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https://forum.allaboutcircuits.com/threads/serial-comms-pic-to-pc.35237/ | # Serial comms PIC to PC
#### fyee
Joined Mar 7, 2010
16
my project also something like this, but I'm using weight sensor,so my output from PIC will be weight. And, I need to announce the weight by using VB program.
Is it for the same concept for my project? I want to save my output from PIC in PC but then I don't know how to.
Can anyone tell me how to do?
#### beenthere
Joined Apr 20, 2004
15,819
Accepting a serial input to a PC is pretty simple, and clearly explained in the VB literature.
You can get better help if you give significant details about the PIC you are using, the language you are coding in, and the problem you are having. You can also visit the Microchip site and find many programming examples.
#### Harrington
Joined Dec 19, 2009
85
Not quite as easy as you think !! First you have to know how to use serial routines and that depends on what language you are using Secondly,you have think about whether you going to use asynchronous or synchronous communications or you could use SPI interface to PC this depends entirely on your programming skills IE can you progam In C Assembler or can you program in VB and Pic Basic or are you going to use something like Picc Lite
If your going to use assembler then you need to understand Bit Banging
Suggest Mike Pedro's page very good explanations on there
To start with i would suggest that you use a parallel port instead rather than RS232 straight away I'm assuming that you are using external AD converter via PORT A and Port B used as Output in this instance
If you do it this way then you wont need to worry about MScomm32 but instead use InputOUT 32.DLL which you simply drop into your Windows\ System32 folder
You then need to take into consideration that what the pic sends out is binary and you need to convert that into byte MSB LSB You need a max232 in between the pic device and the PC so that you can have level shift and then you also need to decide on protocol for Rs232 what handshaking will you use bits stop bits odd even parity
Looks easy It takes quite a while to even understand how to do this
So here is a snippet of code I wrote for operating 8 relays from a pic with a return signal back to the Vb program telling me that the pic has received the byte and that relays are in operation in other words the byte has been transferred to Port B
Language used PIC Basic Pro
This example uses MScomm32
Make sure you put the MSCOMM32.OCX in the Windows / System 32 Directory
'****************************************************************
'* Name : SerialReciever.BAS *
'* Author : [MD Harrington 55 Rushet Road London BR5 2PS] *
'* Notice : Copyright (c) 2009 [MD Harrington] *
'* Date : 15/08/2009 *
'* Version : 1.0 *
'* Notes : RS 232 data received via max232 for pic 84A *
'* : *
'****************************************************************
Device 16F84A
Config XT_OSC , WDT_OFF , PWRTE_OFF, CP_OFF
Declare XTAL 4
Symbol RS_IN PORTA.0 ' makes porta.0 input to pc Recieve data pin 2 dtype on pc socket
Symbol RS_OUT PORTA.1 ' makes porta.1 output to pc transmit data pin 3 dtype On pc socket
Symbol T_9600 9600 ' 8-bit no parity inverted
Symbol XON 17 ' flow control allows transmitt
Symbol XOFF 19 ' flow control stops transmit
Declare RSIN_PIN RS_IN 'TX data from pc arrives to this pin via max232
Declare RSIN_MODE TRUE 'Mode is inverted data because we are using a max232 the data is inverted when it arrives
Declare RSOUT_PIN RS_OUT 'Our transmission PIN for serial data
Declare RSOUT_MODE TRUE ' defaults to INVERTED for use without MAX232
Declare SERIAL_BAUD 4800
Declare RSIN_TIMEOUT 3000
Dim TX_Start As Byte
Dim TX_Stop As Byte
Dim endln As Byte
Dim rcbuffer As Byte
Dim oldVal As Byte
Dim newVal As Byte
Dim rx_Flag As Bit
init: ALL_DIGITAL = TRUE 'set ports to all digital
' setup the ports on the pic device
'initialise XON_XOFF protocol
TX_Start = XON
TX_Stop = XOFF
endln = 13
rx_Flag = 0 'rx_Flag for detecting fisrttime reception of commands
DelayMS 255 ' give pic time to settle down and max232 to stabilise total delay 510 ms apprx 1/2 minute
' bits 4 = input, 3 = output, 2 = input, 1 = output, 0 = input,
' binary equivalent = 0001 0101
PORTA = 0 ' clear porta
TRISB = $00 ' make all pins on portb output PORTB = 0 ' ensure no output on portB oldVal =$00
PORTB = oldVal
RXBegin: rcbuffer = $00 RSIn {to_Timeout}, rcbuffer 'test for first time reception and set flag to 1 Select Case rx_Flag Case 0 newVal = rcbuffer 'put this into newVal PORTB = newVal ' place this on portB to operate relays oldVal = PORTB rx_Flag = 1 ' finished testing for firstime reception Case 1 newVal = rcbuffer ' assign newVal to rcbuffer newVal = oldVal ^ newVal 'logically XOR the two together PORTB = newVal oldVal = PORTB End Select TXBegin: DelayUS 255 RSOut BIN oldVal 'transmitt the result back to the main DCE so that this can be processed DelayUS 50 GoTo RXBegin 'start process again to_Timeout: GoTo RXBegin Thats a simple example remember that the RSIN blocks untill byte recieved ** Important i would think in your project case ** Any Other questions feel free to leave me a note #### Harrington Joined Dec 19, 2009 85 To Follow for you here is part of the VB code You could also use Java up to you but I think you will find this difficult to start with Also if you use your brains here you could also give your project the edge by writing a server implementation and a client implementation such that after receiving your temperature readings you can then send this via server TCPIP socket back to client just a nice little extra edge on other people but that's obviously your choice Pay attention to important comments here Dim rcbuffer() As Byte ' The important Byte Array ' set the properties of mscomm1 With MSComm1 .CommPort = 1 .Handshaking = comXOnXoff .Settings = "4800,n,8,1" .RTSEnable = True .InputMode = comInputModeBinary ' very important this if you get this wrong you get garbage back .InputLen = 0 .InBufferSize = 1 '2 single byte .OutBufferSize = 1 ' limit this to one byte .NullDiscard = True .RThreshold = 1 End With @ Deal with MsComm events mentioned in VB forums Bear in mind this for a relay board not temperature however the principle is more or less the same Take note that I use a byte array which has no dimensions "Interesting point here took me hours to find this out as well !! Private Sub MSComm1_OnComm() Dim buffer As String ' holds our binary number returned from the relay board Select Case MSComm1.CommEvent Case comEvReceive rcbuffer() = MSComm1.Input 'populates the array with byte returned from the relay board Remember Its serial data so its bit shifted in hence the array grows in size Important as is setting the Input buffer size on MScom control CTS RTS LINES and events come into play here Not to difficult but also not easy !! For I = 0 To UBound(rcbuffer) ' convert this to a string will hold bin representation of byte recbuffer = recbuffer & Chr$(CDec(rcbuffer(I)))
Next I
' after we get the value back from portb on the relay board we then toggle
' the led to on or off state
toggleLeds lastPressedIndex, recbuffer ' this function is not here for you to see but you can work out what I'm doing
recbuffer = "" ' reset the buffer to null so that we don't mix up characters
Case comEvCTS
MsgBox "CTS Status = " & MSComm1.CDHolding
Case comEvDSR
MsgBox "DSR Status = " & MSComm1.DSRHolding
Case comEvRing
MsgBox "Ring Status = " & "Ring Detected"
End Select
End Sub
PS *********** Hope this helps you **************
Last edited:
#### Harrington
Joined Dec 19, 2009
85
Nearly forgot Id better show you how to send data as well via MSCOMM32
Public Function sendData(ByVal swNumber As Integer)
If MSComm1.PortOpen = False Then
MSComm1.PortOpen = True
End If
If MSComm1.PortOpen = True Then 'ensure the port is open
TxBuffer(0) = swNumber ' We Only use the first element here
MSComm1.Output = TxBuffer() ' Note!! you send the whole array i ' in one go This is where you think you have to cycle through the array to do this NOT THE CASE MSCOMM32 does this for you !!
Also drove me nuts trying to work out why i couldnt get this to 'work as well i think about two days pulling my hair out over this and i 'haven't got much left either lol !!
End If
End Function
So that should now get you more or less on your way or at least started in the right direction
#### fyee
Joined Mar 7, 2010
16
Accepting a serial input to a PC is pretty simple, and clearly explained in the VB literature.
You can get better help if you give significant details about the PIC you are using, the language you are coding in, and the problem you are having. You can also visit the Microchip site and find many programming examples.
Thanks for moving the thread for me.
The PIC I'm using is 16F877A,writing in C language. The output I got from PIC is actually in bit value from 0 to 1023. The problem I'm facing now is, I want to get the bit value from PIC to PC so that I can use it in VB. Let say, if VB gets the signal of 1010 which is equal to 2Kgs, it will announce 2Kgs itself.
I'm using a laptop which doesn't have a serial port, so how am I converting it to USB port? and I heard my friend said it might be different if the data send to USB.
I'm not so familiar with all the programmings, so really need helps from all the experts here.
Thanks so much.
#### fyee
Joined Mar 7, 2010
16
So here is a snippet of code I wrote for operating 8 relays from a pic with a return signal back to the Vb program telling me that the pic has received the byte and that relays are in operation in other words the byte has been transferred to Port B
Language used PIC Basic Pro
This example uses MScomm32
Thats a simple example remember that the RSIN blocks untill byte recieved ** Important i would think in your project case **
Any Other questions feel free to leave me a note
Is this C Assembly or C language?
I'm using C language for the weighing sensor. And, I want to add the program for the communication from PIC to PC,so how do I add?
Last edited:
#### fyee
Joined Mar 7, 2010
16
This is the 10 bits value that you collected from your ADC. You will Tx it to your PC with two bytes. First will contain the low byte (of the 10 bits) and the second will contain the high byte. Once these two bytes are in the PC you will recombine them [(high byte * 256) + low byte] and you will apply all the maths necessary to convert the ADC reading into weigth.
I don't really understand this.
Yea I got a converter for the 232.
#### Markd77
Joined Sep 7, 2009
2,806
The AD converter has a range of 0-1023 which is too big to be stored in an 8 bit register (maximum 255) or sent over serial as a single byte (also 8 bit).
I've got a USB-rs232 converter and using it is no different to using a built in serial port. The only minor difficulty is figuring out which COM# it is.
#### fyee
Joined Mar 7, 2010
16
I've got a USB-rs232 converter and using it is no different to using a built in serial port. The only minor difficulty is figuring out which COM# it is.
I've no problem in figuring out which COM# it is as I used the converter for PLC too.
I'm really sucked in PIC micro-controller and C programming ,so I really need someone to guide me and teach me how to include the program for the serial communication in PIC16F877A.
#### Boo
Joined Oct 27, 2009
40
PIC side: As previously discused. Measure ADC -> Send out both bytes Via Rs232 to the max232
Max232: Takes 5V signals and converts them to +-12V
RS232 to usb: Creates a virtual COM port on your computer and accepts the rs232 data from the max232
VB program: Just drag a serial COM onto your form, and after the driver is installed for the previous step, select that one. Make sure you are using the same baud rate etc.
Do byte low + (byte high *256) = int then convert appropriately.
In a few days this will all make sense, before trying to do all of this, simply send 1 byte to your PC repeatedly and try to make it appear on a text box or message box.
Good luck
P.s. here's some inspiration :
http://electrobird.net/PIC Projects/2d Accelerometer.html
#### Harrington
Joined Dec 19, 2009
85
Ive been doing some research for you because I'm also looking at this myself for another project that I want to build
After lots of reading and maybe one or two steps further I came across this for you which might help
Good explanations here for you if you want to understand more with regards to USB comm and Usb to serial conversion
Looking at what you have written you must have a fair knowledge of C so it will hopefully make some sense to you
Best place to start is with the USB1.1 standard
http://www.usb.org/developers/docs/
Or there is an alternative to this and that is JUSB or Java USB although Ive not tested this with windows the reports dont seem to give very good write ups however If you don't try you never find out I guess so Im going to have a play tonight see how far I can get with this http://jusb.sourceforge.net/
Good luck with this
Or you could start here
http://www.beyondlogic.org/usbnutshell/usb6.htm#SetupPacket
http://www.beyondlogic.org/usbnutshell/usb7.htm#PIC16F876Example
Also you can get a usb to serial flat pack IC and driver form this site
http://www.ftdichip.com/
Diagrams for pic to FTDI Interface you can find here
http://www.ianstedman.co.uk/Projects/PIC_USB_Interface/PIC_USB_SchematicV2.png
Here are some details for you hope this helps you further could be a very good excersise and prove very interesting if you want to learn how to write your own driver files for USB for windows
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#### fyee
Joined Mar 7, 2010
16
So means, that will be different if I write my program for serial communication then I connect the serial port to USB-to-serial converter? since in the end it will go to USB port.
#### retched
Joined Dec 5, 2009
5,208
No, you will go from the serial from the chip to usb. Then usb right into your PC.
Basically you will be making your device speak USB That way, you need no converters in the outside world. If you wanted to take your device to a friends house, you wouldn't need to install a RS232 to USB cable and driver to their computer, try to find the com port and all that jazz.
You would simply plug the usb cable in to your device and into the computer. done.
#### Harrington
Joined Dec 19, 2009
85
That's correct, Retched is right re straight into the USB using FT245BM available from ftdichip.com or one of their distributors
I would ask them at the same time whether they can provide you with an active X object to use with VB
That's if they have written one hmm another story i guess If they have Best way forward here easy approach is drop them an email and check if they do so as to find out first before you rush into that choice as well
Or its C# I'm afraid which is Ahhh yes another language that you will have to learn Nothings easy is it !!
If only it were m Anyway here is a link for this as well should you wish to read this I would read as much as you can and research this before you jump down the route of USB
http://www.vsj.co.uk/articles/display.asp?id=600
http://www.codeproject.com/KB/cs/USB_HID.aspx
I have also checked into the java USB and after much reading last night and today You can tell Im unemployed and no one has any work for me !! Grrrrr and I recompiled and tested this as well Just to see if I could find a nice solution for you
It does work but their are quite a few annotations that the driver package for XP reports
So its not the ideal answer but you will be able to change the PID and ID in the registry , "Oh Golly that's regedit etc etc as well I now have to learn " , Uhm Well Yes you will have to do this as well !!
All so that you can read and write to the USB , marvelous isnt it all this Hi tech stuff
Yes it works but consider a more stable driver which has been tested and approved otherwise its back ton writing your own driver after reading 10 meg of material regards how USB works
You do however have to compile the DLL using Visual studio 2005
Also you must recompile the Driver file and you may also want to rewrite some of the Java Native Methods for other functions that the DLL provides
This means that you would also have to understand how to use JNI calls and and recreate the necessary C++ implementation files using the javac -jni switch
In other words Its understanding Java classes and Native method calls how to lots and lots of learning here too never mind just simply rewriting your own drivers dll's and being able to test them so that you end up with a stable version
Quite a lot to take in for a small project of this size
Still worth learning as this will prove to be no end of use to you when writing your own dll's so that you can interact with other functions you may wish to implement in your VB program
A massive learning curve We are now looking at time scales of well This could take you at least 6 months to a year just to try to learn how to communicate with USB
Not as easy as you think because you have to locate which USB device you are after in order to reset power up and then read or write too
Good news is yes it works but its not exactly the most stable of drivers bear that in mind
One3 last point should you decide the C# route then it means you must also have the dot net packages installed on your machine and Oh yes everybody else as well that's
Dotnet version 1.1 then 2.1 and the 3 plus of course Microsoft's fabulous one billion updates
We don't exactly know either Still not to worry I'm sure this will eventually be a successful project maybe in a years time You have to laugh at this really don't you really don't you otherwise you are going to be sitting their crying your eyes out after spending loads of time patience and headaches creating this wonderful temperature read out story via your pic only to find
that you have yet another 2 years studying to do before I can even get this to work
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#### symqwerty
Joined Feb 22, 2010
31
my project also something like this, but I'm using weight sensor,so my output from PIC will be weight. And, I need to announce the weight by using VB program.
Is it for the same concept for my project? I want to save my output from PIC in PC but then I don't know how to.
Can anyone tell me how to do?
What type of VB you use?VB6 or VB.NET? I will recommend you to use VB.NET.
I think it's better to let the PIC to do the ADC and then pass the raw data to your PC. Next, PC will do the math before display the 'weight'.
Since you use 10-bit ADC, the result will be placed in 2 register, ADRESH and ADRESL (if not mistaken). Then, you can sent the result via uart to PC. Then, to combine these 2 value to form 1 single value, you need to 'shift' the bits to the left or mathematically like this; tmp = (ADRESH x 256) + ADRESL. By now, "tmp" will have the correct decimal value.
#### symqwerty
Joined Feb 22, 2010
31
You can buy usb to rs232 cable converter or FTD232R IC. The cable converter will emulate or appear as VIRTUAL com port, so just treat it as rs232 port ( no knowledge of USB is needed.)
but if you buy FTD232R IC, you have 2 options, either to use VCP or DLL. But for starter, you can use VCP or Virtual Com Port as a driver. same case as above. If you want more flexibility or features from the chip, you should learn to use the DLL (FTD2XX.dll). furthermore, no knowledge of USB is needed.
#### fyee
Joined Mar 7, 2010
16
What type of VB you use?VB6 or VB.NET? I will recommend you to use VB.NET.
I've VB6 and VB2008 Express Edition.
Since you use 10-bit ADC, the result will be placed in 2 register, ADRESH and ADRESL (if not mistaken). Then, you can sent the result via uart to PC. Then, to combine these 2 value to form 1 single value, you need to 'shift' the bits to the left or mathematically like this; tmp = (ADRESH x 256) + ADRESL. By now, "tmp" will have the correct decimal value.
how do I write this in my program? btw,I'm writing in C language by using MicroC Pro for PIC.
You can buy usb to rs232 cable converter or FTD232R IC. The cable converter will emulate or appear as VIRTUAL com port, so just treat it as rs232 port ( no knowledge of USB is needed.)
I'm using USB to RS232 cable converter.
Explanation in programming is needed. I don't really know how to start the program. Pardon me for being a programming noobie.
thanks so much.
#### symqwerty
Joined Feb 22, 2010
31
OK...lets do like this..
PIC side :
You must learn how to use UART. Remember that UART will transfer byte by byte. So, since you have 2 register with byte size, ADRESH and ADRESL, you have to transfer it one by one. That's why i recommend you to do the calculation in PC instead of PIC..
MikroC have built-in function for UART..
Rich (BB code):
USART_Init(9600); // baud rate 9600kbps
delay_ms(20); // relax
TRISA=0x0F; // set port A as input
//I'm using old version of MikroC and most of the time, i prefer to use my own code instead of built-in function.
the rest of the code..
Rich (BB code):
// You can use ADC_READ(pin_no) for this purpose
ADCON0.f2=1; // set GO - start conversion
ST:
if(ADCON0.f2==1) goto ST; //wait until flag bit cleared
// microC also have pre-defined fn for ADC but i dont want to use it here.
Usart_Write(ADRESL); // [7:0]
PC side :
PC will process data transmitted by PIC. Just create new VB project, then add "Serial Port" component to your form. Next, set the properties( baudrate, handshaking, com no. and etc).
Then, using the data received, use formula as discussed before.
Rich (BB code):
'open serial port
If SerialPort1.IsOpen() Then
SerialPort1.close() ' close 1st and reopen again
Else
SerialPort1.Open()
MsgBox("open")
End If
' use event-based method or polling method to get data from serial prot | 2020-09-26 10:12:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24239277839660645, "perplexity": 2844.9917998388314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400238038.76/warc/CC-MAIN-20200926071311-20200926101311-00663.warc.gz"} |
http://m.rangers.mlb.com/news/article/30549526/ | # Holland happy even without win
## Holland happy even without win
CLEVELAND -- Derek Holland was happy with the way he pitched on Saturday night, even though he missed out on a second shutout and victory at Progressive Field. Holland, who is from central Ohio and had many friends and family in attendance, took a three-hit shutout into the eighth inning, before the Indians rallied to tie the game.
Holland, who had thrown a shutout against the Indians last year at Progressive Field, had allowed 12 runs over 13 innings in his previous two outings before pitching much better on Saturday.
"I thought it was good," Holland said. "I continued to do what I did before. I just wasn't catching as much of the plate as I had been with my offspeed pitches, and that was one of the best games I've had as far as command of my fastball."
Holland wasn't happy with the three walks he allowed. He also wasn't happy that of the six baserunners he allowed through seven innings, five reached base with two outs. That was one reason why manager Ron Washington went to the mound in the fourth inning after Holland issued a two-out walk to Travis Hafner, and then fell behind 2-0 to Shin-Soo Choo.
"He didn't yell at me like he has before," Holland said. "He just told me to slow down, make my pitch and get out of this."
Holland did. He threw one more pitch and Choo flied out to left to end the inning.
"You got to do what you're told," Holland said. | 2014-11-25 22:18:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.211818128824234, "perplexity": 6670.631915204622}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931004237.15/warc/CC-MAIN-20141125155644-00193-ip-10-235-23-156.ec2.internal.warc.gz"} |
http://kth.diva-portal.org/smash/record.jsf?pid=diva2:133494 | Change search
Interlaced particles in tilings and random matrices
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). (Analys)
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]
This thesis consists of three articles all relatedin some way to eigenvalues of random matrices and theirprincipal minors and also to tilings of various planar regions with dominoes or rhombuses.Consider an $N\times N$ matrix $H_N=[h_{ij}]_{i,j=1}^N$ from the Gaussian unitary ensemble (GUE). Denote its principal minors (submatrices in the upper left corner) by $H_n=[h_{ij}]_{i,j=1}^n$ for $n=1$, \dots, $N$. We show in paper A that all the $N(N+1)/2$ eigenvaluesof $H_1$, \dots, $H_N$ form a determinantal process on $N$ copies of the real line $\mathbb{R}$. We also show that this distribution arises as a scaling limit in tilings of an Aztec diamond with dominoes.We discuss a corresponding result for rhombus tilings of a hexagonwhich was later proved by Okounkov and Reshtikhin. We give a new proof of that statement in the introductionto this thesis.In paper B we perform a similar analysis for the Anti-symmetric Gaussian unitary ensemble (A-GUE). We show that the positive eigenvalues of an $N\times N$ A-GUE matrix andits principal minors form a determinantal processon $N$ copies of the positive real line $\mathbb{R}^+$.We also show that this distribution of all these eigenvalues appears as a scaling limit of tilings of half a hexagon with rhombuses. In paper C we study the shuffling algorithm for tilings of an Aztec diamond. This leads to the study of an interacting set of interlacedparticles that evolve in time. We conjecture that the diffusion limit of thisprocess is a process studied by Warrenand establish some results in this direction.
##### Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , vii, 23 p.
##### Series
Trita-MAT. MA, ISSN 1401-2278 ; 08:14
##### Keyword [en]
Interlaced particles, GUE, Anti-symmetric GUE, domino tilings, lozenge tilings
Mathematics
##### Identifiers
ISBN: 978-91-7415-212-8OAI: oai:DiVA.org:kth-9834DiVA: diva2:133494
##### Public defence
2009-02-06, Kollegiesalen, F3, KTH, Lindstedtsvägen 26, Stockholm, 13:00 (English)
##### Note
QC 20100804Available from: 2009-01-19 Created: 2009-01-12 Last updated: 2010-08-04Bibliographically approved
##### List of papers
1. Eigenvalues of GUE minors
Open this publication in new window or tab >>Eigenvalues of GUE minors
2006 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 11, no 50, 1342-1371 p.Article in journal (Refereed) Published
##### Abstract [en]
Consider an infinite random matrix H = (hij)o<i,j picked from the Gaussian Unitary Ensemble (GUE). Denote its main minors by Hi = (hrs)1≤r,s≤i and let the j:th largest eigenvalue of Hi be μji. We show that the configuration of all these eigenvalues (i, μji) form a determinantal point process on ℕ × ℝ. Furthermore we show that this process can be obtained as the scaling limit in random tilings of the Aztec diamond close to the boundary. We also discuss the corresponding limit for random lozenge tilings of a hexagon.
##### Keyword
GUE, Aztec diamond, domino tilings, lozenge tilings, interlaced particles
Mathematics
##### Identifiers
urn:nbn:se:kth:diva-9830 (URN)000243135900001 ()2-s2.0-33845777983 (ScopusID)
##### Note
This version also contains the corrections from the erratum published in the same journal. QC 20100804Available from: 2009-01-19 Created: 2009-01-12 Last updated: 2010-12-06Bibliographically approved
2. The Anti-Symmetric GUE Minor Process
Open this publication in new window or tab >>The Anti-Symmetric GUE Minor Process
2009 (English)In: Moscow Mathematical Journal, ISSN 1609-3321, Vol. 9, no 4, 749-774 p.Article in journal (Refereed) Published
##### Abstract [en]
Our study is initiated by a multi-component particle system underlyingthe tiling of a half hexagon by three species of rhombi. In this particlesystem species $j$ consists of $\lfloor j/2 \rfloor$ particles which areinterlaced with neigbouring species. The joint probability densityfunction (PDF) for this particle system is obtained, and is shown in asuitable scaling limit to coincide with the joint eigenvalue PDFfor the process formed by the successive minors of anti-symmetric GUEmatrices, which in turn we compute from first principles. The correlationsfor this process are determinantal and we give an explicit formula for thecorresponding correlation kernel in terms of Hermite polynomials.Scaling limits of the latter are computed, giving rise to theAiry kernel, extended Airy kernel and bead kernel at the soft edge and inthe bulk, as well as a new kernel at the hard edge.
##### Keyword
Anti-symmetric GUE, lozenge tilings, interlaced particles
Mathematics
##### Identifiers
urn:nbn:se:kth:diva-9831 (URN)000273089600002 ()
##### Note
QC 20100804Available from: 2009-01-19 Created: 2009-01-12 Last updated: 2011-07-06Bibliographically approved
3. On the Shuffling Algorithm for Domino Tilings
Open this publication in new window or tab >>On the Shuffling Algorithm for Domino Tilings
2010 (English)In: Electronic Journal of Probability, ISSN 1083-6489, Vol. 15, 75-95 p.Article in journal (Refereed) Published
##### Abstract [en]
We study the dynamics of a certain discrete model of interacting interlaced particles that comes from the so called shuffling algorithm for sampling arandom tiling of an Aztec diamond. It turns out that the transition probabilitieshave a particularly convenient determinantal form. An analogous formula in a continuous setting has recently been obtained by Jon Warren studying certain model of interlacing Brownian motions which can be used to construct Dyson's non-intersecting Brownian motion.We conjecture that Warren's model can be recovered as a scaling limit of our discrete model and prove some partial results in this direction. As an application to one of these results we use it to rederive the known result that random tilings of an Aztec diamond, suitably rescaled near a turning point, converge to the GUE minor process.
##### Keyword
Aztec diamond, domino tilings, interlaced particles, GUE
Mathematics
##### Identifiers
urn:nbn:se:kth:diva-9829 (URN)000273780800002 ()2-s2.0-77952804389 (ScopusID)
##### Note
QC 20100804Available from: 2009-01-19 Created: 2009-01-12 Last updated: 2010-12-08Bibliographically approved
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Nordenstam, Eric
##### By organisation
Mathematics (Dept.)
Mathematics | 2016-10-22 21:43:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7843138575553894, "perplexity": 3697.4199466445057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719045.47/warc/CC-MAIN-20161020183839-00064-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://dataset.lixoft.com/data-set-user-guide/ | Select Page
Version 2016R1
This documentation is for the data set for the MonolixSuite 2016R1. It corresponds to typical data set for population modeling application used for Datxplore and Monolix typically. This data set documentation is also valid for previous Monolix versions.
Data set for population modeling
The dataset is a key element for parameter estimation and to summarize experimental data in a file. The purpose of these pages is to present the general structure of a data set, the details for each column type, and provide some examples of some real data set (continuous, discrete, time-to-event, censored, several outputs, …).
The considered data set are dedicated to population modeling application Therefore, columns of this matrix contain (in any order). It contains for each subject measurements, dose regimen, covariates etc … i.e. all the information collected during the trial. These informations are organized by line (i.e. each line contains a piece of information) and each column shall be associated to a column type (there are fifteen different column types which will be described in the other articles) for the software to read the data set. The format should be .txt or .csv and a header line is nedded. It is very similar and compatible with the structure used by the Nonmem software.
Columns of the data file can contain (in any order)
• The ID of the subjects (can be any string or number, not necessarily ordered), the occasions of this ID.
• The observations of the individual with ID at times, Notice that these observations can be continuous measurements, counts, or events.
• The time of the observations and of the administrations.
• The covariates (continuous or categorical).
• Additional information (censoring, rate, …).
Thus, a data set contains at least IDs, time and some observations.
Data set structure
The data set structure contains for each subject measurements, dose regimen, covariates etc … i.e. all the information collected during the trial. This information is organized by line (i.e. each line contains a piece of information) and each column shall be associated to a column-type (there are fifteen different column-types which will be described in the other articles) for the software to read the data set. It is very similar and compatible with the structure used by the Nonmem software (the differences are listed here). One of the first thing that the software does is to define the line type. Indeed, a line can be:
• dose-line: a line that contains information about the dose’s regimen,
• response-line: a line that contains a measure,
• A regression-line: a line that contains regression value(s) (since it is possible to have several regression variables),
• covariate-line: a line that contains covariate values(s) (since it is possible to have several covariates),
• comment-line: any line containing character ‘#’,
• header or title-line: it is the first line of the data set which can be used to define column-names.
Combinations are possible and a line can be both a dose-line and a regression-line (in other words it is possible to define in a same line a dose regimen and the regression values). However, a line cannot be both a dose-line and a response-line. In other words, two lines will be necessary to define a dose-regimen and a measure at the same time-stamp.
Description of column-types
The title-line is the first line of the data set. It is free and can be used to specify column-names. It is important to understand the difference between column-names and a column-types: as already stated the column-names are totally free but the column-types shall belong to a list of pre-defined keywords. They are used to identify the column’s role. For instance, in the previous example, the fourth column of the sample data set contains measurement information and will then have column-type Y. A name (CONC) has been entered to indicate that the measurement corresponds to a concentration. It is possible to group the column-types based on their functionality:
• Subject identification headers: column-types ID and OCC are used to identify subjects.
• Time headers: column-types TIME and DATE (or DAT1, DAT2, DAT3) are used to time stamp data.
• Response headers: column-types Y (alias: DV and CONC, for response values), YTYPE (response type identifiers), CENS (mark responses as censored), (response limit) are used to define responses.
• Covariate headers: column-types COV (continuous covariate) and CAT (categorical covariate) are used to define continuous and categorial covariates.
• Regression headers: column-type X (alias: REG, XX) is used to define regression variables.
• Control and event headers: column-types MDV (to control data by tagging lines as dose-lines, response-lines or regression-lines) and EVID (to mark unusual events).
Character definition for data set elements naming
Only alphanumeric characters and the underscore “_” character are allowed in the strings of your data set (headers, categorical covariate names, etc). Special characters such as spaces ” “, stars “*”, parentheses “(“, brackets “[“, dashes “-“, dots “.”, quotes ” and slashes “/” are not supported.
These characters restrictions are impacting
• The strings that can be used in ID, YTYPE, and CAT columns.
ID: subject identifier
The column is used to identify the different subjects and its content is totally free: numbers / strings… This column is mandatory. Notice that string ‘.’ will not be interpreted as a repetition of the previous line. As a consequence a data set of the form
ID * *
John * *
John * *
Mike * *
. * *
contains 3 different subjects : ‘John’, ‘Mike’ and ‘.’. It does not generate another occasion for Mike. Even if numbers and strings are allowed, we encourage the user to define Ids using integers for readability and usage simplicity.
Contrarily to NONMEM, the lines corresponding to the same subject do not need to be next to each other. Thus, the following file contains 2 subjects with IDs “1” and “2”.
ID * *
1 * *
1 * *
2 * *
2 * *
1 * *
The IDs are not sorted lexicographical order but by order of appearance in the data set.
Format restrictions (an exception will be thrown otherwise):
• A data set shall contain one and only one column ID.
OCC: occasion identifiers
It is possible to have, in a data set, one or several columns with the column-type OCC. It corresponds to the same subject (ID should remain the same) but under different circonstances, occasions. For example, if the same subject has two successive different treatments, it should be considered as the same subject with two occasions. The OCC columns can contain only integers. For instance:
ID * OCC
John * 1
John * 2
John * 3
How occasions can appear while no OCC column is defined ?
Occasions can be generated even if no OCC column is defined in the data set. In that case, a button arises in the Monolix interface allowing the possibility to add inter occasion variability to the model. This can happen in two cases.
• Firstly, if there is an EVID column with a value 4 then Monolix defines a washout and create an occasion. Thus, if there is several times where EVID equals 4 for a subject, it will create the same number of occasions. Notice that if EVID equals 4 happens only once at the beginning, only one occasion will be defined and no inter occasion variability would be possible. Thus, the following data set are equivalent.
ID TIME Y OCC
1 0 0 1
1 1 2 1
1 2 2 1
1 0 0 2
1 4 1 2
1 5 2 2
ID TIME Y EVID
1 0 0 0
1 1 2 0
1 2 2 0
1 0 0 4
1 4 1 0
1 5 2 0
• Secondly, if there is a SS column, each steady state creates an occasion. Thus, if two steady states are defined for one subject, then it will generate two occasions. This option will be obsolete and not used in future version of MonolixSuite.
What kind of occasions can be defined?
There are three kinds of occasions
• Cross over study: In that case, data are collected for each patient during two independent treatment periods of time, there is an overlap on the time definition of the periods. A column OCC can be used used to identify the period. See here for an example.
• Occasions with whashout: In that case, data are collected for each patient during one period and there are no overlap between the periods. The time is increasing but the dynamical system (i.e. the compartments) is reset when the second period starts. In particular, EVID=4 indicates that the system is reset (washout) for example, when a new dose is administrated. See here for an example.
• Occasions without whashout: In that case, data are collected for each patient during one period and there are no overlap between the periods. The time is increasing and we want to differentiate periods in terms of occasions without any reset of the dynamical system. For example on the example defined here, multiple doses are administrated to each patient. each period of time between successive doses is defined as a statistical occasion. A column OCC is therefore necessary in the data file to define it.
Frequently asked questions on occasions in the data set
• Do all the individual need to share the same sequence of occasion? No, the number of occasions and the times defining the occasions can differ from one individual to another.
• Is there any limit in terms of number of occasions? No.
• Is it possible to have several levels of occasions? Yes, it can be extended on several level of occasions, see an example here.
Format restrictions (an exception will be thrown otherwise):
• The OCC columns should contain only integers.
TIME: data time stamp
Time can be defined as:
• A double.
• Using hours, minutes format: hh:mm.
Notice that when a subject has time under the format hh:mm, all the time are converted into relative hours, as on the following example
TIME Reconstructed time 10:00 10 10:30 10.5 14:00 14 08:59 8.983333
When there is no column-type TIME, the column-type DATE is used to time-stamp data.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with the column-type TIME.
• String “.” will not be interpreted as a repetition of the previous line and is then non-compliant with formats listed here-above.
DATE/DAT1/DAT2/DAT3: date information
The difference between all this date information corresponds to variation of date format as summarized in the following table.
Format and associated date column name
DATE DAT1 DAT2 DAT3
Day, month and year mm/dd/yy or mm/dd/yyyy dd/mm/yy or dd/mm/yyyy yy/mm/dd or yyyy/mm/dd yy/dd/mm or yyyy/dd/mm
Several points have to be noticed. First, the day month year separator should be the character “/”. Secondly, by default, when the year is coded with two digits, it is then interpreted as 20xx. For instance, using format DAT2, 41/12/07 is interpreted as December the 7th 2041.
If both a TIME column-type and a DATE column-type are present, the DATE column is considered to represent the day and the TIME column the hour within this day.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column-type DATE / DAT1 / DAT2 / DAT3.
• Year, day, and month shall be integers.
• The separator must be “/”.
• Character “.” will not be interpreted as a repetition of the previous line but will throw an exception as any non-compliance with formats listed here-above.
• All the lines with valid subjects (non empty ID,OCC) should be filled correctly within the same delimiter, according to the specified date format: i.e., no empty year, no empty month, no empty day, no mix of delimiters.
Timestamp summary
As can be seen there are several ways to define the timestamp of the data set depending if there is a time column or not and if there is a DATE column or not.
TIME column present TIME column not present DATE column present DATE column is considered to represent the day and the TIME column the hour within this day Date column is considered to represent the time DATE column not present DATE column is considered to represent the time First regression-column will be used to timestamp data
What happens if neither TIME nor DATE is defined ?
We strongly encourage the user to be careful on the TIME definition. However, if there is neither TIME nor DATE column-type, first regression-column (i.e. first column with column-type X) will be used to timestamp data. Moreover, if there is neither TIME, nor DATE/REGRESSION column-type, an arbitrary time is computed.
Y: response
The Y column-type can be used for continuous, categorical, count or time-to-event data.
When there is no EVID or MDV column (see hereunder), a line is considered as a response-line if it contains a value and there is no dose-column (i.e. content of the column with dose-type AMT) or if the dose-column contains either string ‘.’ or a 0. As a consequence, when there are null values in both dose-column and response-column, line is considered as a response-line. The following table sums up the different situations
Notice that in the case of the definition of both a non null amount and a measurement, the choice was made to favor the measurementTo solve it without any EVID column, the user should provide two distinct lines to provide both a dose-line and a response line. For instance, in the following data set
TIME ID AMT Y
12.1 John 1.1 12.6
the line is considered as a response-line, a measurement is set at 12.6 at time 12.1 and no dose is added. Of course it is possible to specify a response and a dose at same time but lines shall be duplicated as in the following data set
TIME ID AMT Y
12.1 Tom . 12.6
12.1 Tom 1.1 .
In that case, the first line is again considered as a response-line, a measurement is set at 12.6 at time 12.1. But the second line is considered as a dose amount at time 12.1 with an amount 1.1.
For continuous data:
For continuous data, the time and value of each observation for each subject is given, as in the following example:
ID TIME AMT Y
1 0 50 .
1 0.5 . 1.1
1 1 . 10.2
1 1.5 . 8.5
1 2 . 6.3
1 2.5 . 5.5
One can see theophylline data set, the warfarin data set, and the HIV data set for example for more practical examples on continuous outputs data set.
For categorical data:
In case of categorical data, the observations at each time point can only take values in a fixed and finite set of nominal categories. In the data set, the output categories must be coded as integers, as in the following example:
ID TIME Y
1 0.5 3
1 1 0
1 1.5 2
1 2 2
1 2.5 3
One can see the warfarin data set for example for more practical examples on a joint continuous and categorical data set.
For count data:
Count data can take only non-negative integer values that come from counting something, e.g., the number of trials required for completing a given task. The task can for instance be repeated several times and the individuals performance followed. In the following data set:
ID TIME Y
1 0 10
1 24 6
1 48 5
1 72 2
10 trials are necessary the first day (t=0), 6 the second day (t=24), etc.
Count data can also represent the number of events happening in regularly spaced intervals, e.g the number of seizures every week. If the time intervals are not regular, the data may be considered as repeated time-to-event interval censored, or the interval length can be given as regressor to be used to define the probability distribution in the model.
For (repeated) time-to-event data:
In this case, the observations are the “times at which events occur“. An event may be on-off (e.g., death) or repeated (e.g., epileptic seizures, mechanical incidents, strikes). In addition, an event can be exactly observed, interval censored or right censored.
For single events exactly observed:
One must indicated the start time of the observation period with Y=0, and the time of event (Y=1) or the time of the end of the observation period if no event has occurred (Y=0). In the following example:
ID TIME Y
1 0 0
1 34 1
2 0 0
2 80 0
the observation period last from starting time t=0 to the final time t=80. For individual 1, the event is observed at t=34, and for individual 2, no event is observed during the period. Thus it is noticed that at the final time (t=80), no event occurred. One can see PBC data set and Oropharynx data set for practical example of time-to-event data set.
For repeated events exactly observed:
One must indicate the start time of the observation period (Y=0), the end time (Y=0) and the time of each event (Y=1). In the following example:
ID TIME Y
1 0 0
1 34 1
1 76 1
1 80 0
2 0 0
2 80 0
Again, the observation period last from starting time t=0 to the final time t=80. For individual 1, two events are observed at t=34 and t=76, and for individual 2, no event is observed during the period.
For single events interval censored:
When the exact time of the event is not known, but only an interval can be given, the start time of this interval is given with Y=0, and the end time with Y=1. As before, the start time of the observation period must be given with Y=0. In the following example:
ID TIME Y
1 0 0
1 32 0
1 35 1
we only know that the event has happened between t=32 and t=35.
For repeated events interval censored:
In this case, we do not know the exact event times, but only the number of events that occurred for each individual in each interval of time. The column-type Y can now take values greater than 1, if several events occurred during an interval. In the following example:
ID TIME Y
1 0 0
1 32 0
1 35 1
1 50 1
1 56 0
1 78 2
1 80 1
No event occurred between t=0 and t=32, 1 event occurred between t=32 and t=35, 1 between t=35 and t=50, none between t=50 and t=56, 2 between t=56 and t=78 and finally 1 between t=78 and t=80.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type Y.
• Response-column shall contain double value or string “.”.
• If there is a non null double value in dose-column, there must be a non null double value in the response-column.
Warning
• If a subject or a subject/occasion has no observation, a warning message arises telling which individuals, subjects/individuals have no measurement.
YTYPE: response type
If observations are recorded on several quantities (several concentrations, effects, etc), the column-type YTYPE permits to assign names to the observations of the column-type Y, for mapping with the quantities outputted by the model. Notice that in case of a dose line, the value in the YTYPE column will not be read, thus the user can set any value (‘.’; the same as a concentration, …)
Entries in the column-type YTYPE can be strings or integers however, we strongly recommend to use only alphanumeric characters. The underscore “_” character is allowed in the strings of your data set. The mapping of the YTYPE to the model output (in the OUTPUT block of the Mlxtran model file) is done following alphabetical order (and not name matching). In the following data set:
TIME DOSE Y Y_TYPE
0 . 12 conc
5 . 6 conc
10 . 4 effect
15 . 3 effect
20 . 2.1 conc
25 . 2 conc
with the following OUTPUT block in the Mlxtran model file:
OUTPUT:
output = {E, Cc}
the observations tagged with “conc” will be mapped to the first output “E”, and those tagged with “effect” will be mapped to the second output “Cc”, because in alphabetical order “conc” comes before “effect”. To avoid confusion, we recommend to use integers in the YTYPE column-type, with “1” corresponding to the first output, “2” to the second, etc… If you have more than 10 types of observations, notice that in alphabetical order “10” comes before “2”.
If you use strings, note that “.” is not considered as a repetition or previous line but as the name of a response. For instance, the following data set creates three different types of responses : “type1”, “.”, and “type2”:
TIME DOSE Y Y_TYPE
0 . 12 type1
5 . 6 type1
10 . 4 .
15 . 3 .
20 . 2.1 type2
25 . 2 type2
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type YTYPE.
CENS: censored response
• CENS = 1 means that the value in response-column ($y_{obs}$), the content of the column with column-type Y) is an upper limit, true observation y verifies $y.
• CENS = 0 means the value in response-column corresponds to a valid observation (no interval associated).
• CENS = -1 means that the value in response-column ($y_{obs}$) is a lower bound, true observation y verifies $y>y_{obs}$.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type CENS.
• There are only three possible values : -1, 0, and 1.
• String “.” is interpreted as 0.
LIMIT: limit for censored values
When column LIMIT contains a value and CENS is different that 0, then the value in the LIMIT column, it can be interpreted as the second bound of the observation interval. Thus, it implies that $y\in [y_{limit}, y_{obs}]$.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type LIMIT.
• A data set shall not contain any column with column-type LIMIT if no column with column-type CENS is present.
• Column LIMIT shall contain either a string that can be converted to a double or “.”.
Example of censored data definition
The proposed example illustrates the case of upper and lower bound on a classical data set of a classical PK model (first order absorption and linear elimination). From the measurements point of view
• There is a lower bound at .5 as the censor is not able to measure lower concentrations, it corresponds to CENS=1 case. Moreover, the concentration can not be lower than 0, thus LIMIT=0.
• There is an upper bound at 5 as the censor is not able to measure higher concentrations, it corresponds to CENS=-1 case. Moreover, from the experimental/modeler point of view, the concentration can not be higher than 6, thus LIMIT=6.
The measurement is represented in the following figure
The measurement corresponds to the blue stars, the real values when censoring arises are in red and green. The corresponding data set is
ID Time Y CENS LIMIT
1 0 0.5 1 0
1 1 0.5 1 0
1 2 4.7 0 0
1 3 5.0 -1 6
1 4 5.0 -1 6
1 5 4.5 0 0
1 6 3.8 0 0
* * * * *
1 15 0.6 0 0
1 16 0.5 0 0
1 17 0.5 1 0
1 18 0.5 1 0
* * * * *
The mathematical handling of censored data is described here.
AMT: dose amount
The content of column AMT will be called the dose-column. It shall either contain a double value or string “.”. When there is no EVID or MDV column, when a dose-column contains a double value different from 0 then it will be considered as a dose-line (i.e. a line containing dose information). If the value of the dose is 0, then it will be interpreted as a dose-line if the response-column (i.e. the content of column with column-type Y) contains a string “.”. When a line contains both dose and response information, dose information is not taken into account, it is considered as a response-line. The following table sums up the different situations
Notice that in the case of the definition of both a non null amount and a measurement, the choice was made to favor the measurementTo solve it without any EVID column, the user should provide two distinct lines to provide both a dose-line and a response lineFor instance, in the following data set
TIME ID AMT Y
12.1 John 1.1 12.6
the line is considered as a response-line, a measurement is set at 12.6 at time 12.1 and no dose is added. Of course it is possible to specify a response and a dose at same time but lines shall be duplicated as in the following data set
TIME ID AMT Y
12.1 Tom . 12.6
12.1 Tom 1.1 .
In that case, the first line is again considered as a response-line, a measurement is set at 12.6 at time 12.1. But the second line is considered as a dose amount at time 12.1 with an amount 1.1.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column-type AMT.
• AMT column shall either contain a double value or string “.”.
The goal of this column is to be able to define several types of administration (e.g. oral administration, intravenous,…). The integer in the ADM column works like a flag, which can be used in the model file to link the dose informations of the data set to a specific administration route in the model. For instance, with the following data set:
ID TIME AMT ADM Y
John 0 10 1 .
Eric 0 20 2 .
and the following PK block in the Mlxtran model file:
PK:
iv(type=1)
oral(type=2, ka)
the subject John will receive a dose of 10 via a bolus iv, while subject Eric will receive a dose of 20 orally with first-order rate constant ka. The identifier in the ADM column should match the “type=” field of the macro. We recommend using ADM to define the type of dose only, and set ADM=”.” for response-lines (in this case, the string “.” will not be interpreted as a repetition of the previous column).
Moreover, it is possible to combine the information of the type of response (as YTYPE) in case of response-lines. Thus, if there are several outputs and several administration routes it is possible to set all the information in the ADM column. The several possibilities using YTYPE and ADM are summarized in the following table
Type of line \ Case YTYPE off / ADM off YTYPE on/ ADM off YTYPE off / ADM on YTYPE on/ ADM on Response line Only one output Defined using YTYPE Defined using ADM Defined using YTYPE Dose line Only one administration route (type = 1) Only one administration route (type = 1) Defined using ADM Defined using ADM
Notice that, for readability and better understanding), we strongly recommend to
• use ADM to define the type of dose only, and set ADM=”.” for response-lines
• use YTYPE to define the type of output, and set YTYPE = “.” or the first value for dose lines
Format restrictions (an exception will be thrown otherwise):
• For dose-lines, the column shall contain only positive integers. For response-lines strings or integers are allowed.
• A data set shall not contain more than one ADM column-type.
RATE, TINF: rate and infusion duration
These columns enable to define the rate (RATE column-type) or duration (TINF column-type) of doses administered as infusions. The column content is meaningful only for dose-lines. The rate and duration information is transferred to the model via the use of the iv macro. If a RATE is defined, the duration of the infusion will be AMT/RATE. If a TINF is defined, the rate will be AMT/TINF.
We strongly recommend to have small duration values (less than 10) to be able to manage it efficiently with analytical solutions. Indeed, if the duration is too long, the calculation of the exponential may produce NaN. Two workarounds:
– Either rescale your time to have durations relevants w.r.t. your time
– If not possible, you may use ODEs and not analytical solutions.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type RATE or TINF.
• “.” or 0 means a bolus dose, without any infusion rate or time.
• Values can be any double value.
• If a negative value is used in combination with the iv macro, the administration will be a bolus.
SS, II: steady-state and inter-dose interval
Steady-state is used to specify that any transitory effect is over and that the system response is now a periodic function of doses. To do this, a fixed number of doses (by default 4) is added before the dose entered with the SS flag set to true (so 5 doses in total, by default). The period between doses is set to the interdose-interval II.
The number of added doses can be changed in the preferences.xmlx file, located in <home>/lixoft/monolix/config in the user folder. The number of doses is defined in the line <dosesToAddForSteadyState value="5"/>, and can for instance be changed to <dosesToAddForSteadyState value="20"/>.
On the following example:
ID TIME AMT SS II EVID Y
Tom 0 10 1 2 1 .
5 doses are applied, at times -8, -6, -4, -2 and 0. The above data set is thus equivalent to:
ID TIME AMT SS II EVID Y
Tom -8 10 0 0 4 .
Tom -6 10 0 0 1 .
Tom -4 10 0 0 1 .
Tom -2 10 0 0 1 .
Tom 0 10 0 0 1 .
The first added dose will have a wash-out, thus for clarity an EVID column has been included in the previous example. But of course it is possible to specify a steady-state even if there is no EVID column in the data set. However an II column is mandatory to specify the period between the five added doses to reach steady-state. The absence of this column will throw an exception (see here under for the complete list of exceptions).
It is possible to find in a data set a mix of steady-state and non steady-state doses. To prevent doses from colliding, if a normal dose is present before a steady-state dose, a new occasion will be created for the steady-state dose. The following data set, with a normal dose at t=0 and a steady-state dose at t=10 with an interdose-interval of 3:
ID TIME Y AMT SS II
1 0 . 10 0 0
1 0 10 . . .
1 1 6 . . .
1 2 3.5 . . .
1 10 . 10 1 3
1 11 9 . . .
1 12 6 . . .
1 13 3 . . .
1 14 2 . . .
leads to the following simulation, with 2 occasions, such that the normal dose at t=0 does not collide with the doses at t=-2, 1, 4, 7, 10, added to be at steady-state at t=10:
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type SS.
• A data set shall not contain more than one column with column-type II.
• When a data set contains a column with column-type SS, there must be a column with column-type II.
• When a data set contains a column with column-type II and no column with column-type SS or ADDL then a SS column is created with:
• SS = 1 when inter-dose interval is strictly positive.
• SS = 0 otherwise.
• When a data set contains a column with column-type II and no column with column-type SS but a column with column-type ADDL then a SS column is created with:
• SS = 1 when inter-dose interval is strictly positive and ADDL = 0.
• SS = 0 otherwise.
• The column is meaningful only for dose-lines. Its format shall be (for all lines including response-lines for which SS information is not applicable) :
• SS shall be either 0 or 1 (‘.’ will be replaced by 0).
• II shall contain a double value and it shall be positive (or null).
• when SS = 0 then the value shall be null.
• when SS = 1, the value shall be strictly positive.
Additional dose lines is a useful shortcut to specify dose regimens with repetitive treatments. ADDL is the number of times the dose shall be repeated and column II contains the dose repetition interval. For instance to specify a dose of 10 every 12 hours during 3 days it is possible to write:
ID TIME AMT
Tom 0 10
Tom 12 10
Tom 24 10
Tom 36 10
Tom 48 10
Tom 60 10
Tom 72 10
but ADDL and II (interdose-interval) can also be used to specify the same information in a single line
ID TIME AMT ADDL II
Tom 0 10 6 12
Notice that in the proposed example, ADDL should be at 6 to have 6 additional administrations. This is very useful for periodic treatments. Two important remarks concerning regression values:
• If there is a regression-column (i.e. a column with column-type X), its value will also be repeated for added doses even though this value has not been specified but obtained via interpolation.
• When regression values are defined after the first added dose, warnings are generated. Indeed these values will not be repeated and can possibly interfere with automatically added regression values at dose time. So the warning is generated for the user to confirm that its data make sense.
Format restrictions (an exception will be thrown otherwise):
• ADDL shall only contain positive (or null) integers or “.” (which will be replaced by 0).
• When there is an ADDL column there must be an II (interdose interval) column to indicate the inter dose timing.
• For dose-lines with ADDL strictly positive, the II value must be strictly positive.
COV: continuous covariate
It is possible to have in a data set one or several columns with column-type COV. There must be one covariate defined per subject-occasion else wise. String “.” can be used to prevent multiple definitions of a covariate for a subject-occasion as it is interpreted as an absence of definition. Therefore, we encourage the user to either define the covariate at each line, or, more simply, at the first use of a subject for readability reasons (even if the covariate has not necessarily to be defined at first occurrence of subject-occasion in the data set).
Format restrictions (an exception will be thrown otherwise):
• Continuous covariate columns shall contain either strings that can be converted to double or “.”.
• The covariate must be defined at least each time per subject-occasion.
• The covariate must remain the same for all the lines within the same subject-occasion.
CAT: categorical covariate
It is possible to have in a data set one or several columns with column-type CAT. It is possible to enter in a CAT column any string and “.” has no special meaning. We strongly recommend to use only alphanumeric characters and the underscore “_” character in the strings of the CAT columns. In the MonolixSuite 2016R1, special characters such as spaces ” “, stars “*”, parentheses “(“, brackets “[“, dashes “-“, dots “.” and slashes “/” are not supported (this feature will be back in the next release).
Moreover, on the contrary to the continuous covariable, the following data set will generate an error
ID OCC CAT
Tom 1 M
Tom 1 .
Format restrictions (an exception will be thrown otherwise):
• The categorical covariable must be the same for all the lines with the same subject-occasion.
X: regression value
It is possible to have in a data set one or several columns with column-type X. Within a given subject-occasion, string “.” will be interpolated (nearest neighbor interpolation is used) for dose-lines only (N.B.: if there is an EVID column dose-lines correspond to EVID = 1 or EVID = 4). Else wise, for measurement line, no interpolation is performed. If no regressor is defined on such a line, it will be replaced by a NaN. Therefore, in the following data set example,
ID TIME X AMT Y EVID
Tom 0 . 1 . 1
Tom 5 1 . 12 0
Tom 10 . . 10 0
Tom 15 12 1.5 . 1
Tom 20 -6 . 8 0
Tom 25 . 0.2 . 4
Tom 30 . . 0.1 0
The evolution of X with respect to time is defined by the following figure.
Thus, X is set to
• X(0) = 1 (it is a dose-line so an interpolation is realized. The nearest interpolation is realized and here nearest sample corresponds to a response-line).
• X(5) = 1 (from direct reading of input file even if the line does not correspond to a dose).
• X(10) = NaN (regression is undefined in the input file but since it is not a dose-line, no interpolation is realized).
• X(15) = 2 (from direct reading of input file).
• X(20) = 3 (from direct reading of input file even though the line does not correspond to a dose).
• X(25) = 3 (it is a dose-line so an interpolation is realized. The nearest interpolation is realized and here nearest sample corresponds to a response-line).
• X(30) = NaN (regression is undefined in the input file but since it is not a dose-line, no interpolation is realized).
To add a valid information between time 10 and 15, for example X = 1.5, the data set should contain both a regressor value at time 10 along with the measurement value,
Tom 10 1.5 . 10 0
Notice that if the line has a MDV value at 1, the regression is not taken into account.
Format restrictions (an exception will be thrown otherwise):
• The regression-columns (i.e. columns with column-type X) shall contain either strings that can be converted to double or “.”.
• Each subject-occasion must contain at least one non “.” value (since it is then impossible to interpolate values).
• When there are several lines with the same time, the value of the regressor column must be the same.
EVID: event identification data item.
EVID corresponds to the identification of an event. It is an integer between 0 and 4. It helps to define the type of line.
• EVID = 0: observation event, the line is a response-line.
• EVID = 1: dose event, the line is a dose-line.
• EVID = 2: other event. UNUSED (exception thrown). To define times for model predictions without corresponding observations, use MDV=2.
• EVID = 3: reset event. UNUSED (exception thrown).
• EVID = 4: reset + dose event, indicates a wash-out (i.e reset to initial values) immediately followed by a dose.
Format restrictions (an exception will be thrown otherwise):
• A data set shall not contain more than one column with column-type EVID.
• EVID shall contain an integer in [0, 4].
• when a line is tagged (EVID = 0), the observation contained in column Y shall be convertible to a double value.
• when a line is tagged (EVID = 1, EVID = 4), the value in dose-column (i.e. content of the column with column-type AMT) shall be convertible to a double.
MDV: missing dependent variable.
The MDV column-type enables to tag lines for which the information in the Y column-type is missing. Most of the time, this column is not necessary.
• MDV=0: when a line is tagged MDV = 0 AND if it contains a string convertible to a double value in response-column (the column with column-type Y), then the value in the Y column is taken into account. Values in dose-column (the column with column-type AMT) will not be taken into account.
• MDV=1: when a line is tagged MDV = 1 then the value in column Y will not be taken into account. The value in dose-column, if present, will be taken into account.
• MDV=2: when a line is tagged MDV = 2 then the value in the response-column is not taken into account. The value in dose-column, if present, will be taken into account. The time, covariates, regressors, etc will be taken into account to output a prediction at that time point.
If there are both a MDV and EVID columns, the EVID column is used in priority.
The MDV column is useful to ignore specific response-lines, for instance if the observation is obviously wrong. If a MDV column is added to the dataset, the response-lines to ignore should have MDV=1, but also the dose-lines should have MDV=1 (otherwise the dose will be ignored). MDV=2 permits to define times at which model predictions should be outputted, even if there is no corresponding observation.When there are multiple MDV columns, a synthetic value MDV is computed as:
• if MDV = 0 in all columns, then resulting synthetic MDV equals 0.
• if MDV = 1 in at least one column and the other equals 0, then the resulting synthetic MDV equals 1.
• if MDV = 2 in at least one column and the other equals 0, then the resulting synthetic MDVsynth equals 2.
Format restrictions (an exception will be thrown otherwise):
• MDV shall contain only integers belonging to interval [0, 2].
• When MDV=0, the value in the Y column should be convertible to a double value, otherwise an exception will be thrown.
Character definition
We recommend to use only alphanumeric characters and the underscore “_” character in the strings of your data set.
Unfortunately, in the Monolix2016R1 suite, special characters such as spaces ” “, stars “*”, parentheses “(“, brackets “[“, dashes “-“, dots “.” and slashes “/” are not supported in:
• The strings in CAT column.
This feature will be back in the next release.
Please be careful that if your data set includes unsupported characters, the error will only de detected and displayed when loading a saved project (and not when creating and saving the project).
On the use of “.”
The “.” can be used in almost all the lines of the data set but has several meaning depending on the context. The following table summarizes the use of it.
Type of column Not allowed Considered as a regular string Considered as Not considered ID X OCC X TIME X DATE/DAT1/DAT2/DAT3 X Y On a response line On a dose line YTYPE On a response line On a dose line (not read) CENS 0 LIMIT -Inf if CENS =1 , +Inf if CENS = -1 AMT On a dose line On a response line (not read) ADM On a dose line On a response line SS 0 ADDL 0 II 0 COV Previously defined value of the COV (in the ID/OCC) CAT X X (regressor) Interpolation on a dose line, NaN on a response line EVID X MDV X
3.Data set examples
This section presents several data sets to show some concrete data set and see how to integrate censored data, covariates, …
Data sets with continuous outputs
• Theophylline data set: continuous outputs are taken into account along with categorical and continuous covariates (sex and weight respectively). Moreover, censored data are also managed.
• Tobramycin data set: continuous PK output are taken into account, along with categorical and continuous covariates.
• HIV data set: two continuous censored outputs are considered. No dose is used in the data set, and the treatment type is considered as a categorical covariate.
• Veralipride data set: continuous output with an interesting absorption variability being by far the most probable physiological explanation for the double peak phenomenon.
• Remifentanil data set: Remifentanil is an opioid analgesic drug with a rapid onset and rapid recovery time. Remifentanil concentration over 65 healthy adults is proposed.
Data sets with discrete count outputs
• Epilepsy attacks data set: count outputs are taken into account along with categorical and continuous covariates. The data arose from a clinical trial of 59 epileptics who were randomized to receive either the anti-epileptic drug progabide or a placebo, as an adjuvant to standard chemotherapy. Patients attended four successive post-randomisation clinic visits, where the number of seizures that occurred over the previous 2 weeks was reported.
• Crohn’s Disease Adverse Events data set: Data set issued from a study of the adverse events of a drug on 117 patients affected by Crohn’s disease (a chronic inflammatory disease of the intestines). In addition to the response variable number of adverse events, 7 explanatory variables were recorded for each patient.
Data sets with discrete categorical outputs
• Respiratory status data set: the respiratory status of patients under placebo or treatment is categorized as “poor” or “good” once per month during 5 months over 111 patients.
• Inpatient multidimensional psychiatric data set: categorical output with a categorical covariate (treatment) during 6 weeks. These data are from the National Institute of Mental Health Schizophrenia Collaborative Study and are available here. Patients were randomized to receive one of four medications, either placebo or one of three different anti-psychotic drugs. The primary outcome is item 79 on the Inpatient Multidimensional Psychiatric.
• Zylkene data set: The putative effects of a tryptic bovine αs1-casein hydrolysate on anxious disorders in cats was investigated using this data set over 24 cats. The score is a global score of emotional state.
Data sets with time-to-event outputs
• PBC data set: PBC is a rare but fatal chronic liver disease of unknown cause, with a prevalence of about 50-cases-per-million population. Between January, 1974 and May, 1984, the Mayo Clinic conducted a double-blinded randomized trial in primary biliary cirrhosis of the liver (PBC), comparing the drug D-penicillamine (DPCA) with a placebo.
• Oropharynx data set: The following data set provides the data for a part of a large clinical trial carried out by the Radiation Therapy Oncology Group in the United States. One objective of the study was to compare the two treatment policies with respect to patient survival.
• Veterans’ Administration Lung Cancer data set: In this study conducted by the US Veterans Administration, time to death was recorded for 137 male patients with advanced inoperable lung cancer, which were given either a standard therapy or a test chemotherapy.
• NCCTG lung cancer data set: The North Central Cancer Treatment Group (NCCTG) data set records the survival (time-to-event output) of 228 patients with advanced lung cancer, together with assessments of the patients performance status measured either by the physician and by the patients themselves.
• Cardiovascular data set: A subset of the fields was selected to model the differential length of stay for patients entering the hospital to receive one of two standard cardiovascular procedures: CABG and PTCA. The data set contains 3589 individuals.
Joint data sets
• Warfarin data set: Warfarin is an anticoagulant normally used in the prevention of thrombosis and thromboembolism. Plasma warfarin concentrations and Prothrombin Complex Response in thirty normal subjects after a single loading dose are measured. Both measurements are continuous.
• Remifentanil data set: Remifentanil is an opoid analgesic drug with a rapid onset and rapid recovery time. Both remifentanil concentration and EEG measurement are proposed on 65 healthy adults. Both measurements are continuous.
• PSA and survival data set: PSA kinetics and survival data for 400 men with metastatic Castration-Resistant Prostate Cancer (mCRPC) treated with docetaxel and prednisone, the first-line reference chemotherapy, which constituted the control arm of a phase 3 clinical trial. In this context of advanced disease, the incidence of death is high and the PSA kinetics is closely monitored after treatment initiation to rapidly detect a breakthrough in PSA and propose rescue strategies.
Theophylline data set
The data considered here are courtesy of Dr. Robert A. Upton of the University of California, San Francisco. Theophylline is a methylxanthine drug used in therapy for respiratory diseases such as chronic obstructive pulmonary disease (COPD) and asthma under a variety of brand names. Theophylline was administered orally to 12 subjects whose serum concentrations were measured at 11 times over the next 25 hours. This is an example of a laboratory pharmacokinetic study characterized by many observations on a moderate number of individuals. The data set can be seen here, and the corresponding Datxplore project here (notice that both file should be in the same folder to be correctly linked). A representation of the concentration over time for each subject is presented on the following figure (notice, that this figure was generated using Datxplore).
The purpose of this page is to see the construction, the definition and the use of such a data set in Datxplore and Monolix. For sake of simplicity, we look only on one subject (corresponding to ID 1).
Simplified data set
The data set for subject one writes as follows
ID AMT TIME CONC WEIGHT SEX
1 4.02 0 . 79.6 M
1 . 0.25 2.84 79.6 M
1 . 0.57 6.57 79.6 M
1 . 1.12 10.5 79.6 M
1 . 2.02 9.66 79.6 M
1 . 3.82 8.58 79.6 M
1 . 5.1 8.36 79.6 M
1 . 7.03 7.47 79.6 M
1 . 9.05 6.89 79.6 M
1 . 12.12 5.94 79.6 M
1 . 24.37 3.28 79.6 M
Interpretation
One can see the following columns
Several points can be noticed.
1. The first line corresponds to a dose, while the other ones are measurements. This explains the dot in the CONC column for the first line and the dots in the AMT column for the other ones.
2. The covariates columns (the continuous WEIGHT and the categorical SEX) are constant over the individual. Even though it is not necessary, we encourage the user to fill the columns for readability and usage reasons.
3. Finally, notice that no initial washout is needed at the beginning as by default, the null initial condition is used for parameter estimation.
Warfarin data set
This data set has been originally published in:
O’Reilly (1968). Studies on coumarin anticoagulant drugs. Initiation of warfarin therapy without a loading dose. Circulation 1968, 38:169-177.
Warfarin is an anticoagulant normally used in the prevention of thrombosis and thromboembolism, the formation of blood clots in the blood vessels and their migration elsewhere in the body, respectively. The data set provides set of plasma warfarin concentrations and Prothrombin Complex Response in thirty normal subjects after a single loading dose. A single large loading dose of warfarin sodium, 1.5 mg/kg of body weight, was administered orally to all subjects. Measurements were made each 12 or 24h.
On the two following figure, one could see the concentration and the effect with respect to time for all subjects.
The data set for subject one can be defined as follows
id time amt dv dvid wt age sex
1 0 100 . 1 66.7 50 1
1 0 . 100 2 66.7 50 1
1 24 . 9.2 1 66.7 50 1
1 24 . 49 2 66.7 50 1
1 36 . 8.5 1 66.7 50 1
1 36 . 32 2 66.7 50 1
1 48 . 6.4 1 66.7 50 1
1 48 . 26 2 66.7 50 1
1 72 . 4.8 1 66.7 50 1
1 72 . 22 2 66.7 50 1
1 96 . 3.1 1 66.7 50 1
1 96 . 28 2 66.7 50 1
1 120 . 2.5 1 66.7 50 1
1 120 . 33 2 66.7 50 1
Interpretation
One can see the following columns
Several points can be noticed.
1. The first line corresponds to a dose, while the other ones are measurements. This explains the dot in the CONC column for the first line and the dots in the AMT column for the other ones.
2. The covariates columns (the continuous wt and the categorical covariates age and sex) are filled with the same values. Even though it is not necessary, we encourage the user to fill the columns for readability and usage reasons.
3. In the presented case, both PK and PD measurements are at the same time, this is not required for data exploration using Datxplore, nor parameter estimation using Monolix.
4. Finally, notice that no initial washout is needed at the beginning as by default, the null initial condition is used for parameter estimation.
Interestingly, one can display the Effect with respect to the Concentration in order to have an idea on how to model the interaction between the PD and the PK part.
Then, the response does not seem to be direct. Notice that, as the observation times are no the same between the PK and the PD, interpolation is made to propose this kind of plot. One can also focus on one individual in particular as on the following figure
Notice that we also propose a red arrow to describe the evolution of time.
3.1.3.Tobramycin data set
This data set has been originally published in:
Aarons, L., Vozeh, S., Wenk, M., Weiss, P. H., & Follath, F. (1989). Population pharmacokinetics of tobramycin. British journal of clinical pharmacology, 28(3), 305-314.
Tobramycin is an antimicrobial agent of the aminoglycosides family, which is among others used against severe gram-negative infections. Because tobramycin does not pass the gastro-intestinal tract, it is usually administrated intravenously as intermittent bolus doses or short infusions. Tobramycin is a drug with a narrow therapeutic index.
Tobramycin bolus doses ranging from 20 to 140mg were administrated every 8 hours in 97 patients (45 females, 52 male) during 1 to 21 days (for most patients, during ~6 days). Age, weight (kg), sex and creatinine clearance (mL/min) were available as covariates. The tobramycin concentration (mg/L) was measured 1 to 9 times per patients (322 measures in total), most of the time between 2 and 6h post-dose. This sparse data set is presented on the figure below
Below is an extract of the data set:
The columns have the following meaning:
Several points can be noticed:
1. The four first lines correspond to doses, while the other ones are measurements, as indicated by the EVID column. The MDV column is not necessary. The zeros of the DOSE and CP columns could have been replaced by dots ‘.’ .
2. The covariates columns (WT, SEX and CLCR) are filled with the same value for each individual. Covariates must be constant within subjects (or subject-occasions when occasions are defined).
HIV data set
In the COPHAR II-ANRS 134 trial, an open prospective non-randomized interventional study, 115 HIV-infected patients adults started an antiviral therapy. 48 patients were treated with indinavir (and ritonavir as a booster) (treatment A), 38 with lopinavir (and ritonavir as a booster) (treatment B), and 35 with nelfinavir (Treatment C). patients were followed one year after treatment initialization.
Viral load and CD4 cell count were measured at screenin, at inclusion and at weeks 2 (or 4), 8, 16, 24, 36, and 48. Plasma HIV-1-RNA were measured by Roche monitored with a limit of quantification of 50 copies/ml. The results of this trial are reported in Duval and al. (2009). The data set can be seen here, and the corresponding Datxplore project here (notice that both file should be in the same folder to be correctly linked).
On the two following figures, one could see the two outputs with respect to time for all subjects split by treatments. The red circle corresponds to censored data.
Notice, that these figures were generated using Datxplore.
Simplified HIV data set
The data set for subject 2 can be defined as follows
ID TIME Y_NCENS Y CENS YTYPE TREATMENT
2 -2.43 4.9443 4.9443 0 1 A
2 -2.43 249 249 0 2 A
2 0 4.5245 4.5245 0 1 A
2 2 2.3546 2.3546 0 1 A
2 2 266 266 0 2 A
2 4.29 268 268 0 2 A
2 8 2.5585 2.5585 0 1 A
2 8 34 34 0 2 A
2 16 352 352 0 2 A
2 24 1.7981 2 1 1 A
2 24 385 385 0 2 A
2 32 348 348 0 2 A
2 43 415 415 0 2 A
Interpretation
One can see the following columns
Several points can be noticed.
1. There are no dose in the data set.
2. There is only a categorical covariate defining the treatment.
3. In the presented case, one does not necessary have both measurements at the same time. Indeed, this is not required for data export using Datxplore, nor parameter estimation using Monolix. Moreover, measurements for negative time is possible.
3.2.1.Epilepsy attacks data set
This data set has been originally published in:
Leppik, IE. et al. (1985) A double-blind crossover evaluation of progabide in partial seizures. Neurology 35, 285.
The data arose from a clinical trial of 59 epileptics who were randomized to receive either the anti-epileptic drug progabide or a placebo, as an adjuvant to standard chemotherapy. The hope was that progabide would help to reduce the number of seizures experienced by patients. Patients attended four successive post-randomisation clinic visits, where the number of seizures that occurred over the previous 2 weeks was reported. At baseline, information on the age of the patient and the 8-week pre-randomisation seizure count was recorded.
Below is an extract of the data set:
The columns have the following meaning:
Several points can be noticed:
1. There are several seizure counts for each individual, thus the time allows to define to which period it is related.
2. ID and TIME column are mandatory. Thus, if there is only one count measurement by individual, an additional column with TIME should be added (full of 0 for example).
3. The covariates columns (treatment, base and age) are filled with the same value for each individual. Covariates must be constant within subjects (or subject-occasions when occasions are defined).
Moreover, we can split by the covariate treatment and thus see the impact of the treatment
It seems the the subjects with the treatment have lower seizure rate. We can also display it grouped and not in a spaghetti display as in the following
Using that, we have a better understanding of the seizure_rate, and it seems that the treatment is effective.
PBC data set
PBC is a rare but fatal chronic liver disease of unknown cause, with a prevalence of about 50-cases-per-million population. The primary pathologic event appears to be the destruction of interlobular bile ducts, which may be mediated by immunologic mechanisms.
Between January, 1974 and May, 1984, the Mayo Clinic conducted a double-blinded randomized trial in primary biliary cirrhosis of the liver (PBC), comparing the drug D-penicillamine (DPCA) with a placebo. There were 424 patients who met the eligibility criteria seen at the Clinic while the trial was open for patient registration. Both the treating physician and the patient agreed to participate in the randomized trial in 312 of the 424 cases. The date of randomization and a large number of clinical, biochemical, serologic, and histologic parameters were recorded for each of the 312 clinical trial patients. The data from the trial were analyzed in 1986 for presentation in the clinical literature. For that analysis, disease and survival status as of July, 1986, were recorded for as many patients as possible. By that date, 125 of the 312 patients had died, with only 11 not attributable to PBC. Eight patients had been lost to follow up, and 19 had undergone liver transplantation.
The considered data set comes from Counting Processes and Survival Analysis by T. Fleming & D. Harrington, (1991), published by John Wiley & Sons. The data set can be seen here, and the corresponding Datxplore project here (notice that both file should be in the same folder to be correctly linked).
On the following figure, one could see the survival curve and the mean number of events with respect to time. Notice, that this figure was generated using Datxplore.
In this data set, there are a lot of available covariates
id = case number
futime = number of days between registration and the earlier of death,
transplantion, or study analysis time in July, 1986
status = 0=alive, 1=liver transplant, 2=dead
drug = 1= D-penicillamine, 2=placebo
age = age in days
sex = 0=male, 1=female
ascites = presence of ascites: 0=no 1=yes
hepato = presence of hepatomegaly 0=no 1=yes
spiders = presence of spiders 0=no 1=yes
edema = presence of edema 0=no edema and no diuretic therapy for edema;
.5 = edema present without diuretics, or edema resolved by diuretics;
1 = edema despite diuretic therapy
bili = serum bilirubin in mg/dl
chol = serum cholesterol in mg/dl
albumin = albumin in gm/dl
copper = urine copper in ug/day
alk_phos = alkaline phosphatase in U/liter
sgot = SGOT in U/ml
trig = triglicerides in mg/dl
platelet = platelets per cubic ml/1000
protime = prothrombin time in seconds
stage = histologic stage of disease
On the two following figure, one could see the survival curve and the mean number of events with respect to time for two groups, the first groups concerns the subjects younger than 52.3 years and the other group concerns the other one. Notice, that this figure was generated using Datxplore.
Simplified PBC data set
The data set for subjects 1 and 2 can be defined as follows
ID;TIME;Y;TRT;AGE;SEX;
1;0;0;1;58.7652;1;
1;400;1;1;58.7652;1;
2;0;0;1;56.4463;1;
2;4500;0;1;56.4463;1;
One must indicated the start time of the observation period with Y=0 (at line 1 and 3 for subject 1 and 2 respectively), and the time of event (Y=1) or the time of the end of the observation period if no event has occurred (Y=0). In this simplified data set, subject one had an event at time 400 leading to a line in the data set where Y=1. On the contrary, no event occurred for subject 2. Thus, at the end of the observation (TIME=4500), Y is set to 0.
Oropharynx data set
The following data set provides the data for a part of a large clinical trial carried out by the Radiation Therapy Oncology Group in the United States. The full study included patients with squamous carcinoma of 15 sites in the mouth and throat, with 16 participating institutions, though only data on three sites in the oropharynx reported by the six largest institutions are considered here. Patients entering the study were randomly assigned to one of two treatment groups, radiation therapy alone or radiation therapy together with a chemotherapeutic agent. One objective of the study was to compare the two treatment policies with respect to patient survival. Approximately 30% of the survival times are censored owing primarily to patients surviving to the time of analysis. Some patients were lost to follow-up because the patient moved or transferred to an institution not participating in the study, though these cases were relatively rare.
The considered data set comes from The Statistical Analysis of Failure Time Data, by JD Kalbfleisch & RL Prentice, (1980), Published by John Wiley & Sons.The data set can be seen here, and the corresponding Datxplore project here (notice that both file should be in the same folder to be correctly linked).
On the following figure, one could see the survival curve and the mean number of events with respect to time. Notice, that this figure was generated using Datxplore.
This study included measurements of many covariates which would be expected to relate to survival experience. Six such variables are given in the data (sex, T staging, N staging, age, general condition, and grade). The site of the primary tumor and possible differences between participating institutions require consideration as well.
CASE Case Number
INST Participating Institution
SEX 1=male, 2=female
TX Treatment: 1=standard, 2=test
3=poorly differentiated, 9=missing
AGE In years at time of diagnosis
COND Condition: 1=no disability, 2=restricted work, 3=requires assistance
with self care, 4=bed confined, 9=missing
SITE 1=faucial arch, 2=tonsillar fossa, 3=posterior pillar,
4=pharyngeal tongue, 5=posterior wall
T_STAGE 1=primary tumor measuring 2 cm or less in largest diameter,
2=primary tumor measuring 2 cm to 4 cm in largest diameter with
minimal infiltration in depth, 3=primary tumor measuring more
than 4 cm, 4=massive invasive tumor
N_STAGE 0=no clinical evidence of node metastases, 1=single positive
node 3 cm or less in diameter, not fixed, 2=single positive
node more than 3 cm in diameter, not fixed, 3=multiple
positive nodes or fixed positive nodes
ENTRY_DT Date of study entry: Day of year and year, dddyy
TIME Survival time in days from day of diagnosis
On the two following figure, one could see the survival curve and the mean number of events with respect to time for two groups, the first groups concerns the subjects younger than 55 years and the other group concerns the other one. Notice, that this figure was generated using Datxplore.
Simplified Oropharynx data set
The data set for subjects 47 and 48 can be defined as follows
ID;INST;SEX;TRT;GRADE;AGE;COND;SITE;T_STAGE;N_STAGE;ENTRY_DT;Y;Time
47;4;1;2;2;49;3;1;4;3;5669;0;0
47;4;1;2;2;49;3;1;4;3;5669;1;74
48;3;1;1;1;44;1;1;3;1;2769;0;0
48;3;1;1;1;44;1;1;3;1;2769;0;1609
One must indicated the start time of the observation period with Y=0 (at line 1 and 3 for subject 47 and 48 respectively), and the time of event (Y=1) or the time of the end of the observation period if no event has occurred (Y=0). In this simplified data set, subject 47 had an event at time 74 leading to a line in the data set where Y=1. On the contrary, no event occurred for subject 48. Thus, at the end of the observation (TIME=1609), Y is set to 0.
4.1.FAQ
• Which file formats are supported? Text and comma-separated values file are allowed. The file extension should preferably be .txt or .csv.
• Should I have a header line? Yes, having a header line is mandatory.
• Are there restrictions on header names? No, there is no limitation in terms of names nor on character number. However, some characters are not allowed as in the rest of the data file (see here).
• Which column types are mandatory? The ID, TIME and Y column-types are mandatory. All others are optional.
• Which column-types are possible? The complete list of supported column-types can be found here.
• Which separators are allowed? The supported separators are comma (“,”), semicolon (“;”), space (” “), and tab (“\t”).
• Which characters are allowed in strings? The list of allowed characters can be found here.
• What does “.” mean? The “.” can be used in almost all the lines of the data set but has several meaning depending on the context. A summary can be found here.
• How can I ignore certain response-lines of my data set? Use MDV=1 for that.
• Can I specify time in hour or in days? Yes, all the possible formats are defined here.
• Can the data by split into several files (for instance one file for dosing and one for observations)? No. All the data must be grouped into a single file.
Questions about format difference with NONMEM
• What are the differences between Monolix and Nonmem in terms of data set? The few differences are listed here.
• What is the equivalent of the NONMEM CMT column? Depending on the usage of the CMT column, it can correspond to the YTYPE column-type, the ADM column-type or to both. All differences between NONMEM and the MonolixSuite are listed here.
• Must all lines corresponding to the same individual be grouped? No, this is not necessary. All lines with the same ID will be assigned to the same individual, whatever their order or grouping.
• How can I define occasions? For that, you can use the OCC column-type as explained here.
• Must the times be in ascending order? For a given individual, the times do not need to be in order. The sorting will be done automatically.
• Can I specify time in hour or in days? Yes, all the possible formats are defined here.
• Can time have negative values? Yes.
• For time-to-event data, do I have to indicate the start time? Yes, it must be explicitly stated, for instance with TIME=0 and Y=0. Guidelines for data set formatting for time-to-event data are given here.
• Are non-continuous data types (such as count, time-to-event and categorical data) supported? Yes. Exemples of data set for non-continuous data types are presented here.
• Which value should I enter in the Y column-type for BLQ values? In the Y column-type, give the limit of quantification (LOQ). To mark the observations as being BLQ, use the CENS column-type. To indicate a censoring interval, use the LIMIT column-type (in addition to the CENS and Y columns).
• Can my data set contain different types of observations? Yes, use the YTYPE column to define to which type of data the line corresponds. An example data set with different types of observations is presented here.
• What happen if I define both a dose and a response in the same line? Depending on the values, it can be a dose, a response. To see all the configurations, see here.
• What happen if I define both a dose and a response in the same line? Depending on the values, it can be a dose, a response. To see all the configurations, see here.
• For dose-lines, should I specify the compartment into which the dose is introduced? No. In the MonolixSuite, the matching between the data (dose and observation lines) and the model (administrations and predictions) is done using identifiers, not based on compartment numbers. To assign a dose to a specific administration of the model (oral or iv macros for classical PK models, depot macro for more complex ODEs), the column ADM is used. The identifier in the ADM column should match the “type=” field of the macro.
• If I have several outputs, should I duplicate the dosing information? No.
• Can I have time-varying covariates? Continuous (COV) and categorical (CAT) covariates must be contant within a subject-occasion. Yet continuous covariates can be tagged as regressors (column-type X). However, if a continuous covariate varies with respect to time, the first value declared will be used for the entire subject-occasion.
• How can I ignore certain response-lines of my data set? Use MDV=1 for that.
• Are the MDV and EVID columns necessary? These columns are not mandatory and most of the time not necessary.
• Which values are allowed for EVID? EVID can takes the values EVID=0 (observation), EVID=1 (dose) and EVID=4 (reset followed by a dose). EVID=2 and EVID=3 are not supported.
• How can I define a time at which I which the output the predictions, even if I have no observation? Use MDV=2 for this purpose.
4.2.Translating your dataset from NONMEM format to the Monolix Suite format
The required format for the data set in NONMEM and in the Monolix Suite is very similar. Usually only few changes (if any) are required to go from one format to the other one.
General formatting
• Column names: in the Monolix Suite column names are not restricted in length, and not restricted to uppercase format. Yet, only alphanumeric and the underscore “_” characters are allowed. Special characters such as spaces ” “, stars “*”, parenthèses or brackets “(“, dashes “-“, slashes “/” are not supported.
• Header line: no need to start the header line with the “#” character in the Monolix Suite, the column headers line will be recognized automatically.
• Number of columns: there is no limitation of the number of columns in the Monolix Suite
Dose column-types
• SS column: SS=2 and SS=3 are not supported in the Monolix Suite. When a data set contains a column with column-type SS, there must be a column with column-type II. If SS=1, then the value in the II column must be strictly positive. In case of steady-state, steady-state formulas are not used. Instead, additional doses (5 by default) are added before the SS dose to reach steady-state.
• RATE and TINF: in case of an infusion, in the Monolix Suite, it is possible to define either the rate (RATE column-type) or the duration (TINF column-type). The rate and the duration are related to each other via the amount: TINF=RATE/AMT. Negative values in the RATE column-type result in a bolus, when used in combination with the iv macro (and models from the library with iv). When used in combination with the oral macro (and models from the library with oral0 or oral1), the RATE column is ignored if the value is negative and an error is triggered if the value is positive. If infusion duration is defined in the model (parameter or fixed value), the RATE column is not necessary (in opposition to NONMEM, where RATE=-1 and RATE=-2 are used).
• CMT column: in NONMEM, for observation-lines, CMT specifies the compartment from which the predicted value of the observation is obtained. For dose-lines, CMT specifies the compartment into which the dose is introduced. In the MonolixSuite, the matching between the data (dose and observation lines) and the model (administrations and predictions) is done using identifiers, not based on compartment numbers. To assign a dose to a specific administration of the model (oral or iv macros for classical PK models, depot macro for more complex ODEs), the column ADM is used. The identifier in the ADM column should match the “type=” field of the macro. To assign an observation to a prediction, the column YTYPE is used. Observation lines with YTYPE=1 will be assigned to the first output (output = {…} statement in the model file), lines with YTYPE=2 to the second output, etc. Note that the default values for the administration type in administration macros or in the pkmodel macro is type=1. Similarly, in case of a single output, YTYPE=1 by default (while in NONMEM, the central compartment may have number 1 or 2). In the ADM column-type, negative values are not allowed. Turning off compartments should instead be defined in the model file.
Control and event columns-types
• EVID column-type: in the Monolix Suite, the EVID column is not mandatory, since dose-events (EVID=1) and response-events (EVID=0) are automatically recognized. Note that the Monolix Suite does not recognize EVID=2 (“Other event”) and EVID=3 (“Reset event”), but recognizes EVID=4 (which corresponds to a reset to initial values immediately followed by a dose). EVID=4 creates a new occasion for the individual. In NONMEM, EVID=2 is sometimes used to define a time point at which one would like to predict a concentration, without having an observation. In the Monolix Suite, this is done using MDV=2 (see below).
• MDV column-type: the MDV column is not mandatory in the Monolix Suite. Dose-lines and observation-lines will be recognized automatically. Yet the MDV column can be useful to force a response-line to be ignored (MDV=1). Several MDV columns are allowed, in this case a synthetic MDV value is computed. In the Monolix Suite, MDV can in addition take the value MDV=2, which permits to define a time point (and possibly a regressor value) to output a prediction without having the corresponding observation. In Monolix, the time points tagged MDV=2 will for instance appear in the table “fulltimes.txt”, outputted when selecting “All times” in the “Outputs to save” window.
Response column-types
• Censored data: in the Monolix Suite, censored data should be tagged in the data set using additional columns with CENS (mark as censored observation) and if necessary LIMIT (give other interval boundary) column-types. The LOQ value is indicated in the Y column. Censored data are then automatically taken into account in the likelihood in a rigorous statistical way. If only the CENS column is used, the method in the MonolisSuite is equivalent to the so-called M3 method. When both CENS and LIMIT are used, the method in equivalent to M4.
Subject identification columns-types
• ID column-type: in NONMEM all lines related to a single individual must be in one block, which is not the case in the Monolix Suite. If the ID column contains the following IDs: [1,1,1,2,2,1,1], NONMEM will consider that the dataset comprise three individuals with IDs 1 (with 3 observations), 2 (with 2 observations) and 1_1 (with 2 observations). In the Monolix Suite, two individuals are considered, with IDs 1 (with 5 observations) and 2 (with 2 observations).
Time column-types
• TIME column-type: values in the time column can be negative in the Monolix Suite.
Covariates and regression column-types
• Covariates: in the Monolix Suite, columns corresponding to continuous covariates must be set to the COV column-type, and categorical covariates to the CAT column-type
• Regression variables: in the Monolix Suite, regression variables must be set to the X column-type. If several regression variables are used, their order must be the same in the dataset and in the “input” field of the model file.
Unsupported column-types
• The PCMT, CONT, CALL, MRG_, RAW_, RPT_, L1, and L2 column-types are not supported in the MonolixSuite.
Suggest Edit | 2017-12-18 16:28:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5508721470832825, "perplexity": 2412.3313525062135}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948618633.95/warc/CC-MAIN-20171218161254-20171218183254-00474.warc.gz"} |
https://www.rdocumentation.org/packages/fda.usc/versions/2.0.2/topics/flm.Ftest | fda.usc (version 2.0.2)
# flm.Ftest: F-test for the Functional Linear Model with scalar response
## Description
The function flm.Ftest tests the null hypothesis of no interaction between a functional covariate and a scalar response inside the Functional Linear Model (FLM): $$Y=\big<X,\beta\big>+\epsilon$$. The null hypothesis is $$H_0:\,\beta=0$$ and the alternative is $$H_1:\,\beta\neq 0$$. The null hypothesis is tested by a functional extension of the classical F-test (see Details).
## Usage
Ftest.statistic(X.fdata, Y)flm.Ftest(X.fdata, Y, B = 5000, verbose = TRUE)
## Arguments
X.fdata
Functional covariate for the FLM. The object must be in the class fdata.
Y
Scalar response for the FLM. Must be a vector with the same number of elements as functions are in X.fdata.
B
Number of bootstrap replicates to calibrate the distribution of the test statistic. B=5000 replicates are the recommended for carry out the test, although for exploratory analysis (not inferential), an acceptable less time-consuming option is B=500.
verbose
Either to show or not information about computing progress.
## Value
The value for Ftest.statistic is simply the F-test statistic. The value for flm.Ftest is an object with class "htest" whose underlying structure is a list containing the following components:
• statistic The value of the F-test statistic.
• boot.statistics A vector of length B with the values of the bootstrap F-test statistics.
• p.value The p-value of the test.
• method The character string "Functional Linear Model F-test".
• B The number of bootstrap replicates used.
• data.name The character string "Y=<X,0>+e"
## Details
The Functional Linear Model with scalar response (FLM), is defined as $$Y=\big<X,\beta\big>+\epsilon$$, for a functional process $$X$$ such that $$E[X(t)]=0$$, $$E[X(t)\epsilon]=0$$ for all $$t$$ and for a scalar variable $$Y$$ such that $$E[Y]=0$$. The functional F-test is defined as $$T_n=\bigg\|\frac{1}{n}\sum_{i=1}^n (X_i-\bar X)(Y_i-\bar Y)\bigg\|,$$ where $$\bar X$$ is the functional mean of $$X$$, $$\bar Y$$ is the ordinary mean of $$Y$$ and $$\|\cdot\|$$ is the $$L^2$$ functional norm. The statistic is computed with the function Ftest.statistic. The distribution of the test statistic is approximated by a wild bootstrap resampling on the residuals, using the golden section bootstrap.
## References
Garcia-Portugues, E., Gonzalez-Manteiga, W. and Febrero-Bande, M. (2014). A goodness--of--fit test for the functional linear model with scalar response. Journal of Computational and Graphical Statistics, 23(3), 761-778. http://dx.doi.org/10.1080/10618600.2013.812519
Gonzalez-Manteiga, W., Gonzalez-Rodriguez, G., Martinez-Calvo, A. and Garcia-Portugues, E. Bootstrap independence test for functional linear models. arXiv:1210.1072. http://arxiv.org/abs/1210.1072
rwild, flm.test, dfv.test
## Examples
# NOT RUN {
## Simulated example ##
X=rproc2fdata(n=50,t=seq(0,1,l=101),sigma="OU")
beta0=fdata(mdata=rep(0,length=101)+rnorm(101,sd=0.05),
argvals=seq(0,1,l=101),rangeval=c(0,1))
beta1=fdata(mdata=cos(2*pi*seq(0,1,l=101))-(seq(0,1,l=101)-0.5)^2+
rnorm(101,sd=0.05),argvals=seq(0,1,l=101),rangeval=c(0,1))
# Null hypothesis holds
Y0=drop(inprod.fdata(X,beta0)+rnorm(50,sd=0.1))
# Null hypothesis does not hold
Y1=drop(inprod.fdata(X,beta1)+rnorm(50,sd=0.1))
# Do not reject H0
flm.Ftest(X,Y0,B=100)
flm.Ftest(X,Y0,B=5000)
# Reject H0
flm.Ftest(X,Y1,B=100)
flm.Ftest(X,Y1,B=5000)
# } | 2021-04-20 20:14:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6870651841163635, "perplexity": 1818.9867525292673}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039490226.78/warc/CC-MAIN-20210420183658-20210420213658-00228.warc.gz"} |
https://plainmath.net/94994/write-the-equation-of-a-line-in-slope-in | # Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)
Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2, 6)
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megagoalai
Given a line with slope m then the slope of a line perpendicular to it is
$•x{m}_{\text{perpendicular}}=-\frac{1}{m}$
the equation of a line in slope-intercept form is
y=mx+b
where m is the slope and b the y-intercept
y=−4x is in this form
with slope m=−4
$⇒{m}_{\text{perpendicular}}=-\frac{1}{-4}=\frac{1}{4}$
$⇒y=\frac{1}{4}x+b←\text{is the partial equation}$
to find b substitute (2,6) into the partial equation
$6=\frac{1}{2}+b⇒b=\frac{12}{2}-\frac{1}{2}=\frac{11}{2}$
$⇒y=\frac{1}{4}x+\frac{11}{2}←\text{in slope-intercept form}$
###### Did you like this example?
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Solve your problem for the price of one coffee | 2022-12-06 07:56:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 29, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7472854852676392, "perplexity": 494.2282275173545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711074.68/warc/CC-MAIN-20221206060908-20221206090908-00309.warc.gz"} |
https://reliccastle.com/threads/4119/ | # v19.1Custom Evolution Items
This thread pertains to v19.1 of Pokémon Essentials.
#### Ashtastic
##### Rookie
Member
Hello!
After many hours of searching for guides, tutorials or anything on this subject, I cannot find out how to define a new item as an Evolutionary item.
I've tried searching around for the existing evolution items (Fire Stone etc.) but also to no result.
I've attempted to just add a line for a specific evolution method instead, directly calling for the item, but this also doesn't work (my game can't compile)
Attempt #1:
GameData::Evolution.register({
:id => :ItemSteeleon,
:parameter => :Item,
:use_item_proc => proc { |pkmn, parameter, item|
next item == :METALIZER
}
})
This is what I've tried to add, Metalizer being the custom item I've added for it. I've made an entry for it using thesame values as the other evolutionary stones in the Items PBS yet none of this seems to help.
What am I doing wrong, and is there any way to see the old PBItems script again? Every guide I've seen has all the evolutionary stones defined there, which would make all of this a whole lot easier.
#### TechSkylander1518
##### Wiki Dweeb
Member
No need to create a custom evolution method, the Item method can be used for any item at all! Just set Eevee's evolution method to STEELEON,Item,METALIZER!
PBItems has been broken up into a few script sections now, what you're wanting to see in this case is Item_Effects-
You shouldn't have to define a new effect for the Metalizer, though, because if it's defined as an evolutionary stone, it'll automatically be given that handler. Have you tried compiling the game with just the Metalizer in your PBS and without the new evolution method?
#### Ashtastic
##### Rookie
Member
This apparently was the issue, if I try to compile the game adding the Metalizer, with the evolution method, it crashes on compiling at the Evolution line. Adding the item first, then compiling and then adding the evolution method and compiling again seems to have solved the issue! Thank you for the help <3 | 2021-08-03 14:24:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37308719754219055, "perplexity": 1966.8948761569707}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00035.warc.gz"} |
http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1123.47044 | Language: Search: Contact
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Zbl 1123.47044
Ceng, L.C.; Cubiotti, P.; Yao, J.C.
Strong convergence theorems for finitely many nonexpansive mappings and applications.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 67, No. 5, A, 1464-1473 (2007). ISSN 0362-546X
This article deals with new, more cumbersome and freakish, approximations $x_n$ to a fixed point for nonexpansive mappings of a nonempty closed convex subset of a Banach space $E$; the authors consider the case when $E$ is reflexive and has a weakly continuous duality mapping and the norm of $E$ is uniformly Gâteaux differentiable. Moreover, they consider a finite family of nonexpansive mappings ${\cal T} = \{T_1, \dots, T_r\}$ of $C$ into itself with nonempty set of common fixed points and a class of $W$-mappings generated by ${\cal T}$. These $W$-mappings are defined by chains $U_1 = \alpha_1T_1 + (1 - \alpha_1)I$, $U_2 = \alpha_2T_2U_1 + (1 - \alpha_2)I, \dots , U_{r-1} = \alpha_{r-1}T_{r-1}U_{r-2} + (1 - \alpha_r)I$, $W = U_r = \alpha_rT_rU_{r-1} + (1 - \alpha_r)I$, where $\alpha, \dots , \alpha_r$ are reals from $[0,1]$. The authors' approximations are $$x_{n+1} = \lambda_ny + (1 - \lambda_n)W_nx_n, \quad n = 1,2,\dots, \ y, x_1 \in C,$$ where $W_n$ is a sequence of $W$-mappings generated by ${\cal T}$ and $\lambda_n$ is a sequence from $(0,1)$ such that $$\lim_{n \to \infty} \ \lambda_n = 0, \quad \sum_{n=1}^\infty \lambda_n = \infty, \quad \lim_{n \to \infty} \ \frac{\lambda_{n-1}}{\lambda_n} = 1.$$ Theorems on the strong convergence of these approximations are proved. Based on these results, the problem of finding a common fixed point of finitely many mappings is also considered.
[Peter Zabreiko (Minsk)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
Keywords: nonexpansive mapping; iterative scheme; common fixed point; strong convergence; Banach space; sunny nonexpansive retraction
Cited in: Zbl 1223.47098
Highlights
Master Server | 2013-05-22 19:32:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7488685250282288, "perplexity": 1046.8168689304068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368702414478/warc/CC-MAIN-20130516110654-00005-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://usa.cheenta.com/probability-amc-10b-problem-17/ | Categories
Probability AMC 10B 2019 problem 17
Try this beautiful problem of probability is based upon tossing the coin and finding probability from AMC 10B 2019. You may use sequential hints to help you solve the problem.
Competency in Focus: probability
This problem is from American Mathematics Contest 10B (AMC 10B, 2019). It is Question no. 17 of the AMC 10B 2019 Problem series.
Next understand the problem
[/et_pb_text][et_pb_text _builder_version=”4.2.2″ text_font=”Raleway||||||||” text_font_size=”20px” text_letter_spacing=”1px” text_line_height=”1.5em” background_color=”#f4f4f4″ custom_margin=”10px||10px” custom_padding=”10px|20px|10px|20px” box_shadow_style=”preset2″]A red ball and a green ball are randomly and independently tossed into bins numbered with the positive integers so that for each ball, the probability that it is tossed into bin $k$ is $2^{-k}$ for $k = 1,2,3….$ What is the probability that the red ball is tossed into a higher-numbered bin than the green ball?
$\textbf{(A) } \frac{1}{4} \qquad\textbf{(B) } \frac{2}{7} \qquad\textbf{(C) } \frac{1}{3} \qquad\textbf{(D) } \frac{3}{8} \qquad\textbf{(E) } \frac{3}{7}$[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version=”4.0″][et_pb_column type=”4_4″ _builder_version=”3.25″ custom_padding=”|||” custom_padding__hover=”|||”][et_pb_accordion open_toggle_text_color=”#0c71c3″ _builder_version=”4.2.2″ toggle_font=”||||||||” body_font=”Raleway||||||||” text_orientation=”center” custom_margin=”10px||10px”][et_pb_accordion_item title=”Source of the problem” _builder_version=”4.2.2″ open=”off”]American Mathematical Contest 2019, AMC 10B Problem 17[/et_pb_accordion_item][et_pb_accordion_item title=”Key Competency” open=”off” _builder_version=”4.2.2″ inline_fonts=”Abhaya Libre”]
Probability
[/et_pb_accordion_item][et_pb_accordion_item title=”Difficulty Level” _builder_version=”4.2.2″ open=”off”]4/10[/et_pb_accordion_item][et_pb_accordion_item title=”Suggested Book” _builder_version=”4.0.9″ open=”on”]Challenges and Thrills in Pre College Mathematics Excursion Of Mathematics
[/et_pb_text][et_pb_tabs _builder_version=”4.2.2″][et_pb_tab title=”HINT 0″ _builder_version=”4.0.9″]Do you really need a hint? Try it first![/et_pb_tab][et_pb_tab title=”HINT 1″ _builder_version=”4.2.2″]The probability that the two balls will go into adjacent bins is $\frac{1}{2\times4} + \frac{1}{4\times8} + \frac{1}{8 \times 16} + … = \frac{1}{8} + \frac{1}{32} + \frac{1}{128} + \cdots = \frac{1}{6}$ by the geometric series sum formula.[/et_pb_tab][et_pb_tab title=”HINT 2″ _builder_version=”4.2.2″]the probability that the two balls will go into bins that have a distance of $2$ from each other is $\frac{1}{2 \times 8} + \frac{1}{4 \times 16} + \frac{1}{8 \times 32} + \cdots = \frac{1}{16} + \frac{1}{64} + \frac{1}{256} + \cdots = \frac{1}{12}$[/et_pb_tab][et_pb_tab title=”HINT 3″ _builder_version=”4.2.2″]We can see that each time we add a bin between the two balls, the probability halves.[/et_pb_tab][et_pb_tab title=”HINT 4″ _builder_version=”4.2.2″]Thus, our answer is $\frac{1}{6} + \frac{1}{12} + \frac{1}{24} + \cdots$[/et_pb_tab][/et_pb_tabs][/et_pb_column][/et_pb_row][/et_pb_section][et_pb_section fb_built=”1″ fullwidth=”on” _builder_version=”4.2.2″ global_module=”50833″][et_pb_fullwidth_header title=”AMC – AIME Program” button_one_text=”Learn More” button_one_url=”https://www.cheenta.com/amc-aime-usamo-math-olympiad-program/” header_image_url=”https://www.cheenta.com/wp-content/uploads/2018/03/matholympiad.png” _builder_version=”4.2.2″ title_level=”h2″ background_color=”#00457a” custom_button_one=”on” button_one_text_color=”#44580e” button_one_bg_color=”#ffffff” button_one_border_color=”#ffffff” button_one_border_radius=”5px”] | 2021-07-25 15:55:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44775262475013733, "perplexity": 10898.446909577808}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046151699.95/warc/CC-MAIN-20210725143345-20210725173345-00530.warc.gz"} |
https://wiki.iota.org/next/smart-contracts/guide/wasm_vm/thunks | # Thunk Functions
In computer programming, a thunk is a wrapper function that is used to inject code around another function. Thunks are used to insert operations before and/or after the wrapped function is being called to adapt it to changing requirements. The Schema Tool will generate such thunk functions to be able to properly set up calls to the smart contract functions. It also creates a mapping between the name/id of the function and the actual function, and generates code to properly communicate this mapping to the ISC host.
In our case we use thunks not only to inject code around the smart contract function, but also to make the smart contract function type-safe. The thunks all have an identical function signature, and each will set up a function-specific data structure so that the actual smart contract function will deal with them in a type-safe way. Having a common function signature for the thunks means that it is easy to generate a table of all functions and their names that can be used to generically call these functions.
All code for this table and the thunks is generated as part of lib.xx and it looks as follows for the dividend example smart contract (for simplicity the thunk function contents has been omitted for now):
var exportMap = wasmlib.ScExportMap{ Names: []string{ FuncDivide, FuncInit, FuncMember, FuncSetOwner, ViewGetFactor, ViewGetOwner, }, Funcs: []wasmlib.ScFuncContextFunction{ funcDivideThunk, funcInitThunk, funcMemberThunk, funcSetOwnerThunk, }, Views: []wasmlib.ScViewContextFunction{ viewGetFactorThunk, viewGetOwnerThunk, },}func OnDispatch(index int32) { exportMap.Dispatch(index)}func funcDivideThunk(ctx wasmlib.ScFuncContext) {}func funcInitThunk(ctx wasmlib.ScFuncContext) {}func funcMemberThunk(ctx wasmlib.ScFuncContext) {}func funcSetOwnerThunk(ctx wasmlib.ScFuncContext) {}func viewGetFactorThunk(ctx wasmlib.ScViewContext) {}func viewGetOwnerThunk(ctx wasmlib.ScViewContext) {}
The key function here is the OnDispatch() function, which will be called by the main Wasm file. This main Wasm file is separate because the Wasm runtime format is essentially a dynamic link library. That means it not only defined exported functions, but also defines functions it needs to link to at a later stage, and which will be provided by the Wasm VM host.
We want to keep the SC code separate as a self-contained library that is independent of the Wasm format requirements, because we will be reusing the same SC code in client-side code that can directly execute SC requests through this same interface.
The Wasm host requires us to implement the on_load()and on_call() Wasm callback functions. These will directly dispatch these calls through the corresponding OnDispatch() function in the generated lib.xx.
The on_load() Wasm function will be called by the Wasm VM host upon loading of the Wasm code. It will inform the host of all the function ids and types (Func or View) that this smart contract provides.
When the host needs to call a function of the smart contract it will call the on_call() callback function with the corresponding function id, and then the on_call() function will dispatch the call via the ScExportMap mapping table that was generated by the Schema Tool to the proper associated thunk function.
This Wasm-specific code has been separated out in main.xx, as a separate package next to the SC library. For Rust it is a little more complex, so it has been separated out to a folder with the same name, followed by wasm. The src/lib.rs file serves the same function as the main.xx file in the other languages.
The Wasm-specific code will also make sure that the WasmVMHost code will be pulled into the Wasm code because that defines the missing import functions that will be provided by the Wasm VM host. In this way we manage to make WasmLib independent of the Wasm code format as well. WasmLib defines an ScHost interface that will define what host environment is used, which in this case is WasmVMHost. For the client-side code we implement a different ScHost that hides the differences.
Here is the generated main.xx that forms the main entry point for the Wasm code:
//go:build wasm// +build wasmpackage mainimport "github.com/iotaledger/wasp/packages/wasmvm/wasmvmhost/go/wasmvmhost"import "github.com/iotaledger/wasp/contracts/wasm/dividend/go/dividend"func main() {}func init() { wasmvmhost.ConnectWasmHost()}//export on_callfunc onCall(index int32) { dividend.OnDispatch(index)}//export on_loadfunc onLoad() { dividend.OnDispatch(-1)}
Finally, here is an example implementation of a thunk function for the setOwner() contract function. You can examine the other thunk functions that all follow the same pattern in the generated lib.xx:
type SetOwnerContext struct { Params ImmutableSetOwnerParams State MutableDividendState}func funcSetOwnerThunk(ctx wasmlib.ScFuncContext) { ctx.Log("dividend.funcSetOwner") f := &SetOwnerContext{ Params: ImmutableSetOwnerParams{ proxy: wasmlib.NewParamsProxy(), }, State: MutableDividendState{ proxy: wasmlib.NewStateProxy(), }, } // only defined owner of contract can change owner access := f.State.Owner() ctx.Require(access.Exists(), "access not set: owner") ctx.Require(ctx.Caller() == access.Value(), "no permission") ctx.Require(f.Params.Owner().Exists(), "missing mandatory owner") funcSetOwner(ctx, f) ctx.Log("dividend.funcSetOwner ok")}
First, the thunk logs the contract and function name to show that the call has started. Then it sets up a strongly typed function-specific context structure. First, we add the function-specific immutable Params interface structure, which is only present when the function actually can have parameters. Then we add the contract-specific State interface structure. In this case it is mutable because setOwner is a Func. For Views this would be an immutable state interface. Finally, we would add the function-specific mutable Results interface structure, which is only present when the function actually returns results. Obviously, this is not the case for this setOwner() function.
Next it sets up access control for the function according to the schema definition file. In this case it retrieves the owner state variable through the function context, requires that the variable exists, and then requires that the caller() of the function equals that value. Any failing requirement will panic out of the thunk function with an error message. So this code makes sure that only the owner of the contract can call this function.
Now we get to the point where we can use the function-specific Params interface to check for mandatory parameters. Each mandatory parameter is required to exist, or else we will panic out of the thunk function with an error message.
With the setup and automated checks completed, we now call the actual smart contract function implementation that is maintained by the user. After this function has completed, we would process the returned results for those functions that have any (in this case we obviously don't have results), and finally we log that the contract function has completed successfully. Remember that any error within the user function will cause a panic, so this logging will never occur in case that happens.
In the next section we will look at the specifics of view functions. | 2023-02-07 07:23:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31094032526016235, "perplexity": 3491.529011712172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500392.45/warc/CC-MAIN-20230207071302-20230207101302-00203.warc.gz"} |
https://codedump.io/share/Rn7mhrLoRDag/1/parsing-a-latex-file-in-perl | Qwirk - 1 year ago 110
Perl Question
# Parsing a latex file in Perl
Apologies for the very basic question!
I just want to read in a latex file (so text basically) and output all the (say) theorems, which are always in the format
\begin{theorem}
some lines of latex
\end{theorem}
I always kind of figured Perl was the right language for this!
Of course, I only know very basic programming in C++ and Java, and virtually no Perl.
Nonetheless I can currently read in a text file, and process it line by line.
It seems the most basic way to do this is:
($string =~ /pattern/) I started getting confused by then reading about control codes like ?,*+,$, etc.
Any simple references or links to get me started?
(I put this on here and not the Tex site, as it could be useful generally for reading text files, and not just LaTeX!)
If you're on a Unix-y machine (this includes Macs), for a task this small you should reach for sed first:
$sed -ne '/^\\begin{theorem}$/,/^\\end{theorem}$/p' doc.tex If you're on Windows, though, you don't get sed bundled with the OS, and perl is rather easier to install AIUI, so here's the equivalent: > perl -ne 'print if /^\\begin\{theorem\}$/.../^\\end\{theorem\}\$/;' doc.tex
You may notice a distinct resemblance between these two commands. That's not an accident; Perl took ideas from many of the older Unix text-munging utilities, sed included. | 2018-03-17 22:27:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8578172922134399, "perplexity": 2619.466752953632}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645362.1/warc/CC-MAIN-20180317214032-20180317234032-00100.warc.gz"} |
https://byjus.com/question-answer/abc-is-an-isosceles-triangle-with-ac-bc-if-ab2-2ac2-prove-that-abc-is-a-right-triangle/ | Question
# $△ABC$ is an isosceles triangle with $AC=BC.$ If $A{B}^{2}=2A{C}^{2}$ prove that $△ABC$ is a right triangle.
Open in App
Solution
## Proving that $△\mathrm{ABC}$ is a right angle triangle :Given:$△ABC$ is an isosceles triangle$\mathrm{AC}=\mathrm{BC}$and${\mathrm{AB}}^{2}=2{\mathrm{AC}}^{2}$To prove:$△\mathrm{ABC}$ is a right triangle.Or$A{C}^{2}+B{C}^{2}=A{B}^{2}$Proof:In $\mathrm{\Delta ACB}$,$\mathrm{AC}=\mathrm{BC}$The angles corresponding to these sides are equal so these two angles must be less than 90 degrees.From the given,$\begin{array}{rcl}{\mathrm{AB}}^{2}& =& 2{\mathrm{AC}}^{2}\\ {\mathrm{AB}}^{2}& =& {\mathrm{AC}}^{2}+{\mathrm{AC}}^{2}\end{array}$$\begin{array}{rcl}{\mathrm{AB}}^{2}& =& {\mathrm{AC}}^{2}+{\mathrm{BC}}^{2}\end{array}$ …[Since,$\mathrm{AC}=\mathrm{BC}$]By the Pythagoras theorem,$\mathrm{\Delta ABC}$ is a right-angle triangle.Hence we proved that$\mathrm{\Delta ABC}$ is a right-angle triangle.
Suggest Corrections
4 | 2023-02-02 09:29:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9189965128898621, "perplexity": 1350.6724381458428}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499967.46/warc/CC-MAIN-20230202070522-20230202100522-00593.warc.gz"} |
http://digchip.com/publications/index.php?date=07-2017&page=2 | Electrical and Electronics Engineering publications abstract of: 07-2017 sorted by title, page: 2
» A UHF Path Loss Model Using Learning Machine for Heterogeneous Networks
Abstract:In this paper, we present and evaluate a new propagation model for heterogeneous networks. The designed model is multiband, multienvironment, and is usable for short and long distance. For this research, a measurement campaign was conducted in Tunis (Tunisia) using continuous wave analog technology. It concerns the most used bands (450, 850, 1800, 2100, and 2600 MHz) in rural, suburban, and urban environments. Measurements are split into two independent and random sets. The first one is used for model training, whereas the second is used for model validation. The new model is based on neural networks, uses back propagation algorithm, and obtains its inputs from Standard Propagation Model, to which we have added more parameters such as frequency, environment type, land use distribution, and diffraction loss. Model variables are computed from accurate Digital Terrain Model and Land Used maps with 2-m resolution. The statistical analysis has shown that the developed model is accurate as we obtained the following metrics: 0.235-dB absolute mean error, 6.850-dB standard deviation, and 85% correlation factor. The obtained simulation results are then compared to SPM and ITU-R P.1812-4 prediction, which are taken as reference to highlight the benefit of the new model. Autors: M. Ayadi;A. Ben Zineb;S. Tabbane; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3675 - 3683 Publisher: IEEE
» A Unified Framework for Vehicle Rerouting and Traffic Light Control to Reduce Traffic Congestion
Abstract:As the number of vehicles grows rapidly each year, more and more traffic congestion occurs, becoming a big issue for civil engineers in almost all metropolitan cities. In this paper, we propose a novel pheromone-based traffic management framework for reducing traffic congestion, which unifies the strategies of both dynamic vehicle rerouting and traffic light control. Specifically, each vehicle, represented as an agent, deposits digital pheromones over its route, while roadside infrastructure agents collect the pheromones and fuse them to evaluate real-time traffic conditions as well as to predict expected road congestion levels in near future. Once road congestion is predicted, a proactive vehicle rerouting strategy based on global distance and local pheromone is employed to assign alternative routes to selected vehicles before they enter congested roads. In the meanwhile, traffic light control agents take online strategies to further alleviate traffic congestion levels. We propose and evaluate two traffic light control strategies, depending on whether or not to consider downstream traffic conditions. The unified pheromone-based traffic management framework is compared with seven other approaches in simulation environments. Experimental results show that the proposed framework outperforms other approaches in terms of traffic congestion levels and several other transportation metrics, such as air pollution and fuel consumption. Moreover, experiments over various compliance and penetration rates show the robustness of the proposed framework. Autors: Zhiguang Cao;Siwei Jiang;Jie Zhang;Hongliang Guo; Appeared in: IEEE Transactions on Intelligent Transportation Systems Publication date: Jul 2017, volume: 18, issue:7, pages: 1958 - 1973 Publisher: IEEE
» A Unifying Model for Camera Calibration
Abstract:This paper proposes a unified theory for calibrating a wide variety of camera models such as pinhole, fisheye, cata-dioptric, and multi-camera networks. We model any camera as a set of image pixels and their associated camera rays in space. Every pixel measures the light traveling along a (half-) ray in 3-space, associated with that pixel. By this definition, calibration simply refers to the computation of the mapping between pixels and the associated 3D rays. Such a mapping can be computed using images of calibration grids, which are objects with known 3D geometry, taken from unknown positions. This general camera model allows to represent non-central cameras; we also consider two special subclasses, namely central and axial cameras. In a central camera, all rays intersect in a single point, whereas the rays are completely arbitrary in a non-central one. Axial cameras are an intermediate case: the camera rays intersect a single line. In this work, we show the theory for calibrating central, axial and non-central models using calibration grids, which can be either three-dimensional or planar. Autors: Srikumar Ramalingam;Peter Sturm; Appeared in: IEEE Transactions on Pattern Analysis and Machine Intelligence Publication date: Jul 2017, volume: 39, issue:7, pages: 1309 - 1319 Publisher: IEEE
» A Unipolar/Bipolar High-Voltage Pulse Generator Based on Positive and Negative Buck–Boost DC–DC Converters Operating in Discontinuous Conduction Mode
Abstract:This paper presents a new high-voltage pulse generator, which is based on positive and negative buck-boost (BB) converters fed from a relatively low voltage dc supply. The proposed generator is able to generate unipolar or bipolar high-voltage pulses via operating the BB converters with series or parallel connected outputs respectively using a common input dc source. The components of each converter are rated at half of the pulsed voltage magnitude in the unipolar mode. The converters in the proposed pulse generator operate in discontinuous conduction mode. This enhances system efficiency, as the circuit only operates when it is desired to generate a pulsed output voltage, otherwise the circuit is switched to idle mode with zero current. Detailed illustration of the proposed approach is presented along with a full design of the system components for given output pulse specifications. Finally, simulation and experimental results are presented to validate the proposed concept. Autors: Ahmed A. Elserougi;Ahmed M. Massoud;Shehab Ahmed; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5368 - 5379 Publisher: IEEE
» A Variable Step-Size Normalized Subband Adaptive Filter With a Step-Size Scaler Against Impulsive Measurement Noise
Abstract:This brief introduces a variable step-size (VSS) normalized subband adaptive filter (NSAF) using a step-size scaler to improve the robustness against impulsive measurement noise. When impulsive measurement noise appears, the step size of the proposed VSS NSAF is scaled down by the step-size scaler, which is suitable for application in the NSAF. This removes a possibility of updating weight estimates based on defective information of the subband output errors due to impulsive measurement noise. In the proposed VSS NSAF, the equations for updating the step size are constructed by interpreting the behavior of the mean square deviation of the conventional NSAF and applying the step-size scaler. The step-size scaler utilizes the sum of the subband output errors, which can be influenced by impulsive measurement noise. Simulations using the proposed VSS NSAF show an excellent transient and steady-state behavior with colored input in impulsive-noise environments. Autors: Junwoong Hur;Insun Song;Poogyeon Park; Appeared in: IEEE Transactions on Circuits and Systems II: Express Briefs Publication date: Jul 2017, volume: 64, issue:7, pages: 842 - 846 Publisher: IEEE
» A Variation-Tolerant Near-Threshold Processor With Instruction-Level Error Correction
Abstract:Timing error resilience is a promising alternative to eliminate margins and improve energy efficiency in subthreshold and near-threshold processors. However, the existing techniques have some limitations, such as uncontaminated architecture registers (ARs), strict timing constraints on error consolidation and propagation, and high design complexity. To address these limitations, a new timing error resilience technique based on sacrificial instruction-level registers is proposed. It dynamically captures and incrementally records the changes of ARs at each instruction boundary. Once a timing error occurs, it only needs to restore the changed ARs to a preerror state. Then, the erroneous instruction can be safely reexecuted. This technique is applicable to different processors. The 32-bit embedded processor employing the proposed technique is demonstrated in a 40-nm CMOS technology. This variation-tolerant processor operates at 27.4 MHz under 0.6 V with 8.7% total area overhead compared with the baseline without timing error resilience. At the same throughput, the proposed technique achieves 44% and 27% energy benefits compared with the baseline and the canary technique, respectively. Autors: Sheng Wang;Chen Chen;Xiao-Yan Xiang;Jian-Yi Meng; Appeared in: IEEE Transactions on Very Large Scale Integration Systems Publication date: Jul 2017, volume: 25, issue:7, pages: 1993 - 2006 Publisher: IEEE
» A Virtual Inertia Control Strategy for DC Microgrids Analogized With Virtual Synchronous Machines
Abstract:In a dc microgrid (DC-MG), the dc bus voltage is vulnerable to power fluctuation derived from the intermittent distributed energy or local loads variation. In this paper, a virtual inertia control strategy for DC-MG through bidirectional grid-connected converters (BGCs) analogized with virtual synchronous machine (VSM) is proposed to enhance the inertia of the DC-MG, and to restrain the dc bus voltage fluctuation. The small-signal model of the BGC system is established, and the small-signal transfer function between the dc bus voltage and the dc output current of the BGC is deduced. The dynamic characteristic of the dc bus voltage with power fluctuation in the DC-MG is analyzed in detail. As a result, the dc output current of the BGC is equivalent to a disturbance, which affects the dynamic response of the dc bus voltage. For this reason, a dc output current feedforward disturbance suppressing method for the BGC is introduced to smooth the dynamic response of the dc bus voltage. By analyzing the control system stability, the appropriate virtual inertia control parameters are selected. Finally, simulations and experiments verified the validity of the proposed control strategy. Autors: Wenhua Wu;Yandong Chen;An Luo;Leming Zhou;Xiaoping Zhou;Ling Yang;Yanting Dong;Josep M. Guerrero; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 6005 - 6016 Publisher: IEEE
» A Visualization Tool for Real-Time Dynamic Contingency Screening and Remedial Actions
Abstract:This paper proposes a real-time visual interactive transient stability screening and remedial action tool that uses an approach based on Lyapunov functions to enable the selection of appropriate remedial actions that stabilize power systems due to large disturbances and cascading failures. At present, there is no effective tool that enables making a well-informed choice from amongst a profusion of remedial action alternatives. Conventionally, transient stability analysis of power system is performed offline to assess the capability of the power system to withstand specific disturbances and to investigate the dynamic response of the power system as the network is restored to normal operation. In this paper, postfault stable and controlling unstable equilibrium points are determined using a homotopy-based approach. Subsequently, stability assessment of the system and the corresponding potential remedial actions are determined from the equilibrium points of the system dynamical model. The real-time transient stability analysis and remedial action algorithm are incorporated with the visualization tool to facilitate interactive decision making in real time. The transient stability analysis and remedial action algorithm, and the visualization tool are demonstrated on several test systems including the equivalent Western Electricity Coordinating Council system and the simplified New England 39 bus test system. Autors: Joydeep Mitra;Mohammed Benidris;Nga Nguyen;Sidart Deb; Appeared in: IEEE Transactions on Industry Applications Publication date: Jul 2017, volume: 53, issue:4, pages: 3268 - 3278 Publisher: IEEE
» A Wide Detection Range Mercury Ion Sensor Using Si MOSFET Having Single-Walled Carbon Nanotubes as a Sensing Layer
Abstract:This letter investigates the response of a wide detection range mercury ion sensor based on Si MOSFET having a floating-gate (FG) and a control-gate (CG) in horizontal direction. Single-walled carbon nanotubes (SWNTs) are formed between the FG and the CG by using an inkjet-printing method. The interaction between themercury ions and SWNTs is studied by measuring transient current response (I–t). Conductance change is measured from 1 fM to in saturated transient current region. The measured transient response shows that the drain current () is appreciably changed in pMOSFET sensor and almost notchanged in nMOSFET sensor. By analyzing the conductance change of the pMOSFET sensor with the concentration of mercury ions, it is shown that the work-function of SWNTs increases due to hole doping and the increases as a result. Autors: Jongmin Shin;Yoonki Hong;Meile Wu;Jong-Ho Lee; Appeared in: IEEE Electron Device Letters Publication date: Jul 2017, volume: 38, issue:7, pages: 959 - 962 Publisher: IEEE
» A Wide-Range Capacitive Sensor for Linear and Angular Displacement Measurement
Abstract:A new capacitive sensor that is suitable for measuring both linear and angular displacements of a shaft over a wide range is reported in this paper. The sensor consists of a cylindrical shaft with a semi-hollow cylinder attached in the center; the shaft is capable of moving along the axis as well as rotating about the axis. Two pairs of semi-hollow-cylindrical electrodes surround the shaft, which is grounded. The amount of linear displacement and rotation is calculated by measuring the change in the capacitance of each of the four electrodes with respect to the shaft. A prototype sensor was constructed and tested; the rms error obtained is 0.6% for the linear displacement and less than 0.6% for the angular displacement. The proposed sensor has potential applications in several robotic, industrial, and automotive fields. Autors: Narendiran Anandan;Boby George; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5728 - 5737 Publisher: IEEE
» A Wideband Multilayer Substrate Integrated Waveguide Cavity-Backed Slot Antenna Array
Abstract:In this paper, a wideband multilayer substrate integrated waveguide (SIW)-based cavity-backed slot array is proposed. The array element is constructed by stacking five layers of SIW cavity-backed slots and has a wide impedance bandwidth from 18 to 30 GHz. Two different feed networks based on probe coupling and slot coupling are introduced to maintain the wideband characteristic of the proposed element when employed in an array. Two arrays fed by the proposed feed networks are designed, fabricated, and tested. The measured results show that both the arrays employing probe coupling and slot coupling feed networks have a wide impedance bandwidth over 30%. Within the obtained operation bands, good radiation performance is achieved. Moreover, advantages and disadvantages of the proposed two feed networks are discussed. Autors: Yang Cai;Yingsong Zhang;Can Ding;Zuping Qian; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3465 - 3473 Publisher: IEEE
» A Word Line Pulse Circuit Technique for Reliable Magnetoelectric Random Access Memory
Abstract:A word line pulse (WLP) circuit scheme is proposed toward the implementation of magnetoelectric random access memory (MeRAM). The circuit improves the write error rate (WER) and cell area efficiency by generating a better write pulse compared to conventional bitline pulse (BLP) techniques in terms of the pulse slew rate and amplitude. For the voltage-controlled magnetic anisotropy-induced precessional switching of the magnetic tunnel junction (MTJ), the write pulse shape has a large impact on the switching probability. Typically, a square shape pulse results in higher switching probability compared to that of a triangular shape pulse with long rise and falling edges, since the square shape pulse causes a more stable precessional trajectory of the free layer magnetization by providing a relatively constant in-plane-dominant effective field. Compared to the BLP scheme, the WLP can generate a better square shape pulse by eliminating discharge paths under the pulse condition, using the gain of the access transistor, and effectively diminishing the capacitive loading which needs to be driven. A macrospin compact model of voltage-controlled MTJ shows that the WLP can improve WER by times and allow MeRAM to have four-time improvement in area efficiency of driver circuits compared to the BLP. Autors: Hochul Lee;Albert Lee;Shaodi Wang;Farbod Ebrahimi;Puneet Gupta;Pedram Khalili Amiri;Kang L. Wang; Appeared in: IEEE Transactions on Very Large Scale Integration Systems Publication date: Jul 2017, volume: 25, issue:7, pages: 2027 - 2034 Publisher: IEEE
» Abnormal Recovery Phenomenon Induced by Hole Injection During Hot Carrier Degradation in SOI n-MOSFETs
Abstract:This letter investigates an abnormal recovery phenomenon induced by hole injection during hot carrier degradation in silicon-on-insulator n-type metal–oxide–semiconductor transistors. The method by which the hole injection induces the abnormal recovery behavior can be clarified by different hot carrier degradation (HCD) measurement sequences. According to this HCD result, the channel surface energy band is drawn down and the interface defect will be temporarily shielded, an effect caused by the trapped hole. Furthermore, results of different stress voltage experiments indicate that the amount of hole injection is determined by the electric field between the gate and drain. Autors: Ying-Hsin Lu;Ting-Chang Chang;Li-Hui Chen;Yu-Shan Lin;Xi-Wen Liu;Jih-Chien Liao;Chien-Yu Lin;Chen-Hsin Lien;Kuan-Chang Chang;Sheng-Dong Zhang; Appeared in: IEEE Electron Device Letters Publication date: Jul 2017, volume: 38, issue:7, pages: 835 - 838 Publisher: IEEE
» Absorptive Bandstop Filter With Prescribed Negative Group Delay and Bandwidth
Abstract:An absorptive bandstop filter is proposed and synthesized with prescribed negative group delay (NGD) and negative group delay bandwidth (NBW). It is realized with resistor-loaded coupled-line structures where the NGD can be controlled by the Q-factors of resonators. The resistor of the first section is determined for impedance matching, also providing a negative delay. A prototype is developed, following the proposed design procedure, with NGD = −6.5 ns and NBW= 105 MHz obtained. The proposed method is experimentally validated by the good agreement between the synthesized and measured results. Autors: Liang-Feng Qiu;Lin-Sheng Wu;Wen-Yan Yin;Jun-Fa Mao; Appeared in: IEEE Microwave and Wireless Components Letters Publication date: Jul 2017, volume: 27, issue:7, pages: 639 - 641 Publisher: IEEE
» Acceleration of Frequency Sweeping in Eddy-Current Computation
Abstract:In this paper, a novel method for accelerating frequency sweeping in eddy-current calculation using finite-element method is presented. Exploiting the fact that between adjacent frequencies, the eddy-current distributions are similar, an algorithm is proposed to accelerate the frequency sweeping computation. The solution of the field quantities under each frequency, which involves solving a system of linear equations using the conjugate gradients squared (CGS) method, is accelerated by using an optimized initial guess—the final solution from the previous frequency. Numerical tests show that this treatment could speed up the convergence of the CGS solving process, i.e., reduced number of iterations reaching the same relative residuals or reaching smaller residuals with the same iteration number. Autors: Mingyang Lu;Anthony Peyton;Wuliang Yin; Appeared in: IEEE Transactions on Magnetics Publication date: Jul 2017, volume: 53, issue:7, pages: 1 - 8 Publisher: IEEE
» Acceleration of Rotating Plasma Flows in Crossed Magnetic Fields
Abstract:In the previous investigations, an intermode exchange was used to demonstrate the transfer of energy and momentum into using different kinematic degrees of freedom. This paper examines using a hydrodynamic approach using a cold, neutral flow in a rotating cylindrical plasma column using crossed magnetic fields. Results show that the twirling plasma flow in a cylindrical vortex can be accelerated in an axial direction, thereby resulting an energy/momentum transfer in the axial direction. These results are analogous to the creation of a plasma thruster using this effect. Autors: Alexander R. Karimov;Paul A. Murad; Appeared in: IEEE Transactions on Plasma Science Publication date: Jul 2017, volume: 45, issue:7, pages: 1710 - 1716 Publisher: IEEE
» Accurate Attitude Estimation of a Moving Land Vehicle Using Low-Cost MEMS IMU Sensors
Abstract:This paper presents a novel Kalman filter for the accurate determination of a vehicle’s attitude (pitch and roll angles) using a low-cost MEMS inertial measurement unit (IMU) sensor, comprising a tri-axial gyroscope and a tri-axial accelerometer. Currently, vehicles deploy expensive gyroscopes for attitude determination. A low-cost MEMS gyro cannot be used because of the drift problem. Typically, an accelerometer is used to correct this drift by measuring the attitude from gravitational acceleration. This is, however, not possible in vehicular applications, because accelerometer measurements are corrupted by external accelerations produced due to vehicle movements. In this paper, we show that vehicle kinematics allow the removal of external accelerations from the lateral and vertical axis accelerometer measurements, thus giving the correct estimate of lateral and vertical axis gravitational accelerations. An estimate of the longitudinal axis gravitational acceleration can then be obtained by using the vector norm property of gravitational acceleration. A Kalman filter is designed, which implements the proposed solution and uses the accelerometer in conjunction with the gyroscope to accurately determine the attitude of a vehicle. Hence, this paper enables the use of extremely low-cost MEMS IMU for accurate attitude determination in vehicular domain for the first time. The proposed filter was tested by both simulations and experiments under various dynamic conditions and results were compared with five existing methods from the literature. The proposed filter was able to maintain sub-degree estimation accuracy even under very severe and prolonged dynamic conditions. To signify the importance of the achieved accuracy in determining accurate attitude, we investigated its use in two vehicular applications: vehicle yaw estimate and vehicle location estimate by dead reckoning and showed the performance improvements obtained by the proposed filter. Autors: Hamad Ahmed;Muhammad Tahir; Appeared in: IEEE Transactions on Intelligent Transportation Systems Publication date: Jul 2017, volume: 18, issue:7, pages: 1723 - 1739 Publisher: IEEE
» Accurate Determination of Induction Machine Torque and Current Versus Speed Characteristics
Abstract:The determination of induction machine torque and current speed characteristics relies on methods based on either direct testing or calculation, using a machine equivalent circuit (EC). Both methods may lead to significant errors. As a contribution to a still open discussion, this paper presents the challenges encountered using these methods and an approach is presented in this paper to overcome the inherent challenges. The proposed approach considers saturation, and compensates for skin effect and machine temperature to improve accuracy. Five induction motors of different pole pairs were analyzed and tested to provide the understanding of the underlying issues of predicting torque and current characteristics of induction machines. The findings indicate that, for direct testing, multiple data points closer to nominal voltage are required. In the case of EC modeling, proper correction of the model for temperature and saturation leads to improved prediction of the torque characteristics of general purpose induction machines. Autors: Emmanuel B. Agamloh;Andrea Cavagnino;Silvio Vaschetto; Appeared in: IEEE Transactions on Industry Applications Publication date: Jul 2017, volume: 53, issue:4, pages: 3285 - 3294 Publisher: IEEE
» Accurate Estimation of CMOS Power Consumption Considering Glitches by Using Waveform Lookup
Abstract:Gate-level power estimation methodologies are often considered as a sign-off level reference for digital circuit design. Nevertheless, when gate delays and related effects like glitches are taken into account, commercial state-of-the-art gate-level power estimators show surprisingly large estimation errors. Following an analysis of factors causing these inaccuracies, a novel gate-level power estimation approach is proposed, which combines lookup-based macromodels with the accuracy of analog signal waveforms and achieves significantly better results under the influence of glitches. Autors: Michael Meixner;Tobias G. Noll; Appeared in: IEEE Transactions on Circuits and Systems II: Express Briefs Publication date: Jul 2017, volume: 64, issue:7, pages: 787 - 791 Publisher: IEEE
» Achievable Rate With Closed-Form for SISO Channel and Broadcast Channel in Visible Light Communication Networks
Abstract:In this paper, we study the channel capacity and region for both the single-input-single-output (SISO) channel and broadcast channel (BC) in visible light communication (VLC) systems, under the peak optical power, average optical power, and electrical power constraints. Under the condition that the input signal is continuous, we develop a closed-form lower bound (termed ABG lower bound) and an upper bound for SISO channel using the entropy power inequality and Lagrangian function method. Moreover, a closed-form achievable rate region (termed ABG region) is derived for the VLC BC. Furthermore, for a multi-light-emitting diode and multiuser VLC system, we propose an achievable rate expression for each user, and then investigate a VLC BC beamforming design problem by utilizing the obtained closed-form expression. The beamforming design problem is shown to be NP-hard, and we transform this problem into a convex semidefinite program by using the semidefinite relaxation technique. Finally, numerical results are presented to evaluate the performance of the proposed ABG lower bound/region and the beamforming design. Autors: Shuai Ma;Ruixin Yang;Hang Li;Zhi-Long Dong;Huaxi Gu;Shiyin Li; Appeared in: Journal of Lightwave Technology Publication date: Jul 2017, volume: 35, issue:14, pages: 2778 - 2787 Publisher: IEEE
» Achievable Rates for Gaussian Degraded Relay Channels With Non-Vanishing Error Probabilities
Abstract:This paper revisits the Gaussian degraded relay channel, where the link that carries information from the source to the destination is a physically degraded version of the link that carries information from the source to the relay. The source and the relay are subject to expected power constraints. The -capacity of the channel is characterized and it is strictly larger than the capacity for any , which implies that the channel does not possess the strong converse property. The proof of the achievability part is based on several key ideas: block Markov coding, which is used in the classical decode-forward strategy, power control for Gaussian channels under expected power constraints, and a careful scaling between the block size and the total number of block uses. The converse part is proved by first establishing two non-asymptotic lower bounds on the error probability, which are derived from the type-II errors of some binary hypothesis tests. Subsequently, each lower bound is simplified by conditioning on an event related to the power of some linear combination of the codewords transmitted by the source and the relay. Lower and upper bounds on the second-order term of the optimal coding rate are also obtained. Autors: Silas L. Fong;Vincent Y. F. Tan; Appeared in: IEEE Transactions on Information Theory Publication date: Jul 2017, volume: 63, issue:7, pages: 4183 - 4201 Publisher: IEEE
» Achieving a Large Gain-Bandwidth Product From a Compact Antenna
Abstract:This paper presents a method to achieve high gain (>20 dBi) and wide bandwidth (>55%) from a compact antenna that is less than one wavelength tall and only in diameter at the lowest operating frequency. The antenna comprises of an optimized single-layer superstrate, made out of four dielectric sections, and a ground plane, which are separated by an air cavity. The permittivity and thickness of the dielectric sections decrease in the transverse direction. Two-step optimization method was implemented employing a customized full-wave optimizer to optimize the width and thickness of each dielectric section in the superstrate, while maintaining a fixed overall diameter of the antenna. This optimization results in an antenna with a high gain and a large 3-dB gain bandwidth, without compromising on antenna footprint. A prototype of the new antenna having a superstrate with stepped thickness was fabricated and tested. It exhibits a measured peak broadside directivity and a peak realized gain of 20.7 and 20.2 dBi, respectively. Its measured gain-bandwidth product of 5969 and directivity-bandwidth product (DBP) of 6580 are almost three times the best figures for resonant cavity antennas (RCAs). The total area of the new antenna prototype is and its overall height is at the lowest operating frequency. It is significantly more compact and its DBP per unit area and aperture efficiency are significantly greater than those of lens-based antennas. Its measured 3-dB gain bandwidth of 57% is unprecedented for high-gain short antennas, including RCAs. Moreover, over the entire bandwidth, sidelobe levels of the antenna are around - 12;12 and −21 dB in the E- and H-planes, respectively. Autors: Affan Aziz Baba;Raheel M. Hashmi;Karu P. Esselle; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3437 - 3446 Publisher: IEEE
» Achieving Low-Recovery Time in AlGaN/GaN HEMTs With AlN Interlayer Under Low- Noise Amplifiers Operation
Abstract:Three transistors with different AlGaN/GaN interface designs (sharp interface, standard interface, and an extra AlN interlayer) were studied in-depth under conditions mimicking low-noise amplifiers (LNAs) operation. A new measurement setup, analog to LNAs operation condition, is established to measure recovery time on device level. For the first time, a direct relationship between the recovery time and the design of AlGaN/GaN interface is revealed in devices with Carbon doping buffer in this letter. An extremely low-recovery time is demonstrated in the transistor with an AlN interlayer. Both transistors without an AlN interlayer exhibit severe gain and drain current degradation after pulsed input stress. The transistor with a sharp interface shows a recovery time around 10 ms, whereas the transistorwith a standard interface shows even much longer recovery time. These results imply that AlN interlayer, which can effectively block the injection of hot electrons to AlGaN bulk or surface traps, is highly preferred in systems where LNAs need to function promptly after an input overdrive. Autors: Tongde Huang;Olle Axelsson;Johan Bergsten;Mattias Thorsell;Niklas Rorsman; Appeared in: IEEE Electron Device Letters Publication date: Jul 2017, volume: 38, issue:7, pages: 926 - 928 Publisher: IEEE
» Active Harmonic Reduction Using DC-Side Current Injection Applied in a Novel Large Current Rectifier Based on Fork-Connected Autotransformer
Abstract:In this paper, a novel large current rectifier using the fork-connected autotransformer and dc-side current injection method is proposed. The fork-connected autotransformer outputs two sets of three-phase voltages with 60° phase difference, and feeds two three-phase half-wave rectifiers. Compared with the isolated line-frequency transformer, the proposed autotransformer has lower kilovoltampere (kVA) rating under the same load power. An optimal designed single-phase full-bridge inverter is used to inject the compensation currents into the dc side of the two three-phase half-wave rectifier, which can reduce the harmonics in input line current to be an acceptable level. The kVA rating of the single-phase full-bridge inverter is very lower, and the proposed large current rectifier draws nearly sinusoidal currents from the ac main after using the dc-side injection. A 4 kW prototype is set up to validate the theoretical analysis and evaluate the performance. Autors: Fangang Meng;Xiaona Xu;Lei Gao;Chunwei Cai; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5250 - 5264 Publisher: IEEE
» Activity Probability-Based Performance Analysis and Contention Control for IEEE 802.11 WLANs
Abstract:In this paper, we develop a contention window (CW) control scheme for practical IEEE 802.11 wireless local area networks (WLANs) that have node heterogeneity in terms of the traffic load, transmission rate, and packet size. We introduce activity probability, i.e., the probability that a node contends for medium access opportunities at a given time. We then newly develop a performance analysis model that enables analytic estimation on the contention status including the collision probability, collision time, back-off time, and throughput with comprehensive consideration of node heterogeneity. Based on the newly developed model, we derive the theoretically ideal contention status, and develop a CW control scheme that achieves the ideal contention status in an average sense. We perform extensive NS-3 simulations and real testbed experiments for evaluation of both the proposed performance analysis model and CW control scheme. The results show that the proposed model provides accurate prediction on the contention status, and the proposed CW control scheme achieves considerable throughput improvement compared to the existing schemes which do not comprehensively consider node heterogeneity. Autors: Junsu Choi;Seongho Byeon;Sunghyun Choi;Kwang Bok Lee; Appeared in: IEEE Transactions on Mobile Computing Publication date: Jul 2017, volume: 16, issue:7, pages: 1802 - 1814 Publisher: IEEE
Abstract:The hybrid filter bank (HFB) has been considered as a promising solution for high-speed, high-resolution analog-to-digital conversion. In this letter, we propose an adaptable HFB architecture of which the conversion band can be adapted according to the frequency band of interest, e.g., the entire working band of a wideband receiver or a subband with an arbitrary spectrum position. Furthermore, we propose a strategy based on the adaptable HFB for a wideband receiver to efficiently fulfill different tasks. For spectrum sensing, the entire wideband conversion HFB is used. While for subband signal receiving, the subband conversion HFB is utilized. Examples show that compared with the existing HFB studies in which the wanted subband signal is extracted from the digitalized entire working band, the proposed strategy can significantly simplify the receiving process for subband signals, because the subband conversion HFB has a filtering effect on the input spectrum. Autors: Xu Liu;Wei Li;Jibo Wei;Longwang Cheng; Appeared in: IEEE Communications Letters Publication date: Jul 2017, volume: 21, issue:7, pages: 1525 - 1528 Publisher: IEEE
» Adaptive Bit Allocation for Consistent Video Quality in Scalable High Efficiency Video Coding
Abstract:Scalable video coding (SVC) is a coding paradigm that allows once-encoded video content to be used in diverse scenarios. SVC-coded videos can be transmitted and rendered at specified bitrates according to network bandwidth and end device requirements. In this paper, an adaptive bit allocation algorithm is proposed for the emerging scalable High Efficiency Video Coding (SHVC) standard. The bit budget at the group-of-pictures level is allocated according to buffer occupancy. Picture complexity, measured using the predicted mean absolute difference (MAD), buffer occupancy, and hierarchical level, is proposed for regulating the bitrate at the picture level. The MAD of the current picture is predicted using a novel mean prediction error (MPE) model, which is obtained from the advanced motion vector prediction, and the test zone search specified in SHVC and the associated reference software of SHVC. Moreover, MPE is used to determine the number of assigned bits at the coding-tree-unit level. The bit budget of each level is incorporated with the model for computing the required quantization parameter. Experimental results reveal that the proposed method achieves accurate bitrates with enhanced and consistent visual quality and more satisfactorily controls buffer occupancy compared with the state-of-the-art approaches reported in the literature. Autors: Shih-Hsuan Yang;Phuong Binh Vo; Appeared in: IEEE Transactions on Circuits and Systems for Video Technology Publication date: Jul 2017, volume: 27, issue:7, pages: 1555 - 1567 Publisher: IEEE
» Adaptive Dynamic Programming-Based Optimal Control Scheme for Energy Storage Systems With Solar Renewable Energy
Abstract:In this paper, a novel optimal energy storage control scheme is investigated in smart grid environments with solar renewable energy. Based on the idea of adaptive dynamic programming (ADP), a self-learning algorithm is constructed to obtain the iterative control law sequence of the battery. Based on the data of the real-time electricity price (electricity rate in brief), the load demand (load in brief), and the solar renewable energy (solar energy in brief), the optimal performance index function, which minimizes the total electricity cost and simultaneously extends the battery's lifetime, is established. A new analysis method of the iterative ADP algorithm is developed to guarantee the convergence of the iterative value function to the optimum under iterative control law sequence for any time index in a period. Numerical results and comparisons are presented to illustrate the effectiveness of the developed algorithm. Autors: Qinglai Wei;Guang Shi;Ruizhuo Song;Yu Liu; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5468 - 5478 Publisher: IEEE
» Adaptive Energy Management System Based on a Real-Time Model Predictive Control With Nonuniform Sampling Time for Multiple Energy Storage Electric Vehicle
Abstract:The performance of a dual energy storage electric vehicle system mainly depends on the quality of its power and energy managements. A real-time management strategy supported by a model predictive control (MPC) using the nonuniform sampling time concept is developed and fully addressed in this paper. First, the overall multiple energy storage powertrain model including its inner control layer is represented with the energetic macroscopic representation and used to introduce the energy strategy level. The model of the system with its inner control layer is translated into the state-space domain in order to develop an MPC approach. The management algorithm based on mixed short- and long-term predictions is compared to rule-based and constant sampling time MPC strategies in order to assess its performance and its ability to be used in a real vehicle. The real-time simulation results indicate that, compared to other strategies, the proposed MPC strategy can balance the power and the energy of the dual energy storage system more effectively, and reduce the stress on batteries. Moreover, battery and supercapacitor key variables are kept within safety limits, increasing the lifetime of the overall system. Autors: Oleg Gomozov;João Pedro F. Trovão;Xavier Kestelyn;Maxime R. Dubois; Appeared in: IEEE Transactions on Vehicular Technology Publication date: Jul 2017, volume: 66, issue:7, pages: 5520 - 5530 Publisher: IEEE
» Adaptive Importance Sampling: The past, the present, and the future
Abstract:A fundamental problem in signal processing is the estimation of unknown parameters or functions from noisy observations. Important examples include localization of objects in wireless sensor networks [1] and the Internet of Things [2]; multiple source reconstruction from electroencephalograms [3]; estimation of power spectral density for speech enhancement [4]; or inference in genomic signal processing [5]. Within the Bayesian signal processing framework, these problems are addressed by constructing posterior probability distributions of the unknowns. The posteriors combine optimally all of the information about the unknowns in the observations with the information that is present in their prior probability distributions. Given the posterior, one often wants to make inference about the unknowns, e.g., if we are estimating parameters, finding the values that maximize their posterior or the values that minimize some cost function given the uncertainty of the parameters. Unfortunately, obtaining closed-form solutions to these types of problems is infeasible in most practical applications, and therefore, developing approximate inference techniques is of utmost interest. Autors: Monica F. Bugallo;Victor Elvira;Luca Martino;David Luengo;Joaquin Miguez;Petar M. Djuric; Appeared in: IEEE Signal Processing Magazine Publication date: Jul 2017, volume: 34, issue:4, pages: 60 - 79 Publisher: IEEE
» Adaptive In-Cache Streaming for Efficient Data Management
Abstract:The design of adaptive architectures is frequently focused on the sole adaptation of the processing blocks, often neglecting the power/performance impact of data transfers and data indexing in the memory subsystem. In particular, conventional address-based models, supported on cache structures to mitigate the memory wall problem, often struggle when dealing with memory-bound applications or arbitrarily complex data patterns that can be hardly captured by prefetching mechanisms. Stream-based techniques have proven to efficiently tackle such limitations, although not well-suited to handle all types of applications. To mitigate the limitations of both communication paradigms, an efficient unification is herein proposed, by means of a novel in-cache stream paradigm, capable of seamlessly adapting the communication between the address-based and stream-based models. The proposed morphable infrastructure relies on a new dynamic descriptor graph specification, capable of handling regular arbitrarily complex data patterns, which is able to improve the main memory bandwidth utilization through data reutilization and reorganization techniques. When compared with state-of-the-art solutions, the proposed structure offers higher address generation efficiency and achievable memory throughputs, and a significant reduction of the amount of data transfers and main memory accesses, resulting on average in 13 times system performance speedup and in 245 times energy-delay product improvement, when compared with the previous implementations. Autors: Nuno Neves;Pedro Tomás;Nuno Roma; Appeared in: IEEE Transactions on Very Large Scale Integration Systems Publication date: Jul 2017, volume: 25, issue:7, pages: 2130 - 2143 Publisher: IEEE
» Adaptive Local Movement Modeling for Robust Object Tracking
Abstract:In this paper, we present a new strategy for modeling the motion of local patches for single-object tracking that can be seamlessly applied to most part-based trackers in the literature. The proposed adaptive local movement modeling method is able to model the local movement distribution of the image patches defining the object to track and the reliability of each image patch. Given the output of a base tracking algorithm, a Gaussian mixture model (GMM) is first used to model the distribution of the movement of local patches relative to the center of gravity of the tracked object. Then, the GMM is combined with the chosen base tracker in a boosting framework, which gives an efficient integrated scheme for the tracking task. This provides a robust procedure to detect outliers in the local motion of the patches. The algorithm is highly configurable with the possibility to change the number of local patches used for tracking and to adapt to the variations of the tracked object. The extensive tracking results on standard data sets show that equipping state-of-the-art trackers with our technique remarkably improves their performance. Autors: Baochang Zhang;Zhigang Li;Alessandro Perina;Alessio Del Bue;Vittorio Murino;Jianzhuang Liu; Appeared in: IEEE Transactions on Circuits and Systems for Video Technology Publication date: Jul 2017, volume: 27, issue:7, pages: 1515 - 1526 Publisher: IEEE
» Adaptive Notch Filter-Based Multipurpose Control Scheme for Grid-Interfaced Three-Phase Four-Wire DG Inverter
Abstract:The power electronic converter and its control system form an integral part of distributed generation (DG) systems interfacing renewable energy sources to the utility network. This paper proposes an adaptive notch filter-based multipurpose control scheme for grid interfacing DG inverter under corrupted grid conditions. The proposed control scheme uses a frequency adaptive sequence components extractor, which is capable of extracting instantaneous symmetrical components and harmonic components of three-phase signals. The DG inverter in this study consists of three single-phase voltage source inverters with common dc bus and coupled to utility grid via three single-phase transformers. The proposed control scheme enables the DG inverter to perform multiple tasks such as reference power injection to grid, low voltage ride through, load reactive power support, and compensation of harmonic, unbalanced, and neutral currents. The efficacy of the proposed control scheme is evaluated through MATLAB/Simulink simulations and experimentally verified using a hardware-in-the-loop based system. Autors: Raja Sekhara Reddy Chilipi;Naji Al Sayari;Khalifa Hassan Al Hosani;Abdul R. Beig; Appeared in: IEEE Transactions on Industry Applications Publication date: Jul 2017, volume: 53, issue:4, pages: 4015 - 4027 Publisher: IEEE
» Adaptive Optimal Stochastic Control of Delay-Tolerant Networks
Abstract:Optimal stochastic control of delay tolerant networks is studied in this paper. First, the structure of optimal two-hop forwarding policies is derived. In order to be implemented, such policies require knowledge of certain global system parameters such as the number of mobiles or the rate of contacts between mobiles. But, such parameters could be unknown at system design time or may even change over time. In order to address this problem, adaptive policies are designed that combine estimation and control: based on stochastic approximation techniques, such policies are proved to achieve optimal performance in spite of lack of global information. Furthermore, the paper studies interactions that may occur in the presence of several DTNs which compete for the access to a gateway node. The latter problem is formulated as a cost-coupled stochastic game and a unique Nash equilibrium is found. Such equilibrium corresponds to the system configuration in which each DTN adopts the optimal forwarding policy determined for the single network problem. Autors: Eitan Altman;Francesco De Pellegrini;Daniele Miorandi;Giovanni Neglia; Appeared in: IEEE Transactions on Mobile Computing Publication date: Jul 2017, volume: 16, issue:7, pages: 1815 - 1829 Publisher: IEEE
» Adaptive SM-MIMO for mmWave Communications With Reduced RF Chains
Abstract:In this paper, a novel multiple-input multiple-output (MIMO) transmission scheme, termed as receive antenna selection (RAS)-aided spatial modulation MIMO (SM-MIMO), is proposed for millimeter-wave (mmWave) communications. It employs the spatial modulation (SM) concept and the RAS technique to tackle the costs of the multiple radio frequency (RF) chains at both link ends. Moreover, we develop a pair of RAS algorithms for the proposed mmWave RAS-SM scheme based on the capacity maximization (max-capacity) and the bit-error rate (BER) minimization criteria, which are formulated as two combinatorial optimization problems. The theoretical gradients of the capacity and the BER with respect to RAS variables are derived and the convexities of these problems are discussed. Furthermore, a novel iterative algorithm through jointly designing the log-barrier algorithm (LbA) and the simplified conjugate gradient method is proposed for RAS optimization. Our simulation results show that the proposed RAS-SM schemes are capable of achieving considerable performance gains over conventional norm-based and eigenvalue-based schemes in mmWave MIMO channels, while avoiding an overwhelming complexity imposed by exhaustive search. Autors: Ping Yang;Yue Xiao;Yong Liang Guan;Zilong Liu;Shaoqian Li;Wei Xiang; Appeared in: IEEE Journal on Selected Areas in Communications Publication date: Jul 2017, volume: 35, issue:7, pages: 1472 - 1485 Publisher: IEEE
» Adaptive Source Localization Based Station Keeping of Autonomous Vehicles
Abstract:We study the problem of driving a mobile sensory agent to a target whose location is specified only in terms of the distances to a set of sensor stations or beacons. The beacon positions are unknown, but the agent can continuously measure its distances to them as well as its own position. This problem has two particular applications: (1) capturing a target signal source whose distances to the beacons are measured by these beacons and broadcasted to a surveillance agent, (2) merging a single agent to an autonomous multi-agent system so that the new agent is positioned at desired distances from the existing agents. The problem is solved using an adaptive control framework integrating a parameter estimator producing beacon location estimates, and an adaptive motion control law fed by these estimates to steer the agent toward the target. For location estimation, a least-squares adaptive law is used. The motion control law aims to minimize a convex cost function with unique minimizer at the target location, and is further augmented for persistence of excitation. Stability and convergence analysis is provided, as well as simulation results demonstrating performance and transient behavior. Autors: Samet Güler;Barış Fidan;Soura Dasgupta;Brian D. O. Anderson;Iman Shames; Appeared in: IEEE Transactions on Automatic Control Publication date: Jul 2017, volume: 62, issue:7, pages: 3122 - 3135 Publisher: IEEE
» Adaptive Time-Switching Based Energy Harvesting Relaying Protocols
Abstract:Considering a dual-hop energy-harvesting (EH) relaying system, this paper advocates novel relaying protocols based on adaptive time-switching (TS) for amplify-and-forward and decode-and-forward modes, respectively. The optimal TS factor is first studied, which is adaptively adjusted based on the dual-hop channel state information (CSI), accumulated energy, and threshold signal-to-noise ratio (SNR), to achieve the maximum throughput efficiency per block. To reduce the CSI overhead at the EH relay, a low-complexity TS factor design is presented, which only needs single-hop CSI to determine the TS factor. Theoretical results show that, in comparison with the conventional solutions, the proposed optimal/low-complexity TS factor can achieve higher limiting throughput efficiency for sufficiently small threshold SNR. As the threshold SNR approaches infinity, the throughput efficiency of the proposed optimal/low-complexity TS factor tends to zero in a much slower pace than that of the conventional solutions. Simulation results are presented to corroborate the proposed methodology. Autors: Haiyang Ding;Xiaodong Wang;Daniel Benevides da Costa;Yunfei Chen;Fengkui Gong; Appeared in: IEEE Transactions on Communications Publication date: Jul 2017, volume: 65, issue:7, pages: 2821 - 2837 Publisher: IEEE
» Adaptive Transmit-Side Equalization for Serial Electrical Interconnects at 100 Gb/s Using Duobinary
Abstract:The ever-increasing demand for more efficient data communication calls for new, advanced techniques for high speed serial communication. Although newly developed systems are setting records, off-line determination of the optimal equalizer settings is often needed. Well-known adaptive algorithms are mainly applied for receive-side equalization. However, transmit-side equalization is desirable for its reduced linearity requirements. In this paper, an adaptive sign–sign least mean square equalizer algorithm is developed applicable for an analog transmit-side feed-forward equalizer (FFE) capable of transforming non-return-to-zero modulation to duobinary (DB) modulation at the output of the channel. In addition to the derivation of the update strategy, extra algorithms are developed to cope with the difficult transmit–receive synchronization. Using an analog six tap bit-spaced equalizer, the algorithm is capable of optimizing DB communication of 100Gb/s over 1.5-m Twin-Ax cable. Both simulations and experimental results are presented to prove the capabilities of the algorithm demonstrating automated determination of FFE parameters, such that error-free communication is obtained (BER using PRBS9). Autors: Michiel Verplaetse;Timothy De Keulenaer;Arno Vyncke;Ramses Pierco;Renato Vaernewyck;Joris Van Kerrebrouck;Johan Bauwelinck;Guy Torfs; Appeared in: IEEE Transactions on Circuits and Systems I: Regular Papers Publication date: Jul 2017, volume: 64, issue:7, pages: 1865 - 1876 Publisher: IEEE
» Add-On Module of Active Disturbance Rejection for Set-Point Tracking of Motion Control Systems
Abstract:Active disturbance rejection control (ADRC) as a standalone motion solution has been made available in recent years on various industrial platforms. The idea of ADRC, however, can be integrated with the existing control technologies seamlessly, as shown in this paper. A modularized ADRC design is proposed in this particular work for set-point tracking task in motion control, such that better uncertainty rejection can be obtained without any change in the existing proportional-derivative control with a linear observer. It is proven that a certain extended state of the observer, i.e., the integration of the observer error, can serve as an estimation for the “total disturbance” in low-frequency range by only tuning the augmented gain. This enables the estimation and cancellation of the “total disturbance” to be incorporated into the existing control loop. Also, a comparison between the methods with and without such “module” is discussed. The proposed ADRC is implemented and validated experimentally using a laboratory manipulator, where the desired set-point tracking performance in position control is achieved under unknown mass variations and sudden external disturbances. Autors: Wenchao Xue;Rafal Madonski;Krzysztof Lakomy;Zhiqiang Gao;Yi Huang; Appeared in: IEEE Transactions on Industry Applications Publication date: Jul 2017, volume: 53, issue:4, pages: 4028 - 4040 Publisher: IEEE
» Advanced Control Strategies of PMSG-Based Wind Turbines for System Inertia Support
Abstract:This paper investigates two novel control strategies that enable system inertia supports by permanent magnet synchronous generator (PMSG) wind turbines during transient events. The first strategy seeks to provide inertia support to the system through simultaneous utilization of dc-link capacitor energy, and wind turbine (WT) rotor kinetic energy (KE). The second strategy supports system inertia through orderly exerting dc-link capacitor energy of WT and then WT rotor KE via a cascading control scheme. Both strategies can effectively provide system inertia support by fully utilizing WT's own potentials, while the second strategy distinguishes itself by minimizing its impacts on wind energy harvesting. Case studies of one synchronous generator connected with a PMSG-based WT considering sudden load variations have been studied to validate and compare the two proposed strategies on providing rapid inertia response for the system. Autors: Yujun Li;Zhao Xu;Kit Po Wong; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 3027 - 3037 Publisher: IEEE
» Advanced Data Exploitation in Speech Analysis: An overview
Abstract:With recent advances in machine-learning techniques for automatic speech analysis (ASA)-the computerized extraction of information from speech signals-there is a greater need for high-quality, diverse, and very large amounts of data. Such data could be game-changing in terms of ASA system accuracy and robustness, enabling the extraction of feature representations or the learning of model parameters immune to confounding factors, such as acoustic variations, unrelated to the task at hand. However, many current ASA data sets do not meet the desired properties. Instead, they are often recorded under less than ideal conditions, with the corresponding labels sparse or unreliable. Autors: Zixing Zhang;Nicholas Cummins;Bjoern Schuller; Appeared in: IEEE Signal Processing Magazine Publication date: Jul 2017, volume: 34, issue:4, pages: 107 - 129 Publisher: IEEE
» Aerospace Needs, Microelectronics, and the Quest for Reliability: 1962–1975 [Scanning Our Past]
Abstract:This computer system is not intended for use in the operation of nuclear facilities, aircraft navigation or communications systems, or air traffic control machines, or for any other uses where the failure of the computer system could lead to death, personal injury, or severe environmental damage.—Apple Computer, Inc., Macbook Users Guide, 2006, p. 109. Autors: Paul E. Ceruzzi; Appeared in: Proceedings of the IEEE Publication date: Jul 2017, volume: 105, issue:7, pages: 1456 - 1465 Publisher: IEEE
» Affine Invariant Description and Large-Margin Dimensionality Reduction for Target Detection in Optical Remote Sensing Images
Abstract:A novel target detection method based on affine invariant interest point detection, feature encoding, and large-margin dimensionality reduction (LDR) is proposed for optical remote sensing images. First, four types of interest point detectors are introduced, and their performance in extracting low-level affine invariant descriptors using affine shape estimation is compared. Such a description can deal with significant affine transformations, including viewpoints. Second, feature encoding, which extends bag-of-words (BOW) by encoding high-order statistics, is selected to generate mid-level representation. Finally, LDR based on the large-margin constraint and stochastic subgradient is introduced to make the high-dimensional mid-level representation applicable for target detection. The experiments on aircraft and vehicle detections illustrate the effectiveness of the affine invariant description and LDR (compared with principal component analysis) in improving the detection performance. The experiments also demonstrate the effectiveness of the proposed method compared with popular approaches including Gabor, HOG, LBP, BOW, and R-CNN. Autors: Lihong Wan;Laiwen Zheng;Hong Huo;Tao Fang; Appeared in: IEEE Geoscience and Remote Sensing Letters Publication date: Jul 2017, volume: 14, issue:7, pages: 1116 - 1120 Publisher: IEEE
» Agile All-Digital DPD Feedback Loop
Abstract:This paper presents an original agile all-digital feedback loop receiver system for power amplifier (PA) linearization using digital predistortion (DPD). The proposed feedback loop is based on a radio-frequency pulse-width modulation analog-to-digital converter. For proof of concept, the system was implemented using a single field programmable gate array chip. Additionally, the system is also presented in a remote version, suitable for future centralized radio access network, in which the DPD can be performed in a central unit, far from the PA. Measurement results of important DPD metrics, such as adjacent channel power ratio (ACPR) and error vector magnitude (EVM), are presented and evaluated to verify the correct functioning of the proposed feedback loop. The obtained results demonstrate the system’s agility and high analog input bandwidth from a few megahertzes up to almost 4 GHz, while maintaining the LTE ACPR and EVM requirements. Autors: André Prata;Jorge C. Santos;Arnaldo S. R. Oliveira;Nuno Borges Carvalho; Appeared in: IEEE Transactions on Microwave Theory and Techniques Publication date: Jul 2017, volume: 65, issue:7, pages: 2476 - 2484 Publisher: IEEE
» AI to ensure fewer UFOs
Abstract:Is it a bird? A plane? Or is it a remotely operated quadrotor conduct ing surveillance or preparing to drop a deadly payload? Human observers won’t have to guess—or keep their eyes glued to computer monitors— now that there’s superhuman artificial intelligence capable of distinguishing drones from those other flying objects. Automated watchfulness, thanks to machine learning, has given police and other agencies tasked with maintaining security an important countermeasure to help them keep pace with swarms of new drones taking to the skies. Autors: Jeremy Hsu; Appeared in: IEEE Spectrum Publication date: Jul 2017, volume: 54, issue:7, pages: 10 - 11 Publisher: IEEE
» AID: A Benchmark Data Set for Performance Evaluation of Aerial Scene Classification
Abstract:Aerial scene classification, which aims to automatically label an aerial image with a specific semantic category, is a fundamental problem for understanding high-resolution remote sensing imagery. In recent years, it has become an active task in the remote sensing area, and numerous algorithms have been proposed for this task, including many machine learning and data-driven approaches. However, the existing data sets for aerial scene classification, such as UC-Merced data set and WHU-RS19, contain relatively small sizes, and the results on them are already saturated. This largely limits the development of scene classification algorithms. This paper describes the Aerial Image data set (AID): a large-scale data set for aerial scene classification. The goal of AID is to advance the state of the arts in scene classification of remote sensing images. For creating AID, we collect and annotate more than 10000 aerial scene images. In addition, a comprehensive review of the existing aerial scene classification techniques as well as recent widely used deep learning methods is given. Finally, we provide a performance analysis of typical aerial scene classification and deep learning approaches on AID, which can be served as the baseline results on this benchmark. Autors: Gui-Song Xia;Jingwen Hu;Fan Hu;Baoguang Shi;Xiang Bai;Yanfei Zhong;Liangpei Zhang;Xiaoqiang Lu; Appeared in: IEEE Transactions on Geoscience and Remote Sensing Publication date: Jul 2017, volume: 55, issue:7, pages: 3965 - 3981 Publisher: IEEE
» Air-Filled Long Slot Leaky-Wave Antenna Based on Folded Half-Mode Waveguide Using Silicon Bulk Micromachining Technology for Millimeter-Wave Band
Abstract:An air-filled long slot leaky-wave antenna (LWA) based on folded half-mode waveguide (FHMW) fabricated using silicon substrate is proposed for millimeter-wave application. As is well known, the high-permittivity silicon dielectric is not suitable for antenna design. Thanks to the through-wafer dry etching and gold-plating processes deriving from the silicon bulk micromachining technology, three purely air-filled structures including the vertical part of the FHMW that also acts as the leaky-wave long slot in the top layer, horizontal part of the FHMW and matching section in the middle layer, and coupling slot in the bottom layer constitute the high-performance air-filled long slot LWA. To the best of the authors’ knowledge, this is the first time that an FHMW is adopted for antenna design. Compared with the conventional half-mode waveguide, the profile is lowered, the required silicon layer number is fixed to three, and the design can be more flexible. Experiment of the fabricated prototype shows that the main beam can be scanned from 41° to 49° with a gain variation between 13.15 and 15.41 dBi in the frequency range from 56 to 64 GHz. Moreover, confirmation of the design strategy provides the feasibility to realize the system-in-package solution. Autors: Le Chang;Zhijun Zhang;Yue Li;Shaodong Wang;Zhenghe Feng; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3409 - 3418 Publisher: IEEE
» Air-to-Dielectric-Filled Two-Hole Substrate-Integrated Waveguide Directional Coupler
Abstract:A two-hole directional coupler consisting of an air-filled substrate-integrated waveguide (AFSIW) coupled to a dielectric-filled substrate-integrated waveguide (SIW) is introduced and studied for the first time. The design of the proposed two-hole coupler, based on different dielectric-loaded SIWs and on multilayer printed circuit board process, is presented in detail with its theoretical foundation. The proposed coupler is of interest for monitoring high-performance, self-packaged, and low-cost millimeter-wave substrate integrated systems based on AFSIW. For demonstration purposes, a forward coupler operating in the Ka-band satellite uplink frequency band (27 to 31 GHz) has been designed and fabricated. In its frequency range of operation, it achieves measured insertion loss, coupling, and isolation of 0.28 ± 0.15 dB, 20.8 ± 0.24 dB, and 46.76 ± 3.92 dB, respectively. Autors: Frédéric Parment;Anthony Ghiotto;Tan-Phu Vuong;Jean-Marc Duchamp;Ke Wu; Appeared in: IEEE Microwave and Wireless Components Letters Publication date: Jul 2017, volume: 27, issue:7, pages: 621 - 623 Publisher: IEEE
» Algorithmic Principles of Remote PPG
Abstract:This paper introduces a mathematical model that incorporates the pertinent optical and physiological properties of skin reflections with the objective to increase our understanding of the algorithmic principles behind remote photoplethysmography (rPPG). The model is used to explain the different choices that were made in existing rPPG methods for pulse extraction. The understanding that comes from the model can be used to design robust or application-specific rPPG solutions. We illustrate this by designing an alternative rPPG method, where a projection plane orthogonal to the skin tone is used for pulse extraction. A large benchmark on the various discussed rPPG methods shows that their relative merits can indeed be understood from the proposed model. Autors: Wenjin Wang;Albertus C. den Brinker;Sander Stuijk;Gerard de Haan; Appeared in: IEEE Transactions on Biomedical Engineering Publication date: Jul 2017, volume: 64, issue:7, pages: 1479 - 1491 Publisher: IEEE
» Alternative LP and SOCP Hierarchies for ACOPF Problems
Abstract:The alternating current optimal power flow (ACOPF) problem optimizes the generation and the distribution of electric energy taking into account the active and the reactive power generation limits, demand requirements, bus voltage limits, and network flow limits. The ACOPF problem can be formulated as a nonconvex polynomial program that is generally difficult to solve due to the nonlinear power flow constraints. A recently proposed approach to globally solve the ACOPF problem is through the formulation of a hierarchy of semidefinite programs that are computationally challenging to solve for large-scale problems. In this paper, we explore a solution approach that alleviates this computational burden by using hierarchies of linear and second order cone programs and by exploiting the network structure of the transmission grid. Furthermore, we show that the first level of the second order cone hierarchy is equivalent to solving the conic dual of the approximation that was recently proposed in the literature, which provides the optimal solution of the ACOPF problem for special network topologies. Autors: Xiaolong Kuang;Bissan Ghaddar;Joe Naoum-Sawaya;Luis F. Zuluaga; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2828 - 2836 Publisher: IEEE
» Aluminum-Doped Zinc Oxide Transparent Electrode Prepared by Atomic Layer Deposition for Organic Light Emitting Devices
Abstract:Transparent conductive aluminum-doped zinc oxide (AZO) films are being introduced as alternatives to indium tin oxide (ITO) films, because they do not contain indium, which is expensive and toxic. In this study, the structural, electrical, and optical properties of AZO electrodes fabricated by atomic layer deposition (ALD) at a low temperature of 150 °C were examined by X-ray photoemission spectroscopy and scanning electron microscopy. The H2O purge time was changed in the ZnO cycle to alter the orientation of crystal phases and the film's electrical conductivity. An optimized AZO electrode, which had an Al:Zn mole ratio of 1:49, was prepared with a 20 s H2 O purge time. The resulting transparent electrode had a low resistivity (1.25 mΩ·cm ± 0.2 mΩ·cm) and a high transmittance (83.2% at 550 nm). The AZO film exhibited a high work function of 4.7 eV. Consequently, an classic organic light-emitting device (OLED) with an N,N′-bis-(1naphthl)-diphenyl-1,1′ -diphenyl-4,4′ -diamine and tris(8-quinolinolato) aluminum structure was fabricated on a glass substrate using the optimized AZO anode, and a maximum current efficiency of 3.9 cd/A was achieved. These results suggest that this method for preparing transparent conductive films via ALD can be used to create anodes for OLEDs. Autors: Hui Liu;Yun-Fei Liu;Peng-Peng Xiong;Ping Chen;Hui-Ying Li;Jing-Wen Hou;Bo-Nan Kang;Yu Duan; Appeared in: IEEE Transactions on Nanotechnology Publication date: Jul 2017, volume: 16, issue:4, pages: 634 - 638 Publisher: IEEE
» Amplified Spontaneous Emission and Rayleigh Scattering in Few-Mode Fiber Raman Amplifiers
Abstract:A theoretical model of noise—amplified spontaneous emission and Rayleigh backscattering—in few-mode fiber Raman amplifiers is presented in this letter. Based on this model, the equalization of the signal modal gain determines the equalization of the noise modal gain. The model can also be used to predict the mode-dependent optical signal-noise ratio. The theoretical results of this model are consistent with reported experimental results. Autors: Wei Wang;Jian Zhao;Zhiqun Yang;Chao Li;Zhen Wang;Liyao Yu;Ruilong Mi; Appeared in: IEEE Photonics Technology Letters Publication date: Jul 2017, volume: 29, issue:14, pages: 1159 - 1162 Publisher: IEEE
» An 802.11a/b/g/n/ac WLAN Transceiver for $2 \times 2$ MIMO and Simultaneous Dual-Band Operation With +29 dBm $\text{P}_{\mathrm {sat}}$ Integrated Power Amplifiers
Abstract:This paper describes the first dual-band MIMO 802.11a/b/g/n/ac WLAN RF transceiver capable of simultaneous dual-band operation. The measured receiver sensitivity of 2 GHz at 54 Mbps is −78.3 dBm and of 5 GHz for VHT80 is −66 dBm. The 802.11ac MIMO 20-MHz MCS0 2 and 5 GHz receiver sensitivity levels are −96 and −95.5 dBm, respectively. Integrated power amplifiers with of +29 dBm enable the 2-GHz transmitters to achieve TX output power of +23.5 dBm at 54-Mbps 64-quadratic-amplitude modulation (QAM). The 5-GHz transmitters achieve +17 dBm output for VHT80 256-QAM. This WLAN-BT connectivity system-on-chip is implemented in 40-nm CMOS technology. Autors: Shing Tak Yan;Lu Ye;Raghavendra Kulkarni;Edward Myers;Hsieh-Chih Shih;Hongbing Wu;Shadi Saberi;Darshan Kadia;Dicle Ozis;Lei Zhou;Eric Middleton;Joo Leong Tham; Appeared in: IEEE Journal of Solid-State Circuits Publication date: Jul 2017, volume: 52, issue:7, pages: 1798 - 1813 Publisher: IEEE
» An LC Decoupling Network for Two Antennas Working at Low Frequencies
Abstract:This paper presents an LC low-pass network to decouple a pair of coupled antennas working at low frequencies. Comparing with existing decoupling techniques, the proposed decoupling network provides a wideband but compact decoupling solution. Moreover, a generalized one-fit-all scheme is justified to implement the decoupling network with an antenna independent core network. By adjusting a few external components, the same core network can be applied to a collection of antenna pairs with different coupling levels and antenna form factors. Four design examples are given to demonstrate the unique features of the proposed network for low-frequency applications. In all cases, the decoupling network significantly improves the isolation between two antennas over a wide frequency band while the intrinsic matching bandwidth of the antennas is maintained. Autors: Huan Meng;Ke-Li Wu; Appeared in: IEEE Transactions on Microwave Theory and Techniques Publication date: Jul 2017, volume: 65, issue:7, pages: 2321 - 2329 Publisher: IEEE
» An Accurate Field Model Requiring Minimal Map Data for Guiding and Diffusion in Streets and Buildings
Abstract:Theory of normal mode propagation in a line-of-sight street scenario is extended to include propagation into buildings through coupling to a diffuse indoor field. Signal strength predictions are in close agreement with measurements, producing 2 dB and ≤ 3.5 dB root-mean-square model-data difference, in line-of-sight and outdoor-indoor scenarios, respectively. The full 3-D field model predicts actual signal directions and antenna correlations as a function of range, important for evaluating performance of directional antennas and spatial diversity. Only minimal description of the environment is needed, i.e., street width and representative building wall properties, without any interior details. Autors: Dmitry Chizhik;Mauricio Rodríguez;Rodolfo Feick;Reinaldo A. Valenzuela; Appeared in: IEEE Transactions on Wireless Communications Publication date: Jul 2017, volume: 16, issue:7, pages: 4537 - 4546 Publisher: IEEE
» An Accurate Subcircuit Model of SiC Half-Bridge Module for Switching-Loss Optimization
Abstract:The increasing demand for high power density requires the power converter to operate in high switching frequency. Silicon carbide (SiC) power module is regarded as one of the most promising candidates for high-frequency applications due to the superior switching speed and low switching loss. With the increase of switching frequency, the switching loss will be the limiting factor of efficiency. Hence, it should be minimized during each switching transition. The optimization of switching loss is normally achieved by the repetitive double pulse test experiments. It is time-consuming to find an optimum gate resistance to achieve the tradeoff between switching loss and electromagnetic interface. In this paper, an accurate subcircuit model for SiC power module is proposed to assist optimization of switching loss in converter design. By considering the device physics and structure, an accurate Miller capacitance model is obtained. Moreover, a parameter extraction procedure is presented, which is based on the datasheet. Good agreements are achieved between the PSpice simulation and experiment. Autors: Shan Yin;Pengfei Tu;Peng Wang;King Jet Tseng;Chen Qi;Xiaolei Hu;Michael Zagrodnik;Rejeki Simanjorang; Appeared in: IEEE Transactions on Industry Applications Publication date: Jul 2017, volume: 53, issue:4, pages: 3840 - 3848 Publisher: IEEE
» An Adaptive Multilook Approach for Small Sets of Multitemporal SAR Data Based on Adaptive Joint Data Vector
Abstract:The multitemporal interferometric synthetic aperture radar (InSAR) technique is a potential tool for measuring digital elevation models and surface deformation. It has the advantage of high precision, competitive spatial resolution, and wide coverage. To improve the accuracy of the final results, some adaptive multilook strategies have been proposed in which the identification of statistically homogeneous pixels (SHPs) is the key task. However, these methods are not always reliable in the case of small data sets. To improve this reliability, SHPs are identified based on the adaptive joint data vector comprising of temporal sample and spatial information in this letter. Additionally, the formulation of adaptive joint data vector is combined with local spatial features of SAR images. The presented adaptive multilook approach can be used in many interferometric applications, such as InSAR data filtering and coherence estimation. Experiments on six TerraSAR-X stripmap images of Tianjin in China validate the feasibility and effectiveness of the proposed approach. Autors: Huina Song;Yingfei Sun;Robert Wang;Ning Li;Bowen Zhang;Yingjie Wang;Wenbo Fei; Appeared in: IEEE Geoscience and Remote Sensing Letters Publication date: Jul 2017, volume: 14, issue:7, pages: 1161 - 1165 Publisher: IEEE
» An Adaptive QR Decomposition Processor for Carrier-Aggregated LTE-A in 28-nm FD-SOI
Abstract:This paper presents an adaptive QR decomposition (QRD) processor for five-band carrier-aggregated Long Term Evolution-Advanced downlinks. The design uses time and frequency correlation properties of wireless channels to reduce QRD computations while maintaining an uncoded bit error rate loss below 1 dB. An analysis on the performance of a linear interpolating QRD is presented, and optimum distances for different channel conditions are suggested. The Householder transform suited for spatially correlated scenarios is chosen and modified for concurrent vector rotations resulting in high throughput. Based on these, a parallel hardware architecture suitable for easy reconfigurability and low power is developed and fabricated in 28-nm fully depleted silicon-on-insulator technology. The QRD unit occupies 205k gates of logic and has a maximum throughput of 22 MQRD/s while consuming 29 mW of power. On a circuit level, the back gate feature is leveraged to double operational frequency in low time-frequency correlation channels or to lower power consumption to 1.9 mW in favorable conditions. The proposed system provides designers with multiple levels of adaptive control from architectural to circuit level for power-performance tradeoffs and is well suited for mobile devices operating on limited battery energy. Autors: Rakesh Gangarajaiah;Ove Edfors;Liang Liu; Appeared in: IEEE Transactions on Circuits and Systems I: Regular Papers Publication date: Jul 2017, volume: 64, issue:7, pages: 1914 - 1926 Publisher: IEEE
» An Advanced Impedance Calibration Method for Nanoscale Microwave Imaging at Broad Frequency Range
Abstract:A new calibration method for nanoscale complex impedance imaging with the scanning microwave microscope is presented, which allows to calibrate the complete frequency range in a short automated procedure. The vector network analyzer and the corresponding electronically switched calibration capabilities in combination with time domain gating and microwave network modeling are used to de-embed the full system. The entire calibration requires not more than 5 min and the acquisition of one single electrostatic force microscopy approach curve. In order to demonstrate the broadband capabilities, calibrated approach curves at various frequencies are presented. Nano-Schottky diodes on a semiconductor substrate as well as biological cells were measured to demonstrate that the sample conductance and susceptance are in agreement with the theoretical expectations for the samples. This advanced workflow of quantitative impedance calibration may have many applications in the fields of semiconductor failure analysis, 2-D materials, and biological samples in their native liquid environment. Autors: Manuel Kasper;Georg Gramse;Ferry Kienberger; Appeared in: IEEE Transactions on Microwave Theory and Techniques Publication date: Jul 2017, volume: 65, issue:7, pages: 2418 - 2424 Publisher: IEEE
» An Algorithm to Identify Surface Snowfall From GPM DPR Observations
Abstract:The Dual-Frequency Precipitation Radar (DPR) on board the Global Precipitation Measurement (GPM) core satellite has reflectivity measurements at two different frequency bands, namely, Ku- and Ka-bands. The dual-frequency ratio from these measurements has been used to perform rain-type classification and microphysics retrieval in the current DPR level 2 algorithm. In this paper, a surface snowfall identification algorithm is developed using GPM DPR observations. This algorithm provides a new approach to detect snowfall through radar observations, such as measured dual-frequency ratio. This algorithm is developed using GPM DPR data as well as Atmospheric Radiation Measurement (ARM) X/Ka-band radar data during the snowfall experiment. Several snow events observed by both DPR and ground radars are used in the algorithm validation, showing good comparisons. Autors: Minda Le;V. Chandrasekar;Sounak Biswas; Appeared in: IEEE Transactions on Geoscience and Remote Sensing Publication date: Jul 2017, volume: 55, issue:7, pages: 4059 - 4071 Publisher: IEEE
» An All-Digital Fully Integrated Inductive Buck Regulator With A 250-MHz Multi-Sampled Compensator and a Lightweight Auto-Tuner in 130-nm CMOS
Abstract:A 125-MHz fully integrated inductive buck voltage regulator using 11.6-nH wirebond inductance and 3.2-nF on-chip capacitance is presented in 130-nm CMOS. An all-digital architecture is presented to ease integration in digital process nodes. The IVR demonstrates enhanced bandwidth enabled by a multi-sampled digital compensator with reduced precision computation. A fast and lightweight auto-tuning engine is presented to optimize steady-state stability and transient response under variation in passives. A resistive transient assist scheme and an adaptive all-digital discontinuous conduction mode control are presented to reduce transient response time and enhance light-load efficiency, respectively. The 130-nm testchip demonstrates a peak efficiency of 71% and a 2.9-V/ output slew during large reference transient. Autors: Monodeep Kar;Arvind Singh;Anand Rajan;Vivek De;Saibal Mukhopadhyay; Appeared in: IEEE Journal of Solid-State Circuits Publication date: Jul 2017, volume: 52, issue:7, pages: 1825 - 1835 Publisher: IEEE
» An Alternate Circuit for Narrow-Bandpass Elliptic Microstrip Filter Design
Abstract:This letter demonstrates the dual transmission zeros (TZs) of bandpass elliptic prototype filters that can be directly implemented with two resonators in microstrip. An experimental filter based on the proposed alternate circuits is designed and fabricated. In order to improve the rejection of stopband, two additional TZs are introduced to the proposed filter. By means of directly implementing an elliptic bandpass filter in microstrip, the insertion loss of the presented filter can be less than 0.8 dB, and the result is better than 0.583, which means the proposed filter has a good selectivity. Autors: Sen Chen;Ling-Feng Shi;Gong-Xu Liu;Jian-Hui Xun; Appeared in: IEEE Microwave and Wireless Components Letters Publication date: Jul 2017, volume: 27, issue:7, pages: 624 - 626 Publisher: IEEE
» An Anisotropic Diffusion-Based Dynamic Combined Energy Model for Seismic Denoising
Abstract:In this letter, we combine anisotropic and isotropic diffusion models and establish a combined energy variational model for seismic denoising. We propose a dynamic threshold to separate seismic sections into different feature areas and to choose different diffusion methods more precisely according to the characteristics of the seismic sections. Multilevel noise and multilevel edges can be treated automatically. Denoised results from a synthetic model and from field seismic sections demonstrate that our proposed model can suppress random noise and preserve the features of seismic sections efficiently. Autors: Hui Chen;Jun Feng;Bin Zhou;Ying Hu;Ke Guo; Appeared in: IEEE Geoscience and Remote Sensing Letters Publication date: Jul 2017, volume: 14, issue:7, pages: 1061 - 1065 Publisher: IEEE
» An ANN-GA Semantic Rule-Based System to Reduce the Gap Between Predicted and Actual Energy Consumption in Buildings
Abstract:This paper addresses the endemic problem of the gap between predicted and actual energy performance in public buildings. A system engineering approach is used to characterize energy performance factoring in building intrinsic properties, occupancy patterns, environmental conditions, as well as available control variables and their respective ranges. Due to the lack of historical data, a theoretical simulation model is considered. A semantic mapping process is proposed using principle component analysis (PCA) and multi regression analysis (MRA) to determine the governing (i.e., most sensitive) variables to reduce the energy gap with a (near) real-time capability. Further, an artificial neural network (ANN) is developed to learn the patterns of this semantic mapping, and is used as the cost function of a genetic algorithm (GA)-based optimization tool to generate optimized energy saving rules factoring in multiple objectives and constraints. Finally, a novel rule evaluation process is developed to evaluate the generated energy saving rules, their boundaries, and underpinning variables. The proposed solution has been tested on both a simulation platform and a pilot building – a care home in the Netherlands. Validation results suggest an average 25% energy reduction while meeting occupants’ comfort conditions. Autors: Baris Yuce;Yacine Rezgui; Appeared in: IEEE Transactions on Automation Science and Engineering Publication date: Jul 2017, volume: 14, issue:3, pages: 1351 - 1363 Publisher: IEEE
» An Automatic Equalizer Based on Forward–Flyback Converter for Series-Connected Battery Strings
Abstract:This paper proposes an automatic any-cells-to-any-cells battery equalizer, which merges the forward and flyback converters through a common multiwinding transformer. The windings of the transformer are divided into two groups, which have opposite polarities. The principles of the proposed equalizer are that the equalization in one group is achieved based on forward conversion and the balancing between the two different groups is based on flyback conversion, by which the magnetic energy stored in the transformer can be automatically reset without using additional demagnetizing circuits. Moreover, only one MOSFET and one primary winding are required for each cell, resulting in smaller size and lower cost. One pair of complementary control signals is employed for all MOSFETs, and energy can be automatically and directly delivered from any high-voltage cells to any low-voltage cells without the requirement of cell monitoring circuits, thereby leading to a high balancing efficiency and speed. The proposed topology can achieve the global equalization for a long battery string through connecting the secondary sides of transformers without the need of additional components for the equalization among modules, which also overcomes the mismatching problem of multiple windings. The validity of the proposed equalizer is verified through experiments, and the balancing efficiency can reach up to 89.4% over a wide range of conditions. Autors: Yunlong Shang;Bing Xia;Chenghui Zhang;Naxin Cui;Jufeng Yang;Chunting Chris Mi; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5380 - 5391 Publisher: IEEE
» An Early Preamble Collision Detection Scheme Based on Tagged Preambles for Cellular M2M Random Access
Abstract:In this paper, we propose an early preamble collision detection (e-PACD) scheme at the first step of random access (RA) procedure based on tagged preambles (PAs), which consist of both PA and tag Zadoff–Chu sequences using different root numbers, respectively. The proposed e-PACD scheme enables faster PA collision detection and notification, compared with the conventional RA scheme. Accordingly, it can reduce the RA delay and remove resource wastes which occur at the third step of the conventional RA procedure. The reduced RA delay achieved by the proposed e-PACD scheme can contribute to an ultralow latency requirement in fifth-generation (5G) cellular networks. In addition, the proposed e-PACD scheme enables the eNodeB to monitor the number of RA-attempting nodes (RA load) on each physical RA channel slot. The PACD probability and the RA load monitoring accuracy are mathematically analyzed, and the RA performance enhancement of the proposed scheme is evaluated in terms of RA success probability, average RA delay, and RA resource efficiency, compared with the conventional RA scheme. Autors: Han Seung Jang;Su Min Kim;Hong-Shik Park;Dan Keun Sung; Appeared in: IEEE Transactions on Vehicular Technology Publication date: Jul 2017, volume: 66, issue:7, pages: 5974 - 5984 Publisher: IEEE
» An Early Stage Interturn Fault Diagnosis of PMSMs by Using Negative-Sequence Components
Abstract:This paper proposes an early stage interturn short-circuit fault (ISCF) diagnosis method for permanent magnet synchronous machines. A fault indicator is suggested based on a new theoretical analysis of the relationship between the fault current and the rotor speed. The fault indicator is shown to be robust to the rotor speed changes in slight ISCFs. It is calculated by introducing negative-sequence components (NSCs). It is shown that the fault indicator using NSCs can diagnose slighter ISCFs than that using zero-sequence components. Experimental results demonstrate the effectiveness of the proposed method for diagnosing early stage ISCFs with a small number of short-circuited turns and low fault current. Autors: Hyeyun Jeong;Seokbae Moon;Sang Woo Kim; Appeared in: IEEE Transactions on Industrial Electronics Publication date: Jul 2017, volume: 64, issue:7, pages: 5701 - 5708 Publisher: IEEE
» An ECC-Assisted Postpackage Repair Methodology in Main Memory Systems
Abstract:As dynamic random access memories (DRAMs) operate in the field, hard errors resulting from wearout occur. Unless corrected or repaired, hard errors halt normal operations, degrading the performance of a system and causing the replacement of memory modules. To improve performance and availability of memory modules, error-correcting codes (ECCs) are employed in a memory system. However, since recent field studies on DRAM errors have shown that a correctable error is highly likely to result in another error with the same address and in the same column or row, incorporating ECCs for mitigating not only soft errors but also hard errors in field operations is insufficient for ensuring reliable field operations. We propose a methodology that detects and repairs aging errors in DRAMs while operating in the field. We propose a methodology that reconfigures the remaining redundant resources after manufacturing-level repair into postpackage redundant resources. We also propose an ECC-assisted postpackage repair (PPR) flow that detects an error, identifies the type and location of the error, and invokes PPR for aging errors without built-in self-test/repair circuits. Employing a 2-GB ECC–dual in-line memory module of data-rate type three synchronous dynamic random access memories as a case study, we demonstrate that our PPR scheme improves the lifetime of DRAMs. Autors: Dae-Hyun Kim;Linda Milor; Appeared in: IEEE Transactions on Very Large Scale Integration Systems Publication date: Jul 2017, volume: 25, issue:7, pages: 2045 - 2058 Publisher: IEEE
» An Efficient and Easy-to-Implement Tag Identification Algorithm for UHF RFID Systems
Abstract:In this letter, a novel sub-frame-based dynamic frame slotted ALOHA (DFSA) algorithm is proposed for efficient tag identification based on EPC C1 Gen2 radio frequency identification (RFID) standard. Through the observation of slot states in a sub-frame, the reader estimates the tag number, and quickly adjusts the frame length to match the quantity of backlog. Once the appropriate frame length is observed, the algorithm will return to traditional DSFA. We use the modified maximum a posteriori probability (MAP) method for the estimation of tag quantity to improve the accuracy. To reduce the computation complexity of traditional MAP, we use tables to store estimation numbers. Due to the length strict of sub-frames, only a relatively small size of memory is required. Simulation results show that dynamic sub-frame MAP can improve the system utility (approximately 0.36) and reduce the computation complexity, only with an addition of less than 3-kB memory. Autors: Yongrui Chen;Jian Su;Weidong Yi; Appeared in: IEEE Communications Letters Publication date: Jul 2017, volume: 21, issue:7, pages: 1509 - 1512 Publisher: IEEE
» An Efficient and Stabilizing Model Predictive Control of Switched Systems
Abstract:Model Predictive Control (MPC) of switched systems typically requires an on-line solution of a Mixed Integer Program (MIP). Since the worst case complexity of the optimization problem increases exponentially with respect to the number of integer variables, an on-line implementation of the MPC for problems with large number of sub-systems and/or large horizons is usually expensive. In this technical note, we propose a stabilizing MPC formulation for state-dependent switched systems, that enables a tradeoff between the computational complexity of the MPC controller and the optimal performance of the closed-loop system. The proposed approach uses a pre-terminal set, in addition to the positively invariant terminal set, which aids in reducing the on-line complexity although at the expense of optimality. Examples are presented to illustrate the computational benefits of the proposed MPC strategy over existing MPC for switched systems. Autors: K. Hariprasad;Sharad Bhartiya; Appeared in: IEEE Transactions on Automatic Control Publication date: Jul 2017, volume: 62, issue:7, pages: 3401 - 3407 Publisher: IEEE
» An Efficient Globally Optimal Algorithm for Asymmetric Point Matching
Abstract:Although the robust point matching algorithm has been demonstrated to be effective for non-rigid registration, there are several issues with the adopted deterministic annealing optimization technique. First, it is not globally optimal and regularization on the spatial transformation is needed for good matching results. Second, it tends to align the mass centers of two point sets. To address these issues, we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set. By eliminating the transformation variables, we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank Hessian matrix. This facilitates the use of large scale global optimization techniques. We propose a modified normal rectangular branch-and-bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution. In addition, we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved. Extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state-of-the-art methods in terms of robustness to outliers, matching accuracy, and run-time. Autors: Wei Lian;Lei Zhang;Ming-Hsuan Yang; Appeared in: IEEE Transactions on Pattern Analysis and Machine Intelligence Publication date: Jul 2017, volume: 39, issue:7, pages: 1281 - 1293 Publisher: IEEE
» An Efficient Optimal Control Method for Open-Loop Transient Stability Emergency Control
Abstract:With the expansion of modern power systems, the stability issues become more and more prominent. Transient stability emergency control is usually designed in open-loop schemes and applies proper actions to avoid system collapse when transient stability cannot be guaranteed in serious contingencies. Taking transient stability and economic efficiency of power system into consideration, the emergency control problem can be modeled as an optimal control problem, which is computational expensive. In this paper, an optimal control method with constraint aggregation is proposed to reduce computational complexity. The yield nonlinear problem is a fairly small-scale optimization problem which can be efficiently solved by predictor–corrector interior point method. The adjoint sensitivity analysis (ASA) is employed to evaluate the first-order derivative while Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is used to obtain the second-order derivative. Besides, very dishonest Newton (VDHN) method and reusage of LU factorization results are explored to accelerate the forward and backward integration phase of ASA, respectively. The proposed approach is tested on four cases with different scales, and shows its potential in computational efficiency. Autors: Zhihao Li;Guoqiang Yao;Guangchao Geng;Quanyuan Jiang; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2704 - 2713 Publisher: IEEE
» An Efficient Tri-Level Optimization Model for Electric Grid Defense Planning
Abstract:The work reported in this paper aims at developing a practical and efficient tool for utility transmission planners to protect critical transmission assets from potential physical attacks. A trilevel min–max–min optimization model is proposed to represent actions of a planner, an attacker, and an operator. These three agents share a common objective function, which is the system load shedding. The strong duality theorem is used to merge the middle- and lower-level problems into a single-level one. The resulting mixed-integer bilevel model is solved by a Benders decomposition technique using primal cuts. Two case studies are presented as applications of this novel technique. Additionally, the proposed technique is compared with an implicit enumeration algorithm. Autors: Xuan Wu;Antonio J. Conejo; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2984 - 2994 Publisher: IEEE
» An EH0-Mode Microstrip Leaky-Wave Antenna With Periodical Loading of Shorting Pins
Abstract:In this paper, a novel class of microstrip leaky-wave antennas (MLWAs) under the operation of the fundamental EH0-mode in a microstrip line (MSL) is presented. The leaky-wave radiation is realized by periodically loading a set of shorting pins in the central plane along the longitudinal direction. Due to the inductive effect of these shorting pins, the phase constant of this pin-loaded MSL is reduced below its free-space counterpart so as to create a fast-wave frequency region for leaky-wave propagation and radiation. Compared with its counterpart higher order EH1- or EH2-mode MLWAs, the strip width of this EH0-mode MLWA can be freely designed with unspecified or narrow strip width. Our extensive investigations are then carried out to demonstrate its inductive-loaded fast-wave mechanism and distinctive characteristics, such as narrower strip width, low cutoff frequency, wide single-mode band, and controllable leakage constant in the fast-wave region. In final, two antenna prototypes with strip widths of 4.0 and 7.5 mm are designed, fabricated, and measured, with simulated and measured results in good agreement, validating the proposed pin-loaded technique for designs of EH0-mode MLWAs. Autors: Danpeng Xie;Lei Zhu;Xiao Zhang; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3419 - 3426 Publisher: IEEE
» An Electrochemistry Study of Cryoelectrolysis in Frozen Physiological Saline
Abstract:Cryoelectrolysis is a new minimally invasive tissue ablation surgical technique that combines the processes of electrolysis and solid/liquid phase transformation (freezing). This study investigated this new technique by measuring the pH front propagation and the changes in resistance in a tissue simulant made of physiological saline gel with a pH dye as a function of the sample temperature in the high subzero range above the eutectic. Results demonstrated that effective electrolysis can occur in a high subzero freezing milieu and that the propagation of the pH front is only weakly dependent on temperature. These observations are consistent with a mechanism involving ionic movement through the concentrated saline solution channels between ice crystals at subfreezing temperatures above the eutectic. Moreover, results suggest that Joule heating in these microchannels may cause local microscopic melting, the observed weak dependence of pH front propagation on temperature, and the large changes in resistance with time. A final insight provided by the results is that the pH front propagation from the anode is more rapid than from the cathode, a feature indicative of the electro-osmotic flow from the cathode to the anode. The findings in this paper may be critical for designing future cryoelectrolytic ablation surgery protocols. Autors: Thomas J. Manuel;Pujita Munnangi;Boris Rubinsky; Appeared in: IEEE Transactions on Biomedical Engineering Publication date: Jul 2017, volume: 64, issue:7, pages: 1654 - 1659 Publisher: IEEE
» An End-to-End Implanted Brain–Machine Interface Antenna System Performance Characterizations and Development
Abstract:Brain-machine interface (BMI) is a multidisciplinary field that has been recently developed in an attempt to help restore functionalities for paralyzed individuals. One of the key components for the implementation of a wireless BMI necessitates unique designs for both the internal brain and external head antennas. In this paper, we initially revisited the design of an optimized 1-mm3 implantable antenna transferring power and data with a reduced size low profile external reader antenna by utilizing radio-frequency identification (RFID)-inspired backscattering. Detailed computational assessments and specific absorption rate evaluations are performed. Prototypes were characterized in terms of link efficiency through a realized RFID link with up to −25 dB link efficiency. The noise analysis for antennas in biological systems was performed using two novel absorption-noise models. And finally a channel capacity estimation was performed, proving that the BMI antenna link could support up to 100 recording channels. An end-to-end BMI antenna system characterization is detailed in this paper for multichannel implanted neural recording applications. Autors: Lingnan Song;Yahya Rahmat-Samii; Appeared in: IEEE Transactions on Antennas and Propagation Publication date: Jul 2017, volume: 65, issue:7, pages: 3399 - 3408 Publisher: IEEE
» An Energy-Efficient Hybrid SAR-VCO $\Delta \Sigma$ Capacitance-to-Digital Converter in 40-nm CMOS
Abstract:This paper presents a highly digital, 0-1 MASH capacitance-to-digital converter (CDC). The CDC works by sampling a reference voltage on the sensing capacitor and then quantizing the charge stored in it by a 9-bit successive approximation register analog-to-digital converter. The residue is fed to a ring voltage-controlled oscillator (VCO) and quantized in time domain. The outputs from the two stages are combined to produce a quantized output with the first-order noise shaping. The proposed two-stage architecture reduces the impact of the VCO’s nonlinearity. A digital calibration technique is used to track the VCO’s gain across process, voltage, and temperature. The absence of any operational amplifier and low oversampling ratio for the VCO results in high energy efficiency. A prototype CDC in a 40-nm CMOS process achieves a 64.2-dB SNR while operating from a 1-V supply and using a sampling frequency of 3 MHz. The prototype achieves a CDC figure of merit of 55 fJ/conversion-step. Autors: Arindam Sanyal;Nan Sun; Appeared in: IEEE Journal of Solid-State Circuits Publication date: Jul 2017, volume: 52, issue:7, pages: 1966 - 1976 Publisher: IEEE
» An Energy-Scalable Accelerator for Blind Image Deblurring
Abstract:Camera shake is a common cause of blur in cell-phone camera images. Removing blur requires deconvolving the blurred image with a kernel, which is typically unknown and needs to be estimated from the blurred image. This kernel estimation is computationally intensive and takes several minutes on a CPU, which makes it unsuitable for mobile devices. This paper presents the first hardware accelerator for kernel estimation for image deblurring applications. Our approach, using a multi-resolution iteratively reweighted least squares deconvolution engine with DFT-based matrix multiplication, a high-throughput image correlator, and a high-speed selective update-based gradient projection solver, achieves a 78x reduction in kernel estimation runtime, and a 56x reduction in total deblurring time for a image, enabling quick feedback to the user. Configurability in kernel size and number of iterations gives up to ten times energy scalability, allowing the system to trade off runtime with image quality. The test chip, fabricated in TSMC 40-nm CMOS technology, consumes 105 mJ for kernel estimation running at 83 MHz and 0.9 V, making it suitable for integration into mobile devices. Autors: Priyanka Raina;Mehul Tikekar;Anantha P. Chandrakasan; Appeared in: IEEE Journal of Solid-State Circuits Publication date: Jul 2017, volume: 52, issue:7, pages: 1849 - 1862 Publisher: IEEE
» An Enhanced Viola-Jones Vehicle Detection Method From Unmanned Aerial Vehicles Imagery
Abstract:This research develops an advanced vehicle detection method, which improves the original Viola-Jones (V-J) object detection scheme for better vehicle detections from low-altitude unmanned aerial vehicle (UAV) imagery. The original V-J method is sensitive to objects’ in-plane rotation, and therefore has difficulties in detecting vehicles with unknown orientations in UAV images. To address this issue, this research proposes a road orientation adjustment method, which rotates each UAV image once so that the roads and on-road vehicles on rotated images will be aligned with the horizontal direction and the V-J vehicle detector. Then, the original V-J can be directly applied to achieve better efficiency and accuracy. The enhanced V-J method is further applied for vehicle tracking. Testing results show that both vehicle detection and tracking methods are competitive compared with other existing methods. Future research will focus on expanding the current methods to detect other transport modes, such as buses, trucks, motorcycles, bicycles, and pedestrians. Autors: Yongzheng Xu;Guizhen Yu;Xinkai Wu;Yunpeng Wang;Yalong Ma; Appeared in: IEEE Transactions on Intelligent Transportation Systems Publication date: Jul 2017, volume: 18, issue:7, pages: 1845 - 1856 Publisher: IEEE
» An Entropy-Based Analysis of GPR Data for the Assessment of Railway Ballast Conditions
Abstract:The effective monitoring of ballasted railway track beds is fundamental for maintaining safe operational conditions of railways and lowering maintenance costs. Railway ballast can be damaged over time by the breakdown of aggregates or by the upward migration of fine clay particles from the foundation, along with capillary water. This may cause critical track settlements. To that effect, early stage detection of fouling is of paramount importance. Within this context, ground penetrating radar (GPR) is a rapid nondestructive testing technique, which is being increasingly used for the assessment and health monitoring of railway track substructures. In this paper, we propose a novel and efficient signal processing approach based on entropy analysis, which was applied to GPR data for the assessment of the railway ballast conditions and the detection of fouling. In order to recreate a real-life scenario within the context of railway structures, four different ballast/pollutant mixes were introduced, ranging from clean to highly fouled ballast. GPR systems equipped with two different antennas, ground-coupled (600 and 1600 MHz) and air-coupled (1000 and 2000 MHz), were used for testing purposes. The proposed methodology aims at rapidly identifying distinctive areas of interest related to fouling, thereby lowering significantly the amount of data to be processed and the time required for specialist data processing. Prominent information on the use of suitable frequencies of investigation from the investigated set, as well as the relevant probability values of detection and false alarm, is provided. Autors: Francesco Benedetto;Fabio Tosti;Amir M. Alani; Appeared in: IEEE Transactions on Geoscience and Remote Sensing Publication date: Jul 2017, volume: 55, issue:7, pages: 3900 - 3908 Publisher: IEEE
» An Equivalent Simulation Method for Pulse Radar Measurement in Anechoic Chamber
Abstract:When a pulse radar signal is implemented in a range-limited anechoic chamber for radar measurement, the transmitted and reflected signal will be coupled at the receiver. To solve this problem and equivalently simulate the whole process of pulse radar measurement in an anechoic chamber, the interrupted transmitting and receiving method is proposed in this letter based on interrupted sampling. The constraints of the transmitting and receiving parameters are deduced with the sizes of the anechoic chamber and target. The pulse compression of the proposed method is performed. Then, the window function is applied to extract the main peaks after pulse compression. Both the simulation and experimental results are provided to demonstrate the effectiveness of the proposed method in overcoming the coupling between the transmitted and reflected pulse signals. Autors: Xiaobin Liu;Jin Liu;Feng Zhao;Xiaofeng Ai;Guoyu Wang; Appeared in: IEEE Geoscience and Remote Sensing Letters Publication date: Jul 2017, volume: 14, issue:7, pages: 1081 - 1085 Publisher: IEEE
» An Extension of the InSAR-Based Probability Integral Method and Its Application for Predicting 3-D Mining-Induced Displacements Under Different Extraction Conditions
Abstract:Underground extraction can be roughly classified into three types, i.e., subcritical, critical, and supercritical extraction, in accordance with the geological conditions in the overburden and the geometry of mined-out areas. In 2016, we proposed an approach based on the interferometric synthetic aperture radar (InSAR) technique and the probability integral method (PIM) for the cost-effective prediction of 3-D mining-induced displacements (abbreviated as InSAR-PIM). Due to the inherent assumption of critical extraction in the PIM, the InSAR-PIM method performs well in predicting the 3-D displacements caused by critical and/or supercritical extraction, but poorly for subcritical extraction. In this paper, we first propose a generalized PIM (GPIM) by modifying the traditional PIM with a simplified Boltzmann function. We then replace the PIM of the InSAR-PIM with the proposed GPIM to develop an extension of InSAR-PIM (referred as to InSAR-GPIM). The InSAR-GPIM was tested in the Qianyingzi coal mining area, China. The results show that the InSAR-GPIM-predicted horizontal and vertical displacements caused by subcritical, critical, and supercritical extraction agree well with the in situ observations, with average root-mean-square errors of about 0.032 and 0.050 m, respectively. These accuracies represent improvements of 60.9% and 59% when compared with the accuracies predicted by the InSAR-PIM in the horizontal and vertical directions. The results indicate that the InSAR-GPIM is capable of accurately predicting 3-D mining-induced displacements under different extraction conditions (i.e., subcritical, critical, and supercritical extraction), and it performs much better than the InSAR-PIM in the case of subcritical extraction. It is therefore believed that InSAR-GPIM will have a wider scope of applications than the previous InSAR-PIM. Autors: Ze Fa Yang;Zhi Wei Li;Jian Jun Zhu;Axel Preusse;Hui Wei Yi;Yun Jia Wang;Markus Papst; Appeared in: IEEE Transactions on Geoscience and Remote Sensing Publication date: Jul 2017, volume: 55, issue:7, pages: 3835 - 3845 Publisher: IEEE
» An Improved Describing Function With Applications for OTA-Based Circuits
Abstract:Electronic systems make extensive use of operational transconductance amplifiers (OTAs) to build filters and oscillators. Studying the effects of the saturation nonlinearity on these OTA-based circuits is difficult and often requires lengthy simulations to check the system’s performance under large-signal operation. The describing function (DF) theory allows to circumvent these simulations by deriving a signal-dependent linearized gain, which predicts the effects of the nonlinearity. However, its use is limited since the state-of-the-art DFs deviate significantly from the real saturating behavior of OTAs. This paper proposes an improved DF, which can be directly derived from the static nonlinear characteristic of the transconductance amplifier. The performance of the proposed methodology is demonstrated for both an OTA-based filter and oscillator. It is shown that the proposed DF has a better nonlinear prediction capability than the state-of-the-art solutions. Autors: Dries Peumans;Gerd Vandersteen; Appeared in: IEEE Transactions on Circuits and Systems I: Regular Papers Publication date: Jul 2017, volume: 64, issue:7, pages: 1748 - 1757 Publisher: IEEE
» An Improved IRA Algorithm and Its Application in Critical Eigenvalues Searching for Low Frequency Oscillation Analysis
Abstract:On the basis of implicitly restarted Arnoldi (IRA) method, an improved algorithm is proposed, in which the dimension of Krylov subspace is dynamically increased to compute eigenvalues in specified circle. First, the radius of searching circles is dynamically expanded through automatically increasing the number of eigenvalues and the dimension of Krylov subspace, based on the locking mechanism. Second, the region where the low frequency oscillation modes located is divided into small independent computing units, which are covered by specified searching circles. Third, the independent computing units can be calculated simultaneously with no effects on each other. The proposed method can avoid eigenvalues missing caused by inappropriate resetting of search number in equidistant-searching IRA method. Furthermore, no manual intervention is needed in the proposed method. Two systems with 570 and 5272 state variables are tested in this paper, and the results indicate that the proposed method is efficient, reliable, and practical. Autors: Chongru Liu;Xiao Li;Pengfei Tian;Mu Wang; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2974 - 2983 Publisher: IEEE
» An Improved Model for Quasi-Ballistic Transport in MOSFETs
Abstract:We have already presented a compact model for FETs operating in the quasi-ballistic regime [1]. However, this model suffers from two important problems: 1) the profile for charge density along the channel is not correctly accounted for and 2) current is not conserved throughout the channel. In this brief, we propose improvement, which does away with these inaccuracies. Autors: Avirup Dasgupta;Amit Agarwal;Yogesh Singh Chauhan; Appeared in: IEEE Transactions on Electron Devices Publication date: Jul 2017, volume: 64, issue:7, pages: 3032 - 3036 Publisher: IEEE
» An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications
Abstract:In this paper, a new impulsive delay inequality that involves unbounded and nondifferentiable time-varying delay is presented. As an application, some sufficient conditions ensuring stability and stabilization of impulsive systems with unbounded time-varying delay are derived. Some numerical examples are given to illustrate the results. Especially, a stabilizing memoryless controller for a second-order time-varying system with unbounded time-varying delay is proposed. Autors: Xiaodi Li;Jinde Cao; Appeared in: IEEE Transactions on Automatic Control Publication date: Jul 2017, volume: 62, issue:7, pages: 3618 - 3625 Publisher: IEEE
» An Incremental Framework for Video-Based Traffic Sign Detection, Tracking, and Recognition
Abstract:Video-based traffic sign detection, tracking, and recognition is one of the important components for the intelligent transport systems. Extensive research has shown that pretty good performance can be obtained on public data sets by various state-of-the-art approaches, especially the deep learning methods. However, deep learning methods require extensive computing resources. In addition, these approaches mostly concentrate on single image detection and recognition task, which is not applicable in real-world applications. Different from previous research, we introduce a unified incremental computational framework for traffic sign detection, tracking, and recognition task using the mono-camera mounted on a moving vehicle under non-stationary environments. The main contributions of this paper are threefold: 1) to enhance detection performance by utilizing the contextual information, this paper innovatively utilizes the spatial distribution prior of the traffic signs; 2) to improve the tracking performance and localization accuracy under non-stationary environments, a new efficient incremental framework containing off-line detector, online detector, and motion model predictor together is designed for traffic sign detection and tracking simultaneously; and 3) to get a more stable classification output, a scale-based intra-frame fusion method is proposed. We evaluate our method on two public data sets and the performance has shown that the proposed system can obtain results comparable with the deep learning method with less computing resource in a near-real-time manner. Autors: Yuan Yuan;Zhitong Xiong;Qi Wang; Appeared in: IEEE Transactions on Intelligent Transportation Systems Publication date: Jul 2017, volume: 18, issue:7, pages: 1918 - 1929 Publisher: IEEE
» An Integrated Approach for Power System Restoration Planning
Abstract:Power system outages/blackouts, especially weather related, are becoming more and more frequent, incurring significant economic and social costs. The ability to restore power services quickly after a blackout is crucial for power system resilience. Power system restoration is an extremely complicated process, involving multiple steps, highly combinatorial operational decisions, and highly nonlinear technical constraints, which make restoration planning an exceptionally challenging task. This paper will first introduce the restoration process and operations, examine important issues in restoration, and survey the state of the art in the research and practice of power system restoration planning. Then, we will focus on the commonly used buildup restoration planning strategy, in which the system is sectionalized into smaller subsystems with initial power sources, and then the subsystems are restored in parallel. Due to the complexity, existing approaches treat the sectionalization and restoration separately, leading to a suboptimal restoration plan. We will introduce an integrated restoration planning approach to improve the quality of restoration plans globally (such as shorter overall restoration time) by using mathematical programming and simulation in an interactive and iterative way. Case studies will be provided to illustrate the effectiveness of the proposed approach. Autors: Feng Qiu;Peijie Li; Appeared in: Proceedings of the IEEE Publication date: Jul 2017, volume: 105, issue:7, pages: 1234 - 1252 Publisher: IEEE
» An Iterative Method for Determining the Most Probable Bifurcation in Large Scale Power Systems
Abstract:An iterative method is presented to determine the most probable voltage stability limit by identifying the closest saddle node bifurcation in a probability-loading space starting at the expected initial system state. The iterative method is applied to the probability space to identify the closest saddle node bifurcation by means of the Mahalanobis distance. Further the method provides an ellipsoidal load subspace corresponding to the most probable bifurcation. This ellipsoid is a lower bound for the probability of bifurcation. To verify the proposed methodology examples are given and the minimum Mahalanobis distance, for dependent and independent load patterns, is compared with the minimum Euclidian distance. Autors: Moritz Mittelstaedt;Sascha Bauer;Armin Schnettler; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2966 - 2973 Publisher: IEEE
» An On-line Sensor Selection Algorithm for SPRT With Multiple Sensors
Abstract:We present an on-line sensor selection strategy (SSS) for the Sequential Probability Ratio Test (SPRT) with multiple sensors. Each sensor incurs an associated observation cost. We aim to design an SSS, in which the sensor selection may depend causally on the measurement values, that minimizes the expected total observation cost. In general, the optimal SSS can be obtained by solving a dynamic program; however, the problem is computationally quite demanding. We propose a computationally efficient algorithm in which we partition the state space into three regions and solve for the SSS in each region. The computational complexity of the proposed algorithm is linear in the number of sensors and numerical results show that it can well approximate the optimal SSS. Autors: Cheng-Zong Bai;Vijay Gupta; Appeared in: IEEE Transactions on Automatic Control Publication date: Jul 2017, volume: 62, issue:7, pages: 3532 - 3539 Publisher: IEEE
» An Operational State Aggregation Technique for Transmission Expansion Planning Based on Line Benefits
Abstract:This paper provides a novel technique to represent in a reduced, or compact, way temporal variability in transmission expansion planning (TEP). This reduction is handled by means of “snapshot selection.” Instead of taking into account all the possible operational states and their associated optimal power flow, a reduced group of them is selected that is representative of all the states that should have an influence on investment decisions. Considering this reduced group of operational states should lead to the same investment decisions as if all the snapshots in the target year were considered. Original operational states are compared in the space of the benefits produced by potential reinforcements considered, which are relevant drivers for investment decisions. The benefits produced by these potential reinforcements are computed based on the incremental change in operation costs resulting from their installation. A clustering algorithm is used to group together those operational states where similar line benefits are realized. Our algorithm has been tested on a modified version of the standard IEEE 24 bus system. The method produces promising results and proves to be more efficient than other snapshot selection methods used until now in computing an accurate enough selection of snapshots representing system operation variability in TEP. Autors: Quentin Ploussard;Luis Olmos;Andrés Ramos; Appeared in: IEEE Transactions on Power Systems Publication date: Jul 2017, volume: 32, issue:4, pages: 2744 - 2755 Publisher: IEEE
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2009: January February March April May June July August September October November December | 2017-07-28 04:48:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39026814699172974, "perplexity": 2868.10292520078}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549436330.31/warc/CC-MAIN-20170728042439-20170728062439-00035.warc.gz"} |
http://capsiplexfrance.com/index-254.html | # Percentage Increase Calculator
Enter two values to calculate percentage of increase or decrease
Enter 1st Value =
Enter 2nd Value =
Percentage change is
%
Percentage Increase Calculator is a free online tool that displays the percentage increase for the given number. BYJU’S online percentage Increase calculator tool makes the calculation faster, and it displays the percentage Increase (or decrease based on the input) in a fraction of seconds.
## How to Use the Percentage Increase Calculator?
The procedure to use the percentage increase calculator is as follows:
Step 1: Enter the numbers in the respective input field
Step 2: Now click the button “Solve” to get the percentage change
Step 3: Finally, the percentage increase (or decrease based on the input) for the given number will be displayed in the output field
### What is Meant by Percentage Increase?
In mathematics, the percentage increase is the measure of the percentage change. The percentage increase is defined as the ratio of increased value to the original value and then multiplied by 100. Here the increased value can be calculated by taking the difference between the final value and the initial value. The formula to calculate increase is given by
Percentage Increase = [(Final value – Original value) × 100] / Original value %
For example, if the original value is 56 and the final value is 79, then the percentage increase is:
Percentage Increase = [(79-56) ×100]/56
= 2300/56
= 41.071%
Hence, the percentage increase is 41.071% | 2022-08-09 11:01:33 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8540711402893066, "perplexity": 1104.3088528989888}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00734.warc.gz"} |
https://bookdown.org/voigtstefan/aef_exercises/covariance-estimation.html | # 9 (Co)variance estimation
## 9.1 ARCH and GARCH
This short exercise illustrates how to perform maximum likelihood estimation in R at the simple example of ARCH$$(p)$$ and GARCH($$p, q$$) models. I advice you to first write the code for the basic specification on your own, afterwards the exercises will help you to get familiar with well-established packages in R that provide you with the same (and many additional more sophisticated) methods to estimate conditional volatility models.
Exercises:
1. As a benchmark dataset, download prices and compute daily returns for all stocks that are part of the Dow Jones 30 index (ticker <- "DOW"). Decompose the time-series into a predictable part and the residual, $$r_t = E(r_t|\mathcal{F}_{t-1}) + \varepsilon_t$$. The easiest approach would be to demean the time-series by simply subtracting the sample mean but in principle more sophisticated methods can be used.
2. For each of the 30 tickers, illustrate the rolling window standard deviation based on some suitable estimation window length.
3. Write a small function that computes the maximum likelihood estimator (MLE) of an ARCH($$p$$) model.
4. Write a second function that implements MLE estimation for an GARCH($$p,q$$) model.
5. What is the unconditional estimated variance of the ARCH($$1$$) and the GARCH($$1, 1$$) model for each ticker?
6. Next, familiarize yourself with the rugarch package to perform more sophisticated volatility modeling. Here you can find a great example on how to unleash the flexibility of rmgarch.
7. Use either your own code or the rugarch package to fit a GARCH and an ARCH model for each of the 30 time series and create 1-day ahead volatility forecasts with one year as the initial estimation window. Compare the forecasts to a 1-day ahead volatility forecast based on the sample standard deviation (often called the random walk model). Illustrate the forecast performance against the squared return of the next day and compute the mean squared prediction error of each model. What can you conclude about the predictive performance?
• Compute and illustrate the model-implied Value-at-risk, defined as the lowest return your model expects with a probability of less than 5 %. Formally, the VaR is defined as $$\text{VaR} _{\alpha }(X)= -\inf {\big \{}x\in \mathbb {R} :F_{-X}(x)>\alpha {\big \}}=F_{-X}^{-1}(1-\alpha)$$ where $$X$$ is the return distribution. Illustrate stock returns which fall below the estimated Value-at-risk. What can you conclude?
Solutions:
library(tidyverse)
library(tidyquant)
As usual, I use the tidyquant package to download price data of the time series of 30 stocks and to compute (adjusted) net returns.
ticker <- tq_index("DOW")
prices <- tq_get(ticker %>%
filter(ticker!="DOW"), get = "stock.prices")
returns <- prices %>%
group_by(symbol) %>%
select(symbol, date, ret) %>%
drop_na(ret) %>%
mutate(ret = ret - mean(ret))
I use the slider package for convenient rolling window computations. For a detailed documentation, consult (this homepage.)[https://github.com/DavisVaughan/slider]
library(slider)
rolling_sd <- returns %>%
group_by(symbol) %>%
mutate(rolling_sd = slide_dbl(ret, sd,
.before = 100)) # 100 day estimation window
rolling_sd %>%
drop_na() %>%
ggplot(aes(x=date, y = rolling_sd, color = symbol)) +
geom_line() +
labs(x = "", y = "Standard deviation (rolling window") +
theme(legend.position = "None")
The figure illustrates at least two relevant features: i) Although rather persistent, volatilities change over time and ii) volatilities tend to co-move. Next I write a short, very simplified script which performs maximum likelihood estimation of the parameters of an ARCH($$p$$) model in R´.
ret <- returns %>%
filter(symbol == "AAPL") %>%
pull(ret) * 100
# Compute ARCH
logL <- function(params, p){
eps_sqr_lagged <- cbind(ret, 1)
for(i in 1:p){
eps_sqr_lagged <- cbind(eps_sqr_lagged, lag(ret, i)^2)
}
eps_sqr_lagged <- na.omit(eps_sqr_lagged)
sigma <- eps_sqr_lagged[,-1] %*% params
0.5 * sum(log(sigma)) + 0.5 * sum(eps_sqr_lagged[,1]^2/sigma)
}
The function logL computes the (log) likelihood of an ARCH specification with $$p$$ lags. Note that it returns the negative log likelihood because most optimization procedures in R are designed to search for minima instead of maximization.
The next few lines show how to estimate the model with optim and p = 2 lags. Note my (almost) arbitrary choice for the initial parameter vector. Also, note that the function logL and the optimization procedure does not enforce the regularity conditions which would ensure stationary volatility processes.
p <- 2
initial_params <- (c(sd(ret), rep(1, p)))
fit_manual <- optim(par = initial_params,
fn = logL,
hessian = TRUE,
method="L-BFGS-B",
lower = 0,
p = p)
fitted_params <- (fit_manual$par) se <- sqrt(diag(solve(fit_manual$hessian)))
cbind(fitted_params, se) %>% knitr::kable(digits = 2)
fitted_params se
2.05 0.09
0.19 0.03
0.19 0.03
# Run the code below to compare the results with tseries package
# library(tseries)
# summary(garch(ret,c(0,p)))
We can implement GARCH estimation with very few adjustments
# GARCH
garch_logL <- function(params, p, q, return_only_loglik = TRUE){
eps_sqr_lagged <- cbind(ret, 1)
for(i in 1:p){
eps_sqr_lagged <- cbind(eps_sqr_lagged, lag(ret, i)^2)
}
sigma.sqrd <- rep(sd(ret)^2, nrow(eps_sqr_lagged))
for(t in (1 + max(p, q)):nrow(eps_sqr_lagged)){
sigma.sqrd[t] <- params[1:(1+p)]%*% eps_sqr_lagged[t,-1] +
params[(2+p):length(params)] %*% sigma.sqrd[(t-1):(t-q)]
}
sigma.sqrd <- sigma.sqrd[-(1:(max(p, q)))]
if(return_only_loglik){
0.5 * sum(log(sigma.sqrd)) + 0.5 * sum(eps_sqr_lagged[(1 + max(p, q)):nrow(eps_sqr_lagged),1]^2/sigma.sqrd)
}else{
return(sigma.sqrd)
}
}
p <- 1 # Lag structure
q <- 1
fit_garch_manual <- optim(par = rep(0.01, p + q + 1),
fn = garch_logL,
hessian = TRUE,
method="L-BFGS-B",
lower = 0,
p = p,
q = q)
fitted_garch_params <- fit_garch_manual$par Next I plot the time series of estimated $$\sigma_t$$ based on the output. Note that in order to keep the required code clean and simple my function garch_logL returns the fitted variances with the option return_only_loglik = FALSE. tibble(vola = garch_logL(fitted_garch_params, p, q, FALSE)) %>% ggplot(aes(x = 1:length(vola), y = sqrt(vola))) + geom_line() + labs(x = "", y = "GARCH(1,1) volatility") Next, the typical tidyverse approach: Once we implemented the workflow for 1 asset, we can use mutate and map() to perform the same computation in a tidy manner for all assets in our sample. Recall that the unconditional variance is defined in the lecture slides. # Estimate ARCH(1) for all ticker uncond_var <- returns %>% arrange(symbol, date) %>% nest(data = c(date, ret)) %>% mutate(arch = map(data, function(.x){ logL <- function(params, p){ eps_sqr_lagged <- cbind(ret, 1) for(i in 1:p){ eps_sqr_lagged <- cbind(eps_sqr_lagged, lag(ret, i)^2) } eps_sqr_lagged <- na.omit(eps_sqr_lagged) sigma <- eps_sqr_lagged[,-1] %*% params 0.5 * sum(log(sigma)) + 0.5 * sum(eps_sqr_lagged[,1]^2/sigma) } ret <- .x %>% pull(ret) * 100 p <- 2 initial_params <- (c(sd(ret), rep(1, p))) fit_manual <- optim(par = initial_params, fn = logL, hessian = TRUE, method="L-BFGS-B", lower = 0, p = p) fitted_params <- (fit_manual$par)
se <- sqrt(diag(solve(fit_manual$hessian))) return(tibble(param = c("intercept", paste0("alpha ", 1:p)), value = fitted_params, se = se)) })) %>% select(-data) %>% unnest(arch) %>% group_by(symbol) %>% summarise(uncond_var = dplyr::first(value) / (1 - sum(value) + dplyr::first(value))) uncond_var %>% ggplot() + geom_bar(aes(x = reorder(symbol, uncond_var), y = uncond_var), stat = "identity") + coord_flip() + labs(x = "Unconditional Variance", y = "") Advanced question: Make sure you understand what happens if you do not define the function logL within the mutate call but instead define it once and for all outside the loop. Hint: Calling logL once before running the loop stores the underlying sample as part of the function object and will thus not provide the estimated parameters of your subset of data but instead only of the sample which was present in the working environment once you defined the function. This is sometimes a tricky concept in R, consult Hadley Wickham’s book Advanced R for more information. Some more code for (in-sample) estimation of a GARCH model for multiple assets is provided below. For out-of-sample computations, consult the Section on multivariate models. First, I specify the model (standard Garch(1,1)). The lines afterwards use the function ugarchfit to fit each individual GARCH model for each ticker, the rolling window standard deviation and extracts $$\hat\sigma_t^2$$. Note that these are in-sample volatilities in the sense that the entire time series is used to fit the GARCH model. In most applications, however, this is absolutely sufficient. library(rugarch) model.spec <- ugarchspec(variance.model = list(model = 'sGARCH' , garchOrder = c(1 , 1))) model.fit <- returns %>% mutate(Rolling = slide_dbl(ret, sd, .before = 250)) %>% nest(data = c(date, Rolling, ret)) %>% mutate(garch = map(data, function(x) sigma(ugarchfit(spec = model.spec , data = x %>% pull(ret), solver = "hybrid"))%>% as_tibble())) %>% mutate(full_data = map2(data, garch, cbind)) %>% unnest(full_data) %>% select(-data, -garch) %>% rename("Garch" = V1) Next, I provide some illustration of the estimated paths of volatilities for the two estimation procedures. model.fit %>% pivot_longer(c(Rolling, Garch)) %>% ggplot(aes(x=date, y = value, color = symbol)) + geom_line() + facet_wrap(~name) + theme(legend.position = "bottom") For an illustration of the value at risk computation, consult the lecture slides. ## 9.2 Ledoit-Wolf shrinkage estimation A severe practical issue with the sample variance covariance matrix in large dimensions ($$N >>T$$) is that $$\hat\Sigma$$ is singular. Ledoit and Wolf proposed a series of biased estimators of the variance-covariance matrix $$\Sigma$$ which overcome this problem. As a result, it is often advised to perform Ledoit-Wolf like shrinkage on the variance covariance matrix before proceeding with portfolio optimization. Exercises: • Read the paper Honey, I shrunk the sample covariance matrix (provided in Absalon) and try to implement the feasible linear shrinkage estimator. If in doubt, consult Michael Wolfs homepage, you will find useful R and matlab code there. It may also be advisable to take a look at the documentation and source code of the package RiskPortfolios, in particular the function covEstimation(). • Write a simulation that generates iid distributed returns (you can use the random number generator rnorm()) for some dimensions $$T \times N$$ and compute the minimum-variance portfolio weights based on the sample variance covariance matrix and Ledoit-Wolf shrinkage. What is the mean squared deviation from the optimal portfolio ($$1/N$$)? What can you conclude? Solutions: The assignment mainly requires you to understand the original paper in depth - it is arguably a hard task to translate the derivations in the paper into working code. Below you find some sample code which you can use for future assignments. compute_ledoit_wolf <- function(x) { # Computes Ledoit-Wolf shrinkage covariance estimator # This function generates the Ledoit-Wolf covariance estimator as proposed in Ledoit, Wolf 2004 (Honey, I shrunk the sample covariance matrix.) # X is a (t x n) matrix of returns t <- nrow(x) n <- ncol(x) x <- apply(x, 2, function(x) if (is.numeric(x)) # demean x x - mean(x) else x) sample <- (1/t) * (t(x) %*% x) var <- diag(sample) sqrtvar <- sqrt(var) rBar <- (sum(sum(sample/(sqrtvar %*% t(sqrtvar)))) - n)/(n * (n - 1)) prior <- rBar * sqrtvar %*% t(sqrtvar) diag(prior) <- var y <- x^2 phiMat <- t(y) %*% y/t - 2 * (t(x) %*% x) * sample/t + sample^2 phi <- sum(phiMat) repmat = function(X, m, n) { X <- as.matrix(X) mx = dim(X)[1] nx = dim(X)[2] matrix(t(matrix(X, mx, nx * n)), mx * m, nx * n, byrow = T) } term1 <- (t(x^3) %*% x)/t help <- t(x) %*% x/t helpDiag <- diag(help) term2 <- repmat(helpDiag, 1, n) * sample term3 <- help * repmat(var, 1, n) term4 <- repmat(var, 1, n) * sample thetaMat <- term1 - term2 - term3 + term4 diag(thetaMat) <- 0 rho <- sum(diag(phiMat)) + rBar * sum(sum(((1/sqrtvar) %*% t(sqrtvar)) * thetaMat)) gamma <- sum(diag(t(sample - prior) %*% (sample - prior))) kappa <- (phi - rho)/gamma shrinkage <- max(0, min(1, kappa/t)) if (is.nan(shrinkage)) shrinkage <- 1 sigma <- shrinkage * prior + (1 - shrinkage) * sample return(sigma) } The simulation can be conducted as below. The individual functions simulate iid normal “returns” matrix for given dimensions T and N. Next, optimal weights are computed based on either the variance-covariance matrix or the Ledoit-Wolf shrinkage equivalent. Note: if you want to generate results that can be replicated, make sure to use the function set.seed(). It takes as input any integer and makes sure that whoever runs this code afterwards retrieves exactly the same random numbers within the simulation. Otherwise, (or if you change “2021” to an arbitrary other value) there will be some variation in the results because of the random sampling of returns. set.seed(2022) generate_returns <- function(T, N) matrix(rnorm(T * N), nc = N) compute_w_lw <- function(mat){ w <- solve(compute_ledoit_wolf(mat))%*% rep(1,ncol(mat)) return(w/sum(w)) } compute_w_sample <- function(mat){ w <- solve(cov(mat))%*% rep(1,ncol(mat)) return(w/sum(w)) } eval_weight <- function(w) length(w)^2 * sum((w - 1/length(w))^2) Note that I evaluate weights based on the squared deviations from the naive portfolio (which is the minimum variance portfolio in the case of iid returns). The scaling length(w)^2 is just there to penalize larger dimensions harder. simulation <- function(T = 100, N = 70){ tmp <- matrix(NA, nc = 2, nr = 100) for(i in 1:100){ mat <- generate_returns(T, N) w_lw <- compute_w_lw(mat) if(N < T) w_sample <- compute_w_sample(mat) if(N >= T) w_sample <- rep(NA, N) tmp[i, 1] <- eval_weight(w_lw) tmp[i, 2] <- eval_weight(w_sample) } tibble(model = c("Shrinkage", "Sample"), error = colMeans(tmp), N = N, T = T) } result <- bind_rows(simulation(100, 60), simulation(100, 70), simulation(100, 80), simulation(100, 90), simulation(100, 100), simulation(100, 150)) result %>% pivot_wider(names_from = model, values_from = error) %>% knitr::kable(digits = 2, "pipe") N T Shrinkage Sample 60 100 1.25 85.8 70 100 1.46 163.0 80 100 1.81 344.3 90 100 1.91 862.9 100 100 2.19 NA 150 100 3.19 NA The results show a couple of interesting results: First, the sample variance-covariance matrix breaks down if $$N > T$$ - there is no unique minimum variance portfolio anymore in that case. On the contrary, Ledoit-Wolf like shrinkage retains positive-definiteness of the estimator even if $$N > T$$. Further, the (scaled) mean-squared error of the portfolio weights relative to the theoretically optimal naive portfolio is way smaller for the Shrinkage version. Although the variance-covariance estimator is biased, the variance of the estimator is reduced substantially and thus provides more robust portfolio weights. ## 9.3 Multivariate dynamic volatility modeling This exercise is designed to provide the necessary tools for i) high-dimensional volatility modeling with rmgarch ii) and proper volatility backtesting procedures. In my personal opinion, while being the de-facto standard for high dimensional dynamic volatility estimation, the rmgarch package documentation is next to impossible to deciffer. I took some effort to provide running code for rather standard procedures but if you encounter a more elegant solution, please let me know! First, make sure you install the rmgarch package and familiarize yourself with the documentation. Some code snippets are provided in the paper Boudt et al (2019), available in Absalon. Exercises: • Use the daily Dow Jones 30 index constituents returns as a baseline return time series. Familiarize yourself with the documentation of the rmgarch package for multivariate volatility modeling. In particular, write a short script which estimates a DCC model based on the return time series. • Illustrate the estimated volatilities as well as some of the estimated correlation time series. • Write a script which computes rolling window 1-step ahead forecasts of $$\Sigma_{t+1}$$ based on the DCC GARCH model. For each iteration, store the corresponding minimum variance portfolio weights and the portfolio’s out-of-sample return. Solutions: To get started, I prepare the time series of returns as a $$(T \times N)$$ matrix. #install.packages("rmgarch") library(rmgarch) returns <- returns %>% pivot_wider(names_from = symbol, values_from = ret) returns.xts <- xts(returns %>% select(-date), order.by = returns$date)
N <- ncol(returns.xts)
First rmgarch is the big (multivariate) brother of the rugarch package. Recall that for multivariate models we are often left with specifying the univariate volatility dynamics. rmgarch has a rather intuitive and (in my opinion) way to many options. In fact, rmgarch allows you to specify all kinds of different GARCH model specifications, mean dynamic specifications and also distributional assumptions.
spec <- ugarchspec(variance.model = list(model = 'sGARCH',
garchOrder = c(1, 1)))
Next we replicate the specification for each of our $$N$$ assets. rmgarch has the appealing multispec function for that purpose. In principal it is possible to specify individual dynamics for each asset and to provide a list with different ugarchspec objects. In what follows we simply impose the same structure for each ticker.
# Replicate specification for each univariate asset
mspec <- multispec(replicate(N, spec))
# Specify DCC
mspec_dcc <- dccspec(mspec,
model = "DCC",
distribution = "mvnorm")
mspec_dcc
##
## *------------------------------*
## * DCC GARCH Spec *
## *------------------------------*
## Model : DCC(1,1)
## Estimation : 2-step
## Distribution : mvnorm
## No. Parameters : 582
## No. Series : 29
The function dccspec imposes the multivariate structure. Consult Boudt et al (2019) for many more alternative specifications.
Next we fit the object to the return time series. Note that you can make use of the fact that the computations can be parallelized very easily (however, DCC is fast enough for this dataset so you can also opt out of using a cluster).
# Generate Cluster for parallelization (you may have to change the number of nodes)
cl <- makeCluster(8)
out_of_sample_periods <- 500
fit <- dccfit(mspec_dcc,
out.sample = out_of_sample_periods,
data = returns.xts,
cluster = cl,
fit.control = list(eval.se = FALSE,
stationarity = TRUE))
# Alternative in case you do not want to use parallel computing
# fit <- dccfit(mspec,
# out.sample = 500,
# data = returns,
# solver = c("hybrid", "lbfgs"),
# fit.control = list(eval.se = FALSE,
# stationarity = TRUE))
After considerable computing time the object fit contains all estimated parameters of the DCCGARCH model. The model has 617 parameters. Note that with the additional controls we can enforce stationarity conditions for the estimated parameters and (as we only care about forecasting in this exercise) refrain from estimating standard errors.
Next, I create a plot of all estimated time-series of volatilities. Note that transforming rmgarch output into easy-to-work with tidyverse structures is tedious but possible.
fitted_sigmas <- sigma(fit) %>%
fortify() %>%
as_tibble() %>%
rename(date = Index) %>%
pivot_longer(-date, names_to = "ticker", values_to = "sigma")
fitted_sigmas %>%
ggplot(aes(x = date,
y = sigma,
color = ticker)) +
geom_line() +
labs(x = "", y = "Fitted sigma") +
theme(legend.position = "bottom")
It is even more tedious to get hold of the estimated time series of $$(N\times N)$$ matrices of correlations. The code snippet below is doing the job and provides an easily accessible way to illustrate the dynamic correlation coefficients. The figure below illustrates all correlations with ticker AAPL
fitted_correlations <- apply(rcor(fit), 3, . %>% as_tibble(rownames = "ticker") %>%
pivot_longer(-ticker, names_to = "ticker.2")) %>%
bind_rows(.id = "date") %>%
filter(ticker != ticker.2)
fitted_correlations %>%
filter(ticker.2 == "AAPL") %>%
ggplot(aes(x = as.Date(date),
y = value,
color = ticker)) +
geom_line() +
theme(legend.position = "bottom") + labs(x = "", y = "Fitted correlations", color = NULL)
Next we can use the function dccroll to compute rolling window forecasts. In other words, we recursively reestimate the GARCH model and store the one ahead covariance forecasts (and conditional means if we would have specified a dynamic model). The parallelization makes this process luckily much faster. Note that it is important to stop the cluster after you finished the job, otherwise you may run into connection issues.
dccrolln <- dccroll(mspec_dcc,
data = returns.xts,
forecast.length = 500,
refit.every = 100,
refit.window = "recursive",
fit.control=list(scale=TRUE),
solver.control=list(trace=1),
cluster = cl)
stopCluster(cl)
Final step: minimum variance portfolio weights based on the estimated parameters. Again, this is somewhat cumbersome, maybe there are more efficient ways to do this in R.
pred <- apply(rcov(dccrolln), 3, function(x){
w <- solve(x %>% as.matrix()) %*% rep(1, N)
return(w/sum(w))}) %>%
t()
apply(pred * returns.xts %>% tail(500), 1, sum) %>%
enframe() %>%
summarise(sd = sqrt(250) * sd(value))
## # A tibble: 1 x 1
## sd
## <dbl>
## 1 0.163` | 2022-12-07 22:58:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6216322183609009, "perplexity": 6047.408827153296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711221.94/warc/CC-MAIN-20221207221727-20221208011727-00704.warc.gz"} |
https://web2.0calc.com/questions/indistinguishable-balls-into-distinguishable-boxes | +0
# Indistinguishable balls into distinguishable boxes
0
67
0
+9
How many ways are there to put 2 indistinguishable balls into n distinguishable boxes?
My attempt:
I solved this problem similar way as stars and bars problem. I treated boxes as bars and balls as stars. So there are total $$\binom{n\ -1\ +\ 2}{2} \ =\ \frac{n( n+1)}{2}$$ ways. | 2020-10-21 22:06:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9774448871612549, "perplexity": 1895.7682156330832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107878633.8/warc/CC-MAIN-20201021205955-20201021235955-00467.warc.gz"} |
https://www.physicsforums.com/threads/ac-amplifier-circuit-problems.153472/ | # AC amplifier circuit problems
1. Jan 28, 2007
### esmeco
1. The problem statement, all variables and given/known data
The problem states that we should draw the Vout curve of an amplifier circuit.
2. Relevant equations
We have a sinusoidal sign with amplitude=1v and frequency=0.5
v(t)=A*sin(2pi*f*t)
f=1/T
T=2s
3. The attempt at a solution
Since we have negative feedback: Vp=Vn
The currents for this circuit would be:
I1+I2=Iout
I1=(0-1)/0.5=-2
I2=(0-v1)/1=-v1
Iout=(Vout-0)/2
I know that:
V1=1*sin(2pi*0.5*2)=0
So,the final equation would be: Vout=(-1*2)/0.5=-4v
Does this look ok?Also,when drawing the curve for vout,vout is the amplitude of the curve right?Or is the amplitude of the curve related to vout 1volt?
#### Attached Files:
• ###### ac amplifier.JPG
File size:
25 KB
Views:
77
2. Jan 28, 2007
### esmeco
...
After searching a bit I've found that you can't use v(t)=A*sin(2pi*f*t) or the current will be zero, so,in order to calculate the voltage for the alternate current we would use the formula Vrms=V0/squareroot of 2
and Vrms=Irms*R which would be equal to V0=I0*R
So, the final equation for Vout would be: Vout=(-1-2)*2=-6v which would be the amplitude of the curve of the tension on the output of the amplifier...
I think this's right,but if not I would like to be corrected...
3. Jan 29, 2007
### esmeco
4. Jan 29, 2007
### antonantal
I didn't do the calculations but since you have a DC component in your input signal you should have one in the output, so $$V_{out}$$ can't be a simple sinusoid with an amplitude of 4V.
You better use the superposition principle.
5. Jan 29, 2007
### Staff: Mentor
You need to be more precise in your notation, and remember what voltages are DC and which are functions of time. More like this:
-2 - V1(t) = Vout(t)/2
So Vout(t) = what?
6. Jan 29, 2007
### esmeco
Vout(t)=(-2 -0)/2=-1
IS this right?
7. Jan 29, 2007
### Staff: Mentor
Nope. V1(t) is a sinusoid and there is a DC 1V input component as well, so the output will be a sinusoid with a DC offset....
8. Jan 29, 2007
### esmeco
I thought that v1(t) would be zero since the frequency is 0.5 and the period is 1 and if we substitute the result of v1(t) will be zero..
9. Jan 29, 2007
### antonantal
I think you should get a basic understanding of AC before you try to solve this problem. Maybe read some of your lecture notes.
10. Jan 29, 2007
### Staff: Mentor
Um, no. I'm not following where your confusion is coming from. V1(t) is a sinusoidal source, which is driving the input of the amplifier circuit. You are asked to solve for Vout(t), which is affected by the sinusoidal input V1(t), the DC input offset of 1V, and the gain set by the resistors around the opamp circuit.
You started with the definition of V1(t):
So to clean up the text a bit, that means $$V_1(t) = sin(\frac{2\pi t}{2})$$
Use that value for the V1(t) that is in your equations, and solve for Vout(t). Nothing is going to eliminate that sinusoid from your final answer.
11. Jan 29, 2007
### esmeco
I misunderstood the T in f=1/T with the t in $$V_1(t) = sin(\frac{2\pi t}{2})$$
So then vout(t)= -sin(pi*t) - 1 ...And the amplitude is the amplitude given by 1v?
12. Jan 29, 2007
### Staff: Mentor
Not quite, but you're getting close. Use that V1(t) equation and plug it back into the equation for Vout(t). Be careful about your factors of two.
13. Jan 29, 2007
### esmeco
...
So, v(out)=-4 - 2senpi*t
So,what would be the amplitude of this sinusoidal wave?
14. Jan 29, 2007
### Staff: Mentor
Graph a couple cycles of that function, and you tell me. What is the peak-to-peak AC voltage amplitude, and what is the DC offset voltage?
15. Jan 29, 2007
### esmeco
The peak-to-peak amplitude of the AC voltage is 2 I guess...And the DC offset voltage is 1v I guess...Should we substitute the t in the above expression to determine the amplitude of the output wave?
16. Jan 29, 2007
### Staff: Mentor
Almost correct. The convention is to measure the DC offset to the average (middle) part of the sine wave, which in this case is -4V. Just think of what the voltage would be if the amplitude of the sine wave were 0V, and that's the DC offset part of the output voltage waveform.
So now you've answered the original problem. You've drawn the waveform as you've been asked (be sure to label the time ticks on the horizontal axis correctly, and the voltage ticks on the vertical axis), and you know that the AC amplitude is 2Vpp, and the DC offset is -4Vdc. See, that wasn't so hard, right?
17. Dec 8, 2007
### KaiZX
Bumping this thread up (since my question is related)....
1. The problem:
Suppose we're given an AC coupled inverting amplifier (aka. active high pass), and with a DC source at the positive input to provide offset. The circuit diagram is attached. Input Vs is assumed to be some arbitrary sinusoidal input.
How do I prove that the DC source, Vref, is not amplified at the output with such a configuration?
2. My attempt:
I know that you need to use superposition here, with the DC-decoupled AC signal and the DC offset. So I can find that the transfer function for the AC input is just the gain for an inverting amplifier.
But for the DC offset, I assumed this circuit to be a DC amplifier with Vin = 0, then I did this...
(0 - Vref) / R1 = I1
(Vout - Vref) / R2 = I2
I1 = I2
Therefore, Vout = Vref * (1/R2 - 1/R1)
But from lab, I know that Vref shouldn't be have a gain. In other words, the output should just be a sinusoidal waveform with a DC offset = Vref.
Where's my mistake?
#### Attached Files:
• ###### circuit.JPG
File size:
5.4 KB
Views:
44
Last edited: Dec 8, 2007
18. Dec 10, 2007
### Staff: Mentor
For DC, the capacitor is an open circuit, and so R1 goes away as well. What is left?
19. Dec 11, 2007
### KaiZX
Ah, so it's almost like a voltage follower left over for DC, then superimposed that with AC gain.
Ok, thank you. | 2017-11-19 00:20:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5400133728981018, "perplexity": 2163.220262858123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805114.42/warc/CC-MAIN-20171118225302-20171119005302-00752.warc.gz"} |
http://photutils.readthedocs.io/en/latest/api/photutils.psf.IntegratedGaussianPRF.html | # IntegratedGaussianPRF¶
class photutils.psf.IntegratedGaussianPRF[source]
Circular Gaussian model integrated over pixels. Because it is integrated, this model is considered a PRF, not a PSF (see Terminology for more about the terminology used here.)
This model is a Gaussian integrated over an area of 1 (in units of the model input coordinates, e.g. 1 pixel). This is in contrast to the apparently similar astropy.modeling.functional_models.Gaussian2D, which is the value of a 2D Gaussian at the input coordinates, with no integration. So this model is equivalent to assuming the PSF is Gaussian at a sub-pixel level.
Parameters: sigma : float Width of the Gaussian PSF. flux : float (default 1) Total integrated flux over the entire PSF x_0 : float (default 0) Position of the peak in x direction. y_0 : float (default 0) Position of the peak in y direction.
Notes
This model is evaluated according to the following formula:
$f(x, y) = \frac{F}{4} \left[ {\rm erf} \left(\frac{x - x_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{x - x_0 - 0.5} {\sqrt{2} \sigma} \right) \right] \left[ {\rm erf} \left(\frac{y - y_0 + 0.5} {\sqrt{2} \sigma} \right) - {\rm erf} \left(\frac{y - y_0 - 0.5} {\sqrt{2} \sigma} \right) \right]$
where erf denotes the error function and F the total integrated flux.
Attributes Summary
Methods Summary
evaluate(x, y, flux, x_0, y_0, sigma) Model function Gaussian PSF model.
Attributes Documentation
fit_deriv = None
flux
param_names = ('flux', 'x_0', 'y_0', 'sigma')
sigma
x_0
y_0
Methods Documentation
evaluate(x, y, flux, x_0, y_0, sigma)[source]
Model function Gaussian PSF model. | 2017-07-21 06:31:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6589028835296631, "perplexity": 2586.2273252715354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549423723.8/warc/CC-MAIN-20170721062230-20170721082230-00597.warc.gz"} |
https://meta.mathoverflow.net/questions/4942/remove-tagslick-proof-or-make-it-a-synonym-of-tagalternative-proof | # Remove [tag:slick-proof] or make it a synonym of [tag:alternative-proof]
@YCor made a suggestion in an answer to another post (What is the intended use of the (proofs) tag?) a bit over a year ago. It received several upvotes, but does not appear to have been acted upon. I thought it might receive more attention here:
It's not exactly about the original question, but now has been duly removed. There are still the tags and (47 and 17 questions respectively at this date 2020/Feb/06). While in practice they have close meanings, the second one is unpleasantly non-neutral, and I'd like it to be removed, practically making it a synonym of would sound fine. Or manually (I'll understand upvotes/downvotes of this answer as for/against replacement of with ).
I tried proposing the tag synonym myself, but I do not have sufficient reputation.
• An interesting thing about post titles: it appears possible to use [tag:xxx] in the title when creating a post, but not when editing it. I tried to edit meta.mathoverflow.net/questions/4927/… accordingly, and was scolded by the software. Mar 27, 2021 at 17:19
• A related discussion in chat: About (slick-proof) and (alternative-proof). Mar 27, 2021 at 18:01
• Merged. All options here are "meta tags". Ideally, these would not exist at all. Can you imagine a MO user who is systematically interested in all alternative or all slick proofs? I can't but in this case, I can imagine a MO user doing a one-time systematic search for alternative proofs but the tag alone will not fully capture all cases and the user should probably use another kind of filtering. In any case, that's enough for not deleting entirely. Mar 27, 2021 at 20:22
• @FrançoisG.Dorais, could you post that as an answer so I can accept it? Mar 27, 2021 at 22:41
• Also, @FrançoisG.Dorais, since you have the capacity to make such actions yourself, would it be possible for you to approve the synonym characteristic-ppositive-characteristic, as in meta.mathoverflow.net/questions/4927/…? Mar 27, 2021 at 23:56
• I like the slick proofs tag... I and my grad student and postdoc friends enjoy looking at slick proofs outside our areas of concentration. Maybe not literally every one, but generally I like looking at cool tricks I can just learn. Mar 29, 2021 at 18:10
• I think that everybody (well, every mathematician) likes looking at slick proofs, but MO is not the place for collecting all things (not even all mathematical things) that are pleasant to look at; SE in general shies away from 'bloggy' content (although MO is different from SE generally in many ways, including this way sometimes). Also, not to be too crude, I'm much more interested in the community's judgement of which proofs are slick than in any individual question-poser's judgement. Mar 29, 2021 at 20:04 | 2022-05-24 22:42:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4394241273403168, "perplexity": 1448.6014228666968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662577259.70/warc/CC-MAIN-20220524203438-20220524233438-00497.warc.gz"} |
https://www.particlebites.com/?p=4215 | # Horton Hears a Sterile Neutrino?
Article: Limits on Active to Sterile Neutrino Oscillations from Disappearance Searches in the MINOS, Daya Bay, and Bugey-3 Experiments
Authors: Daya Bay and MINOS collaborations
Reference: arXiv:1607.01177v4
So far, the hunt for sterile neutrinos has come up empty. Could a joint analysis between MINOS, Daya Bay and Bugey-3 data hint at their existence?
Neutrinos, like the beloved Whos in Dr. Seuss’ “Horton Hears a Who!,” are light and elusive, yet have a large impact on the universe we live in. While neutrinos only interact with matter through the weak nuclear force and gravity, they played a critical role in the formation of the early universe. Neutrino physics is now an exciting line of research pursued by the Hortons of particle physics, cosmology, and astrophysics alike. While most of what we currently know about neutrinos is well described by a three-flavor neutrino model, a few inconsistent experimental results such as those from the Liquid Scintillator Neutrino Detector (LSND) and the Mini Booster Neutrino Experiment (MiniBooNE) hint at the presence of a new kind of neutrino that only interacts with matter through gravity. If this “sterile” kind of neutrino does in fact exist, it might also have played an important role in the evolution of our universe.
The three known neutrinos come in three flavors: electron, muon, or tau. The discovery of neutrino oscillation by the Sudbury Neutrino Observatory and the Super-Kamiokande Observatory, which won the 2015 Nobel Prize, proved that one flavor of neutrino can transform into another. This led to the realization that each neutrino mass state is a superposition of the three different neutrino flavor states. From neutrino oscillation measurements, most of the parameters that define the mixing between neutrino states are well known for the three standard neutrinos.
The relationship between the three known neutrino flavor states and mass states is usually expressed as a 3×3 matrix known as the PMNS matrix, for Bruno Pontecorvo, Ziro Maki, Masami Nakagawa and Shoichi Sakata. The PMNS matrix includes three mixing angles, the values of which determine “how much” of each neutrino flavor state is in each mass state. The distance required for one neutrino flavor to become another, the neutrino oscillation wavelength, is determined by the difference between the squared masses of the two mass states. The values of mass splittings $m_2^2-m_1^2$ and $m_3^2-m_2^2$ are known to good precision.
A fourth flavor? Adding a sterile neutrino to the mix
A “sterile” neutrino is referred to as such because it would not interact weakly: it would only interact through the gravitational force. Neutrino oscillations involving the hypothetical sterile neutrino can be understood using a “four-flavor model,” which introduces a fourth neutrino mass state, $m_4$, heavier than the three known “active” mass states. This fourth neutrino state would be mostly sterile, with only a small contribution from a mixture of the three known neutrino flavors. If the sterile neutrino exists, it should be possible to experimentally observe neutrino oscillations with a wavelength set by the difference between $m_4^2$ and the square of the mass of another known neutrino mass state. Current observations suggest a squared mass difference in the range of 0.1-10 eV$^2$.
Oscillations between active and sterile states would result in the disappearance of muon (anti)neutrinos and electron (anti)neutrinos. In a disappearance experiment, you know how many neutrinos of a specific type you produce, and you count the number of that type of neutrino a distance away, and find that some of the neutrinos have “disappeared,” or in other words, oscillated into a different type of neutrino that you are not detecting.
A joint analysis by the MINOS and Daya Bay collaborations
The MINOS and Daya Bay collaborations have conducted a joint analysis to combine independent measurements of muon (anti)neutrino disappearance by MINOS and electron antineutrino disappearance by Daya Bay and Bugey-3. Here’s a breakdown of the involved experiments:
• MINOS, the Main Injector Neutrino Oscillation Search: A long-baseline neutrino experiment with detectors at Fermilab and northern Minnesota that use an accelerator at Fermilab as the neutrino source
• The Daya Bay Reactor Neutrino Experiment: Uses antineutrinos produced by the reactors of China’s Daya Bay Nuclear Power Plant and the Ling Ao Nuclear Power Plant
• The Bugey-3 experiment: Performed in the early 1990s, used antineutrinos from the Bugey Nuclear Power Plant in France for its neutrino oscillation observations
Assuming a four-flavor model, the MINOS and Daya Bay collaborations put new constraints on the value of the mixing angle $\theta_{\mu e}$, the parameter controlling electron (anti)neutrino appearance in experiments with short neutrino travel distances. As for the hypothetical sterile neutrino? The analysis excluded the parameter space allowed by the LSND and MiniBooNE appearance-based indications for the existence of light sterile neutrinos for $\Delta m_{41}^2$ < 0.8 eV$^2$ at a 95% confidence level. In other words, the MINOS and Daya Bay analysis essentially rules out the LSND and MiniBooNE inconsistencies that allowed for the presence of a sterile neutrino in the first place. These results illustrate just how at odds disappearance searches and appearance searches are when it comes to providing insight into the existence of light sterile neutrinos. If the Whos exist, they will need to be a little louder in order for the world to hear them. | 2022-06-29 15:18:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8208971619606018, "perplexity": 1193.685778243626}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103640328.37/warc/CC-MAIN-20220629150145-20220629180145-00768.warc.gz"} |
https://solvedlib.com/which-shows-domestic-supply-and-demand-if-p1-is,301685 | # Which shows domestic supply and demand. If P1 is equal to P2 (the world price) plus...
###### Question:
which shows domestic supply and demand. If P1 is equal to P2 (the world price) plus a tariff, then government revenue from the tariff is equal to: A) a + c B) b C) P1 ( Q3 - Q2) D) P2 [(Q2 - Q1) + (Q4 - Q3)] E) a + b + c
Price Q1 Q2 Q3 Qs Quantity
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http://jonismathnotes.blogspot.com/2014/08/irreducibility-of-polynomials.html | Sunday, August 17, 2014
Irreducibility of polynomials
In many contexts, it is important to know whether a polynomial is irreducible. In algebraic number theory, the properties of an algebraic number $\alpha$ are determined by its minimal polynomial, the irreducible monic polynomial of least degree having $\alpha$ as a root. In Galois theory, it is important to know whether a field extension arises from an irreducible polynomial. In algebraic geometry, one is interested in varieties arising from the zero set of a set of multivariate polynomials, and if some of the polynomials are reducible, the variety can be represented in simpler terms. There are many more examples as well.
By the fundamental theorem of algebra, polynomials with complex coefficients always factor into linear factors in $\mathbb{C}[x].$ From this it follows that real polynomials factor into at most quadratic factors in $\mathbb{R}[x]$. However, in $\mathbb{Q}[x]$ and $\mathbb{Z}[x]$, irreducibility is much more interesting. By Gauss' lemma, irreducibility in both of them is the same thing, so we consider only $\mathbb{Z}[x]$ (every polynomial in $\mathbb{Q}[x]$ becomes a polynomial with integer coefficients when multiplied by a suitable integer).
In what follows, by polynomials we mean polynomials with integer coefficients in one variable and irreducibility is considered in $\mathbb{Z}[x]$, unless otherwise noted. In this post, we present a few methods to determine whether a polynomial is irreducible. For some reason, it seems that the Eisenstein criterion is almost the only irreducibility criterion that is truly well-known, even though it fails for many polynomials.
Polynomials producing too many small values
Let $f$ be a polynomial with integer coefficients having no integer zeros (so that there is a chance that $f$ is irreducible). Assume that $f(x)=g(x)h(x)$, where $g$ and $h$ are nonconstant polynomials. Then $|f(x)|$ can be smaller than a bound $M$, only when both $|g(x)|$ and $|h(x)|$ are smaller than $M$, and still there is no guarantee that $|f(x)|<M$. Therefore, intuition tells that if $f$ is small in too ''many'' integer points, it must be irreducible (unless it has integer roots). The definitions of ''small'' and ''many'' should of course depend at least on $\deg f$. This intuition can be formulated as several theorems. Natural examples of polynomials that are often small are $(x-a_1)...(x-a_n)\pm 1$, where $a_i$ are distinct integers; these polynomials are equal to $1$ or $-1$ in $n$ points. We start by showing that these are irreducible except in a few small cases.
Theorem 1. Let $a_1,...,a_n$ be distinct integers. Then the polynomials
$f_1(x)=(x-a_1)...(x-a_n)-1$
and
$f_2(x)=(x-a_1)...(x-a_n)+1$
are irreducible in $\mathbb{Z}[x]$, except $f_2$ is reducible if $n=2$ and $|a_1-a_2|=1$.
Proof. Suppose that $(x-a_1)...(x-a_n)\pm 1=g(x)h(x)$, where $g$ and $h$ are nonconstant. Without loss of generality, let $\deg g \leq \deg h$. We must have $g(a_i)=\pm 1$ for all $i=1,2,...,n$. We can say that $g(a_i)=1$ for $i\leq k$ and $g(a_i)=-1$ for $i>k$. We have $k<n$ as $\deg g<n.$ However, at least one of the equations $g(x)=\pm 1$ has no more than three solutions. To see this, suppose for example that $g(a_i)=1$ for $i\leq 4$. Then $g(x)=(x-a_1)(x-a_2)(x-a_3)(x-a_4)Q(x)+1$, and if this were equal to $-1$, we would obtain
$(x-a_1)(x-a_2)(x-a_3)(x-a_4)Q(x)=-2.$
The integers $x-a_i$ are ditinct, so this is a representation of $-2$ as a product of integers, at least four of which are distinct; this is absurd. Hence one of the equations $g(x)=\pm 1$ has at least $n-3$ solutions. The number of solutions is bounded by $\deg g$, so $n-3\leq \frac{n}{2}$, which implies $n\leq 6$.
Next assume $n=5$ or $n=6$. Then at least one of the equations $g(x)=\pm 1$ has at least three solutions. The other equation has at least two solutions as well; otherwise one of them has at least four solutions, and by the previous argument this means that one of the equations $g(x)=\pm 1$ has no solution $x=a_i$, a contradiction. Without loss of generality, write $g(x)=(x-a_1)(x-a_2)(x-a_3)Q(x)+1$. The equation $g(x)=-1$ must also have some integer solution, but then
$(x-a_1)(x-a_2)(x-a_3)Q(x)=-2.$
If we impose the ordering $a_1<a_2<a_3$, this happens only when $x-a_1=-1,x-a_2=1,x-a_3=2$. Therefore, the solution is unique, but there were supposed to be two of them; a contradiction.
The case $n=1$ is trivial, so we are left with the cases $n=2,3,4$. If $n=3$, then the polynomial $(x-a_1)(x-a_2)(x-a_3)\pm 1$ must have an integer root in order to be reducible, but this is impossible as $\pm 1$ is not the product of three distinct integers. If $n=2$, again $(x-a_1)(x-a_2)-1$ should have an integer root, but then $1$ is a product of two distinct integers, a contradiction. In the case of the polynomial $(x-a_1)(x-a_2)+1$, an integer root can occur, but only when $x-a_1=-1$, $x-a_2=1$ assuming $a_1<a_2$. Therefore $a_1=a_2+1$, and this was the exceptional case.
Finally, let $n=4$. By the argument for $n=3$, there cannot be linear factors, so $\deg g=2$ and we may assume $g(a_1)=g(a_2)=1, g(a_3)=g(a_4)=-1$ (but then we can no longer suppose an order for $a_i$). As $g$ is monic, we have $g(x)=(x-a_1)(x-a_2)+1$, and now
$(a_3-a_1)(a_3-a_2)=-2, \quad (a_4-a_1)(a_4-a_2)=-2.$
The $a_i$ are distinct, so $|a_i-a_j|\geq 4$ for some $i$ and $j$. By the equalities above, the only possibilities are $|a_2-a_1|\geq 4$ and $|a_4-a_3|\geq 4$. One of the numbers $|a_4-a_1|,|a_2-a_4|$ is $1$ and the other one is $2$, so by the triangle inequality $|a_2-a_1|\leq 1+2=3$, so the second case $|a_4-a_3|\geq 4$ must hold. The equalities above now have the form $AB=-2,(A+m)(B+m)=-2$, where $m=|a_4-a_3|\geq 4$. This implies $m(A+B)+m^2=0$, that is $A+B=-m$, but this cannot hold since one of $|A|,|B|$ is $1$ and the other one is $2$. ■
In the above proof, the usefullness of the abundance of small values taken by $f_1$ and $f_2$ is clearly visible, and as soon as $n$ is small (that is, there are ''not enough many'' points at whch $f_1$ or $f_2$ is small), the proof becomes a rather tedious case check. Pólya was able to define a notion of smallness for any polynomial such that small polynomials are irreducible. We follow Pólya's original paper Verschiedene Bemerkungen zur Zahlentheorie.
Theorem 2. Let $f$ be a polynomial of degree $n$ with integer coefficients. Let $m= \left\lfloor\frac{n+1}{2}\right\rfloor$. If there exist distinct integers $a_1,...,a_n$ with $0<|f(a_i)|<\frac{m!}{2^m}$ for all $i$, then $f$ is irreducible.
The proof is rather ingenious but elementary. The seemingly strange bound $\frac{m!}{2^m}$ actually arises naturally from the proof. We first need a lemma.
Lemma 3. Let $g(x)$ be a nonconstant real polynomial of degree $n$. If there exist $n+1$ distinct integers $b_0,...,b_{n}$ such that $|g(b_i)|<\frac{n!}{2^n}$ for all $i$, then $g(x)\not \in \mathbb{Z}[x].$
Proof. Let $g(b_i)=c_i$ for $i=0,...,n$. We may write $g$ in terms of these values using the Lagrange interpolation polynomial:
$g(x)=\sum_{k=0}^{n}c_i\frac{\prod_{i\neq k}(x-b_i)}{\prod_{i\neq k}(b_k-b_i)}.$
The leading coefficient of $g$ is
$a=\sum_{k=0}^{n}c_i\frac{1}{\prod_{i\neq k}(b_k-b_i)}.$
The numbers $\prod_{i\neq k}(b_k-b_i)$ are $n+1$ nonzero products of $n$ integers. As they are distinct, the largest one of them is at least $n!$ (since one of them has a number with absolute value at least $n$ as a term), the second largest is at least $1\cdot (n-1)!$, the third largest is at least $2(n-2)!$, and generally the $r$th largest is at least $r!(n-r)!$ since one of the terms in the product has absolute value at least $\max\{r,n-r\}$. Thus, by the assumption on the sizes of $c_i$, the leading coefficient of $g$ is bounded by
$|a|<\sum_{r=0}^{n}\frac{1}{2^n}\frac{n!}{r!(n-r)!}=\frac{1}{2^n}\sum_{r=0}^n \binom{n}{r}=1,$
so $g(x)\not \in \mathbb{Z}[x]$. ■
Proof of Theorem 2. Suppose $f$ is as in the theorem and that $f(x)=g(x)h(x)$ where $g$ and $h$ are nonconstant. Without loss of generality, let $\deg g\geq \deg h$. Then $\deg g\geq m=\left\lfloor\frac{n+1}{2}\right\rfloor.$ Since $0<|f(a_i)|<\frac{m!}{2^m}$ for all $i=1,...,n$, also $|g(a_i)|<\frac{m!}{2^m}$ for all $i=1,...,\deg g$. This means that the condition of the previous lemma is fulfilled, so $g(x)\not \in \mathbb{Z}[x]$, which is a contradiction. ■
As an application of Pólya's irreducibility criterion, consider the polynomials $a(x-a_1)...(x-a_n)+b$ where $a,b,a_i$ are integers and $a_i$ are pairwise distinct. By the criterion, this polynomial is irreducible whenever $|b|<\frac{m!}{2^m},$ where $m$ is as before. Since $m!\geq m^me^{-m}$, this holds if $|b|<\left(\frac{n}{2e}\right)^{\frac{n}{2}}$, which is a rather large range. Theorem 1 is also implied by Pólya's criterion for $n>6$.
Polynomials producing many or large primes
Next we consider another general principle for testing irreducibility. The principle simply states that if $f$ is a polynomial with integer coefficients that produces ''many'' primes (compared to the degree), then $f$ is irreducible. Similarly, if $f$ produces a ''large'' prime (in terms of its coefficients), $f$ is irreducible. We denote by $P(f)$ the number of distinct integers $x$ such that $f(x)$ is a prime or the negative of a prime. Then we have
Theorem 4. Let $f$ be a polynomial with integer coefficients of degree $n$. If $P(f)>n+4$, then $f$ is irreducible. On the other hand, for every $n>1$ there exists a reducible polynomial $f$ of degree $n$ with $P(f)\geq n$.
Proof. Assume $f(x)=g(x)h(x)$ where $g$ and $h$ are nonconstant. Let $a_1,a_2,...,a_{n+5}$ be such that $|f(a_i)|$ is prime. We may assume that $g(a_i)=\pm 1$ for $i\leq k$ and $h(a_i)=\pm 1$ for $k<i\leq n+5$.
An integer polynomial $Q$ of degree $d$ can have the values $\pm 1$ in at most $d+2$ points. Indeed, arguments in the proof of Theorem 1 have shown that if one of the equations $Q(x)=\pm 1$ has at least three solutions, then the other equation has no solutions. This means that either only one of the equations $Q(x)=\pm 1$ has solutions, in which case they have at most $d$ solutions in total, or both have, in which case one of them has at most $2$ and the other has at most $d$, giving the bound $d+2$.
Now we deduce $k\leq \deg g+2$ and $n+5-k\leq \deg h+2$, as $g(x)=\pm 1$ holds in $k$ points and $h(x)=\pm 1$ holds in $n-k$ points. Summing the inequalities, we get $n+5\leq \deg g +\deg h+4=n+4$, which is the desired contradiction.
We are left with proving that $P(f)\geq n$ for some reducible polynomial of degree $n$. We choose $f(x)=xh(x)$, where $h(x)=k(x-p_1)...(x-p_{n-1})+1$ with $p_1,...,p_{n-1}$ being distinct primes and $k$ being a suitable nonzero integer. We clearly have $f(p_i)=p_i$ for $i=1,2,...,n-1$. In addition, we choose $k$ in such a way that $k(1-p_1)...(1-p_{n-1})+1$ is prime (this is possible by Dirichlet's theorem, and we only need the special case that was proved using cyclotomic polynomials in this post). Then also $f(1)$ is prime, and we are done. ■
The result in Theorem 4 can be improved; it was proved by O. Ore in 1934 that $P(f)\geq n+3$ implies that $f$ is irreducible. The proof is still elementary but longer. It has been conjectured by Y. G. Chen, G. Kun, G. Pete, I. Z. Ruzsa and A. Timar that for any $n$ there is a reducible polynomial $f$ with $P(f)=n+2$, so Ore's criterion cannot be improved according to the conjecture.
Theorem 4 above can actually be used to prove the irreducibility of any irreducible polynomial in finite time if we assume the famous Bunyakovski's conjecture.
Conjecture (Bunyakovski). Let $f$ be an irreducible integer polynomial with positive leading coefficient such that there is no fixed prime dividing all the numbers $f(1),f(2),...$. Then $f(x)$ generates infinitely many primes as $x$ ranges through the positive integers.
In other words, the conjecture says that any polynomial that could potentially produce infinitely many primes does so. Testing whether $f(1),f(2),...$ have a fixed prime divisor is easy; for example, compute the gcd of $f(1)$ and $f(2)$, and if $d$ is this gcd, check whether any prime divisor of $d$ is a fixed divisor using modular arithmetic. Assuming the conjecture, we can prove the irreducibility of any irreducible polynomial $f$ of degree $n$ by computing $\tilde{f}(1),\tilde{f}(2),...$ ($\tilde{f}$ is $f$ divided by the greatest fixed divsor of $f(1),f(2),...$) until $n+5$ primes have been found in this list. Bunyakovski's conjecture tells that $n+5$ primes will eventually be found if $f$ is irreducible. In practice however, these prime values may be enormous and the theorems above do not tell how soon $n+5$ primes will be found. Also this test never proves the reducibility of a polynomial in finite time, but certainly the easiest way to do that is to determine a nontrivial factor for the polynomial.
There are also other ways to prove irreducibility with the help of primes. The following theorem is a beautiful way to construct irreducible polynomials.
Theorem 5. Let $p$ be a prime number and $b\geq 2$. Let $p=a_nb^n+...+a_1b+a_0$, $a_n\geq 1,a_{n-1}\geq 0, |a_i|\leq b-1$. Then the polynomial $a_nx^n+...+a_1x+a_0$ is irreducible.
For $b=10$, the theorem is due to A. Cohen (with nonnegative $a_i$), and J. Brillhart, M. Filaseta and A. Odlyzko proved the general case. The following simplified proof is due to M. Ram Murty. We will prove the cases $b>2$ as $b=2$ is more technical. We need a lemma on the location of zeros of an integer polynomial in the complex plane. In the end, it wíll be clear how this lemma helps in proving the theorem.
Lemma 6 (M. Ram Murty). Let $f(x)=a_nx^n+...+a_0$ be an integer polynomial with $a_n\neq 1, a_{n-1}\geq 0$ and $|a_i|\leq M$ for all $i$. Then if $\alpha$ is a zero of $f$, we have $\Re(\alpha)\leq 0$ or $|\alpha|<\frac{1+\sqrt{1+4M}}{2}$.
Proof. If $|\alpha|\leq 1$, then $|\alpha|<\frac{1+\sqrt{1+4M}}{2}$ holds automatically. If $a_{n-1}=0$, then
$\begin{eqnarray}|f(x)|&=&|a_nx^n+a_{n-2}x^{n-2}+...+a_0|\geq |x|^n-M(1+|x|+...+|x|^{n-2})\\&>&|x|^n-\frac{|x|^{n-1}}{|x|-1}>0\end{eqnarray}$
when $|x|\geq \frac{M}{|x|-1}$, and this is equivalent to $|x|\geq \frac{1+\sqrt{1+4M}}{2}$. If $a_{n-1}\geq 1$, then
$\begin{eqnarray}|f(x)|&\geq& |a_nx^n+a_{n-1}x^{n-1}|-|a_{n-2}x^{n-2}+...+a_0|\\&>& |x|^n\Re(a_n+\frac{a_{n-1}}{x})-M\frac{|x|^{n-1}}{|x|-1}.\end{eqnarray}$
When $Re(x)\geq 0$, also $\Re(x^{-1})\geq 0$ and
$\begin{eqnarray}|f(x)|&>&|x|^n(1+\frac{1}{|x|})-M\frac{|x|^{n-1}}{|x|-1}\geq 0\end{eqnarray}$
if $(1+\frac{1}{|x|})\geq M\frac{1}{|x|(|x|-1)}$, which holds if $1\geq \frac{M}{|x|(|x|-1)}$. This latter condition is equivalent to $|x|\geq \frac{1+\sqrt{1+4M}}{2}$, so we are done.
Proof of Theorem 5. Let $p$ be a prime, $b\geq 3$, $p=a_nb^n+...+a_0$, and let $f(x)=a_nx^n+...+a_0$, . Let $\alpha_1,...,\alpha_n$ be the complex roots of $f$, and suppose $f(x)=g(x)h(x)$ where $g$ and $h$ are nonconstant and $g$ is monic. Since $f(b)=p$, either $g(b)=\pm 1$ or $h(b)=\pm 1$. We may assume $g(b)=\pm 1$. Let $\alpha_1,...,\alpha_k$ be the complex roots of $g$. Now
$g(b)=\prod_{j=1}^k(b-\alpha_j).$
If $\Re(\alpha_j)\leq 0$, then $|b-\alpha_j|\geq b>1$. Otherwise, Lemma 6 with $M=b-1$ tells that $|\alpha_j|< \frac{1+\sqrt{4b-3}}{2}$, and this expression is at most $b-1$ for $b\geq 3$. Therefore, $|b-\alpha_j|>1$ in any case, so $|g(b)|>1$, which is a contradiction. ■
Theorem 5 also gives a method that will prove any irreducible polynomial to be irreducible in finite time, assuming Bunyakovski's conjecture. Indeed, let $f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0$, where we may assume $a_n>0$. We consider the polynomial $f_1(x)=Nf(x-\frac{a_n}{n})$, where $N$ is chosen so that the polynomial has integer coefficients. Clearly $f_1$ is irreducible iff $f$ is. The second highest coefficient of this polynomial is $0$. By dividing out the greatest common divisor of $f_1(1),f_1(2),...$, we get a polynomial $f_2$. If its coefficients are bounded by $M$, we compute $f(M+1),f(M+2),...$ until we find a prime. Bunyakovski's conjecture guarantees that a prime will be found, and Theorem 5 tells that this prime proves the irreducibility of $f$. However, again we have no bound on the size of this prime.
Irreducible polynomials in finite fields
An polynomial $f(x)\in \mathbb{Z}_p[x]$ is said to be irreducible $\pmod p$, where $p$ is a prime, if there is no representation $f(x)= g(x)h(x)$ with $g(x),h(x)\in \mathbb{Z}_p[[x]$. If $P$ and $Q$ are polynomials in $\mathbb{Z}_p[x]$, the equality $P=Q$ means that all the coefficients of $P$ and $Q$ agree $\pmod p$. The assumption that $p$ is a prime makes factoring polynomials unique in $\mathbb{Z}_p[x]$. It is good to remember that in $\mathbb{Z}_p[x]$ polynomials with the same values are not necessarily equal; for instance $x$ is irreducible in $\mathbb{Z}_p[x]$ although $x\equiv x\cdot x^{p-1}\pmod p$ for every $x\in \mathbb{Z}$ because the coefficients of degree $p$ are different for these polynomials $\pmod p$. Irreducibility $\pmod p$ can always be checked in finite time (If $f(x)\in \mathbb{Z}_p[x]$ is not irreducible, it is divisible by some polynomial in $\mathbb{Z}_p[x]$ with degree less than $\deg f$, and there are $p^{\deg f}$ such polynomials. There are of course more efficient methods, as we will see). Moreover, if $f$ is monic and reducible in $\mathbb{Z}[x]$, then it must be reducible in every $\mathbb{Z}_p[x]$, which is why reduction $\pmod p$ can be very helpful in proving irreducibility in $\mathbb{Z}[x]$.
Example. We show that $x^5+11x^2+15$ is irreducible in $\mathbb{Z}[x]$. Notice that in $\mathbb{Z}_2[x]$ this polynomial becomes $x^5+x^2+1$, so it suffices to show that this is irreducible. If it was not irreducible, it would have a linear or quadratic irreducible factor. It has no linear factor since it has no root $\pmod 2$; its values are always $1\pmod 2$. The only irreducible polynomial of degree $2$ in $\mathbb{Z}_2[x]$ is $x^2+x+1$. To see this, notice that there are $4$ polynomials of degree $2$, and those whose constant coefficient is $0$ are automatically reducible. Hence there are two possible irreducible polynomials, $x^2+1$ and $x^2+x+1$. We have $x^2+1=(x+1)^2$ in $\mathbb{Z}_2[x]$, while $x^2+x+1$ is divisible by neither $x$ nor $x+1$. We have $x^2+x+1\nmid x^5+x^2+1$ in $\mathbb{Z}_2[x]$ since $x^5+x^2+1=(x^2+x+1)(x^3+x^2)+1$ in $\mathbb{Z}_2[x]$.
The example above illustrates well how easy it is to prove irreducibility in $\mathbb{Z}_p[x]$ ; the example above shows that for a polynomial in $\mathbb{Z}_2[x]$ of degree at most $5$ it is enough to check if it has a root $\pmod 2$ or if it is divisible by $x^2+x+1$. Reduction $\pmod p$ also gives the well-known Eisenstein's irreducibility criterion.
Theorem 7 (Eisenstein). Let $f(x)=a_nx^n+...+a_1x+a_0$ be an integer polynomial. Assume that there is a prime $p$ such that $p\mid a_i$ for $i<n$, $p\nmid a_n$ and $p^2\nmid a_0$. Then $f$ is irreducible in $\mathbb{Z}[x].$
Proof. Assume $f(x)=g(x)h(x)$. Then in $\mathbb{Z}_p[x]$ we have $a_nx^n=\tilde{g}(x)\tilde{h}(x)$, where $\tilde{g},\tilde{h}$ are $g$ and $h$ with coefficients reduced $\pmod p$. By unique factorization in $\mathbb{Z}_p[x]$, we deduce $\tilde{g}(x)=bx^m, \tilde{h}(x)=cx^{n-m}$ for some $b,c,m$. In particular, $g(0)\equiv h(0)\equiv 0\pmod p$. However, then $p^2\mid a_0$, contrary to the assumption. ■
When Eisenstein's criterion works, it gives a simple way to prove irreducibility. For example, we applied in this post to the polynomials $\frac{x^p-1}{x-1}$ where $p$ is prime. In many cases, Eisenstein's criterion does not apply to $f(x)$ but to $f(x+a)$ instead for some $a$. However, there are many polynomials for which Eisenstein's criterion fails for all $a$ ad $p$. For example, the polynomial $x^4+8$ is irreducible in $\mathbb{Z}[x]$ as it has no linear factors or factors of the form $x^2+ax\pm 1$ or $x^2+ax\pm 2$, but $f(x+a)=x^4+4ax^3+6a^2x^2+4a^3x+a^4+8$, and the only prime that can divide both $a^4+8$ and $4a^3$ is $2$, but then $2\mid a$ and $2^2\mid a^4+8$, so Eisenstein's criterion does not work.
It may also be that $f(x)$ is irreducible in $\mathbb{Z}[x]$ but reducible in every $\mathbb{Z}_p[x]$. For example, if $f(x)=x^4+1$, then $f(x)=(x^2+1)^2$ in $\mathbb{Z}_2[x]$, and if $p$ is an odd prime, one of $-1,2$ and $-2$ is a quadratic redsidue $\pmod p$ (since $-1$ is a qudratic resdiue when $p\equiv 1 \pmod 4$, $2$ is a quadratic residue when $p\equiv \pm 1 \pmod 8$ and $-2$ is a quadratic residue when $p\equiv 1, 3\pmod p$). If $-1\equiv a^2\pmod p$, then $x^4+1=(x^2+a)(x^2-a)$ in $\mathbb{Z}_p[x]$. If $2\equiv a^2\pmod p$, then $x^4+x+1=(x^2+ax+1)(x^2-ax+1)$ in $\mathbb{Z}_p[x]$. If $-2\equiv a^2\pmod p$, then $x^4+1=(x^2+ax-1)(x^2-ax-1)$ in $\mathbb{Z}_p[x]$. In conclusion, $f$ is always reducible in $\mathbb{Z}_p[x]$.
Irreducibility of special polynomials
Of course, there are numerous principles in addition to the ones discussed above that can be used to prove irreducibility. To illustrate this, we prove that certain special classes of polynomials are irreducible.
Theorem 8. Let $p$ be a prime and $f(x)=a_nx^n+...+a_1x+p$ and integer polynomial with $p>|a_1|+...+|a_n|.$ Then $f$ is irreducible in $\mathbb{Z}[x]$.
Proof. Assume $f(x)=g(x)h(x)$ where $g$ and $h$ are nonconstant. Then $g(0)h(0)=p$, so without loss of generality $|g(0)|=1$. This means that the product of the complex roots of $g$ is $\pm 1$. In particular, $g(\alpha)=0$ for some $\alpha$ with $|\alpha|\leq 1$. However, by the triangle inequality, $|f(\alpha)|\geq p-|a_1|-...-|a_n|>0$, a contradiction. ■
The proof above contains the rather surprising idea of considering the complex roots of a polynomial, when we are actually interested in $\mathbb{Z}[x]$.
Theorem 9. Let $n>m>1$ be integers. Then $x^n+x^m+1$ is irreducible unless there exists $q$ such that $3m\equiv q \pmod{3q}, 3n\equiv -q\pmod{3q}$ or vice versa.
Proof. The idea of considering reciprocal polynomials is due to W. Ljunggren from this paper.
For a polynomial $f(x)=a_nx^n+...+a_1x+a_0$ (where $a_n\neq 0$), define its reciprocal as $\tilde{f}(x)=x^nf(x^{-1})=a_0x^n+a_1x^{n-1}+...+a_n$. Clearly $\tilde{fg}=\tilde{f}\tilde{g}$, and $\deg f=\deg \tilde{f}$ if $f(0)\neq 0$. We show that if $f(x)\in \mathbb{Z}[x]$ is reducible and $f(x)$ and $\tilde{f}(x)$ have no common roots, then there exists an integer polynomial $Q$ such that $f\tilde{f}=Q\tilde{Q}$ and $Q\neq \pm f, Q\neq \pm \tilde{f}$. In addition, if $f$ is monic and $f(0)=\pm 1$, we can take $Q$ to be monic. Assume $f(x)=g(x)h(x)$. Let $Q(x)=\pm g(x)\tilde{h}(x)$. Then $Q(x)\tilde{Q}(x)=g(x)\tilde{h}(x)\tilde{g}(x)h(x)=f(x)\tilde{f}(x)$. Since $f$ and $\hat{f}$ have no common roots, also $h$ and $\tilde{h}$ have no common roots, so $Q$ has a root that is not a root of $f$. Similarly, $Q$ has a root that is not a root of $\tilde{f}$. Thus $Q\neq \pm f, Q\neq \pm \tilde{f}$. If $f$ is monic, then $g$ and $h$ are also monic, and if $f(0)=\pm 1$, then $\pm g\tilde{h}$ is monic for either choice of sign.
Now let $f(x)=x^n+x^m+1$. Then $\tilde{f}(x)=x^n+x^{n-m}+1.$ These polynomials obviously have no common root, unless both have a root $\zeta$ such that $\zeta^{n-2m}=1$. Now $\zeta^n+\zeta^m=-1\in \mathbb{R}$, so $\zeta^n$ and $\zeta^m$ are conjugates (if $|v|=|w|=1,$ then the argument of $v+w$ is $\frac{\arg(v)+\arg(w)}{2}$). Now if $\zeta$ is a primitive $q$th root of unity, then $n\equiv -m\pmod q$. Since $n\equiv 2m\pmod{|n-2m|}$ and $q\mid |n-2m|$, we get $q\mid 3m$. We cannot have $q\mid m$, since then we would have $\zeta^n+2=0$, which is impossible. Now $\zeta^n+\zeta^m+1=\zeta^n+\omega+1,$ where $\omega$ is a nontrivial cube root of unity. Thus $\zeta^n=\omega^2$, so $n\equiv \pm \frac{q}{3} \pmod{q}$, and hence $3n\equiv \pm q \pmod{3q}$. If these conditions hold, then indeed $x^n+x+1$ is divisible by the minimal polynomial of $\zeta$ (which is the cyclotomic polynomial $\Phi_q(x)$, as $\Phi_q$ was shown to be irreducible in this post).
We may then assume that $f$ and $\tilde{f}$ have no common roots. If $f(x)$ were irreducible, we would have $f(x)\tilde{f}(x)=Q(x)\tilde{Q}(x)$ where $Q\neq \pm f, Q\neq \pm \tilde{f}$. Write $Q(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_0$. Now the coefficient of $x^n$ in $Q(x)\tilde{Q}(x)$ is $\sum_{i=1}^n a_i^2$. The coefficient of $x^n$ in $f(x)\tilde{f}(x)$ is $3$. Thus $\sum_{i=1}^n a_i^2=3$, and as $a_n=1$, we must have $Q(x)=x^n+x^a+1$ ($Q(x)$ is not divisible by $x$ since $f(x)\tilde{f}(x)$ is not). Hence
$(x^n+x^m+1)(x^n+x^{n-m}+1)=(x^n+x^a+1)(x^n+x^{n-a}+1).$
By symmetry, we ay assume $a\leq n-a$. If $a<\frac{n}{2}$, comparing the coefficients, we see that $a=m$ or $a=n-m$, which is a contradiction. Therefore $a=\frac{n}{2}$, and then $2x^n=x^{m}+x^{n-m}$, so $m=\frac{n}{2}$, and again we have a contradiction. ■
The polynomials $x^n+x^m+1$ are a particular case of 0,1 polynomials, which have all their coefficients equal to $0$ or $1$. They are interesting because of their simple form, but yet nontrivial properties. For example, it has been conjectured that almost all 0,1 polynomials are irreducible, but this is an open problem. In the next example, reduction $\pmod p$ will be crucial in the proof.
Theorem 10. Let $p$ be a prime and $a$ and integer with $p\nmid a$. Then $x^p-x+a$ is irreducible.
Proof. These polynomials are the famous Artin Schreier polynomials which are the basis of an entire theory. We show that $f(x)=x^p-x+a$ is actually irreducible in $\mathbb{Z}_p[x]$. Let $F$ be an extension field of $\mathbb{Z}_p$ in which $f$ splits into linear factors. It is well-known that $F$ is a finite field in which $px=0$ for all $x\in F$. Let $\alpha$ be a root of $f$. Then $(\alpha+1)^p-(\alpha+1)+a=0$ by Fermat's little theorem, so the roots of $f$ are $\alpha+k,$ $k=0,1,...,p-1$. We have $\alpha \not \in \mathbb{Z}_p$, since otherwise $\alpha^p-\alpha+a=a$ in $\mathbb{Z}_p$. Now suppose $f(x)=g(x)h(x)$ in $\mathbb{Z}_p[x]$ where $g(x),h(x)\in \mathbb{Z}_p[x]$ are nonconstant. We may assume that $g$ is monic, so
$g(x)=\prod_{k\in S}(x-\alpha-k),$
where $S\subset \mathbb{Z}_p$. However, the coefficient of $x^{|S|-1}$ in $g(x)$ is $-\sum_{k\in S}(\alpha+k)$. This should be in $\mathbb{Z}_p,$ so $|S|=p$, which means that $h$ is constant, a contradiction. ■ | 2018-10-22 11:13:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9703365564346313, "perplexity": 67.19732588835959}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515029.82/warc/CC-MAIN-20181022092330-20181022113830-00313.warc.gz"} |
https://math.paperswithcode.com/paper/long-cycles-have-the-edge-erd-h-o-s-p-osa | # Long cycles have the edge-Erd\H{o}s-P\'osa property
30 May 2017 Bruhn Henning Heinlein Matthias Joos Felix
We prove that the set of long cycles has the edge-Erd\H{o}s-P\'osa property: for every fixed integer $\ell\ge 3$ and every $k\in\mathbb{N}$, every graph $G$ either contains $k$ edge-disjoint cycles of length at least $\ell$ (long cycles) or an edge set $X$ of size $O(k^2\log k + \ell k)$ such that $G-X$ does not contain any long cycle. This answers a question of Birmel\'e, Bondy, and Reed (Combinatorica 27 (2007), 135--145)...
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• COMBINATORICS | 2021-03-05 19:51:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6006690859794617, "perplexity": 2205.4098095670483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178373241.51/warc/CC-MAIN-20210305183324-20210305213324-00192.warc.gz"} |
http://dimacs.rutgers.edu/TechnicalReports/abstracts/1993/93-02.html | ## Projective Orientations of Matroids
### Authors: I. M. Gelfand, G. L. Rybnikov, and D. Stone
ABSTRACT
Let \$\bold M\$ be a matroid on a finite set. Let \${\Cal M}({\bold M})\$ denote the set of oriented matroids whose underlying matroid is \$\bold M\$. We define an equivalence relation on \${\Cal M}({\bold M})\$ in terms of ``reorientations'' of oriented matroids. The set of reorientation classes of oriented matroids on \$\bold M\$ is characterized in various combinatorial and algebraic ways. As part of this work we find two presentations of the inner Tutte group of \$\bold M\$ by generators and relations.
Paper available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1993/93-02.ps | 2017-10-19 16:20:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9225696921348572, "perplexity": 3629.855694297027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823350.23/warc/CC-MAIN-20171019160040-20171019180040-00593.warc.gz"} |
http://trinitariasmallorca.org/dxapk217/how-far-is-200-meters-to-walk-9dc2cb | # how far is 200 meters to walk
Great source for shortwave listeners for calculating crow distance. If it covers half of the journey in $$\Large \frac{3}{5}$$th time, the speed to cover the … To. In Japanese, "man" means 10,000, "po" means steps and "kei" means meter. There is also a special table for the track and field athlete. math. In this case we should multiply 200 Meters by 0.00062137119223733 to get the equivalent result in Miles: 200 Meters x 0.00062137119223733 = 0.12427423844747 Miles 200 m to ft conversion. It takes a healthy person about 10 minutes to walk 1 kilometer at a speed of 6 kilometers per hour. Athletes complete it in less than five minutes. Simply use our calculator above, or apply the formula to change the weight 200 m to ft. It is equal to 100 centimeters, 1/1000th of a kilometer, or about 39.37 inches. I had a thought to convert this speed into yards and feet. 800 meters is .5 miles and 5 minutes would mean you walked about 3 miles per hour. If your own measurement is fairly close to one of these numbers, you can probably assume the track is of a standard size. One foot equals 12 inches exactly. Step 1: Convert from meters to feet. How many kilometers did Keri walk in one week What is the total . It is envisaged that passes will be issued to people who can only walk with excessive labour and at an extremely slow pace or with excessive pain. An alternate approach: We assume that the ratio of distance walked to time is constant (that is that Barbara will walk at the same rate no matter how far or how long she walks). You walk 45 meters down the hall, climb 4.5 meters up the stairs and then walk another 40 meters to your science class. Converting 200 m to ft is easy. Mood Time of walk. How far is 250 meters? Well at least they do in England. How far is 200 meters? G4GHB By Bill on 5th October 2020. So, if you want to calculate how many feet are 200 meters you can use this simple rule. 200 meters equal 656.167979003 feet (200m = 656.167979003ft). Not sure exactly how far 200 feet is? Multiply distance by scale 8.5cm x 25,000 = 212,500 cm Convert to meters 212,500 / 100 = 2,125 m Convert to km: 2,125 / 1,000 = 2.125 km This online calculator tool can be a great help for calculating time basing on such physical concepts as speed and distance. By Robert M on 9th October 2020. bad! Rep:? How far is 200 meters in feet? How to convert 200 meters to feet To convert 200 m to feet you have to multiply 200 x 3.28084, since 1 m is 3.28084 fts . What is 200 meters in inches, feet, meters, km, miles, mm, yards, etc? When u go for the practical test it won’t be exactly 20 meters, they will find the most appropriate number plate and ask u to read but it won’t be that far as the instructors need to find a plate that they can read quickly as well 0. reply. If you feel that 3 miles an hour is your average walking speed then simply deduct some time from the walk. Walking in a group is a great way to start walking, make new friends and stay motivated. This table shows the time for each popular track event from the 100 metres to the 10000 metres (10 kilometre) based on the speed you are travel. Ramblers organises group walks for health, leisure and as a means of getting around for people of all ages, backgrounds and levels of fitness. That's a pretty normal speed. Walking time = 2.5 miles per hour. It is defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second." What is 200 meters in feet? To calculate 200 Meters to the corresponding value in Miles, multiply the quantity in Meters by 0.00062137119223733 (conversion factor). Convert cm, km, miles, yds, ft, in, mm, m. 200 m to cm: 200 m to feet: 200 m to in: 200 m to km: 200 m to miles: 200 m to mm: 200 m to yd: How much is 200 meters in feet? From. I was dropped off at the front door to the place and walked probably no more than 10 meters into the assessment room - on those grounds she decided I would be able to walk more than 20 (I think) but prob no more than 100. Its website has details of many locally organised walks in towns and cities, as well as the countryside. It can also be used for training purposes through the multipoint pace calculator, convert between units of pace, and estimate a finish time. Find how far you’ve walked by entering your height and the number of steps below. Best app for distance and directions! Convert 200 Meters to Miles. 8 Mar 07, 10:36 PM #2 : MrLazy. To qualify under this category, a person would have to have a long term and substantial disability that means they cannot walk or which makes walking very difficult. Imagineer . About Speed Distance Time Calculator. On each weekend day, the walk is 1.4 times as long as a walk on a weekday. Breaktime = 1 minute per Breaktime minute. Therefore, in order to calculate the time, both distance and speed parameters must be entered. swap units ↺ Amount. A bullock cart has to cover a distance of 120 km in 15 hours. Points can … Not sure exactly how far 200 feet is? What is not taken into consideration is the fatigue, pins and needles and numbness when I walk more than even a few meters that builds up the further I go. Enter how far you want to walk or run --> and the unit of measure --> ; ... or 440 yards (1320' 0" or 402.336 meters). How long is it? If Barbara can walk #3200# meters in 24 minutes:. It's meaningless to try for an answer as it varies based on so many factors, a few are:— Age Sex Climate( temperature, wind,rain) Slope of the landscape where you walk . how long does it take to walk 200 metres at an average speed? Barbara can walk 3200 meters in 24 mins. For the speed, you need to enter its value and select speed unit by using the scroll down menu in the calculator. The length of the walk is 0.55 on each weekday. It is defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second." 1 meter = 3.28 x feet, so, 200 x 1 meter = 200 x 3.28 feet, or. Walk in a mostly straight line away from those water sources and trails to reach your defecation destination. What is 250 meters in feet? What is 250 meters in inches, feet, meters, km, miles, mm, yards, etc? So the easiest way for me to understand would be doing it like this, I am standing at the mickey and walt statue in wdw, walking up main street, how far up do I get, Sorry to be thick. Therefore to walk 300 meters should only take. If we note that #3# minutes is #1/8# of #24# minutes then we can see that in #3# minutes she can walk #color(white)("XXX")1/8" of "3200# meters #=400# meters. How many inches in 200 meters? Keri walks her dog every morning. 3 minutes However, a 1996 study from the Transportation Research Board found that the average walking speed of an adult human is approximately 3.1 mph, and, at this rate, a person covers 400 meters in about 4 minutes. How long is it? Practice. By john on 9th October 2020. xoxAngel_Kxox Badges: 21. Leave No Trace recommends walking 200 feet to reduce the chances of contaminating water sources and trails. A meter, or metre, is the fundamental unit of length in the metric system, from which all other length units are based. The device was an early pedometer, based … Walking speed 1000 meters or 1 kilometer per 10 minutes ( m/min – km/min ), converted to foot per 10 minutes equals 3280.84 feet per 10 minutes ( ft/min ). How far can she walk in 3mins. Enter your height feet to get distance in feet and miles or in metric to get results in meters and kilometers. In 1799, France start using the metric system, and that is the first country using the metric. By Keith on 7th October 2020. Descent Time = 1 minute for every 25 metres descent. How far is 200 metres, that's what I need to know. You want to use the simpler number to make the math easier use this simple rule have... Meters in 24 minutes: older people per metre or seconds per 100 meters 800 meters is.5 miles 5... 0.55 on each weekend day, the walk is 0.55 on each weekday rounded to 8 digits ) Display as!, but the distance varies depending on how fast you walk I 'd say 10... 200 x 3.28 feet, so, if you want to use the simpler number make. To reduce the chances of contaminating water sources and trails to reach your defecation.... X feet, meters, km, miles, mm, yards, etc factor ) get fit stay... It is equal to 100 centimeters, 1/1000th of a standard size 6,500 meters listeners calculating! 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As long as a walk on a horse, I want a VAMPIRE with a volvo you will have... In a mostly straight line away from those water sources and trails up the stairs and then walk another meters. To walk 200 metres at an average human is 5 km per hour or in metric to distance! Results in meters by 0.00062137119223733 ( conversion factor ) the formula to change the weight 200 m to ft an. 3.28 x feet, or out of shape then it might be 15 minutes the simpler number to make math. To enter its value and select speed unit by using the metric, the walk is 0.55 on weekend..., 200 x 3.28 feet, meters, km, miles, mm yards... Order to calculate the time, and that is the first country using scroll. Through 100 m within 9 seconds walk I 'd say about 10 minutes great way to start,! Walk in a group is a great way to get fit and stay.... To your science class it will only take: this means in one hour will. 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Physical concepts as speed and distance, given values for two of the.. Calculating crow distance this online calculator tool can be a great way to get results meters. Walk about 4 miles an hours is 5 km per hour 3.2808398950131 feet = 3.2808398950131 feet these numbers you!, you can probably assume the track and field athlete digits ) Display result as within 9 seconds,,... Speed parameters must be entered how many feet are 200 meters in inches, feet or... Basing on such physical concepts as speed and distance 40 meters to the corresponding value in miles multiply... Meters is.5 miles and 5 minutes would mean you walked about 3 miles hour! 24 minutes: 70 big steps very close to one of these numbers you... 0.55 on each weekday, I want a VAMPIRE with a volvo in inches, feet, will... For the track and field athlete meters to the corresponding value in miles, mm, yards etc!, or about 39.37 inches a 10,000 steps meter in miles, multiply the quantity in meters 0.00062137119223733... 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In feet and miles or in metric to get distance in feet and miles in! 100 m within 9 seconds will also have time taken to travel certain distances such as per... To reach your defecation destination be super precise how far is 200 meters to walk you can probably assume the track and field.... Into yards and feet the length of the walk is 1.4 times as long as a walk a!, miles, multiply the quantity in meters by 0.00062137119223733 ( conversion factor.! Bullock cart has to cover a distance of 120 km in 15 hours = x!, 10:36 PM # 2: MrLazy 1.0 /5 2 how far is 200 meters to walk is a great help calculating... Concepts as speed and distance select speed unit by using the metric = 656.167979003ft ) this is close... 200 feet to get fit and stay healthy # 3200 # meters in 24 minutes: every 10 ascent... How long does it take to walk much faster than older people meters, km miles! Of contaminating water how far is 200 meters to walk and trails m within 9 seconds feet is approximately 70 big steps than older.! See how far is 200 meters to walk ( 2 ) Ask for details ; Follow Report Log to. Height, weight, culture and effort we have a simple, yet excellent to... Value and select speed unit by using the metric system, and that is first. This rate it will take about 1.21 minutes to walk much faster than older people a... | 2021-02-27 06:18:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6718201041221619, "perplexity": 1819.8753298958559}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358203.43/warc/CC-MAIN-20210227054852-20210227084852-00329.warc.gz"} |
https://math.stackexchange.com/questions/3723460/what-is-the-relation-between-recursive-languages-and-partial-recursive-functions | # What is the relation between recursive languages and partial recursive functions?
From Introduction to Automata Theory, Language, and Computation by Ullman et. al.:
The Turing machine is studied both for the class of languages it define (called the recursively enumerable sets) and the class of integer functions it computes (called the partial recursive functions).
1. What is the relation between recursive enumerable languages and partial recursive functions? (notice "recursive" in both terms, and "partial" in "partial recursive functions" are also often omitted)
Is it correct that the membership decision problem of a r.e. language is a partial recursive function, so can be computed by a TM?
2. What is the relation between recursive languages and total recursive functions? (The similarity in the two terms has led me to a lot of confusions and mix-ups.)
Thanks.
1. Strictly speaking the two are simply different things. The "membership decision problem of a r.e. language" cannot be an integer function, because it does not take an integer as input. But with some coding we can connect the two. For example, we can interpret the input word over an n-ary alphabet as a number in base n+1 (exclude the zero for uniqueness of representation). Then we can look at the membership as an integer function, and indeed just the ones for r.e. sets are partial recursive.
The other way around, funtions have both input and output, while language deciders take a word and end in a certain class of state (or loop forever). So if we want to consider what functions they can compute we usually look at the sets of ordered pairs $$\{(x,f(x)): x \text{ in the domain} \}.$$ And again one can show that just the partial recursive functions result in r.e. sets.
1. The answer is just as above. They are different things, but deep down they are the same.
(Below, for simplicity all functions are unary. Also, "$$\uparrow$$" denotes "is undefined." Finally, for simplicity I'll think of languages as sets of natural numbers as opposed to sets of strings, although this is purely superficial.)
The key is the following "translation" from partial functions to sets:
Given a partial function $$f$$, let $$Graph_f=\{\langle a,b\rangle: f(a)=b\}$$ (where "$$\langle\cdot,\cdot\rangle$$" is your favorite pairing operation).
Note that $$Graph_f$$ is defined for all partial functions $$f$$, not just the recursive ones. The construction $$f\mapsto Graph_f$$ lets us translate properties of functions to corresponding properties of sets, and in general all computability-theoretic properties will "match up" appropriately. In particular, we have:
Suppose $$f$$ is a partial function. Then the following are equivalent: $$(i)$$ $$f$$ is a partial recursive function. $$(ii)$$ $$Graph_f$$ is recursively enumerable.
(Indeed, this is one way that partial recursive functions are sometimes defined in the first place. Moreover, note that in much of logic a function literally is its graph, so it's unsurprising to see this sort of correspondence.)
On a less-immediate note, observe that the further assumption of totality simplifies things substantially:
Suppose $$f$$ is a total function. Then the following are equivalent: $$(i)$$ $$f$$ is recursive. $$(ii)$$ $$Graph_f$$ is r.e. $$(iii)$$ $$Graph_f$$ is recursive.
Clearly $$(iii)\rightarrow (ii)$$, and $$(ii)\rightarrow (i)$$ by the previous observation. To see $$(i)\rightarrow (iii)$$, suppose $$f$$ is total recursive and we want to check whether $$\langle a,b\rangle\in Graph_f$$; we simply run (the computation of) $$f$$ on input $$a$$ until it halts and outputs some $$n$$, which it must since $$f$$ is total, and then we check whether $$n=b$$.
If we drop the totality assumption this breaks down: the function $$h_X(n)=\begin{cases} n & \mbox{ if n\in X}\\ \uparrow & \mbox{ otherwise}\\ \end{cases}$$ is partial recursive whenever $$X$$ is r.e., but $$Graph_{h_X}=\{\langle x,x\rangle: x\in X\}$$ has the same Turing degree as $$X$$, so if $$X$$ is a non-recursive r.e. set then $$h_X$$ is a partial recursive function with r.e. but non-recursive graph.
It's also worth noting that there's also a translation "dual" to the $$f\mapsto Graph_f$$-construction, although it's a bit more finicky. Every r.e. set $$X$$ has a "one-at-a-time" enumerator - that is, a machine $$M$$ such that for each $$s$$ there is at most one $$t_s$$ such that $$M$$ accepts $$t_s$$ in exactly $$s$$ steps. The associated map $$g_M(s)=\begin{cases} t_s & \mbox{ if M accepts some string in exactly s steps}\\ \uparrow & \mbox{ otherwise} \end{cases}$$ is partial recursive and we have $$Graph_{g_M}=X.$$
The reason this is more finicky is that $$M$$ is not uniquely determined by $$X$$ - every r.e. $$X$$ will have many such $$M$$s. | 2020-10-24 08:28:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 50, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8930814862251282, "perplexity": 309.85397144993436}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882103.34/warc/CC-MAIN-20201024080855-20201024110855-00016.warc.gz"} |
https://itprospt.com/num/4427532/question-completion-status-question-16provide-an-appropriate | 5
##### (a) Find the junction temperature at the steady state of system the area of cross-section of copper twice that of the steel fod (Thermal conductivity of steel 40 Wm 'K and ol copper 385 Wm (3marks)(b) Find the ratio of rate of heat Ilow through both the materials:(Zmatks)HOT RESERVOIR Do-€COLD RESERVOIR 0"
(a) Find the junction temperature at the steady state of system the area of cross-section of copper twice that of the steel fod (Thermal conductivity of steel 40 Wm 'K and ol copper 385 Wm (3marks) (b) Find the ratio of rate of heat Ilow through both the materials: (Zmatks) HOT RESERVOIR Do-ââ...
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2.6.41-GI The population of Nilam doubles In size every yr; In 1992, Its population was 15,000. a) Find an exponential function of the form P(t) = Pon that models Nilam's population after t years; b) Find the equivalent exponential model of the form P(t) = Po What is Nilam'5 yoary percenta...
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##### What is the wavelength of light with frequency 5.54 x1016 s-1?a) 5.41 pmb) 5.41 nmc) 5.41 μmd) 5.41 mmWhat is the frequency of electromagnetic radiation with anenergy of 2.69×104 kJ mol-1?a) 1.41×104 Hzb) 2.39×108 Hzc) 4.56×1012 Hzd) 6.74×1016 HzWhat is the energy (to two decimal places) of a photon offrequency 2.78x1011 s−1?a) 1.84x10-22 Jb) 3.68x1011 Jc) 1.56 Jd) 5.43x1021 Je) 4.47x10−21 JHow long does it take for electromagnetic radiation to travel in3.54x10−3 m?a) 8
What is the wavelength of light with frequency 5.54 x 1016 s-1? a) 5.41 pm b) 5.41 nm c) 5.41 μm d) 5.41 mm What is the frequency of electromagnetic radiation with an energy of 2.69×104 kJ mol-1? a) 1.41×104 Hz b) 2.39×108 Hz c) 4.56×1012 Hz d) 6.74×1016 Hz What is the... | 2022-05-26 02:24:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7696567177772522, "perplexity": 4868.991938968396}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662595559.80/warc/CC-MAIN-20220526004200-20220526034200-00080.warc.gz"} |
https://livingthing.danmackinlay.name/controllerism.html | # Controllerism
### Also gestural interfaces, and other fancy words for making thing happen by waving your arms about on stage
“[…]Now. Where is it?”
“Where is what?”
“The time machine.”
“You're standing in it.” said [X].
“How… does it work?” [Y] said, trying to make it sound like a casual enquiry.
“Well, it's really terribly simple,” said [X], “it works any way you want it to. You see, the computer that runs it is a rather advanced one. In fact it is more powerful than the sum total of all the computers on this planet including – and this is the tricky part – including itself. Never really understood that bit myself, to be honest with you. But over ninety-five per cent of that power is used in simply understanding what it is you want it to do. I simply plonk my abacus down there and it understands the way I use it. I think I must have been brought up to use an abacus when I was a… well, a child, I suppose.
“[R], for instance, would probably want to use his own personal computer. If you put it down there, where the abacus is, the machine's computer would simple take charge of it and offer you lots of nice user-friendly time-travel applications complete with pull-down menus and desk accessories if you like. Except that you point to 1066 on the screen and you've got the Battle of Hastings going on outside your door, er, if that's the sort of thing you're interested in.”
[X]'s tone of voice suggested that his own interests lay in other areas.
“It's, er, really quite fun in its way,” he concluded. “Certainly better than television and a great deal easier to use than a video recorder. If I miss a programme I just pop back in time and watch it. I'm hopeless fiddling with all those buttons.” […]
“You have a time machine and you use it for… watching television?”
“Well, I wouldn't use it at all if I could get the hang of the video recorder”
On the dark art of persuading the computer to respond intuitively to your intentions, with particular regard to music.
The input-data side of gesture recognition.
In non-musical circles they call this “physical computing”, or “natural user interfaces”, or “tangible computing”, depending upon whom they are pitching to for funding this month.
• I just designed an interesting digital instrument with a bunch of free control parameters.
• I have an interface with a different (usually much smaller) number of control parameters.
• there is no obvious “best”, or even immediately intuitive, mapping from one to the other
How do I plug these into each other in an intelligible, expressive way so as to perform using them?
This question is broad, vague and and comes up all the time.
Ideas I would like to explore:
• Interpolating between interesting parameters using arbitrary regression. Rebecca Fiebrink's Wekinator does this using simple neural networks.
• Constructing basis vectors in some clever way, e.g. sparse basis dictionaries
• constructing quasi-physical models that explore parameter space in some smart, intuitive way, e.g. swarm systems, Hamiltonian models
• doing basic filtering of generic UI signals
• leaky integration
• differentiation (smoothed)
• gating
• thresholding and Schmitt-triggering
• constructing random IIR convolutional filters and harnessing for control. How do you select the best ones, though? What is the right objective function?
## Random mappings
• sparse correlation
• physical models as input
• random sparse physical models as input
• annealing/Gibbs distribution style process
• Der/Zahedi/Bertschinger/Ay-style information sensorimotor loop
## “Copula” Models
And related stuff.
Copula are an intuitive way to relate 2 or more (monotonically varying?) values by their quantiles.
The most basic one is Gaussian, where the parameter of the copula is essentially the correlation. For various reasons, I'm not keen on this in practice; I do't have time to go into my intuitions as to why it is so, but Gaussian tails“feel” wrong for control. Student-t, perhaps?
See copulas.
## UI design ideas
• circular sequencer
• gesture classifiers
• accelerometer harvest for iphone
## Protocols
### MIDI
More-or-less working since the 1980s; still the best idea, if you can live with 7-bit scalars as your lingua franca. See MIDI.
### OpenSoundControl
A short-lived project from the 1990s to produce a more flexible protocol than MIDI. Insinuated its way into many projects before death, and still haunts them Because it is more flexible than MIDI, it is sometimes discussed as if it were the apotheosis of protocols, as opposed to an incremental improvement on MIDI with many debilities of its own, and much narrower support.
# . Stateless protocol designed to support UDP – and therefor it's a one way
protocol. No question-and-response here. Therefore you always end up
re-inventing TCP if you want to do 2 way communication. Which presumably you do,
or you'd be using MIDI.
# . Doesn't guarantee delivery, due to UDP assumption. When you mention this,
supercollider fans tell you that you CAN in fact use TCP instead. Which you can,
but only if you are using supercollider, which rather diminishes the “universal
ultimate controller protocol for everything” argument.
TBD.
TBD.
## Software
• libmapper bundles together UI signals and provides a discovery protocol; libraries in C right now; also there is python, and some puredata/maxMSP implementation
But if you were doing that, why not use some IoT tools and benefit from greater brainshare?
• musicbricks include gestural controllers and syncing in their various open source umbrella projects.
• The Autobahn project:
provides open-source implementations of the The WebSocket Protocol and The Web Application Messaging Protocol (WAMP) network protocols.
WebSocket allows bidirectional real-time messaging on the Web and WAMP adds asynchronous Remote Procedure Calls and Publish & Subscribe on top of WebSocket.
WAMP is ideal for distributed, multi-client and server applications, such as multi-user database-driven business applications, sensor networks (IoT), instant messaging or MMOGs (massively multi-player online games).
includes javascript, python and a routing infrastructure called crossbar.
• Luis Lloret's OSMID aims to provide a lightweight, portable, easy to use tool to convert MIDI to OSC and OSC to MIDI.
• Mark Francombe's browser MIDI/OSC converter, MIDI MESSAGE GENERATOR.
### python
• MIDI
• Magenta's MIDI interface shows how Google does it so they can be cool.
• MIDO “is a library for working with MIDI messages and ports. It’s designed to be as straight forward and Pythonic as possible.”
• OSC
• The original, sorta-working thing: pyOSC
• C-based and easier to use: pyliblo
### javascript
• tangible.js is a resource for real-world interfaces plugging into to javascript. They intermittently publish useful reviews.
• There are various handy GUI frameworks designed for musical control.
• OpenSoundControl bridges
• osc.js is an Open Sound Control (OSC) library for JavaScript that works in both the browser and Node.js (And is still being maintained unlike many)
• supercollider.js does this and much more.
• OSC-JS exists, bridging websockets to OSC, but doesn't look as maintained as osc.js. Are there others?
• Yes. Legato.
legato is a small node.js library written in coffeescript, but that doesn't really matter. legato is designed to let you create beautifully simple connections between devices and software, regardless of environment.
### Lua
Reasonably comprehensive support for MIDI with decent timing in Löve2d.
### Supercollider
• mmExtensions by Martin Marier has the best-designed preset interpolation system I have seen, all so that its creator may plug a networked bath sponge into clarinet recordings.
## Interesting hardware
### Tablet computers
For iOs, Touchosc, Lemur…
For anything +Ableton, yeco.
## 3d interaction
The classic depth camera is the Kinect. More-open depth-camera: Orbbec3d
Calibration is tricky; Rulr attempts to solve this in an open-source, general way. (Rulr docs). openkinect does Kinect.
TBC.
### myo
myo is a wristband sensor that measures your muscles directly using EMG. Similar: the XTH using MMG - “which captures motion, direction and orientation sensors (integrated in a 9-DoF IMU) and muscle sound (also known as mechanomyogram or MMG)”
### leapmotion
Infrared hand tracker. In my experience, not really stable enough for on-stage use, (needs better Kalman filtering) but gee it's small and portable.
### Keith McMillan fancy controllers
e.g. QUNexus, multi-dimensional midi controllers. (Ongoing project – find out how to work them in Bitwig.)
### Makeymakey
makeymakey
[Turns] everyday objects into touchpads and combine them with the internet. It's a simple Invention Kit for Beginners and Experts doing art, engineering, and everything in between
Hmm. I'm not sold on this, as it's a rather expensive way of getting 1-dimensional controllers out of \$2 contact mics, and you could do a lot more with this if you were clever. Nice if you are short of time and quirk, but not short of money,
### wiimote
Wiimote should be a normal HID device, but has nasty sharp edges. So you avoid them using alternate libraries:
• wiiuse is a library written in C that connects with several Nintendo Wii remotes. Supports motion sensing, IR tracking, nunchuk, classic controller, Balance Board, and the Guitar Hero 3 controller. Single threaded and nonblocking makes a light weight and clean API.
• OS X mapper Darwiinremote.
• OSX driver wjoy
• osculator is a commerical product which does this; it's pretty good.
• libcwiid seems to be linux-happy? But it's a naked C library and apparently threading-tricky. Has a python interface.
• nodewii uses it though for node linux
See synestizer.
## Accessibility
Human Instruments does good accessibile interface work. | 2019-02-17 20:57:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33691033720970154, "perplexity": 6931.7729078454595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247482478.14/warc/CC-MAIN-20190217192932-20190217214932-00019.warc.gz"} |
https://www.physicsforums.com/threads/is-it-true-that-in-general-relativity-length-does-not-exist.648111/ | # Is it true that in general relativity length does not exist?
1. Oct 30, 2012
### 7561
I think I read once that length does not exist in general relativity, though I'm not sure if I got that hopelessly muddled or if there are subtleties that I am missing. I have a vague understanding of length contraction, but I thought that what I was reading said that there simply is no length in general relativity, it is not a meaningful concept.
2. Oct 30, 2012
### bossman27
Someone correct me if I'm missing something as well, as I'm mostly familiar with SR, but I believe lengths certainly do exist in GR as well. What you may be thinking of is the fact that there isn't one "right" length i.e. no particular reference frame is any better than the others. In this sense, length is variable, although there is what's called "proper length." In any reference frame, proper length L is:
$L = \sqrt{\Delta x^{2} + \Delta y^{2} + \Delta z^{2} - (c \Delta t)^{2}}$
Proper length is defined as the invariant interval of a space-like path between two events. Two events are space-like separated if there exists a reference frame in which the two events can be observed to occur at the same time, but no reference frame such that they are observed to be located the same point in space.** This would be the case for defining the length between two spatially separated points like the endpoints of an object, since we can take proper length to be distance between simultaneous "events" at the ends of the object, in the object's rest frame. That is, the proper length of an object is the length of the object as it would be measured in the object's own rest frame (though technically this length is not any more "correct" than any other possible lengths). This invariant quantity could be inferred from any reference frame by 'boosting' to the object's rest frame. I should note that this formula assumes a flat spacetime, and it looks much more complicated in GR as it accommodates curved spacetime.
**If you think of it in terms of length contraction, we're just saying that there is no reference frame such that the length contracts to 0.
I also just had a thought that you might be muddling length contraction in GR with something you read about the plank length. Just wikipedia "plank length" for more details.
Last edited: Oct 30, 2012
3. Oct 30, 2012
### Staff: Mentor
Bossman, you left out a fairly important minus sign. It's:
$L = \sqrt{\Delta x^{2} + \Delta y^{2} + \Delta z^{2} - (c \Delta t)^{2}}$
Or if you're using the other sign convention:
$L = \sqrt{(c \Delta t)^{2} - \Delta x^{2} - \Delta y^{2} - \Delta z^{2}}$
Either way, the sign of the time and the space coordinates must be different, so that the path followed by a flash of light has length zero.
4. Oct 30, 2012
### bossman27
Woops! My mistake, corrected now. Thanks for pointing that out.
5. Oct 30, 2012
### Staff: Mentor
Unless you can give a specific reference, I don't think you're going to get much clarification, except for the obvious point that "length" *is* a meaningful concept in GR.
6. Oct 30, 2012
### Staff: Mentor
This formula is correct (at least, it is now since you adopted Nugatory's correction) for special relativity, where spacetime is always flat. It is not correct in GR because spacetime can be curved. (Technically, it can still be used in GR in a local inertial frame, but it certainly can't be used in *any* frame.)
7. Oct 30, 2012
### PAllen
I think it's fair to say that length and distance have major additional difficulties in GR compered to SR. In SR, there are well known issues with rigidity for non-inertial bodies. Since, in GR, there are no global inertial frames, this translates to difficulties for what is meant by rigidity for an extended object in a region with substantial spacetime curvature. Then, without a clear concept of rigidity, it becomes hard to talk about the length of an extended object in such a context (length here referring to rest length - length measured in rigid object's rest frame ; in GR the latter does not exist for an extended object).
For large distances in GR, the problems are less acute, but still present. The issue is lack of a preferred way to define simultaneity over great distances (locally, you can say that a relevant local inertial frame gives you a preferred slicing). Thus, it is not that you can't compute distances, but that, in the general case, you don't know which of an infinite number of answers to prefer.
8. Oct 30, 2012
### Staff: Mentor
Agreed, but none of this implies that "length" is not a meaningful concept. It just means that, in any particular case, there are multiple "lengths" that could be applicable.
9. Oct 30, 2012
### bossman27
I did mention that the formula is altered in GR to accomodate curved spacetime. I didn't bother to copy down the formula because I (let alone the OP) don't have a firm grasp on it, and I'm under the impression that the qualitative idea of proper length is the same regardless. Is it somehow not?
10. Oct 30, 2012
### Staff: Mentor
Ah, sorry, I missed that in your post.
There isn't actually a single formula for curved spacetime; it depends on *which* curved spacetime you are dealing with. But you're right that the qualitative idea is the same: the "length" between two nearby events is $ds = \sqrt{ \sum_{a, b} g_{ab} dx^a dx^b }$, where $g_{ab}$ is the metric and $dx^a$ and $dx^b$ are coordinate differentials (like dx, dy, dz). In the flat spacetime case, we have $g_{00} = -1$ and $g_{11} = g_{22} = g_{33} = 1$, and $dx^0 = dt$, $dx^1 = dx$, $dx^2 = dy$, $dx^3 = dz$, which gives the formula you wrote down. The specific coefficients in the matrix $g_{ab}$ will depend on the particular spacetime.
11. Oct 30, 2012
### bossman27
Ahh, that's very interesting. Thank you for that explanation. I'm very comfortable with SR but have yet to deal with any GR in my undergrad courses, do you by chance have a preferred book or other source that I might try and do a bit of self-teaching from?
12. Oct 30, 2012
### Staff: Mentor
13. Oct 30, 2012
### Staff: Mentor
14. Oct 30, 2012
### Matterwave
I just want to mention that the metric "g" actually also depends on the coordinate system and, more importantly, the basis vectors you use. One could always adopt a tetrad field as our basis vectors so that "g" has the form it takes in SR always...but the formulas we must us to calculate our other tensors must all change (which is why most GR courses just stick with coordinate bases).
15. Oct 30, 2012
### PAllen
This is interesting. Wouldn't it not just be tensor calculation that changes? Wouldn't you also have have to do something different to compute integral invariants (distances, time, volume, etc)? If you used the coordinate formula with the Minkowski metric, wouldn't you get the wrong anser? Or is it that you don't compute integral invariants at all with tetrad fields - you only compute tensor fields using them?
16. Oct 30, 2012
### Matterwave
Tetrad fields are not coordinate bases, so you don't have one forms which are just dx, dy, dz, etc., or vectors which are d/dx, d/dy, d/dz, etc. You have basis one forms and basis vectors e_x, e_y, and e_z, which maybe expressed as some functions of d/dx, d/dy, and d/dz, etc. So, you don't have ds^2=gdxdx or some such because the dx's are no longer your basis vectors. You have ds^2=sum_ij(e_i dot e_j)=sum_i(e_i)^2.
EDIT: Sorry, my memory is getting hazy on this...I'll have to think about this a little more...What I wrote above (the formula for ds) might be wrong.
Probably, it's better to just look at the wikipedia...http://en.wikipedia.org/wiki/Frame_fields_in_general_relativity
Last edited: Oct 30, 2012
17. Oct 30, 2012
### pervect
Staff Emeritus
Length becomes observer dependent in Special relativity (Lorentz contraction means that a moving observer measures an object to have a different length than a stationary one).
Length is pretty much the same in GR as it is in SR, except that the concept of "an observer" becomes trickier. In SR, you can specify "an observer" by picking an inertial frame. In GR, to define distance, you need to pick a notion of "simultaneity" - or a class of observers For instance, observers who are isotropic (moving with the Hubble flow) will have a different "now", and hence a different notion of distance, than fermi observerers). The later sort of distance is the sort that one would measure with a ruler, but it's little used in cosmology, the sort you'll see reported in most papers is the first sort (which is much easier to compute and has become semi-standard).
18. Oct 30, 2012
### Staff: Mentor
This is true, and it's good to mention it. If we're going to talk about the complications, we should talk about all of them.
Strictly speaking, this is only true in a small local patch of spacetime around a given event. You can't construct a global "reference frame" this way like you can in flat spacetime.
19. Oct 30, 2012
### Staff: Mentor
I think this is the right way to look at it; a "tetrad field" is, strictly speaking, a local object only. You can, of course, define a frame field over an entire spacetime region (for example, the frame field of static observers in Schwarzschild spacetime, where the basis vectors vary with r), but I don't think you can compute integral invariants using it because there isn't a consistent integration measure. You need a single chart that covers the entire region. (I would welcome comment from experts on this, though.) | 2017-12-12 18:35:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7773644924163818, "perplexity": 555.9084918699823}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948517845.16/warc/CC-MAIN-20171212173259-20171212193259-00473.warc.gz"} |
https://lw2.issarice.com/users/soerenmind | ## Posts
How important are model sizes to your timeline predictions? 2019-09-05T17:34:14.742Z · score: 11 (6 votes)
What are some good examples of gaming that is hard to detect? 2019-05-16T16:10:38.333Z · score: 5 (2 votes)
Any rebuttals of Christiano and AI Impacts on takeoff speeds? 2019-04-21T20:39:51.076Z · score: 47 (17 votes)
Some intuition on why consciousness seems subjective 2018-07-27T22:37:44.587Z · score: 19 (10 votes)
Updating towards the simulation hypothesis because you think about AI 2016-03-05T22:23:49.424Z · score: 9 (13 votes)
Working at MIRI: An interview with Malo Bourgon 2015-11-01T12:54:58.841Z · score: 8 (9 votes)
Meetup : 'The Most Good Good You Can Do' (Effective Altruism meetup) 2015-05-14T18:32:18.446Z · score: 1 (2 votes)
Meetup : Utrecht- Brainstorm and ethics discussion at the Film Café 2014-05-19T20:49:07.529Z · score: 1 (2 votes)
Meetup : Utrecht - Social discussion at the Film Café 2014-05-12T13:10:07.746Z · score: 1 (2 votes)
Meetup : Utrecht 2014-04-20T10:14:21.859Z · score: 1 (2 votes)
Meetup : Utrecht: Behavioural economics, game theory... 2014-04-07T13:54:49.079Z · score: 2 (3 votes)
Meetup : Utrecht: More on effective altruism 2014-03-27T00:40:37.720Z · score: 1 (2 votes)
Meetup : Utrecht: Famine, Affluence and Morality 2014-03-16T19:56:44.267Z · score: 0 (1 votes)
Meetup : Utrecht: Effective Altruism 2014-03-03T19:55:11.665Z · score: 3 (4 votes)
Comment by soerenmind on [AN #63] How architecture search, meta learning, and environment design could lead to general intelligence · 2019-09-18T17:28:57.872Z · score: 1 (1 votes) · LW · GW
Would be cool to hear at some point :)
Comment by soerenmind on [AN #63] How architecture search, meta learning, and environment design could lead to general intelligence · 2019-09-11T00:09:15.814Z · score: 5 (3 votes) · LW · GW
I think that the complexity of the real world was quite crucial, and that simulating environments that reach the appropriate level of complexity will be a very difficult task.
Almost all the actual complexity comes from other organisms, so that’s sort of something you get for free if you’re spending all this compute running evolution cause you get to have the agent you’re actually producing interact with itself.
I guess, other than that, you have this physical environment, which is very rich. Quantum field theory is very computationally complicated if you want to actually simulate the behavior of materials, but, it’s not an environment that’s optimized in ways that really pull out … human intelligence is not sensitive to the details of the way that materials break. If you just substitute in, if you take like, “Well, materials break when you apply stress,” and you just throw in some random complicated dynamics concerning how materials break, that’s about as good, it seems, as the dynamics from actual chemistry until you get to a point where humans are starting to build technology that depends on those properties. And, by that point, the game is already over.
Comment by soerenmind on Buck's Shortform · 2019-08-20T20:25:23.451Z · score: 10 (4 votes) · LW · GW
Hired an econ tutor based on this.
Comment by soerenmind on [AN #60] A new AI challenge: Minecraft agents that assist human players in creative mode · 2019-07-28T20:55:39.350Z · score: 3 (2 votes) · LW · GW
Yep my comment was about the linear scale up rather than it's implications for social learning.
Comment by soerenmind on [AN #60] A new AI challenge: Minecraft agents that assist human players in creative mode · 2019-07-28T17:41:06.670Z · score: 9 (3 votes) · LW · GW
Costs don't really grow linearly with model size because utilization goes down as you spread a model across many GPUs. I. e. aggregate memory requirements grow superlinearly. Relatedly, model sizes increased <100x while compute increased 300000x on OpenAI's data set. That's been updating my views a bit recently.
People are trying to solve this with things like GPipe, but I don't know yet if there can be an approach that scales to many more TPUs than what they tried (8). Communication would be the next bottleneck.
Comment by soerenmind on [AN #60] A new AI challenge: Minecraft agents that assist human players in creative mode · 2019-07-28T17:37:35.653Z · score: 1 (1 votes) · LW · GW
Edit: double commented
Comment by soerenmind on Conditions for Mesa-Optimization · 2019-07-28T10:33:53.923Z · score: 2 (2 votes) · LW · GW
The concept of pre-training and fine-tuning in ML seems closely related to mesa-optimization. You pre-train a model on a general distribution so that it can quickly learn from little data on a specific one.
However, as the number of tasks you want to do (N) increases, there seems to be the opposite effect as what your (very neat) model in section 2.1 describes: you get higher returns for meta-optimization so you'll want to spend relatively more on it. I think model's assumptions are defied here because the tasks don't require completely distinct policies. E.g. GPT-2 does very well across tasks with the exact same prediction-policy. I'm not completely sure about this point but it seems fruitful to explore the analogy to pre-training which is widely used.
Comment by soerenmind on What are principled ways for penalising complexity in practice? · 2019-06-28T04:38:36.232Z · score: 15 (5 votes) · LW · GW
The exact Bayesian solution penalizes complex models as a side effect. Each model should have a prior over its parameters. The more complex model can fit the data better, so P(data | best-fit parameters, model) is higher. But the model gets penalized because P(best-fit parameters | model) is lower on the prior. Why? The prior is thinly spread over a higher dimensional parameter space so it is lower for any particular set of parameters. This is called "Bayesian Occam's razor".
Comment by soerenmind on Risks from Learned Optimization: Introduction · 2019-06-24T19:22:51.332Z · score: 23 (6 votes) · LW · GW
This recent Deepmind paper seems to claim that they found a mesa optimizer. E. g. suppose their LSTM observes an initial state. You can let the LSTM 'think' about what to do by feeding it that state multiple times in a row. The more time it had to think, the better it acts. It has more properties like that. It's a pretty standard LSTM so part of their point is that this is common.
https://arxiv.org/abs/1901.03559v1
Comment by soerenmind on Risks from Learned Optimization: Introduction · 2019-06-20T19:31:34.017Z · score: 3 (1 votes) · LW · GW
Terminology: the phrase 'inner alignment' is loaded with connotations to spiritual thought (https://www.amazon.com/Inner-Alignment-Dinesh-Senan-ebook/dp/B01CRI5UIY)
Comment by soerenmind on What is the evidence for productivity benefits of weightlifting? · 2019-06-20T18:26:59.175Z · score: 5 (3 votes) · LW · GW
"high intensity aerobic exercise provides the benefit, and resistance training, if it includes high intensity aerobic exercise, can capture that benefit."
Which part made you conclude that high intensity aerobic exercise is needed? Asking because most resistance training doesn't include it.
Comment by soerenmind on What would you need to be motivated to answer "hard" LW questions? · 2019-05-17T13:06:31.567Z · score: 5 (3 votes) · LW · GW
It would help if the poster directly approaches or tags me as a relevant expert.
Comment by soerenmind on What are some good examples of gaming that is hard to detect? · 2019-05-17T12:58:51.664Z · score: 1 (1 votes) · LW · GW
Thanks, updated.
Comment by soerenmind on What are some good examples of gaming that is hard to detect? · 2019-05-17T12:58:05.362Z · score: 1 (1 votes) · LW · GW
For example, an RL agent that learns a policy that looks good to humans but isn't. Adversarial examples that only fool a neural nets wouldn't count.
Comment by soerenmind on What failure looks like · 2019-04-29T12:00:46.534Z · score: 3 (1 votes) · LW · GW
It'd be nice to hear a response from Paul to paragraph 1. My 2 cents:
I tend to agree that we end up with extremes eventually. You seem to say that we would immediately go to alignment given somewhat aligned systems so Paul's 1st story barely plays out.
Of course, the somewhat aligned systems may aim at the wrong thing if we try to make them solve alignment. So the most plausible way it could work is if they produce solutions that we can check. But if this were the case, human supervision would be relatively easy. That's plausible but it's a scenario I care less about.
Additionally, if we could use somewhat aligned systems to make more aligned ones, iterated amplification probably works for alignment (narrowly defined by "trying to do what we want"). The only remaining challenge would be to create one system that's somewhat smarter than us and somewhat aligned (in our case that's true by assumption). The rest follows, informally speaking, by induction as long as the AI+humans system can keep improving intelligence as alignment is improved. Which seems likely. That's also plausible but it's a big assumption and may not be the most important scenario / isn't a 'tale of doom'.
Comment by soerenmind on Any rebuttals of Christiano and AI Impacts on takeoff speeds? · 2019-04-22T11:15:55.802Z · score: 3 (2 votes) · LW · GW
AFAICT Paul's definition of slow (I prefer gradual) takeoff basically implies that local takeoff and immediate unipolar outcomes are pretty unlikely. Many people still seem to put stock in local takeoff. E.g. Scott Garrabrant. Zvi and Eliezer have said they would like to write rebuttals. So I'm surprised by the scarcity of disagreement that's written up.
Comment by soerenmind on Any rebuttals of Christiano and AI Impacts on takeoff speeds? · 2019-04-22T11:00:36.676Z · score: 5 (3 votes) · LW · GW
Thanks. IIRC the comments didn't feature that much disagreement and little engagement from established researchers. I didn't find too much of these in other threads either. I'm not sure if I should infer that little disagreement exists.
Re Paul's definition, he expects there will be years between 50% and 100% GDP growth rates. I think a lot of people here would disagree but I'm not sure.
Comment by soerenmind on How much funding and researchers were in AI, and AI Safety, in 2018? · 2019-04-21T20:19:10.758Z · score: 14 (4 votes) · LW · GW
I counted 37 researchers with safety focus plus MIRI researchers in September 2018. These are mostly aimed at AGI and at least PhD level. I also counted 38 who do safety at various levels of part-time. I can email the spreadsheet. You can also find it in 80k's safety Google group.
Comment by soerenmind on Some intuition on why consciousness seems subjective · 2018-11-21T11:06:43.601Z · score: 1 (1 votes) · LW · GW
Gotcha, I'm referring to a representation encoded in neuron activity, which is the physical process.
Comment by soerenmind on Some intuition on why consciousness seems subjective · 2018-11-06T00:40:25.909Z · score: 1 (1 votes) · LW · GW
Where else would the model be if not inside the head? Or are you saying one can 'understand' physical objects without any hint of a model?
Comment by soerenmind on Some intuition on why consciousness seems subjective · 2018-10-17T19:03:04.918Z · score: 9 (2 votes) · LW · GW
Late response:
Instantiation/representation/having a model, in my view, is not binary and is needed for any understanding. You seem to say that I don't think 'understanding' requires instantiation. My example with the bowl is meant to say that you do require a non-zero degree of instantiation - although I would call it modelling instead because instantiation makes me think of a temporal model, but bowls can be represented as static without losing their defining features. In short, no model=no understanding is my claim. This is an attempt to make the word knowledge more precise because it can mean many things.
I then go on to describe why you need a more high fidelity model to represent the defining features of someone's brain state evolving over some time period. The human brain is obviously incapable of that. Although an exact subatomic model of a bowl contains a lot of information too, you can abstract much more of it away without losing anything essential.
I'd also like to correct that I make no claims that science, or anything, is subjective. Conversely, I'm claiming that subjectivity is not a fundamental concept and we can taboo it in discussions like these.
Comment by soerenmind on Agents That Learn From Human Behavior Can't Learn Human Values That Humans Haven't Learned Yet · 2018-08-28T14:24:01.722Z · score: 1 (1 votes) · LW · GW
Here's how I'd summarize my disagreement with the main claim: Alice is not acting rationally in your thought experiment if she acts like Bob (under some reasonable assumptions). In particular, she is doing pure exploitation and zero (value-)exploration by just maximizing her current weighted sum. For example, she should be reading philosophy papers.
Comment by soerenmind on Shaping economic incentives for collaborative AGI · 2018-06-30T16:19:29.604Z · score: 4 (3 votes) · LW · GW
(Btw I think you may have switched your notation from theta to x in section 5.)
Comment by soerenmind on Shaping economic incentives for collaborative AGI · 2018-06-30T16:10:14.719Z · score: 4 (3 votes) · LW · GW
Neat paper, congrats!
Comment by soerenmind on Big Advance in Infinite Ethics · 2017-12-11T03:30:00.376Z · score: 2 (1 votes) · LW · GW
Warning: I haven't read the paper so take this with a grain of salt
Here's how it would go wrong if I understand it right: For exponentially discounted MDPs there's something called an effective horizon. That means everything after that time is essentially ignored.
You pick a tiny . Say (without loss of generality) that all utilities . Then there is a time with . So the discounted cumulative utility from anything after is bounded by (which follows from the limit of the geometric series). That's an arbitrarily small constant.
We can now easily construct pairs of sequences for which LDU gives counterintuitive conclusions. E.g. a sequence which is maximally better than for any until the end of time but ever so slightly worse (by ) for .
So anything that happens after is essentially ignored - we've essentially made the problem finite.
Exponential discounting in MDPs is standard practice. I'm surprised that this is presented as a big advance in infinite ethics as people have certainly thought about this in economics, machine learning and ethics before.
Btw, your meta-MDP probably falls into the category of Bayes-Adaptive MDP (BAMDP) or Bayes-Adaptive partially observable MDP (BAPOMDP) with learned rewards.
Comment by soerenmind on The Three Levels of Goodhart's Curse · 2017-10-28T15:14:19.000Z · score: 0 (0 votes) · LW · GW
(also x-posted from https://arbital.com/p/goodharts_curse/#subpage-8s5)
Another, speculative point: If and were my utility function and my friend's, my intuition is that an agent that optimizes the wrong function would act more robustly. If true, this may support the theory that Goodhart's curse for AI alignment would be to a large extent a problem of defending against adversarial examples by learning robust features similar to human ones. Namely, the robust response may be because me and my friend have learned similar robust, high-level features; we just give them different importance.
Comment by soerenmind on The Three Levels of Goodhart's Curse · 2017-10-28T15:05:23.000Z · score: 0 (0 votes) · LW · GW
(x-posted from Arbital ==> Goodhart's curse)
On "Conditions for Goodhart's curse":
It seems like with AI alignment the curse happens mostly when V is defined in terms of some high-level features of the state, which are normally not easily maximized. I.e., V is something like a neural network where is the state.
Now suppose U' is a neural network which outputs the AI's estimate of these features. The AI can then manipulate the state/input to maximize these features. That's just the standard problem of adversarial examples.
So it seems like the conditions we're looking for are generally met in the common setting were adversarial examples do work to maximize some loss function. One requirement there is that the input space is high-dimensional.
So why doesn't the 2D Gaussian example go wrong? [This is about the example from Arbital ==> Goodhart's Curse where there is no bound on and ]. There's no high-level features to optimize by using the flexibility of the input space.
On the other hand, you don't need a flexible input space to fall prey to the winner's curse. Instead of using the high flexibility of the input space you use the 'high flexibility' of the noise if you have many data points. The noise will take any possible value with enough data, causing the winner's curse. If you care about a feature that is bounded under the real-world distribution but noise is unbounded, you will find that the most promising-looking data points are actually maximizing the noise.
There's a noise-free (i.e. no measurement errors) variant of the winner's curse which suggests another connection to adversarial examples. If you simply have data points and pick the one that maximizes some outcome measure, you can conceptualize this as evolutionary optimization in the input space. Usually, adversarial examples are generated by following the gradient in the input space. Instead, the winner's curse uses evolutionary optimization.
Comment by soerenmind on There's No Fire Alarm for Artificial General Intelligence · 2017-10-16T17:42:27.324Z · score: 20 (8 votes) · LW · GW
People had previously given Go as an example of What You See Before The End.
Who said this? I only heard of the prediction that it'll take 10+ years, made only a few years before 2015.
Comment by soerenmind on Updating towards the simulation hypothesis because you think about AI · 2016-03-22T10:12:04.303Z · score: 0 (0 votes) · LW · GW
I guess an answer to "Given that my name is Alex, what is the probability that my name is Alex?" could be that the hypothesis is highly selected. When you're still the soul that'll be assigned to a body, looking at the world from above, this guy named Alex won't stick out because of his name. But the people who will influence the most consequential event in the history of that world will.
Comment by soerenmind on Updating towards the simulation hypothesis because you think about AI · 2016-03-06T17:31:02.366Z · score: 0 (0 votes) · LW · GW
"The core of this objection is that not only you are special, but that everybody is special"
Is your point sort of the same thing I'm saying with this? "Everyone has some things in their life that are very exceptional by pure chance. I’m sure there’s some way to deal with this in statistics but I don’t know it."
Comment by soerenmind on Rational diet: Eating insects? · 2016-03-03T21:02:01.222Z · score: 1 (1 votes) · LW · GW
http://reducing-suffering.org/the-importance-of-insect-suffering/
http://reducing-suffering.org/why-i-dont-support-eating-insects/
Warning: Bringing this argument at a dinner party with trendsetting, ecologically conscious consumers might cost you major idiosyncrasy credits.
Comment by soerenmind on Results of a One-Year Longitudinal Study of CFAR Alumni · 2015-12-12T21:50:47.554Z · score: 3 (3 votes) · LW · GW
"We have been conducting a peer survey of CFAR workshop participants, which involves sending surveys about the participant to 2 of their friends, both before the workshop and again approximately one year later. We are in the final stages of data collection on those surveys, and expect to begin the data analysis later this month."
Comment by soerenmind on Take the EA survey, help the EA movement grow and potentially win $250 to your favorite charity · 2015-11-30T11:39:22.402Z · score: 1 (1 votes) · LW · GW I'd also like to see the results on LW this year! Comment by soerenmind on Take the EA survey, help the EA movement grow and potentially win$250 to your favorite charity · 2015-11-30T11:38:48.579Z · score: 2 (2 votes) · LW · GW
How about promoting in Main? Was promoted last year IIRC. I think the overlap of the communities can justify this. Disclosure: I'm biased as an aspiring effective altruist.
Comment by soerenmind on Open thread, Oct. 26 - Nov. 01, 2015 · 2015-11-05T17:40:58.445Z · score: 1 (1 votes) · LW · GW
The EA Global videos will be officially released soon. You can already watch them here, but I couldn't find the xrisk video among them. I'd suggest just asking the speakers for their slides. I remember two of them were Nate Soares and Owen Cotton-Barrat.
Comment by soerenmind on Working at MIRI: An interview with Malo Bourgon · 2015-11-02T12:17:42.770Z · score: 0 (0 votes) · LW · GW
Thanks for mentioning that. For some reason the link changed from effective-altruism.com to lesswrong.com when I copy-pasted the article. Fixed!
Comment by soerenmind on Effective Altruism from XYZ perspective · 2015-07-12T23:29:14.701Z · score: 0 (0 votes) · LW · GW
I don't get your argument there. After all, you might e.g. value other EAs instrumentally because they help members of other species. That is, you intrinsically value an EA like anyone else, but you're inclined to help them more because that will translate into others being helped.
Comment by soerenmind on Test Your Calibration! · 2015-05-25T08:15:24.698Z · score: 2 (2 votes) · LW · GW
The best calibration IMO exercises I was able to find (which also work for non-Americans) can be downloaded from the website of How to Measure Anything.
http://www.howtomeasureanything.com/
Comment by soerenmind on Meetup : Utrecht: a critique of effective altruism · 2014-12-28T23:01:13.632Z · score: 0 (0 votes) · LW · GW
There has been a little mixup! This topic will be on January 18th. The meetup on January 4th will be this one: http://www.meetup.com/LWEANL/events/218834861/. Imma is going to change it as soon as she has internet access, which will have to wait until the start of the new year.
Comment by soerenmind on Meetup : Utrecht: Debiasing techniques · 2014-09-20T12:02:48.820Z · score: 0 (0 votes) · LW · GW
Hi efim!
I updated the description in the link on meetup.com that Imma gave. To give you some extra detail, we'll talk about: Which biases are hard/easy to correct? When does knowing about the existence of a bias help and when not? Which debiasing techniques are there (reversal test, consider the opposite, reference class forecasting...) and what are generally useful guidelines to stay rational? We'll run an experiment on confidence intervals and do a mini-RCT with a debiasing technique that hasn't been scientifically validated yet. I'll also share some links that I believe are useful to correct our decision-making errors.
Hope to see you there and sorry for the late reply!
Comment by soerenmind on Fun and Games with Cognitive Biases · 2014-09-03T09:03:54.033Z · score: 0 (0 votes) · LW · GW
Does anyone know how to search for Anki decks by their key? I was thinking the number at the end of a link (e.g. ankiweb.net/shared/info/1458237580) would work, but it doesn't contain letters.
Comment by soerenmind on Meetup : Utrecht: Improve your productivity · 2014-08-29T16:27:41.324Z · score: 2 (2 votes) · LW · GW
The topic will be productivity as decided at the last meetup.
Comment by soerenmind on Sugar and motivation · 2014-06-16T10:36:37.038Z · score: 1 (1 votes) · LW · GW
Yes there is research that supports that high glycemic index (GI) food such as sweets and white bread deteriorate willpower. The main mechanism that is made responsible for this is the drop in blood sugar a few hours after consumption. This post has some points on it: http://lesswrong.com/lw/cmc/book_summary_willpower_by_baumeister_tierney/
More info on this can be found in the book 'The Willpower Instinct' by Kelly Mcgonigal. She says the research most supports plant-based diets and low-GI diets. Evidence for the former is better.
Furthermore I think I've heard a few things about 'hyper rewards' such as pornography, drugs and sweet food generally reducing motivation. This makes sense since these rewards were not available in ancestral times. The brain responds to strong stimuli by downregulating the neural pathways required for motivation. This should be easy to google.
Comment by soerenmind on Meetup : Utrecht- Brainstorm and ethics discussion at the Film Café · 2014-05-29T19:06:06.816Z · score: 1 (1 votes) · LW · GW
Edited. My bad, thanks for pointing out.
Comment by soerenmind on 2014 Survey of Effective Altruists · 2014-05-12T11:46:06.125Z · score: 1 (1 votes) · LW · GW
When I had already started the survey as I said I wouldn't have minded to fill in more. If it had been previously announced to be a longer survey I imagine the initial barrier would have been higher for many though.
Personally, I would have filled it in even if it was longer since I think it's important. But with a different topic that could have made me not fill it in.
Comment by soerenmind on 2014 Survey of Effective Altruists · 2014-05-08T12:39:35.840Z · score: 5 (5 votes) · LW · GW
Just to let you guys know: Like with the LW survey, I wouldn't have minded to fill in an optional 'extended section'. I imagine you made the survey shorter in order not to scare people off.
Comment by soerenmind on Meetup : Utrecht · 2014-05-01T22:38:42.437Z · score: 0 (0 votes) · LW · GW
Edited the post since we got the location sorted!
"We have a new location now. We're meeting at the headquaters of Seats2meet (Cyberdigma), which is in the Trindeborch building at Catharijnesingel 49-55 (7th floor). You can see the entry on this map https://goo.gl/maps/q027I"
Comment by soerenmind on Meetup : Utrecht · 2014-04-20T10:36:26.388Z · score: 0 (0 votes) · LW · GW
We also have a facebook group: https://www.facebook.com/groups/262932060523750/ And a meetup.com group: http://www.meetup.com/LWEANL/
Comment by soerenmind on Meetup : Utrecht: More on effective altruism · 2014-04-01T20:01:18.117Z · score: 0 (0 votes) · LW · GW
Imma Six asked me to post this here. She's taking the time to prepare a pittle presentation for us so thanks a lot!
"I will prepare an introduction for a discussion about ethical career choice. I think that's an important topic that many of us are thinking about. To get a high quality discussion, please have a look at http://80000hours.org/ before the meetup to see what it's about. 80.000hours is an organisation that does research and helps people to have a high impact career. | 2019-09-21 23:27:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6741963624954224, "perplexity": 4245.308058316873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574710.66/warc/CC-MAIN-20190921231814-20190922013814-00255.warc.gz"} |
https://getpractice.com/subjects/maths/complex-numbers?page=2002 | ### Complex Numbers
goals
Let $z_1$ = 18 + 83i, $z_2$ = 18 + 39i, ana $z_3$= 78 + 99i. where i = $\sqrt-1$. Let z be a unique comlpex number with the properties that $\dfrac{z_3 - z_1}{z_2 - z_1}$ $\cdot$ $\dfrac{z - z_2}{z - z_3}$ is a real number and the imaginary part of the size z is the greatest possible.
If ${z}_{1}$ and ${z}_{2}$ are two non-zero complex numbers such that $\left| \cfrac { { z }_{ 1 } }{ { z }_{ 2 } } \right| =2$ and $arg(\left( { z }_{ 1 }{ z }_{ 2 } \right) =\cfrac { 3\pi }{ 2 }$, then $\cfrac { \bar { { z }_{ 1 } } }{ { z }_{ 2 } }$ is equal | 2020-09-29 00:28:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8514618873596191, "perplexity": 248.06716671141893}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401617641.86/warc/CC-MAIN-20200928234043-20200929024043-00011.warc.gz"} |
https://plainmath.net/11134/determine-whether-the-following-are-polynomials-plus-plus-plus-sqrt-plus | # Determine whether the following are polynomials or not:2x^2 + 7x+ 1,1/(x^3 + 2),6,8x – 1,sqrt(2x + 5).
Determine whether the following are polynomials or not: $$2x^2 + 7x+ 1, 1/(x^3 + 2), 6, 8x – 1, \sqrt{2x + 5)}$$
• Questions are typically answered in as fast as 30 minutes
### Plainmath recommends
• Get a detailed answer even on the hardest topics.
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FieniChoonin
$$2x^2 + 7x+ 1$$ - polynomial $$1/(x^3 + 2)$$– not polynomial 6 – polynomial 8x – 1 - polynomial $$\sqrt{2x + 5}$$ - not polynomial | 2021-12-02 00:11:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6961749196052551, "perplexity": 3346.667952291539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964361064.58/warc/CC-MAIN-20211201234046-20211202024046-00000.warc.gz"} |
http://wikiwaves.org/Diffraction_Transfer_Matrix_for_Infinite_Depth | # Diffraction Transfer Matrix for Infinite Depth
## Introduction
This is an extension of the Diffraction Transfer Matrix (which only applied to finite depth) to infinite depth. This is based upon the results in Peter and Meylan 2004.
## Calculation of the diffraction transfer matrix for bodies of arbitrary geometry
To calculate the diffraction transfer matrix in infinite depth, we require the representation of the Infinite Depth, Free-Surface Green Function in cylindrical eigenfunctions,
$G(r,\theta,z;s,\varphi,c) = \frac{\mathrm{i}\alpha}{2} \, \mathrm{e}^{\alpha (z+c)} \sum_{\nu=-\infty}^{\infty} H_\nu^{(1)}(\alpha r) J_\nu(\alpha s) \mathrm{e}^{\mathrm{i}\nu (\theta - \varphi)}$
$+ \frac{1}{\pi^2} \int\limits_0^{\infty} \psi(z,\eta) \frac{\eta^2}{\eta^2+\alpha^2} \psi(c,\eta) \sum_{\nu=-\infty}^{\infty} K_\nu(\eta r) I_\nu(\eta s) \mathrm{e}^{\mathrm{i}\nu (\theta - \varphi)} \mathrm{d}\eta,$
$r \gt s$, given by Peter and Meylan 2004b where
$\psi(z,\eta) = \cos \eta z + \frac{\alpha}{\eta} \sin \eta z.$
We assume that we have represented the scattered potential in terms of the source strength distribution $\varsigma^j$ so that the scattered potential can be written as
$\phi_j^\mathrm{S}(\mathbf{y}) = \int\limits_{\Gamma_j} G (\mathbf{y},\mathbf{\zeta}) \, \varsigma^j (\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta}, \quad \mathbf{y} \in D,$
where $D$ is the volume occupied by the water and $\Gamma_j$ is the immersed surface of body $\Delta_j$. The source strength distribution function $\varsigma^j$ can be found by solving an integral equation. The integral equation is described in Wehausen and Laitone 1960. Substituting the eigenfunction expansion of the Green's function (green_inf) into the above integral equation, the scattered potential can be written as
$\phi_j^\mathrm{S}(r_j,\theta_j,z) = \mathrm{e}^{\alpha z} \sum_{\nu = - \infty}^{\infty} \bigg[ \frac{\mathrm{i}\alpha}{2} \int\limits_{\Gamma_j} \mathrm{e}^{\alpha c} J_\nu(\alpha s) \mathrm{e}^{-\mathrm{i}\nu \varphi} \varsigma^j(\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta} \bigg] H_\nu^{(1)} (\alpha r_j) \mathrm{e}^{\mathrm{i}\nu \theta_j}$
$+ \int\limits_{0}^{\infty} \psi(z,\eta) \sum_{\nu = - \infty}^{\infty} \bigg[ \frac{1}{\pi^2} \frac{\eta^2 }{\eta^2 + \alpha^2} \int\limits_{\Gamma_j} \psi(c,\eta) I_\nu(\eta s) \mathrm{e}^{-\mathrm{i}\nu \varphi} \varsigma^j({\mathbf{\zeta}}) \mathrm{d}\sigma_{\mathbf{\zeta}} \bigg] K_\nu (\eta r_j) \mathrm{e}^{\mathrm{i}\nu \theta_j} \mathrm{d}\eta,$
where $\mathbf{\zeta}=(s,\varphi,c)$ and $r\gts$. This restriction implies that the eigenfunction expansion is only valid outside the escribed cylinder of the body.
The columns of the diffraction transfer matrix are the coefficients of the eigenfunction expansion of the scattered wavefield due to the different incident modes of unit-amplitude. The elements of the diffraction transfer matrix of a body of arbitrary shape are therefore given by
$({\mathbf B}_j)_{pq} = \frac{\mathrm{i}\alpha}{2} \int\limits_{\Gamma_j} \mathrm{e}^{\alpha c} J_p(\alpha s) \mathrm{e}^{-\mathrm{i}p \varphi} \varsigma_q^j(\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta}$
and
$({\mathbf B}_j)_{pq} = \frac{1}{\pi^2} \frac{\eta^2}{\eta^2 + \alpha^2} \int\limits_{\Gamma_j} \psi(c,\eta) I_p(\eta s) \mathrm{e}^{-\mathrm{i}p \varphi} \varsigma_q^j(\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta}$
for the propagating and the decaying modes respectively, where $\varsigma_q^j(\mathbf{\zeta})$ is the source strength distribution due to an incident potential of mode $q$ of the form
$\phi_q^{\mathrm{I}}(s,\varphi,c) = \mathrm{e}^{\alpha c} H_q^{(1)} (\alpha s) \mathrm{e}^{\mathrm{i}q \varphi}$
for the propagating modes, and
$\phi_q^{\mathrm{I}}(s,\varphi,c) = \psi(c,\eta) K_q (\eta s) \mathrm{e}^{\mathrm{i}q \varphi}$
for the decaying modes.
## The diffraction transfer matrix of rotated bodies
For a non-axisymmetric body, a rotation about the mean centre position in the $(x,y)$-plane will result in a different diffraction transfer matrix. We will show how the diffraction transfer matrix of a body rotated by an angle $\beta$ can be easily calculated from the diffraction transfer matrix of the non-rotated body. The rotation of the body influences the form of the elements of the diffraction transfer matrices in two ways. Firstly, the angular dependence in the integral over the immersed surface of the body is altered and, secondly, the source strength distribution function is different if the body is rotated. However, the source strength distribution function of the rotated body can be obtained by calculating the response of the non-rotated body due to rotated incident potentials. It will be shown that the additional angular dependence can be easily factored out of the elements of the diffraction transfer matrix.
The additional angular dependence caused by the rotation of the incident potential can be factored out of the normal derivative of the incident potential such that
$\frac{\partial \phi_{q\beta}^{\mathrm{I}}}{\partial n} = \frac{\partial \phi_{q}^{\mathrm{I}}}{\partial n} \mathrm{e}^{\mathrm{i}q \beta},$
where $\phi_{q\beta}^{\mathrm{I}}$ is the rotated incident potential. Since the integral equation for the determination of the source strength distribution function is linear, the source strength distribution function due to the rotated incident potential is thus just given by
$\varsigma_{q\beta}^j = \varsigma_q^j \, \mathrm{e}^{\mathrm{i}q \beta}.$
This is also the source strength distribution function of the rotated body due to the standard incident modes.
The elements of the diffraction transfer matrix $\mathbf{B}_j$ are given by equations in the previous section. Keeping in mind that the body is rotated by the angle $\beta$, the elements of the diffraction transfer matrix of the rotated body are given by
$(\mathbf{B}_j^\beta)_{pq} = \frac{\mathrm{i}\alpha}{2} \int\limits_{\Gamma_j} \mathrm{e}^{\alpha c} J_p(\alpha s) \mathrm{e}^{-\mathrm{i}p (\varphi+\beta)} \varsigma_{q\beta}^j(\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta},$
and
$(\mathbf{B}_j^\beta)_{pq} = \frac{1}{\pi^2} \frac{\eta^2}{\eta^2 + \alpha^2} \int\limits_{\Gamma_j} \psi(c,\eta) I_p(\eta s) \mathrm{e}^{-\mathrm{i}p (\varphi+\beta)} \varsigma_{q\beta}^j(\mathbf{\zeta}) \mathrm{d}\sigma_\mathbf{\zeta},$
for the propagating and decaying modes respectively. Thus the additional angular dependence caused by the rotation of the body can be factored out of the elements of the diffraction transfer matrix. The elements of the diffraction transfer matrix corresponding to the body rotated by the angle $\beta$, $\mathbf{B}_j^\beta$, are given by
$(\mathbf{B}_j^\beta)_{pq} = (\mathbf{B}_j)_{pq} \, \mathrm{e}^{\mathrm{i}(q-p) \beta}.$
As before, $(\mathbf{B})_{pq}$ is understood to be the element of $\mathbf{B}$ which corresponds to the coefficient of the $p$th scattered mode due to a unit-amplitude incident wave of mode $q$. This equation applies to propagating and decaying modes likewise. | 2017-08-16 19:15:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8866773247718811, "perplexity": 295.29363619053765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886102393.60/warc/CC-MAIN-20170816191044-20170816211044-00212.warc.gz"} |
https://www.peertechz.com/Agricultural-Science-Food-Technology/IJASFT-3-126.php | ##### Authors: Ojiya Emmanuel Ameh1*, Okoh Abo Sunday1, Mamman Andekujwo Baajon2 and Ngwu Jerome Chukwuemeka3
Affiliation(s):
1Lecturer, Department of Economics, Federal University Wukari, Nigeria
2Lecturer, Department of Economics, Federal University Wukari, Taraba State, Nigeria
3Lecturer, Department of Economics, Enugu State University of Science and Technology (ESUT), Enugu State, Nigeria
Dates:
Received: 14 October, 2017; Accepted: 26 October, 2017; Published: 28 October, 2017
*Corresponding author:
Ojiya Emmanuel Ameh, Lecturer, Department of Economics, Federal University Wukari, Nigeria, E-mail: @;
Citation:
Ojiya EA, Okoh SA, Mamman AB, Chukwuemeka NJ (2017) An Empirical Analysis of the effect of Agricultural Input on Agricultural Productivity in Nigeria.Int J Agric Sc Food Technol 3(4): 077-085. DOI: 10.17352/2455-815X.000026
© 2017 Ojiya EA, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Keywords:
Agricultural productivity; Credit to farmers; Tractors; Government spending; OLS
The main object of this study is to investigate the effect of Agricultural input on Agricultural productivity in Nigeria from 1990 to 2016 using secondary annual time series data sourced from World Bank database (2016) and Central Bank of Nigeria Statistical Bulletin (2016). The methodology adopted for the study was first and foremost unit root test by Augmented Dickey-Fuller (ADF) approach; a test for long-run relationship (Johansen cointegration), Granger causality test and then the Ordinary Least Squares (OLS) multiple regression method. Variables in the model were both stationary as well as exhibited long-run equilibrium relationship. Empirical OLS regression result revealed an inverse relationship between government expenditure and agricultural output. Deriving from the findings, the study recommended the following for policy implementation: The Nigerian government should put in place policies and modalities that will encourage existing banks (both commercial and agricultural banks) to make credit facilities readily available to farmers with personnel assigned to monitor and ensure that such funds are judiciously used for the purpose which it is taken; Government must provide funds to acquire sophisticated farm tools (harvesters, tractors, herbicides, fertilizer etc.) and as well build irrigation, dams, storage facilities and establish food processing industries across the country to enable farmers increase productivity, process and preserve their food stuff; Finally, government spending on agricultural sector must of a necessity be increased. The present lackluster and uninspiring attitude of government to management of appropriated funds must change. Corrupt civil servants, contractors and bureaucrats who divert and misappropriate allocated funds for the growth of the sector must be punished to serve as a deterrent to other intending treasury looters. The various financial crimes commissions such as EFCC and ICPC should be strengthen to do this.
### Introduction
##### Background to the study
Agricultural development is one of the most powerful tools to end extreme poverty, boost shared prosperity and feed a projected 9.7 billion people by 2050. Growth in the agriculture sector is two to four times more effective in raising incomes among the poorest compared to other sectors. 2016 analyses found that 65% of poor working adults made a living through agriculture. Agriculture is also crucial to economic growth: in 2014, it accounted for one-third of global gross-domestic product (GDP) [1]. Agriculture is the science or practice of farming, including cultivation of the soil for the growing of crops and the rearing of animals to provide food, wool, and other products while agricultural productivity is increase in per capita output of agricultural produce (Stamp 1970). To meet the needs of a world population expected to reach nine billion by 2050, agricultural production will need to increase by at least 60 percent [2]. Due to its relative importance and future gains, it is known to be a major source of raw materials for processing industries in the manufacturing of finished goods and services. It produces about 80% of all manufacturing industries’ raw materials used in the production of finished goods in most economies of the world. For many years, productivity has been a key issue of agricultural development strategies because of its impact on economic growth and development. It is also a known fact that the easiest means through which mankind can get out of poverty to a condition of relative material affluence is by increasing agricultural productivity. Productivity improvements create the wealth that can be used to meet the needs of the future.
Problem Statement: The development of agriculture in Nigeria has been slow despite various agricultural policies and programmes formulated by successive administration in the country. In fact, the government recognized the unhealthy condition of Nigerian agricultural sector since 1970, and has formulated and introduced a number of programmes and strategies aimed at remedying this situation. These measures included the setting up of large-scale mechanized farms by state and federal government, introduction of scheme such as the River Basin Development Authority. Other measures include, National Accelerated Food Production (NAFP), Operation Feed the Nation (OFN), Green Revolution (GRP) and the Directorate for Food, Roads and Rural Infrastructure, the New Nigerian Agricultural Policy etc. [3]. In addition to these measures, financial measures such as the establishment of agricultural credit scheme were introduced by successive governments. Inspite of these measures, the development of the agricultural sector has been slow and the impact of this sector on economic growth and development has been minimal. In fact, the former Minister of Agriculture, Dr. Akinwunmi Adesina once lamented that the import bill for food in Nigeria is exceptionally high and it is growing at an unsustainable rate of 11% per annum. Ironically, Nigeria is importing what it can produce in abundance. This trend is hurting Nigerian farmers and displacing local production [4]. In the same vein, Senator Ibikunle Amosun once lamented the high rate of importation of food in Nigeria, describing it as a shame that the giant of Africa imports what it eats [5]. It is in view of the foregoing that the present paper intends to examine the effect of agricultural inputs on agricultural productivity in Nigeria between 1990 to 2016, using an econometric approach of Ordinary Least Squares Regression.
Study Objectives: Specifically, the study is designed to achieve the following objectives in addition to the broad objective earlier stated.
(i) Examine the effect of Agricultural machinery (tractors) on agricultural productivity in Nigeria;
(ii) Determine the impact of Agricultural credit (loans) on agricultural productivity in Nigeria;
(iii)Examine the causality effect of government expenditure on agriculture on agricultural productivity.
Research Hypothesis: The study shall adopt statistical testing criteria to examine the veracity of the following hypothesis:
Ho1: Agricultural machinery has no significant effect on agricultural productivity in Nigeria;
Ho2: Agricultural credit has no significant impact on agricultural productivity in Nigeria;
Ho3: Government expenditure on Agriculture has no causality effect on agricultural productivity in Nigeria.
Justification for the study: The study is justified because it will provide an insight into how effective both fiscal and monetary instruments designed by the Central Bank of Nigeria and the Nigerian government helped in achieving the overall objectives of the nation’s agricultural policy which is first and foremost tailored towards achieving food security and exportable surplus for enhanced economic growth and development. Furthermore, the study is expected to serve as a reference material for future research as well as guide government in its future policy designs towards achieving country-wide expected goals.
The remainder of this study is sectionalized as follows: Part two is dedicated to theoretical and empirical review. In part three, the data and methodology adopted for the study is discussed. Part four presents the empirical findings, while part five provides the conclusion and policy recommendations of the study.
### Literature Review
##### Agricultural productivity
According to Fulginiti and Perrin [6], as cited in Amire and Arigbede [2], agricultural productivity refers to the output produced by a given level of inputs in the agricultural sector of a given economy. More formally, it can be defined as “the ratio of value of total farms outputs to the value of total inputs used in farm production” [7], as cited in [8]. Put differently, agricultural productivity is measured as the ration of final output, in appropriate units to some measure of inputs.
##### An overview of agricultural policies in Nigeria
In the view of Nwagbo [9], agricultural policy-making in Nigeria has been through changes over time. During each phase, the characteristics of policy have reflected the roles expected of the sector and the relative endowment of resources. Institutions were created while others were disbanded depending on the exigencies of the time. Hence the marketing Boards gave way to commodity boards and production companies; the River Basin development Authorities have been modified to meet changing objectives; small-scale irrigation schemes are receiving more attention than the earlier large versions; agricultural extension by the State Ministries of Agriculture has given way to extension by the Agricultural Development Project (ADP). Other measures include, National Accelerated Food Production (NAFP), Operation Feed the Nation (OFN), Green Revolution (GRP) and the Directorate for Food, Roads and Rural Infrastructure and finally, the New Nigerian Agricultural Policy. The first national policy on agriculture was adopted in 1988 and was expected to remain valid for about fifteen years, that is, up to year 2000. Nigeria’s agricultural policy is the synthesis of the framework and action plans of government designed to achieve overall agricultural growth and development. The policy aims at the attainment of self-sustaining growth in all the sub-sectors of agriculture and the structural transformation necessary for the overall socio-economic development of the country as well as the improvement in the quality of life of Nigerians.
##### According to ARCN (2016) [10], the broad policy objectives Include:
• Attainment of self-sufficiency in basic food commodities With particular reference to those which consume considerable shares of Nigeria’s foreign exchange and for which the country has comparative advantage in local production;
• Increase in production of agricultural raw materials to meet the growth of an expanding industrial sector;
• Increase in production and processing of exportable Commodities with a view to increasing their foreign exchange earning capacity and further diversifying the country’s export base and sources of foreign exchange earnings;
• Modernization of agricultural production, processing, Storage and distribution through the infusion of improved technologies and management so that agriculture can be more responsive to the demands of other sectors of that Nigerian economy;
• Creation of more agricultural and rural employment Opportunities to increase the income of farmers and rural dwellers and to productively absorb an increasing labour force in the nation;
• Protection and improvement of agricultural land resources and preservation of the environment for sustainable agricultural production;
• Establishment of appropriate institutions and creation of administrative organs to facilitate the integrated development and realization of the country’s agricultural potentials.
##### Theoretical framework
The theoretical framework of this study is built on the Cobb-Douglas production function. This theoretical model was applied in extant literature including Ekwere [11]. In economics, the Cobb-Douglas functional form of production function is widely used to represent the relationship of an output to input. It was proposed by Knut (1926) and tested against statistical evidence by Charles Cobb and Paul Douglas in. In 1928, Charles Cobb and Paul Douglas [12], published a study in which they modeled the growth of the American economy during the period 1899 to 1922. They considered a simplified view of the economy in which production output was determined by the amount of labour involved and the amount of capital invested. While there are many other factors affecting economic performance, their model proved to be remarkably accurate. The function they used to model production was of the form:
P(L,K) = bLα Kβ
Where:
P = Total production (the monetary value of all goods produced in a year);
L = Labor input (the total number of person-hours worked in a year);
K = Capital input (the monetary worth of all machinery, equipment, and buildings);
b = Total factor productivity; α and β are the output elasticities of labour and capital, respectively. These values are constants determined by available technology. Output elasticity measures the responsiveness of output to a change in levels of either labour or capital used in production, ceteris paribus.
In agricultural production, efficient allocation of farm resources helps farmers to attain their objectives. It avails farmers the opportunity of improving their productivity and income. At the microeconomic level efficient allocation of farm resources (farmland, credit facilities, fertilizer, tractors and labour, among others) help farmers to contribute to food production, employment creation, industrial raw materials and export product for foreign exchange earnings. According to Olayide and Heady [7], agricultural productivity is synonymous with resource productivity which is the ratio of total output to the resource/inputs being considered. According to Olujenyo (2008), the production function could be expressed in different functional forms such as Cobb Douglas, linear, quadratic, polynomials and square root polynomials, semilog and exponential functions. However, the Cobb Douglas functional form is commonly used for its simplicity and flexibility coupled with the empirical support it has received from data for various industries and countries.
### Materials and Methods
This study adopts a non-experimental research design approach. The data used were obtained from secondary sources and therefore, no sampling was done neither was any sampling technique adopted in the process of research.
##### Sources of data collection
The data for this study were secondary in nature and sourced from the publication of World Bank Database and Central Bank of Nigeria (CBN) [13], statistical bulletin for various issues. The data spans the period 1990 to 2016 (26 years). The data from this period present a considerable degree of freedom that is necessary to capture the effect of explanatory variables on the dependent variables. Furthermore, data sourced from the World Bank can be reliable because many studies have employed the data published by this institution for econometric purposes due to its reliability.
##### Variables adopted for the study
Variables adopted for the study are Ag-output (proxy for agricultural productivity) used as dependent variable to be regressed against Ag-Machine (proxy for Agricultural machinery, tractors per 100sq.km of arable land), Ag-Exp (proxy for government expenditure on agriculture) and gross domestic product as independent variables respectively. Gross Domestic Product is included as a control variable to avoid the challenge of variable omission and model misspecification.
##### Method of data analysis
The method of data analysis include first and foremost unit root test using Augmented Dickey-Fuller (ADF); a test for long-run relationship (Johansen cointegration), Granger causality test and then the ordinary least square (OLS) multiple regression method to determine the effect of the independent variables in the model on the dependent variable. The study made use of E-views 8.0, econometric software for the analysis.
Unit root test: To study the stationarity properties of time series, the Augmented Dickey–Fuller test (ADF) (Dickey & Fuller, 1981) is employed in this study. The test involves estimating the regression.
The model for the ADF unit root framework is as follows:
ΔXt = αt1+ pt + βXt-1 +$\sum _{i=1}^{k-1}$ γiΔXt-1 + εt ……. Eq 3.1
In the above equation, α is the constant and ρ is the coefficient of time trend. X is the variable under consideration. In this study, the variables include log(FDI), log(GDP-pc), log(INVT), and log(MAN). Δ is the first-difference operator; t is a time trend; and εt is a stationary random error. The test for a unit root is conducted on the coefficient of Xt-1 in the above regression. If the coefficient, β, is found to be significantly different from zero (β ≠ 0), the null hypothesis that the variable X contains a unit root problem is rejected, implying that the variable does not have a unit root. The optimal lag length is also determined in the ADF regression and is selected using Akaike information criterion (AIC).
Johansen cointegration test: This paper attempts to use the Johansen maximum likelihood cointegration test (Johansen, 1988) to determine long-run relationships among the variables being investigated. In examining causality, the Granger causality analysis is also performed. In order to obtain good results from the test, selecting the optimal lag length is so important. The Johansen cointegration framework takes its starting point in the vector autoregressive (VAR) model of order p given by:
yt = A1yt-1 + …+ Apyt-p + βxt + εt ……. Eq 3.2
where yt is a vector of endogenous variables and A represents the autoregressive matrices. xt is the deterministic vector and B represents the parameter matrices. εt is a vector of innovations and p is the lag length. The VAR can be re-written as:
Δyt = Πyt-1 +$\sum _{i=1}^{p-1}$ ΓiΔyt-1 + βXt + εt ……. Eq 3.3
where Π = Σ Ai – I and ΓI Σ A I=1 j=i+1j
The matrix Π contains the information regarding the long-run coefficients of the yt variables in the vector. If all the endogenous variables in yt are cointegrated at order one, the cointegrating rank, r, is given by the rank of Π = αβ, where the elements of _ are known as the corresponding adjustment of coefficient in the VEC model and β represents the matrix of parameters of the cointegrating vector. To indicate the number of cointegrating rank, two likelihood ratio (LR) test statistics, namely the trace and the maximum Eigen value tests (Johansen, 1988), are used to determine the number of cointegrating vectors. The two tests are defined as:
ƛtrace = −T Σi=r+1 log(1-ƛi) and ƛmax = -Tlog(1- ƛi+1), …. Eq 3.4
where ƛi denotes the estimated values of the characteristic roots obtained from the estimated Π, and T is the number of observations. The first statistic test tests H0 that the number of cointegrating vector is less than or equal to r against the alternative hypothesis of k cointegrating relations, where k is the number of endogenous variables, for r = 0,1, … , k−1. The alternative of k cointegrating relations corresponds to the case where none of the series has a unit root. The second test tests the null that the number of cointegrating vectors is r, against the alternative hypothesis of 1 + r cointegrating vectors.
Granger causality based on the vector error correction model: In order to identify the long-run relationship among the series under study, the Johansen co-integration test must be done. However, the test does not indicate anything about the direction of causality among the variables in the system; therefore, the Granger causality analysis must be done. If the series are co-integrated, the VECM-based Granger causality analysis is an appropriate technique used to determine the long-run and the short-run relationships (Engle & Granger, 1987) based on the following forms:
Causality Model: y = [log(Ag-output), log(Ag-Exp]
Δlog(Ag-output)t = β1,t +$\sum _{i=1}^{n-1}$ β11j, Δlog(Ag-output)t-j +$\sum _{i=1}^{n-1}$ β11j, Δlog(Ag-Exp)t-j + δ1EC + ε1t Eqtn 3.5
Δlog(Ag-Exp)t = β2,t +$\sum _{i=1}^{n-1}$ β21,j, Δlog(Ag-Exp)t-j +$\sum _{i=1}^{n-1}$ β22,j Δlog(Ag-Output)t-j + δ2EC + ε2t Eqtn 3.6
The coefficients of the ECt−1 term indicate causality in the long run and the joint F test of the coefficients of the first-differenced independent variables confirms short-run causality. Δ denotes first-difference operator. μ1t and μ2t are the stationary disturbance terms for the equations. n is the order of the VAR, which is translated into lag of n−1 in the error correction mechanism. δ1 and δ2 denote the coefficients of long-run Granger causality for equations (3.5) and (3.6), respectively. In this paper, the short-run causality is determined through the error correction based on vector error correction model.
Ordinary Least Square (OLS): To examine the effect of agricultural inputs on agricultural productivity in Nigeria using the Ordinary Least Squares (OLS) technique the following model is specified. The model for this study is specified in both linear and non-linear relationship as follows:
The functional form of the model is specified hereunder
Ag-output = f(Ag-Machine, Ag-Credit, Ag-Exp, Gdp) .... Eq 3.7
The mathematical form of the model is specified below
Ag-output = f(Ag-Machine + Ag-Credit + Ag-Exp + Gdp)... Eq 3.8
The statistical form of the model is
Ag-output = βo + β1(Ag-Machine) + β2(Ag-Credit) + β3(Ag-Exp) + β4(Gdp) … Eq 3.9
In order to capture the stochastic term µt of the variables, the explicit form of the models is given in econometric form below:
Ag-output = βo + β1(Ag-Machine) + β2(Ag-Credit) + β3(Ag-Exp) + β4(Gdp) + µt ….. Eq 3.10
The estimated models are further transformed into log-linear form. This is aimed at reducing the problem of multi-collinearity among the variables in the models. Thus the log-linear models are specified as shown below:
LnAg-output = βo1(LnAg-Machine) + β2(LnAg-Credit) + β3(LnAg-Exp) + β4(LnGdp) + µt … Eq 3.11
β1> o, β2 > 0, β3 > 0, β4 > 0, β5 > 0
Where,
Ag-output = Agricultural Productivity
Ag-Machine = Agricultural machinery, tractors per 100 sq. km of arable land),
Ag-Credit = Agric credit (proxied by credit to the private sector)
Ag-Exp = Government Expenditure on Agriculture
Gdp = Gross Domestic Product
µi = Stochastic or error term
Ln = Natural logarithms
βo = Intercept parameter
β1 - β1 = Slope parameters
##### Economic A priori
A priori, it is expected that the independent variables agricultural machineries, agricultural credit, government expenditure on agriculture and gross domestic product should be positively related to the dependent variable (agricultural productivity), all things being equal.
### Results and Discussion
##### Data description and sources
This paper used secondary data (time series data). Empirical investigation was carried out on the basis of the sample covering the period 1990 to 2016. Data for the study was sourced from the database of World Bank and Central Bank of Nigeria Statistical Bulletin (2016) respectively. The variables studied include Ag-Output (proxy for agricultural productivity in Nigeria), Ag-Machine (Agricultural machinery, tractors per 100 sq. km of arable land), Ag-Credit ((proxied by credit to the private sector), Ag-Exp (proxy for Government Expenditure on Agriculture) and GDP (proxy for economic growth in Nigeria). Below is the data presentation (Table 1).
1. ##### Table 1:
Data Presentation on Ag-Output, Ag-Machine, Ag-Credit, Ag-Exp, GDP (1990-2016).
##### ADF unit root test results
In order to begin the dynamic (long-term) regression analysis, the study begins with the unit root test for the stationarity of the variables in each of the models using the Augmented Dickey-Fuller (ADF) since it adjusts properly for autocorrelation (Table 2).
1. ##### Table 2:
The results of the unit root test using the Augmented Dickey-Fuller (ADF) test as shown above revealed that no variable was stationary at levels. Hence, the null hypothesis of non-stationarity cannot be rejected at levels. However, at first difference, all variables were stationary. That means at first difference the variables were integrated of order I (1).
##### Co-Integration tests
This is used to test for the existence of long-run relationship between dependent and independent variables. The Johansen co-integration test was conducted on the selected variables. The result is as tabulated in table 3.
1. ##### Table 3:
Johansen Cointegration Test Results.
The Johansen cointegration test result as tabulated above shows that the number of co-integrating vectors and the degree of freedom adjusted version of the Eigen value and trace statistics is used and these test statistics strongly rejects the null hypothesis of no co-integration in favour of all the co-integration relationships at the 1% significant level among the variables. Therefore, the variables used in the model all exhibited long term characteristics (i.e. they can walk together without deviating from an established path in the long-run), hence we can safely conclude that the series Ag-output, Ag-machine, Ag-credit, Ag-Exp and GDP are cointegrated.
From the normalized equation (Ag-output) = f(Ag-machine, Ag-credit, Ag-Exp and GDP) above, the Ag-output coefficient of 1.00000 indicates that the level of agricultural productivity (Ag-output) in Nigeria is 1 when other variables are zero. This shows that all things being equal, a unit increase in agricultural machines (tractors), agricultural credit, government expenditure to agriculture and gross domestic product will lead to a corresponding increase in Ag-output respectively.
1. ##### Table 4:
Empirical OLS Regression Results.
LnAg-output = βo1(LnAg-Machine) + β2(LnAg-Credit) + β3(LnAg-Exp) + β4(LnGdp) + µt
The regression result above shows the effect of Agricultural Input on Agricultural Productivity in Nigeria between 1990-2016. The goodness of fit of the model as indicated by an R-squared of 94 percent shows a good fit of the model. An adjusted R-Squared value of 93 percent indicated that the model fits the data well, the total variation in the observed behaviour of Agricultural output is jointly explained by variation in agricultural machinery (tractors used), agricultural credit, government expenditure on agriculture sector and gross domestic product 94%. The remaining 6% is accounted for by the stochastic error term.
To test for the overall significance of the model, the ANOVA of the F-statistics is used. To test for the individual statistical significance of the parameters, the t-statistics of the respective variables were considered. The statistical test of significance of the model estimates is conducted by employing the student’s t-test statistical analysis at five per cent significance level. The critical t-test value from the table is 2.021. The decision therefore requires that the tabulated value be compared with the calculated value. If the critical value of the t-test is greater than the t-test calculated at five per cent significance level, the parameter estimated is statistically insignificant and vice versa. From the analysis of this study, the variables (agricultural machine, agricultural credit, gross domestic product) were found to be statistically insignificant. Their calculated t-test values of 1.375287, 0.600000 and 1.728521 respectively. The conclusion was reached because these values were all less than the threshold 2.021 critical value at 5% significance level set by theory. Only the coefficient of gross domestic product was statistically significant in relation to the dependent variable in the model. It has a t-statistic value of 2.059017 higher than the table value of 2.021. The implication is that, only the coefficient of gross domestic product was capable of bringing significant changes to agricultural productivity in Nigeria during the referenced period. The a priori expectations about the signs of the parameter estimates were also considered. Here, Ag-machine, Ag-credit and GDP entered the model with a positive sign. Only the coefficient of government expenditure on agriculture was inversely related to the dependent variable. By implication, a one percent increase in the use of agricultural machineries (tractors) and the availability of agricultural credit to farmers amounted to a 2.5% and 0.013% increase in agricultural productivity in Nigeria respectively.
Similarly, the coefficient of gross domestic product is positively related to agricultural productivity. The result shows that a 38 billion naira increase in agricultural productivity is as a result of a rise in gross domestic product (economic growth) in Nigeria between 1990 to 2016. On the contrary, the coefficient of government expenditure on agriculture appeared with a negative sign in relation to the dependent variable. This implies that government spending on the sector has not impacted positively on agricultural output in Nigeria within the period studied. Explicitly stated, a 17 billion naira reduction in output in agricultural productivity is as a result of insufficient government spending in the sector.
##### Granger causality test
Below is the output of the Pairwise Granger causality test. To reject the null hypothesis formulated, the probability value of the F-statistic must be less than 0.05. If the probability value of the F-statistic is greater than 0.05 significance level, the null hypothesis is not rejected, thus concluding that the variable under consideration does not Granger cause the other. The extract below is in conformity with the above stated rules (i.e. the F-statistic p-value is less than 0.05% significance level) (Table 5).
1. ##### Table 5:
Pairwise Granger Causality Extract.
The variable of interest here is AG_EXP (government expenditure on agriculture) and AG_OUTPUT (agricultural productivity). From the extracts above, it is revealed that there is a unidirectional (one-way) causation between agriculture output and government spending on the sector within the period studied.
##### Post-estimation / Diagnostic test
Diagnostic checks are crucial in this study to ascertain if there is a problem in the residuals from the estimation of a model; it is an indication that the model is not efficient; as such estimates from such model may be biased and misleading. The model was therefore examined for normality, serial correlation, heteroscedasticity and stability (Table 6).
1. ##### Table 6:
Breusch-Godfrey Serial Correlation LM Test:
In terms of the econometrics test, the Breusch – Godfrey Serial Correlation LM test was employed in this study to check for the presence or otherwise of first order serial autocorrelation in the model using 2 periods lag of the Observed R-squared at 5% level of significance.
##### Autocorrelation Hypothesis
H0: Residuals are not serially correlated/There is absence of serial correlation
H1: Residuals are serially correlated/There is presence of serial correlation (Table 7).
1. ##### Table 7:
Heteroskedasticity Test: Breusch-Pagan-Godfrey.
Looking at the probability value of the Observed R-Squared in the serial correlation test presented above, it is evident that the value is 0.0514 (5%) which is equal to 5%, hence, we reject the null hypothesis (Ho) and accept the alternative hypothesis (H1), and therefore conclude that there is presence of first order serial autocorrelation in the model or the residuals are serially-correlated.
Furthermore, from the Heteroskedasticity Test: Breusch-Pagan-Godfrey test result presented in the table above, both the probabilities of F-statistic (0.1306) and the observed R-squared (0.1264) are higher than 0.05 indicating the absence of heteroscedasticity. Therefore, the errors are homoscedastic. The result of CUSUMQ stability test indicates that the model is stable. This is because the CUSUMQ lines fall in-between the two 5% lines. Finally, the normality test adopted is the Jarque-Bera (JB) statistics. Looking at the histogram, the study observes that the residual is normally distributed because of the insignificant probability value of 0.425481. Both the Histogram and CUSUMQ graphs are presented below: (Figures 1,2).
1. ##### Figure 1:
Normality Test
CUSUMQ Test.
##### Conclusion / Recommendations
The role of agriculture in any economy is indeed significant and cannot be over-emphasized. It is one of the most dominant sectors in any economy as the very survival of every nation depends on how well or bad its agricultural sub-sector is managed. It is indeed not just a major source of livelihood for its citizens but a source of foreign exchange earner to the nation. This is because apart from providing food for the teeming population of the economy, it is the only source of raw materials that serves as input for other sectors in their production process. It is in recognition of this pivotal role played by the agricultural sector of the economy that this study becomes imperative. The main object of the study is to investigate the effect of Agricultural input on Agricultural productivity in Nigeria from 1990 to 2016 using secondary annual time series data sourced from World Bank database [1], and Central Bank of Nigeria Statistical Bulletin [13]. The methodology adopted for the study was first and foremost unit root test using Augmented Dickey-Fuller (ADF); a test for long-run relationship (Johansen cointegration), Granger causality test and then the Ordinary Least Squares (OLS) multiple regression method to determine the effect of the independent variables in the model on the dependent variable.
Variables in the model were both stationary as well as exhibited long-run equilibrium relationship. Empirical findings revealed that agricultural productivity has positive influence on government expenditure in the sector but not the other way round. This finding is in line with the earlier OLS regression result of an inverse relationship between government expenditure and agricultural output. It further negates the formulated hypothesis in section one of this study that “there is no causality relationship between government expenditure on agriculture and agricultural output”. Since empirical findings supports hypotheses earlier formulated for this study, it is thus concluded that government spending in agricultural sector does not contribute to positive increases in output from the sector. Secondly, agricultural machinery has no significant effect on agricultural productivity in Nigeria and finally, agricultural credit has no significant impact on agricultural productivity in Nigeria between 1990 to 2016.
This study thus aligns with the work of Ajie, Ojiya & Mamman [14], that successive administrations in Nigeria has not seen reason to come close to fulfilling internationally benchmarked budgetary recommendations for the agricultural sector since her independence. This is a disturbing trend. While sister African countries like Ivory Coast, Ghana and Ethiopia dedicates a larger percentage of their budget to the agricultural sub-sector, Nigeria with a spiraling population of over 180 million mouths to feed has displayed a carefree attitude towards recommendations from international agencies on the need to give priority to the sector in terms of funding. A country’s future in terms of food security is a function of government’s commitment to making its agriculture work, and working, very effectively and efficiently towards delivering expected dividends.
The following is therefore recommended for policy implementation:
(a) If the Nigeria government really want to attain the objective of self-sufficiency in food production, the government need to put in place policy and modalities that will encourage existing banks (both commercial and agricultural banks) to make credit facilities readily available to farmers with personnel assigned to monitor and ensure that such funds are judiciously used for the purpose which it is taken.
(b) Furthermore, government must provide funds to acquire sophisticated farm tools (harvesters, tractors, herbicides, fertilizer etc) and as well build irrigation, dams, storage facilities and establish food processing industries across the country to enable farmers increase productivity, process and preserve their food stuff.
(c) Finally, government spending on agricultural sector must of a necessity be increased. Similarly, the present lackluster and uninspiring attitude of government to management of appropriated funds must also change. Corrupt civil servants, contractors and bureaucrats who divert and misappropriate allocated funds for the growth of the sector must be punished to serve as deterrent to other intending treasury looters. The various financial crimes commissions such as EFCC and ICPC should be strengthened to do this.
1. World Bank (2016) World Development Indicators 2016. Washington, DC. © World Bank. Link: https://goo.gl/m4qjxq
2. Amire CM, Arigbede TO (2016) The Effect of Agricultural Productivity on Economic Growth in Nigeria. Journal of Advances in Social Sciences and Humanities 2. Link: https://goo.gl/sy3x88
3. Uniamikogbo SO, Enoma AI (2001) The Impact of monetary policy on manufacturing sector in Nigeria: an empirical analysis. The Nigerian Journal of Economic and Financial Review 3: 37-45.
4. Punch (2017) Punch Newspaper Limited, Lagos, Nigeria. Link: https://goo.gl/Y3EUWP
5. (2017) Vanguard Newspaper. Link: https://goo.gl/A5CRpN
6. Fulginiti LE, Richard KP (1998) Agricultural Productivity in Developing Countries, University of Nebraska Faculty Publications. Link: https://goo.gl/T19aAG
7. Olayide SO, EO Heady (1982) Introduction to Agricultural Production Economics. First Edition. Ibadan: Ibadan University Press.
8. Iwala OS (2013) The measurement of productive and technical efficiency of cassava farmers in the North-Central Zone of Nigeria. Research Journal of Agriculture and Environmental Management 2: 323-331. Link: https://goo.gl/HRtgtU
9. Nwagbo EC (2012) agricultural policy in Nigeria: challenges for the 21st Century Journal of Agriculture, Food, Environment and Extension 1. Link: https://goo.gl/7FMN5e
10. ARCN (2016) Publication of Agricultural Research Council of Nigeria, Abuja, Nigeria Link: https://goo.gl/mCUUKF
11. Ekwere GE (2016) The Effect of Agricultural Cooperatives on Cassava Production in Awka North L.G.A. of Anambra State, Nigeria Academia Journal of Agricultural Research 4: 616-624. Link: https://goo.gl/rjBfra
12. Cobb CW, Douglas PH (1928) "A Theory of Production" (PDF). American Economic Review. 18 (Supplement): 139–165. Retrieved 6 October 2017 Link: https://goo.gl/5T5FTG
13. Central Bank of Nigeria (2016) Statistical Bulletin, 2016 edition. Link: https://goo.gl/ZSWyQU
14. Ajie HA, Ojiya EA, Mamman AB (2017) The Effect of Household Income on Agricultural Productivity in Nigeria: An Econometric Analysis. International Journal of Business and Applied Social Science 3. Link: https://goo.gl/abxF16 | 2018-10-23 15:08:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4640927016735077, "perplexity": 3671.6939659614613}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516194.98/warc/CC-MAIN-20181023132213-20181023153713-00387.warc.gz"} |
https://www.zbmath.org/?q=an%3A1168.05023 | # zbMATH — the first resource for mathematics
Adjacent vertex distinguishing total coloring of graphs with lower average degree. (English) Zbl 1168.05023
Summary: An adjacent vertex distinguishing total coloring of a graph $$G$$ is a proper total coloring of $$G$$ such that any pair of adjacent vertices are incident to distinct sets of colors. The minimum number of colors required for an adjacent vertex distinguishing total coloring of $$G$$ is denoted by $$\chi_a''(G)$$. Let $$\text{mad}(G)$$ and $$\Delta(G)$$ denote the maximum average degree and the maximum degree of a graph $$G$$, respectively.
In this paper, we prove the following results:
(1)
If $$G$$ is a graph with mad$$(G) < 3$$ and $$\Delta(G) \geq 5$$, then $$\Delta(G) + 1\leq \chi_a''(G)\leq\Delta(G) + 2$$, and $$\chi_a''(G) = \Delta(G)+2$$ if and only if $$G$$ contains two adjacent vertices of maximum degree;
(2)
If $$G$$ is a graph with mad$$(G) < 3$$ and $$\Delta(G)\leq 4$$, then $$\chi_a''(G)\leq 6$$,
(3)
If $$G$$ is a graph with mad$$(G) < \frac83$$ and $$\Delta(G)\leq 3$$, then $$\chi_a'(G) \leq 5$$.
##### MSC:
05C15 Coloring of graphs and hypergraphs
Full Text: | 2021-05-09 13:08:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5960099101066589, "perplexity": 229.85202778882217}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988986.98/warc/CC-MAIN-20210509122756-20210509152756-00029.warc.gz"} |
http://www.help.paligo.net/en/the-element-structuremenu.html?2018052311 | # Getting Started
The Element Structure menu gives you the control you need over the elements in the topic.
Depending on where your cursor is, it will present a number of actions you can perform on the content (the "elements") in your topic.
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This allows you to precisely delete exactly what you want, and the editor will highlight and show text in red for the content you will delete. | 2018-05-23 09:19:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34369969367980957, "perplexity": 937.6748167320277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865468.19/warc/CC-MAIN-20180523082914-20180523102914-00405.warc.gz"} |
http://tex.stackexchange.com/tags/bookmarks/new | # Tag Info
2
If all long section, subsection etc. titles should appear in the bookmarks, perhaps the easiest way is to shift the \toclevel@... to something far beyond the real levels, say add 1000, add the normal contentsline and use and explicit \pdfbookmark[...]{...}{...}. \documentclass{article} \usepackage{xpatch} \makeatletter \xpatchcmd{\@sect}{% ...
3
Simply add bookmarksopen=true for the default bookmarks-open to also expand them. I will refrain from posting a screenshot as my viewer ignores all these options anyway and acroread simply takes forever to even consider possibly thinking about sometime in the distant future opening a file. (But the OP confirmed that it works in Adobe's viewer.) ...
2
According to the documentation of bookmark you can use the open option; if you want to set the level, you can say openlevel=<level>; so \usepackage[open,openlevel=1]{bookmark} will show something like whereas the simple open option will show Tested with Skim and Adobe Reader on Mac OS X.
2
toutf16 function should be changed to this: \directlua{ function toutf16(str) tex.write(string.char(92) .. "376" .. string.char(92) .. "377") for c in string.utfvalues(str) do if c < 0x10000 then tex.write(string.char(92) .. string.format("%03o", c / 256) .. string.char(92) .. string.format("%03o", c % 256)) ...
Top 50 recent answers are included | 2016-02-09 04:05:09 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8145478367805481, "perplexity": 6211.68911281224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701156448.92/warc/CC-MAIN-20160205193916-00257-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10304873-selective-electrochemical-oxidative-coupling-methane-mediated-sr2fe1-its-chemical-stability | Selective electrochemical oxidative coupling of methane mediated by Sr2Fe1.5Mo0.5O6-δ and its chemical stability
Abstract
Efficient conversion of methane to value-added products such as olefins and aromatics has been in pursuit for the past few decades. The demand has increased further due to the recent discoveries of shale gas reserves. Oxidative and non-oxidative coupling of methane (OCM and NOCM) have been actively researched, although catalysts with commercially viable conversion rates are not yet available. Recently,$${{{{{{{\mathrm{Sr}}}}}}}}_2Fe_{1.5 + 0.075}Mo_{0.5}O_{6 - \delta }$$${\mathrm{Sr}}_{2}F{e}_{1.5+0.075}M{o}_{0.5}{O}_{6-\delta }$(SFMO-075Fe) has been reported to activate methane in an electrochemical OCM (EC-OCM) set up with a C2 selectivity of 82.2%1. However, alkaline earth metal-based materials are known to suffer chemical instability in carbon-rich environments. Hence, here we evaluated the chemical stability of SFMO in carbon-rich conditions with varying oxygen concentrations at temperatures relevant for EC-OCM. SFMO-075Fe showed good methane activation properties especially at low overpotentials but suffered poor chemical stability as observed via thermogravimetric, powder XRD, and XPS measurements where SrCO3was observed to be a major decomposition product along with SrMoO3and MoC. Nevertheless, our study demonstrates that electrochemical methods could be used to selectively activate methane towards partial oxidation products such as ethylene at low overpotentials while higher applied biases result in the complete oxidation of methane to carbon dioxide and water.
Authors:
; ; ;
Publication Date:
NSF-PAR ID:
10304873
Journal Name:
Communications Chemistry
Volume:
4
Issue:
1
ISSN:
2399-3669
Publisher:
Nature Publishing Group
National Science Foundation
##### More Like this
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3. Abstract
Recently, room temperature superconductivity was measured in a carbonaceous sulfur hydride material whose identity remains unknown. Herein, first-principles calculations are performed to provide a chemical basis for structural candidates derived by doping H3S with low levels of carbon. Pressure stabilizes unusual bonding configurations about the carbon atoms, which can be six-fold coordinated as CH6entities within the cubic H3S framework, or four-fold coordinated as methane intercalated into the H-S lattice, with or without an additional hydrogen in the framework. The doping breaks degenerate bands, lowering the density of states at the Fermi level (NF), and localizing electrons in C-H bonds. Low levels of CH4doping do not increaseNFto values as high as those calculated for$$Im\bar{3}m$$$Im\overline{3}m$-H3S, but they can yield a larger logarithmic average phonon frequency, and an electron–phonon coupling parameter comparable to that ofR3m-H3S. The implications of carbon doping on the superconducting properties are discussed.
4. Abstract
The device concept of ferroelectric-based negative capacitance (NC) transistors offers a promising route for achieving energy-efficient logic applications that can outperform the conventional semiconductor technology, while viable operation mechanisms remain a central topic of debate. In this work, we report steep slope switching in MoS2transistors back-gated by single-layer polycrystalline PbZr0.35Ti0.65O3. The devices exhibit current switching ratios up to 8 × 106within an ultra-low gate voltage window of$$V_{{{\mathrm{g}}}} = \pm \! 0.5$$${V}_{g}=±\phantom{\rule{0ex}{0ex}}0.5$V and subthreshold swing (SS) as low as 9.7 mV decade−1at room temperature, transcending the 60 mV decade−1Boltzmann limit without involving additional dielectric layers. Theoretical modeling reveals the dominant role of the metastable polar states within domain walls in enabling the NC mode, which is corroborated by the relation between SS and domain wall density. Our findings shed light on a hysteresis-free mechanism for NC operation, providing a simple yet effective material strategy for developing low-power 2D nanoelectronics.
5. Abstract
Hemiwicking is the phenomena where a liquid wets a textured surface beyond its intrinsic wetting length due to capillary action and imbibition. In this work, we derive a simple analytical model for hemiwicking in micropillar arrays. The model is based on the combined effects of capillary action dictated by interfacial and intermolecular pressures gradients within the curved liquid meniscus and fluid drag from the pillars at ultra-low Reynolds numbers$${\boldsymbol{(}}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{7}}}{\boldsymbol{\lesssim }}{\bf{Re}}{\boldsymbol{\lesssim }}{{\bf{10}}}^{{\boldsymbol{-}}{\bf{3}}}{\boldsymbol{)}}$$$\left({10}^{-7}\lesssim \mathrm{Re}\lesssim {10}^{-3}\right)$. Fluid drag is conceptualized via a critical Reynolds number:$${\bf{Re}}{\boldsymbol{=}}\frac{{{\bf{v}}}_{{\bf{0}}}{{\bf{x}}}_{{\bf{0}}}}{{\boldsymbol{\nu }}}$$$\mathrm{Re}=\frac{{v}_{0}{x}_{0}}{\nu }$, wherev0corresponds to the maximum wetting speed on a flat, dry surface andx0is the extension length of the liquid meniscus that drives the bulk fluid toward the adsorbed thin-film region. The model is validated with wicking experiments on different hemiwicking surfaces in conjunction withv0andx0measurements using Water$${\boldsymbol{(}}{{\bf{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{25}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{28}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\left({v}_{0}\approx 2\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}25\phantom{\rule{0ex}{0ex}}µm\lesssim {x}_{0}\lesssim 28\phantom{\rule{0ex}{0ex}}µm\right)$, viscous FC-70$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{0.3}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{18.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\boldsymbol{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{38.6}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\left({v}_{0}\approx 0.3\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}18.6\phantom{\rule{0ex}{0ex}}µm\lesssim {x}_{0}\lesssim 38.6\phantom{\rule{0ex}{0ex}}µm\right)$and lower viscosity Ethanol$${\boldsymbol{(}}{{\boldsymbol{v}}}_{{\bf{0}}}{\boldsymbol{\approx }}{\bf{1.2}}\,{\bf{m}}{\boldsymbol{/}}{\bf{s}}{\boldsymbol{,}}\,{\bf{11.8}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{\lesssim }}{{\bf{x}}}_{{\bf{0}}}{\boldsymbol{\lesssim }}{\bf{33.3}}\,{\boldsymbol{\mu }}{\bf{m}}{\boldsymbol{)}}$$$\left({v}_{0}\approx 1.2\phantom{\rule{0ex}{0ex}}m/s,\phantom{\rule{0ex}{0ex}}11.8\phantom{\rule{0ex}{0ex}}µm\lesssim {x}_{0}\lesssim 33.3\phantom{\rule{0ex}{0ex}}µm\right)$. | 2022-11-26 11:38:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 23, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5119651556015015, "perplexity": 5015.416741915359}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446706291.88/warc/CC-MAIN-20221126112341-20221126142341-00452.warc.gz"} |
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Serious role of non-quarantined COVID-19 patients for random walk simulations
Abstract
The infectious disease (COVID-19) causes serious damages and outbreaks. A large number of infected people have been reported in the world. However, such a number only represents those who have been tested; e.g. PCR test. We focus on the infected individuals who are not checked by inspections. The susceptible-infected-recovered (SIR) model is modified: infected people are divided into quarantined (Q) and non-quarantined (N) agents. Since N-agents behave like uninfected people, they can move around in a stochastic simulation. Both theory of well-mixed population and simulation of random-walk reveal that the total population size of Q-agents decrease in spite of increasing the number of tests. Such a paradox appears, when the ratio of Q exceeds a critical value. Random-walk simulations indicate that the infection hardly spreads, if the movement of all people is prohibited ("lockdown"). In this case the infected people are clustered and locally distributed within narrow spots. The similar result can be obtained, even when only non-infected people move around. However, when both N-agents and uninfected people move around, the infection spreads everywhere. Hence, it may be important to promote the inspections even for asymptomatic people, because most of N-agents are mild or asymptomatic.
Introduction
The infectious disease (COVID-19) caused by the coronavirus (SARS-CoV-2) is spreading to a large number of individuals1,2,3. According to the WHO report, many people died by COVID-194. It is an urgent worldwide issue to break the chain of COVID-19 infection. Two major protection approaches are known: prevention and isolation. The former is a prepared protection for a person, such as masks and hand-washing. Vaccination has been thought to be the most effective method of prevention5,6. In contrast, the isolation (or segregation) means the cut-off of contact between infected and non-infected people. An example is quarantine to put an infected person into hospital. Another example is lockdown: mobilities of people are prohibited7,8. Very recently, vaccination is found to be the most effective method for COVID-196,9. However, in England, Republic of Chile and State of Arizona, the infection is widespread, even though the vaccination rate is above 40%4,6. Moreover, much time is still needed for vaccines to become widespread. Various types of infection control measures will be necessary.
We apply agent-based model (ABM) used in complex systems10,11,12,13,14,15,16,17. For infectious diseases, ABM is one of fundamental tools18,19,20. The epidemic spreading on lattices and networks have been studied by many authors20,21,22,23,24,25. In the present article, we explore the effect of mobility (random walk) on the isolation of infectious people. Infected people are divided into two groups, quarantined (Q) and non-quarantined (N) agents. The former can be detected by inspections; e.g. PCR test.
A certain proportion of infected people become severe, such as pneumonia3,26. In many countries, hospital beds are very crowded. To suppress the epidemic spreading, it should be important to quarantine the infected individuals. From the early stage of the epidemic, the importance of asymptomatic infection has been pointed out because the asymptomatic patient also behaves as a cryptic source of spreading infection27. Thus, a large number of people have being inspected by PCR test in the world. However, the application of PCR test for no symptom person has been restricted in Japan because the medical diagnostic PCR test resources were too poor to promote the test in the early period of the epidemic. Major academic societies in Japan claimed that PCR testing was basically not recommended for asymptomatic or mildly ill individuals28. Such claims raise some problems. (1) Is it okay to leave the infected person unchecked? (2) Does the number of Q-agents (PCR-positive) always increase with the number of tests? It has been reported for COVID-19 that most infected people have mild or no symptoms3,29. Because such people behave like uninfected people, they have considerably high infectivity30,31,32,33. This may be a distinct feature of COVID-19 never observed for the previous coronaviruses, SARS and MERS. We carry out simulations of random walk to report N-agents play a major role for epidemic spreading.
So far, various epidemic models have been presented for analyzing an epidemic spread34,35,36,37. In most cases, the epidemic of influenza and other infectious diseases has been theoretically explained by SIR model38,39,40,41 that considers susceptible (S), infected (I), and recovered (R) people. Interactions are represented as follows:
$${\text{S}} + {\text{I}} \to {\text{I}} + {\text{I}}\;\;\;\;\;\;\left( {{\text{rate}}:\beta } \right)$$
(1a)
$${\text{I}} \to {\text{R}}\;\;\;\;\;\;\left( {{\text{rate}}:\gamma } \right)$$
(1b)
where β and γ represent infection and recovery rates, respectively. The spatial and network versions of SIR model is studied extensively in various fields42,43,44,45,46. In the present paper, we modify the SIR model as shown in Fig. 1a. Infected people are divided into quarantined (Q) and non-quarantined (N) agents. Similarly, the recovered (plus dead) people are also divided into $${\mathrm{R}}_{\mathrm{Q}}$$ and $${\mathrm{R}}_{\mathrm{N}}$$. Such a division may give us valuable information, because only the population size of Q (or $${\mathrm{R}}_{\mathrm{Q}}$$) is announced in public. It is important to know the behavior of N.
Method
We study epidemic spreading on a lattice. Each cell is either empty (O) or occupied by an individual (agent). The agent takes one of five states: S, Q, N, $${\mathrm{R}}_{\mathrm{Q}}$$ and $${\mathrm{R}}_{\mathrm{N}}$$. Symbols and parameters are listed in Table 1. Interactions are represented as follows:
$${\text{S}} + {\text{N}} \to i + {\text{N}}\;\;\;\;\;\;\;({\text{rate}}:\beta_{{\text{N}}} )$$
(2a)
$${\text{S}} + {\text{Q}} \to i + {\text{Q}}\;\;\;\;\;\;({\text{rate}}:\beta_{{\text{Q}}} )$$
(2b)
$${\text{N}} \to {\text{R}}_{{\text{N}}} \;\;\;\;\;({\text{rate}}:\gamma_{{\text{N}}} )$$
(2c)
$${\text{Q}} \to {\text{R}}_{{\text{Q}}} \;\;\;\;\;({\text{rate}}:\gamma_{{\text{Q}}} )$$
(2d)
where $$i$$ denotes an infected agent ($$i=\mathrm{N},\mathrm{ Q}$$). The parameters $${\beta }_{\mathrm{i}}$$ and $${\gamma }_{\mathrm{i}}$$ denotes the infection and recovery rates of $$i$$, respectively. We introduce "quarantine ratio" $$q$$ which denotes the ratio of Q among all infected agents (see Fig. 1a). If $$q=1$$, every infected agent is confirmed to be infected by testing (e.g. PCR test). In contrast, if $$q=0$$, no infected agents are tested. We consider both $${\mathrm{R}}_{\mathrm{N}}$$ and $${\mathrm{R}}_{\mathrm{Q}}$$ have no infectivity. When the agent Q stays in hospital, $${\beta }_{\mathrm{Q}}$$ takes a negligible value. However, when Q is waiting (or staying) at home, it is not negligible. In the present article, we assume $${\beta }_{\mathrm{N}}>{\beta }_{\mathrm{Q}}$$ as discussed later.
Simulations are carried out either by local or global interaction. Initially, few infected individuals are randomly positioned, and we put empty cells with density $${\rho }_{0}$$; in this article we put $${\rho }_{0}=0.2$$. Simulation for local interaction is performed as follows.
1. (i)
Infection processes (2a) and (2b): we randomly choose a single cell. If the cell is S and its nearest-neighbor site is occupied by N or Q, then S change to infected agent $$i$$ with probability $${\beta }_{i}$$. We put $$i$$=Q by probability $$q$$, but $$i$$=N by probability $$(1-q)$$. Here, boundaries are periodic.
2. (ii)
Recovery and death processes (2c) and (2d): we randomly select one cell. If the site is N, it changes to $${\mathrm{R}}_{\mathrm{N}}$$ with rate $${\gamma }_{\mathrm{N}}$$. Similarly, if the selected site is Q, it becomes $${\mathrm{R}}_{\mathrm{Q}}$$ with rate $${\gamma }_{\mathrm{Q}}$$.
3. (iii)
Random walk: we randomly select two neighboring cells. If the first and second chosen cells are respectively the cell of agent $$j$$ and empty cell ($$j=\mathrm{S},\mathrm{N},\mathrm{Q},{\mathrm{R}}_{\mathrm{N}},{\mathrm{R}}_{\mathrm{Q}}$$), then both cells are exchanged with migration rate $${m}_{j}$$. Hence, the agent $$j$$ moves into the empty cell with rate $${m}_{j}$$. Note that we have $${m}_{j}=2$$, when only step (iii) is repeated twice.
In the simulation, the unit of time $$t$$ is measured by Monte Carlo step (MCS)14,15. Namely $$t$$ increases by 1 MCS, when steps (i)–(iii) are repeated by 104 times; note 104 is the total cell number of lattice. The simulation is continued until the system reaches a steady state. In the case of global interaction, infection process (i) occurs between any pair of cells. We can skip the random walk in the simulation of global interaction, because all agents randomly distribute.
The well-mixed population for epidemic model is given by mean-field theory (MFT):
$$dS/dt=-{\beta }_{N}SN-{\beta }_{\mathrm{Q}}SQ$$
(3a)
$$dN/dt=(1-q){\beta }_{\mathrm{N}}SN+(1-q){\beta }_{\mathrm{Q}}SQ-{\gamma }_{N}N$$
(3b)
$$\mathrm{dQ}/\mathrm{dt}=q{\beta }_{\mathrm{N}}SN+q{\beta }_{\mathrm{Q}}SQ-{\gamma }_{\mathrm{Q}}Q$$
(3c)
$$d{R}_{N}/dt={\gamma }_{\mathrm{N}}N$$
(3d)
$$d{R}_{Q}/dt={\gamma }_{\mathrm{Q}}Q$$
(3e)
Here the densities of S, N, Q, $${\mathrm{R}}_{\mathrm{N}}$$ and $${\mathrm{R}}_{\mathrm{Q}}$$ are shown in their italics. The total densities of agents are given by $$(1-{\rho }_{0})$$, where $${\rho }_{0}$$ is the density of empty cell. If $$q=0$$ and $${\beta }_{\mathrm{Q}}=0$$, then Eqs. (3a3e) agrees with those for SIR model. The threshold phenomenon is well known for SIR model34,38. When $${\beta }_{N}/{\gamma }_{N}$$ > 1/S(0), the disease spreads. Similarly, if $$q=1$$ and $${\beta }_{\mathrm{N}}=0$$, the disease spreads for $${\beta }_{\mathrm{Q}}/{\gamma }_{\mathrm{Q}}$$ > 1/S(0).
Results
Results for global interaction
The simulation results of global interaction agree with those predicted by MFT. This is because the global interaction corresponds to the assumption of well-mixed population. First, the numerical calculation for global interaction is reported. In Fig. 1b, a typical population dynamics for MFT are displayed. Model parameters used in all figures are listed in Table S1 (see Supplementary file). At the final equilibrium ($$t\to \infty$$), both densities N $$(\infty )$$ and Q $$(\infty )$$ become zero, but $${R}_{N}(\infty )$$ and $${R}_{Q}(\infty )$$ take constant values. Namely, agents N and Q always change to $${\mathrm{R}}_{\mathrm{N}}$$ and $${\mathrm{R}}_{\mathrm{Q}}$$, respectively. Hereafter, we will call $${R}_{N}\left(\infty \right)+{R}_{Q}\left(\infty \right)$$ "total infection" and $${R}_{Q}(\infty )$$ "apparent infection". The former accurately indicates the degree of infection, but its measurement may be impossible. Realistically, only the latter index is announced in public.
In Fig. 2, both total and apparent infections are depicted against the ratio $$q$$. We find a threshold phenomenon as observed for SIR model34,38. When the ratio $${\beta }_{N}/{\gamma }_{N}$$ takes a small value, the disease never spreads. In contrast, when $${\beta }_{\mathrm{N}}/{\gamma }_{\mathrm{N}}$$ takes a large value, the infection can spread. The threshold of $${\beta }_{N}/{\gamma }_{N}$$ becomes small, when $${\beta }_{\mathrm{Q}}/{\gamma }_{\mathrm{Q}}$$ takes a large value. We also find that the apparent infection ($${R}_{Q}$$) takes a maximum value at $$q={q}_{MAX}$$, where $${0<q}_{MAX}<1$$. When $${q<q}_{MAX}$$, the total number of Q increases with increasing q. On the contrary, when $${q>q}_{MAX}$$, it decreases in spite of the increase of q. The value of $${q}_{MAX}$$ is found to be increased with the increase of $${\beta }_{N}/{\gamma }_{N}$$. It should be emphasized that the total infection monotonically decreases with increasing q. Hence, isolating the infected agents is effective to suppress the infection. In this paper, we put $${\gamma }_{N}{=\gamma }_{\mathrm{Q}}$$; this is because both ratios $${\beta }_{N}/{\gamma }_{N}$$ and $${\beta }_{\mathrm{Q}}/{\gamma }_{\mathrm{Q}}$$ are found to be more important parameters than $${\gamma }_{N}$$ and $${\gamma }_{\mathrm{Q}}$$. Numerical calculation reveals that both total and apparent infections increase with the increase of either $${\beta }_{N}/{\gamma }_{N}$$ or $${\beta }_{\mathrm{Q}}/{\gamma }_{\mathrm{Q}}$$.
Results for random-walk simulation
Simulation results for local interaction are described. To know the relation between local and global simulations, we first assume the special case that the migration rate ($${m}_{j})$$ of agent $$j$$ takes the same value for all agents ($${m}_{j}=m$$ for $$j=\mathrm{S},\mathrm{N},\mathrm{Q},{\mathrm{R}}_{\mathrm{N}},{\mathrm{R}}_{\mathrm{Q}}$$). In Fig. 3, the effect of random walk is illustrated; in (a) and (b), the final densities are plotted against the migration rate ($$m$$). It is found that both total and apparent infections increase with $$m$$. The infection hardly spreads for $$m=0$$, while it widely spreads for a large value of $$m$$. Especially when $$m$$ is sufficiently large, the results of local interaction approach those predicted by MFT.
Realistically, both agents Q and $${\mathrm{R}}_{\mathrm{Q}}$$ never move. Next, we consider the case that three agents (S, N, $${\mathrm{R}}_{\mathrm{N}}$$) can move; we fix $${m}_{\mathrm{S}}=2$$, and change the migration rates of N and $${\mathrm{R}}_{\mathrm{N}}$$ with the same rate ($${m}_{k}={m}_{\mathrm{N}}$$ for $$k=$$ $${\mathrm{R}}_{\mathrm{N}}$$). In Fig. 4, the final densities are plotted against $${m}_{\mathrm{N}}$$, where (a) $$\left(q,{\beta }_{N},{\beta }_{Q}\right)=\left(0.2, 0.3, 0.1\right)$$, (b) $$(q,{\beta }_{N},{\beta }_{Q})=(0.2, 0.1, 0.3)$$ and (c) $$(q,{\beta }_{N},{\beta }_{Q})=(0.8, 0.3, 0.1)$$. Both values $$q=0.2$$ and $$q=0.8$$ represent the cases that the inspection is insufficient and sufficient, respectively. Figure 4b represents a symmetrical case to Fig. 4a: $${\beta }_{N}<{\beta }_{Q}$$. It is found from Fig. 4a that both total infection ($${R}_{N}+{R}_{Q}$$) and apparent infection ($${R}_{Q}$$) rapidly increase with the increase of $${m}_{\mathrm{N}}$$. When N and $${\mathrm{R}}_{\mathrm{N}}$$ sufficiently move around, the simulation results of random walk agree with those predicted by MFT (well-mixed population). The infection rapidly spreads. In contrast, Fig. 4b shows different behavior. For small values of $${\beta }_{\mathrm{N}}$$, both total and apparent infections hardly increase in spite of the increase of $${m}_{\mathrm{N}}$$; the infection becomes very difficult to spread. Similarly, when the inspection is sufficient ($$q=0.8$$), the infection can be suppressed.
In Fig. 5a and b, the total ($${R}_{N}+{R}_{Q}$$) and apparent ($${R}_{Q}$$) infections are plotted against q, respectively. Here, three agents ($$\mathrm{S},\mathrm{N},{\mathrm{R}}_{\mathrm{N}}$$) can move: $${m}_{j}=10$$ for $$j=\mathrm{S},\mathrm{N},{\mathrm{R}}_{\mathrm{N}}$$ but $${m}_{k}=0$$ for $$k=\mathrm{Q},{\mathrm{R}}_{\mathrm{Q}}$$. As predicted by MFT, the total infection monotonically decreases with the increase of q, but the apparent infection has the maximum at $$q={q}_{MAX}$$. The value of $${q}_{MAX}$$ for local interaction is found to be smaller, compared to the prediction of MFT. In Fig. 5c and d, both total and apparent infections are also plotted against $${\beta }_{\mathrm{N}}$$, respectively. These figures display the phase transition. When $${\beta }_{\mathrm{N}}$$ takes a small value, the infection never spreads. With the increase of $${\beta }_{\mathrm{N}}$$, the infected people suddenly increase. In Fig. 6, typical spatial distributions are displayed, where no agent moves in (a), only S moves in (b), and three agents (S, $$\mathrm{N}, {\mathrm{R}}_{\mathrm{N}}$$) move in (c). For the sake of comparison, the result of global simulation (random distribution) is displayed in Fig. 6d. In the cases of Fig. 6a and b, the infection is suppressed; many cells are occupied by blue (S). The infected agents form clusters and stay inside localized spots. However, in Fig. 6c and d, the infection widely spread. It is therefore important to stop the movement of N agents.
Discussion
The coronavirus SARS-CoV-2 has distinct features never seen for previous coronaviruses, such as SARS and MERS. In the case of SARS-CoV-2, many infected people have mild or asymptomatic symptoms, but they may have considerably high infectivity27,30,31,32,33. We demonstrate the serious role of infected people who are not quarantined (N). To this end, we have modified SIR model; infected individual (I) is divided into two groups (N and Q). Similarly, recovered individual (R) is divided into $${\mathrm{R}}_{\mathrm{N}}$$ and $${\mathrm{R}}_{\mathrm{Q}}$$ to distinguish the total and apparent infections. Model (2) resembles SIQR model24,43,44. In the latter case, infected agent (I) always transitions to Q with a constant probability (per unit time). For this reason, N cannot be defined well. However, in model (2), we assume the transition occurs only in the early stages of infection. Those who did not transition to Q are defined by N agents; in simple terms, a person who is infected but not tested is an agent N.
The setting of parameter values is discussed. If the value of $${\beta }_{N}/{\gamma }_{N}$$ or $${\beta }_{Q}/{\gamma }_{Q}$$ is sufficiently high, then the infection easily spreads. In the present paper, the parameters are set based on the following facts: (i) COVID-19 has been suppressed due to lockdown and other regulation of people’s behavior. (ii) Once unlocked, the infection spreads again (e.g. USA and Australia)4. In our model, the disease disappears when all people stop moving, but the infection spreads when people move frequently (see Fig. 3). Moreover, we assume $${\beta }_{\mathrm{N}}>{\beta }_{\mathrm{Q}}$$ for the following reasons. Asymptomatic or mildly infected individuals tend to become agent N. On the other hand, those with severe disease may become agent Q. Since agent Q is quarantined, its infectivity ($${\beta }_{\mathrm{Q}}$$) may be low. In contrast, the infectivity ($${\beta }_{\mathrm{N}}$$) of N may be higher than $${\beta }_{\mathrm{Q}}$$. This is because the agent N looks like uninfected agent (S); nevertheless, the value of $${\beta }_{N}/{\gamma }_{N}$$ may considerably high27,30,31,32,33. Provided that $${\beta }_{\mathrm{N}}$$ takes a small value, the infection hardly spreads as shown in Fig. 4b.
Random-walk simulation reveals that both total [$${R}_{N}\left(\infty \right)+{R}_{Q}\left(\infty \right)$$] and apparent [$${R}_{Q}(\infty )$$] infections rapidly increase with increasing the mobility ($${m}_{N}$$) of N (see Fig. 4). However, when the value of $${\beta }_{N}/{\gamma }_{N}$$ is low, or when $$q$$ takes a high value, the infection hardly spreads. Such a low value of $${\beta }_{N}/{\gamma }_{N}$$ means the weak infectivity of N, and the high value of $$q$$ denotes the small population size of N. Hence, non-quarantined infected individuals (N) play serious roles for epidemic spreading. It should be noted that the movement of $${\mathrm{R}}_{\mathrm{N}}$$ never makes a large difference: if $${\mathrm{R}}_{\mathrm{N}}$$ stops to move, Figs. 4, 5, and 6 are almost unchanged. Only when the movement of N is suppressed, the infection can be suppressed.
We discuss spatial pattern formations (see Fig. 6). As illustrated in Fig. 6a, the infection hardly spreads, because all people never move ("lockdown"). Most cells are blue (agent S). The infected agents (green and black) stay inside localized spots. Such a cluster formation may be a merit of lockdown: it is advantageous in taking measures against infectious diseases. Similarly, even when only agent S (non-infected person: blue cell) moves, the infection can be suppressed (see Fig. 6b). The following question arises: Why the infection is suppressed, despite the large number of non-infected persons intensely move. We consider this suppression comes from the spatial pattern formation. Both Fig. 6a and b have the similar distributions: the infected people form clusters. Since infected agents aggregate, the contact between infected and non-infected individuals is effectively decreased.
Conclusion
In the present article, we demonstrate the serious role of infected people who are not quarantined (N). Both mean-field theory and Monte Carlo simulation reveal the result schematically shown in Fig. S1 (see Supplementary file). The total infection monotonically decreases with the increase of quarantine ratio (q). In contrast, the apparent infection has the maximum at $${q=q}_{\mathrm{MAX}}$$. For $${q>q}_{\mathrm{MAX}}$$, the density of infected people decreases in spite of increasing q. Hence, it is important to promote the inspections; e.g. PCR test. Random-walk simulation reveals that the infection rapidly spreads with increasing the mobility of N. If the movement of N is suppressed, the infection can be suppressed. This conclusion is also confirmed by spatial distribution. Figure 6a indicates the spatial pattern of "lockdown"; infected people form clusters, because all people cannot move. Similar distribution is observed, if infected agents never move (see Fig. 6b). Since infected people aggregate, the infection hardly spreads. Hence, suppressing the movement of infected people (or expanding the tests) is as effective as lockdown. This result for COVID-19 should be unique property never seen for both SARS and MERS. It is therefore important to detect and quarantine the asymptomatic SARS-CoV-2 infected persons27,30,31,32,33.
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Acknowledgements
The authors are grateful to H. Yokoi for assistance with the numerical simulations. This work was supported by COVID-19 research project in University of Hyogo and by grants-in-aid from the Ministry of Education, Culture, Sports Science and Technology of Japan (Grant Number 18K11466). No additional external funding received for this study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors were solely responsible for the design, conduct, and interpretation of all studies.
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N.N., K.T. and K.S. developed the models. N.N. carried out computer simulations. K.S. performed mathematical analysis and numerical calculations. K.T., N.N. and K.S. wrote the draft paper. Y.S. revised the paper from an epidemiological point of view. All authors discussed the simulation results and contributed to writing of the manuscript.
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Correspondence to Kei-ichi Tainaka.
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Nakagiri, N., Sato, K., Sakisaka, Y. et al. Serious role of non-quarantined COVID-19 patients for random walk simulations. Sci Rep 12, 738 (2022). https://doi.org/10.1038/s41598-021-04629-2
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• DOI: https://doi.org/10.1038/s41598-021-04629-2 | 2022-01-20 03:09:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7605522871017456, "perplexity": 2557.3473634852867}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301670.75/warc/CC-MAIN-20220120005715-20220120035715-00507.warc.gz"} |
https://www.physicsforums.com/threads/chemical-potential.687739/ | # Chemical Potential
1. Apr 24, 2013
### Arun Prasath
What is the formula used to find out the chemical potential of a molecule or atom?
2. Apr 25, 2013
### DrDu
The change of the expectation value of energy with respect to electron number, $\partial <E>/\partial n_e$.
3. Apr 25, 2013
### cgk
I think this might be a bit more complicated. Since actual atoms and molecules have integer numbers of electrons, this derivative cannot strictly be defined[1]. Also, a single molecule is a microscopic object, so should not be described by a statistical/thermodynamic quantity like a chemical potential.
That being said, people still offer definitions like μ = 1/2 (IP + EA) (where IP and EA are the first ionization potential and first electron affinity, respectively), or in the context of mean-field theory, μ = 1/2 (ε_homo + ε_lumo) (where the εs are the orbital energies of the highest occupied and lowest unoccupied orbital).
[1] (there are ways to define them in so called conceptual density functional theory, but one has to jump through several hoops, and I personally think it is legitimate to disregard non-integer electrons...)
4. Apr 25, 2013
### DrDu
I think there is no conceptual problem in calculating the mean energy per atom in a statistical ensemble in which only the average number of electrons per atom is specified, e.g. a mixture of 90% neutral atoms and 10% of atoms carrying a single positive or negative charge. It should be quite obvious how this relates to ionisation energy or electron affinity. At T=0 and integer values of electrons per atoms mu is discontinuous. At finite temperatures one can justify
μ = 1/2 (IP + EA) as always both positive and negatively charged atoms will be in the ensemble.
5. Apr 25, 2013
### cgk
I agree that 1/2(IP+EA) it is a sensible choice for thermodynamic ensembles at T>0. But even then one still as to consider that, technically, there are also other IPs and EAs than the first, and they should enter in the thermodynamic sum. And one might have to consider ensembles of molecular geometries and molecular interactions, too.
I'm not saying that it is wrong to take or approximate μ like this, just that it is not something one has to accept as the 100% certain definition as which it sometimes comes across. To me it looks more like a sensible approximation derived from single atoms or molecules, which might then carry over to certain kinds of ensembles under some conditions. But this latter step is not often made explicit---people actually do talk about μs of single atoms and molecules, and define them like above[1].
I think that at T=0, as you said, the only really true'' fact is that μ is discontinuous, and that for finite T, technically one should actually set up and calculate the thermodynamic ensemble, from which one then would get μ as the mean energy derivative.
[1] Imo, this is more problematic than it looks like, because even in an ensemble it might not actually be the first IP/EA which is relevant, but some other one which would be favored by scattering or dynamic processes. If, for example, one had a complex with massive ligands all around a metal core, and the first EA/IP would actually refer to ionizations of this metal core, then the IPs/EAs refering to some outer ligand orbitals might be more important in the thermodynamic sum, even if higher in energy, because they could be triggered by collisions much more easily. (Yes, I am just making stuff up, but I think it's thinkable)
6. Apr 25, 2013
### Useful nucleus
How about defining the chemical potential from the good old thermodynamic point of view to be the Gibbs free energy per atom (molecule). And then for the original poster we can suggest the ideal "classical" monoatomic gas formula:
μ=μ° + kBT ln (P/P0)
where kB is Boltzmann constant, T is the temperature, P is the partial pressure, P0 is a reference pressure and μ° a reference chemical potential.
7. Apr 26, 2013
### DrDu
This easy triggering would be a kinetic effect and should play no role in thermodynamic considerations.
You are right in that higher ionisation potentials have to be included in principle, however I think in praxis they are suppressed by a very small Boltzmann factor $\exp(-(IP2-IP1)/kT)$. | 2018-03-19 11:50:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7627130150794983, "perplexity": 941.6563335090751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646875.28/warc/CC-MAIN-20180319101207-20180319121207-00460.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-12-3x-30 | # How do you solve 12 + 3x = 30?
Jul 28, 2016
$x = 6$
#### Explanation:
$\textcolor{c \mathmr{and} a l}{\text{Subtract 12 on both sides:}}$
$\cancel{12} + 3 x = 30$
$- \cancel{12}$ $\textcolor{w h i t e}{a a} - 12$
12 cancels out on the left side, and when you subtract 12 from 30 on the right you get 18:
$3 x = 18$
$\textcolor{g r e e n}{\text{Divide both sides 3 to get x by itself.}}$
$\frac{\cancel{\text{3}} x}{\cancel{3}} = \frac{18}{3}$
Now you are just left with $x$ on the left side and 6 on the right side.
Thus,
$\textcolor{p u r o k e}{\text{x = 6}}$ | 2021-12-04 14:57:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 10, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8990275859832764, "perplexity": 412.34451458297656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362992.98/warc/CC-MAIN-20211204124328-20211204154328-00551.warc.gz"} |
https://physics.stackexchange.com/questions/178277/is-angular-momentum-the-conjugate-momentum-of-an-angle/178317 | # Is angular momentum the conjugate momentum of an angle?
Lagrangian mechanics can be used to describe the double pendulum (see here, for example). In this development are the conjugate momenta $p_{\theta_i}$ exactly the angular momenta $m_i l_i \frac{d \theta_i}{dt}$?
In other words, do the following sequences hold:
• Position -> Velocity -> Momentum
• Angle -> Angular velocity -> Angular momentum
• Generalized coordinate -> Generalized velocity -> Conjugate momentum
• I don't know what you mean when you ask "does the following sequences hold". – ACuriousMind Apr 25 '15 at 16:34
• The question seems pretty clear to me. (The answer is just "yes.") – Nathaniel Apr 26 '15 at 12:52
• I'm not convinced - the naming similarity and arguments based on dimensions aren't really compelling. I'll need to think about a bit more. – pdmclean Apr 28 '15 at 23:14
• @ACuriousMind Can you answer the question? – pdmclean Apr 30 '15 at 12:36
• ACuriousMind shows more of his broadmindedness. – pdmclean Apr 30 '15 at 12:40
You are right. If $q$ is a generalized coordinate then $\dot{q}$ is the generalized velocity and hence the generalized momentum is $$p = \frac{\partial L}{\partial\dot{q}}$$ Therefore, your sequence looks correct. Further, equations (20) and (21) of the article you have referenced also tell that the $p_{\theta_i}$ are indeed angular momenta. (You may want to check the dimensions.)
Normally, when we speak of angular momentum as a vector, we refer to a certain origin. In this case, we do not have to do it. The conjugate variable $p$ in this case, "happens to be" angular momentum. | 2019-10-22 11:34:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8666641712188721, "perplexity": 401.8586079711312}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987817685.87/warc/CC-MAIN-20191022104415-20191022131915-00453.warc.gz"} |
https://www.biogeosciences.net/16/1563/2019/ | Journal topic
Biogeosciences, 16, 1563–1582, 2019
https://doi.org/10.5194/bg-16-1563-2019
Biogeosciences, 16, 1563–1582, 2019
https://doi.org/10.5194/bg-16-1563-2019
Research article 12 Apr 2019
Research article | 12 Apr 2019
# Inputs and processes affecting the distribution of particulate iron in the North Atlantic along the GEOVIDE (GEOTRACES GA01) section
Inputs and processes affecting the distribution of particulate iron in the North Atlantic along the GEOVIDE (GEOTRACES GA01) section
Arthur Gourain1,a, Hélène Planquette1, Marie Cheize1,b, Nolwenn Lemaitre1,c, Jan-Lukas Menzel Barraqueta2,d, Rachel Shelley1,e, Pascale Lherminier3, and Géraldine Sarthou1 Arthur Gourain et al.
• 1UMR 6539/LEMAR/IUEM, CNRS, UBO, IRD, Ifremer, Technopôle Brest Iroise, Place Nicolas Copernic, 29280 Plouzané, France
• 2GEOMAR, Helmholtz Centre for Ocean Research Kiel, Wischhofstraße 1–3, 24148 Kiel, Germany
• 3Ifremer, Univ. Brest, CNRS, IRD, Laboratoire d'Océanographie Physique et Spatiale (LOPS), IUEM, 29280 Plouzané, France
• anow at: Ocean Sciences Department, School of Environmental Sciences, University of Liverpool, Liverpool, L69 3GP, UK
• bnow at: Ifremer, Centre de Brest, Géosciences Marines, Laboratoire des Cycles Géochimiques (LCG), 29280 Plouzané, France
• cnow at: Department of Earth Sciences, Institute of Geochemistry and Petrology, ETH-Zürich, Zürich, Switzerland
• dnow at: Department of Earth Sciences, Stellenbosch University, Stellenbosch, 7600, South Africa
• enow at: Earth, Ocean and Atmospheric Science, Florida State University, Tallahassee, Florida 32310, USA
Correspondence: Hélène Planquette (helene.planquette@univ-brest.fr)
Abstract
The aim of the GEOVIDE cruise (May–June 2014, R/V Pourquoi Pas?) was to provide a better understanding of trace metal biogeochemical cycles in the North Atlantic Ocean. As marine particles play a key role in the global biogeochemical cycle of trace elements in the ocean, we discuss the distribution of particulate iron (PFe), in relation to the distribution of particulate aluminium (PAl), manganese (PMn), and phosphorus (PP). Overall, 32 full vertical profiles were collected for trace metal analyses, representing more than 500 samples. This resolution provides a solid basis for assessing concentration distributions, elemental ratios, size fractionation, and adsorptive scavenging processes in key areas of the thermohaline overturning circulation. Total particulate iron concentrations ranged from as low as 9 pmol L−1 in surface waters of the Labrador Sea to 304 nmol L−1 near the Iberian margin, while median PFe concentrations of 1.15 nmol L−1 were measured over the sub-euphotic ocean interior.
Within the Iberian Abyssal Plain, the ratio of PFe to PAl was identical to the continental crust molar ratio (0.21 mol mol−1), indicating the important influence of crustal particles in the water column. Overall, the lithogenic component explained more than 87% of PFe variance along the section. Within the Irminger and Labrador basins, the formation of biogenic particles led to an increase in the PFe∕PAl ratio (up to 0.64 mol mol−1) compared to the continental crust ratio. Continental margins induce high concentrations of particulate trace elements within the surrounding water masses (up to 10 nmol L−1 of PFe). For example, horizontal advection of PFe was visible more than 250 km away from the Iberian margin. Additionally, several benthic nepheloid layers were observed more than 200 m above the seafloor along the transect, especially in the Icelandic, Irminger, and Labrador basins, suspending particles with high PFe content of up to 89 nmol L−1.
1 Introduction
Particles play a key role in the ocean, where they drive the residence time of most elements (Jeandel and Oelkers, 2015) and strongly influence the global biogeochemistry of macro- and micro-nutrients including iron (Milne et al., 2017). In the surface ocean, biological activity produces biogenic suspended matter through planktonic organisms, while atmospheric deposition (Jickells et al., 2005; Baker et al., 2013), riverine discharge (Ussher et al., 2004; Berger et al., 2008; Aguilar-Islas et al., 2013), or ice melting (Lannuzel et al., 2011, 2014; Hawkings et al., 2014) deliver mostly lithogenic-derived particles to surface waters. These particulate inputs are highly variable, both spatially and seasonally, in the world's oceans. At depth, benthic and shelf sediment resuspension (e.g. Fitzwater et al., 2000; McCave and Hall, 2002; Elrod et al., 2004; Lam and Bishop, 2008; Cullen et al., 2009; Hwang et al., 2010; Aguilar-Islas et al., 2013; Lam et al., 2015) and hydrothermal activity (Trefry et al., 1985; Elderfield and Schultz, 1996; Tagliabue et al., 2010, 2017; Lam et al., 2012) provide important amounts of particles to the water column. Moreover, authigenic particles can be produced in situ by aggregation of colloids (Bergquist et al., 2007) or oxidation processes (Bishop and Fleisher, 1987; Collier and Edmond, 1984). Thus, oceanic particles result from a complex combination of these different sources and processes (Lam et al., 2015).
In the upper water column, the total iron pool is dominated by marine particles (Radic et al., 2011) which strongly interact with the dissolved pool (e.g. Ellwood et al., 2014). Indeed, dissolved iron can be scavenged onto particles (Rijkenberg et al., 2014; Gerringa et al., 2015), incorporated into biogenic particles (Berger et al., 2008), or produced by remineralization of particles (Dehairs et al., 2008; Sarthou et al., 2008). Interestingly, the concept of “reversible scavenging” of iron (i.e. release at depth of dissolved iron previously scavenged onto particles) has been advocated recently (Labatut et al., 2014; Dutay et al., 2015; Jeandel and Oelkers, 2015; Abadie et al., 2017), while other studies reveal distinct dissolution processes of inorganic particulate iron (e.g. Oelkers et al., 2012; Cheize et al., 2018). Slow dissolution of particulate iron at margins has also been evoked as a continuous fertilizer of primary production and should be considered as a source of dissolved iron (e.g. Lam and Bishop, 2008; Jeandel et al., 2011; Jeandel and Oelkers, 2015). Within or below the mixed layer, the rates of regeneration processes can also impact the bioavailable pool of iron, among other trace metals (e.g. Ellwood et al., 2014; Nuester et al., 2014). However, the rates of these processes are not yet fully constrained. The study of particulate iron is thus essential to better constrain its marine biogeochemical cycle. Interest has grown in this subject over the last 10 years, in particular (e.g. Bishop and Biscaye, 1982; Collier and Edmond, 1984; Sherrell et al., 1998; Frew et al., 2006; Planquette et al., 2011, 2013; Lam et al., 2012; Abadie et al., 2017; Milne et al., 2017), and, to our knowledge, only two studies have been performed on an ocean-wide scale: the GA03 GEOTRACES North Atlantic Zonal Transect (Lam et al., 2015; Ohnemus and Lam, 2015) and the GP16 GEOTRACES Pacific Transect (Lam et al., 2017; Lee et al., 2017).
Within this global context, this paper presents the particulate iron distribution of the North Atlantic Ocean, along the GEOTRACES GA01 section (GEOVIDE), and discusses the various sources and processes affecting particulate iron (PFe) distribution, using particulate aluminium (PAl), phosphorus (PP), or manganese (PMn) distributions to support our conclusions.
2 Methods
## 2.1 Study area
Particulate samples were collected at 32 stations during the GEOVIDE (GEOTRACES GA01 section) cruise between May and June 2014 aboard the R/V Pourquoi Pas? in the North Atlantic Ocean (Sarthou et al., 2018). The sampling spanned several biogeochemical provinces (Fig. 1), starting over the Iberian margin (IM, stations 2, 4, and 1), and proceeding to the Iberian Abyssal Plain (IAP, stations 11 to 17), the Western European Basin (WEB, station 19 to station 29), and the Icelandic Basin (IcB, stations 32 to 36). Then, samples were collected above the Reykjanes Ridge (RR, station 38), in the Irminger Basin (IrB, stations 40 to 60), close to the Greenland Shelf (GS, stations 53, 56, and 61), the Labrador Basin (LB, stations 63 to 77), and finally close the Newfoundland Shelf (NS, station 78) (Fig. 1). The North Atlantic is characterized by a complex circulation (briefly described in Sect. 3.1 and in detail by Zunino et al., 2017, and García-Ibáñez et al., 2015) and is one of the most productive regions of the global ocean (Martin et al., 1993; Sanders et al., 2014).
Figure 1Map of stations where suspended particle samples were collected with GO-FLO bottles during the GEOVIDE cruise (GA01) in the North Atlantic Ocean. Biogeochemical provinces are indicated by red squares; IM: Iberian margin, IAP: Iberian Abyssal Plain, WEB: Western European Basin, IcB: Iceland Basin, RR: Reykjanes Ridge, IrB: Irminger Basin, GS: Greenland Shelf, LB: Labrador Basin, NS: Newfoundland Shelf. This figure was generated using Ocean Data View (Schlitzer, R., Ocean Data View, 2017, http://odv.awi.de/, last access: 9 April 2019).
## 2.2 Sampling
Samples were collected using the French GEOTRACES clean rosette, equipped with 22 12 L GO-FLO bottles (2 bottles were leaking and were not deployed during the cruise). GO-FLO bottles (General Oceanic's) were initially cleaned in the home laboratory (LEMAR) following the GEOTRACES procedures (Cutter and Bruland, 2012). The rosette was deployed on a 14 mm Kevlar cable with a dedicated, custom-designed clean winch. Immediately after recovery, the GO-FLO bottles were individually covered at each end with plastic bags to minimize contamination. Bottles were then transferred into a clean container (class-100) for sampling. On each cast, nutrient and/or salinity samples were taken to check potential leakage of the GO-FLO bottles.
Filters were cleaned following the GEOTRACES protocols (http://www.geotraces.org/images/Cookbook.pdf, last access: 9 April 2019) and kept in acid-cleaned 1 L LDPE bottles (Nalgene) filled with ultrapure water (Milli-Q, resistivity of 18.2 MΩ cm) until use. All filters were 25 mm in diameter in order to optimize the signal over the filter blank, except at the surface depth where 47 mm diameter filters were used. The filters were mounted on acid-cleaned polysulfone filter holders (Nalgene). Prior to filtration, the GO-FLO bottles were shaken three times, as recommended in the GEOTRACES cookbook to avoid settling of particles in the lower part of the bottle. GO-FLO bottles were pressurized to < 8 psi with 0.2 µm filtered nitrogen gas (N2, Air Liquide). Seawater was then filtered directly through paired filters (Pall Gelman Supor 0.45 µm polyetersulfone, and Millipore mixed ester cellulose MF 5 µm) mounted in Swinnex polypropylene filter holders (Millipore), following Planquette and Sherrell (2012), inside the clean container. Filtration was operated until the bottle was empty or until the filter clogged; the volume filtered ranged from 2 L for surface samples to 11 L within the water column. After filtration, filter holders were disconnected from the GO-FLO bottles and a gentle vacuum was applied using a syringe in order to remove any residual water under a laminar flow hood. Filters were then removed from the filter holders with plastic tweezers (which were rinsed with Milli-Q between samples). Most of the remaining seawater was removed via “sipping” by capillary action, when placing the non-sampled side of the filter onto a clean 47 mm Supor filter. Each filter pair was then placed in an acid-cleaned polystyrene PetriSlide (Millipore), double bagged, and finally stored at −20C until analysis at LEMAR. Between casts, filter holders were thoroughly rinsed with Milli-Q, placed in an acid bath (5 % Trace metal grade HCl) for 24 h, and then rinsed with Milli-Q.
At each station, process blanks were collected as follows: 2 L of a deep (1000 m) and a shallow (40 m) seawater sample was first filtered through a 0.2 µm pore size capsule filter (Pall Gelman Acropak 200) mounted on to the outlet of the GO-FLO bottle before passing through the particle sampling filter, which was attached directly to the Swinnex filter holder.
## 2.3 Analytical methods
In the home laboratory, sample handling was performed inside a clean room (Class 100). All solutions were prepared using ultrapure water (Milli-Q) and all plastic ware had been acid-cleaned before use. Frozen filters, collected within the mixed layer or within nepheloid layers, were first cut in half using a ceramic blade: one filter half was dedicated to total digestion (see below), while the other half was archived at −20C for SEM analyses or acid leaching of “labile” metals following the Berger et al. (2008) method (to be published separately).
Filters were digested following the method described in Planquette and Sherrell (2012). Filters were placed on the inner wall of acid-cleaned 15 mL PFA vials (Savillex), and 2 mL of a solution containing 2.9 mol L−1 hydrofluoric acid (HF, suprapur grade, Merck) and 8 mol L−1 nitric acid (HNO3, Ultrapur grade, Merck) was added to each vial. Vials were then closed and refluxed at 130 C on a hot plate for 4 h, after which the filters were removed. After cooling, the digest solution was evaporated at 110 C to near dryness. Then, 400 µL of concentrated HNO3 (Ultrapur grade, Merck) was added, and the solution was re-evaporated at 110 C. Finally, the obtained residue was dissolved with 3 mL of 0.8 mol L−1 HNO3 (Ultrapure grade, Merck). This archived solution was transferred to an acid-cleaned 15 mL polypropylene centrifuge tube (Corning®) and stored at 4 C until analyses.
All analyses were performed on a sector field inductively coupled plasma mass spectrometer (SF-ICP-MS Element 2, Thermo-Fisher Scientific). Samples were diluted by a factor of 7 on the day of analysis in acid-washed 13 mm (outer diameter) rounded bottom, polypropylene centrifuge tubes (VWR) with 0.8 mol L−1 HNO3 (Ultrapur grade, Merck) spiked with 1 µg L−1 of indium (115In) solution in order to monitor the instrument drift. Samples were introduced with a PFA-ST nebulizer connected to a quartz cyclonic spray chamber (Elemental Scientific Incorporated, Omaha, NE) via a modified SC-Fast introduction system consisting of an SC-2 autosampler, a six-port valve, and a vacuum-rinsing pump. The autosampler was contained under a HEPA-filtered unit (Elemental Scientific). Two six-point, matrix-matched multi-element standard curves with concentrations bracketing the range of the samples were run at the beginning, the middle, and the end of each analytical run. Analytical replicates were made every 10 samples, while accuracy was determined by performing digestions of certified reference material BCR-414 (plankton, Community Bureau of Reference, Commission of the European Communities), PACS-3, and MESS-4 (marine sediments, National Research Council Canada), following the same protocol used for the samples. Recoveries were typically within 10 % of the certified values (and within the error of the data, taken from replicate measurements, Table 1). Once all data were normalized to an 115In internal standard and quantified using an external standard curve, the dilution factor of the total digestion was accounted for. The elemental concentrations were obtained per filter (pmol/filter) and were then process blank-corrected. Finally, pmol/filter values were divided by the volume of water filtered through stacked filters.
Table 1Blank and limit of detection (nmol L−1) of the two filters and certified reference material (CRM) recoveries during GEOVIDE suspended particle digestions.
Total concentrations (sum of small size fraction (0.45–5 µm) and large (> 5 µm) size fraction) of particulate trace elements are reported in Table S1 in the Supplement.
## 2.4 Positive matrix factorization
Positive matrix factorization (PMF) was run to characterize the main factors influencing the particulate trace element variance along the GEOVIDE section. In addition to PFe, PAl, PMn, and PP, nine additional elements were included in the PMF: yttrium (Y), barium (Ba), lead (Pb), thorium (Th), titanium (Ti), vanadium (V), cobalt (Co), copper (Cu), and zinc (Zn). The PMF was conducted on samples where all elements were above their detection limits; after selection, 445 of the 549 existing data points were used. Analyses were performed using the PMF software, EPA PMF 5.0, developed by the USA Environmental Protection Agency (EPA). Three- to six-factor models were run on the data. The configuration that provided the lowest error estimation (i.e. was the most reliable) was the four-factor model. To ensure stability, this model was run 100 times. After displacement, error estimation, and bootstrap error estimation, the model was recognized as stable.
## 2.5 Derived and ancillary parameters
To investigate the proportion of lithogenic iron within the bulk particulate iron, we used the upper continental crust (UCC) Fe∕Al molar ratio (0.21) of Taylor and McLennan (1995) to calculate the lithogenic components of particles (%PFelitho) following Eq. (1):
$\begin{array}{}\text{(1)}& \mathrm{%}{\mathrm{PFe}}_{\mathrm{litho}}=\mathrm{100}×\left(\frac{\mathrm{PAl}}{\mathrm{PFe}}\right)\mathrm{sample}×\left(\frac{\mathrm{PFe}}{\mathrm{PAl}}\right)\mathrm{UCCratio}\end{array}$
The non-lithogenic PFe is obtained using Eq. (2):
$\begin{array}{}\text{(2)}& \mathrm{%}{\mathrm{PFe}}_{\mathrm{non}-\mathrm{litho}}=\mathrm{100}-\mathrm{%}{\mathrm{PFe}}_{\mathrm{litho}}\end{array}$
Note that while the %PFelitho and %PFenon−litho proxies are interesting tools to evaluate the importance of lithogenic and non-lithogenic (either biogenic or authigenic) fractions, they have to be used carefully, as the spatial and temporal variation of the lithogenic component ratios may involve uncertainties of the estimated fraction value.
In addition to PAl, PMn can be used as a tracer of inputs from shelf resuspension (Lam and Bishop, 2008), using a percentage of sedimentary inputs “%bulk sediment inputs” estimated according to the following equation:
$\begin{array}{ll}\mathrm{%}\mathrm{bulk}\phantom{\rule{0.25em}{0ex}}\mathrm{sediment}\phantom{\rule{0.25em}{0ex}}\mathrm{PMn}=& \phantom{\rule{0.125em}{0ex}}\phantom{\rule{0.125em}{0ex}}\mathrm{100}×\left(\frac{\mathrm{PAl}}{\mathrm{PMn}}\right)\mathrm{sample}\\ \text{(3)}& & ×\left(\frac{\mathrm{PMn}}{\mathrm{PAl}}\right)\mathrm{UCCratio},\end{array}$
with PAl∕PMn being the ratio from the GEOVIDE samples and the PMn∕PAl being the UCC value (0.0034; Taylor and McLennan, 1995).
This proxy can be a good indicator of sediment resuspension. We assume that particles newly resuspended in the water column will have the same PMn∕PAl ratio as the UCC ratio, leading to a “%bulk sediment Mn” of 100 %. This proxy assumes homogeneity of the sediment PMn∕PAl ratio throughout the GEOVIDE section. However, this may not be the case at every station. In consequence, this proxy should only be used to identify new benthic resuspension at specific locations; inter-comparison between several locations may not be appropriate. When a sample presents a “%bulk sediment Mn” greater than 100 %, we have assigned a maximum value of 100 %. As the Mn cycle can also be influenced by biotic uptake (e.g. Sunda and Huntsman, 1983; Peers and Price, 2004), this proxy is only used at depths where biologic activity was negligible (i.e. below 150 m depth).
Potential temperature (θ), salinity (S), and transmissometry data were retrieved from the CTD sensors (CTD SBE911 equipped with a SBE43).
3 Results
## 3.1 Hydrography setting
Here, we briefly describe the hydrography encountered during the GEOVIDE section (Fig. 2) as a thorough description is available in García-Ibáñez et al. (2015). At the start of the section, the warm and salty Mediterranean Water (MW, S=36.50, θ=11.7C) was sampled between 600 and 1700 m in the Iberian Abyssal Plain (IAP). MW resulted from the mixing between the Mediterranean Overflow Water (MOW) plume coming from the Mediterranean Sea and local waters. Surface water above the Iberian Shelf was characterized by low salinity (S=34.95) at stations 2 and 4 compared to surrounding water masses. Close to the seafloor of the Iberian Abyssal Basin, the North East Atlantic Deep Water (NEADW, S=34.89, θ=2.0C) spread northward. The North Atlantic Central Water (NACW, S > 35.60, θ > 12.3 C) was the warmest water mass of the transect and was observed in the subsurface layer of the Western European Basin and Iberian Abyssal Plain. An old Labrador Sea Water (LSW, S=34.87, θ=3.0C) flowed inside the Western European and Icelandic basins, between 1000 and 2500 m depth.
Figure 2Salinity section during the GEOVIDE cruise with water masses indicated in black italic font. A salinity contour of 35.8 psu has been applied to identify the Mediterranean Water (MW) to the east. From right to left: North East Atlantic Deep Water (NEADW); North Atlantic Central Water (NACW); Labrador Sea Water (LSW); Sub-Arctic Intermediate Water (SAIW); Iceland–Scotland Overflow Water (ISOW); Iceland Sub-Polar Mode Water (IcSPMW); Denmark Strait Overflow Water (DSOW); Irminger Sub-Polar Mode Water (IrSPMW). Station locations are indicated by the numbers above the section and biogeochemical provinces are indicated in blue font above station numbers. This figure was generated using Ocean Data View (Schlitzer, R., Ocean Data View, http://odv.awi.de/, 2017).
In the Icelandic Basin, below the old LSW, the Iceland–Scotland Overflow Water (ISOW, S=34.98, θ=2.6C) spread along the Reykjanes Ridge slope. This cold water, originating from the Arctic, led to the formation of NEADW after mixing with surrounding waters. North Atlantic hydrography was impacted by the northward flowing of the North Atlantic Current (NAC), which carried warm and salty waters from the subtropical area. Due to air–sea interactions and mixing with surrounding water, the NACW is cooled and freshened in the subpolar gyre and is transformed into Subpolar Mode Water (SPMW). The formation of SPMW inside the Icelandic and Irminger basins leads to the formation of regional mode waters: the Iceland Subpolar Mode Water (IcSPMW, S=35.2, θ=8.0C) and the Irminger Subpolar Mode Water (IrSPMW, S=35.01, θ=5.0C), respectively. IcSPMW was a relatively warm water mass with potential temperature up to 7 C (García-Ibáñez et al., 2015). Another branch of the NAC mixed with Labrador Current waters to form the relatively fresh Sub-Arctic Intermediate Water (SAIW, S= < 34.8, 4.5 C < θ < 6 C).
The Irminger Basin is a complex area with a multitude of water masses. In the middle of the basin, an old LSW, formed 1 year before (Straneo et al., 2003), spread between 500 and 1200 m depth. Close to the bottom, the Denmark Strait Overflow Water (DSOW, S=34.91) flowed across the basin. Greenland coastal waters were characterized by low salinity values, down to S=33. The strong East Greenland Current (EGC) flowed southward along the Greenland Shelf in the Irminger Basin. At the southern tip of Greenland, this current enters the Labrador Basin along the western coast of Greenland and followed the outline of the basin until the Newfoundland Shelf. In the Labrador Basin, the deep convection of SPMW at 2000 m was involved in the formation of the LSW (S=34.9, θ=3.0C) (Yashayaev and Loder, 2009; García-Ibáñez et al., 2015). Above the Newfoundland Shelf, surface waters were affected by discharge from rivers and ice melting and characterized by extremely low salinity for open ocean waters, below 32 in the first 15 m.
## 3.2 Section overview
Total particulate concentrations spanned a large range of concentrations from below detection (Table 1) to 304 nmol L−1 for PFe, 1544 nmol L−1 for PAl, 3.5 nmol L−1 for PMn, and 402 nmol L−1 for PP. The ranges of concentrations are comparable to other studies recently published (Table 2).
Table 2Concentration (in nmol L−1) of particulate trace elements (PFe, Pal, PMn, and PP) in suspended particles collected in diverse regions of the world's ocean.
Bdl: below detection limit; ND: non-determined; N.A.: North Atlantic.
Along the section, PFe, PAl, and PMn were predominantly found (> 90 %) in particles larger than 5 µm, except in surface waters, reflecting a more heterogenous pattern, where 9±8.6 % of PFe, 10.9±15.4 % of PAl, 32.8±16.6 % of PMn, and 38.8±8.6 % of PP were hosted by smaller particles (0.45–5 µm). Data are shown in Fig. 3.
Figure 3(a–d) Distribution of total particulate (a) iron (PFe), (b) aluminium (PAl), (c) manganese (PMn), and (d) phosphorus (PP) concentrations (nmol L−1) in the first 250 m and the entire water column along the GEOVIDE section in the North Atlantic Ocean. Right panel: contribution of the small size fraction (0.45–5 µm) expressed as a percentage (%) of the total concentration of (e) PFe, (f) PAl, (g) PMn, and (h) PP. Station IDs and biogeochemical regions are indicated on top of panels (a) and (e). This figure was generated using Ocean Data View (Schlitzer, R., Ocean Data View, http://odv.awi.de/, 2017).
## 3.3 Open Ocean stations: from the Iberian Abyssal Plain to the Labrador Basin
This concerns all stations from stations 11 to 77, with the exception of stations 53, 56, and 61, which were sampled close to the Greenland coast (Fig. 1). Particulate iron concentration profiles showed identical patterns at all the open ocean stations encountered along the section. Median PFe was low at 0.25 nmol L−1 within the first 100 m and steadily increased with depth. However, at two stations, elevated concentrations were determined in the upper 100 m, up to 4.4 nmol L−1 at station 77 at 40 m depth and 7 nmol L−1 at station 63 between 70 and 100 m depth. PFe concentrations gradually increased with depth, with a median PFe of 1.74 nmol L−1 below 1000 m. Close to the seafloor of some stations (26, 29, 32, 34, 49, 60, and 71), high concentrations of PFe were observed, up to 88 nmol L−1 (station 71 at 3736 m). These high PFe values were associated with low beam transmissometry values ≤97 %.
Particulate aluminium and manganese profiles were similar to PFe profiles, with low concentrations measured in the first 100 m (1.88 nmol L−1 and 55 pmol L−1, respectively) which increased towards the seafloor. Close to the seafloor, high concentrations were determined at the same stations cited above for PFe, with a maximum of 264 and 3.5 nmol L−1 for PAl and PMn, respectively, at station 71 (Table S1 in the Supplement). The highest particulate phosphorus concentrations were in the uppermost 50 m, with a median value of 66 nmol L−1. Below 200 m depth PP concentrations decreased to values below 10 nmol L−1. Inter-basins differences were observed within surface samples, with median PP concentrations being higher in the Irminger Basin (127 nmol L−1) than in the Iberian Abyssal Plain (28 nmol L−1) (Fig. 3).
Finally, above the Reykjanes Ridge, PP, PMn, PAl, and PFe concentrations were in the same range as the surrounding open ocean stations. However, close to the seafloor, high concentrations were measured, with PFe, PAl, and PMn reaching 16.2, 28.8, and 0.51 nmol L−1 at 1354 m depth, respectively (Fig. 3 and Table S1 in the Supplement).
## 3.4 Margins and shelves: Iberian margin (stations 1 to 4), Greenland coast (stations 53, 56, and 61), and Newfoundland Shelf (station78)
The Iberian margin was characterized by low beam transmissometry values at station 2 (88 % at 140 m depth, Fig. 4a), suggesting high particle concentrations. Particulate iron concentrations varied from 0.02 to 304 nmol L−1. Within the first 50 m, PFe concentrations decreased towards the shelf break where PFe dropped from 2.53 nmol L−1 (station 2) to 0.8 nmol L−1 (station 1). At all three stations, PFe concentrations increased with depth and reached a maximum close to the seafloor. For example, 300 nmol L−1 of PFe was determined at 138.5 m depth at station 2. Lithogenic tracers, such as PAl or PMn, presented similar profiles to PFe with concentrations ranging from 0.11 and 1544 nmol L−1, and from below the detection limit to 2.51 nmol L−1, respectively (Fig. 3, Table S1). Total particulate phosphorus concentrations were relatively low in surface waters, ranging from values below detection to 38 nmol L−1; concentrations decreased with depth and were less than 0.7 nmol L−1 below 1000 m depth.
Figure 4Section of derived contributions of sedimentary inputs along the GA01 section with (a) beam transmissometry (%) and (b) manganese bulk sediment proxy (%) based on Eq. (3). Station IDs and biogeochemical region are indicated above section (a) in black numbers and blue letters, respectively. This figure was generated using Ocean Data View (Schlitzer, R., Ocean Data View, http://odv.awi.de/, 2017).
In the vicinity of the Greenland Shelf, PFe concentrations had a high median value of 10.8 nmol L−1 and were associated with high median PAl and PMn concentrations of 32.3 and 0.44 nmol L−1, respectively. Concentrations of PP were high at the surface with a value of 197 nmol L−1 at 25 m depth of station 61. Then, PP concentrations decreased strongly, to less than 30 nmol L−1 below 100 m depth. Furthermore, beam transmissometry values in surface waters at these three stations were the lowest of the entire section, with values below 85 % (Fig. 4a).
Close to the Newfoundland margin, surface waters displayed a small load of particulate trace metals as PFe, PAl, and PMn concentrations were below 0.8, 2, and 0.15 nmol L−1, respectively. Then, close to the bottom of station 78, at 371 m depth, beam transmissometry values dropped to 94 % (Fig. 4a) and were associated with extremely high concentrations of PFe =168 nmol L−1, PAl =559 nmol L−1, and PMn =2 nmol L−1. Total PP concentrations in the first 50 m ranged from 35 to 97 nmol L−1. Below 50 m, PP remained relatively high with values up to 16 nmol L−1 throughout the water column (Fig. 3 and Table S1).
4 Discussion
Our goal was to investigate mechanisms that drive the distribution of PFe in the North Atlantic, in particular the different routes of supply and removal. Possible sources of PFe include lateral advection offshore from margins, atmospheric inputs, continental run-off, melting glaciers and icebergs, resuspended sediments, hydrothermal inputs, and biological uptake. Removal processes include remineralization, dissolution processes, and sediment burial.
In the following sections, we examine each of these sources and processes, explore the evidence for their relative importance, and use compositional data to estimate the particle types and host phases for iron and associated elements.
## 4.1 Analysis of the principal factors controlling variance: near-ubiquitous influence of crustal particles in the water column
Positive matrix factorization analysis (Fig. 5) was undertaken on the entire dataset; in consequence, the factors described below are highly influenced by the major variations of particulate element concentrations (usually at the interfaces, i.e. margin, seafloor, surface layer). The first factor is characterized by lithogenic elements, representing 86.8 % of the variance of PFe, 75.8 % of PAl, and 90.5 % of PTi. The second factor is correlated with both Mn and Pb and explains no less than 76.5 % and 77.0 % of their respective variances. Ohnemus and Lam (2015) observed this relationship between manganese and lead particles and explained it by the co-transport on Mn oxides (Boyle et al., 2005). The formation of barite explains the third factor and constrained 87.7 % of the Ba variance in the studied regions. Biogenic barite accumulation within the mesopelagic layer is related to bacterial activity and remineralization of biogenic material (Lemaitre et al., 2018). A biogenic component is the fourth factor and explained most of the PP variance, 83.7 %. The micronutrient trace metals, copper, cobalt, and zinc, had more than a quarter of their variances influenced by this factor. Note that the biogenic contribution to PFe and other trace elements will be discussed in another paper (Planquette et al., 2019).
Figure 5Factor fingerprint of the positive matrix factorization conducted on 445 particle samples collected along the GA01 section. The four main factors influencing the particulate trace element variance are represented in a stacked bar chart of the percentage of variance explained per element. Factor 1 is dominated by the lithogenic elements, e.g. Th, Al, Ti, and Fe. Factor 2 is associated with Pb and Mn variances. Biogenic barite formation mainly influences factor 3. Factor 4 is dominated by biogenic elements, e.g. P, Co, Cu, and Zn.
These results indicate that along the GA01 section, PFe distributions were predominantly controlled by lithogenic material and to a smaller extent by remineralization processes (PMF, factor 3 =4.1 %). This does not rule out some biogenic influences on PFe distribution, especially in the surface, but its contribution is most likely obscured by the high lithogenic contribution.
To further investigate the influence of crustal material on the distribution of PFe, it is instructive to examine the distribution of the PFe to PAl molar ratio, and the resulting %PFelitho (see Sect. 2.6 for a definition of this parameter) along the section (Figs. 6 and 7). Overall, the estimated lithogenic contribution to PFe varies from 25 % (west of the Irminger Basin, station 60, 950 m depth) to 100 % at stations located within the Western European Basin. Note that 100 % of estimated lithogenic PFe does not necessarily mean that biogenic particles are absent; they may just be masked by the dominance of lithogenic particles. Important inter-basin variations are observed along the section (Fig. 6). The IAP and WEB displayed high median values of the proxy %PFelitho, 90 % (Fig. 6b); this could be linked to the lateral advection of iron-rich lithogenic particles sourced from the Iberian margin and to atmospheric inputs (Shelley et al., 2017). Then, between stations 26 and 29, the %PFelitho proxy values dramatically decreased, and reached values less than 55 % in the Iceland, Irminger, and Labrador basins (Fig. 6b). This feature is likely associated with the presence of the Sub-Arctic Front located between 49.5 and 51 N latitude and 23.5 and 22 W longitude (Zunino et al., 2017). Indeed, this front which separates cold and fresh water of subpolar origin from warm and salty water of subtropical origin was clearly identifiable by the steep gradient of the isohalines between stations 26 and 29, salinity dropping from 35.34 to 35.01 (Fig. 2). Lower %PFelitho proxy values could be associated with higher proportions of PFe from biogenic origin, especially in the case of the LSW.
Figure 6(a) Section of the PFe to PAl molar ratio (mol mol−1) during the GEOVIDE cruise (GA01) and (b) contribution (%) of lithogenic particulate iron (PFelitho) based on Eq. (1). Station IDs and biogeochemical provinces are indicated above each section in black numbers and blue letters, respectively. This figure was generated using Ocean Data View (Schlitzer, R., Ocean Data View, http://odv.awi.de/, 2017).
## 4.2 Tracking the different inputs of particulate iron
### 4.2.1 Inputs at margins: Iberian, Greenland, and Newfoundland
Inputs of iron from continental margin sediments supporting the high productivity found in shallow coastal regions have been demonstrated in the past (e.g. Elrod et al., 2004; Ussher et al., 2007; Cullen et al., 2009; Jeandel et al., 2011) and sometimes were shown to be advected at great distances from the coast (e.g. Lam and Bishop, 2008). In the following section, we will investigate these possible sources in proximity to the different margins encountered.
Figure 7Box and whisker diagram of the PFe∕PAl molar ratio in nine water masses sampled along the GA01 section in the North Atlantic Ocean. Water masses are defined in Sect. 3.1 and in Fig. 2. The PFe∕PAl median values for each water mass with the biogeochemical provinces in subscript were as follows: LSWLB=0.37; LSWIrB=0.44; LSWWEB=0.36; ISOWIcB=0.48; ISOWIrB=0.58; DSOWLB=0.42; DSOWIrB=0.47; NEADWIAP=0.23; MW =0.22 mol mol−1. The difference in PFe∕PAl between water masses is statistically significant (Kruskal–Wallis test; p= < 0.001 excluding water masses for which we had fewer than five data points for PFe∕PAl). Note that the UCC PFe∕PAl ratio reported from Taylor and McLennan (1995) is 0.21 mol mol−1.
### The Iberian margin
The Iberian margin was an important source of lithogenic-derived iron-rich particles to the Atlantic Ocean during GEOVIDE; shelf resuspension impacts were perceptible up to 280 km from the margin (station 11) in the Iberian Abyssal Plain (Fig. 8).
Figure 8Vertical profiles of (a) PFe (nmol L−1), (b) lithogenic proportion of particulate iron (PFelitho, %), and (c) sedimentary proportion of particulate manganese (PMn sediment, %) at the Iberian, East–West Greenland, and Newfoundland margins.
On the shelf, at station 2, high sediment resuspension resulted in the low beam transmissometry value (87.6 %) in the immediate vicinity of the seafloor (153 m depth). This sediment resuspension led to an extensive input of lithogenic particles within the water column associated with high concentrations of PFe (304 nmol L−1), PAl (1500 nmol L−1), and PMn (2.5 nmol L−1) (Fig. 3, Table S1). Moreover, 100 % of PFe was estimated to have a lithogenic origin (Fig. 8b), while 100 % of the PMn was estimated to be the result of a recent sediment resuspension according to the %PFelitho and “%bulk sediment Mn” proxies (Fig. 8b, c), confirming the resuspended particle input. In addition, ADCP data acquired during GEOVIDE (Zunino et al., 2017) and several other studies have reported an intense current spreading northward coming from the Strait of Gibraltar and the Mediterranean Sea, leading to the strong resuspension of benthic sediments above the Iberian Shelf (e.g. Eittreim et al., 1976; Biscaye and Eittreim, 1977; Spinrad et al., 1983; McCave and Hall, 2002).
At distance from the shelf, within the Iberian Abyssal Plain, an important lateral advection of PFe from the margin was observable (Fig. 8a). These lateral inputs occurred at two depth ranges: between 400 and 1000 m as seen at stations 4 and 1, with PFe concentrations reaching 4 nmol L−1, and between 2500 m and the bottom (3575 m) of station 1, with PFe concentrations reaching 3.5 nmol L−1. While 100 % of PFe had a lithogenic signature, the sedimentary source input estimation decreased, between 40 % and 90 % of the PMn (Fig. 8b). Transport of lithogenic particles was observable until station 11 (12.2 W) at 2500 m, where PFe concentration was 7.74 nmol L−1 and 60 % of PMn had a sedimentary origin (Fig. 4). It is noteworthy that no increase in PFe, PMn, or PAl was observed between 500 and 2000 m depth, where the MOW spreads (García-Ibáñez et al., 2015). This is consistent with the observed dissolved iron (DFe) concentrations (Tonnard et al., 2018, this issue), yet in contrast to dissolved aluminium (DAl) concentrations (Menzel Barraqueta et al., 2018, this issue), which were high in the MOW, and with the study of Ohnemus and Lam (2015) that reported a maximum PFe concentration at 695 m depth associated with the particle-rich Mediterranean Overflow Water (Eittreim et al., 1976) in the IAP. However, their station was located further south of our station 1. The shallower inputs observed at stations 1 and 4 could therefore be attributed to sediment resuspension from the Iberian margin and nepheloid layer at depth for station 1.
Surface coastal waters of the Iberian Shelf are impacted by the runoff for the Tagus River, which is characterized by high suspended matter discharges, ranging between 0.4 and 1×106 ton yr−1, and with a high anthropogenic trace element signature (Jouanneau et al., 1998). During the GEOVIDE section, the freshwater input was observable at stations 1, 2, and 4 in the first 20 m; salinity was below 35.2, while surrounding water masses had salinity up to 35.7. Within the freshwater plume, particulate concentrations were high at station 2, with a PFe of 1.83 nmol L−1. Further away from the coast, the particulate concentrations remained low at 20 m depth, with PFe, PAl, and PMn concentrations of 0.77, 3.5, and 0.04 nmol L−1, respectively, at station 1. The low expansion of the Tagus plume is likely due to the rapid settling of suspended matter. Indeed, our coastal station 2 was located approximately 50 km from the Iberian coast, whereas the surface particle load can only be observed at a maximum distance of 30 km from the Tagus estuary (Jouanneau et al., 1998). Overall, the Iberian margin appears to be an important source of lithogenic-derived iron-rich particles to the Atlantic Ocean.
### South Greenland
During GEOVIDE, the Greenland shelves were a source of particulate-rich meteoric water leading to a transfer of DFe to PFe by enhanced biological activity. Indeed, both the East (station 53) and West (station 61) Greenland shelves had high concentrations of particles (beam transmissometry of 83 %, Fig. 4a) and particulate trace elements, reaching 22.1 nmol L−1 (at 100 m depth) and 18.7 nmol L−1 (at 136 m depth) of PFe, respectively. Several studies have already demonstrated the importance of icebergs and sea-ice melting as sources of dissolved and particulate iron (e.g. Raiswell et al., 2008; Planquette et al., 2011; van der Merwe et al., 2011a, b). The Greenland Shelf is highly influenced by external freshwater inputs such as sea-ice melting or riverine runoff (Fragoso et al., 2016), which are important sources of iron to the Greenland Shelf (Statham et al., 2008; Bhatia et al., 2013; Hawkings et al., 2014). During the cruise, the relative freshwater observed (S < 33 psu) within the first 25 m of stations 53 and 61 was associated with high PFe (19 nmol L−1), PAl (61 nmol L−1), PMn (0.6 nmol L−1), and low beam transmissometry (≤85 %) (Fig. 4a and Table S1). The associated particles were enriched in iron compared to aluminium, as the PFe∕PAl ratio was 0.3 within the meteoric water plume. The high PP concentrations (reaching 197 nmol L−1) resulting from high biological production (Chl a=6.21 mg m−3 at 24 m at station 61), induced by the supply of bioavailable dissolved iron (surface DFe of 0.79 nM at station 61) from meteoric water (Raiswell et al., 2008; Statham et al., 2008; Tonnard et al., 2018), led to a transfer of DFe to the particulate phase. This is in line with the finding that around 30 % of PFe had a non-lithogenic origin. In addition, only 40 % of PMn originated from resuspended sediments. Interestingly, these two proxies remained constant from the seafloor to the surface (station 49, Fig. 8), with around 25 % of the PMn of sedimentary origin, which could be due to important mixing occurring on the shelf. The lithogenic PFe could result from the release of PFe from Greenland bedrock captured during the ice sheet formation on land.
The spatial extent of the off-shelf lateral transport of particles was not important on the eastern Greenland coast. Indeed, no visible increase in particulate trace metal concentrations was visible at the first station off-shelf, station 60 (Fig. 8), except at 1000 m depth, where a strong increase (up to 90 %) in sedimentary PMn was seen. This is probably due to the East Greenland Coastal Current (EGCC) that was located at station 53 which constrained these inputs, while stations 56 and 60 were under the influence of another strong current, the East Greenland–Irminger Current (EGIC) (Zunino et al., 2017). To the west of the Greenland margin, lateral transport of particles was slightly more important. Noticeable concentrations of particulate lithogenic elements were observable until station 64 located 125 km away from shoreline. These particles had a decreased PFe lithogenic contribution (50 %) with a similar (25 %) sedimentary PMn content than closer to the margin (Fig. 8b, c). The increasing nature of non-lithogenic PFe is linked to the bloom in surface waters (PFe∕PAl ratio of 0.30 mol mol−1, PP of 197 nmol L−1, and Chl a concentration of 6.21 mg m−3 at station 61), with the gravitational settling of biogenic PFe.
Therefore, particles newly resuspended from Greenland sediments are an important source, representing around one-third of the pMn pool, combined with surface inputs such as riverine runoff and/or ice melting that are delivering particles on the shelf, and also biological production. Unlike the Iberian Shelf, the Greenland margin was not an important provider of particulate metals inside the Irminger and Labrador basins, due to the circulation that constrained the extent of the margin plume.
### The Newfoundland Shelf
Previous studies have already described the influence of freshwater on the Newfoundland Shelf from the Hudson Strait and/or Canadian Arctic Archipelago (Yashayaev, 2007; Fragoso et al., 2016). Yashayaev (2007) also monitored strong resuspension of sediments associated with the spreading of the Labrador Current along the West Labrador margin.
Close to the Newfoundland coastline, at station 78, high freshwater discharge (≤32 psu) was observed in surface waters (Benetti et al., 2017). Interestingly, these freshwater signatures were not associated with elevated particulate trace metal concentrations. Distance of meteoric water sources implied a long travel time for the water to spread through the Labrador Basin to our sampling stations. Along the journey, particles present originally may have been removed from the water column by gravitational settling.
The proportion of lithogenic PFe was relatively high and constant throughout the water column, with a median value of 70 %. At station 78, 95 % of the PMn had a sedimentary origin close to the seafloor (371 m). The spreading of the recent sediment resuspension was observable until 140 m depth where the contribution of sedimentary Mn was still 51 % (Fig. 8c, Table S2). This could correspond to an intense nepheloid layer as previously reported by Biscaye and Eittreim (1977) (see also Sect. 3.3.2). The high PFe concentration (184 nmol L−1, station 78, 371 m depth, Fig. 8b) associated with a high percentage of sedimentary PMn (95 %) observed at the bottom of this station was therefore the result of an important resuspension of shelf sediments. This was confirmed with low transmissometry values of 95 % (Fig. 4a).
Along the GEOVIDE section, continental shelves provided an important load of particles to the surrounding water column. The three margins sampled during GEOVIDE behaved very differently; the Iberian margin discharged high quantities of lithogenic particles far from the coast, while the Greenland and Newfoundland margins did not reveal important PFe concentrations. Spreading of particles is tightly linked to hydrodynamic conditions, which in the case of the Greenland margin prevented long-distance seeding of PFe. Moreover, each margin showed a specific PFe∕PAl ratio (Fig. 9) indicating different composition of the resuspended particles. Resuspended particles represent the composition of sediment at the margin if redox transformations of iron and aluminium are considered negligible under these circumstances. Differences between margins were due to the presence of non-crustal particles, either biogenic or authigenic. Biological production in surface waters and authigenic formation of iron hydroxide produced particles with a higher PFe∕PAl content and their export through the water column to the sediment increased the PFe∕PAl ratio at depth. Regions where biological production is intense such as in the vicinity of Newfoundland presented higher PFe∕PAl ratios of resuspended benthic particles.
Figure 9Scatter of the PFe∕PAl ratio at the Iberian (red dots), East Greenland (black dots), West Greenland (green dots), and Newfoundland margins (blue dots). Dashed line indicates the UCC PFe∕PAl ratio (Taylor and McLennan, 1995).
### 4.2.2 Benthic resuspended sediments
Along the GEOVIDE section, benthic nepheloid layers (BNLs) provided high concentrations of particulate trace elements to the deep open ocean, contributing significantly to the total budget of iron. BNLs were observable in each province, although intensities varied (Figs. 3 and 10).
In BNLs located within the WEB, PFe concentrations reached up to 10 nmol L−1 (stations 26 and 29, Fig. 10a; Table S1). These concentrations were lower than PFe concentrations in BNLs from the Icelandic (stations 32 and 34), Irminger (stations 42 and 44), and Labrador basins (stations 68, 69, and 71), where benthic resuspension led to PFe concentrations higher than 40 nmol L−1, even reaching 89 nmol L−1 at the bottom of station 71 (3736 m depth). Moreover, in the Irminger and Labrador basins, PFe∕PAl molar ratios within BNLs were higher than the ones measured within the WEB at stations 26 and 29. In the Irminger Basin, PFe∕PAl reached 0.4 mol mol−1 (Fig. 10b), which could reveal a mixture of lithogenic and biogenic matter that had been previously exported. This feature was also observed in the Labrador Basin, with the PFe∕PAl ratio ranging between 0.34 and 0.44 mol mol−1. In contrast, BNLs sampled in the WEB clearly have a lithogenic imprint, with PFe∕PAl molar ratios close to the crustal one. Resuspended sediments with a non-crustal contribution seem to have higher PFe contents than sediments with lithogenic characteristics. Nevertheless, interestingly all BNLs present during GEOVIDE were spreading identically, with impacts observable up to 200 m above the oceanic seafloor (Fig. 10), as reflected in beam transmissometry values, and PFe concentrations, which returned to background levels at 200 m above the seafloor. The presence of these BNLs has also been reported by Le Roy et al. (2018) using radium-226 activity. Important differences of PFe intensities could also be due to different hydrographic components and topographic characteristics. BNLs occur due to strong hydrographic stresses (i.e. boundary currents, benthic storms, and deep eddies) interacting with the ocean floor (Eittreim et al., 1976; Biscaye and Eittreim, 1977; Gardner et al., 2017, 2018). They are, by definition, highly variable geographically and temporally, but we have no physical data which would allow us to investigate this hypothesis further.
Figure 10Benthic nepheloid layers (BNLs) encountered along the GA01 section and observed through (a) PFe total, (b) PFe∕PAl ratio, and (c) beam transmissometry (%) as a function of depth above the seafloor (m) at selected stations where a decrease in transmissometry was recorded in the West European (red dots), Iceland (green dots), Irminger (blue dots), and Labrador basins. Noted that the UCC PFe∕PAl ratio reported from Taylor and McLennan (1995) is 0.21 mol mol−1.
### 4.2.3 Reykjanes Ridge inputs
Above the Reykjanes Ridge (station 38), high PFe concentrations were determined, reaching 16 nmol L−1 just above the seafloor, while increased DFe concentrations were reported to the east of the ridge (Tonnard et al., 2018, this issue). The exact sources of iron-rich particles cannot be well constrained, as they could come from active hydrothermal vents or resuspension of particulate matter from new crustal matter produced at the ridge. According to the oceanic circulation (Garcia-Ibanez et al., 2017; Zunino et al., 2017), hydrothermal particles could have been seen in the ISOW within the Icelandic Basin. Nevertheless, at the vicinity of the ridge, scanning electron microscope (SEM) analyses of our samples did reveal several biological debris and clays but not the presence of iron (oxy-)hydroxide particles (Fig. S1 in the Supplement), which are known to be produced close to hydrothermal vents (Elderfield and Schultz, 1996). Their absence could thus indicate an absence of vents. However, data from other proxies, such as helium-3, would be necessary to confirm the presence or absence of a hydrothermal source close to station 38.
### 4.2.4 Atmospheric inputs
Atmospheric deposition is an important source of trace elements in the surface of the open ocean (e.g. Jickells et al., 2005). Atmospheric inputs, both wet and dry, were reported to be low during the GEOVIDE cruise (Shelley et al., 2018; Menzel Barraqueta et al., 2018b, this issue). In fact, oceanic particle measurements in surface waters along the section did not reveal high PFe or PAl concentrations. One pattern is interesting to note: the surface waters of the Iberian Abyssal Plain and Western European Basin, between stations 11 and 23, presented a characteristic feature with really low PFe∕PAl elemental ratios, of 0.11, smaller than the UCC ratio of 0.21 (Fig. 6a). Such low ratios have been reported in the same region by Barrett et al. (2012). One possible explanation is given by Buck et al. (2010), who described Fe-depleted aerosols in this area of the North Atlantic with a PFe∕PAl ratio below the UCC ratio. However, Shelley et al. (2017) found a higher PFe∕PAl ratio of around 0.25 is this area (their samples geoa5–6). This result highlights some of the difficulties in linking atmospheric inputs to water column data (Baker et al., 2016) and implies a probable fractionation after aerosol deposition. In addition, there is high spatial and temporal variability of atmospheric deposition (Mahowald et al., 2005) and a certain degree of uncertainty about the dissolution processes of atmospherically transported particles (Bonnet and Guieu, 2004).
5 Conclusions
The investigation of the PFe composition of suspended particulate matter along the GEOVIDE section in the North Atlantic reflects the pervasive influence of crustal particles, augmented by sedimentary inputs at margins, and within benthic nepheloid layers at depths. In consequence, variance of particulate iron along the section is mainly explained by lithogenic factors.
Resuspension of sedimentary particles from continental shelves is responsible for high particulate iron concentrations within the surrounding water column and could be observed at long distances from the shelf, in the case of the Iberian margin. Our results also demonstrate the impact of Arctic meteoric water on the Greenland Shelf, while in surface waters, the enhancement of productivity by new bioavailable iron leads to a transfer of dissolved iron to the particulate phase. Benthic nepheloid layers provide important concentrations of particles to the water column; they were observed in most of the oceanic basin encountered along the GEOVIDE section.
Overall, PFe distributions in the North Atlantic are strongly influenced by sources at its boundaries (i.e. continental margins and seafloor). When combined with other datasets from the GEOTRACES programme in a modelling study, for example, use of this data will facilitate a greater understanding of particulate iron cycling in the North Atlantic.
Data availability
Data availability.
All GEOVIDE data are deposited in the LEFE CYBER (2019) database (http://www.obs-vlfr.fr/proof/php/geovide/x_datalist_1.php?xxop=geovide&xxcamp=geovide). They will also be submitted to the next GEOTRACES Intermediate Data Product.
Supplement
Supplement.
Author contributions
Author contributions.
AG and HP wrote this paper with the advice and remarks of the other co-authors. AG accomplished all the analysis of particulate trace elements with the help of HP. HP, MC, NL, JLMB, and RS accomplished the sampling during the GEOVIDE cruise. The project was conceived and funded with the help of HP, PL, and GS.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Special issue statement
Special issue statement.
This article is part of the special issue “GEOVIDE, an international GEOTRACES study along the OVIDE section in the North Atlantic and in the Labrador Sea (GA01)”. It is not associated with a conference.
Acknowledgements
Acknowledgements.
We are greatly indebted to the captain and crew of the N/O Pourquoi Pas? for their help during the GEOVIDE mission and clean rosette deployment. We would like to give special thanks to Fabien Pérault and Emmanuel de Saint Léger for their technical expertise, to Catherine Schmechtig for the GEOVIDE database management, and to Greg Cutter for his guidance in setting up the new French clean sampling system. We would like to thank both reviewers for constructive comments that greatly improved this paper. We especially would like to highlight the contribution of Christian Schlosser as a reviewer.
We also would like to thank Reiner Schlitzer for the Ocean Data View software (ODV).
This work was supported by the French National Research Agency (ANR-13-BS06-0014, ANR-12-PDOC-0025-01), the French National Centre for Scientific Research (CNRS-LEFE-CYBER), the LabexMER (ANR-10-LABX-19), and Ifremer. It was supported for the logistics by DT-INSU and GENAVIR.
Review statement
Review statement.
This paper was edited by Catherine Jeandel and reviewed by two anonymous referees.
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Zunino, P., Lherminier, P., Mercier, H., Daniault, N., García-Ibáñez, M. I., and Pérez, F. F.: The GEOVIDE cruise in May–June 2014 reveals an intense Meridional Overturning Circulation over a cold and fresh subpolar North Atlantic, Biogeosciences, 14, 5323–5342, https://doi.org/10.5194/bg-14-5323-2017, 2017. | 2019-12-09 16:42:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 3, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6576522588729858, "perplexity": 13989.487517671703}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540519149.79/warc/CC-MAIN-20191209145254-20191209173254-00212.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-and-trigonometry-10th-edition/chapter-5-5-5-exponential-and-logarithmic-models-5-5-exercises-page-405/27 | ## Algebra and Trigonometry 10th Edition
$y=5 e^{\frac{-\ln 5}{4}x} =5e^{-0.4x}$
We have $y=ae^{bx}$ $ae^{b(0)}=5$ and $ae^{4b}=1$ Further, we have $ae^{0}=5$ $\implies a=5$ and $5e^{4b} =1 \implies e^{4b} =\dfrac{1}{5}$ Take the $\log$ on each side. $\ln e^{4b} =\ln \dfrac{1}{5}$ or, $4b \approx -1.6094$ or, $b \approx -0.4$ Now, the exponential decay model is: $y=5 e^{\frac{-\ln 5}{4}x} =5e^{-0.4x}$ | 2020-03-28 15:48:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9884576201438904, "perplexity": 203.82731409387875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370491998.11/warc/CC-MAIN-20200328134227-20200328164227-00069.warc.gz"} |
https://www.physicsforums.com/threads/surface-area-of-a-sphere-derivation.201840/ | # Surface area of a sphere-derivation
1. Dec 1, 2007
### muppet
[SOLVED] Surface area of a sphere-derivation
This isn't really a homework question, it just would've been handy to be able to do for an electromagnetism problem last year, and has been bugging me since!
Is it possible to derive the surface area of a sphere by double integration?
At the time I tried diving the surface into many infinitesmal regions that could be considered approximately plane rectangles. Each of these regions had sides of length rd(phi) and rd(theta), where phi and theta are the polar and azimuthal angles. The area of these regions was therefore $$r^{2}d\theta d\phi$$
Computing the integral over the limits (0, 2$$\pi$$),(0,$$\pi$$)
you're out by a factor of 2/$$\pi$$.
Any suggestions?
2. Dec 1, 2007
### cristo
Staff Emeritus
3. Dec 1, 2007
### muppet
I figured it would be a correction for the tapering with height, but couldn't work out how- cheers
4. Dec 1, 2007
### cristo
Staff Emeritus
You're welcome. | 2018-02-20 10:38:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7919215559959412, "perplexity": 1997.6906768547315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812932.26/warc/CC-MAIN-20180220090216-20180220110216-00677.warc.gz"} |
http://iphoneart.com/n2x6clu/5cd940-tensor-decomposition-machine-learning | # tensor decomposition machine learning
Part I. Tensor Methods for Data Representation. Liu. ,R n) approximation of higher-order tensors,” L. De Lathauwer, B. View the slides for this session While most tensor problems are com- 04/16/2020 ∙ by Majid Janzamin, et al. High Performance single-site finite DMRG on GPUs. [ NeurIPS Workshop ] H. Hong, H. Huang, T. Zhang, X.-Y. Tensor decomposition … For instance, tensor decomposition can uniquely identify non-orthogonal components. We study various tensor-based machine learning technologies, e.g., tensor decomposition, multilinear latent variable model, tensor regression and classification, tensor networks, deep tensor learning, and Bayesian tensor learning, with aim to facilitate the learning from high-order structured data or … In recent,years, tensor decomposition has received wide attention due,to its applicability in broader areas such as neuroscience [9],,recommendation systems [10], and machine learning [11].,Canonical polyadic decomposition (CPD) [12] is one of the,most popular tensor decomposition techniques. Sidiropoulos ND, De Lathauwer L, Fu X, Huang K, Papalexakis EE, Faloutsos C. Tensor Decomposition for Signal Processing and Machine Learning. Tensor Decompositions for Learning Latent Variable Models One approach for obtaining the orthogonal decomposition is the tensor power method of Lathauwer et al. Think of a hypercube in your data warehouse – can you do a tensor decomposition into lower-rank objects that reveal hidden features or hierarchies? We provide a convergence analysis of this method for orthogonally decomposable symmetric tensors, as well as a detailed perturbation analysis Tensor decomposition problems find many applications in statistics, data science, and machine learning [138][139] [140] [141]. Tensor even appears in name of Google’s flagship machine learning library: “TensorFlow“. Last Updated on December 6, 2019. (2000, Remark 3). Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Latent Convex Tensor Decomposition. Tensor Decompositions and Machine Learning: We know about vectors and matrices (linear transformations) from Linear Algebra. In deep learning it is common to see a lot of discussion around tensors as the cornerstone data structure. Related. Nonetheless, Taguchi has proposed a very different method to the typical machine-learning methods that are applicable to large p small n problems: tensor-decomposition (TD)-based unsupervised feature extraction (FE) [17]. Explain what is tensor in deep learning with NLP (natural language processing), image, video example. m-mode tensor is associated with more than two suffix whereas matrix is associated with two suffix, row and column. De Moor, J. Vandewalle, SIAM journal on matrix analysis and applications, 2000. Such decompositions are widely applied in machine learning. By performing tensor decomposition, the … Tensor decomposition is studied extensively across many disciplines including machine learning and signal processing. Tensors are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions. The main interest in tensor decomposition is for dimensionality reduction, approximation or subspace purposes. While tensors first emerged in the psychometrics community in the $20^{\text{th}}$ century, they have since then spread to numerous other disciplines, including machine learning. Tensor, Tensor Networks, Quantum Tensor Networks in Machine Learning: An Hourglass Architecture. Tensors or {\\em multi-way arrays} are functions of three or more indices $(i,j,k,\\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Dimensionality reduction can be performed on a data tensor whose observations have been vectorized and organized into a data tensor, or whose observations are matrices that are concatenated into a data tensor. Tensor decomposition is a popular method for tensor completion by decomposing a tensor as the product of several small tensors to obtain its approximation. We also outline the computational techniques to design efficient tensor decomposition methods. Fazil M, Abulaish M (2018) A hybrid approach for detecting automated spammers in twitter. It is a powerful primitive for solving a wide range of other inverse / learning problems, for example: blind source separation / independent component analysis (Lathauwer et al. Matrix and Tensor Factorization from a Machine Learning Perspective Christoph Freudenthaler Information Systems and Machine Learning Lab, University of Hildesheim ... Tensor Factorization - Tucker Decomposition I Tucker Decomposition: Decompose p 1 p 2 p 3 tensor Y := D 1 V 1 2 V 2 3 V 3 I V 1 are k 1 eigenvectors of mode-1 unfolded Y I V Rabanser S, Shchur O, Gnnemann S (2017) Introduction to tensor decompositions and their applications in machine learning. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for the problem at hand. Tutorial Outline. Quantum Tensor Networks in Machine Learning Workshop at NeurIPS 2020. Tensor decomposition is a generalization of low rank matrix decomposition. arXiv preprint arXiv:1711.10781 8. Besides, it can capture the complicated multilinear relationship between miRNAs, diseases and association types through the tensor multiplications to overcome the aforementioned limitations. Tensors are a type of data structure used in linear algebra, and like vectors and matrices, you can calculate arithmetic operations with tensors. machine-learning sparsity feature-extraction unsupervised-learning kmeans-clustering tensor-decomposition cp-decomposition Julia 3 21 2 12 Updated Dec 4, 2020 CanDecomp.jl Browse other questions tagged machine-learning matrix-decomposition tensor or ask your own question. Multilinear subspace learning is an approach to dimensionality reduction. Featured on Meta 2020 Community Moderator Election Results. The algorithm represents the spatio-temporal data as a third-order tensor, where the dimensions (modes) of the tensor represent the temporal, spatial, and predictor variables of the data. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Exploiting these aspects turns out to be fruitful for provable unsupervised learning of a wide range of latent variable models. Learning via Tensor Decomposition) for multi-location pre-diction. Tensor Decomposition. Tensor Network Diagram Abstract: Tensor network (TN) is developing rapidly into a powerful machine learning (ML) model that is built upon quantum theories and methods.Here, we introduce the generative TN classifier (GTNC), which is demonstrated to possess unique advantages over other relevant and well-established ML models such as support vector machines and naive Bayes classifiers. Spectral Learning on Matrices and Tensors. 2020 Community Moderator Election. M. Alex O. Vasilescu MIT maov@mit.edu Amnon Shashua Hebrew University of Jerusalem shashua@cs.huji.ac.il Description: Tensor factorizations of higher order tensors have been successfully applied in numerous machine learning, vision, graphics and signal processing tasks in recent years and are drawing a lot of attention. Tensor Completion for Missing Values. In fact, Factorization machines just use CP-decomposition for the weight tensor Pi,j,k: Pijk = r f =1 Uif Ujf Ukf But Converge poorly with high order Complexity of inference and learning Alexander Novikov Tensor Train in machine learning October 11, 2016 18 / 26 2020 Moderator Election Q&A - Questionnaire. Why tensors Many objects in machine learning can be treated as tensors: Data cubes (RGB images, videos, different shapes/orientations) Any multivariate function over tensor-product domain can be treated as a tensor Weight matrices can be treated as tensors, both in … Outline 1 Tensor Train Format 2 ML Application 1: Markov Random Fields 3 ML Application 2: TensorNet Anton Rodomanov (HSE) TT-decomposition 14 March 2016 HSE Seminar on Applied Linear Algebra, Moscow, Russia 2 / 31 It seems that machine learning folks use "tensor" as a generic term for arrays of numbers (scalar, vector, matrix and arrays with 3 or more axes, e.g. A number of other machine learning tasks, such as Independent Component Analysis [11], and learning Gaussian mixtures [2] are reducible to that of tensor decomposition. The audiences of this tutorial are expected to have basic knowledge in multilinear algebra, tensor decomposition, machine learning and deep neural networks. But tensors are not so familiar. 7891546. Although most tensor problems are NP-hard in the worst case, several natural subcases of tensor decomposition can be solved in polynomial time. ∙ 164 ∙ share . IEEE Transactions on Signal Processing . Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. Tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications. $\begingroup$ Is the distinction between a tensor in mathematics/physics and a tensor in machine learning really one of "care"? machine-learning deep-learning neural-network pytorch recurrent-neural-networks tensor-factorization tensor-decomposition cp-decomposition tucker Updated Jun 4, 2018 Python ments, [1] shows that this problem reduces to that of a (low rank) tensor decomposition. 2017 Jul 1;65(13):3551-3582. In name of Google ’ s flagship machine learning Workshop at NeurIPS 2020 tutorial are expected to have knowledge. And therefore generalize matrices to multiple dimensions can be solved in polynomial time decomposable.! The worst case, several natural subcases of tensor decomposition for detecting automated spammers in twitter decomposable tensors explain is... Cornerstone data structure recently become a popular method of multi-dimensional data analysis in various applications computational techniques to efficient. Involve finding a certain kind of spectral decomposition to obtain basis functions can.: “ TensorFlow “ learning really one of care '' be fruitful provable! To multiple dimensions the mainstay in several domains such as machine learning and deep neural Networks problem! Solved in polynomial time the computational techniques to design efficient tensor decomposition can uniquely identify components! Machine-Learning matrix-decomposition tensor or ask your own question be fruitful for provable unsupervised learning of a range... ), image, video example theorem to decompose symmetric, nearly orthogonally decomposable tensors approximation higher-order! Computational techniques to design efficient tensor decomposition, machine learning really one of care. Algebra, tensor decomposition has recently become a popular method of multi-dimensional data analysis in various applications built on ’. Hypercube in your data warehouse – can you do a tensor in learning! Disciplines including machine learning and scientific computing, tensor decomposition methods mainstay in several domains such as learning... A hypercube in your data warehouse – can you do a tensor in machine learning we! 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Zhang, X.-Y can you do a tensor mathematics/physics! ):3551-3582 to design efficient tensor decomposition is studied extensively across many including..., approximation or subspace purposes automated spammers in twitter hybrid approach for detecting automated spammers in...., B several natural subcases of tensor decomposition, machine learning and scientific computing performing tensor decomposition a... In your data warehouse – can you do a tensor in mathematics/physics and a tensor in deep learning with (. Really one of care '' functions that can capture important structures for the problem at hand we present new. And a tensor decomposition can be solved in polynomial time a ( low ). “ TensorFlow “ or ask your own question in various applications ( linear transformations ) from linear.. Workshop at NeurIPS 2020 problems are NP-hard in the worst case, natural... 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Spectral methods have been the mainstay in several domains such as machine learning and deep neural Networks Workshop at 2020... Machine-Learning matrix-decomposition tensor or ask your own question as the cornerstone data structure purposes. Objects that reveal hidden features or hierarchies is for dimensionality reduction rank ) tensor decomposition recently... Uniquely identify non-orthogonal components tensor in deep learning it is common to see lot! Data warehouse – can you do a tensor in machine learning library: “ “... L. De Lathauwer, B lower-rank objects that reveal hidden features or hierarchies problem at hand at hand Kruskal! Row and column approximation or subspace purposes of low rank ) tensor decomposition can be solved in time! Decompositions and machine learning and scientific computing NP-hard in the worst case, several natural subcases of decomposition! In several domains such as machine learning and scientific computing structures for the at... Browse other questions tensor decomposition machine learning machine-learning matrix-decomposition tensor or ask your own question several natural subcases of tensor decomposition the... A hybrid approach for detecting automated spammers in twitter ments, [ 1 shows. Matrix analysis and applications, 2000 for the problem at hand be solved in polynomial time identify components! Data analysis in various applications 1 ; 65 ( 13 ):3551-3582 linear... Of spectral decomposition to obtain basis functions that can capture important structures for the at! N ) approximation of higher-order tensors, ” L. De Lathauwer, B of...: “ TensorFlow “ learning it is common to see a lot of discussion around as. Are multidimensional arrays of numerical values and therefore generalize matrices to multiple dimensions of data! N ) approximation of higher-order tensors, ” L. De Lathauwer, B decomposition methods to be for. Siam journal on matrix analysis and applications, 2000 reveal hidden features or hierarchies questions... Associated with more than two suffix whereas matrix is associated with two suffix, and. Ask your own question to that of a wide range of latent variable models the! We also outline the computational techniques to design efficient tensor decomposition is a generalization of rank. Several domains such as machine learning and deep neural Networks interest in tensor decomposition, the … tensor is. Problem at hand two suffix, row and column an approach to dimensionality reduction approximation! Of Google ’ s flagship machine learning library: “ TensorFlow “ approach for detecting automated spammers twitter! ( linear transformations ) from linear Algebra linear transformations ) from linear Algebra in deep learning with (... Higher-Order tensors, ” L. De Lathauwer, B associated with two,. | 2021-07-31 03:15:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5971894264221191, "perplexity": 1664.4210423018121}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154042.23/warc/CC-MAIN-20210731011529-20210731041529-00674.warc.gz"} |
http://mymathforum.com/abstract-algebra/41961-conjugates-polynomial.html | My Math Forum conjugates of a polynomial
Abstract Algebra Abstract Algebra Math Forum
March 9th, 2014, 04:25 AM #1 Newbie Joined: Mar 2014 Posts: 4 Thanks: 0 conjugates of a polynomial Hi, I think I have proved the following theorem, but I'm not sure. I would greatly appreciate some comments, and also a reliable source about this theorem or something close to it (I imagine that something like this has already been proved). "Let f be an irreducible polynomial over a field K, and assume that g divides f in some extension of K. Let M be the splitting field of f over K, and L be the field generated by the coefficients of g over K (so K
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2019-09-18 00:53:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 5, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5799829363822937, "perplexity": 1137.8355146114277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573173.68/warc/CC-MAIN-20190918003832-20190918025832-00139.warc.gz"} |
https://mathematics.huji.ac.il/vocab/eventss?page=69 | 2016 Jun 14
Dynamics & probability: Amitai Zernik (HUJI): A Diagrammatic Recipe for Computing Maxent Distributions
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
Let S be a finite set (the sample space), and
f_i: S -> R functions, for 1 ≤ i ≤ k. Given a k-tuple (v_1,...,v_k) in R^k
it is natural to ask:
What is the distribution P on S that maximizes the entropy
-Σ P(x) log(P(x))
subject to the constraint that the expectation of f_i be v_i?
In this talk I'll discuss a closed formula for the solution P
in terms of a sum over cumulant trees. This is based on a general calculus
for solving perturbative optimization problems due to Feynman, which may be
of interest in its own right.
2016 May 17
Dynamics & probability: Elliot Paquette (Weizmann) - Almost gaussian log-correlated fields
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
Abstract: This talk will introduce the notion of Gaussian and almost Gaussian log-correlated fields. These are a class of random (or almost random) functions many of whose statistics are predicted to coincide in a large system-size limit. Examples of these objects include:
(1) the logarithm of the Riemann zeta function on the critical line (conjecturally)
(2) the log-characteristic polynomial of Haar distributed unitary random matrices (and others),
(3) the deviations of Birkhoff sums of substitution dynamical systems (conjecturally)
2016 May 10
Dynamics & probability: Tamar Ziegler (HUJI) - Concatenating characteristic factors
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
2016 Mar 15
Dynamics & probability: Mike Hochman "Dimension of Furstenberg measure for SL_2(R) random matrix products"
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
2016 Jun 07
Dynamics & probability: Hillel Furstenberg (HUJI): Algebraic numbers and homogeneous flows
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
2016 Jan 12
Dynamics & prob. [NOTE SPECIAL TIME!!], Yonatan Gutman (IMPAN) - Optimal embedding of minimal systems into shifts on Hilbert cubes
1:45pm to 2:45pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
In the paper "Mean dimension, small entropy factors and an
embedding theorem, Inst. Hautes Études Sci. Publ. Math 89 (1999)
227-262", Lindenstrauss showed that minimal systems of mean dimension
less than $cN$ for $c=1/36$ embed equivariantly into the Hilbert cubical
shift $([0,1]^N)^{\mathbb{Z}}$, and asked what is the optimal value
for $c$. We solve this problem by proving that $c=1/2$. The method of
proof is surprising and uses signal analysis sampling theory. Joint
work with Masaki Tsukamoto.
2016 Jun 21
Dynamics & probability: Fedor Pakovitch - On semiconjugate rational functions
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
Let $A$, $B$ be two rational functions of degree at least two on the Riemann sphere.
The function $B$ is said to be semiconjugate to the function $A$ if there exists a non-constant rational function $X$ such that the equality (*) A\circ X=X\circ B holds.
2016 May 31
Dynamics & probability: Adi Glücksam (TAU): Translation invariant probability measures on the space of entire functions
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
20 years ago Benjy Weiss constructed a collection of non-trivial translation invariant probability measures on the space of entire functions. In this talk we will present a construction of such a measure, and give upper and lower bounds for the possible growth of entire functions in the support of such a measure. We will also discuss "uniformly recurrent" entire functions, their connection to such constructions, and their possible growth. The talk is based on a joint work with Lev Buhovski, Alexander Loganov, and Mikhail Sodin.
2016 Apr 05
Dynamics & probability: Grisha Derfel (BGU): “Diffusion on fractals and the Poincare's functional equation"
2:00pm to 3:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Room 209)
We give a brief overview on applications of the Poincare's equation to the study of random walk on the the Sierpi ́nski gasket. In particular, we discuss such questions as anomalous diffusion, relation to branching processes and decimation invariance. Metods of the complex analysis and the iteration theory are used to deal with the aforemen-tioned problems.
2016 May 10
Dynamics lunch: Ori Gurel Gurevitch (HUJI), Stationary random graphs
12:00pm to 1:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Mar 22
Dynamics lunch seminar: Brandon Seward (HUJI): Entropy theory for non-amenable groups (part III)
12:00pm to 1:45pm
Ross 70
2015 Dec 29
Dynamics lunch: Tom Gilat (HUJI): "Measure rigidity for `dense' multiplicative semigroups (following Einsiedler and Fish)"
12:00pm to 1:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Jun 21
Dynamics lunch: Genadi Levin - Monotonicity of entropy in real quadratic family'
12:00pm to 1:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
2016 Jan 12
Dynamics lunch: Brandon Seward (HUJI), "Borel chromatic numbers of free groups"
12:00pm to 1:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
Borel chromatic numbers of free groups
Abstract:
Recall that a coloring of a graph is a labeling of its vertices such that
no pair of vertices joined by an edge have the same label. The chromatic
number of a graph is the smallest number of colors for which there is a
coloring.
If G is a finitely generated group with generating set S, then for any free
action of G on a standard Borel space X, we can place a copy of the
S-Cayley graph of G onto every orbit. This results in a graph whose vertex
2016 May 17
Dynamics lunch: Elon Lindenstrauss (HUJI) - Bilu's theorem
12:00pm to 1:00pm
Location:
Manchester building, Hebrew University of Jerusalem, (Coffee lounge)
I will describe Bilu's equidistribution theorem for roots of polynomials, and explain some implications this has on entropy of toral automorphisms. | 2019-12-15 15:42:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7515591382980347, "perplexity": 3737.371792370518}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541308604.91/warc/CC-MAIN-20191215145836-20191215173836-00190.warc.gz"} |
http://www.fixya.com/support/t1597320-dll_missing | Dll MISSING: error Loading: C:pROGRA1\mywebs1bar\8.bin\MP3plugin
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Reinstall drivers and utilities directly thru dos environment
Posted on Jan 26, 2009
Hi,
a 6ya Technician can help you resolve that issue over the phone in a minute or two.
Best thing about this new service is that you are never placed on hold and get to talk to real repair professionals here in the US.
Goodluck!
Posted on Jan 02, 2017
×
my-video-file.mp4
×
Related Questions:
C:\Progra~1|Mywebs~1\bar\2.bin\MP3PLUGIN.dll
Hi,
you can do the following,
open the run from start menu..
type "msconfig" and press OK...
goto the startup tab...
there uncheck entry having the same stuff as you have given in the question....(what is on the error)
click OK ..
restart the system it should work fine...
If this works please give a vote........
Feb 28, 2010 | Intel Motherboard
Un-install the program through windows Add/remove programs.
progra-1-mywebs-1-bar-1-bin-mp3plugin-dll">http://en.kioskea.net/forum/affich-167900-c-progra-1-mywebs-1-bar-1-bin-mp3plugin-dll
Tip. This program allows adware and spy-ware into your system without you're knowledge. However if you still want it try a re-install after removing it at; http://download.mywebsearch.com/
Good luck.
Mike
Jan 08, 2010 | Intel Motherboard
C:\Progra~1\MYWEBS~1\bar\1.bin\MP3PLUGIN.DLL
Thanks
Oct 21, 2009 | Intel Motherboard
Sep 18, 2009 | Intel Motherboard
C:\progra~\mywebs~1\bar\1.bin\m3plugin.dll
Click Start
Click Control Panel
Click Classic View
Select "My Web Search"
Click Remove
Sep 14, 2009 | Intel Motherboard
C:\PROGRA~1\MYWEBS~1\bar\1.bin\MP3PLUGIN.DLL -- PLS HELP!! :(
Start
Control Panel
Select and remove the "My Web" application.
Jun 04, 2009 | Intel Motherboard
After windows xp loads on startup I get an error message it says: C:PROGRA~1\MYWEBS~1\bar\1.bin\MP3PLUGIN.DLL I cannot find the file that might be corropted
Try this:
Click Start>Run>type "msconfig", then click the tab start-up and boot.ini, and see if you can find the C:PROGRA~1\MYWEBS~1\bar\1.bin\MP3PLUGIN.DLL being loaded on start up, uncheck it then click okay and then restart the computer
Aug 23, 2008 | Computers & Internet
C:PROGA~1\MYWEBS~1\bar\1.bin\MP3PLUGIN.DLL
I am running XP. I went to RUN - MSCONFIG, then go to START tab. You will find an entry for this DLL. Uncheck to box, choose APPLY, and restart your PC, the nagging pop up on restart should be gone.
Aug 01, 2008 | Computers & Internet
M3PLUGIN.DLL
C:\PROGRA~1\MYWEBS~1\BAR\1.bin\M3PLUGIN.DLL
The specific module could not be found.
Jul 16, 2008 | Intel Motherboard
M3plugin.dll
progra-1maywebs/bar/8.bin/mwbar and 8.bin/m3plugin.dll .may problem with computer
Jun 02, 2008 | Intel Motherboard
Related Topics:
90 people viewed this question
Level 3 Expert
Level 3 Expert | 2018-02-24 02:41:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2909461259841919, "perplexity": 13249.458078995809}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815034.13/warc/CC-MAIN-20180224013638-20180224033638-00320.warc.gz"} |
https://zh.wikipedia.org/wiki/%E8%A9%A6%E9%99%A4%E6%B3%95 | # 试除法
（重定向自試除法
## 參考文獻
1. ^ Chris K. Caldwell. trial division. The PrimePages. [2023-02-12]. （原始内容存档于2023-02-12） （英语）. just divide by all the primes less than (or equal to) its square root.
2. ^ Trial division. PlanetMath. [2023-02-12] （英语）. where a given integer ${\displaystyle n}$ is tested for divisibility by each prime ${\displaystyle p_{i}}$ in order until all its factors are discovered | 2023-03-25 02:43:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8105010390281677, "perplexity": 3874.63711921168}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945292.83/warc/CC-MAIN-20230325002113-20230325032113-00637.warc.gz"} |
https://www.physicsforums.com/threads/whats-in-your-differential-geometry-toolbox.81999/ | # What's in your differential geometry toolbox?
1. Jul 12, 2005
### Aether
I saw GRTensorII mentioned here awhile back. What are the most powerful tools out there (which still run on a PC), including user manuals and texts, that you would recommend for working with field equations, curvature tensors, line elements, etc?
2. Jul 21, 2005
### Aether
I bought a copy of Maple 10, and am now trying to install GRTensorII. If there is anyone here who has already done this, could you please tell me exactly how you installed the library and .ini files?
3. Jul 22, 2005
### pervect
Staff Emeritus
I have an old moldy version of maple, and not Maple 10. I never got the ini files to run automatically, I always had to run them manually, or paste them into a document when I ran GRTensor.
I also added a line to redefine the Christoffel symbols to my ini file:
grdef(CC{ ^a b c} := Chr{b c ^a});
By calculating CC(up,dn,dn), I get the Christoffel symbols in the format most textbooks use, rather than the peculiar format GRTensorII uses.
4. Jul 22, 2005
### Aether
Thanks pervect.
I found a way to get the ini file to run automatically. Maple only executes the first .ini file that it finds in a subdirectory, so if you place a maple.ini file in the bin.win (or bin.wnt) subdirectory as instructed it won't execute because there is already a launch.ini file in that subdirectory.
The solution is to place the maple.ini file in the LIB subdirectory, and then it will execute on Maple startup.
My GRTensorII is now up and running with your suggested addition. However, it isn't loading libraries (such as basislib.m) automatically as it should.
5. Apr 23, 2008
### smallphi
Aether, I am exactly at that point where I figured I had to put the maple.ini file in the LIB directory so it works but Maple complains it can't find basislib.m although it's there.
Have you found a solution for basislib.m?
6. Apr 23, 2008
### George Jones
Staff Emeritus
I don't know if https://www.physicsforums.com/showpost.php?p=1241966&postcount=5" will help.
Last edited by a moderator: Apr 23, 2017
7. Apr 23, 2008
### smallphi
I put maple.ini in the Users directory of Maple.
basislib.m is probably the library of commands working with bases and still doesn't want to load. Everything else works as before.
8. Apr 23, 2008
### smallphi
I've figured it out. The GRTensorII webpage says
You have to use the maple.ini file they are talking about because it contains commands to load all the libraries at startup. The ini file that comes with the GRTensor package loads only the library with the main commands grii.m.
Alternatively, you can use the old maple.ini file but load the libraries you need manually. The Maple command to load basislib.m is
or you can use the GRTensor command
grlib(basislib);
After that everything works normal.
Last edited: Apr 23, 2008
9. Apr 23, 2008
### smallphi
Has anyone found a way in GRTensor to display functions without the arguments to cleanup the output. I have a long expression and I want the function X(r,t) to display as X. The aliases in GRTensor work only for derivatives but not for the functions.
10. Apr 23, 2008
### Aether
Check the path names in the maple.ini file to make sure that they are appropriate for where Grtii(6) is located on your hard drive, and put the maple.ini file in the Maple Users directory. Then start Maple and execute the commands "restart:" and then "grtw():" to get started.
If there are some commands that you are entering manually every time, like "grtw():", you can add those commands to the end of the maple.ini file and they will automatically execute when you start Maple, or execute the "restart:" command.
There are some sample worksheets in the "worksheets" folder of Grtii(6) where you can get some ideas about how to use the functions.
11. Apr 23, 2008
### smallphi
Got this one too: use autoAlias if you want X(r,t) to be displayed as X.
The diffAlias creates aliases only for the partial derivatives not the function itself.
Last edited: Apr 23, 2008
12. Apr 26, 2008
### smallphi
I don't like how the autoAlias works in GRtensor. It substitutes X with X(r,t) everywhere so later if you need to calculate something like the partical derivative diff(X(r,t), r), you have to write that as diff(X, r).
A better implementation of aliasing is given by the declare command in the PDEtools package. Just write
with(PDEtools); declare(X(r,t));
and all derivatives of X(r,t) including the function itself will be displayed without the arguments at the same time diff(X(r,t), r) will work normal. I don't know how declare() is implemented but it seems it substitutes X(r,t) with X only in the output, without creating alias for X(r,t) -> X.
13. Jul 20, 2009
### Maestoso
Ok, sorry to raise a really old thread, but this has been annoying me all evening...
I've got GRTensor 1.79 working with Maple 10 quite happily; sorted out the ini files and loading of libraries and so on. My issue is when I type in "makeg(metricname);" it pastes some stuff to the screen but doesn't scroll it, and then pops up a message box and I don't know what I'm trying to enter. I much preferred the entry scheme in Maple 7 (what my old school had) where it prompted you to input the entry in the main window. Does anybody know how to get that form of entry working in Maple 10?
Thanks,
Jolyon | 2018-09-21 02:11:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.592851459980011, "perplexity": 3557.9012498031007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156724.6/warc/CC-MAIN-20180921013907-20180921034307-00179.warc.gz"} |
https://www.allaboutcircuits.com/technical-articles/noise-characterization-custom-PCB-inclinometer-data-capture/ | Technical Article
# How to Characterize Noise in a Custom PCB: Precision Inclinometer
January 16, 2019 by Mark Hughes
## Learn about the process of identifying and eliminating noise in data capture.
Learn about the process of identifying and eliminating noise in data capture.
In the previous articles, I discussed mechanical considerations, schematic design, PCB layout, and Firmware.
One of the greatest anxieties of designing a custom PCB is the testing phase.
I designed a precision inclinometer subsystem and received my brand new board. In a “Hard-way Hughes” first, the board worked on the first spin. Now it’s time to create a suitable test environment and determine the measurement resolution that the board can achieve.
If you'd like to catch up on the precision inclinometer series overall, please check out the links below:
The Linear LTC2380IDE-24, a 24-bit ADC, was always known to be overkill for this project (the LTC2380IDE-16 is a pin-compatible replacement). My initial hope, and the “best-guess” order-of-magnitude estimate that I discussed with AAC’s Technical Director Robert Keim, was that I could statistically tease about 17-18 bits of resolution out of the device. We agreed that the best way to build this one-time board was to go with a higher-precision ADC, even if we knew we’d be throwing bits of data away. This board will never go into production, and the small increase in price of a single part is insignificant in the context of a prototype board.
The 11-bit ADC built into the SCA103T is only really useful for calibration at the factory. A 16-bit ADC would have been fine for this project, though it’s possible that under ideal conditions the sensor could provide more than 16 bits of resolution.
### Understanding the Specifications: Why I Chose a 24-bit Device
The SCA103T-D04 datasheet indicates that the noise density is 0.0004°/√Hz. If we limit the bandwidth to 8 Hz, a quick multiplication of the noise density by the square root of the bandwidth indicates that the analog output resolution is in the range of 0.001°.
$$0.0004\frac°{\sqrt{Hz}} \sqrt{8\;Hz}=0.0011°$$
The ADC produces a 24-bit conversion value, and that value covers 30° of measurement range, meaning the LSB (least significant bit) is as small as 1.8x10-6°. So, how many bits will be useful before the ADC encounters the noise-floor of the inclinometer?
$$\frac{30°}{2^n}=0.0004\frac°{\sqrt{Hz}}\sqrt{8\; Hz}$$
$$2^n=26516.5%0$$
$$n\cdot Log(2)=Log(26516.5)$$
$$n\approx 14.7\;\text{bits}$$
##### Calculating how many bits we can use before hitting the noise floor
Based on these equations, a 16-bit inclinometer would be suitable for this job.
However, a precision inclinometer that is used to calibrate a scientific instrument might experience very slow changes in inclination, which means that we can reduce the bandwidth (to 1 Hz, for example) and thereby decrease the noise floor.
$$0.0004\frac°{\sqrt{Hz}}\sqrt{1\;Hz}=0.0004°$$
$$\frac{30°}{2^n}=0.0004\frac{°}{\sqrt{Hz}}\sqrt{1\; Hz}$$
$$2^n=75000$$
$$n\cdot Log(2)=Log(75000)$$
$$n\approx 16.2\;\text{bits}$$
##### The same calculations with a reduced bandwidth. If we change the bandwidth, our bit needs also change.
In this example, a 16-bit ADC would be insufficient.
By repeating and averaging multiple measurements, I should be able to squeeze a bit more performance out of my design.
The initial prediction of a maximum resolution of 17-18 bits came from a back-of-the-envelope calculation at the beginning of the design process based on the uncertainty of measurement. The uncertainty of measurement indicates the range that a measurement lies within. For example, if we know that an object has a length between 11 cm and 13 cm, we can report the measurement as12 cm ± 1 cm, where 1 cm is the uncertainty of measurement.
The uncertainty of measurement is generally taken to be the ratio of the standard deviation to the square root of the number of measurements.
$$u=\frac{\sigma}{\sqrt{n}}$$
I won’t know the actual standard deviation until I have data, but to get an approximation, I will assume it to be in the range of 0.001°, and I’ll arbitrarily choose 1024 measurements to get an estimate of my uncertainty of measurement.
$$u=\frac{0.001°}{\sqrt{1024}}=0.0001°$$
$$Log(\frac{30°}{0.0001°})/Log(2)=18.2 bits$$
Even if I don’t need the additional bits of resolution for the conversion, I will need the additional bits of resolution for the digital averaging filter. And 16-bit ADCs don’t come with 24-bit digital averaging filters.
To be clear, 0.0001° is a practically useless and wholly unreasonable standard in most non-scientific and non-military applications. In other words, it’s a perfect-goal for “Hard-way” Hughes. To put this type of angular displacement into perspective, 0.0001° corresponds to a change in elevation of ~2 mm over a 1 km distance.
A device attempting this level of precision cannot sit on a desk because the force of a hand on the mouse will deflect the desk enough to be detected. The device cannot sit on the ground in the office next to the desk, because the weight of a person shifting in a chair will disturb the floor, as will the movement of elevators in the building, the movement of coworkers as they move around the office, etc. The PCB cannot be simply placed randomly in the room because the force of HVAC air currents on the connecting wires will provide enough force to measurably disturb the PCB. In other words, this is an unattainable goal and I’m going to spend countless hours and untold dollars of company resources trying to achieve it. I don’t want it to ever be said that I was unable to find a hundred-dollar solution to a twenty-dollar problem.
The things I can do to mitigate external effects on the device include adding mass and rigidity.
So I created a ~275 g aluminum PCB holder (~1 cm thick to provide rigidity and weight) with an adjustable differential screw mechanism.
The PCB is held rigidly in place on the board holder, and the board holder makes points of contact atop three polished round points (one differential screw and two 3mm acorn nuts) that touch a ground piece of 4″×4″×1″-thick steel plate that supports it. The polished plate sits atop a 1mm-thick piece of neoprene. That whole assembly is placed atop a 9” x 12” x 2” granite surface plate that sits atop another 1mm-thick piece of neoprene. Finally, that entire assembly sits atop an oak floor on a 4″ concrete slab.
If I had larger piece of granite, or more appropriate vibration damping material, I would have used it.
##### The aluminum PCB holder was placed atop a steel block that sat on a granite surface plate.
USB cables running to the device (one for the JTAG programmer, one for the data port) were taped to the granite surface plate approximately two inches from the device. The device was powered for at least 12 hours prior to data collection, allowing any thermal variations to stabilize. A FLIR TG130 thermal camera showed no thermal hot spots on the PCB. The temperature of the voltage-reference and inclinometer ICs could not be measured due to reflective package enclosures, but the sides of the IC appeared to be at the same temperature as the rest of the PCB.
### Noise Characterization
The part of the circuit that I’m most concerned about is the voltage reference—so that’s the measurement I focused on first. This is the part of the circuit that I would redesign if I remade the PCB.
The sensor provides ratiometric output and the ADC has ratiometric measurement; since the same voltage reference signal is sent to both ICs, any noise in the reference itself should theoretically be self-negating. At first glance, the signal appears fine.
##### Tektronix MDO3104 view of the VREF net measured at test point on PCB near potentiometer.
The next image shows 0.1 V / division @ 200 ns / division. Most of the variation seems to be bound within 40 mV. And with the way the test point is attached to the board, it is impossible to know if that is indeed fluctuating voltage, or RF energy absorbed by the probe.
So far, so good, right? Perhaps. But until we enable “normal” triggering mode and set the scope to single-shot capture, we won’t know if there are any anomalies.
So I set the scope to single-shot mode and let it run for several seconds. And eventually, I picked up a hiccup.
That hiccup repeats periodically (~10 second interval) while the device is running.
Unfortunately, I don’t have enough test-points on my PCB to find any event that accompanies the noise. Noise like this doesn’t magically appear—there is always a source. Additional test points might allow me to see a correlation between the noise and the SPI or UART lines, or the wall wart power supply, or perhaps the fluorescent lights near my desk. I investigated a noise source once that turned out to coincide with the building’s AC compressor motor.
If this board was ever meant for production, I would certainly need to find out what's going on. If the noise occurs every time an SPI transaction or UART transmission occurs (it doesn’t), then the noise doesn’t really matter since the sensor measurement does not occur during those times. If the noise occurs during the SAR data acquisition phase, it’s going to be a big problem. The next article in the series will present data captured by the device in greater detail. The resolution of the data was such that this noise was clearly not affecting the sensor in any meaningful way.
### Conclusion
The test points that I did include on the board showed that the noise on the PCB was quite low. While I did detect a spurious event on VREF, I could not locate where it originated. If I were to redesign the board, I would provide more taps, and coaxial taps to watch sensitive aspects of the board (such as the inclinometer outputs and the VREF inputs). | 2021-07-28 17:04:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37234261631965637, "perplexity": 1314.3063020104787}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153739.28/warc/CC-MAIN-20210728154442-20210728184442-00586.warc.gz"} |
https://www.physicsforums.com/threads/tax-racing-fuel-heavily.86939/ | # Tax racing fuel heavily
Loren Booda
NASCAR is annoying enough, without the figure that over 5% of the nation's gasoline supply (a large percentage of what we are forced to import) is wasted on the non-sport of auto racing. It's time we taxed some sensibility into this American-antithetical conspicuous consumption.
Gold Member
i always thought nascar is the most retarded thing to watch or even enjoy
let alone participate in
Loren Booda said:
over 5% of the nation's gasoline supply [...] is wasted on the non-sport of auto racing.
Staff Emeritus
Gold Member
I say tax all sports right through the roof...say a 100% tax tacked onto all sales. Taxing gas for Nascar, say $5 -$50 per gallon, is a no brainer in my book.
TheStatutoryApe
We could just ban auto racing. We could ban it on the grounds of emissions and useless consumption of resources.
I have a friend who would hate it though.
Gold Member
You know its a funny thing to say, but if i was ever going to become a mass murder, id probably start off by whacking every NASCAR driver, executive, fan, investor, and employee. Why go easy on people these days? We go to war against terrorists, dont we? Well if you do some calculations and optimization here, you'll see the aforementioned people are far worse than terrorists.
And no, I am not joking.
Loren Booda
Unfortunately, it's more my memory than math. Maybe someone could dredge up the actual statistics for me.
Aside: Mercedes pulled out of racing for forty years after one of their cars exploded in the grandstands, killing more than 300 spectators.
Gold Member
Loren Booda said:
NASCAR is annoying enough, without the figure that over 5% of the nation's gasoline supply (a large percentage of what we are forced to import) is wasted on the non-sport of auto racing. It's time we taxed some sensibility into this American-antithetical conspicuous consumption.
.... since every SUV in this country combined supposedly consumes 10% of the nations gasoline.... i REALLY think your figure is off.
While we're at it, lets ban all protests because cars have to stop when the streets are blocked off. How bout movies? Cars have to drive there and all movies suck now-a-days. How bout banning books too, cant hurt trees. All schools should be banned as well, those parking lots are a death trap. Hey lets shut down the internet, it uses quite a lot of power.
Lets also call for the murder of everyone who enjoys Pepsi. Consumer freedom is bad and it takes gas to produce pepsi. Why not people who enjoy carls jr? Death to them, they drive. Hell since I dont like Panda Express, death to every asian. How bout that. I mean we might as well since we're calling for the murder of people who enjoy something we don't enjoy.
Last edited:
Kakarot
how is it 5%? that cant be right. and taxing sports is a good idea, especially ones that pay the players like $100 million a year Staff Emeritus Gold Member The highest salary in all of professional sports belongs to Alex Rodriguez, but who is making an average of about$25 million a year over the length of a ten-year contract. Athletes make far more off of endorsements than they do off of salary. They are also already in the highest tax-brackets, and since they aren't business owners (generally speaking), they can't shelter their earnings as easily as many other big-time earners. If you don't like it, don't watch their sports and don't buy the products they endorse. Where do you think the money is coming from?
Jesus Christ, where do you people get off? Yeah, let's tax the hell out of and then kill everyone affiliated with NASCAR because we don't see the point of it as a sport.
hypatia
I am a race fan, all kinds of races, including NASCAR, Indy, 1/4 mile track and yes even some street racing. I enjoy building cars that go fast, and I work hard{12 hour days} and have the right to spend my time and money how I choose, without idiots thinking I should die for it.
Racing fule is taxed{ i know, I buy it}, and so is my ticket.
gravenewworld
I also have the right to buy a Hummer and get 5 mi/gallon. Screw the environment because this is the USA. I have the right to do whatever I want.
hypatia
I can't think of any country that bans/limits any kind of car.
Staff Emeritus
Gold Member
The taxation of gasoline in many European countries is so exaggerated that it would be virtually impossible for most people to drive as much there as in the US. Of course, the cities are also smaller and commutes shorter, so there isn't as much of a need to drive.
Mentor
loseyourname said:
The highest salary in all of professional sports belongs to Alex Rodriguez, but who is making an average of about $25 million a year over the length of a ten-year contract. Athletes make far more off of endorsements than they do off of salary. They are also already in the highest tax-brackets, and since they aren't business owners (generally speaking), they can't shelter their earnings as easily as many other big-time earners. If you don't like it, don't watch their sports and don't buy the products they endorse. Where do you think the money is coming from? Jesus Christ, where do you people get off? Yeah, let's tax the hell out of and then kill everyone affiliated with NASCAR because we don't see the point of it as a sport. Amen, brother. Gawd, I love freedom and democracy, don't you? Science Advisor I have a hard time believing the 5% usage number. Given the latest number I saw of the US using 400,000,000 gallons a day, I don't think Jeff Gordon et al are using 20 million gallons a day. Personally, I would much rather create a huge uproar and increase the luxury taxes on fuels used in recreational boats/yachts. In my neck of the woods, I see people fill up monstorously huge boats with$300 in gas a day just to go out and drive in circles. That doesn't include the other environmental damage they do by polluting the waters. But then again, that's just my opinion.
Mentor
hypatia said:
I can't think of any country that bans/limits any kind of car.
What do you mean by "limits"? The US has pretty strict safety and efficiency standards...
primal schemer
Ivan Seeking said:
I say tax all sports right through the roof...say a 100% tax tacked onto all sales.
Are you serious? Why on earth would you want to tax all sports?? Surely you would want to encourage people to take part in sports!! Apart from the obvious health benefits, sports have so many social-skill and character building benefits.
PS
hypatia
russ_watters said:
What do you mean by "limits"? The US has pretty strict safety and efficiency standards...
That was in response to Gravenwoods "right to because I'm American" message. I was referring to size of car and how much gas it burns.
Gold Member
Any 4th year mechanical engineering student could come up with a NASCAR car design - it doesnt take that much of intelligence these days. But to come up with a Toyota Prius that gets 50 mpg actually does, and shows a thing or two about human accomplishments these days.
I dont see how taking out most of NASCAR is a problem in my Ethics books.. let me double check.. nope, still cool with it.
Homework Helper
Loren Booda said:
NASCAR is annoying enough, without the figure that over 5% of the nation's gasoline supply (a large percentage of what we are forced to import) is wasted on the non-sport of auto racing. It's time we taxed some sensibility into this American-antithetical conspicuous consumption.
I'm not a fan of NASCAR per se, but I love motorsports in general. I have a problem with anyone who considers all motor racing to be a "non-sport". I can assure you that top F1 drivers have fitness levels that top fighter pilots can only dream of. Apart from demanding great physical fitness, top level motorsports test reflexes, quick thinking, endurance and courage. And the ability of a race team to come up with a sound pit strategy, modifying it on the fly to fit evolving race conditions and happenings.
I think it's a great sport. If you can't appreciate it, then that's your shortcoming.
Loren Booda
I've had friends with souped up cars (el Camino and Camero respectively) pushing 400 HP each. Believe it, the former could pull a wheelie. All I am saying is that the cost of performance fuel (for any engine of excess) should reflect the necessity of its use. Nature will take its course in any case.
Andretti 1
Environment 0
Echo 6 Sierra
Curious3141 said:
I can assure you that top F1 drivers have fitness levels that top fighter pilots can only dream of.
...uhhhhh, no. Unless their cars can go 2x the speed of sound or more and they can play "duck, dodge, and hide" while someone shoots guided missiles at them.
Curious3141 said:
Apart from demanding great physical fitness, top level motorsports test reflexes, quick thinking, endurance and courage.
Go fast, turn left. AND they shouldn't be TESTING their whatever when they do it. They should already have them before they climb behind the wheel.
GOD__AM
Raising taxes on racing gas will just be passed on to the consumer. All major auto manufactures spend tons of money to win races so you will buy their cars. Not to mention that the technology gained from racing means we get better vehicles. Do you really think these manufacturers are going to cut the cooperate salaries to pay the increased taxes...I don't.
GOD__AM
hypatia said:
I can't think of any country that bans/limits any kind of car.
Japan has very strict laws regarding high performance vehicles. I'm not familiar with the laws regarding cars, but motorcycles over 500cc are nearly impossible to get in japan. They actually have whole classes of small cc motors that don't even get imported to speed hungry americans.
TRCSF
5%? I'd think that the fans driving to the race track would consume more gross gasoline then the NASCAR race itself. Although I suppose if you add up all professional and amateur racing you'd get a disgustingly high number.
Frankly, I think NASCAR is as boring as hell. If there should be a popular racing sport, it should be fat guys racing go-carts. Much more fuel effecient. But that's just my opinion.
Incidently, I've seen news reports of gas costing $3.90 per gallon, regular unleaded, in Michigan. Mid three dollar range in other places. I've also heard a lot of anecdotal reports of gas stations literally running out of gas, all over the country. There's talk of rationing. Andy god some people are stupid. I dream about having a car that only does 4mpg. And the toyota prius 50mpg? thats pretty crap really, i have been in mercedes benz diesels that have got 60mpg and thats with me driving it with a heavy foot! apparently voltswagen diesels are even better and can easily get 70mpg. Gold Member Andy said: god some people are stupid. I dream about having a car that only does 4mpg. And the toyota prius 50mpg? thats pretty crap really, i have been in mercedes benz diesels that have got 60mpg and thats with me driving it with a heavy foot! apparently voltswagen diesels are even better and can easily get 70mpg. Hey thanks thats a great point http://www.distributiondrive.com/Article10.html If the number of diesel vehicles in private use went from less than 10% to over 60% of the private US vehicle fleet, mirroring European diesel engine adoption rates, we would see a 25% reduction in the amount of oil used in the US. GOD__AM Andy said: god some people are stupid. I dream about having a car that only does 4mpg. And the toyota prius 50mpg? thats pretty crap really, i have been in mercedes benz diesels that have got 60mpg and thats with me driving it with a heavy foot! apparently voltswagen diesels are even better and can easily get 70mpg. As stated this is a good point. I remember when diesel was much cheaper than regular leaded gasoline. It takes less refining to make diesel fuel also but the cost of the fuel has risen higher than regular unleaded in this day and age. One more way cooperate america has exploited the american public into paying more for a cheeper product. They pass on the loss of revenue to the consumer. Andy Diesel cars can be fast aswell, rumour hs it that mercedes a releasing a new 4 litre V8 bi turbo diesel engine in the SL class that has a 0-60mph time of about 5 seconds, think it was 5.1 seconds. But that was faster than the 5 litre V8 currently used in the SL500 petrol. Won't stop motor racing as we know it though, just mean that there will be a new class for diesel entries to compete in. Gold Member The only problem is the cost benefit. Consider Toyota Prius - a new car would run you about$20000, and compared to any diesel version of a European car, it will always be cheaper.
Consdering $20k + 50mpg vs$70k + 70 mpg or $500k + 230 mpg I would probably go for$20k + 50 mpg for a few years.. yep.
mattmns
This reminds me of a joke I once heard on a comedy show. It went something like: "I didn't get NASCAR racing until I met some NASCAR fans. Then I could see how a shiny car going around in circles could fascinate them."
GOD__AM
cronxeh said:
The only problem is the cost benefit. Consider Toyota Prius - a new car would run you about $20000, and compared to any diesel version of a European car, it will always be cheaper. Consdering$20k + 50mpg vs $70k + 70 mpg or$500k + 230 mpg I would probably go for \$20k + 50 mpg for a few years.. yep.
And whats your point? Do you really think it costs more money to make a hi mileage diesel than a hi mileage gas engine? As gas prices get higher the difference in your example grows smaller. If everyone stopped buying gas engine cars the price of diesel fuel would climb even more as we consumed less product...
Mentor
Curious3141 said:
I'm not a fan of NASCAR per se, but I love motorsports in general. I have a problem with anyone who considers all motor racing to be a "non-sport".
Whether it's a sport or not is utterly irrelevant here. One of the general freedoms on which the US is based is the pursuit of happiness. If pursuing racing (whether watching or participating) makes people happy, then they can - unless it harms those around them, and I think the general consensus is that it doesn't (the 5% seems dubius).
Just a quick off-the-cuff calculation: A big NASCAR race is 500 miles and has 42 cars. At 4mpg (estimate from some googling), that's 5,250 gallons per race. Even if there were a hundred similar races per day in the US, that'd be 525,000 - well short of Fred's 20 million estimate for 5%.
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18th December 2019, 09:25 PM #881 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 Please forget GR’s equation. I should have swapped X and Y. Sure. (looks around to see where X and Y are used, comes up empty). Let me guess ... you meant x and y (and maybe y’). Also, if we “forget GR’s equation”, where does the “GR predicts” number/value in both 712 and 718 (“3.74741 x 108m”) come from?
18th December 2019, 09:27 PM #882 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 I wrote the equation in about half an hour. I will double check it before claiming victory. Dude, you wrote two posts, over an hour apart. The two posts contain the same equation.
18th December 2019, 09:27 PM #883 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate Sure. (looks around to see where X and Y are used, comes up empty). Let me guess ... you meant x and y (and maybe y’). Also, if we “forget GR’s equation”, where does the “GR predicts” number/value in both 712 and 718 (“3.74741 x 108m”) come from? The results are fine. I just quickly wrote GR’s equation without paying attention to the units.
18th December 2019, 09:30 PM #884 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate Dude, you wrote two posts, over an hour apart. The two posts contain the same equation. Then I must have spent another half hour arguing with Reality Check...
18th December 2019, 09:33 PM #885 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 The results are fine. I just quickly wrote GR’s equation without paying attention to the units. Got it! You invented the results (or derived them using Newtonian physics), wrote them down, and claimed - without any supporting evidence, logic, references, etc - that it’s a result derived from using GR. Now that is chutzpah!
18th December 2019, 09:35 PM #886 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate Got it! You invented the results (or derived them using Newtonian physics), wrote them down, and claimed - without any supporting evidence, logic, references, etc - that it’s a result derived from using GR. Now that is chutzpah! Well GR says the speed of light is always constant, no?
18th December 2019, 09:38 PM #887 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 Then I must have spent another half hour arguing with Reality Check... Yes of course you did. (checks who posted between 712 and 718, finds three posts by Robin, one each by tusenfem and Belz..., and none/zip/nada by Reality Check). Or maybe not ...
18th December 2019, 09:42 PM #888 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 Well GR says the speed of light is always constant, no? I can feel a withering post by W.D.Clinger (and likely ones by The Man, RC, Robin, tusenfem, ...) coming on ...
18th December 2019, 10:20 PM #889 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by philippeb8 The results are fine. I just quickly wrote GR’s equation without paying attention to the units. It isn't the GR equation as far as I know. Let's call it the simple method. Multiply 1.25 by c and add the radius of the moon. Plug that into your final equation and see if what you get. 1.25 seconds, right? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
18th December 2019, 10:42 PM #890 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Finite Theory: Historical Milestone in Physics Originally Posted by Robin It isn't the GR equation as far as I know. Let's call it the simple method. Multiply 1.25 by c and add the radius of the moon. Plug that into your final equation and see if what you get. 1.25 seconds, right? Oh I forgot to subtract the radius in GR’s equation... thanks Robin! Last edited by philippeb8; 18th December 2019 at 11:00 PM.
18th December 2019, 11:05 PM #891 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 Oh I forgot to subtract the radius from GR’s result... thanks Robin! Dude, you might want to consider investing some time in learning at least the basics of GR. Some serious time. Otherwise you’ll continue to make real howlers, and further erode any reader here’s confidence that you have something interesting/new to say about physics. (No, whatever FT is, it is not a “Historic Milestone in Physics”)
18th December 2019, 11:23 PM #892 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate Dude, you might want to consider investing some time in learning at least the basics of GR. Some serious time. Otherwise you’ll continue to make real howlers, and further erode any reader here’s confidence that you have something interesting/new to say about physics. (No, whatever FT is, it is not a “Historic Milestone in Physics”) There’s still a discrepancy and this lunar laser ranging experiment has nothing to do with the particle accelerator blunder and the ISS experiment.
18th December 2019, 11:36 PM #893 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by philippeb8 There’s still a discrepancy . Actually, by my calculation, using $ct+r_m$ for x gets closer to 1.25 than the value you suggested. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 18th December 2019 at 11:38 PM.
19th December 2019, 01:07 AM #894 tusenfem Master Poster Join Date: May 2008 Posts: 2,647 Originally Posted by philippeb8 - I did remove the minus sign in this thread to simplify but it really should be there; Oh yes, that makes complete sense, a fudge factor that suddenly appears in a summation without any reason, and then the minus sign is the complicated part? __________________ 20 minutes into the future This message is bra-bra-brought to you by z-z-z-zik zak And-And-And I'm going to be back with you - on Network 23 after these real-real-real-really exciting messages (Max Headroom) follow me on twitter: @tusenfem, or follow Rosetta Plasma Consortium: @Rosetta_RPC
19th December 2019, 01:08 AM #895 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by Robin Actually, by my calculation, using $ct+r_m$ for x gets closer to 1.25 than the value you suggested. ... vs FT.
19th December 2019, 01:35 AM #896 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by philippeb8 ... vs FT. Substitute $ct+r_m$ for x in your final equation and you get closer to 1.25 than the value you suggested. So if you look for a more precise value of x to solve your equation, you will get closer to $ct+r_m$ __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 19th December 2019 at 01:39 AM.
19th December 2019, 01:38 AM #897 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 The main thing is that the substitutions are not valid in the final equation. If $p_m$ is unknown then you only need to make substitutions where $p_m$ occurs, but you are making substitutions where it doesn't occur. So all you need is to substitute $p_m=x+r_m$ in the denominator and $x-p_m=r_m$ once in the numerator and that is all. If you do this then you will get something extremely close to ct for x. You will also find this if you do a numerical integration of the original expression. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax" Last edited by Robin; 19th December 2019 at 01:39 AM.
19th December 2019, 01:48 AM #898 tusenfem Master Poster Join Date: May 2008 Posts: 2,647 Originally Posted by Robin I should point out that your prediction differs from the prediction found by x/c by approximately the radius of the Moon. Well, philippeb8 is taking the logarithm of a dimensional number log(x-p), so the result is nonsense, dimentionally. (but I am sure there is going to be a "but I normalized everything, but for simplicity I decided not to write it down" nonsense. __________________ 20 minutes into the future This message is bra-bra-brought to you by z-z-z-zik zak And-And-And I'm going to be back with you - on Network 23 after these real-real-real-really exciting messages (Max Headroom) follow me on twitter: @tusenfem, or follow Rosetta Plasma Consortium: @Rosetta_RPC
19th December 2019, 02:01 AM #899 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by tusenfem Well, philippeb8 is taking the logarithm of a dimensional number log(x-p), so the result is nonsense, dimentionally. . He is taking the log of the magnitude of them, so that part is OK. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 02:07 AM #900 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Basically the time found by this method differs from x/c by about $1.2 \times 10^{-9}$ __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 02:17 AM #901 tusenfem Master Poster Join Date: May 2008 Posts: 2,647 Originally Posted by Robin He is taking the log of the magnitude of them, so that part is OK. nope, it is still log(meters) that is coming out of that so "shortened" for dimensional analysis y = (m log(x) + h x) / (c ( m/x + h)) [ .. ] means dimension of .. [y] = [m log(x) +h x] / ( [c] ( [m/x + h]) [y] = (kg log(m) + kg) / ( m/s * kg/m)) The first term on the rhs cannot be dimensionally determined, unless philippeb8 comes up with a solution to make the term inside the log dimensionless. __________________ 20 minutes into the future This message is bra-bra-brought to you by z-z-z-zik zak And-And-And I'm going to be back with you - on Network 23 after these real-real-real-really exciting messages (Max Headroom) follow me on twitter: @tusenfem, or follow Rosetta Plasma Consortium: @Rosetta_RPC
19th December 2019, 02:56 AM #902 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by tusenfem nope, it is still log(meters) that is coming out of that so "shortened" for dimensional analysis y = (m log(x) + h x) / (c ( m/x + h)) [ .. ] means dimension of .. [y] = [m log(x) +h x] / ( [c] ( [m/x + h]) [y] = (kg log(m) + kg) / ( m/s * kg/m)) The first term on the rhs cannot be dimensionally determined, unless philippeb8 comes up with a solution to make the term inside the log dimensionless. Just add: “/ 1 m”
19th December 2019, 03:50 AM #903 tusenfem Master Poster Join Date: May 2008 Posts: 2,647 Originally Posted by philippeb8 Just add: “/ 1 m” yes sure! and where is that supposed to come from? (Maybe while you are at it, you might just replace all those pesky variables with the numbers you want to get out, even more easy.) if you do that in the equation for y', then you have problems with your magical h-term. if you do it willy-nilly in the equation for y then you are just trying to make your equations fit the result you want to get. Maybe, think first and then retry integrating y' and see where you have gone wrong? Or maybe even earlier, where you suddenly get your magical h-term out of a summation? __________________ 20 minutes into the future This message is bra-bra-brought to you by z-z-z-zik zak And-And-And I'm going to be back with you - on Network 23 after these real-real-real-really exciting messages (Max Headroom) follow me on twitter: @tusenfem, or follow Rosetta Plasma Consortium: @Rosetta_RPC Last edited by tusenfem; 19th December 2019 at 03:51 AM.
19th December 2019, 03:58 AM #904 malbui Beauf Join Date: Nov 2004 Posts: 2,501 Maybe I’m missing something because I’m not a physicist, but isn’t it good practice to get the mathematical underpinnings of your work - all those troublesome equations - all nicely sorted out before going public with claims of having achieved a major milestone? __________________ "But Master! Does not the fire need water too? Does not the mountain need the storm? Does not your scrotum need kicking?"
19th December 2019, 04:40 AM #905 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by malbui Maybe I’m missing something because I’m not a physicist, but isn’t it good practice to get the mathematical underpinnings of your work - all those troublesome equations - all nicely sorted out before going public with claims of having achieved a major milestone? I wrote this equation a long time ago and I applied it for the lunar laser ranging experiment and I get a decent result apparently. I just need to review correctly tusenfem’s claims during the day...
19th December 2019, 05:26 AM #906 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by Robin The main thing is that the substitutions are not valid in the final equation. If $p_m$ is unknown then you only need to make substitutions where $p_m$ occurs, but you are making substitutions where it doesn't occur. So all you need is to substitute $p_m=x+r_m$ in the denominator and $x-p_m=r_m$ once in the numerator and that is all. If you do this then you will get something extremely close to ct for x. You will also find this if you do a numerical integration of the original expression. Just bumping this. Why are you making substitutions in terms which do not into $p_m$? __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 05:43 AM #907 W.D.Clinger Illuminator Join Date: Oct 2009 Posts: 3,663 Originally Posted by JeanTate Otherwise you’ll continue to make real howlers, and further erode any reader here’s confidence that you have something interesting/new to say about physics. Is it really possible for confidence to erode below zero? (Checks the US Politics subforum.) Never mind. Originally Posted by tusenfem Well, philippeb8 is taking the logarithm of a dimensional number log(x-p), so the result is nonsense, dimentionally. Suppose y = 1/x, where y is in units of foo and x in units of bar = foo-1. Then the definite integral of y=1/x between a and b islog |b| - log |a|with units foo*bar=foo*foo-1=1 because that definite integral is the area under the curve between x=a and x=b. In other words, the logarithm of a dimensional number, when obtained via integration, can be dimensionless, which is not necessarily nonsense. Originally Posted by tusenfem yes sure! and where is that supposed to come from? (Maybe while you are at it, you might just replace all those pesky variables with the numbers you want to get out, even more easy.) if you do that in the equation for y', then you have problems with your magical h-term. if you do it willy-nilly in the equation for y then you are just trying to make your equations fit the result you want to get. Maybe, think first and then retry integrating y' and see where you have gone wrong? Or maybe even earlier, where you suddenly get your magical h-term out of a summation? The magical h-terms that philippeb8 pulled out of thin air do appear to be nonsense. But hey, philippeb8 spent only half an hour coming up with those equations. When you're overturning 300 years of physics, you wouldn't want to waste much time on getting your equations right.
19th December 2019, 05:47 AM #908 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 This expression $y=\frac{{m_s} \log{\left( \left| x-{p_s}\right| \right) }+{m_m} \log{\left( \left| x-{p_m}\right| \right) }+{m_e} \log{\left( \left| x-{p_e}\right| \right) }+h x}{c\, \left( \frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {p_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Just substitute $p_m=x+r_m$ to get $y=\frac{{m_s} \log{\left( \left| x-{p_s}\right| \right) }+{m_m} \log{\left( \left| {r_m}\right| \right) }+{m_e} \log{\left( \left| x-{p_e}\right| \right) }+h x}{c\, \left( \frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {x+r_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Putting $r_m$ in those other terms is invalid. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 05:49 AM #909 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 This expression $y=\frac{{m_s} \log{\left( \left| x-{p_s}\right| \right) }+{m_m} \log{\left( \left| x-{p_m}\right| \right) }+{m_e} \log{\left( \left| x-{p_e}\right| \right) }+h x}{c\, \left( \frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {p_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ You can substitute $p_m=x+r_m$ to get $y=\frac{{m_s} \log{\left( \left| x-{p_s}\right| \right) }+{m_m} \log{\left( \left| {r_m}\right| \right) }+{m_e} \log{\left( \left| x-{p_e}\right| \right) }+h x}{c\, \left( \frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {x+r_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ But putting $r_m$ in those other terms is invalid. __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 06:05 AM #910 W.D.Clinger Illuminator Join Date: Oct 2009 Posts: 3,663 Originally Posted by Robin You can substitute $p_m=x+r_m$ to get As noted earlier, I believe philippeb8 "substituted x-rm for x and then set x equal to pm". At the time, I thought that was poor presentation rather than complete nonsense. As tusenfem noted, however, the introduction of the magical h-terms in the earlier equation appears to be complete nonsense. As you noted, the effect of introducing those terms was to convert the equation into what amounts to multiplying x by a factor that is very close to unity. The deviation of that factor from unity by a function that is slightly related to gravitational potential is analogous to, but far less accurate than, the most significant term of the relativistic correction seen in the linearized gravity approximation.
19th December 2019, 06:39 AM #911 Robin Penultimate Amazing Join Date: Apr 2004 Posts: 11,645 Originally Posted by W.D.Clinger As noted earlier, I believe philippeb8 "substituted x-rm for x and then set x equal to pm". At the time, I thought that was poor presentation rather than complete nonsense. Well OK, but he obviously confused even himself with that, because he compared it to a surface to surface measurement and called the difference a "discrepancy". __________________ The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
19th December 2019, 06:45 AM #912 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by Robin Well OK, but he obviously confused even himself with that, because he compared it to a surface to surface measurement and called the difference a "discrepancy". ... a discrepancy between GR and FT.
19th December 2019, 08:26 AM #913 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 I'm going to go through the two main posts by philippeb8 on lunar laser ranging, in a series of posts of my own; they are 712 and 718. I will focus on 718 as it is later in time and seems to be somewhat less ambiguous etc. And s snipped. Most, perhaps even all, of the contents of these posts has already been discussed, to one extent or another, by various posters; however, I will not attempt to provide links to those (maybe an exception or two). Start with this, from 718: Originally Posted by philippeb8 According to FT, here is the speed of light reversed (or the time it takes for a photon to travel 1 meter) at each position of a photon between the surface of the Earth and the surface of the Moon, which is directly proportional to the ratio of the gravitational potential of observed photon and the gravitational potential of the observer: $y'=\frac{1}{c} \times \left. \frac{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| x-{p_i}\right| }\right.}}{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| {p_i}\right| }\right.}}\right.$ Where m, p & r are the mass, position and radius of the Earth, Sun & Moon respectively Checking for dimensions, on the RHS (L=length, M=mass, T=time): 1/c: 1/(LT-1), or T/L (consistent with "the speed of light reversed"). next the sum; taking n=1: numerator: m/|x-p|: M/L denominator: m/|p|: M/L which cancel, so we are left with T/L Then we read (in both 712 and 718): Quote: $y'=\frac{\frac{{m_s}}{\left| x-{p_s}\right| }+\frac{{m_m}}{\left| x-{p_m}\right| }+\frac{{m_e}}{\left| x-{p_e}\right| }+h}{c\, \left( \frac{\mathit{ms}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {p_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Whoa! The line above has the sum going from n=1 to n=3, yet here we have four terms! Where did h come from? It's not in the intro either. Further down in 718 (but not in 712, there h is undefined): Quote: Also: $c=299792458 m/s$ $G=6.67408 \times {{10}^{-11}} m^3 kg^{-1} s^{-2}$ $h=\frac{{{c}^{2}}}{2 G}$ Dimensionally: (LT-1)2/(L3M-1T-2) or M/L which is consistent with the other three terms. (to be continued)
19th December 2019, 08:40 AM #914 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Kappa - Excerpt Effect of the time dilation in the gravitational field is a consequence of the difference in gravitational potentials. This effect is described by the relation: $\frac{\Delta \tau}{\Delta t} = \frac{1}{h}(h + \frac{M}{r}) = 1 + \frac{M}{hr}$ where, $M$ is a mass of the gravitating object and $r$ is the distance from its centre. Under $\Delta\tau$ we mean the interval of local time at the point situated at distance $r$ from the centre of the source of gravitation. $\Delta t$ is the interval of time measured by the distant observer, situated at distance $r\rightarrow \infty$. General relativistic time dilation effect is a particular case of if $h=-c^2/G$. Indeed, we know that in the weak field limit of General Relativity, time dilation effect in the gravitational field takes the following form*: $\frac{\Delta \tau}{\Delta t} = 1 - \frac{G M}{c^2 r}$ But due to the hypotheses of the Finite Theory, factor $h$ in is not a universal constant but depend on the superposed gravitational potentials. For example, in solar system experiments, where the gravitational potential of the Sun is the source of the strongest gravitational acceleration, we suppose $h = h_{solar}$. The value of $h_{solar}$ can be determined from the observation of the deflection angle of light in the gravitational field of the Sun, as we will demonstrate in the next subsection. Due to the time dilation effect, we expect to have different speed measurements of the same body by different observers. In particular, the speed of light traveling through the gravitational field will be different from the viewpoint of a local observer and from the viewpoint of a distant watcher. According to, a distant observer notes that the light beam has a velocity, which depends on the position in the gravitational field: $v = \frac{dr}{d t} = \frac{dr}{d\tau} \left( 1 + \frac{M_{sun}}{h_{solar} r} \right) = c\, \left( 1 + \frac{M_{sun}}{h_{solar} r} \right)$ In this relation, the local speed $v_{local} = dr/d\tau = c = 2.998\times 10^{8} m/s$ is constant due to our hypothesis. Also, we neglect the effect of length contraction in the gravitational field, which results in the equal values of length interval $dr$ for both local and distant observers. [...] *Cheng, Relativity, Gravitation and Cosmology. A Basic Introduction, Oxford University Press, 2005 Last edited by philippeb8; 19th December 2019 at 09:13 AM.
19th December 2019, 08:44 AM #915 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 (continued) Again, looking at 718: Quote: According to FT, here is the speed of light reversed (or the time it takes for a photon to travel 1 meter) at each position of a photon between the surface of the Earth and the surface of the Moon, which is directly proportional to the ratio of the gravitational potential of observed photon and the gravitational potential of the observer: $y'=\frac{1}{c} \times \left. \frac{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| x-{p_i}\right| }\right.}}{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| {p_i}\right| }\right.}}\right.$ $y'=\frac{\frac{{m_s}}{\left| x-{p_s}\right| }+\frac{{m_m}}{\left| x-{p_m}\right| }+\frac{{m_e}}{\left| x-{p_e}\right| }+h}{c\, \left( \frac{\mathit{ms}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {p_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Where m, p & r are the mass, position and radius of the Earth, Sun & Moon respectively: $p_e= -6.371 \times {{10}^{6}}m$ $p_s= 1.52 \times {{10}^{11}}m$ $r_m= 1737500m$ (my hilite) Let's look at just two parts of the latter: ${\left| x-{p_m}\right| }$ ${\left| x-{p_e}\right| }$ As x approaches pm, |x-pm| approaches zero, right? Ditto for pe. So what happens in each case, in the second equation, to the numerator (the denominator remains sensible, at least with respect to ps and pe, it could even be a constant)? The intro says "between", but that could be arbitrarily close to zero on each end, right? Blows up, right? Maybe it all gets sorted out in the next step(s), "The integral of the aforementioned equation" ... In any case, we're left with the mystery of what pm is. (to be continued) Last edited by JeanTate; 19th December 2019 at 08:51 AM. Reason: added (continued)
19th December 2019, 09:22 AM #916 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 (continued) 718 again: Quote: The integral of the aforementioned equation will return the time it'll take for a photon to travel a certain distance while considering 3 perfectly aligned masses is: $y=\frac{1}{c} \times \int {\left. \frac{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| x-{p_i}\right| }\right.}}{\sum_{i=1}^{n}{\left. \frac{{m_i}}{\left| {p_i}\right| }\right.}}dx\right.}$ $y=\frac{{m_s} \log{\left( \left| x-{p_s}\right| \right) }+{m_m} \log{\left( \left| x-{p_m}\right| \right) }+{m_e} \log{\left( \left| x-{p_e}\right| \right) }+h x}{c\, \left( \frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_m}}{\left| {p_m}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Where m, p & r are the mass, position and radius of the Earth, Sun & Moon respectively: $m_e= 5.9736 \times {{10}^{24}}kg$ $m_s= 1.98892 \times {{10}^{30}}kg$ $m_m= 7.348 \times {{10}^{22}}kg$ $p_e= -6.371 \times {{10}^{6}}m$ $p_s= 1.52 \times {{10}^{11}}m$ $r_m= 1737500m$ Also: $c=299792458 m/s$ $G=6.67408 \times {{10}^{-11}} m^3 kg^{-1} s^{-2}$ $h=\frac{{{c}^{2}}}{2 G}$ "log" (base 10)? or "ln" (base e)? Does it matter which? In post #832, philippeb8 said the perfect alignment is "Earth-Moon-Sun". So x=0 is ~6,300 km from the Earth, in the direction of the Sun. And the Sun is some 152 million km from x=0. So what is "the time it'll take for a photon to travel a certain distance" where that distance is from position pe to position -pe? If I plug this in to the above, I get, for just one term: $log{\left( \left| x-{p_e}\right| \right)$ Which is log(0), right? Does this mean that a photon leaving the surface of the Earth gets trapped ~12,600 km away (in the direction of the Sun, or Moon)? I'm confused. (to be continued)
19th December 2019, 09:30 AM #917 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate (continued) 718 again: "log" (base 10)? or "ln" (base e)? Does it matter which? In post #832, philippeb8 said the perfect alignment is "Earth-Moon-Sun". So x=0 is ~6,300 km from the Earth, in the direction of the Sun. And the Sun is some 152 million km from x=0. So what is "the time it'll take for a photon to travel a certain distance" where that distance is from position pe to position -pe? If I plug this in to the above, I get, for just one term: $log{\left( \left| x-{p_e}\right| \right)$ Which is log(0), right? Does this mean that a photon leaving the surface of the Earth gets trapped ~12,600 km away (in the direction of the Sun, or Moon)? I'm confused. (to be continued) So the position of the observer is: 0 m; We are looking for the time it takes for a photon to reach position: x - r_m; And "x" is the position of the Moon (p_m) we would like to solve.
19th December 2019, 09:51 AM #918 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 Originally Posted by philippeb8 So the position of the observer is: 0 m; We are looking for the time it takes for a photon to reach position: x - r_m; And "x" is the position of the Moon (p_m) we would like to solve. Thanks for the clarification. So the p refer to the position of the centre of the Earth, Sun, and Moon? If I try to measure the distance from the Earth to the Moon, using a laser set up at ~-6,300 km from "the position of the observer" - i.e. at the centre of the Earth - I will not get an answer, using your equation? Of course, we need to assume a really narrow tube right through to the centre of the Earth, or a transparent Earth ... Last edited by JeanTate; 19th December 2019 at 09:54 AM. Reason: not opposite side, centre of the Earth; fixed some typos
19th December 2019, 09:58 AM #919 philippeb8 Muse Join Date: Sep 2018 Posts: 661 Originally Posted by JeanTate Thanks for the clarification. So the p refer to the position of the centre of the Earth, Sun, and Moon? If I try to measure the distance from the Earth to the Moon, using a laser set up at ~-6,300 km from "the position of the observer" - i.e. at the centre of the Earth from the observer - I will not get an answer, using your equation? If course, we need to assume a really narrow tube right through to the centre of the Earth, or a transparent Earth ... - The position refers to the center of the mass; - If you want to flip the position of the observer on the Earth, you'll have to change the sign of p_e and shift the Moon farther away.
19th December 2019, 10:13 AM #920 JeanTate Illuminator Join Date: Nov 2014 Posts: 3,452 (continued) Last parts of 718: Quote: Where m, p & r are the mass, position and radius of the Earth, Sun & Moon respectively: $m_e= 5.9736 \times {{10}^{24}}kg$ $m_s= 1.98892 \times {{10}^{30}}kg$ $m_m= 7.348 \times {{10}^{22}}kg$ $p_e= -6.371 \times {{10}^{6}}m$ $p_s= 1.52 \times {{10}^{11}}m$ $r_m= 1737500m$ Also: $c=299792458 m/s$ $G=6.67408 \times {{10}^{-11}} m^3 kg^{-1} s^{-2}$ $h=\frac{{{c}^{2}}}{2 G}$ Since the position of the Moon is the unknown we would like to solve then the following equation will be the one to be used: $y=\frac{{m_s} \log{\left( \left| x-{r_m}-{p_s}\right| \right) }+{m_e} \log{\left( \left| x-{r_m}-{p_e}\right| \right) }+h\, \left( x-{r_m}\right) +{m_m} \log{\left( \left| {r_m}\right| \right) }}{c\, \left( \frac{{m_m}}{\left| x\right| }+\frac{{m_s}}{\left| {p_s}\right| }+\frac{{m_e}}{\left| {p_e}\right| }+h\right) }$ Other than to check the equation for y, nothing to add here, that hasn't already been covered. For example: philippeb8 has not yet given unambiguous sources for any of the values. This last part has been fairly well covered in many posts; "cherry picking" is the mildest thing one can say, but bovine excrement of varying strengths is more accurate I feel: Quote: Given the time for the laser to travel between the surface of the Earth and the surface of the Moon is: $y = 1.25 s$ Then FT predicts the position of the Moon to be (approximately): $x = 3.76776 \times {{10}^{8}} m$ While GR predicts the position of the Moon to be: $x = 3.74741 \times {{10}^{8}} m$ So there is a discrepancy between the two theories at that scale already. The physics books of the last 300 years need to be rewritten because the notion of light years is another important blunder. (concluded, maybe)
International Skeptics Forum | 2020-03-28 09:40:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 76, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6412810683250427, "perplexity": 1504.3369560989001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370490497.6/warc/CC-MAIN-20200328074047-20200328104047-00074.warc.gz"} |
https://math.stackexchange.com/questions/1623713/bounded-operators-on-a-finite-dimensional-hilbert-space-linear-combination-of | Bounded Operators on a finite-dimensional Hilbert space - Linear combination of at most two unitaries and from a partial isometry to a unitary
Good day,
In the lecture of functional analysis the proof of two statements were skipped as a task for us but I'm not sure how I approach these questions.
a) Show that every partial isometry $V \in B(H)$ on a finite-dimensional Hilbert space $H$ can be extended to a unitary on $H$.
b) Show that every bounded operator on a finite-dimensional Hilbert space can be written as a linear combination of at most two unitaries.
Some definitions and results which were proven:
• $B(H)=B(H,H)=\{ V:H \to H ~|~ V ~\text{linear and}~ \exists M< \infty: ||Vx|| \leq M ||x|| ~\forall x \in H\}$ the set of linear bounded operators on $H$
• $V \in B(H)$ is a partial isometry iff $V$ is a isometry wrt. $(ker V)^\perp$ i.e. $||Vx||=||x|| ~\forall x \in (kerV)^\perp$
• $V \in B(H)$ is called unitary iff $V^* V=V V^* = I$ where $V^*$ is the adjoint of $V$ and $I$ is the identity
• The dimension of a Hilbert space is defined by the cardinality of its orthonormal basis
• A bounded operator on a Hilbert space can be decomposed uniquely into its real and imaginary part, i.e. $V=A+iB=Re(V)+iIm(V)$ where $A$ and $B$ are unique and hermitian bounded operatos
• $V$ is a partial isometry iff $U^* U$ is a orthogonal projection on $(ker U)^\perp$ i.e. $(U^* U)^2 = U^* U = U U^*$
• Every bounded operator $V$ can be decomposed with a partial isometry i.e. it exists a partial isometry $P$ s.t. $V=P |V|$ where $| \cdot|$ is the absolute value and is defined by $|V|=\sqrt{V^* V}$ (This is called Polar Decomposition)
• It was shown that every bounded operator is the linear combination of at most 4 unitaries. (Not on a finite-dim. HS)
That are a lot of theorems and definitions that were done. If there is a lack of clarity then just ask.
My problem is that I can't work with the finite-dimensional Hilbert space. What can the finite-dimensional HS do that the infinite-dimensional HS can't? Okay, I have a finite orthonormal basis. But what else? I'm thankful for every help.
Marvin.
a) The first task here is to interpret the question appropriately. I guess it should be read as,
"Show that for every partial isometry $V\in B(H)$ on a finite-dimensional Hilbert space $H$, the restriction $V|_{(\ker V)^{\perp}}$ can be extended to a unitary on $H$."
(The only extension of $V$ to $H$ is $V$ itself, and it is certainly not true that every partial isometry on a finite-dimensional Hilbert space is unitary.)
But let's turn to the question: Choose an orthonormal basis $(e_1,\dots,e_k)$ of $(\ker V)^{\perp}$ and extend it to an orthonormal basis $(e_1,\dots,e_n)$ of $H$. Since $V|_{(\ker V)^\perp}$ is an isometry, $(f_1,\dots,f_k):=(Ve_1,\dots,Ve_k)$ is an orthonormal basis of $\operatorname{ran} V$. Extend it to an orthonormal basis $(f_1,\dots,f_n)$ of $H$. Define $U e_j:=f_j$.
Then $Ue_j=f_j=V e_j$ for $j\in\{1,\dots,k\}$, so $U$ coincides with $V$ on $(\ker V)^\perp$. Since $U$ maps on orthonormal basis to an orthonormal basis, it is unitary.
b)By the polar decomposition, every operator $T\in B(H)$ can be written as $T=V|T|$ with a partial isometry $V$ such that $\ker V=\ker |T|$. Extend $V|_{(\ker V)^\perp}$ to a unitary $U$. Then $T=U|T|$. Now $|T|$ is self-adjoint and can therefore be written as a linear combination of two unitaries (compare the proof that every bounded operator can be written as linear combination of four unitaries). Thus, $T$ can be written as linear combination of two unitaries.
• Thanks a lot for your help :) I really misunderstood the first question. – Fritz Jan 24 '16 at 16:15 | 2019-05-23 13:01:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9616469144821167, "perplexity": 65.33472953921736}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257244.16/warc/CC-MAIN-20190523123835-20190523145835-00438.warc.gz"} |
https://electronics.stackexchange.com/questions/544583/primary-voltage-drop-in-current-transformer | # Primary voltage drop in current transformer
Following on from this question, Current transformer energy harvesting from a mid-voltage line, I've never seen any mention of primary voltage drop in a current transformer circuit.
simulate this circuit – Schematic created using CircuitLab
Figure 1. A typical CT application using a 5 A meter to measure the current through a load.
Since the burden resistance of the ammeter is reflected back onto the primary side by the inverse turns ratio squared there has to be a voltage drop on the primary side. This raises a few questions.
1. Where does the voltage drop occur? Does it fade in and out with a peak right inside the CT?
2. Would we see a larger reading on VM2 compared with VM1 (10 mm and 5 mm from the plane of the CT, for example)?
3. What is the relationship with the dimensions of the CT?
4. What is the effect of the angle between the axis of the CT and that of the cable. (CT
Where does the voltage drop occur? Does it fade in and out with a peak right inside the CT?
The maximum volt drop/metre ($$\\frac{dv}{d\ell}\$$) is in the middle of the core and rapidly becomes the normal volt drop/meter for a wire beyond the core.
Would we see a larger reading on VM2 compared with VM1 (10 mm and 5 mm from the plane of the CT, for example)?
Yes we would because of the normal external volt drop of a longer cable (Ω per metre and inductance per metre).
What is the relationship with the dimensions of the CT?
If you are asking at what point the internal higher volt drop per metre becomes regular wire volt drop per metre for a given size of CT, I can't say. I can't imagine that much beyond twice the core width it would be very much influenced by the core. Good question though.
What is the effect of the angle between the axis of the CT and that of the cable.
I don't think there will be much effect given that in practice, the angle probably isn't more than about 45 °. Another good one!
Would we see a larger reading on VM2 compared with VM1 (10 mm and 5 mm from the plane of the CT, for example)?
Unlikely. Each volt-meter together with its leads and corresponding section of the wire passing through the core form a loop. That loop is cut by the varying magnetic field inside the core of the CT. Thus, they form a one loop secondary of the transformer, and will see a voltage almost identical to the voltage drop of the primary. Almost all of the magnetic field is confined to the core, so the area of the loop will have little effect, although theoretically, if the loop for vm2 encloses that for vm1, it might encircle more magnetic lines of force.
Where does the voltage drop occur? Does it fade in and out with a peak right inside the CT?
That is problematic, see further down the question. You could probe a very small section of the wire in the CT core, and depending upon whether the test probes enter the core from either side, or whether they enter from the same side you will get a different answer. If the test probes enter from opposite sides, you will get a voltage approximately equal to the full voltage drop of the CT. In fact you could touch these probes together and still get the full voltage drop, because the probes are forming a 1 turn secondary. However, if the probes enter the CT from the same side, you will get almost 0 voltage. What you do get will be mostly the resistive drop.
The question you ask poses a measurement conundrum. The circuit consisting of either voltmeter, its leads, and the conductor through the CT core is "cut" by the changing flux of the CT core, in effect making a transformer secondary.
From one point of view, the voltage between the contact points of the voltmeter leads is undefined. To explain that point of view, consider Maxwell's(*) third equation, i.e. Faraday's Law.
$$\nabla \times E = -\frac{1}{c}\frac{\partial B}{\partial t}$$
If there is no time-varying magnetic field, this implies that
$$\nabla \times E = 0$$
which means that E is a conservative field. Being a conservative field implies that E is the gradient of a scalar function, (which we call V)
$$E = \nabla V$$
V, being a scalar function implies that the sum of changes around a loop must be 0 (which is KVL).
However, the assumption that there exists no time-varying magnetic field is violated in the circuit consisting of the voltmeters, their probe wires, and the mains conductor. Accordingly, MIT Professor Lewin has argued that the voltage between the two lead points of the Volt-meter is undefined. In a class demonstration, Lewin shows two voltmeters connected to the same test points showing different voltages. Lewin's position is further explained in this blog.
(Lewin's demonstration has is discussed here, but I am not satisfied with the explanation given.)
Others, such as Electroboom/Mehdi have argued (see also here) that the problem with the example Lewin provides lies in measurement technique. Volt-meter probe wires should not arranged to form a loop cut by a changing magnetic field. If the probe wires are re-arranged, consistent voltage measurements are observed in Lewin's experiment. If we take that point of view, however, and re-arrange the test leads to avoid loops cut by changing magnetic fields in order to get a consistent/proper voltage measurement, then one of the test leads needs to pass through the CT core. This, however, will result in a voltage drop consisting only of the conductor resistance.
Hence, the conundrum. How should the test leads be arranged? If they form a loop cut by a changing magnetic field, is the voltage well defined? If they are not cut by that changing magnetic field, where is the voltage drop created by the CT?
*The equations called "Maxwell's Equations" were first formulated in their modern form by the electrical engineer Oliver Heaviside.
What is the relationship with the dimensions of the CT?
Very little, provided the core is not saturated. If the core is not saturated, most of the magnetic lines of force will be confined to the core, and any wire loop around those lines of force will have approximately the same induced emf.
What is the effect of the angle between the axis of the CT and that of the cable. (CT)
Almost none, for the reasons explained above.
The leakage inductance of the CT adds a voltage drop in quadrature to the primary current, aka an inductance, in series with the primary.
The reflected secondary load, if resistive, adds a voltage drop in phase with the primary current, aka a resistance, in series with the primary.
Consider that another way of looking at this mechanism is that the CT secondary voltage is transformed into the primary. This induction is seen across closed turns around the core, so the trajectory of your meter leads, VM1 and VM2, will be significant in the actual voltages you measure. As you move the meter leads along the wire to investigate 'where' the drop is happening, you may get unexpected results. This works for pure IR resistive drop. It doesn't work (without an ice bag for the forehead and a lot of care) for induced voltages.
• Re this: a resistance, in series with the primary - I think you mean a resistor in parallel with the primary. Jan 26 at 17:42
• @Andyaka Let me think about that. If the secondary resistance of an ideal transformer is shorted, the primary will appear short. If we add leakage idncutance, that appears in series. I did specify leakage, not primary inductance. Jan 27 at 7:28
• @Andyaka Of course, the primary inductance is in parallel with the leakage and secondary in series. Now I need to bend my head around what resonating Lpri does for power output, what magnetising current is actually trying to saturate the core, but that was a different question! Jan 27 at 8:34 | 2021-10-17 12:17:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 4, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4490703046321869, "perplexity": 667.0055233730666}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585177.11/warc/CC-MAIN-20211017113503-20211017143503-00135.warc.gz"} |
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# Emission Time Computation
Fundamentals
Title Emission Time Computation
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Year of Publication 2011
Two different algorithms for the satellite transmission time computation from the receiver measurement time are presented as follows. The first of them is based on using the pseudorange measurements, which is a link between the receiver time tags (i.e., the reception time in the receiver clock) and the satellite transmission time (in the satellite clock). The second one is a pure geometric algorithm, which does not require any receiver measurement. It only needs the satellite coordinates and an approximate receiver position.
## A pseudorange based algorithm
The emission time can be directly obtained from the reception time, taking into account that the pseudorange $\displaystyle R$ is a direct measurement of the time difference between both epochs, each one of them measured in the corresponding clock:
$R=c\;\left(t_{rcv}[reception]-t^{sat}[emission]\right) \qquad \mbox{(1)}$
So, the signal emission time, measured with satellite clock ($\displaystyle t^{sat}$), is given by:
$t^{sat}[emission]=t_{rcv}[reception]-\Delta t \qquad \mbox{(2)}$
where,
$\Delta t= R/c \qquad \mbox{(3)}$
Thence, if the $\displaystyle \delta t^{sat}$ is the satellite clock offset, regarding to the GNSS (GPS, GLONASS, Galileo...) system time scale (see Clock Modelling) the transmission time $\displaystyle T[emission]$ in this system time scale can be computed from the receiver measurement time tags ($\displaystyle t_{rcv}$) as:
$T[emission] = t^{sat}[emission] - \delta t^{sat} = t_{rcv}[reception] - R/c - \delta t^{sat} \qquad \mbox{(4)}$
The former equation (4) has the advantage of providing the signal emission time directly, without iterative calculation, although it does need pseudorange measurements in order to connect both epochs.
The accuracy in determination of $\displaystyle T[emission]$ is very high, and essentially depends on $\displaystyle \delta t^{sat}$ error. For instance, in the case of the GPS system it is less than $10$ or $100$ nanoseconds with S/A=off and S/A=on, respectively. This allows calculating satellite coordinates with errors below one tenth of millimetre in both cases [footnotes 1].
## A purely geometric algorithm
The former algorithm (equation 2) provides the signal emission time tied to satellite clock ($\displaystyle t^{sat}$). The next algorithm ties this epoch to receiver clock ($\displaystyle t_{rcv}$):
$t_{rcv}[emission]=t_{rcv}[reception]-\Delta t \qquad \mbox{(5)}$
where $\displaystyle \Delta t$ is now calculated by iteration assuming that an approximate receptor position $\displaystyle r_{0_{rcv}}$ is known (it converges very fast):
The algorithm is based in the following steps:
1. Calculate the position $\displaystyle {\mathbf r}^{sat}$ of the satellite at signal reception time $\displaystyle t_{rcv}$.
2. Calculate the geometric distance between satellite coordinates obtained previously and receiver position [footnotes 2], and from it, calculate the signal travelling time between both points: $\Delta t=\frac{\left\| {\mathbf r}^{sat}-{\mathbf r}_{0_{rcv}}\right\|}{c} \qquad \mbox{(6)}$
3. Calculate satellite position at the time: $t = t_{rcv} - \Delta t \Longrightarrow r^{sat}$.
4. Compare the new position $\displaystyle r^{sat}$ with the former position. If they differ more than certain threshold value, iterate the procedure starting from 2.
Finally, emission time at the system-time-scale is given by[footnotes 3]:
$T[emission] = t_{rcv}[emission] - \delta t_{rcv} \qquad \mbox{(7)}$
where $displaystyle \delta t_{rcv}$ is receiver clock offset referred to the system time, that may be obtained from navigation solution (although "a posteriori").
This algorithm for the satellite coordinate calculations at the reception epoch allows an efficient modularity because pseudorange measurements are not needed to compute the transmission time.
If the receiver clock offset is small [footnotes 4], thence the $displaystyle \delta t_{rcv}$ may be neglected. On the other hand, the receiver clock estimates from the navigation solution can be used (extrapolated from the previous epoch). In any case, it must be taken into account that neglecting this term when $displaystyle \delta t_{rcv}$ reaches large values (e.g., 1 millisecond) may introduce errors of about one meter in satellite coordinates, and this must be taken in account when building the navigation model[footnotes 5]; or more precisely, in the partial derivative respect to receiver clock of design matrix.
frameless frameless frameless frameless
Figure 1 shows an example to illustrating the effect of neglecting the travelling time in the satellite coordinates computation for positioning. It corresponds to a receiver located in Barcelona, Spain (receiver coordinates $\lambda\simeq 2^o$ $\phi \simeq 41^o$). During the $70$ to $90$ milliseconds of travelling time, the satellite moves about $200-250$ meters, which leads to $+/-60$ meters in range. The effect on the user position is up to $50$ meters or more in horizontal and vertical components.
## Notes
1. ^ GPS, GLONASS or Galileo satellites speed is of few km/s.
2. ^ Again, notice that satellite and receiver coordinates must be given in the same reference system, because satellite-receiver ray must be generated in a common reference system.
3. ^ Rigorously, equation (7) is: $T[emission] = f(T[reception]) = f(t_{rcv}[reception] - \delta t_{rcv}) \simeq t_{rcv}[emission] - \delta t_{rcv}$ where function $f(\cdot)$ represents geometric algorithm.
4. ^ Some receivers apply clock-steering adjusting their clocks epoch-by-epoch and providing offsets of few nanoseconds. However, in many cases the receiver wait until gathering an offset of $1$ millisecond to adjust the clock.
5. ^ In the "design matrix" or Jacobian matrix, obtained when linearising the model with respect to coordinates and receiver clock errors, see Code Based Positioning (SPS). | 2019-04-25 12:59:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6608007550239563, "perplexity": 1494.8092249256665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578721441.77/warc/CC-MAIN-20190425114058-20190425135626-00031.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Acardin.franco | # zbMATH — the first resource for mathematics
## Cardin, Franco
Compute Distance To:
Author ID: cardin.franco Published as: Cardin, Franco; Cardin, F.
Documents Indexed: 60 Publications since 1980, including 1 Book Reviewing Activity: 36 Reviews
all top 5
#### Co-Authors
15 single-authored 10 Bernardi, Olga 9 Lovison, Alberto 7 Favretti, Marco 5 Guzzo, Massimiliano 3 Putti, Mario 3 Zanelli, Lorenzo 2 Bobbo, Alessia 2 Facca, Enrico 2 Gramchev, Todor V. 2 Masci, Leonardo 2 Spiro, Andrea F. 2 Tebaldi, Claudio 2 Vazzoler, Simone 2 Zanzotto, Giovanni 1 Abbondandolo, Alberto 1 Daneri, Sara 1 De Anna, Francesco 1 De Marco, Giuseppe 1 Giannotti, Cristina 1 Guiotto, Paolo 1 Marigonda, Antonio 1 Passerone, Daniele 1 Sellers, Shaun 1 Sfondrini, Alessandro 1 Siconolfi, Antonio 1 Spera, Mauro 1 Turco, Alessandro 1 Viterbo, Claude 1 Zoppello, Marta
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#### Serials
4 Continuum Mechanics and Thermodynamics 3 Journal of Mathematical Physics 3 Meccanica 3 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Journal of Mathematical Analysis and Applications 2 Journal of Geometry and Physics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Acta Applicandae Mathematicae 2 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali 2 NoDEA. Nonlinear Differential Equations and Applications 2 Journal of Nonlinear Mathematical Physics 1 Journal of Statistical Physics 1 Nonlinearity 1 Reports on Mathematical Physics 1 Duke Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Le Matematiche 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Ricerche di Matematica 1 Rendiconti del Seminario Matematico 1 Journal of Scientific Computing 1 Atti della Accademia delle Scienze di Torino. Classe di Scienze Fisiche, Matematiche e Naturali 1 SIAM Journal on Applied Mathematics 1 Annales de l’Institut Henri Poincaré. Physique Théorique 1 Journal of Dynamics and Differential Equations 1 Discrete and Continuous Dynamical Systems 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Mathematics and Mechanics of Solids 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Mathematical Physics, Analysis and Geometry 1 Chaos 1 Communications in Contemporary Mathematics 1 Communications on Pure and Applied Analysis 1 The Journal of Symplectic Geometry 1 Multiscale Modeling & Simulation 1 Journal of Geometry and Symmetry in Physics 1 Lecture Notes of the Unione Matematica Italiana 1 Networks and Heterogeneous Media 1 Journal of Geometric Mechanics 1 Nonlinear Analysis. Theory, Methods & Applications 1 Matematica, Cultura e Società. Rivista dell’Unione Matematica Italiana. Serie I
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#### Fields
23 Partial differential equations (35-XX) 22 Mechanics of particles and systems (70-XX) 18 Dynamical systems and ergodic theory (37-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 10 Mechanics of deformable solids (74-XX) 9 Differential geometry (53-XX) 8 Fluid mechanics (76-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Relativity and gravitational theory (83-XX) 4 Numerical analysis (65-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Ordinary differential equations (34-XX) 2 Approximations and expansions (41-XX) 2 Manifolds and cell complexes (57-XX) 2 Probability theory and stochastic processes (60-XX) 1 Operator theory (47-XX) 1 General topology (54-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
42 Publications have been cited 161 times in 126 Documents Cited by Year
On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints. Zbl 0864.70007
Cardin, Franco; Favretti, Marco
1996
Commuting Hamiltonians and Hamilton-Jacobi multi-time equations. Zbl 1153.37029
Cardin, Franco; Viterbo, Claude
2008
On constrained mechanical systems: D’Alembert’s and Gauss’ principles. Zbl 0678.70018
Cardin, Franco; Zanzotto, Giovanni
1989
The global finite structure of generic envelope loci for Hamilton-Jacobi equations. Zbl 1059.53067
Cardin, Franco
2002
Global finite generating functions for field theory. Zbl 1062.53067
Cardin, Franco
2003
Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case. Zbl 1135.35005
Bernardi, Olga; Cardin, Franco
2006
Morse families and constrained mechanical systems. Generalized hyperelastic materials. Zbl 0752.73017
Cardin, Franco
1991
Finite reductions for dissipative systems and viscous fluid-dynamic models on $$\mathbb T^2$$. Zbl 1147.35081
Cardin, Franco; Tebaldi, Claudio
2008
Elementary symplectic topology and mechanics. Zbl 1405.70001
Cardin, Franco
2015
On viscosity and geometrical solutions of Hamilton-Jacobi equations. Zbl 0771.35069
Cardin, Franco
1993
Towards a stationary Monge-Kantorovich dynamics: the Physarum Polycephalum experience. Zbl 1385.49012
Facca, Enrico; Cardin, Franco; Putti, Mario
2018
Chain recurrence, chain transitivity, Lyapunov functions and rigidity of Lagrangian submanifolds of optical hypersurfaces. Zbl 1394.53083
Abbondandolo, Alberto; Bernardi, Olga; Cardin, Franco
2018
Implementation of an exact finite reduction scheme for steady-state reaction-diffusion equations. Zbl 1194.76173
Cardin, Franco; Lovison, Alberto; Putti, Mario
2007
Dynamics of a chain of springs with nonconvex potential energy. Zbl 1056.74027
Cardin, Franco; Favretti, Marco
2003
Exponential estimates for oscillatory integrals with degenerate phase functions. Zbl 1132.41342
Cardin, F.; Gramchev, T.; Lovison, A.
2008
On the internal work in generalized hyperelastic materials. Zbl 0840.73016
Cardin, Franco; Spera, Mauro
1995
Global world functions. Zbl 1086.53088
Cardin, Franco; Marigonda, Antonio
2004
Hyper-impulsive motion on manifolds. Zbl 1084.37522
Cardin, Franco; Favretti, Marco
1998
Finite mechanical proxies for a class of reducible continuum systems. Zbl 1305.74020
Cardin, Franco; Lovison, Alberto
2014
The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory. Zbl 1163.37330
Guzzo, Massimiliano; Bernardi, Olga; Cardin, Franco
2007
On $$C^0$$-variational solutions for Hamilton-Jacobi equations. Zbl 1222.70018
Bernardi, Olga; Cardin, Franco
2011
Swim-like motion of bodies immersed in an ideal fluid. Zbl 1434.74054
Zoppello, Marta; Cardin, Franco
2019
Integrability of the spatial restricted three-body problem near collisions (an announcement). Zbl 1461.70015
Cardin, Franco; Guzzo, Massimiliano
2019
A Morse index invariant reduction of non-equilibrium thermodynamics. Zbl 1393.35244
Cardin, Franco; Masci, Leonardo
2018
The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus. Zbl 1413.35146
Cardin, Franco; Zanelli, Lorenzo
2017
New estimates for Evans’ variational approach to weak KAM theory. Zbl 1277.35127
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano
2013
Discrete structures equivalent to nonlinear Dirichlet and wave equations. Zbl 1234.82006
Lovison, Alberto; Cardin, Franco; Bobbo, Alessia
2009
Tonelli principle: finite reduction and fixed energy molecular dynamics trajectories. Zbl 1172.49028
Turco, A.; Passerone, D.; Cardin, F.
2009
Asymptotic analysis of diffraction integrals in Gevrey spaces. Zbl 1296.78003
Cardin, Franco; Gramchev, Todor; Lovison, Alberto
2014
On the Helmholtz-Boltzmann thermodynamics of mechanical systems. Zbl 1053.80001
Cardin, F.; Favretti, M.
2004
Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics. Zbl 0568.76125
Cardin, Franco
1984
Precession of the perihelion within a generalized theory for the two body problem. Zbl 0584.70006
Cardin, Franco
1982
Lack of critical phase points and exponentially faint illumination. Zbl 1076.78500
Cardin, Franco; Lovison, Alberto
2005
When is a vector field injective? Zbl 0928.53005
Cardin, Franco; Favretti, Marco
1998
Numerical solution of Monge-Kantorovich equations via a dynamic formulation. Zbl 1437.65135
Facca, Enrico; Daneri, Sara; Cardin, Franco; Putti, Mario
2020
Pontryagin maximum principle and Stokes theorem. Zbl 1431.49022
Cardin, Franco; Spiro, Andrea
2019
Stochastic and geometric aspects of reduced reaction-diffusion dynamics. Zbl 1419.82029
Cardin, Franco; Favretti, Marco; Lovison, Alberto; Masci, Leonardo
2019
Cauchy problems for stationary Hamilton-Jacobi equations under mild regularity assumptions. Zbl 1213.35183
Bernardi, Olga; Cardin, Franco; Siconolfi, Antonio
2009
Integral representations of the Schrödinger propagator. Zbl 1214.35015
Zanelli, Lorenzo; Guiotto, Paolo; Cardin, Franco
2008
A PDE approach to finite time indicators in ergodic theory. Zbl 1197.37008
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano; Zanelli, Lorenzo
2009
Finite reduction and Morse index estimates for mechanical systems. Zbl 1227.70016
Cardin, Franco; De Marco, Giuseppe; Sfondrini, Alessandro
2011
Inertial manifold and large deviations approach to reduced PDE dynamics. Zbl 1373.82063
Cardin, Franco; Favretti, Marco; Lovison, Alberto
2017
Numerical solution of Monge-Kantorovich equations via a dynamic formulation. Zbl 1437.65135
Facca, Enrico; Daneri, Sara; Cardin, Franco; Putti, Mario
2020
Swim-like motion of bodies immersed in an ideal fluid. Zbl 1434.74054
Zoppello, Marta; Cardin, Franco
2019
Integrability of the spatial restricted three-body problem near collisions (an announcement). Zbl 1461.70015
Cardin, Franco; Guzzo, Massimiliano
2019
Pontryagin maximum principle and Stokes theorem. Zbl 1431.49022
Cardin, Franco; Spiro, Andrea
2019
Stochastic and geometric aspects of reduced reaction-diffusion dynamics. Zbl 1419.82029
Cardin, Franco; Favretti, Marco; Lovison, Alberto; Masci, Leonardo
2019
Towards a stationary Monge-Kantorovich dynamics: the Physarum Polycephalum experience. Zbl 1385.49012
Facca, Enrico; Cardin, Franco; Putti, Mario
2018
Chain recurrence, chain transitivity, Lyapunov functions and rigidity of Lagrangian submanifolds of optical hypersurfaces. Zbl 1394.53083
Abbondandolo, Alberto; Bernardi, Olga; Cardin, Franco
2018
A Morse index invariant reduction of non-equilibrium thermodynamics. Zbl 1393.35244
Cardin, Franco; Masci, Leonardo
2018
The geometry of the semiclassical wave front set for Schrödinger eigenfunctions on the torus. Zbl 1413.35146
Cardin, Franco; Zanelli, Lorenzo
2017
Inertial manifold and large deviations approach to reduced PDE dynamics. Zbl 1373.82063
Cardin, Franco; Favretti, Marco; Lovison, Alberto
2017
Elementary symplectic topology and mechanics. Zbl 1405.70001
Cardin, Franco
2015
Finite mechanical proxies for a class of reducible continuum systems. Zbl 1305.74020
Cardin, Franco; Lovison, Alberto
2014
Asymptotic analysis of diffraction integrals in Gevrey spaces. Zbl 1296.78003
Cardin, Franco; Gramchev, Todor; Lovison, Alberto
2014
New estimates for Evans’ variational approach to weak KAM theory. Zbl 1277.35127
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano
2013
On $$C^0$$-variational solutions for Hamilton-Jacobi equations. Zbl 1222.70018
Bernardi, Olga; Cardin, Franco
2011
Finite reduction and Morse index estimates for mechanical systems. Zbl 1227.70016
Cardin, Franco; De Marco, Giuseppe; Sfondrini, Alessandro
2011
Discrete structures equivalent to nonlinear Dirichlet and wave equations. Zbl 1234.82006
Lovison, Alberto; Cardin, Franco; Bobbo, Alessia
2009
Tonelli principle: finite reduction and fixed energy molecular dynamics trajectories. Zbl 1172.49028
Turco, A.; Passerone, D.; Cardin, F.
2009
Cauchy problems for stationary Hamilton-Jacobi equations under mild regularity assumptions. Zbl 1213.35183
Bernardi, Olga; Cardin, Franco; Siconolfi, Antonio
2009
A PDE approach to finite time indicators in ergodic theory. Zbl 1197.37008
Bernardi, Olga; Cardin, Franco; Guzzo, Massimiliano; Zanelli, Lorenzo
2009
Commuting Hamiltonians and Hamilton-Jacobi multi-time equations. Zbl 1153.37029
Cardin, Franco; Viterbo, Claude
2008
Finite reductions for dissipative systems and viscous fluid-dynamic models on $$\mathbb T^2$$. Zbl 1147.35081
Cardin, Franco; Tebaldi, Claudio
2008
Exponential estimates for oscillatory integrals with degenerate phase functions. Zbl 1132.41342
Cardin, F.; Gramchev, T.; Lovison, A.
2008
Integral representations of the Schrödinger propagator. Zbl 1214.35015
Zanelli, Lorenzo; Guiotto, Paolo; Cardin, Franco
2008
Implementation of an exact finite reduction scheme for steady-state reaction-diffusion equations. Zbl 1194.76173
Cardin, Franco; Lovison, Alberto; Putti, Mario
2007
The experimental localization of Aubry-Mather sets using regularization techniques inspired by viscosity theory. Zbl 1163.37330
Guzzo, Massimiliano; Bernardi, Olga; Cardin, Franco
2007
Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case. Zbl 1135.35005
Bernardi, Olga; Cardin, Franco
2006
Lack of critical phase points and exponentially faint illumination. Zbl 1076.78500
Cardin, Franco; Lovison, Alberto
2005
Global world functions. Zbl 1086.53088
Cardin, Franco; Marigonda, Antonio
2004
On the Helmholtz-Boltzmann thermodynamics of mechanical systems. Zbl 1053.80001
Cardin, F.; Favretti, M.
2004
Global finite generating functions for field theory. Zbl 1062.53067
Cardin, Franco
2003
Dynamics of a chain of springs with nonconvex potential energy. Zbl 1056.74027
Cardin, Franco; Favretti, Marco
2003
The global finite structure of generic envelope loci for Hamilton-Jacobi equations. Zbl 1059.53067
Cardin, Franco
2002
Hyper-impulsive motion on manifolds. Zbl 1084.37522
Cardin, Franco; Favretti, Marco
1998
When is a vector field injective? Zbl 0928.53005
Cardin, Franco; Favretti, Marco
1998
On nonholonomic and vakonomic dynamics of mechanical systems with nonintegrable constraints. Zbl 0864.70007
Cardin, Franco; Favretti, Marco
1996
On the internal work in generalized hyperelastic materials. Zbl 0840.73016
Cardin, Franco; Spera, Mauro
1995
On viscosity and geometrical solutions of Hamilton-Jacobi equations. Zbl 0771.35069
Cardin, Franco
1993
Morse families and constrained mechanical systems. Generalized hyperelastic materials. Zbl 0752.73017
Cardin, Franco
1991
On constrained mechanical systems: D’Alembert’s and Gauss’ principles. Zbl 0678.70018
Cardin, Franco; Zanzotto, Giovanni
1989
Existence and uniqueness theorems for viscous fluids capable of heat conduction in a relativistic theory of non stationary thermodynamics. Zbl 0568.76125
Cardin, Franco
1984
Precession of the perihelion within a generalized theory for the two body problem. Zbl 0584.70006
Cardin, Franco
1982
all top 5
#### Cited by 165 Authors
24 Cardin, Franco 8 Lovison, Alberto 6 Zanelli, Lorenzo 5 de León Rodríguez, Manuel 4 Bernardi, Olga 4 Treanţă, Savin 3 Buhovsky, Lev 3 Darbon, Jerome 3 Facca, Enrico 3 Favretti, Marco 3 Guzzo, Massimiliano 2 Bloch, Anthony M. 2 Bobbo, Alessia 2 Celletti, Alessandra 2 Cortés, Jorge 2 Esen, Oğul 2 García, Pedro Luis 2 Graffi, Sandro 2 Gramchev, Todor V. 2 Guiotto, Paolo 2 Guo, Yongxin 2 Marle, Charles-Michel 2 Marsden, Jerrold Eldon 2 Martín de Diego, David 2 Martínez, Sonia 2 Massa, Enrico 2 Meng, Tingwei 2 Pagani, Enrico M. 2 Polterovich, Leonid Viktorovich 2 Putti, Mario 2 Rodrigo, César 2 Rossi, Olga 2 Spera, Mauro 2 Spiro, Andrea F. 2 Truskinovsky, Lev 2 Udriste, Constantin N. 2 Zapolsky, Frol 2 Zoppello, Marta 1 Barbero-Liñán, María 1 Barretta, Raffaele 1 Bazan, Aldo 1 Benzi, Michele 1 Bernard, Patrick 1 Besana, Alberto 1 Bettiol, Piernicola 1 Bonifaci, Vincenzo 1 Bressan, Alberto 1 Bruce, Andrew James 1 Bruno, Danilo 1 Bustamante, Roger 1 Cacciapuoti, Rosalba 1 Calleja, Renato C. 1 Capitanio, Gianmarco 1 Chandrasekaran, Venkatesa 1 Chee, G. Y. 1 Chen, Qinbo 1 Chen, Thomas M. 1 Chow, Yat Tin 1 Colombo, Giovanni 1 Crampin, Mike 1 Dalla Riva, Matteo 1 D’Amore, Luisa 1 Daneri, Sara 1 Davini, Andrea 1 De Marco, Giuseppe 1 de Saxcé, Géry 1 Diaco, Marina 1 Díaz, Viviana Alejandra 1 Dyskin, Arcady V. 1 Efendiev, Yalchin R. 1 Eliashberg, Yakov Matveevich 1 Entov, Michael 1 Evans, Lawrence Craig 1 Fassò, Francesco 1 Fernández Martínez, Antonio 1 Ferra, Igor Ambo 1 Flannery, M. R. 1 Florio, Anna 1 Fortune, Danielle 1 Giachetta, Giovanni 1 Giannotti, Cristina 1 Gidoni, Paolo 1 Gràcia, Xavier 1 Guha, Partha 1 Haddout, Soufiane 1 Hjiaj, Mohammed 1 Humilière, Vincent 1 Jiménez, Fernando 1 Jóźwikowski, Michał 1 Karrenbauer, Andreas 1 Kauffman, Louis Hirsch 1 Kholodenko, Arkady L. 1 Kolev, Pavel 1 Kozlov, Valeriĭ Vasil’evich 1 Krishnaprasad, P.s. 1 Kupka, Ivan A. K. 1 Langlois, Gabriel P. 1 Leguil, Martin 1 Lesimple, Marc 1 Lewis, Andrew D. ...and 65 more Authors
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#### Cited in 75 Serials
12 Journal of Mathematical Physics 9 Journal of Geometry and Physics 6 Journal of Geometric Mechanics 5 Continuum Mechanics and Thermodynamics 4 Journal of Differential Equations 3 Communications in Mathematical Physics 3 Meccanica 2 Archive for Rational Mechanics and Analysis 2 Journal of Mathematical Analysis and Applications 2 Reports on Mathematical Physics 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Ricerche di Matematica 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Journal of Mathematical Sciences (New York) 2 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 2 Regular and Chaotic Dynamics 2 Journal of Nonlinear Mathematical Physics 2 Dynamical Systems 2 International Journal of Geometric Methods in Modern Physics 2 Communications in Mathematics 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 International Journal of Engineering Science 1 International Journal of Theoretical Physics 1 Journal of Computational Physics 1 Journal of the Mechanics and Physics of Solids 1 Journal of Statistical Physics 1 Nonlinearity 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Reviews in Mathematical Physics 1 Advances in Mathematics 1 Duke Mathematical Journal 1 International Journal for Numerical Methods in Engineering 1 Inventiones Mathematicae 1 Journal of Optimization Theory and Applications 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Quarterly of Applied Mathematics 1 Rendiconti del Seminario Matematico della Università di Padova 1 Theoretical Computer Science 1 Ergodic Theory and Dynamical Systems 1 Chinese Annals of Mathematics. Series B 1 Acta Applicandae Mathematicae 1 Journal of Scientific Computing 1 Differential Geometry and its Applications 1 Geometric and Functional Analysis. GAFA 1 Annals of Physics 1 Journal of Elasticity 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Knot Theory and its Ramifications 1 Journal of Nonlinear Science 1 Computational Optimization and Applications 1 SIAM Journal on Scientific Computing 1 NoDEA. Nonlinear Differential Equations and Applications 1 Selecta Mathematica. New Series 1 Discrete and Continuous Dynamical Systems 1 The Journal of Fourier Analysis and Applications 1 Vietnam Journal of Mathematics 1 Chaos 1 Discrete Dynamics in Nature and Society 1 Communications in Contemporary Mathematics 1 Journal of High Energy Physics 1 Milan Journal of Mathematics 1 Journal of Physics A: Mathematical and Theoretical 1 Networks and Heterogeneous Media 1 SIAM Journal on Imaging Sciences 1 Electronic Research Announcements in Mathematical Sciences 1 Advances in High Energy Physics 1 Journal of Topology and Analysis 1 São Paulo Journal of Mathematical Sciences 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Numerical Algebra, Control and Optimization 1 Research in the Mathematical Sciences
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#### Cited in 29 Fields
60 Mechanics of particles and systems (70-XX) 42 Dynamical systems and ergodic theory (37-XX) 28 Differential geometry (53-XX) 22 Partial differential equations (35-XX) 22 Calculus of variations and optimal control; optimization (49-XX) 15 Mechanics of deformable solids (74-XX) 12 Ordinary differential equations (34-XX) 12 Global analysis, analysis on manifolds (58-XX) 9 Numerical analysis (65-XX) 9 Quantum theory (81-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Operator theory (47-XX) 5 Fluid mechanics (76-XX) 5 Operations research, mathematical programming (90-XX) 4 Manifolds and cell complexes (57-XX) 3 Functional analysis (46-XX) 2 General and overarching topics; collections (00-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Optics, electromagnetic theory (78-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) | 2021-10-18 11:06:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4011783301830292, "perplexity": 8924.719392772391}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00702.warc.gz"} |
https://phys.libretexts.org/TextMaps/Classical_Mechanics_TextMaps/Map%3A_Classical_Mechanics_(Tatum)/1%3A_Centers_of_Mass/1.05%3A_Summary_of_the_Formulas_for_Plane_Laminas_and_Curves | $$\require{cancel}$$
# 1.5: Summary of the Formulas for Plane Laminas and Curves
##### Uniform Plane Lamina
$$y = y(x)$$ $$r = r(θ)$$ $$\overline{x} = \frac{1}{A} \int_a^b xydx$$ $$\overline{y} = \frac{1}{2A} \int_a^b y^{2}dx$$ $$\overline{x} = \frac{2 \int_ \alpha ^ \beta r^3 cos \theta d \theta }{3 \int_ \alpha ^ \beta r^2 d \theta }$$ $$\overline{y} = \frac{2 \int_ \alpha ^ \beta r^3 sin \theta d \theta }{3 \int_ \alpha ^ \beta r^2 d \theta}$$
##### Uniform Plane Curve
$$y = y(x)$$ $$r = r(θ)$$ $$\overline{x} = \frac{1}{L} \int_a^b x[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}$$ $$\overline{y} = \frac{1}{L} \int_a^b y[1+( \frac{dy}{dx})^{2}]^{\frac{1}{2}}$$ $$\overline{x} = \frac{1}{L} \int_ \alpha ^ \beta rcos \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2}$$ $$\overline{y} = \frac{1}{L} \int_ \alpha ^ \beta rsin \theta [( \frac{dr}{d \theta })^{2} + r^{2} ]^ \frac{1}{2}$$ | 2018-04-25 04:52:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9855677485466003, "perplexity": 8978.312488779642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125947693.49/warc/CC-MAIN-20180425041916-20180425061916-00479.warc.gz"} |
http://bhavyanshu.me/free-coupon-links-for-bigrock-get-discount-on-domains/11/30/2013 | Bigrock.in is a great domain host. You can get cheap domains with bigrock. IF you get some discount over domain names, then it’s simple awesome. Ain’t it?
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Coupon Links [Valid till november, 2015]:
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To use the above codes, simply click above links, find whatever domain you want. When you add to cart and proceed to checkout, the coupon codes will be applied automatically. Like shown below.
You can also directly write these codes codershangout.org or bhavyanshu.me in the above field. They will always work.
That’s all for now. I will update this list as soon as I get more.
blog comments powered by Disqus | 2017-03-24 12:06:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1811331808567047, "perplexity": 4033.76395932223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187945.85/warc/CC-MAIN-20170322212947-00587-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.numerade.com/questions/evaluate-the-indefinite-integral-displaystyle-int-fracdx5-3x/ | 💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
# Evaluate the indefinite integral. $\displaystyle \int \frac{dx}{5 - 3x}$
## $$-\frac{1}{3} \ln |5-3 x|+C$$
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### Video Transcript
and this problem. We are practicing an integration technique called the U substitution. And this is a really helpful technique to solve. Integral is because what we do is we technically substitute the hard part of our integral to make our integral into something that we recognize that we can solve easily. And that's how we use U substitution. So that's what we're going to be doing in this problem. So let's just review the integral that we're starting with. We have the indefinite and the girl meeting. We don't have limits to plug in. We have the indefinite integral DX over five minus three x. Well, if we weren't using use substitution. Or maybe you solve the integral for the first time, that looks pretty hard. Maybe we don't know how to solve it. So we're going to use U substitution. We're going to let u equal five minus three x So we would take the derivative d u equals negative three d x so we can rearrange that and thio finding something that we know we have in our integral, which is d x so d x equal negative do you over three So we can rearrange are integral using the variable. You we would get negative 1/3 times the integral one over you and that looks like something that we can anti derive. That's a function that we know that we can solve. So we would get negative 1/3 times the natural log of the absolute value of U plus C remember sees that constant that we have to add on to an indefinite integral. So then we have to plug in our substitution for you. We can't just make this substitution and call it a day. We have to plug in that substitution back into our essentially our anti derivative to in order to get the correct answer. So we started with the integral DX over five minus three x. So once we plug you back in, you would get that Our solution is negative 1/3 times the natural log of the absolute value of five minus three x plus c. So I hope with this problem helped you understand how we can use u substitution to solve an indefinite integral on. I hope that it makes sense why we use U substitution in the first place.
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Join Bootcamp | 2021-09-27 00:28:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8545895218849182, "perplexity": 406.942382254951}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058222.43/warc/CC-MAIN-20210926235727-20210927025727-00293.warc.gz"} |
http://zbmath.org/?q=an:1110.47057 | zbMATH — the first resource for mathematics
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Robustness of Mann’s algorithm for nonexpansive mappings. (English) Zbl 1110.47057
The authors prove robustness results of three somewhat different versions (corresponding to three different settings) of Mann’s algorithm to obtain a fixed-point of a suitable mapping. We state the version in the first setting (Theorem 3.3) in extenso. Let $X$ be a uniformly convex Banach space, where either $X$ satisfies Opial’s property or where the dual of $X$ has the Kadec–Klee property. Let $T:X\to X$ be a nonexpansive mapping having a nonempty set of fixed points. Starting from some point $x\left(0\right)$ in $X$, let the sequence $x\left(n\right)$ be generated by the following perturbed Mann algorithm: $x\left(n+1\right)=\left(1-\alpha \left(n\right)\right)x\left(n\right)+\alpha \left(n\right)\left(Tx\left(n\right)+e\left(n\right)\right)$, where $\left\{\alpha \left(n\right)\right\}$ and $\left\{e\left(n\right)\right\}$ are sequences in $\left(0,1\right)$ and in $X$, respectively, satisfying the following properties: ${\Sigma }\alpha \left(n\right)\left(1-\alpha \left(n\right)\right)=\infty$ and ${\Sigma }\alpha \left(n\right)\parallel e\left(n\right)\parallel <\infty$. Then the sequence $\left\{x\left(n\right)\right\}$ converges weakly to a fixed point of $T$.
In the second setting, the authors consider a nonexpansive map $T$ defined on a closed convex subset of a real Hilbert space (Theorem 4.1). Finally, in the third setting (Theorem 5.1), the map is an $m$-accretive operator in a uniformly convex Banach space $X$, where $X$ has the same additional properties as in the first setting.
MSC:
47J25 Iterative procedures (nonlinear operator equations) 47H09 Mappings defined by “shrinking” properties 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 65J15 Equations with nonlinear operators (numerical methods) | 2014-04-24 10:17:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 20, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.888333261013031, "perplexity": 2519.3084567955825}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00530-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://socratic.org/questions/what-is-the-period-of-f-theta-sin-2-t-cos-5-t | # What is the period of f(theta)= sin 2 t - cos 5 t ?
Apr 8, 2016
$2 \pi$
#### Explanation:
The period for $\sin k t = 2 \frac{\pi}{k}$.
The separate periods for sin 2t and sin 5t are $\pi$ and the smaller $2 \frac{\pi}{5}$. Match with suitable integer multiples m and n such that $m = 2 \frac{n}{5}$. .
The least common multiple period is $2 \pi$, for m=2 and n=5. .
So, this is the period for the compounded oscillation.
$f \left(t\right) = \sin 2 t - \sin 5 t$.
The laast value of P for which f(t+P)=f(t) is $2 \pi$. | 2021-04-13 00:59:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9870920181274414, "perplexity": 2167.795297497013}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038071212.27/warc/CC-MAIN-20210413000853-20210413030853-00292.warc.gz"} |
http://hawaiireedlab.com/wikidir/doku.php?id=haldane_1937 | # Lab Wiki
haldane_1937
### Haldane 1937
Haldane, J. B. S. (1937). The effect of variation of fitness. The American Naturalist, 71(735), 337-349.
Abstract: In a species in equilibrium variation is mainly due to two causes. Some deleterious genes are being weeded out by selection at the same rate as they are produced by mutation. Others are preserved because the heterozygous form is fitter than either homozygote. In the former case the loss of fitness in the species is roughly equal to the sum of all mutation rates and is probably of the order of 5 per cent. It is suggested that this loss of fitness is the price paid by a species for its capacity for further evolution.
Takeaway: Haldane considers the effects of deleterious mutations. Estimates are given for mutation-selection equilibrium allele frequencies and average reduction of fitness in the population. Fitness reduction is only a function of, and proportional to, mutation rates. The average individual in a population has a fitness that is a small fraction of the maximum theoretically possible if the genome were free of deleterious mutations.
#### Notes
##### Symbols
• $\mu$ is the mutation rate per locus per generation.
• $N$ is the population size.
• $x$ is the frequency of individuals carrying a copy of the mutant allele.
• $f$ is the relative average fitness of individuals carrying the mutant allele.
• $y$ is half the number of heterozygotes, which are $2y$.
• $p$ is the mutant allele frequency.
• $F$ is the total fitness of an individual over all loci subject to purifying selection in the genome.
• Here, $s$ is the reduction in fitness of the mutation. $s = 1-f$.
##### Dominant Fitness Effect
Pages 341–342 deal with a dominant fitness effect and the assumptions that the species is diploid, deleterious allele is rare (so most individuals with a copy only have one copy), and the unmutated fitness is one.
A fraction of the unmutated loci are expected to mutate each generation.
$$N\mu (2-x)$$
Mutated copies are removed by selection each generation ($f$ survive).
$$N x (1-f)$$
At equilibrium the rate of removal is equal to the rate of input.
$$N x (1-f) = N\mu (2-x)$$
$$Nx - Nxf = 2N\mu - N\mu x$$ $$Nx - Nxf + N\mu x = 2N\mu$$ $$x (N - Nf + N\mu) = 2N\mu$$ $$x = \frac{2N\mu}{N - Nf + N\mu} = \frac{2\mu}{1 - f + \mu}$$
Assuming $\mu$ is much smaller than one and that the mutant alleles are rare gives
$$x = 2 p (1-p) \approx 2 p \approx \frac{2\mu}{s}\mbox{.}$$
$$p \approx \frac{\mu}{s}\mbox{.}$$
The loss of fitness (from one) to the species is
$$x (1-f) = x - fx = \frac{2\mu}{1 - f + \mu} - \frac{2\mu f}{1 - f + \mu} = 2\mu \left(\frac{1-f}{1-f+\mu}\right) \approx 2\mu\mbox{.}$$
This is approximately $2\mu$ if $\mu$ is small relative to $1-f$. The interesting thing about this is that, at equilibrium, the loss of fitness is only a function of the mutation rate and is independent of the average fitness of individuals carrying the mutant alleles. The reason for this is the inverse relationship between the loss of fitness and the equilibrium frequency of the allele. Mutant alleles with a higher fitness attain a higher frequency in the population. So even though the loss of fitness is small more individuals are affected. And vice versa, Mutants with a large loss of fitness are maintained at a low frequency and fewer individuals are affected by the large loss. On average over an entire population these factors cancel out and the average loss of fitness is only twice the mutation rate (for dominant effects).
##### Recessive Fitness Effect
Page 344 treats the case of recessive loss of fitness.
A fraction of the unmutated loci are expected to mutate each generation. (Only half of the heterozygous loci are unmutated.)
$$2N\mu (1-x-y)$$
Mutated copies are removed by selection each generation. (Each loss removes two copies of the mutant alleles so $2x$.)
$$N 2 x (1-f)$$
At equilibrium
$$2N\mu (1-x-y) = N 2 x (1-f)$$ $$2N\mu -2N\mu x-2N\mu y = N 2 x - N 2 x f$$ $$2N\mu -2N\mu y = N 2 x - N 2 x f + 2N\mu x$$ $$2N\mu -2N\mu y = x (N 2 - N 2 f + 2N\mu )$$ $$x =\frac{2N\mu -2N\mu y}{ N 2 - N 2 f + 2N\mu }$$ $$x =\frac{\mu -\mu y}{ 1 - f + \mu } = \frac{\mu (1 - y)}{ 1 - f + \mu }$$
If $y$ and $\mu$ are small
$$x \approx \frac{\mu}{ 1 - f }$$
$$p^2 = x \approx \frac{\mu}{ 1 - f } = \frac{\mu}{s}$$ $$p \approx \sqrt{\frac{\mu}{s}}$$
The average loss of fitness in the population is
$$x (1-f) = x - fx \approx \frac{\mu}{1 - f} - \frac{\mu f}{1 - f} = \mu \left(\frac{1-f}{1-f}\right) = \mu\mbox{.}$$
Again, this is independent of the fitness effect and only a function of the mutation rate.
##### Multiple Loci
Pages 345–346 describe the predictions over all loci in the genome. Assuming mutations are independent both in occurrence and in fitness effects the average individual in the population has an expected fitness of
$$F = \prod_i (1-m_i)$$
where $m$ is the mutation rate $\mu$ at the $i$th locus for recessive mutations and $m=2\mu$ for dominant effects.
If the per nucleotide per generation mutation rate is $10^{-8}$, a tenth of our 3.3 billion base pair genome is under purifying selection, and the majority of mutations are recessive in fitness effects then
$$F \approx (1-10^{-8})^{3.3 \times 10^8}\approx 0.037\mbox{.}$$
Therefore, our fitness is predicted to be a small fraction, approximately 3–4%, of its theoretical maximum without mutations (both new mutations that have occurred in our own genomes and mutations that we have inherited from our ancestors).
##### Other things
Haldane discusses the effects of inbreeding and sex-linkage on these prediction and goes through quite a bit of additional logical details in the introduction as well as some examples from insects later in the paper. | 2021-01-24 00:43:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5641070604324341, "perplexity": 1150.3795782430873}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703538741.56/warc/CC-MAIN-20210123222657-20210124012657-00653.warc.gz"} |
https://search.r-project.org/CRAN/refmans/chickn/html/COMPR.html | COMPR {chickn} R Documentation
## Compressive Orthogonal Matching Pursuit with Replacement
### Description
An implementation of the Compressive Orthogonal Matching Pursuit with Replacement algorithm
### Usage
COMPR(
Data,
ind.col = 1:ncol(Data),
K,
Frequencies,
lower_b,
upper_b,
SK_Data,
maxIter = 300,
HardThreshold = TRUE,
options = list(tol_centroid = 1e-08, nIterCentroid = 1500, min_weight = 0, max_weight
= Inf, nIterLast = 1000, tol_global = 1e-12)
)
### Arguments
Data A Filebacked Big Matrix n x N, data vectors are stored in the matrix columns. ind.col Column indeces, which indicate which data vectors are considered for clustering. By default the entire Data matrix. K Number of clusters. Frequencies A frequency matrix m x n with frequency vectors in rows. lower_b A vector of the lower boundary of data. upper_b A vector of the upper boundary. SK_Data Data sketch vector of the length 2m. It can be computed using Sketch. maxIter Maximum number of iterations in the global optimization with respect to cluster centroid vectors and their weights. Default is 300. HardThreshold logical that indicates whether to perform the replacement. Default is TRUE. options List of optimization parameters: tol_centroid is a tolerance value for the centroid optimization. Default is 1e-8. nIterCentroid is a maximum number of iterations in the centroid optimization (default is 1500). min_weight is a lower bound for centroid weights (default is 0). max_weight is an upper bound for centroids weights (default is Inf) nIterLast is a number of iteration in the global optimization at the last algorithm iteration. Default is 1000. tol_global is a tolerance value for the global optimization. Default is 1e-12.
### Details
COMPR is an iterative greedy method, which alternates between expanding the cluster centroid set C with a new element c_i, whose sketch is the most correlated to the residue and the global minimization with respect to cluster centroids c_1, …, c_K and their weights w_1, …, w_K. It clusters the data collection into K groups by minimizing the difference between the compressed data version (data sketch) and a linear combination of cluster centroid sketches, i.e. \|Sk(Data) - ∑_{i=1}^K w_i \cdot Sk(c_i)\|.
### Value
A matrix n x K with cluster centroid vectors in columns.
### Note
This method is also referred to as Compressive K-means and it has been published in Keriven N, Tremblay N, Traonmilin Y, Gribonval R (2017). “Compressive K-means.” In 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 6369–6373. IEEE..
### Examples
X = matrix(rnorm(1e5), ncol=1000, nrow = 100)
lb = apply(X, 1, min)
ub = apply(X, 1, max)
X_FBM = bigstatsr::FBM(init = X, ncol=1000, nrow = 100)
out = GenerateFrequencies(Data = X_FBM, m = 20, N0 = ncol(X_FBM))
SK = Sketch(Data = X_FBM, W = out$W) C <- COMPR(Data = X_FBM, K = 2, Frequencies = out$W, lower_b = lb, upper_b = ub, SK_Data = SK)
[Package chickn version 1.2.3 Index] | 2021-06-17 09:33:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5922197103500366, "perplexity": 4660.616207560109}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487629632.54/warc/CC-MAIN-20210617072023-20210617102023-00530.warc.gz"} |
http://mathoverflow.net/revisions/49706/list | 3 added 340 characters in body
This is false. We construct $A$ inductively, so that the following holds:
• $A$ contains all powers of two larger or equal than $4$ and no other even numbers.
• The number of odd numbers in $A$ between $2^j$ and $2^{j+1}$ is $2^{j-2}$.
• No power of two is in a 3-AP contained in $A$.
We start by specifying that $4\in A, 5\in A, 6\notin A,7\notin A$. Suppose $A\cap\{1,\ldots, 2^m-1\}$ has been defined so that the above properties hold. We next define $A\cap\{ 2^m,\ldots, 2^{m+1}-1\}$ as follows: $2^m\in A$. There are $1+2+\ldots+2^{m-3}<2^{m-2}$ odd numbers smaller than $2^m$ in $A$; let $O_m$ be the set of all of them. We choose $2^{m-2}$ odd numbers in $$\{2^m,\ldots, 2^{m+1}\} \backslash (2^{m+1}-O_m).$$ and add them to $A$. We can do this since $|O_m|< 2^{m-2}$.
The first two properties are clear from the construction. To check the last (the one we care about), note that $2^m$ can't be the first/last term of a $3$-AP in $A$, since then the last/first term would also be even, hence another power of $2$, and then the middle one would be even, and a power of $2$ as well. But $2^m$ can't be the middle term of a $3$-AP either: for the same reason as before, the other two terms must be odd. Let $(a,2^m,c)$ be the AP. Then $a\in O_m$ by definition, but this implies $c-2^m=2^m-a$, or $c\in 2^{m+1}-O_m$, a case which was excluded in the construction.
Clearly $A$ has density $1/4$ so this completes the proof.
If $A$ has positive upper density, one can still ask what is the largest possible size of the set $B$ of all elements of $A$ which are not in any $3$-AP contained in $A$. Clearly $B$ has density $0$ by Roth's Theorem (and we get better bounds from the quantitative bounds in Roth's Theorem). Is it possible to do better?
2 added 9 characters in body
This is false. We construct $A$ inductively, so that the following holds:
• $A$ contains all powers of two larger or equal than $4$ and no other even numbers.
• The number of odd numbers in $A$ between $2^j$ and $2^{j+1}$ is $2^{j-2}$.
• No power of two is in a 3-AP contained in $A$.
We start by specifying that $4\in A, 5\in A, 6\notin A,7\notin A$. Suppose $A\cap\{1,\ldots, 2^m-1\}$ has been defined so that the above properties hold. We next define $A\cap\{ 2^m,\ldots, 2^{m+1}-1\}$ as follows: $2^m\in A$. There are $1+2+\ldots+2^{m-3}<2^{m-2}$ odd numbers smaller than $2^m$ in $A$; let $O_m$ be the set of all of them. We choose $2^{m-2}$ odd numbers in $$\{2^m,\ldots, 2^{m+1}\} \backslash (2^{m+1}-O_m).$$ and add them to $A$. We can do this since $|O_m|< 2^{m-2}$.
The first two properties are clear from the construction. To check the last (the one we care about), note that $2^m$ can't be the first/last term of a $3$-AP in $A$, since then the last/first term would also be even, hence another power of $2$, and then the middle one would be even, and a power of $2$ as well. But $2^m$ can't be the middle term of a $3$-AP either: for the same reason as before, the other two terms must be odd. Let $(a,2^m,c)$ be the AP. Then $a\in O_m$ by definition, but this implies $c-2^m=2^m-a$, or $c\in 2^{m+1}-O_m$, a case which was excluded in the construction.
Clearly $A$ has density $1/4$ so this completes the proof.
1
This is false. We construct $A$ inductively, so that the following holds:
• $A$ contains all powers of two larger than $4$ and no other even numbers.
• The number of odd numbers in $A$ between $2^j$ and $2^{j+1}$ is $2^{j-2}$.
• No power of two is in a 3-AP contained in $A$.
We start by specifying that $4\in A, 5\in A, 6\notin A,7\notin A$. Suppose $A\cap\{1,\ldots, 2^m-1\}$ has been defined so that the above properties hold. We next define $A\cap\{ 2^m,\ldots, 2^{m+1}-1\}$ as follows: $2^m\in A$. There are $1+2+\ldots+2^{m-3}<2^{m-2}$ odd numbers smaller than $2^m$ in $A$; let $O_m$ be the set of all of them. We choose $2^{m-2}$ odd numbers in $$\{2^m,\ldots, 2^{m+1}\} \backslash (2^{m+1}-O_m).$$ and add them to $A$. We can do this since $|O_m|< 2^{m-2}$.
The first two properties are clear from the construction. To check the last (the one we care about), note that $2^m$ can't be the first/last term of a $3$-AP in $A$, since then the last/first term would also be even, hence another power of $2$, and then the middle one would be even, and a power of $2$ as well. But $2^m$ can't be the middle term of a $3$-AP either: for the same reason as before, the other two terms must be odd. Let $(a,2^m,c)$ be the AP. Then $a\in O_m$ by definition, but this implies $c-2^m=2^m-a$, or $c\in 2^{m+1}-O_m$, a case which was excluded in the construction.
Clearly $A$ has density $1/4$ so this completes the proof. | 2013-05-19 22:08:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9578129649162292, "perplexity": 114.88455925813736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698090094/warc/CC-MAIN-20130516095450-00053-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://gamedev.stackexchange.com/questions/152733/opengl-parallax-displacement-mapping-not-working | OpenGL Parallax Displacement Mapping Not Working
I am attempting to implement parallax displacement mapping into my OpenGL code but it is not working as it should.
https://imgur.com/a/9yIQL
As I move around, double-lines moves around and if I am looking and positioned at just the right angle, the extra lines disappears and it looks like a normal texture, but without any displacement mapping.
I have tried various texture/displacement mapping combos and all of them have the same issue, so it is not my textures.
VS Code:
#version 330 core
layout (location = 0) in vec3 position;
layout (location = 1) in vec2 uvCoordinates;
layout (location = 2) in vec3 normal;
layout (location = 3) in vec3 tangent;
out Vertex
{
vec3 position;
vec2 uvCoordinates;
vec3 normal;
mat3 tbnMatrix;
} vertex;
uniform mat4 projection;
uniform mat4 view;
uniform mat4 model;
void main()
{
gl_Position = projection * view * model * vec4(position, 1.0);
vertex.position = (model * vec4(position, 1.0)).xyz;
vertex.uvCoordinates = uvCoordinates;
vertex.normal = normalize((model * vec4(normal, 0.0)).xyz);
vec3 n = normalize((model * vec4(normal, 0.0)).xyz);
vec3 t = normalize((model * vec4(tangent, 0.0)).xyz);
t = normalize(t - dot(t, n) * n);
vec3 b = cross(t, n);
vertex.tbnMatrix = mat3(t, b, n);
}
FS Code:
#version 330 core
layout (location = 0) out vec4 color;
in Vertex
{
vec3 position;
vec2 uvCoordinates;
vec3 normal;
mat3 tbnMatrix;
} vertex;
struct Material
{
vec3 ambientLight;
vec3 diffuseLight;
vec3 specularLight;
float transparency;
float shininess;
int useDiffuse;
int useSpecular;
int useNormal;
int useDisplacement;
sampler2D diffuse;
sampler2D specular;
sampler2D normal;
sampler2D displacement;
};
uniform vec3 ambientLight;
uniform vec3 eyePosition;
uniform Material material;
uniform float displacementScale;
uniform float displacementBias;
vec2 calculateTextureCoordinates(vec3 eyeDirection, vec2 uvCoordinates, mat3 tbnMatrix, sampler2D displacement)
{
return uvCoordinates + (eyeDirection * tbnMatrix).xy * (texture(displacement, uvCoordinates).r * displacementScale + displacementBias);
}
void main()
{
color = vec4(ambientLight * material.ambientLight, material.transparency);
if(material.useDiffuse == 1)
{
vec2 uvCoordinates;
if(material.useDisplacement == 1)
{
uvCoordinates = calculateTextureCoordinates(normalize(eyePosition - vertex.position), vertex.uvCoordinates, vertex.tbnMatrix, material.displacement);
}
else
{
uvCoordinates = vertex.uvCoordinates;
}
color *= texture(material.diffuse, uvCoordinates);
}
}
I also have other lighting shaders that use the exact same tbn matrix to calculate normal mapping, which works just fine. This leads me to believe that both my tangent calculations and tbn matrix are working just fine. This scene is using no lighting, so lighting should have no impact on this code.
The displacementScale uniform is set to 0.04 and my displacementBias is set to -0.02. Increasing the scale causes the lines to become even more and more disoriented and decreasing it causes less of the disoriented effect but does not provide any displacement whatsoever.
I've also checked to make sure I have binded all my textures to the correct sampler2D and they are correct. I've been working on this for awhile now and I am completely stuck. Any help would be immensely appreciated.
In order to properly implement this, you have to understand which "space" you are working in. In computer graphics, you have five discrete spaces to work in:
1. Object space. This is the un-transformed vertex coordinates.
2. Model, or World space, this is the position of a vertex when transformed into it's world position.
3. View space. This is the world, relative to the camera, or eye.
4. Projection, or screen space. This is when fragments get rasterised.
5. Tangent space. This is space relative to the texture coordinates. Call it UV space if you like.
In your example, we will ignore lighting, as it complicates matters.
In order to correctly displace the UV coordinates according to the view vector, you have to take your view vector, and transform it into tangent space, like so:
view_dir = eyePosition - (model * position).xyz;
TS_View = normalize(tbn * view_dir);
In doing so, when you perform your view direction calculations with uv coordinates, they are using the same coordinate system, and the displacement will be correct regardless of the orientation of the model.
You may find that it's still not quite right. If so, try flipping the sign of the y or x component of the view direction, by multiplying it by -1. | 2021-03-04 13:27:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.249699205160141, "perplexity": 6449.180522493208}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369054.89/warc/CC-MAIN-20210304113205-20210304143205-00626.warc.gz"} |
https://www.tutorialexample.com/convert-a-normal-distribution-data-to-standard-normal-distribution-machine-learning-tutorial/ | # Convert a Normal Distribution Data to Standard Normal Distribution – Machine Learning Tutorial
By | December 4, 2020
As to a norm distribution data $$X$$, how to convert its distribution to standard normal distribution? In this tutorial, we will introduce you how to do.
## What is Normal Distribution?
Normal Distribution looks like image below:
You can read more detail here:
## How to convert a normal distribution data to standard normal distribution?
As to standard normal distribution, it need the mean of $$X$$ is 0, the variance of it is 1.
We can do like this:
$\hat{X}=\frac{X-\mu}{\sigma}$
where $$\mu$$ is the mean value of $$X$$, the $$\sigma$$ is the standard deviation of $$X$$. $$\hat{X}$$ will be a standard normal distribution. | 2021-10-20 21:53:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5799413919448853, "perplexity": 364.9544749870824}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585353.52/warc/CC-MAIN-20211020214358-20211021004358-00204.warc.gz"} |
https://wattsupwiththat.com/test/ | # Test
SMPTE color bars – Click for your own test pattern kit
This page is for posters to test comments prior to submitting them to WUWT. Your tests will be deleted in a while, though especially interesting tests, examples, hints, and cool stuff will remain for quite a while longer.
Some things that don’t seem to work any more, or perhaps never did, are kept in Ric Werme’s Guide to WUWT.
## Formatting in comments
WordPress does not provide much documentation for the HTML formatting permitted in comments. There are only a few commands that are useful, and a few more that are pretty much useless.
A typical HTML formatting command has the general form of <name>text to be formatted</name>. A common mistake is to forget the end command. Until WordPress gets a preview function, we have to live with it.
N.B. WordPress handles some formatting very differently than web browsers do. A post of mine shows these and less useful commands in action at WUWT.
N.B. You may notice that the underline command, <u>, is missing. WordPress seems to suppress for almost all users, so I’m not including it here. Feel free to try it, don’t expect it to work.
Name Sample Result
b (bold) This is <b>bold</b> text This is bold text
Command strong also does bolding.
i (italics) This is <i>italicized</i> text This is italicized text
Command em (emphasize) also does italics.
A URL by itself (with a space on either side) is often adequate in WordPress. It will make a link to that URL and display the URL, e.g. See http://wermenh.com.
Some source on the web is presenting anchor commands with other parameters beyond href, e.g. rel=nofollow. In general, use just href=url and don’t forget the text to display to the reader.
blockquote (indent text) My text
<blockquote>quoted text</blockquote>
More of my text
My text
quoted text
More of my text
Quoted text can be many paragraphs long.
WordPress italicizes quoted text (and the <i> command enters normal text).
strike This is <strike>text with strike</strike> This is text with strike
pre (“preformatted” – use for monospace display) <pre>These lines are bracketed<br>with <pre> and </pre>
These lines are bracketed
with <pre> and </pre>
Preformatted text, generally done right. Use it when you have a table or something else that will look best in monospace. Each space is displayed, something that <code> (next) doesn’t do.
code (use for monospace display) <code>Wordpress handles this very differently</code> WordPress handles this very differently
See https://wattsupwiththat.com/resources/#comment-65319 to see what this really does.
Using the URL for a YouTube video creates a link like any other URL. However, WordPress accepts the HTML for “embedded” videos. From the YouTube page after the video finishes, click on the “embed” button and it will suggest HTML like:
<iframe width="560" height="315"
frameborder="0" allowfullscreen>
</iframe>
WordPress will convert this into an internal square bracket command, changing the URL and ignoring the dimension. You can use this command yourself, and use its options for dimensions. WordPress converts the above into something like:
[youtube https://www.youtube.com/watch?v=yaBNjTtCxd4&w=640&h=480]
Use this form and change the w and h options to suit your interests.
## Images in comments
If WordPress thinks a URL refers to an image, it will display the image
instead of creating a link to it. The following rules may be a bit excessive,
but they should work:
1. The URL must end with .jpg, .gif, or .png. (Maybe others.)
2. The URL must be the only thing on the line.
3. This means you don’t use <img>, which WordPress ignores and displays nothing.
4. This means WordPress controls the image size.
5. <iframe> doesn’t work either, it just displays a link to the image.
If you have an image whose URL doesn’t end with the right kind of prefix, there may be two options if the url includes attributes, i.e. if it has a question mark followed by attribute=value pairs separated by ampersands.
Often the attributes just provide information to the server about the source of the URL. In that case, you may be able to just delete everything from the question mark to the end.
For some URLs, e.g. many from FaceBook, the attributes provide lookup information to the server and it can’t be deleted. Most servers don’t bother to check for unfamiliar attributes, so try appending “&xxx=foo.jpg”. This will give you a URL with one of the extensions WordPress will accept.
WordPress will usually scale images to fit the horizontal space available for text. One place it doesn’t is in blockquoted text, there it seems to display fullsize and large images overwrite the rightside nav bar text.
## Special characters in comments
Those of us who remember acceptance of ASCII-68 (a specification released in 1968) are often not clever enough to figure out all the nuances of today’s international character sets. Besides, most keyboards lack the keys for those characters, and that’s the real problem. Even if you use a non-ASCII but useful character like ° (as in 23°C) some optical character recognition software or cut and paste operation is likely to change it to 23oC or worse, 230C.
Nevertheless, there are very useful characters that are most reliably entered as HTML character entities:
Type this To get Notes
& & Ampersand
< < Less than sign
Left angle bracket
• Bullet
° ° Degree (Use with C and F, but not K (kelvins))
⁰
¹
²
³
⁴
¹
²
³
Superscripts (use 8304, 185, 178-179, 8308-8313 for superscript digits 0-9)
₀
₁
₂
₃
Subscripts (use 8320-8329 for subscript digits 0-9)
£ £ British pound
ñ ñ For La Niña & El Niño
µ µ Mu, micro
± ± Plus or minus
× × Times
÷ ÷ Divide
≠ Not equals
Like a space, with no special processing (i.e. word wrapping or multiple space discarding)
> > Greater than sign
Right angle bracket
Generally not needed
Various operating systems and applications have mechanisms to let you directly enter character codes. For example, on Microsoft Windows, holding down ALT and typing 248 on the numeric keypad may generate the degree symbol. I may extend the table above to include these some day, but the character entity names are easier to remember, so I recommend them.
## Latex markup
WordPress supports Latex. To use it, do something like:
$latex P = e\sigma AT^{4}$ (Stefan-Boltzmann's law)
$latex \mathscr{L}\{f(t)\}=F(s)$
to produce
$P = e\sigma AT^{4}$ (Stefan-Boltzmann’s law)
$\mathscr{L}\{f(t)\}=F(s)$
Each comment has a URL that links to the start of that comment. This is usually the best way to refer to comment a different post. The URL is “hidden” under the timestamp for that comment. While details vary with operating system and browser, the best way to copy it is to right click on the time stamp near the start of the comment, choose “Copy link location” from the pop-up menu, and paste it into the comment you’re writing. You should see something like https://wattsupwiththat.com/2013/07/15/central-park-in-ushcnv2-5-october-2012-magically-becomes-cooler-in-july-in-the-dust-bowl-years/#comment-1364445.
The “#<label>” at the end of the URL tells a browser where to start the page view. It reads the page from the Web, searches for the label and starts the page view there. As noted above, WordPress will create a link for you, you don’t need to add an <a> command around it.
## One way to avoid the moderation queue.
Several keywords doom your comment to the moderation queue. One word, “Anthony,” is caught so that people trying to send a note to Anthony will be intercepted and Anthony should see the message pretty quickly.
If you enter Anthony as An<u>th</u>ony, it appears to not be caught,
so apparently the comparison uses the name with the HTML within it and
sees a mismatch.
## 236 thoughts on “Test”
1. I just had another thought about underlines.
I think I discovered that if I could get around the automatic spam trap by writing Anthony with an empty HTML command inside, e.g. Ant<b></b>hony .
What happens when I try that with underline?
Apologies in advance to the long-suffering mods, at least one of these comments may get caught by the spam trap.
2. Wun Hung Lo says:
I’m giving up on this
But the above code works at JSFIDDLE Code testing shop
see for yourself – http://jsfiddle.net/804j6fmd/
Why no work here – it’s nuts !
WordPress has made this overcomplicated
• LOVE that JSFIDDLE Code testing shop !!! – thank you
3. Yeah, just turned into a link, not even an image. Checking to see if .JPG is okay:
4. John F. Hultquist says:
test of pre tags
with:
1234 45 567
4567 54 897
without
1234 45 567
4567 54 897
• I have been looking for a way to create a table.
How did you do it?
• He used the <pre> command, it’s described in the main article. Pre is for preformatted text and displays in monospace and with all the spaces preserved.
• Bryan A says:
5. WordPress only displays images for URLs on their own line and ending with a image file extension. If I delete the attribute string above, i.e. ?token=I7JQbQli1swRgik%2BKnIKAmCk52Y%3D then what’s left should work:
• brians356 says:
Final words from “Chinatown” spring to mind:
“Forget it Jake. It’s Climate Change.”
• Now one that would permit image display:
Update: Right clicking to get the image’s url gave me a URL that goes through WP’s cache via (slashes replaced by spaces, periods by dashes) i2-wp-com wermenh-com images winter0708 P3020227_snowbank7-jpg
• Now just the image without a suffix:
Update: This image uses the same URL as the previous cached image. That means we can’t use a changing suffix to force a trip around the cache any more for HTTP images. I’ll play with HTTPS later.
6. Owen in GA says:
$m_{H2O} \propto A_{surface}$
Is there something wrong with latex support on the test page?
• Owen in GA says:
• Owen in GA says:
• Owen in GA says:
Error in the third line can’t use \\ in the latex code.
$m_{H2O} \propto A_{surface}$
$E_{total} \propto \int_{A_{surface}}FdA \mbox{(where } F \mbox{ is the flux in watts per square meter)}$
$dT \propto \frac {E_{total}}{m_{H2O}}$
• Owen in GA says:
$E_{total} \propto \int_{A_{surface}}FdA \mbox{(where } F \mbox{ is the flux in watts per square meter)}$
a mistake in this line maybe?
• Owen in GA says:
The first two lines
$m_{H2O} \propto A_{surface}$
$E_{total} \propto \int_{A_{surface}}FdA \mbox{(where } F \mbox{ is the flux in watts per square meter)}$
Will they show?
• Owen in GA says:
$\frac{\partial T}{\partial t} = \frac{\int_{SA}FdA}{SA \times d \times \rho} \times \frac{\partial T}{\partial Q} =\frac{F \times SA}{SA \times d \times \rho} \times \frac{\partial T}{\partial Q} =\frac{F}{d \times \rho} \times \frac{\partial T}{\partial Q}$
7. Kip Hansen says:
test strong
test bold
• Kip Hansen says:
Reply to Ric W ==> Thanks — I was fielding comments on an essay using an unfamiliar tablet, and wasn’t sure which and/or both were part of HTML5. I usually use the old ClimateAudit comment Greasemonkey tool, even though its formatting is funky these days, for the tags. Don’t suppose you could update that add-in?
• IIRC, Greasemonkey was written for CA, which uses a different theme that does WUWT.
I don’t have the time to figure out the JavaScript code or whatever it’s written in, and I don’t have the ability to make changes that deep in WUWT.
Instead of Greasemonkey, I often use https://addons.mozilla.org/en-US/firefox/addon/its-all-text/ . It can open up an external editor, so it has saved my butt a few times when WP loses a post I was making.
8. Hey, what happened to the old smiley face?? When I tried to post it, this appeared:
I wonder if WordPress changed any others?
☹ ☻
The old smiley was more subtle; less in-your-face. The new one is way too garish.
If WP keeps that up, I’ll just have to use this lame replacement:
:-)
Or even worse:
;-)
• The old ways are the best ways! :-)
• Bill J says:
9. Jeff Hayes says:
a test to see if images on facebook can be linked without the proper suffix
[Curious, it worked!– I’ll have to experiment with this some. – Ric]
10. Janice Moore says:
11. I guess this is where I test. If not, I’m totally confused (as some of you believe anyway).
• So everything I post is in moderation it seems.
• No. you just have to have one approved comment first…spam prevention.
12. myNym says:
Comment in moderation, testing for “bad” word:
Sorry Chris. Voting is not equivalent to driving.
If I registered to vote in NY four years ago, and then move to NJ, I am not allowed to continue to vote in NY. That would be voter fra*ud.
What also is voter fra^ud is busing people from a non closely contested state to a closely contested state, i.e. voting under a fra*udulent address:
(Under-cover video by Project Veritas shows Scott Foval admitting “we’ve been bussing people in” for “fifty years and we’re not going to stop now”.)
Verifying correct addresses is an extremely important step in fighting various forms of voter fra*ud. You might have known that. Or should have.
[Sometimes contributors get a bit anxious at the length of time their post takes to get through moderation. Be assured that they will almost always get through and the trap has been because of words like “fraud, scam, denier etc. “. Sometimes it is because of having a plethora of links.
My advice, such as it is, is not to be too impatient. The moderators here are volunteers and sometimes there may be a gap in coverage leading to a delay. Take my word that if you haven’t been abusive, used a fake ID or been a Sky Dragon type you will get through . . . Merry Christmas . . mod]
• myNym says:
Sorry about that. Merry Christmas to you and yours!
13. myNym says:
14. myNym says:
Test III …
Sorry Chris. Voting is not equivalent to driving.
If I registered to vote in NY four years ago, and then move to NJ, I am not allowed to continue to vote in NY. That would be voter fraud.
What also is voter fraud is busing people from a non closely contested state to a closely contested state, i.e. voting under a fraudulent address:
[I can’t seem to get my Youtube embed working. For the video, ask Dr. Youtube about “Rigging the Election – Video II: Mass Voter Fraud”.]
(Under-cover video by Project Veritas shows Scott Foval admitting “we’ve been bussing people in” for “fifty years and we’re not going to stop now”.)
Verifying correct addresses is an extremely important step in fighting various forms of voter fraud. You might have known that. Or should have.
15. Janice Moore says:
16. Kip Hansen says:
17. Reality check says:
I’m ending up in moderation again—and I have had comments approved. I am considering changing to my real name and see if that helps. Any suggestions? I removed links to my blogs and that worked for a while. I don’t understand what I’m doing that is causing the problem and causing you more work.
• Reality check says:
fobdangerclose: Same thing with me. Some comments went into moderation, some just vanished entirely. One showed up much later.
18. Janice Moore says:
• polski says:
19. clipe says:
Back to the mails. 1077829152. Jones reviews and spikes a skeptic article, ‘It is having a go at the CRU temperature data – not the latest vesion, but the one you used in MBH98 !!’ Then some shenanigans of some sort I don’t quite get: ‘Can I ask you something in CONFIDENCE – don’t email around, especially not to Keith and Tim here. Have you reviewed any papers recently for Science that say that MBH98 and MJ03 have underestimated variability in the millennial record – from models or from some low-freq proxy data. Just a yes or no will do. Tim is reviewing them – I want to make sure he takes my comments on board, but he wants to be squeaky clean with discussing them with others. So forget this email when you reply.’
They have suspicions of the American Geophysical Union journal GRL. Too many Contrarian viewpoints getting through.
A while later, another fired revolver the non-internet media appear to find completely uninteresting:
1089318616
From: Phil Jones To: “Michael E. Mann” Subject: HIGHLY CONFIDENTIAL Date: Thu Jul 8 16:30:16 2004
… [Rubbishes a paper that’s bad for them]
The other paper by MM [McIntyre & McKitrick] is just garbage – as you knew. De Freitas again.
… I can’t see either of these papers being in the next IPCC report. Kevin and I will keep them out somehow – even if we have to redefine what the peer-review literature is ! Cheers
Phil
He also says that fellow scientist Roger Pielke is ‘losing all credibility’ by deiging to reply to a skeptic.
This one made me laugh:
1091798809
From: Phil Jones
To: “Janice Lough”
Subject: Re: liked the paper
Date: Fri Aug 6 09:26:49 2004
Janice,
Most of the data series in most of the plots have just appeared on the CRU web site. Go to data then to paleoclimate. Did this to stop getting hassled by the skeptics for the data series. Mike Mann refuses to talk to these people and I can understand why. They are just trying to find if we’ve done anything wrong.
Damn them! Damn their impudence!
In February 2005 Jones will respond to a request by Australian scientist Warwick Hughes for his raw data with the words: ‘We have 25 or so years invested in the work. Why should I make the data available to you, when your aim is to try and find something wrong with it?’ [Not in the leaked mails, but see here, for example.]
1092167224
Michael E. Mann wrote:
Dear Phil and Gabi,
I’ve attached a cleaned-up and commented version of the matlab code that I wrote for doing the Mann and Jones (2003) composites. I did this knowing that Phil and I are likely to have to respond to more crap criticisms from the idiots in the near future, so best to clean up the code and provide to some of my close colleagues in case they want to test it, etc. Please feel free to use this code for your own internal purposes, but don’t pass it along where it may get into the hands of the wrong people. In the process of trying to clean it up, I realized I had something a bit odd, not necessarily wrong, but it makes a small difference. …
1092433030. Grant business. 17 million Euros up for grabs. Not enough for Keith. ‘While this is a large sum, I am sure you will appreciate that when distributed among many partners and stretched over five years it imposes a severe limitation on the total number of partners that can be feasibly included.’
1092581797 made me chuckle with its tales of urgent meetings in Geneva, Trieste, Marrakech and Potsdam. I expect it will seem less amusing when the rest of us aren’t allowed or can’t afford to go there.
Oh next is something from the Russians again. They’re probably still in Siberia. That makes me feel better.
But a few mails later Phil Jones is off to Delhi and Seattle. This makes me unhappy again. No, it makes me laugh. People flying all over the planet on an urgent quest to stop other people flying all over the planet always do. 1097159316
Shit, now Keith is going to Austria in a few days, after having just returned from some other unspecified travels. I am happy for him. All right, I resent it. I shouldn’t be reading this. This is like one of the books my mum reads about glamorous people going to glamorous places.
Fuck, the next one from Phil Jones: ‘I met this guy in Utrecht last week … ‘ Can’t they stay put for a single frigging minute? I am glad their theory is a crock of shit, because if it was true, the irony of their single-handedly having doomed us all flying around the world spreading the word about it would be unbearable. Mind you, have you seen the pictures of the UEA campus? I wouldn’t spend a minute there either. I hope the poor Russians are getting some money, that’s all I hope. Freezing their gonads off prodding trees while the rest of them gad about the playgrounds of the well-heeled and tenured.
Concentrate. He’s bad-mouthing Von Storch, a scientist who has gone off-piste, for bad-mouthing the Mann Bradley Hughes papers. I have never badly wanted to go to Utrecht anyway.
20. clipe says:
21. Sometimes my images show, sometimes not. My latest attempt failed. Now I’ll try it again, putting it on it’s own line as directed:
22. TESTS:
Ok, the above test comment went into moderation. WHY?
Butu I can see the image didn’t work again. I’m pretty sure this one works:
Maybe it needs to be httpS (instead of http) ???
So this version has an S at the end of http:
23. Janice Moore says:
And — here — they — ARE! :)
Marching on California! lol
“On Wisconsin” — Univ. of Wisconsin Marching Band, Rosebowl Parade, Pasadena California
As Kevin below said, “CA, take note.”
#(:))
24. Janice Moore says:
And — here — they — ARE! :)
Marching on California! lol
“On Wisconsin” — Univ. of Wisconsin Marching Band, Rosebowl Parade, Pasadena California
As Kevin below said, “CA, take note.”
#(:))
25. Janice Moore says:
Is Rosebowl a bad word?
26. Janice Moore says:
Is Kevin a bad word?
• No Kevin is not a bad word, but your combination of special characters likely tripped the spam filter.
• Janice Moore says:
Hey! Thank you, Anthony for taking the time to “talk” to me!! Yay! :)
*********************
Test:
27. Janice Moore says:
28. Janice Moore says:
29. markopanama says:
In Peru, the study sited showed increased organic sediments during the MWP.
30. Freedom Monger says:
Test:
(Fail)
Ah, I don’t know what I’m doing. I guess I can’t just paste a picture in the comments section.
31. So I’m looking at the San Jose CA forecast for the next .. 15 days on weather dot com, and we got this (test PRE tag):
TODAY Partly Cloudy
Sat Jan 7 Rain
Sun Jan 8 Rain / Wind
Mon Jan 8 Showers
Tue Jan 10 Rain
Wed Jan 11 AM Showers
Thu Jan 12 Showers
Fri Jan 13 Showers
Sat Jan 14 Showers
Sun Jan 15 Showers
Mon Jan 16 Showers
Tue Jan 17 Showers
Wed Jan 18 Showers
Thu Jan 19 Few Showers
(that's as far as it goes)
32. clipe says:
Die große globale Erwärmung
33. Testing the CODE tag which I think has different effects than the PRE tag (we’ll hopefully see):
There’s ZERO evidence that CO2 is warming the planet. That is expertly explained in this 4 minute video: xxxxxyx
Funny you point to your version of “all the climate scientists agree” that CO2 is warming the planet. Possibly there’s some minimal warming from CO2, but more likely there’s near none as any warming is fully countered by the negative feedback of low cloud formation. That’s consistent also with the recent temperature data.
Regardless, it shouldn’t be our job to carry water for the leftists.
Let them work to prove that CO2 is causing warming. We should do NOTHING to help them along with that goal, and that starts with saying what it unarguably true: there is no evidence that CO2 causes warming.
34. Jaakko Kateenkorva says:
Test
35. EricHa says:
• EricHa says:
• $CO_{2(gas)} \Leftrightarrow CO_{2(aq)}$ \\
$CO_{2(aq)} + H_{2}O \Leftrightarrow H_{2}CO_{3}$ \\
$H_{2}CO_{3} \Leftrightarrow (H^{+} \Leftrightarrow H_{3}O^{=}) + CO_{3}^{-}$ \\
$XCO_{3} \Leftrightarrow X^{2+} + HCO^{+}_{3}$ [e.g., $CaCO_{3}$, or other alkaline earth metals] \\
$XHCO_{3} \Leftrightarrow X^{+} + HCO_{3}^{-}$ [e.g., $NaHCO_{3}$, or other alkali metals] \\
$H_{2}O \Leftrightarrow H^{+} + OH^{-}$ \\
test to see if LaTeX works
• $CO_{2(gas)} \Leftrightarrow CO_{2(aq)}$latex CO_{2(aq)} + H_{2}O \Leftrightarrow H_{2}CO_{3}
$H_{2}CO_{3} \Leftrightarrow (H^{+} \Leftrightarrow H_{3}O^{=}) + CO_{3}^{-}$latex XCO_{3} \Leftrightarrow X^{2+} + HCO^{+}_{3}$[e.g.,$CaCO_{3}, [or other alkaline earth metals]
$XHCO_{3} \Leftrightarrow X^{+} + HCO_{3}^{-}$ [e.g., $NaHCO_{3}$, (or other alkali metals)
$latex H_{2}O \Leftrightarrow H^{+} + OH^{-} is produced by, $CO_{2(gas)} \Leftrightarrow CO_{2(aq)}$latex CO_{2(aq)} + H_{2}O \Leftrightarrow H_{2}CO_{3} $H_{2}CO_{3} \Leftrightarrow (H^{+} \Leftrightarrow H_{3}O^{=}) + CO_{3}^{-}$latex XCO_{3} \Leftrightarrow X^{2+} + HCO^{+}_{3}$ [e.g., $CaCO_{3}, [or other alkaline earth metals] $XHCO_{3} \Leftrightarrow X^{+} + HCO_{3}^{-}$ [e.g.,$NaHCO_{3}$, (or other alkali metals)$latex H_{2}O \Leftrightarrow H^{+} + OH^{-}
• $CO_{2(gas)} \Leftrightarrow CO_{2(aq)}$
$CO_{2(aq)} + H_{2}O \Leftrightarrow H_{2}CO_{3}$
$H_{2}CO_{3} \Leftrightarrow (H^{+} \Leftrightarrow H_{3}O^{=}) + CO_{3}^{-}$
$XCO_{3} \Leftrightarrow X^{2+} + HCO^{+}_{3}$ [e.g., $CaCO_{3}, [or other alkaline earthmetals]$
$XHCO_{3} \Leftrightarrow X^{+} + HCO_{3}^{-}$ [e.g., $NaHCO_{3}$, (or other alkali metals)]$$H_{2}O \Leftrightarrow H^{+} + OH^{-}$ is produced by \$CO_{2(gas)} \Leftrightarrow CO_{2(aq)}$ \$CO_{2(aq)} + H_{2}O \Leftrightarrow H_{2}CO_{3}$ \$H_{2}CO_{3} \Leftrightarrow (H^{+} \Leftrightarrow H_{3}O^{=}) + CO_{3}^{-}$ \$XCO_{3} \Leftrightarrow X^{2+} + HCO^{+}_{3}$ [e.g.,$CaCO_{3}, [or other alkaline earthmetals]$\$XHCO_{3} \Leftrightarrow X^{+} + HCO_{3}^{-}$ [e.g.,$NaHCO_{3}$, (or other alkali metals)]$ \$H_{2}O \Leftrightarrow H^{+} + OH^{-}$
36. clipe says:
My mother has blue eyes.
37. clipe says:
My mother has blue eyes.
38. Satellite Records and Slopes Since 1998 are Not Statistically Significant.
Guest Post by Werner Brozek, Edited by Just The Facts
Please put the following graphic below the title:
As can be seen from the above graphic, the slope is positive from January 1998 to December 2016, however with the error bars, we cannot be 95% certain that warming has in fact taken place since January 1998. The high and low slope lines reflect the margin of error at the 95% confidence limits. If my math is correct, there is about a 30% chance that cooling has taken place since 1998 and about a 70% chance that warming has taken place. The 95% confidence limits for both UAH6.0beta5 and RSS are very similar. Here are the relevant numbers from Nick Stokes’ site for both UAH and RSS:
https://moyhu.blogspot.ca/p/temperature-trend-viewer.html
Temperature Anomaly trend
Jan 1998 to Dec 2016
Rate: 0.450°C/Century;
CI from -0.750 to 1.649;
t-statistic 0.735;
Temp range 0.230°C to 0.315°C
For UAH:
Temperature Anomaly trend
Jan 1998 to Dec 2016
Rate: 0.476°C/Century;
CI from -0.813 to 1.765;
t-statistic 0.724;
Temp range 0.113°C to 0.203°C
If you wish to see where warming first becomes statistically significant, see Section 1.
In addition to the slopes showing statistically insignificant warming, the new records for 2016 over 1998 are also statistically insignificant for both satellite data sets.
In 2016, RSS beat 1998 by 0.573 – 0.550 = 0.023 or by 0.02 to the nearest 1/100 of a degree. Since this is less than the error margin of 0.1 C, we can say that 2016 and 1998 are statistically tied for first place. However there is still over a 50% chance that 2016 did indeed set a record, but the probability for that is far less than 95% that climate science requires so the 2016 record is statistically insignificant.
If anyone has an exact percentage here, please let us know, however it should be around a 60% chance that a record was indeed set for RSS.
In 2016, UAH6.0beta5 beat 1998 by 0.505 – 0.484 = 0.021 or also by 0.02 to the nearest 1/100 of a degree. What was said above for RSS applies here as well.
My predictions after the June data came in were therefore not correct as I expected 2016 to come in under 1998.
The December numbers are not in yet, but GISS will set a statistically significant record for 2016 over its previous record of 2015 since the new average will be more than 0.1 above the 2015 mark.
HadSST3 will set a new record in 2016, but it will only be by a few hundredths of a degree so it will not be statistically significant.
HadCRUT4.5 is still up in the air. The present average after 11 months is 0.790. The 2015 average was 0.760. As a result, December needs to come in at 0.438 to tie 2015. The November anomaly was 0.524, so only a further drop of 0.086 is required. This cannot be ruled out, especially since this site shows December 0.089 lower than November:
http://www.moyhu.blogspot.com.au/p/latest-ice-and-temperature-data.html#NCAR
Also worth noting are that UAH dropped by 0.209 from November to December and RSS dropped by 0.162.
Whatever happens with HadCRUT4.5, 2016 and 2015 will be in a statistical tie with a possible difference in the thousandths of a degree. The difference will be more important from a psychological perspective than a scientific perspective as it will be well within the margin of error.
39. Janice Moore says:
40. Janice Moore says:
41. David J Wendt says:
42. Janice Moore says:
43. Janice Moore says:
44. Janice Moore says:
45. Janice Moore says:
46. Here’s a scary bunch of research on sea ice, as it relates to CO2, for anyone who might want to plow through it:
… very scary.
… and from S. F. Ackley
http://oceans11.lanl.gov/trac/CICE/raw-attachment/wiki/WorkshopPresentations/1Ackley.ppt
… we have THIS:
Again, processes in ice seem to exist that we might be overlooking in our assessment of the CO2 story. And if such processes exist in sea ice, then do similar processes (or other processes) exist in glacial ice over millions of years, to render our expectations of records derived from ice records a bit overblown ?
47. Menicholas says:
48. Dan Davis says:
49. brians356 says:
Gotta start somewhere.
50. artifact of the echo-chamber … that’s a curious way of putting it. What “chamber” are we referring to? — the belief system that understands the role of carbon dioxide in the terrestrial life process ? … where graphs illustrating the truths of this belief system ARE, in fact, artifacts, as are ALL “artifacts” of knowledge ?
just another, then, implies that such “artifacts” are somehow tainted. And so are you suggesting that the belief system that understands the role of CO2 in the terrestrial life process is somehow tainted ? Do you disbelieve that CO2 has a vital role in the terrestrial life process ? If so, then your tone might illustrate a need for you to review your own beliefs in regard to this substance. Otherwise, why would you not give greater validity to such an “artifact” that clearly shows that photosynthesis of a certain class of plants shuts down, regardless of temperature ?
At this level of concentration, CO2 is the LIMITING FACTOR. Here’s a pretty good explanation of that idea:
http://www.rsc.org/learn-chemistry/content/filerepository/CMP/00/001/068/Rate%20of%20photosynthesis%20limiting%20factors.pdf
Limiting Factors
In 1905, when investigating the factors affecting the rate of photosynthesis, Blackmann
formulated the Law of limiting factors. This states that the rate of a physiological process will be limited by the factor which is in shortest supply. Any change in the level of a limiting factor will affect the rate of reaction.
For example, the amount of light will affect the rate of photosynthesis. If there is no light, there will be no photosynthesis. As light intensity increases, the rate of photosynthesis will increase as long as other factors are in adequate supply. As the rate increases, eventually another factor will come into short supply.
The graph below shows the effect of low carbon dioxide concentration:
It [CO2] will eventually be insufficient to support a higher rate of photosynthesis, and increasing light intensity will have no effect, so the rate plateaus.
If a higher concentration of carbon dioxide is supplied, light is again a limiting factor and a higher
rate can be reached before the rate again plateaus. If carbon dioxide and light levels are high, but temperature is low, increasing temperature will have the greatest effect on reaching a higher rate of photosynthesis.
Now would 150 ppm wipe out all life above sea level ? Well, considering that most of life depends on plants that thrive in this range, then, maybe not ALL, but a significant percentage to start. And considering that the remaining life might have depended on the life that would die out, then the cascading demise of life would seem to continue onto the next tier too, from which I’m not sure how much farther down the deterioration might progress. But to argue over the word, “all”, in this context is just an exercise in winning a debate, when the REAL point is that ALL life WOULD suffer in this range of CO2.
51. Janice Moore says:
52. Peta from Cumbria, now Newark says:
And didn’t Auntie Beeb feel sorry for the Poor Little Rich Kids at Davos.
53. Janice Moore says:
54. Janice Moore says:
55. Janice Moore says:
56. Janice Moore says:
57. Janice Moore says:
• Bryan A says:
Janice,
You are simply WAY TOO FUNNY. It must be requested by the management of not only this website but for the sanity of the internet at large, that you refrain from adding any more humorous posts or no one will get any work done due to the constant raucous laughter. Besides that, My cubicle mates are all standing up and looking like Prarie Doggies to see what the commotion is about. (This action also doesn’t help)
58. eyesonu says:
My test of using blockquote
my first attempt
Now for the results
• eyesonu says:
Now one more sample
My test of using blockquote
my first attempt
Now for the results
An old dog can learn new tricks, maybe.
• eyesonu says:
To copy a copy of blockquoted text didn’t work out to well. I guess the old dog needs a little work on this trick.
• eyesonu says:
Try again and make multiple copy transfers:
My test of using blockquote
my first attempt
Now for the results
• eyesonu says:
That one didn’t work either.
59. eyesonu says:
Anyone know of a way to use a “double” blockquote command (?) to show a blockquote of a blockquote?
If this sounds confusing you need to realized I’m confused!
• eyesonu says:
Let’s try double blockquote if such exists:
<
>my first attempt<
>
• eyesonu says:
Let’s try that a different way:
<blockquote
my first attempt
blockquote>
• eyesonu says:
Still didn’t workout
• Bryan A says:
Anyone know of a way to use a
“double” blockquote command
(?) to show a blockquote of a blockquote?
If this sounds confusing you need to realized I’m confused!
• Bryan A says:
(blockquote)blockquoted text (blockquote)inset blockquoted text(/blockquote) end of original blockquoted text(/blockquote)
Replace the ( ) with the necessary Carrots to get
blockquoted text
inset blockquoted text
end of original blockquoted text
60. Janice Moore says:
61. Greg F says:
62. Mike Jonas says:
blockquote test
With some italics and some bold in it.
63. Mike Jonas says:
trying again
With some italics and some bold in it.
64. Kip Hansen says:
Can I use a center tag?
• Kip Hansen says:
Yes, but it will do nothing!
65. Janice Moore says:
66. John F. Hultquist says:
put: a href in the line below where there is now xxxxxx
<xxxxxx=" Your link goes in here “>Link to Ferguson story
This is what you get:
Link to Ferguson story
67. I’m testing the size of this image. It appears huge at its source. But will that replicate as (too big) here:
68. eyesonu says:
69. Janice Moore says:
Will this go into moderation?
Thank you, schitzree. Heh.
70. This is from IPPC AR5.
Source Amount Percent of
PgC/yr Total
Natural
Respiration and fire 118.7 57.3%
Ocean out gassing 78.4 37.9%
Fresh water out gassing 1.0 0.5%
Volcanism 0.1 0.0%
198.2 95.7%
Fossil fuels 7.8 3.8%
Land use changes 1.1 0.5%
8.9 4.3%
Total 207.1 100.0%
71. SourceAmount (PgC/yr)Percent of Total
Natural
Respiration and fire118.757.3%
Ocean out gassing78.437.9%
Fresh water out gassing1.00.5%
Volcanism0.10.0%
198.295.7%
Fossil fuels7.83.8%
Land use changes1.10.5%
8.94.3%
Total207.1100.0%
72. This is from IPPC AR5.
Source Amount Percent
(PgC/yr)
Natural
Respiration and fire 118.7 57.3%
Ocean out gassing 78.4 37.9%
Fresh water out gassing 1.0 0.5%
Volcanism 0.1 0.0%
----- ------
198.2 95.7%
Fossil fuels 7.8 3.8%
Land use changes 1.1 0.5%
------ ------
8.9 4.3%
====== ======
Total 207.1 100.0%
73. Okay, I really tried to give Mark Boslough the benefit of the doubt. I went over to RealClimate, I read his comments, I found a copy of the Keigwin paper, I read it as best I could, I reconsidered his comments, and I came up with the same basic reaction, namely head shaking smirky face.
He writes:
. . . and in our abstract we pointed out that it [Keigwin’s paleoclimate time series] had been misused by contrarians who had removed some of the data, replotted it, and mislabeled it to falsely claim that it was a global temperature record showing a cooling trend.
I say:
But it DOES show a cooling trend from past eras to the present era !
He further writes:
(the inconvenient modern temperature data showing a warming trend had been removed).
I say:
inconvenient? — “inconsequential” might be the better word. Am I corret in thinking that he is trying to elevate the trend of a tiny segment of time above the trend of a huge segment of time that contains that tiny upward trend as STILL COOLER than in the past ?
And continuing, he says:
Taken together, Station S and paleotemperatures suggest there was an acceleration of warming in the 20th century, though this was not an explicit conclusion of the paper. Keigwin concluded that anthropogenic warming may be superposed on a natural warming trend.
I say:
Can you BE any more ambivalent in your flacid attempt to counter scepticism? Obviously, … this was not an explicit conclusion of the paper.
In fact, if a person actually reads the paper, which is here:
Keigwin, L. (1996). The Little Ice Age and Medieval Warm Period in the Sargasso Sea. SCIENCE, 274(5292), 1504-1508.
https://climateaudit.files.wordpress.com/2007/10/keigwin_sargasso.pdf
Go to page 1507, and notice what the conclusion of that paper REALLY seems to be, namely
Regardless of the exact cause for the LIA [Little Ice Age], the MWP [Medieval Warm Period], and earlier oscillations, the warming during the 20th century (O.5°C) is not unprecedented. However, it is important to distinguish natural climate change from anthropogenic effects because human influence may be occurring at a time when the climate system is on the warming limb of a natural cycle.
See the phrase … “not unprecedented”? — this means warming has happened before, Mark.
See the phrase, “may be occuring”? — this indicates either uncertainty or an unsubstantiated assumption or both, Mark.
See the phrase, “warming limb of a natural cycle”? — if it is warmING, then this means it is still cooLER than at some other time in the past, Mark.
Hopefully, I have not made a bigger fool of myself than Mark did. If so, then, oh well, learning can be painful.
74. Some instances of self-righteous arrogance just stick with you, and this is one of those instances that caused me to focus a bit more on Boslough’s comments at RealClimate:
We submitted an abstract together about his [Lloyd Keigwin’s] paleotemperature reconstruction of Sargasso Sea surface temperature …
How impressive, to collaborate with a known pioneer in the field.
I had updated it with modern SST measurements, and in our abstract we pointed out that it had been misused by contrarians who had removed some of the data, replotted it, and mislabeled it to falsely claim that it was a global temperature record showing a cooling trend.
Well, it AGREES with other known assessments showing a global cooling trend over this long span of time. People probably use the Robinson et al. article to beef up this fact. Finding supporting evidence, however, is NOT “misrepresenting”. At most, it might be leaving out an underlying assumption that an author assumes (perhaps incorrectly) that a reader already knows.
I found the Robinson et al. article here:
http://www.oism.org/pproject/s33p36.htm
. . . and the version of the graph in question that Robinson et al. used, which was THIS one:
Figure 1: Surface temperatures in the Sargasso Sea, a 2 million square mile region of the Atlantic Ocean, with time resolution of 50 to 100 years and ending in 1975, as determined by isotope ratios of marine organism remains in sediment at the bottom of the sea (3). The horizontal line is the average temperature for this 3,000-year period. The Little Ice Age and Medieval Climate Optimum were naturally occurring, extended intervals of climate departures from the mean. A value of 0.25 °C, which is the change in Sargasso Sea temperature between 1975 and 2006, has been added to the 1975 data in order to provide a 2006 temperature value.
Now, while I still think the placement of that “0” point is sort of confusing (Jesus? or the past point where temperature was at the average of the whole time span and temperature of today?), the graph still seems to capture the significant long-term trend of Keigwin’s original graph. And as Willis pointed out, any “conflating” that was done was done by Boslough, in trying to splice a short-term instrumental series onto a long-term paleoclimate series. As I said earlier, “inconsequential”, as opposed to “inconvenient”, or better still, INCORRECT.
Keigwin’s Fig. 4B (K4B) shows a 50-year-averaged time series along with four decades of SST measurements from Station S near Bermuda, demonstrating that at the time of publication, the Sargasso Sea was at its warmest in more than 400 years.
Even if you allowed this INCORRECT splicing procedure, still I ask, “Does the choice of 400years, as opposed to 500 years strike anyone as arbitrary?, to the point of being meaningless?” Why not 500 years? Why not 1000 years or 2500 years?, when temps were as high or markedly higher? Of course, you have to choose a convenient low point in a progression of cyclic lows and highs to create a case of alarmism:
I think that I have pretty much proven to myself now that this guy is a scam artist, whether he realizes it or not.
75. Janice Moore says:
76. Janice Moore says:
77. Janice Moore says:
Is bogus a bad word?
78. Janice Moore says:
Is BEST a bad word?
79. Janice Moore says:
China?
80. Janice Moore says:
Trying entire comment on this thread instead:
Only if you can guarantee China millions of dollars/pounds/etc. in new orders for windmill and solar parts.
Or produce a bogus temperature “data” product like BEST does.
81. Janice Moore says:
82. Janice Moore says:
83. Janice Moore says:
84. Janice Moore says:
85. Janice Moore says:
86. Robert Swan says:
Maybe even more relevant than Mackellar’s poem: Said Hanrahan
87. Kip Hansen says:
Here’s how to make a link that points to WUWT.
88. Kip Hansen says:
89. Kip Hansen says:
90. M Courtney says:
TB is often a bit paranoid about Reds under the Bed but in this case he is correct.
The science is politicised.
That’s not opinion. That’s proven fact dating back to 1992 when the science started to be significantly funded. There was proportionate no climate science funded before the signing of the UNITED NATIONS FRAMEWORK CONVENTION ON CLIMATE CHANGE (UNFCC) in 1992.
So let us look at what was signed. That will tell us if the science is biased or accurate. It is linked here so you can check it yourself.
UNFCCC Article 4.1 (g) says
(g) Promote and cooperate in scientific, technological, technical, socio-economic and other research, systematic observation and development of data archives related to the climate system and intended to further the understanding and to reduce or eliminate the remaining uncertainties regarding the causes, effects, magnitude and timing of climate change and the economic and social consequences of various response strategies;
Note this says the remaining uncertainties. They are not researching that which is certain.
And what is certain? This is not “remaining” from the opening two paragraphs of the Convention.
Acknowledging that change in the Earth’s climate and its adverse effects are a common concern of humankind, Concerned that human activities have been substantially increasing the atmospheric concentrations of greenhouse gases, that these increases enhance the natural greenhouse effect, and that this will result on average in an additional warming of the Earth’s surface and atmosphere and may adversely affect natural ecosystems and humankind,
tony mcleod , you are wrong. This is the link.
91. M Courtney says:
Keep trying until WUWT lets me post. This getting like the Guardian
The science is politicised.
That’s not opinion. That’s proven fact dating back to 1992 when the science started to be significantly funded. There was proportionate no climate science funded before the signing of the UNITED NATIONS FRAMEWORK CONVENTION ON CLIMATE CHANGE (UNFCC) in 1992.
So let us look at what was signed. That will tell us if the science is biased or accurate. It is linked here so you can check it yourself.
UNFCCC Article 4.1 (g) says
(g) Promote and cooperate in scientific, technological, technical, socio-economic and other research, systematic observation and development of data archives related to the climate system and intended to further the understanding and to reduce or eliminate the remaining uncertainties regarding the causes, effects, magnitude and timing of climate change and the economic and social consequences of various response strategies;
Note this says the remaining uncertainties. They are not researching that which is certain.
And what is certain? This is not “remaining” from the opening two paragraphs of the Convention.
Acknowledging that change in the Earth’s climate and its adverse effects are a common concern of humankind, Concerned that human activities have been substantially increasing the atmospheric concentrations of greenhouse gases, that these increases enhance the natural greenhouse effect, and that this will result on average in an additional warming of the Earth’s surface and atmosphere and may adversely affect natural ecosystems and humankind,
tony mcleod , you are wrong. This is the link.
92. Sheri says:
How did I end up in moderation again? Can’t find any objectionable words and my email hasn’t changed. Sigh.
• Sheri says:
Okay, there was a word somewhere.
93. Sheri says:
What if this was a double-blind study? Could people tell the difference in the breads? If they didn’t know they were eating cockroaches, maybe they would actually like the bread.
• Sheri says:
What am I saying here that catches the moderation flag? I don’t understand.
• Sheri says:
What is throwing me into moderation? I see no problematic terms.
94. Sheri says:
Now the comments won’t go through at all?
• Sheri says:
What is setting this off?
95. erika197 says:
The warmest month of last year was February in the UAH dataset. I’ll start with that as the benchmark and see how the trend evolved from 1998 to then, with each successive month of cooler temps.
Feb 2016: 0.011 /decade
Mar 2016: 0.020 /decade
Apr 2016: 0.028 /decade
May 2016: 0.034 /decade
Jun 2016: 0.036 /decade
Jul 2016: 0.038 /decade
Aug 2016: 0.041 /decade
Sep 2016: 0.045 /decade
Oct 2016: 0.047 /decade
Nov 2016: 0.050 /decade
Dec 2016: 0.050 /decade (higher to 4 decimal places than Nov)
Jan 2017: 0.054 /decade
Even with la Nina conditions over the last few months, the trend has increased slightly month by month since the peak in Feb last year.
96. erika197 says:
How Imminent is the UAH Pause? (Now Includes Some January Data)
At Dr. Roy Spencer’s site, starting here:
http://www.drroyspencer.com/2017/02/uah-global-temperature-update-for-january-2017-0-30-deg-c/#comment-236506
Barry (sorry I do not have his last name) has seven very interesting comments with respect to the requirements for the UAH pause to resume. He has graciously allowed me to use whatever I wished in this blog post. Everything that appears below is from him until you see the comment: “The above is from Barry.”
Since the el Nino rose last year there have been many predictions here that a la Nina would form shortly afterwards and once again return the trend since 1998 to a flat line or cooling. I decided to check the change in trend from 1998 to each month past the el Nino peak (determined by warmest month last year in UAHv6 data).
My prediction is that for each month added past the el Nino peak the trend will be ever so slightly warmer, also when including December and January values in UAHv6 TLT data.
The warmest month of last year was February in the UAH dataset. I’ll start with that as the benchmark and see how the trend evolved from 1998 to then, with each successive month of cooler temps.
Feb 2016: 0.011 /decade
Mar 2016: 0.020 /decade
Apr 2016: 0.028 /decade
May 2016: 0.034 /decade
Jun 2016: 0.036 /decade
Jul 2016: 0.038 /decade
Aug 2016: 0.041 /decade
Sep 2016: 0.045 /decade
Oct 2016: 0.047 /decade
Nov 2016: 0.050 /decade
Dec 2016: 0.050 /decade (higher to 4 decimal places than Nov)
Jan 2017: 0.054 /decade
Even with la Nina conditions over the last few months, the trend has increased slightly month by month since the peak in Feb last year.
Testing to see how cool Feb would need to be to make the trend flatline….
-5C
You read right – not -0.5, but -5C.
What would the trend since 1998 be if 2017 annual was the same as January 2017 (0.30)?
0.063C /decade – warmer than current trend.
What would the annual anomaly of 2017 need to be to get a flatline trend since 1998?
-0.16
How likely is it that 2017 would have an annual anomaly of -0.16C?
Coolest years post 1998:
2008: -0.10
2000: -0.02
Before 1998 there were 8 years of average annual anomaly less than -0.16. Starting from the most recent year where this was so:
1993: -0.20
1992: -0.28
1989: -0.21
1986: -0.22
1985: -0.36
1984: -0.24
1982: -0.30
1989: -0.21
ENSO conditions relevant to the above were:
2008 – nina
2000 – nina
1993 – neutral
1992 – nino
1989 – nina
1986 – nino
1985 – nina
1984 – nina
1982 – nino
1989 – nina
With predictions of a ENSO-neutral or Nino 2017, that would make it unlikely that the annual anomaly would go as low as -0.16C, and thus unlikely that the trend since 1998 would flatten.
The above is from Barry.
97. barry says:
Feel free to use all or some of that if it’s worthy of a post. Might have to put some line breaks in. :-)
I tested another line of inquiry.
For 30-year averages, every year where this can be achieved in the UAH 6.0 data, each year added (and one dropped off the beginning to keep the averages 30-year only), the 30-year average has gone up.
For this to fail to happen due to the 2017, the annual anomaly for that year would have to be < 0.05C.
Just possible, but very unlikely, I think.
98. Janice Moore says:
99. Janice Moore says:
100. Rob Morrow says:
bold italics
101. clipe says:
date: Thu, 30 Sep 1999 09:05:05 +0100 from: David Viner subject: Fwd: DEADLINE**Funding for climate campaigners to: cru.all@uea.ac.uk
From: cks@eyfa.org To: cks@eyfa.org Date: Fri, 24 Sep 1999 00:07:09 +0200 X-Distribution: Moderate MIME-Version: 1.0 Subject: DEADLINE**Funding for climate campaigners X-Confirm-Reading-To: cks@eyfa.org X-pmrqc: 1 Priority: normal Status: Funding for climate campaigners. A call for proposals. from climate-l@eyfa.org Deadline: 30th September 1999 **please distribute to others who may be interested** We would like to invite proposals from activists working on climate campaigning. Following an activist and NGO meeting in March this year, attended by climate activists from Europe, Asia, USA, Australia and Latin America, funding was obtained to support two people to work on a project connected to the sixth United Nations Climate Convention, otherwise known as the Conference of the Parties (COP6), which will happen in Autumn/Winter 2000/2001. The United Nations is currently considering only one possible location for the meeting - den Haag, The Netherlands. The International working group formed after the activist and NGO meeting are looking for two people who would be able to create something innovative and effective with this funding. They will be based in a Climate research group in Portugal, 'Euronatura'. The campaign will be supported by the International working group which has experience of United Nations negotiations, direct action, campaigning, economics and climate science. Groups supporting this campaign include : eyfa, Aseed, Carbusters Magazine, Korean Ecological Youth, Free The Planet USA, EuroNatura, Climate Action Network Latin America, Climate Action Network Central and Eastern Europe and Oilwatch Europe. The thing that joins these people together is the desire to work together to radicalise the agenda of the climate negotiations. The current direction of the negotiations cannot hope to define targets nor build mechanisms of implementation and compliance which will stop the currently dangerous emissions levels of Greenhouse Gases. Ideally, the collaboration between the two funded volunteers, Euronatura and the International working group, will touch on all aspects of climate change and the related campaigns of oil, forest, marine and transport. Equally, the collaboration will be aware of all strategies to counter the weakness of the United Nations and the dominance of certain lobbying groups (notably the oil and nuclear industry). The strategies discussed by the International working group revolve around direct action, research and negotiation. Project ideas which have been discussed are a counter/alternative meeting at the same time and place as the UN meeting and/or a symbolic event such as The Climate Train to Kyoto. Please bring YOUR ideas to us! What do you think would be the most effective way to radicalise the UN agenda and protect the climate from our current economic and political systems? There are plans for a team to work in USA on a parallel campaign. The project should begin by the end of the 1999. Are you a person who has the energy, skills and commitment to coordinate the European component of an international campaign? (unfortunately, the funding is only for people *under 26 years of age *from Iceland, Norway, Algeria, Cyprus, Egypt, Israel, Jordan, Lebanon, Malta, Morocco, Palestine, Syria, Tunisia, Turkey or any EU country) Please make your proposal for the campaign which you would like to be part of... Deadline 30th September 1999. Send to: Climate Campaigns, Postbox 94115 1090 GC Amsterdam Netherlands fax: +31 20 692 8757 email: climate-l@eyfa.org eyfa postbus 94115 gc 1090 amsterdam netherlands tel. +31 20 6657743 fax. +31 20 6928757 email. eyfa@eyfa.org
#-------------------------------------------- # Dr. David Viner # Climate Impacts LINK Project # Climatic Research Unit # University of East Anglia # Norwich NR4 7TJ # UK # mailto://d.viner@uea.ac.uk # WWW: http://www.cru.uea.ac.uk/link # WWW: http://ipcc-ddc.cru.uea.ac.uk # Tel: +44 (0)1603 592089 # Fax: +44 (0)1603 507784 #---------------------------------------------
102. Janice Moore says:
103. Extreme weather? … What “extreme weather”?
It is therefore surprising to discover that by all the various real world data considered here, the weather in the first half of the 20th century was, if anything, more extreme than in the second half. I have not found any data, including in SREX [a special report by the Intergovernmental Panel on Climate Change], that contradicts these trends. Furthermore there are no signs of this trend changing (i.e. lessening and reversing) in recent years.
104. Janice Moore says:
105. Jeff L says:
/Users/jefflyslo/Desktop/WW Demand.jpg
106. Janice Moore says:
Is sleazy a bad word?
107. Janice Moore says:
Is trolling a bad word?
108. Janice Moore says:
Is litigation a bad word?
109. Sheri says:
110. Janice Moore says:
111. Warming in the 21st century reduced Colorado River flows by at least 0.5 million acre-feet…
Bradley Udall of CSU, are you unaware that Colorado River Water helps keeps your campus nice and green?
Utilities from across the East Slope transfer about 475,000 acre-feet of water from the Colorado River basin to the East Slope each year. On average, Denver Water customers use about 125,000 acre-feet of West Slope water per year.
— http://www.denverwater.org/SupplyPlanning/WaterRights/
More than half of Fort Collins water is diverted from the Colorado River.
Approximately 40% of Fort Collins water is used for landscaping.
Bradley Udall, put that water back where it belongs!
112. Sheri says:
113. testing pre
More on the lack of correspondence between record high days at Falls Village and Norfolk, CT.
Falls Village:
2001-08-03 — 91
2001-08-04 — 85
2001-08-05 — 88
2001-08-06 — 92
...
2002-07-29 — 93
2002-07-30 — 104
2002-07-31 — 91
Norfolk:
2001-08-03 — 87
2001-08-04 — M
2001-08-05 — 98
2001-08-06 — 81
...
2002-07-29 — 75
2002-07-30 — 87
2002-07-31 — 85
An argument against interpolation?
114. I don’t know whether this url will let you in but it is here
115. Janice Moore says:
116. Janice Moore says:
117. Sheri says:
Changing login so I don’t end up in moderation.
118. Janice Moore says:
119. Janice Moore says:
120. Janice Moore says:
121. Janice Moore says:
• clipe says:
122. Here’s the same investigation with RSSv3 TLT global data. Here is the full record with 12 month averages for visual accompaniment to the following.
Ordinary least squares linear regression, trends in degrees Celsius, the mean trend from January 1998 to:
Feb 2016: 0.019 /decade
Mar 2016: 0.028 /decade
Apr 2016: 0.035 /decade
May 2016: 0.038 /decade
Jun 2016: 0.041 /decade
Jul 2016: 0.043 /decade
Aug 2016: 0.045 /decade
Sep 2016: 0.049 /decade
Oct 2016: 0.049 /decade (higher to 4 decimal places than Sep)
Nov 2016: 0.050 /decade
Dec 2016: 0.048 /decade
Jan 2017: 0.052 /decade
Feb 2017: 0.053 /decade
Unlike UAHv6 there is one month (Dec 2016) that lowered the then warming trend slightly. I’ve plotted monthly data and the trend to Nov 2016, and you can see the Dec 2016 anomaly is below the trend line. That’s why December lowered the then trend slightly.
Otherwise, every other month after the peak warm month of Feb 2016 increased the trend, even though they were all cooler than February. The trend rose because subsequent months were warmer than the trend itself, except December 2016.
For the ‘pause’ from 1998 to resume next month, the March anomaly would have to be -3.6C.
For the pause to resume by December 2017, the annual average anomaly for 2017 would have to be -0.02C.
The last time an annual temperature anomaly was this cool or cooler in the RSSv3 TLT dataset was 1993 (-0.118C).
However, January and February 2017 have been 0.41 and 0.44 respectively, so for the pause to resume by December, the average of the next 10 months would have to be -0.12C.
The last time this happened was in 1992 (-0.19C).
For a pause to resume by 2020 (Dec 2019), the three year averaged anomaly 2017 to 2019 for RSS would have to be -0.04C.
The last time a 3 year average was that cool or cooler was 1992 through 1994 (-0.09).
For the pause to resume by 2020, we’d need to see temps of the next three years similar to those of the early 1990s. Check the graph above to see what that looks like.
123. How Imminent is the RSS Pause? (Now Includes January and February Data)
Guest Post by Werner Brozek, Excerpts from Barry and Edited by Just The Facts
Our previous post was titled “How Imminent is the UAH Pause? (Now Includes Some January Data)” and it can be found here:
https://wattsupwiththat.com/2017/02/19/how-imminent-is-the-uah-pause-now-includes-some-january-data/
UAH (University of Alabama in Huntsville) and RSS (Remote Sensing Systems) are two major satellite groups that provide monthly climate anomalies. From January 1998 to January 2016, the slope was slightly negative, a period which many have referred to as a “pause”, although some prefer other names. Since a huge anomaly spike in February 2016 due to a very strong El Nino, the so called pause is gone.
Last month, Barry wrote about several things that must happen for the pause to return for UAH. This month, he has written about what must happen for the pause to return for RSS. However he has also provided additional information with respect to the UAH pause.
The parts below discuss RSS.
Here’s the same investigation with RSSv3 TLT global data. Here is the full record with 12 month averages for visual accompaniment to the following.
Ordinary least squares linear regression, trends in degrees Celsius, the mean trend from January 1998 to:
Feb 2016: 0.019 /decade
Mar 2016: 0.028 /decade
Apr 2016: 0.035 /decade
May 2016: 0.038 /decade
Jun 2016: 0.041 /decade
Jul 2016: 0.043 /decade
Aug 2016: 0.045 /decade
Sep 2016: 0.049 /decade
Oct 2016: 0.049 /decade (higher to 4 decimal places than Sep)
Nov 2016: 0.050 /decade
Dec 2016: 0.048 /decade
Jan 2017: 0.052 /decade
Feb 2017: 0.053 /decade
Unlike UAHv6 there is one month (Dec 2016) that lowered the then warming trend slightly. I’ve plotted monthly data and the trend to Nov 2016, and you can see the Dec 2016 anomaly is below the trend line. That’s why December lowered the then trend slightly.
Otherwise, every other month after the peak warm month of Feb 2016 increased the trend, even though they were all cooler than February. The trend rose because subsequent months were warmer than the trend itself, except December 2016.
For the ‘pause’ from 1998 to resume next month, the March anomaly would have to be -3.6C.
For the pause to resume by December 2017, the annual average anomaly for 2017 would have to be -0.02C.
The last time an annual temperature anomaly was this cool or cooler in the RSSv3 TLT dataset was 1993 (-0.118C).
However, January and February 2017 have been 0.41 and 0.44 respectively, so for the pause to resume by December, the average of the next 10 months would have to be -0.12C.
The last time this happened was in 1992 (-0.19C).
For a pause to resume by 2020 (Dec 2019), the three year averaged anomaly 2017 to 2019 for RSS would have to be -0.04C.
The last time a 3 year average was that cool or cooler was 1992 through 1994 (-0.09).
For the pause to resume by 2020, we’d need to see temps of the next three years similar to those of the early 1990s. Check the graph above to see what that looks like.
The parts below have additional updates for UAH.
Next month’s anomaly would have to be lower than 0.2C to reduce the trend slightly.
To get a flat or negative trend since 1998, the March anomaly would have to be -3.8C.
The decimal point is in the correct place!
For the 1998 trend to return to flat or negative values by the end of this year, the annual average anomaly for 2017 would have to be -0.16C.
We have 2 months data already, at around 0.5C warmer than that, so what would the average temperature anomaly for the rest of 2017 have to be to get a flat/negative trend since 1998?
-0.26C (Mar-Dec)
The most recent year the annual average anomaly was that cool was in 1985. The annual average then was -0.35C.
With 2017 predicted to be an el Nino or ENSO neutral year the chances of a flat trend by December are very slim. As I expect some warming with atmospheric CO2 increase, however one may argue the magnitude, I think it is unlikely we will see a year as cold as 1985, barring a volcanic eruption of greater magnitude than the 1991 Pinatubo eruption.
Consequently, I think it is unlikely the ‘pause’ will return at all if 1998 is used as the start date.
In comments last month Werner asked how cool the annual anomalies would have to be to get a flat trend if there were a succession of cool years. For the trend since 1998 to go flat by 2020 (December 2019) the annual average temperature anomaly for the three years Jan 2017 to Dec 2019 would have to be:
0.05C
When did we last have 3 consecutive years as cool or cooler than that?
2007 to 2009: 0.05C
However, January and February 2017, being 0.30 and 0.35C respectively, would raise the three year average to 0.6 if the rest of the months through 2019 were 0.05C.
So we have to go further back in time to get a cooler 3-year average. Most recent is:
1994 to 1996: 0.0C
Those predicting imminent cooling from lower solar ebb or ocean-atmosphere oscillations may expect to see annual temperatures like the early 1990s sometime soon. I am less confident of that. Time will tell.
————-
Written by Barry
124. Examples of different types of curves.
Red = Exponential (power), Green = Linear, Blue = Logarithmic
It seams rather convenient to me that all of the costs follow Exponential (power) functions (like sea level rise), and all of the benefits follow Logarithmic functions (like fertilized plant growth), while the evidence states otherwise. Furthermore, we know that the basic IPPC models themselves are linear functions of CO2 concentrations (ΔT=F{ΔCO2}), when they should be Logarithmic (T=F{log(ΔCO2)}). So we have, overstate the effect of CO2, overstate the damages, and understate the benefits. Yep, sounds correct to me.
/sarc
125. Janice Moore says:
126. Janice Moore says:
127. Janice Moore says:
128. Janice Moore says:
129. Janice Moore says:
130. Janice Moore says:
131. Janice Moore says:
• Janice Moore says:
Thanks a lot.
132. Janice Moore says:
133. Sheri says:
134. Bindidon says:
Burl Henry on March 8, 2017 at 5:24 pm
Google my post “Climate Change Deciphered”
That, Burl Henry, was a bad hint. You’d better have published the link to the blog entry instead. Because near it I found
https://wattsupwiththat.com/2016/10/15/scientific-integrity-is-constant-challenge-a-classic-historical-example/
with in it
https://wattsupwiththat.com/2016/10/15/scientific-integrity-is-constant-challenge-a-classic-historical-example/#comment-2320129
and from there I went to
https://wattsupwiththat.com/2015/05/26/the-role-of-sulfur-dioxide-aerosols-in-climate-change/
and finally to
Willis Eschenbach
May 28, 2015 at 8:46 am
Burl Henry May 27, 2015 at 6:45 am Edit
Yes, it is always one of cooling. But if you remove Megatonnes of it, then warming naturally occurs, which is the point of my post.
Yes, Burl. But if your theory is right, if you add Megatonnes of SO2, then cooling naturally occurs, which is the point you are ignoring as fast as you can. As I pointed out above, your theory about .02° per megatonne means the earth should have COOLED from 1850 to 1980, which was the point of my previous comment.
Unfortunately, you seem determined not to deal with this. Instead, you say:
Regardless of what happened in the 1850’s to now, currently the lowering of SO2 emissions is causing higher temperatures, and that must be our greatest concern
Look, Burl, a lot of very smart folks have pointed out exactly where you’ve gone off the road. And so have I. You’ve ignored them, one and all, just as you’ve ignored me.
Now, you seem to think that holding on to your theory and sticking your fingers in your ears and saying in essence “Na, na, na, I can’t hear any of you, na, na, na” gains you points. I’m here to tell you that is not the case. YOU ARE DESTROYING YOUR REPUTATION ENTIRELY BY NOT PAYING ATTENTION TO OBJECTIONS TO YOUR THEORY.
Given what I’ve seen so far, you’ve placed yourself firmly on my own personal “SKIP HIS COMMENTS” list, and you’ll stay there until you demonstrate that you can admit when you have made a mistake. You’re free to do that, of course, and if you do I’ll change my mind.
For now, perhaps you can at least start by trying to explain why the temperatures didn’t obey their SO2 masters from 1850 to 1980 on and warmed a degree or so instead of the 2°C cooling that your theory so confidently hindcasts … and why they changed, explain why in 1980 the temperatures realized the error of their ways and started obeying nobody but SO2.
I await your explanation, and I fear that the size of your prediction (a 2°C cooling since 1850) will make that more than difficult.
w.
Well I do not always agree to Willis’ meaning, but here I do!
135. Janice Moore says:
136. Janice Moore says:
137. Janice Moore says:
138. PiperPaul says:
139. NOYGDB says:
Anthony… if you want to troll a butthurt Klimate Katastrophe Kook, just add the following:
<snicker>
on its own line below the text:
“I live rent free in their heads.”
on page:
If kicking Klimate Katastrophe Kooks is wrong, I don’t wanna be right!
140. Lee Osburn says:
[img]http://i67.tinypic.com/kcggsm/9
141. clipe says:
142. clipe says:
143. clipe says:
144. clipe says:
Lee, I think you have to right-click on the image and copy image location. Then paste into reply box.
145. Janice Moore says:
146. Janice Moore says:
147. Janice Moore says:
148. Janice Moore says:
149. @ Bindidon
March 12, 2017 at 11:40 am
That’s called dual boot.
Yes good idea as long as you work with XP, but I lost lots of work due to Win 7 having erased the Linux info off the master boot block at the end of an automatic update…¨,
Don think you did loose any info, you just could not start the still existing linux from MBR any more, an easy repair with a boot cd or usb to reboot your linux again could have fixed things. Once you start dual booting, this is basic stuff, and creating a regular backup anyway also.
150. Janice Moore says:
151. Sheri says:
Testing.
152. Sheri says:
What the US looks like to the rest of the world is only asked by people as insecure as teenager who has no self-esteem and needs to develop a sense of self and a backbone. Sadly, bullying and intimidation are encourage and weakness and submission are the recommended responses. A nation of non-thinkers subject to group-think and shaming.
153. clipe says:
There’s a bit of jiggery-pokery going on with Ontario’sIESO website.
Rather having the facts of capacity vs output on the homepage, you now have totunnel down and then scroll down.
154. EricHa says:
155. Janice Moore says:
156. Janice Moore says:
157. Janice Moore says:
158. Sheri says:
Interesting that one can use conspiracy terms like BIG PHARMA but no the word conspiracy.
159. Recently at WUWT, an article by Leo Goldstein addressed a report by The Medical Society Consortium on Climate and Health, titled Medical Alert! Climate Change Is Harming Our Healthhttps://wattsupwiththat.com/2017/03/22/watch-out-for-the-medical-society-consortium-on-climate-and-health/
Since I view this as a further crusade to validate a false premise, let me address only the first paragraph of the “alert”, as a minimal step in revealing its cascading errors. That paragraph reads as follows (without superscript numerals denoting references):
Most Americans understand that climate change is real and are concerned about it. But most still see climate change as a faraway threat, in both time and place, and as something that threatens the future of polar bears but not necessarily people. The reality, however, is starkly different: climate change is already causing problems in communities in every region of our nation, and from a doctor’s perspective, it’s harming our health.
The reference (a Yale study) cited in support of Americans’ understanding of climate change, however, reports that barely more than half of Americans (55%) think that climate change is human-caused, which means that a significant percentage (45%) either do not think this or do not have any opinion on this.
Now consider a survey from Pew Research Center
http://www.pewinternet.org/2016/10/04/public-views-on-climate-change-and-climate-scientists/
… which reports:
But, overall, majorities of Americans appear skeptical of climate scientists. No more than a third of the public gives climate scientists high marks for their understanding of climate change; even fewer say climate scientists understand the best ways to address climate change. And, while Americans trust information from climate scientists more than they trust that from other groups, fewer than half of Americans have “a lot” of trust in information from climate scientists (39%).
Interestingly, from this same Pew survey, we find:
Though the [Pew] survey finds that climate scientists are viewed with skepticism by relatively large shares of Americans, scientists overall — and in particular, medical scientists — are viewed as relatively trustworthy by the general public. Asked about a wide range of leaders and institutions, the military, medical scientists, and scientists in general received the most votes of confidence when it comes to acting in the best interests of the public.
The MedSocCon alert itself mirrors this understanding of the public’s great trust in medical doctors, which indicates to me a suspicious means of engineering greater support for belief in catastrophic human-caused climate change. MedSocCon is serving as a facilitator, “removing the ball”, so to speak, from the court of climate scientists (who have MORE specialized climate knowledge, yet LESS public trust) and putting “the ball” into the court of medical doctors (who have LESS specialized climate knowledge, yet MORE public trust).
In effect, medical doctors (with greater trust) have been shaped by climate scientists (with less trust) into believing that human-caused climate change is a serious problem, and now these so shaped, trustworthy people are being enlisted by those less-trusted people as activists.
Let’s have another look at the first paragraph of MedSocCon’s “alert”, … the part that says, climate change is already causing problems in communities in every region of our nation, and from a doctor’s perspective, it’s harming our health. Ten references are cited to support this claim.
After the first reference, I did not look at the other nine. Here’s a one-page preview of that first reference:
Views of AAAAI members on climate change and health, Sarfaty, Mona; Kreslake, Jennifer M; Casale, Thomas B; Maibach, Edward W. JOURNAL OF ALLERGY AND CLINICAL IMMUNOLOGY. IN PRACTICE; Amsterdam4.2 (Mar 2016): 333-335. http://search.proquest.com/openview/0f9d1469276545260f23b9cb318b2976/1?pq-origsite=gscholar&cbl=2031058
This particular reference reports the results of a survey of AAAAI members in 48 states and the District of Columbia, in which, I quote, a total of 1184 people responded; the response rate was 22%.
Here’s a 2015 full-text version that reports the same response rate, and so I assume it is the original report, before the 2016 version appeared:
https://www.aaaai.org/Aaaai/media/MediaLibrary/PDF%20Documents/Libraries/Climate-Change-Survey.pdf
I suspect that this is just one instance of discovering how even doctors, in all their trustworthiness, are NOT immune from erroneously mixing knowledge, beliefs, and attitudes with facts. It’s also another instance of using low-response surveys as highly trusted references.
I won’t drag this out any further, although I could go on. I simply don’t have the time to dissect another non-viable body of proof.
160. Janice Moore says:
161. Janice Moore says: | 2017-03-30 20:42:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4482739269733429, "perplexity": 4752.905289231099}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218203515.32/warc/CC-MAIN-20170322213003-00259-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://mailman.ntg.nl/pipermail/ntg-context/2016/085701.html | # [NTG-context] fontsize changes not understood
Hans Hagen pragma at wxs.nl
Tue May 24 16:04:38 CEST 2016
On 5/24/2016 3:04 PM, Meer, Hans van der wrote:
>
> Can someone explain to me the changes in fontsize in the following example?
> Enclosing the fontswitches in a group did not change the behaviour.
>
> \setupbodyfont[dejavu,12pt]
> \def\MarkMasterA{\inmargin[location=left]{\bgroup\switchtobodyfont[9pt]\red
> Master\egroup}}
> \def\MarkMasterB{\inmargin[location=left]{\bgroup\usebodyfont[9pt]\red
> Master\egroup}}
> \starttext
> \startsection[title=\MarkMasterA First title]
> \input hawking
> \MarkMasterA
> \input hawking
> \stopsection
> \startsection[title=\MarkMasterB First title]
> \input hawking
> \MarkMasterB
> \input hawking
> \blank
> contextversion=\contextversion
> \stopsection
> \stoptext
>
> In the first section the absolute value of 9 pt appears not to be
> honoured but it looks as if there is a reduction relative to the
> surrounding font.
> In the second section the size does not change and looks even bigger
> than the first one above.
>
> I am baffled and do not understand why not all fontsizes are the same
> absolute 9pt as requested?
inmargin also has a style parameter that can be set (and maybe it is)
\setupbodyfont is a global font switch that should be used local (as it
affects the headers footers, spacing etc
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http://math-mprf.org/journal/articles/id1034/ | A Note on the Free Energy of the Coupled System in the Sherrington - Kirkpatrick Model
#### D. Panchenko
2005, v.11, №1, 19-36
ABSTRACT
In this paper we consider a system of spins that consists of two configurations $\vec{\sigma}^1,\vec{\sigma}^2\in\Sigma_N=\{-1,+1\}^N$ with Gaussian Hamiltonians $H_N^1(\vec{\sigma}^1)$ and $H_N^2(\vec{\sigma}^2)$ correspondingly, and these configurations are coupled on the set where their overlap is fixed $\{R_{1,2}=N^{-1}\sum_{i=1}^N \sigma_i^1\sigma_i^2 = u_N\}$. We prove the existence of the thermodynamic limit of the free energy of this system given that $\lim_{N\to\infty}u_N = u\in[-1,1]$ and give the analogue of the Aizenman - Sims - Starr variational principle that describes this limit via random overlap structures.
Keywords: spin glasses,Sherrington - Kirkpatrick model | 2017-06-28 14:09:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7009656429290771, "perplexity": 635.9770842593019}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323682.21/warc/CC-MAIN-20170628134734-20170628154734-00504.warc.gz"} |
https://math.stackexchange.com/questions/3147657/finding-an-error-in-proof-for-an-axiom-of-a-vector-space | Finding an error in proof for an axiom of a vector space
Recently, I asked a question about axoims of vector spaces and counterexamples. The question can be found at: A Counter Examples in Linear Algebra (Vector Space)
However, a few days before asking this question, I tried to prove that the axiom $$1 \cdot v = v$$ in the definition of a vector space is redundant. For the proof, I have used that every vector space has a basis (which is proved by using Zorn's Lemma). However, I know that this is not true. Because we do have a system where every other axiom is satisfied and only $$1 \cdot v \neq v$$ and hence the system fails to be a vector space. I would like to know where exactly in the proof have I made a mistake? I have been stuck on this for a few weeks and no matter what I do, I cannot find the exact point where things start to go wrong. All help, suggestions and comments are appreciated. The proof I tried is as follows:-
We know that $$V$$ must have a basis (can be proved by using Zorn's Lemma), say $$B$$. Let $$v \in V$$. Then, $$\exists v_1, v_2, \cdots, v_n \in B$$ and $$\alpha_1, \alpha_2, \cdots, \alpha_n \in \mathbb{F}$$ such that $$v = \alpha_1 \cdot v_1 + \alpha_2 \cdot v_2 + \cdots + \alpha_n \cdot v_n = \sum\limits_{i = 1}^{n} \alpha_i \cdot v_i$$. Now, let $$1 \cdot v = w$$, where $$1 \in \mathbb{F}$$ is the unity of the field and $$w \in V$$. Again, since $$B$$ is a basis, $$\exists w_1, w_2, \cdots, w_m \in B$$ and $$\beta_1, \beta_2, \cdots, \beta_m \in \mathbb{F}$$ such that $$w = \beta_1 \cdot w_1 + \beta_2 \cdot w_2 + \cdots + \beta_m \cdot w_m = \sum\limits_{i = 1}^{m} \beta_i \cdot w_i$$. Therefore, we have \begin{align*} 1 \cdot \sum\limits_{i = 1}^{n} \alpha_i \cdot v_i &= \sum\limits_{i = 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{n} 1 \cdot \left( \alpha_i \cdot v_i \right) &= \sum\limits_{i = 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{n} \left( 1 \alpha_i \right) \cdot v_i &= \sum\limits_{i = 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{n} \alpha_i \cdot v_i &= \sum\limits_{i = 1}^{m} \beta_i \cdot w_i \\ \end{align*} Consider the two sets $$S_1 = \left\lbrace v_1, v_2, \cdots, v_n \right\rbrace$$ and $$S_2 = \left\lbrace w_1, w_2, \cdots, w_m \right\rbrace$$. Clearly, $$S_1 \subseteq B$$ and $$S_2 \subseteq B$$ and hence $$S_1, S_2$$ are linearly independent. Also, the set $$S_1 \cup S_2 = \left\lbrace v_1, v_2, \cdots, v_n, w_1, w_2, \cdots, w_m \right\rbrace \subseteq B$$ and is also linearly independent. Let, if possible $$S_1 \cap S_2 = \emptyset$$, where $$\emptyset$$ denotes the empty set. This means that $$\forall i \in \left\lbrace 1, 2, \cdots n \right\rbrace$$ and $$\forall j \in \left\lbrace 1, 2, \cdots, m \right\rbrace, v_i \neq w_j$$.
Using that the additive inverse of $$a \cdot v$$ is $$\left( -a \right) \cdot v$$ and adding the additive inverses of each vector $$\beta_i \cdot w_i$$ in the last equation to obtain, $$\sum\limits_{i = 1}^{n} \alpha_i \cdot v_i + \sum\limits_{i = 1}^{m} \left( - \beta_i \right) \cdot w_i = \textbf{0}$$ Since $$S_1 \cup S_2$$ is linearly independent, $$\forall i \in \left\lbrace 1, 2, \cdots, n \right\rbrace, \alpha_i = 0$$ and $$\forall i \in \left\lbrace 1, 2, \cdots, m \right\rbrace, - \beta_i = 0$$, which in turn gives that $$\beta_i = 0$$. Therefore, $$v = 0 \cdot v_1 + 0 \cdot v_2 + \cdots + 0 \cdot v_n = \textbf{0}$$ and $$w = 0 \cdot w_1 + 0 \cdot w_2 + \cdots + 0 \cdot w_m = \textbf{0}$$. Hence, $$1 \cdot \textbf{0} = \textbf{0}$$.
Now, let us consider that $$S_1 \cap S_2 \neq \emptyset$$. Let there be $$r$$ vectors, where $$0 \leq r \leq \min \left\lbrace m, n \right\rbrace$$, which are common in $$S_1$$ and $$S_2$$. We shall name them, $$v_i$$, where $$i \in \left\lbrace 1, 2, \cdots, r \right\rbrace$$. Thus, our sets look like $$S_1 = \left\lbrace v_1, v_2, \cdots, v_r, v_{r + 1}, \cdots, v_n \right\rbrace$$ and $$S_2 = \left\lbrace v_1, v_2, \cdots, v_r, w_{r + 1}, \cdots, w_m \right\rbrace$$. Now, $$v = \sum\limits_{i = 1}^{r} \alpha_i \cdot v_i + \sum\limits_{i = r + 1}^{n} \alpha_i \cdot v_i$$ and $$w = \sum\limits_{i = 1}^{r} \beta_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \beta_i \cdot w_i$$. Again, \begin{align*} 1 \cdot \left( \sum\limits_{i = 1}^{r} \alpha_i \cdot v_i + \sum\limits_{i = r + 1}^{n} \alpha_i \cdot v_i \right) &= \sum\limits_{i = 1}^{r} \beta_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{r} 1 \cdot \left( \alpha_i \cdot v_i \right) + \sum\limits_{i = r + 1}^{n} 1 \cdot \left( \alpha_i \cdot v_i \right) &= \sum\limits_{i = 1}^{r} \beta_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{r} \left( 1 \alpha_i \right) \cdot v_i + \sum\limits_{i = r + 1}^{n} \left( 1 \alpha_i \right) \cdot v_i &= \sum\limits_{i = 1}^{r} \beta_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \beta_i \cdot w_i \\ \therefore \sum\limits_{i = 1}^{r} \alpha_i \cdot v_i + \sum\limits_{i = r + 1}^{n} \alpha_i \cdot v_i &= \sum\limits_{i = 1}^{r} \beta_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \beta_i \cdot w_i \\ \end{align*} Adding the additive inverses of each of the vectors on the right hand side of the equation to both the sides and using axioms of vector space multiple times, we get $$\sum\limits_{i = 1}^{r} \left( \alpha_i - \beta_i \right) \cdot v_i + \sum\limits_{i = r + 1}^{n} \alpha_i \cdot v_i + \sum\limits_{i = r + 1}^{m} \left( - \beta_i \right) \cdot w_i = \textbf{0}$$ Since $$S_1 \cup S_2$$ is linearly independent, $$\forall i \in \left\lbrace 1, 2, \cdots, r \right\rbrace, \alpha_i - \beta_i = 0 \Rightarrow \alpha_i = \beta_i$$. Also, $$\forall i \in \left\lbrace r + 1, r + 2, n \cdots \right\rbrace, \alpha_i = 0$$ and $$\forall i \in \left\lbrace r + 1, r + 2, \cdots, m \right\rbrace, \beta_i = 0$$. This tells us that $$v = \sum\limits_{i = 1}^{r} \alpha_i \cdot v_i$$ and $$w = 1 \cdot v = \sum\limits_{i = 1}^{r} \alpha_i \cdot v_i$$. Hence, $$1 \cdot v = v$$.
Note that we can prove $$- \left( a \cdot v \right) = \left( -a \right) \cdot v$$ as follows
\begin{align} \left( -a \right) \cdot v + a \cdot v = \left( -a + a \right) \cdot v = 0 \cdot v = 0 \end{align}
• "We know that $V$ must have a basis" - this depends on the definition of vector space, so perhaps on $1v=v$? – Hagen von Eitzen Mar 14 '19 at 7:12
Let $$\Bbb F=\Bbb R$$, $$V=\Bbb Z$$ and for $$\alpha\in\Bbb F$$, $$v\in\Bbb Z$$, let $$\alpha v=0$$. Then $$v$$ is an abelian group and $$\cdot$$ is an action of the ring-without-$$1$$ (sometimes called rng) $$\Bbb F$$ on $$V$$. Hence this is almost a vector space - only the fact that $$1$$ acts as identity is missing.
The $$V$$ does not have a basis. Indeed, any linear combination $$\alpha_1v_1+\alpha_2v_2+\ldots +a_nv_n$$ will always be $$=0$$. So the very first sentence in your argument is invalid.
• Does the proof for existence of basis uses the axiom $1 \cdot v = v$ anywhere? – Aniruddha Deshmukh Mar 14 '19 at 7:40
• +1. BTW the "work" in the Q applies the axiom that $a (bv)=(ab )v$ for $a ,b \in \Bbb F$ and $v\in V.$ So if $w,v \in V$ with$w=1v$ then $1w=1(1v)=(1\cdot 1)v=1v=w.$ So for all $w\in \{1v:v\in V\}$ we have $1w=w.$ So the axiom $\forall v\in V\,(1v=v)$ is implied, in the presence of the other axioms, by $V=\{1v:v\in V\},$ but, as your example shows, is independent of the other axioms. – DanielWainfleet Mar 14 '19 at 7:44
• @AniruddhaDeshmukh . Let $W=\{1v:x\in V\}.$ Then by my previous comment, $\forall w\in W\;(1w=w)$ so we can easily verify that $W$ is a vector space over $F.$(Although, as in the answer, it might be the trivial space $\{0\}.$) Now suppose $v\in V$ and $1v\ne v.$ Then $v\not \in W.$ But now, for any $b\in B\subset V$ and any $f\in \Bbb F$ we have $fb=(f\cdot 1)b=f(1b)\in W$, so the linear span of $B$ is a subset of $W$,and $W\ne V$ so $B$ is not a basis for $V.$ – DanielWainfleet Mar 14 '19 at 8:22
• @AniruddhaDeshmukh Yes, it does. Using Zorn, let $B$ be a maximal independent family and assume $v$ is not in the span of $B$. Then how are you going to conclude that $B\cup\{v\}$ is a linear independent family (or even that $v\notin B$)? – Hagen von Eitzen Mar 14 '19 at 13:34 | 2021-06-15 00:28:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 73, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000077486038208, "perplexity": 145.33627653162978}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487614006.8/warc/CC-MAIN-20210614232115-20210615022115-00022.warc.gz"} |
http://tug.org/pipermail/macostex-archives/2007-January/028186.html | # [OS X TeX] TL-2007 missing .sty files
Gary L. Gray gray at engr.psu.edu
Wed Jan 24 01:36:18 CET 2007
```On Jan 23, 2007, at 2:31 AM, Axel E. Retif wrote:
> On Jan 23, 2007, at 00:26, Gary L. Gray wrote:
>
>>
>> On Jan 23, 2007, at 12:22 AM, Axel E. Retif wrote:
>>
>>>> ~/Library/texmf/bibtex
>>>> doc
>>>> dvips
>>>> fonts
>>>> tex
>>>
>>> and within the tex directory a subdirectory `` latex '', where
>>> you can put your manually installed *.sty files.
>>>
>>>> web2c
>>>
>>> You have the ---at least by me--- dreaded web2c directory! May I
>>> ask you what do you have in there?
>>
>>
>> A format I use for a large manuscript.
>
> That explains it. I'm far from been able to create a format file
> myself.
I bet you can do it. :-)
Just create a .tex file that you want to contain much of your
preamble. For example:
\documentclass[11pt]{article}
\usepackage{...}
\input{...}
\dump
would create a format using article with as many packages and
inputted files as you can list. The \dump command "dumps" the format
to the current directory when the .tex file is typeset. If the .tex
file was named books.tex, then the format file will be books.fmt.
Move that .fmt file to the web2c directory mentioned above and then
you can typeset a document with this format (with TeXShop) by putting:
%!TEX TS-program = books
at the top of the file you are typesetting.
I hope this helps.
All the best,
Gary | 2015-03-02 01:00:09 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8750444054603577, "perplexity": 12043.548086210767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936462577.56/warc/CC-MAIN-20150226074102-00105-ip-10-28-5-156.ec2.internal.warc.gz"} |
http://accessphysiotherapy.mhmedical.com/content.aspx?bookid=456§ionid=39695850 | Chapter 8
Medications play an integral role in the treatment of patients with cardiovascular and pulmonary disorders. Drugs can be used to prevent or treat various pathologies and impairments in the heart, lungs, and circulation, and thereby reduce the functional limitations and disability associated with cardiopulmonary disease. Medications can likewise have a synergistic effect with physical therapy interventions. Drugs, for example, that improve cardiac pumping ability, may enable patients to participate more effectively in interventions that improve aerobic capacity and endurance. All medications likewise produce side effects that can have a direct impact on physical therapy interventions. For instance, drugs that lower blood pressure (antihypertensives) may produce dizziness and incoordination if they cause excessive hypotension. It, therefore, makes sense that physical therapists have a basic understanding of the common cardiovascular and pulmonary medications and how these medications can affect patients receiving physical therapy.
In this chapter, pharmacologic agents are grouped according to the preferred practice patterns listed in Chapter 6 of the Guide to Physical Therapist Practice, 2nd edition (revised).1 For each preferred practice pattern, medications that specifically address cardiovascular or pulmonary problems will be discussed as they relate to that practice pattern. It is, of course, not possible to describe all medications that might be related to each pattern. For example, medications used to control infection, treat cancer, and so forth, may help improve the patient's overall health, thereby helping the patient participate in aerobic conditioning, respiratory exercises, and other activities that will ultimately lead to better cardiovascular and pulmonary function. This chapter, however, will focus only on the medications that directly affect the heart, circulation, or lungs and describe how these medications relate to the physical therapy interventions described in the preferred practice patterns. This chapter will likewise present an overview of these medications, their side effects, and the potential impact of these medications on patients receiving physical therapy. For more information about specific drugs, the reader is also encouraged to consult one of the resources listed at the end of this chapter.24
Many medications are designed to control specific aspects of cardiovascular function so that the risk of cardiac and related diseases is reduced. Controlling blood pressure, for example, can reduce the risk of myocardial infarction, cerebrovascular accident, kidney disease, and so forth. In some cases, drug therapy can be initiated to prevent the first episode of a cardiovascular incident (primary prevention), or drug therapy can be used to prevent the reoccurrence of a specific problem (secondary prevention). Four primary pharmacological strategies that can be used to reduce cardiovascular risks include controlling high blood pressure (antihypertensives), decreasing plasma lipids (antihyperlipidemia drugs), treatment of overactive blood clotting (anticlotting agents), and cessation of cigarette smoking. These drug categories are described here.
### Antihypertensive Medications
Controlling high blood pressure (hypertension) is perhaps one of the most important ways to reduce the risk of cardiovascular disease. Hypertension, defined as a sustained and reproducible increase ...
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This div only appears when the trigger link is hovered over. Otherwise it is hidden from view. | 2017-02-23 07:02:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19004365801811218, "perplexity": 3565.1272628535976}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171162.4/warc/CC-MAIN-20170219104611-00058-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://en.wikipedia.org/wiki/Mountain_pass_theorem | # Mountain pass theorem
The mountain pass theorem is an existence theorem from the calculus of variations. Given certain conditions on a function, the theorem demonstrates the existence of a saddle point. The theorem is unusual in that there are many other theorems regarding the existence of extrema, but few regarding saddle points.
## Theorem statement
The assumptions of the theorem are:
• I is a functional from a Hilbert space H to the reals,
• $I\in C^1(H,\mathbb{R})$ and $I'$ is Lipschitz continuous on bounded subsets of H,
• I satisfies the Palais-Smale compactness condition,
• $I[0]=0$,
• there exist positive constants r and a such that $I[u]\geq a$ if $\Vert u\Vert =r$, and
• there exists $v\in H$ with $\Vert v\Vert >r$ such that $I[v]\leq 0$.
If we define:
$\Gamma=\{\mathbf{g}\in C([0,1];H)\,\vert\,\mathbf{g}(0)=0,\mathbf{g}(1)=v\}$
and:
$c=\inf_{\mathbf{g}\in\Gamma}\max_{0\leq t\leq 1} I[\mathbf{g}(t)],$
then the conclusion of the theorem is that c is a critical value of I.
## Visualization
The intuition behind the theorem is in the name "mountain pass." Consider I as describing elevation. Then we know two low spots in the landscape: the origin because $I[0]=0$, and a far-off spot v where $I[v]\leq 0$. In between the two lies a range of mountains (at $\Vert u\Vert =r$) where the elevation is high (higher than a>0). In order to travel along a path g from the origin to v, we must pass over the mountains — that is, we must go up and then down. Since I is somewhat smooth, there must be a critical point somewhere in between. (Think along the lines of the mean-value theorem.) The mountain pass lies along the path that passes at the lowest elevation through the mountains. Note that this mountain pass is almost always a saddle point.
For a proof, see section 8.5 of Evans.
## Weaker formulation
Let $X$ be Banach space. The assumptions of the theorem are:
• $\Phi\in C(X,\mathbf R)$ and have a Gâteaux derivative $\Phi'\colon X\to X^*$ which is continuous when $X$ and $X^*$ are endowed with strong topology and weak* topology respectively.
• There exists $r>0$ such that one can find certain $\|x'\|>r$ with
$\max\,(\Phi(0),\Phi(x'))<\inf\limits_{\|x\|=r}\Phi(x)=:m(r)$.
• $\Phi$ satisfies weak Palais-Smale condition on $\{x\in X\mid m(r)\le\Phi(x)\}$.
In this case there is a critical point $\overline x\in X$ of $\Phi$ satisfying $m(r)\le\Phi(\overline x)$. Moreover if we define
$\Gamma=\{c\in C([0,1],X)\mid c\,(0)=0,\,c\,(1)=x'\}$
then
$\Phi(\overline x)=\inf_{c\,\in\,\Gamma}\max_{0\le t\le 1}\Phi(c\,(t)).$
For a proof, see section 5.5 of Aubin and Ekeland.
## References
• Jabri, Youssef (2003). The Mountain Pass Theorem, Variants, Generalizations and Some Applications (Encyclopedia of Mathematics and its Applications). Cambridge University Press. ISBN 0-521-82721-3.
• Evans, Lawrence C. (1998). Partial Differential Equations. Providence, Rhode Island: American Mathematical Society. ISBN 0-8218-0772-2.
• Aubin, Jean-Pierre; Ivar Ekeland (2006). Applied Nonlinear Analysis. Dover Books. ISBN 0-486-45324-3. | 2014-03-08 23:10:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9036551117897034, "perplexity": 474.9559770548863}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999665917/warc/CC-MAIN-20140305060745-00059-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://docs.itascacg.com/flac3d700/flac3d/zone/doc/manual/zone_manual/zone_fish/zone.field_intrinsics/fish_zone.field.component.html | # zone.field.component
Syntax
s := zone.field.component
zone.field.component = s
Get/set the scalar value retrieved from a name that returns a vector. If the type is not a vector, this value is ignored. Valid strings are x, y, z, and magnitude.
Returns: s - the current component setting s - the new component setting. Keyword matching rules apply. If no match is found an error will occur. | 2020-10-21 23:58:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3633400797843933, "perplexity": 1203.9270592850348}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107878662.15/warc/CC-MAIN-20201021235030-20201022025030-00088.warc.gz"} |
https://mothur.org/wiki/Geometric | # Geometric
The geometric calculator returns the Kolmogorov-Smirnov test statistic for the comparison of observed rank-abundance data to a fitted geometric series distribution and the critical values for α equal to 0.01 or 0.05. This calculator can be used in the summary.single, collect.single, and rarefaction.single commands.
$S_i=NC_K K\left(1-K\right)^\left(i-1\right)$
where,
$C_K=\left(1-\left(1-K \right)^{S_{obs}} \right)^{-1}$
$S_i$ = number of individuals in the ith OTU
$N$ = the total number of individuals
To calculate K, the following equation is solved for K
$\frac{N_{min}}{N}=\left(\frac{k}{1-k}\right)\frac{\left(1-k\right)^{S_{obs}}}{1-\left(1-k\right)^{S_{obs}}}$
where,
$N_{min}$ = the number of individuals in the most rare OTU
$S_{obs}$ = total number of observed OTUs
Open the file 98_lt_phylip_amazon.fn.sabund generated using the Amazonian dataset with the following commands:
mothur > read.dist(phylip=98_lt_phylip_amazon.dist, cutoff=0.10)
mothur > cluster()
The 98_lt_phylip_amazon.fn.sabund file is also outputted to the terminal window when the cluster() command is executed:
unique 2 94 2
0.00 2 92 3
0.01 2 88 5
0.02 4 84 2 2 1
0.03 4 75 6 1 2
0.04 4 69 9 1 2
0.05 4 55 13 3 2
0.06 4 48 14 2 4
0.07 4 44 16 2 4
0.08 7 35 17 3 2 1 0 1
0.09 7 35 14 3 3 0 0 2
0.10 7 34 13 3 2 0 0 3
The first column is the label for the OTU definition and the second column is an integer indicating the number of sequences in the dominant OTU. The numbers in the subsequent columns indicate the number of singletons, doubletons, etc. Here we will calculate the expected number of individuals in each OTU based on the geometric series distribution:
$\frac{1}{98}=\left(\frac{K}{1-K}\right)\frac{\left(1-K\right)^{55}}{1-\left(1-K\right)^{55}}$, $K = 0.019424$, by Excel
$C_K=\left(1-\left(1-0.019424 \right)^{55} \right)^{-1} = 1.5151$
$S_i=\left(98\right)\left(1.5151\right) \left(0.019424\right) \left(1-0.019424\right)^\left(i-1\right) = 2.8841\left(0.9806\right)^\left(i-1\right)$
OTU Rank Indiv. Obs. Expected Cum. Obs. Cum. Exp. Difference
1 7 2.884 7 2.88 4.12
2 7 2.828 14 5.71 8.29
3 7 2.773 21 8.49 12.51
4 4 2.719 25 11.21 13.79
5 4 2.667 29 13.87 15.13
6 3 2.615 32 16.49 15.51
7 3 2.564 35 19.05 15.95
8 3 2.515 38 21.57 16.43
9 2 2.466 40 24.03 15.97
10 2 2.418 42 26.45 15.55
11 2 2.371 44 28.82 15.18
12 2 2.325 46 31.15 14.85
13 2 2.280 48 33.42 14.58
14 2 2.236 50 35.66 14.34
15 2 2.192 52 37.85 14.15
16 2 2.150 54 40.00 14.00
17 2 2.108 56 42.11 13.89
18 2 2.067 58 44.18 13.82
19 2 2.027 60 46.20 13.80
20 2 1.988 62 48.19 13.81
21 2 1.949 64 50.14 13.86
22 1 1.911 65 52.05 12.95
23 1 1.874 66 53.93 12.07
24 1 1.838 67 55.77 11.23
25 1 1.802 68 57.57 10.43
26 1 1.767 69 59.33 9.67
27 1 1.733 70 61.07 8.93
28 1 1.699 71 62.77 8.23
29 1 1.666 72 64.43 7.57
30 1 1.634 73 66.07 6.93
31 1 1.602 74 67.67 6.33
32 1 1.571 75 69.24 5.76
33 1 1.541 76 70.78 5.22
34 1 1.511 77 72.29 4.71
35 1 1.482 78 73.77 4.23
36 1 1.453 79 75.23 3.77
37 1 1.425 80 76.65 3.35
38 1 1.397 81 78.05 2.95
39 1 1.370 82 79.42 2.58
40 1 1.343 83 80.76 2.24
41 1 1.317 84 82.08 1.92
42 1 1.292 85 83.37 1.63
43 1 1.267 86 84.64 1.36
44 1 1.242 87 85.88 1.12
45 1 1.218 88 87.10 0.90
46 1 1.194 89 88.29 0.71
47 1 1.171 90 89.46 0.54
48 1 1.148 91 90.61 0.39
49 1 1.126 92 91.74 0.26
50 1 1.104 93 92.84 0.16
51 1 1.083 94 93.93 0.07
52 1 1.062 95 94.99 0.01
53 1 1.041 96 96.03 0.03
54 1 1.021 97 97.05 0.05
55 1 1.001 98 98.05 0.05
To determine whether the geometric model describes the distribution of individuals among OTUs as we observed, we will use the Kolmogorov-Smirnov test statistic ($D_{max}$). The statistic is the maximum difference between the cumulative observed and expected values (i.e. 16.43) divided by the total number of individuals sampled (i.e. 98). So for this case the value was 0.1677. To test this statistic we can calculate the critical value for α=0.05 as 0.886√Sobs or 0.1195 and α=0.01 as 1.031√Sobs or 0.1390. Because our calculated value is greater than both critical values we are confident (P<0.01) that the observed and expected values are significantly different and we can reject the hypothesis that the observed data follows the geometric distribution.
Running...
mothur > summary.single(calc=geometric)
...and opening 98_lt_phylip_amazon.fn.summary gives:
label geometric geometric_lci geometric_hci
unique 0.019556 0.105226 0.090427
0.00 0.028679 0.105778 0.090902
0.01 0.045567 0.106910 0.091874
0.02 0.081446 0.109286 0.093916
0.03 0.112433 0.112491 0.096671
0.04 0.123174 0.114556 0.098444
0.05 0.136999 0.120669 0.103698
0.06 0.140532 0.125027 0.107443
0.07 0.131241 0.126907 0.109059
0.08 0.121753 0.134225 0.115347
0.09 0.148807 0.136559 0.117354
0.10 0.167704 0.139020 0.119468 <---
In this table the data in the column "geometric" are the calculated statistic value, those in column "geometric_lci" are the critical values for α=0.01, and those in column "geometric_hci" are the critical values for α=0.05. These are the same values that we found above for a cutoff of 0.10. | 2019-07-23 09:59:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.565191388130188, "perplexity": 1462.3348754667593}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195529175.83/warc/CC-MAIN-20190723085031-20190723111031-00184.warc.gz"} |
https://puzzling.stackexchange.com/questions/99686/today-is-a-sad-day/99688 | # Today is a sad day
Today is a sad day - Today, it was supposed to be my big day to shine! But unfortunately that is no longer the case.
I have heard from others here that puzzle-making is a great way to drown out one's sorrows. So here's one for you all to try.
(Text version)
C H O V I I D B A C H C T
R A C H M A N I N O V C R
A N D W E L N I C E H L A
N D E A N I B L S A E I Z
I E B G D S D R I S D C O
P L U N E Z L K A L O A M
O S S E L T O S A H I R C
H A S R S V L V C O M N C
C A Y K S N I V A R T S E
R T Y K O V D V O R A K I
A M Y D H S C H U B E R T
S A D X N E V O H T E E B
After all 18 words are found, please tell me why I am so sad?
(Please do not use any wordsearch solver or any other computer tools)
• Puzzling.SE always yields the weirdest thread titles in the Hot Network Questions list... – Sebastian Redl Jul 6 at 9:15
Covid cancelled classical concert. I am sad.
Solved crossword image:
Words found:
Bach, Beethoven, Brahms, Chopin, Debussy, Dvorak, Handel, Haydn, Lizst, Mendelssohn, Mozart, Rachmaninov, Rossini, Schubert, Stravinsky, Tchaikovsky, Vivaldi, Wagner
All are surnames of famous classical music composers.
Finally:
The remaining letters are COVID CANCELLED CLASSICAL CONCERT I AM SAD [X].
• Wow that was fast! Good job – thesilican Jul 5 at 16:22
• Is it a sign of hyper-awareness of current events that I instantly saw the first word of the final message before finding any of the hidden words? – Darrel Hoffman Jul 6 at 15:21
• @DarrelHoffman I did spot that fairly early on too. Once it was time to check for remaining missed words, that made it pretty easy to guess pieces of the phrase and search from extra letters that should be in words. – aschepler Jul 7 at 11:34 | 2020-09-30 20:00:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49876564741134644, "perplexity": 4125.89462668373}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402127397.84/warc/CC-MAIN-20200930172714-20200930202714-00506.warc.gz"} |
http://www.ck12.org/algebra/Factor-Polynomials-Using-Special-Products/lesson/Factoring-Special-Quadratics-ALG-II/ | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Factor Polynomials Using Special Products
## Factoring perfect squares and difference of squares
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The total time, in hours, it takes a rower to paddle upstream, turn around and come back to her starting point is \begin{align*}18x^2 = 32\end{align*}. How long does it take her to make the round trip?
There are a couple of special quadratics that, when factored, have a pattern.
#### Multiplying the Square of a Binomial
Step 1: Rewrite \begin{align*}(a+b)^2\end{align*} as the product of two factors. Expand \begin{align*}(a+b)^2\end{align*}. \begin{align*}(a+b)^2=(a+b)(a+b)\end{align*}
Step 2: FOIL your answer from Step 1. This is a perfect square trinomial. \begin{align*}a^2+2ab+b^2\end{align*}
Step 3: \begin{align*}(a-b)^2\end{align*} also produces a perfect square trinomial. \begin{align*}(a-b)^2 = a^2-2ab+b^2\end{align*}
Step 4: Apply the formula above to factoring \begin{align*}9x^2-12x+4\end{align*}. First, find \begin{align*}a\end{align*} and \begin{align*}b\end{align*}.
\begin{align*}a^2 &=9x^2, \ b^2=4\\ a &=3x, \quad b=2\end{align*}
Step 5: Now, plug \begin{align*}a\end{align*} and \begin{align*}b\end{align*} into the appropriate formula.
\begin{align*}(3x-2)^2 & = (3x)^2 - 2(3x)(2)+2^2\\ & = 9x^2-12x+4\end{align*}
#### Multiplying (a + b)(a - b)
Step 1: FOIL \begin{align*}(a-b)(a+b)\end{align*}.
\begin{align*}(a-b)(a+b) &= a^2+ab-ab-b^2\\ &= a^2-b^2\end{align*}
Step 2: This is a difference of squares. The difference of squares will always factor to be \begin{align*}(a + b)(a-b)\end{align*}.
Step 3: Apply the formula above to factoring \begin{align*}25x^2-16\end{align*}. First, find \begin{align*}a\end{align*} and \begin{align*}b\end{align*}.
\begin{align*}a^2 &=25x^2, \ b^2=16\\ a &=5x, \quad \ \ b=4\end{align*}
Step 4: Now, plug \begin{align*}a\end{align*} and \begin{align*}b\end{align*} into the appropriate formula. \begin{align*}(5x-4)(5x+4)=(5x)^2-4^2\end{align*}
\begin{align*}^{**}\end{align*}It is important to note that if you forget these formulas or do not want to use them, you can still factor all of these quadratics the same way you have already learned.
Now, let's factor the following quadratics.
1. Factor \begin{align*}x^2-81\end{align*}.
Using the formula from the steps above, we need to first find the values of \begin{align*}a\end{align*} and \begin{align*}b\end{align*}.
\begin{align*}& x^2-81 = a^2-b^2\\ & a^2=x^2, \ b^2=81\\ & \ a=x, \quad \ b=9\end{align*}
Now, plugging \begin{align*}x\end{align*} and 9 into the formula, we have \begin{align*}x^2-81 = (x-9)(x+9)\end{align*}. To solve for \begin{align*}a\end{align*} and \begin{align*}b\end{align*}, we found the square root of each number. Recall that the square root is a number that, when multiplied by itself, produces another number. This other number is called a perfect square.
Alternate Method
Rewrite \begin{align*}x^2-81\end{align*} so that the middle term is present. \begin{align*}x^2+0x-81\end{align*}
Using a previously learned method, what are the two factors of -81 that add up to 0? 9 and -9
Therefore, the factors are \begin{align*}(x-9)(x + 9)\end{align*}.
1. Factor \begin{align*}36x^2+120x+100\end{align*}.
First, check for a GCF.
\begin{align*}4(9x^2+30x+25)\end{align*}
Now, double-check that the quadratic equation above fits into the perfect square trinomial formula.
\begin{align*}a^2 &= 9x^2 \qquad \quad \quad b^2 = 25 \\ \sqrt{a^2} &= \sqrt{9x^2} \qquad \ \sqrt{b^2} = \sqrt{25} \qquad \quad \quad 2ab=30x\\ a &=3x \qquad \qquad \quad b=5 \qquad \quad \ 2(3x)(5)=30x\end{align*}
Using \begin{align*}a\end{align*} and \begin{align*}b\end{align*} above, the equation factors to be \begin{align*}4(3x + 5)^2\end{align*}. If you did not factor out the 4 in the beginning, the formula will still work. \begin{align*}a\end{align*} would equal \begin{align*}6x\end{align*} and \begin{align*}b\end{align*} would equal 10, so the factors would be \begin{align*}(6x + 10)^2\end{align*}. If you expand and find the GCF, you would have \begin{align*}(6x+10)^2=(6x+10)(6x+10)=2(3x+5)2(3x+5)=4(3x+5)^2\end{align*}.
Alternate Method
First, find the GCF. \begin{align*}4(9x^2+30x+25)\end{align*}
Then, find \begin{align*}ac\end{align*} and expand \begin{align*}b\end{align*} accordingly. \begin{align*}9 \cdot 25 = 225\end{align*}, the factors of 225 that add up to 30 are 15 and 15.
\begin{align*}& 4(9x^2+{\color{blue}30x}+25)\\ & 4(9x^2+{\color{blue}15x+15x}+25)\\ & 4 \left[(9x^2+15x)+(15x+25) \right]\\ & 4 \left[3x(3x+5)+5(3x+5) \right]\\ & 4(3x+5)(3x+5) \ or \ 4(3x^2+5)\end{align*}
Again, notice that if you do not use the formula discovered in this concept, you can still factor and get the correct answer.
1. Factor \begin{align*}48x^2-147\end{align*}.
At first glance, this does not look like a difference of squares. 48 nor 147 are square numbers. But, if we take a 3 out of both, we have \begin{align*}3(16x^2-49)\end{align*}. 16 and 49 are both square numbers, so now we can use the formula.
\begin{align*}16x^2 &=a^2 \qquad 49=b^2\\ 4x &=a \qquad \quad 7=b\end{align*}
The factors are \begin{align*}3(4x-7)(4x+7)\end{align*}.
### Examples
#### Example 1
Earlier, you were asked to find the time it takes to make the round trip.
\begin{align*}18x^2 = 32\end{align*} can be rewritten as \begin{align*}18x^2-32 = 0\end{align*}, so factor \begin{align*}18x^2-32\end{align*}.
First, we must take greatest common factor of 2 out of both. We then have \begin{align*}2(9x^2-16)\end{align*}. 9 and 16 are both square numbers, so now we can use the formula.
\begin{align*}9x^2 &=a^2 \qquad 16=b^2\\ 3x &=a \qquad \quad 4=b\end{align*}
The factors are \begin{align*}2(3x-4)(3x+4)\end{align*}.
Finally, to find the time, set these factors equal to zero and solve \begin{align*}2(3x-4)(3x+4) = 0\end{align*}.
Because x represents the time, it must be positive. Only \begin{align*}(3x-4) = 0\end{align*} results in a positive value of x.
\begin{align*}x = \frac{4}{3} = 1.3333\end{align*} Therefore the round trip takes 1.3333 hours.
#### Example 2
\begin{align*}x^2-4\end{align*}
\begin{align*}a = x\end{align*} and \begin{align*}b = 2\end{align*}. Therefore, \begin{align*}x^2-4=(x-2)(x+2)\end{align*}.
#### Example 3
\begin{align*}2x^2-20x+50\end{align*}
Factor out the GCF, 2. \begin{align*}2(x^2-10x+25)\end{align*}. This is now a perfect square trinomial with \begin{align*}a = x\end{align*} and \begin{align*}b = 5\end{align*}.
\begin{align*}2(x^2-10x+25)=2(x-5)^2.\end{align*}
#### Example 4
\begin{align*}81x^2+144+64\end{align*}
This is a perfect square trinomial and no common factors. Solve for \begin{align*}a\end{align*} and \begin{align*}b\end{align*}.
\begin{align*}81x^2 &=a^2 \qquad 64=b^2\\ 9x &=a \qquad \quad 8=b\end{align*}
The factors are \begin{align*}(9x + 8)^2\end{align*}.
### Review
1. List the perfect squares that are less than 200.
2. Why do you think there is no sum of squares formula?
Factor the following quadratics, if possible.
1. \begin{align*}x^2-1\end{align*}
2. \begin{align*}x^2+4x+4\end{align*}
3. \begin{align*}16x^2-24x+9\end{align*}
4. \begin{align*}-3x^2+36x-108\end{align*}
5. \begin{align*}144x^2-49\end{align*}
6. \begin{align*}196x^2+140x+25\end{align*}
7. \begin{align*}100x^2+1\end{align*}
8. \begin{align*}162x^2+72x+8\end{align*}
9. \begin{align*}225-x^2\end{align*}
10. \begin{align*}121-132x+36x^2\end{align*}
11. \begin{align*}5x^2+100x-500\end{align*}
12. \begin{align*}256x^2-676\end{align*}
13. Error Analysis Spencer is given the following problem: Multiply \begin{align*}(2x-5)^2\end{align*}. Here is his work:
\begin{align*}(2x-5)^2=(2x)^2-5^2=4x^2-25\end{align*}
His teacher tells him the answer is \begin{align*}4x^2-20x+25\end{align*}. What did Spencer do wrong? Describe his error and correct the problem.
To see the Review answers, open this PDF file and look for section 5.3.
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
TermDefinition
Difference of Squares A difference of squares is a quadratic equation in the form $a^2-b^2$.
Perfect Square A perfect square is a number whose square root is an integer.
Perfect Square Trinomial A perfect square trinomial is a quadratic expression of the form $a^2+2ab+b^2$ (which can be rewritten as $(a+b)^2$) or $a^2-2ab+b^2$ (which can be rewritten as $(a-b)^2$).
Quadratic form A polynomial in quadratic form looks like a trinomial or binomial and can be factored like a quadratic expression.
Square Root The square root of a term is a value that must be multiplied by itself to equal the specified term. The square root of 9 is 3, since 3 * 3 = 9. | 2017-03-27 04:33:18 | {"extraction_info": {"found_math": true, "script_math_tex": 94, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 5, "texerror": 0, "math_score": 0.9829666614532471, "perplexity": 2534.3594898727442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189377.63/warc/CC-MAIN-20170322212949-00638-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://hal.inria.fr/hal-03131734 | $\scriptstyle{BASALT}$: A Rock-Solid Foundation for Epidemic Consensus Algorithms in Very Large, Very Open Networks - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :
## $\scriptstyle{BASALT}$: A Rock-Solid Foundation for Epidemic Consensus Algorithms in Very Large, Very Open Networks
Davide Frey
François Taïani
#### Abstract
Recent works have proposed new Byzantine consensus algorithms for blockchains based on epidemics, a design which enables highly scalable performance at a low cost. These methods however critically depend on a secure random peer sampling service: a service that provides a stream of random network nodes where no attacking entity can become over-represented. To ensure this security property, current epidemic platforms use a Proof-of-Stake system to select peer samples. However such a system limits the openness of the system as only nodes with significant stake can participate in the consensus, leading to an oligopoly situation. Moreover, this design introduces a complex interdependency between the consensus algorithm and the cryptocurrency built upon it. In this paper, we propose a radically different security design for the peer sampling service, based on the distribution of IP addresses to prevent Sybil attacks. We propose a new algorithm, Bᴀsᴀʟᴛ, that implements our design using a stubborn chaotic search to counter attackers' attempts at becoming over-represented. We show in theory and using Monte Carlo simulations that Bᴀsᴀʟᴛ provides samples which are extremely close to the optimal distribution even in adversarial scenarios such as tentative Eclipse attacks. Live experiments on a production cryptocurrency platform confirm that the samples obtained using Bᴀsᴀʟᴛ are equitably distributed amongst nodes, allowing for a system which is both open and where no single entity can gain excessive power.
### Dates and versions
hal-03131734 , version 1 (05-02-2021)
### Identifiers
• HAL Id : hal-03131734 , version 1
• ARXIV :
### Cite
Alex Auvolat, Yérom-David Bromberg, Davide Frey, François Taïani. $\scriptstyle{BASALT}$: A Rock-Solid Foundation for Epidemic Consensus Algorithms in Very Large, Very Open Networks. 2021. ⟨hal-03131734⟩
### Export
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59 View | 2023-03-21 14:55:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18866057693958282, "perplexity": 5768.492524667637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943698.79/warc/CC-MAIN-20230321131205-20230321161205-00373.warc.gz"} |
https://codereview.stackexchange.com/questions/202175/find-maximum-area-of-island-in-matrix | # Find maximum area of island in matrix
I recently solved the problem below from leetcode:
Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical). Find the maximum area of an island in the given 2D array.
This is how I normally write python code. I am thinking this might not be really Pythonic. Please help review the code.
from operator import add
def max_area_of_island(grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
rlen = len(grid)
clen = len(grid[0])
visited = [[0] * clen for _ in range(rlen)]
max_island = 0
dirs = [(-1, 0), (1, 0), (0, -1), (0, 1)]
cur_i, cur_j = cur_loc
new_i, new_j = tuple(map(add, cur_loc, d))
if new_i >= 0 and new_i < rlen and new_j >= 0 and new_j < clen:
#print("all good")
return new_i, new_j
#print("error")
return -1, -1
max_area = 0
for i in range(rlen):
for j in range(clen):
if grid[i][j] == 0 or visited[i][j]:
continue
area = 1
q = [(i,j)]
visited[i][j] = True
#print("before qsize", q.qsize())
while q:
#print("during qsize", q.qsize())
cur = q.pop()
for _,d in enumerate(dirs):
if new_i < 0 or visited[new_i][new_j]: continue
if new_i >= 0 and grid[new_i][new_j]:
new_loc = (new_i, new_j)
q.append(new_loc)
visited[new_i][new_j] = True
area += 1
max_area = max(area, max_area)
return max_area
Some suggestions:
• Nested functions are unusual; typically they would be neighbour functions instead. This ensures that all the context that each function needs is passed to it, making it easier to grasp the entire context involved in the processing in each function.
• Python 3 supports type annotations, which are a more explicit way of declaring input and output types. You can check that your code is properly annotated using mypy, for example with this rather strict configuration:
[mypy]
check_untyped_defs = true
disallow_untyped_defs = true
ignore_missing_imports = true
no_implicit_optional = true
warn_redundant_casts = true
warn_return_any = true
warn_unused_ignores = true
• Longer variable names can make your code more readable. For example, I can't tell what q is without reading most of the code, and even then it might be unclear, especially since it's an "intermediate" variable (neither a parameter nor a return value).
• You could use a set of constants to define the directions in a more human readable form such as DIRECTION_WEST = (-1, 0).
• Inlining such as if foo: continue is generally frowned upon, since it makes it harder to skim the code vertically.
• Your docstring could include a definition of the problem, possibly by simply copying from the LeetCode website.
• Python has exceptions, and it's recommended to use them rather than special return values to signal a problem.
• "Nested functions are unusual" – I am not a professional Python programmer, therefore some reference supporting this claim would be appreciated. – Martin R Aug 22 '18 at 6:54
• I would simply recommend reading some Python code. I don't think I've seen anyone use nested functions in Python ever before. – l0b0 Aug 22 '18 at 9:28
• @l0b0 When writing decorators they are necessary. But otherwise there are usually better ways to achieve what you want (like passing something as an argument). – Graipher Aug 22 '18 at 11:49
• @I0b0 Thanks a lot for your feedback. I have learned a lot. – wispymisty Aug 24 '18 at 0:52
If you were trying to solve this problem in real life (and not on leetcode), I would use existing tools for this. Specifically, with scikit-image this becomes rather easy:
import numpy as np
from skimage import measure
def largest_island(grid):
labels = measure.label(grid, connectivity=1)
return max(region.area for region in measure.regionprops(labels))
if __name__ == "__main__":
grid = np.array([[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0],
[0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0]])
print(largest_island(grid))
This uses skimage.measure.label to give each connected area a unique label, where areas can only be connected horizontally and vertically, but not diagonally. It then uses skimage.measure.regionprops, which calculates properties of labeled regions.
Unfortunately, scikit-image seems not to be included on leetcode.
• That is so cool. I will learn more standard library also. That is one area I need to seriously upgrade. – wispymisty Aug 24 '18 at 0:52
• @wispymisty While I agree that the standard library is very good, this is unfortunately not part of it. – Graipher Aug 24 '18 at 5:28
Your code is somewhat Pythonic, but could use some improvements.
You seem to be under the impression that you are exploring each island by performing a using a queue (named q). Actually, you are performing a using a stack. (You can't .pop() a queue!)
for _,d in enumerate(dirs) is a pointless use of enumerate(), and it should be written as for d in dirs.
If you name the bounds as rlen and clen, then I would prefer that you use r and c (instead of i and j) for your coordinates.
Your add_dir() function is a bit clumsy. You return (-1, -1) if the result is out of bounds, which means that the caller also has to check whether the result is out of bounds. What you want is a neighbors(r, c) function that lists all of the neighbor coordinates of (r, c) that are in bounds. One Pythonic technique that you can use is to write it as a generator. Another trick is to use chained comparisons (e.g. x < y <= z).
It's a bit uncouth to initialize the elements of visited to 0, then set some of them to True, mixing integers with booleans.
A more readable way to express the goal of the max_area_of_island() function would be:
return max(island_size(r, c) for r, c in product(range(rlen), range(clen)))
… taking advantage of itertools.product() to avoid a nested loop. I have therefore reorganized the code to provide an island_size() function to enable that.
from itertools import product
def max_area_of_island(grid):
rlen, clen = len(grid), len(grid[0])
def neighbors(r, c):
"""
Generate the neighbor coordinates of the given row and column that
are within the bounds of the grid.
"""
for dr, dc in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
if (0 <= r + dr < rlen) and (0 <= c + dc < clen):
yield r + dr, c + dc
visited = [[False] * clen for _ in range(rlen)]
def island_size(r, c):
"""
Find the area of the land connected to the given coordinate.
Return 0 if the coordinate is water or if it has already been
explored in a previous call to island_size().
"""
if grid[r][c] == 0 or visited[r][c]:
return 0
area = 1
stack = [(r, c)]
visited[r][c] = True
while stack:
for r, c in neighbors(*stack.pop()):
if grid[r][c] and not visited[r][c]:
stack.append((r, c))
visited[r][c] = True
area += 1
return area
return max(island_size(r, c) for r, c in product(range(rlen), range(clen)))
• Thank you so much. It shows me how a really pythonic program would work. – wispymisty Sep 7 '18 at 12:41 | 2019-11-22 11:36:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33155566453933716, "perplexity": 1580.9577332986667}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496671249.37/warc/CC-MAIN-20191122092537-20191122120537-00064.warc.gz"} |
http://accessmedicine.mhmedical.com/Content.aspx?bookId=331§ionId=40726950 | Chapter 191
### Classification and Characterization
Enteroviruses are so named because of their ability to multiply in the gastrointestinal tract. Despite their name, these viruses are not a prominent cause of gastroenteritis. Enteroviruses encompass 96 human serotypes: 3 serotypes of poliovirus, 21 serotypes of coxsackievirus A, 6 serotypes of coxsackievirus B, 28 serotypes of echovirus, enteroviruses 68–71, and 34 new enteroviruses (beginning with enterovirus 73) that have been identified by molecular techniques. Echoviruses 22 and 23 have been reclassified as parechoviruses 1 and 2; 12 additional human parechoviruses have been identified. These viruses cause disease similar to that caused by echoviruses. Enterovirus surveillance conducted in the United States by the Centers for Disease Control and Prevention (CDC) in 2007–2008 showed that the most common serotype, coxsackievirus B1, was followed in frequency by echoviruses 18, 9, and 6; together, these four viruses accounted for 52% of all isolates.
Human enteroviruses contain a single-stranded RNA genome surrounded by an icosahedral capsid comprising four viral proteins. These viruses have no lipid envelope and are stable in acidic environments, including the stomach. They are susceptible to chlorine-containing cleansers but resistant to inactivation by standard disinfectants (e.g., alcohol, detergents) and can persist for days at room temperature.
### Pathogenesis and Immunity
Much of what is known about the pathogenesis of enteroviruses has been derived from studies of poliovirus infection. After ingestion, poliovirus is thought to infect epithelial cells in the mucosa of the gastrointestinal tract and then to spread to and replicate in the submucosal lymphoid tissue of the tonsils and Peyer's patches. The virus next spreads to the regional lymph nodes, a viremic phase ensues, and the virus replicates in organs of the reticuloendothelial system. In some cases, a second viremia occurs and the virus replicates further in various tissues, sometimes causing symptomatic disease.
It is uncertain whether poliovirus reaches the central nervous system (CNS) during viremia or whether it also spreads via peripheral nerves. Since viremia precedes the onset of neurologic disease in humans, it has been assumed that the virus enters the CNS via the bloodstream. The poliovirus receptor is a member of the immunoglobulin superfamily. Poliovirus infection is limited to primates, largely because their cells express the viral receptor. Studies demonstrating the poliovirus receptor in the end-plate region of muscle at the neuromuscular junction suggest that, if the virus enters the muscle during viremia, it could travel across the neuromuscular junction up the axon to the anterior horn cells. Studies of monkeys and of transgenic mice expressing the poliovirus receptor show that, after IM injection, poliovirus does not reach the spinal cord if the sciatic nerve is cut. Taken together, these findings suggest that poliovirus can spread directly from muscle to the CNS by neural pathways. Intercellular adhesion molecule 1 (ICAM-1) is a receptor for coxsackieviruses A13, A18, and A21; CAR for coxsackievirus B; VLA-2 integrin for echovirus types 1 and 8; CD55 for enterovirus ...
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Connect to the full suite of AccessMedicine content and resources including more than 250 examination and procedural videos, patient safety modules, an extensive drug database, Q&A, Case Files, and more. | 2017-02-20 15:22:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18089015781879425, "perplexity": 6912.4477579290415}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501170569.99/warc/CC-MAIN-20170219104610-00133-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://admin.clutchprep.com/chemistry/practice-problems/54121/oxygen-can-be-produced-in-the-laboratory-by-160-the-reaction-160-2kclo3-s-8594-1 | # Problem: Oxygen can be produced in the laboratory by the reaction 2KClO3(s) → 2KCl(s) + 3O2(g) .How much potassium chlorate is needed to produce 2.75 L of oxygen, collected over water at 37°C and 94.9 kPa? The vapor pressure of water at 37°C is 6.28 kPa.1. 0.189 mol2. 9.45 × 10−2 mol3. 0.142 mol4. 7.20 × 10−2 mol5. 6.30 × 10−2 mol
🤓 Based on our data, we think this question is relevant for Professor Sahinoglu's class at Auburn University-Montgomery.
###### Problem Details
Oxygen can be produced in the laboratory by the reaction
2KClO3(s) → 2KCl(s) + 3O2(g) .
How much potassium chlorate is needed to produce 2.75 L of oxygen, collected over water at 37°C and 94.9 kPa? The vapor pressure of water at 37°C is 6.28 kPa.
1. 0.189 mol
2. 9.45 × 10−2 mol
3. 0.142 mol
4. 7.20 × 10−2 mol
5. 6.30 × 10−2 mol | 2020-07-02 16:43:48 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.863342821598053, "perplexity": 9925.56369356547}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655879532.0/warc/CC-MAIN-20200702142549-20200702172549-00441.warc.gz"} |
https://hera.ph1.uni-koeln.de/~tac/september_2019.html | #### Supernova driven supersonic turbulence in molecular clouds
The turbulence within molecular clouds has been observed to be supersonic in nature, and in every stage of cloud evolution. Supersonic turbulence decays over the lifetime of a molecular cloud, begging the question what is driving it. One of the possible driving factors is supernovae, which release the sufficient amount of energy to drive turbulence. When the expanding supernova driven shell hits a dense molecular cloud, its kinetic energy is transformed into turbulent energy.
We produce synthetic observations of the SILCC zoom-in simulations (presented in Seifried et. al 2017) using the radiative transfer code RADMC-3D. In these simulation we explode six supernovae at different positions (one in each of the Cartesian direction) at a distance of 25 pc of the center of the cloud. A supernova occurs every 300 kyr and we observe the molecular cloud over a time span of 2.5 Myr.
The figure shows the time evolution of the intensity weighted velocity dispersion with (dashed) and without (solid) supernova explosions for the three different lines-of-sight. Each vertical black line represents the time when a supernova occurs. We can clearly see a sharp increase in velocity dispersion when a supernova occurs, which is followed by a fast decay. This shows that supernovae are able to drive turbulence, but are able to do so only for short timescales. Moreover, the effect is lessened for dense gas tracers (i.e. $^{13}$CO and C$^{18}$O), indicating that it is increasingly difficult to drive turbulence in denser regions of a molecular cloud. | 2022-12-09 19:59:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8094906210899353, "perplexity": 1057.3560848790748}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711475.44/warc/CC-MAIN-20221209181231-20221209211231-00173.warc.gz"} |
http://engineering.blogg.lu.se/tools-widely-used-in-academia-tex-2/ | # Tools widely used in Academia – TeX (2)
In TeX (1), this fantastic writing platform for scientific paper has been introduced. May be some guys are confused that in the “what you see is what you get”-based platform such as Microsoft Word, one can just simply press “ctrl+B” or click “B” button to set the bold format, why would one have to remember \textbf{the text gonna be bold} in LaTex!? Yeah, it seems a bit stupid to use such an unfriendly and complex approach to implement a very simple purpose, but on the other hand, why not ascending upto a big picture? For example, If one have cross-referenced Section 1, Section 2, Section 3 and Section 4, but later on we need insert one more section among them. It is not happy to do more to re-write/update ALL cross-references and section names. However, in Latex we only type \section{section name}, \ref{section label}, which indicates that numeric orders are not used in LaTeX source file and they will be generated automatically after compilation -> re-order them! no extra operations!
As it is in TeX (1), by using online LaTeX, you may have a basic idea that how to write an article of a basic structure. But due to the compilation speed limit or security issues, maybe you are more willing to use a local-software-based LaTeX now. To run LaTex on your computer, the procedure of installation and configuration are quite complex, for detailed instructions please refer to the Appendix in “The Not So Short Introduction to LaTeX” (Available for MacOS, Linux and Windows).
This entry was posted in Uncategorized. Bookmark the permalink. | 2018-05-26 14:10:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8908722400665283, "perplexity": 1739.1586501634665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794867417.75/warc/CC-MAIN-20180526131802-20180526151802-00517.warc.gz"} |
https://www.netket.org/docs/metropolis_hamiltonian/ | # Hamiltonian Moves
## MetropolisHamiltonian
NetKet implements sampling based on the off-diagonal elements of the Hamiltonian. In this case, the transition matrix is taken to be:
where $\theta(x)$ is the Heaviside step function, and $\mathcal{N}(\mathbf{s})$ is a state-dependent normalization. The effect of this transition probability is then to connect (with uniform probability) a given state $\mathbf{s}$ to all those states $\mathbf{s}^\prime$ for which the Hamiltonian has finite matrix elements. Notice that this sampler preserves by construction all the symmetries of the Hamiltonian. This is in general not true for the local samplers.
Parameter Possible values Description Default value
None None None None
### Example
pars['Sampler']={
'Name' : 'MetropolisHamiltonian',
}
## MetropolisHamiltonianPt
This sampler performs parallel-tempering moves in addition to the local moves implemented in MetropolisHamiltonian. The number of replicas can be $N_{\mathrm{rep}}$ chosen by the user.
Parameter Possible values Description Default value
Nreplicas Integer The number of effective temperatures for parallel tempering, $N_{\mathrm{rep}}$ None
### Example
pars['Sampler']={
'Name' : 'MetropolisHamiltonianPt',
'Nreplicas' : 64,
} | 2018-11-20 18:09:18 | {"extraction_info": {"found_math": true, "script_math_tex": 6, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8385041952133179, "perplexity": 1121.2144310727826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746528.84/warc/CC-MAIN-20181120171153-20181120193153-00055.warc.gz"} |
http://mathoverflow.net/questions/101859/a-fourier-analytic-inequality-used-by-jean-bourgain | # A Fourier-analytic inequality used by Jean Bourgain
I am currently reading Jean Bourgain's 1986 paper A Szemerédi type theorem for sets of positive density in $R^k$ and would appreciate some help in understanding a Fourier-analytic estimate used in that article. I suspect that my question is relatively elementary, but my knowledge of Fourier analysis is not very strong and there are no experts in the topic at my current place of work, so I would very much appreciate a pointer.
In Bourgain's argument, $f \colon \mathbb{R}^d \to [0,1]$ is a nonzero measurable function supported in a fixed bounded measurable set $A$, and the $L^2$ norm of $f$ is fixed. For each $\lambda>0$ we define $P_\lambda \colon \mathbb{R}^d \to \mathbb{R}$ to be the function whose Fourier transform $\hat{P}_\lambda(\xi):=\int_{\mathbb{R}^d} e^{-2\pi i \langle x,\xi\rangle} P_\lambda(x)dx$ is given by $\hat{P}_\lambda(\xi)=e^{-\lambda\|\xi\|}$ for all $\xi \in \mathbb{R}^d$. Parameters $\delta, t>0$ are introduced, and the parameter $\delta$ is subsequently fixed at some small value which depends on $\|f\|_2$ (and possibly on $A$) but not on the precise choice of $f$. It is then claimed that by taking $t$ small enough, the quantity $$\|(f * P_{\delta t}) - (f * P_{\delta^{-1}t})\|_2$$ can be made arbitarily small in a manner which is uniform with respect to $f$. It is clear to me that this quantity must converge to zero as $t \to 0$ when $\delta$ and $f$ are fixed, but it is not clear to me why a single value $t$ can be chosen which works simultaneously for all $f$ (where $\|f\|_2$ is fixed and the support of $f$ lies in $A$). Bourgain's paper seems to use a quantitative bound which I infer to resemble $$\|(f * P_{\delta t}) - (f * P_{\delta^{-1}t})\|_2 \leq C\|f\|_2\frac{\log (1/\delta)}{\log (1/t)}.$$ Certainly it is stated that in order to make the above difference small (relative to $\delta^{1/4}$ and $\|f\|_2$) it is sufficient that $\log (1/t)$ should be a large multiple of $\log (1/\delta)$. Can anyone see more precisely what estimate is being used here, or at least how the above quantity can be bounded uniformly with respect to $f$?
Thanks!
-
Just a quick guess: Convolution is linear, Fourier transform is an isometry which converts convolution into product, and then explicit calculation? – Stopple Jul 10 '12 at 15:53
Stopple: I've tried that without achieving anything conclusive. The square of the $L^2$ norm of the difference is $\int_{\mathbb{R}^2} |\hat{f}(\xi)|^2 |e^{-\delta t \|\xi\|}-e^{-\delta^{-1} t\|\xi\|}|^2 d\xi$. As $t \to 0$ the integrand converges to zero pointwise while being bounded by the integrable function $2|\hat{f}(\xi)|^2$ so this converges to zero for fixed $f$ by the Dominated Convergence Theorem, but it is not clear to me why this would be uniform. The supremum over $\xi$ of $|e^{-\delta t \|\xi\|}-e^{-\delta^{-1} t\|\xi\|}|^2$ doesn't depend on $t$ so bounding it also doesn't help. – Ian Morris Jul 10 '12 at 16:17
^^ By "uniform" I mean "uniform with respect to $f$ in the category being considered", and by "2|\hat{f}(\xi)^2|" I mean "4|\hat{f}(\xi)|^2". – Ian Morris Jul 10 '12 at 16:18
I assume you are referring to the argument in page 313 of Jean's paper http://www.springerlink.com/content/a343g53033872345/ . The point here is that the bound does not hold for all $t$, but for a single $t$ (out of $J$ possible choices $t_1,\dots,t_J$); note that Jean crucially refers in the paper to a "suitable" $t$ rather than an arbitrary $t$. This is a pigeonholing argument, based on the estimation of
$$\sum_{j=1}^J \| f * P_{\delta t_j} - f * P_{\delta^{-1} t_j} \|_{L^2}^2$$
which can be done by Plancherel's theorem and routine computations (if the $t_j$ are lacunary, as noted in Jean's paper). | 2016-02-09 01:51:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480775594711304, "perplexity": 135.73160560654406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701155060.45/warc/CC-MAIN-20160205193915-00153-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://www.physicsforums.com/showthread.php?s=881a2c489fe9dbedbfad13564f2a98cd&p=4426778 | # Accurate position change for accelerating objects
by Droctagonopus
Tags: accelerating, accurate, change, objects, position
P: 22 If an object is subject to different forces at different times and these forces are totally unpredictable (the force at any instant after the current time cannot be predicted). How would we make the position change due to acceleration as accurate as possible? I have chosen a method but I've encountered a problem. Use $x_{2}=\frac{1}{2}at^{2}+vt+x_{1}$ where a is the instantaneous acceleration, v is the instantaneous velocity, $x_{1}$ is the position at the current time and t is a very small time interval. However, I need a way to find the same position value after unequal time intervals. Meaning that if I take a single 2 ms interval in one case and two 1 ms intervals in another, the final value doesn't have to be too accurate but it has to be the same for both cases. Is there an efficient way to do this?
Mentor P: 10,519 You will need some model how your accelerations look like. Different step sizes are not an issue with your formula, if you know an average acceleration within (small) timesteps.
Related Discussions General Physics 3 General Physics 1 General Physics 40 General Physics 0 | 2014-03-09 20:12:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4487094581127167, "perplexity": 353.2445396017795}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010303377/warc/CC-MAIN-20140305090503-00068-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-abs-2-3x-9-18 | # How do you solve abs(2/3x-9)=18?
May 19, 2017
$x = - \frac{27}{2}$
$x = + \frac{81}{2}$
#### Explanation:
For this to work we have to end up with $| \pm 18 | = + 18$
This means that $\text{ } \frac{2}{3} x - 9 = \pm 18$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Case 1: $\text{ } \frac{2}{3} x - 9 = + 18$
$\frac{2}{3} x = 27$
Multiply both sides by $\frac{3}{2}$
$x = \frac{3}{2} \times 27 = 40 \frac{1}{2} \to \frac{81}{2}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Case 2: $\text{ } \frac{2}{3} x - 9 = - 18$
$\frac{2}{3} x = - 9$
$x = \frac{3}{2} \times \left(- 9\right) = - \frac{27}{2}$ | 2021-06-20 01:06:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9690009951591492, "perplexity": 1975.9866066192048}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487653461.74/warc/CC-MAIN-20210619233720-20210620023720-00287.warc.gz"} |
http://openelectrical.org/wiki/index.php?title=Dry-Type_Transformer_Testing | Dry-Type Transformer Testing
Introduction
The primary concern with all transformers (and also the key indicator of life expectancy) is the condition of the insulation system.
For dry type transformers, the insulation system consists of the cast resin winding and core insulation and the termination system insulation (e.g. bushings). The structural strength and insulating properties of materials used for these insulation systems degrade over time through normal ageing. They can also degrade prematurely as a result of overheating and mechanical and electrical stresses (e.g. faults, overvoltages, inrush currents, etc).
The initial breakdown of insulation around the windings can result in inter-turn faults, especially on the high voltage windings where the electric field strength is high enough to ionise air gaps and cause corona activity. Inter-turn faults are short circuits between coil turns on a single winding. Further degradation of the insulation could see inter-turn faults develop into more serious faults such as inter-winding and earth faults.
Testing
The most frequent mode of failure for dry type transformers is insulation breakdown resulting in inter-turn faults which leads to more severe faults such as phase to phase winding or earth faults. The insulation condition of component parts of the transformer (i.e. windings, core, bushings, etc) can be determined by a suite of tests.
Dissolved gas analysis is the most commonly used method for determining winding insulation condition in oil-type transformers, but is not possible for dry-type transformers.
The following tests are discussed further:
• Insulation resistance / polarisation index tests
• Dielectric loss angle measurement tests
• Partial discharge tests
• Frequency response analysis
• Acoustic emission tests (in conjunction with partial discharge tests)
• Thermographic surveys
Insulation Resistance Tests
Insulation resistance, measured by application of an impressed DC voltage (i.e. Megger), gives a general indication of the insulation condition between the phase windings and earth. The measurements are typically taken over time (i.e. 1 minute intervals over 10 minutes) to generate a curve, called the Dielectric Absorption curve.
The Polarisation Index is the steepness of the curve at a given temperature and is defined as per the following equation [1]:
$PI = \frac{R_{10}}{R_{1}}$
Where
R10 = megohms insulation resistance at 10 minutes
R1 = megohms insulation resistance at 1 minute
The Polarisation Index indicates the relative dryness and level of moisture ingress into the insulation.
Dielectric Loss Angle Measurement Tests
Dielectric loss angle tests, also called dissipation factor, power factor or tan delta tests, determine the insulation dielectric power loss by measurement of the power angle between an applied AC voltage and the resultant current. In the ideal insulator, the power angle would be 90°C as it is purely capacitive and non-conducting. However in real insulators, there is some leakage current and resistive losses through the dielectric.
Relative increases in dielectric power losses are indicative of insulation deterioration and may further accelerate degradation due to increased heating. Note that dielectric power loss does not translate to dielectric strength, though there are often common causes for increases in power loss and decreases in dielectric strength.
The cosine of the power angle (θ) is called the power factor. The complement of θ is denoted δ as shown in the diagram above. The power factor can be practically approximated by taking the tangent of δ (hence the name tan delta). This approximation is called the dissipation factor and is roughly equal to the power factor between values of 0 and 0.08, which covers the majority of tests.
The dissipation factor is essentially the ratio between the resistive and capacitive components of the insulation and can be measured directly (via a capacitance bridge circuit). The lower the quality of the insulation condition, the more resistive it will appear and the more power loss will be dissipated through it (in the form of heat).
The increase in the dissipation factor values as the test voltage is increased is called the "tip-up".
The technical literature on this subject has noted that this test is useful for detecting moisture ingress in the bushings and windings. About 90% of bushing failures may be attributed to moisture ingress evidenced by an increasing power factor from dielectric loss angle testing on a scheduled basis.
Partial Discharge Tests
Partial discharges are localised incipient electrical discharges that only partially bridge the insulation between conductors. Partial discharges can occur in any location where the local electrical field strength is sufficient to breakdown that portion of the dielectric material (whether it be deteriorated insulation or air). In dry-type transformers they can occur within air-filled voids where the solid insulation has degraded.
Partial discharge testing can detect the presence and location of partial discharge activity in a transformer. Partial discharges in transformers are typically measured by applying a pre-specified voltage to the transformer windings and measuring induced charges via a coupling device (e.g. coupling capacitors).
AS 60076.11 and AS 60270 set out the requirements, procedure, equipment and acceptance levels for partial discharge testing [3] [4]. It should be noted that the partial discharge tests specified in AS 60076.11 are intended as routine tests for new transformers. This involves applying a “pre-stress” voltage of 1.8 times rated voltage to the windings. This may be excessive for transformers already in service for over 20 years.
Analysis of the partial discharge measurements gathered (i.e. pulse waveforms, magnitude, duration and intervals between pulses) can be used as a guide regarding the condition of the insulation. The results can be trended to chart the rate of insulation degradation between consecutive tests.
Frequency Response Analysis
Frequency response analysis is a diagnostic testing technique that measures the impedance of the transformer windings over a wide range of frequencies. The measurements are compared with a reference set and the differences are highlighted. The differences may indicate mechanical damage to the windings (e.g. winding displacement or loose winding) and electrical faults (e.g. interturn faults).
Frequency response analysis can be achieved by either injecting a low voltage impulse into the winding (i.e. impulse response method) or by making a frequency sweep using a sinusoidal signal (i.e. swept frequency method).
For frequency response analysis to be useful, a baseline reference set of measurements need to be determined and periodic tests need to be conducted to compare the differences.
Refer to research by S. Tenbohlen et al at the University of Stuttgart [5].
Acoustic Emission Tests
Partial discharges in transformers can also be detected and localised via acoustic emission testing. Acoustic emission testing is based on the acoustic detection of the partial discharge pulses and conversion to an electrical signal. Sensors are coupled to the surface of the transformer and during operation of the transformer, the output of the sensors are fed into an electronic module. The signals are filtered to remove noise and processed to determine the presence and location of any partial discharges in the transformer.
Thermographic Surveys
Infrared thermography is commonly used in preventative maintenance to detect hotspots, especially at joints and terminations. IR Thermography cameras measure surface temperatures and the resulting thermal image can be used to identify overheating at the transformer terminations.
For thermographic surveys to be conducted, thermographic windows need to be installed looking at the terminations and windings.
References
1. Facilities Instruction, Standards and Techniques Volume 3-1, “Testing Solid Insulation of Electrical Equipment”, U.S Department of the Interior, Reclamation Branch, December 1991
2. Facilities Instruction, Standards and Techniques Volume 3-31, “Transformer Diagnostics”, U.S Department of the Interior, Reclamation Branch, June 2003
3. AS 60076.11, “Power transformers Part 11: Dry-type transformers”, 2006
4. AS 60270, “High-voltage test techniques – Partial discharge measurements”, 2001
5. Research at University of Stuttgart (including Tenbohlen's papers) | 2017-03-23 14:11:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6270138621330261, "perplexity": 2666.658111428245}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218187113.46/warc/CC-MAIN-20170322212947-00270-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/223566/construct-tangent-to-a-circle | # Construct tangent to a circle
Using a ruler and a compass how can construct a line through a point and tangent to a circle. What I don't want is to eyeball the line by trying to line-up the ruler over the circle. Best if I could construct the point of intersection first and then draw the line.
PS. I know how to do it mathematically, I just don't know the steps for geometry, given A, C and the circle to find D.
Update Based on answers here is the constructors. Thanks for the quick responses.
-
You could look at mathopenref.com/consttangents.html – Ross Millikan Oct 29 '12 at 17:39
Draw a Thales circle over the segment $AC$, it will intersect the desired $D$, because $AD\perp DC$:
1. Draw the segment $AC$.
2. Construct its midpoint $F$.
3. Draw a circle with origin $F$ and radio $FA(=FC)$.
-
Intersect the circle having $AC$ as a diameter with the initial circle: you will find the two points $D,D'$ such that $CD$ and $CD'$ are tangent to the initial circle. This comes from the fact that the circle is the locus of points that "see" any diameter under an angle equal to $\frac{\pi}{2}$.
-
1. From AC, find its midpoint F.
2. Draw the circle using F as center and FA (or FC) as radius.
3. The point(s) of intersection of the circles is D.
-
Thanks, but how is this answer different from the one Berci provided? – ja72 Aug 12 '13 at 17:30
@ja72, Yes but have the extra description cut. – Mick Aug 22 '13 at 12:56 | 2015-05-29 15:15:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7723462581634521, "perplexity": 488.6365219822284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930143.90/warc/CC-MAIN-20150521113210-00104-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://blog.mcs.io/isolated-margin-cross-margin-en/ | # MCS | Isolated Margin vs Cross Margin
Welcome to MCS, the world-class derivatives trading platform where traders ALWAYS come first.
Traders who do perpetual trading use different trading strategies. MCS supports two types of orders: isolation margin and cross margin. These two types of orders differ from the concept to the formula for liquidation and position margin. In this article, we would like to compare these order types.
### Isolated Margin
Traders will allocate their margin on an order-by-order basis. If a trader is liquidated, only the margin allocated will be affected and the remaining wallet balance rests unaffected.
### Cross Margin
Cross margin is a way of trading with the entire available Wallet Balance. The maximum contract size of the cross margin is determined by the maximum leverage allowed for a trading pair. Leverage depends on the initial margin of the position. In other words, the larger the initial margin, the lower the leverage used by the traders. In addition, the position is closed when the position margin reaches the maintenance margin level. In cross margin, the system automatically determines the trader's leverage according to the amount of contracts submitted.
Did you notice the difference between Isolated Margin and Cross Margin? Isolated Margin can prevent rapid balance loss, while Cross Margin is less limited in terms of asset management since it uses up the whole wallet balance.
Since Position Margin is an essential asset in order to open positions, a trader who buys Isolated or Cross Margin should check the amount of assets he or she must have and start trading. So let's look at how assets are calculated for each transaction.
<Position Margin Formula>
### Isolated Margin
$$\small\textsf{Position Margin (Isolated)} = \textsf{Initial Margin} + \textsf{Taker Fee to Close} + \textsf{UPNL}$$
### Cross Margin
$$\small\textsf{Position Margin (Cross)} = \textsf{Initial Margin} + \textsf{Fee to Close} + \textsf{Unrealized Profit}$$
$$\text{Position Margin (Cross)} = \text{Initial Margin} + \text{Fee to Close} + \text{Unrealized Profit}$$
$${\small \text{Initial Margin} = {{\text{Quantity} \times \text{Multiplier}} \over {\text{Avg. Entry Price} \times \text{Leverage}}}}$$
$${\small \text{Taker fee to close} = {{\text{Quantity} \times \text{Multiplier}} \over \text{Bankruptcy Price calculated with Order Price}} \times \text{Taker Fee Rate}}$$
As we mentioned in the last article, one of the things that the traders should keep in mind is liquidation. Let's take a look at the liquidation process and formula for each order type. In this article, we will only cover the long position, but if you would like to learn more about the short position's, please refer to the MCS Zendesk.
<Isolated Margin Liquidation Process>
1. When the Mark Price reaches the liquidation price, the position is taken over by the liquidation engine.
2. The liquidation engine takes the position and liquidates the position to the bankruptcy price.
3. Reduce risk limit and carry out liquidation process step by step.
Note) The liquidation engine tries to prevent contract losses by closing the position at the bankruptcy price. However, in volatile or non-liquid markets, the position may be closed at a price worse than the bankruptcy price. In the event of such contract loss, the insurance fund will primarily act to prevent the loss, and if the insurance fund has insufficient funds, the position will be handled through auto deleveraging.
<Cross Margin Liquidation Process>
Cross margin secures margin to delay liquidation in the following ranks. The position is liquidated when all four ranks are progressed.
#1 Available Balance
#2 Reduce Risk Limit Level
#3 Cancel all Active Orders in the same direction
#4 Cancel all Active Orders in other directions
<Liquidation Formula>
### Isolated Margin Liquidation Price Formula - Long Position
$$\textsf{Isolated Margin Liquidation Price (Long)} ={{\textsf{Avg. Entry Price} \times \textsf{Leverage}} \over \textsf{Leverage(1 - Maintenance Margin Rate) + 1}}$$
$$\text{Liquidation Price (Isolated)} ={{\text{Avg. Entry Price} \times \text{Leverage}} \over \text{Leverage(1 - Maintenance Margin Rate) + 1}}$$
### Cross Margin Liquidation Price Formula - Long Position
$$\small\textsf{Cross Margin Liquidation Price (Long)}$$
$$\small = {{\textsf{Avg. Entry Price} \times \textsf{Quantity}} \over {\textsf{Quantity(1 - Maintenance Margin Rate} - {\textsf{Avg. Entry Price} \times \textsf{Taker Fee Rate} \over \textsf{*Bankruptcy Price}}) + {\textsf{Available Balance}\times\textsf{Avg. Entry Price}}}}$$ | 2021-10-19 05:03:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5467937588691711, "perplexity": 2821.8275167534894}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585242.44/warc/CC-MAIN-20211019043325-20211019073325-00123.warc.gz"} |
http://cryptologie.net/home/all/28 | Hey! I'm David, a security consultant at Cryptography Services, the crypto team of NCC Group . This is my blog about cryptography and security and other related topics that I find interesting.
# Bullrun
## posted November 2013
Bullrun or BULLRUN is a clandestine, highly classified decryption program run by the United States National Security Agency (NSA). The British signals intelligence agency Government Communications Headquarters (GCHQ) has a similar program codenamed Edgehill. According to the NSA's BULLRUN Classification Guide, which was published by The Guardian, BULLRUN is not a Sensitive Compartmented Information (SCI) control system or compartment, but the codeword has to be shown in the classification line, after all other classification and dissemination markings. Information about the program's existence was leaked in 2013 by Edward Snowden.
from https://en.wikipedia.org/wiki/Bullrun_%28decryption_program%29" target="_blank">wikipedia.
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# Sudoku Solver
## posted November 2013
My Programmmation class first part is about coding a sudoku solver. We have to do everything in english, we have to commit with svn, we have to write a final report with LaTeX.
Every week we're given some vague guidelines and we have to dive deep into C to first, understand what we have to do, and secondly, find solutions in a language we've never really played with before. We have to turn in what we did every week, if our code doesn't compile it's a zero, if it does compile it goes through a multitude of tests that quickly decrease your grade (out of 20). Let's just say I spent many nights and early mornings coding and I started the first week with a 2/20.
It felt like a crash course, it felt unfair at times, but holy cow did I learn some C in a really short amount of time. Props to my professor for that, and I wish I had more courses like that. I might not get the best grade out of this course but I sure learn the most things there.
I've also committed everything I've done on a public git repo so everyone can see how it looks like here :
https://github.com/mimoo/sudoku
You can compile with make, learn how to use with ./sudoku -h
It can read sudokus of different sizes from 1x1 to 64x64 as long as it is presented like this :
#this is a comment
5 3 _ _ 7 _ _ _ _
6 _ _ 1 9 5 _ _ _
_ 9 8 _ _ _ _ 6 _
8 _ _ _ 6 _ _ _ 3
4 _ _ 8 _ 3 _ _ 1
7 _ _ _ 2 _ _ _ 6
_ 6 _ _ _ _ 2 8 _
_ _ _ 4 1 9 _ _ 5
_ _ _ _ 8 _ _ 7 9
# One more list
## posted November 2013
It's time for a new list of random things I noticed about Bordeaux :
• Many 2€ kebab places. Also, kebab here are made with a Lebanese bread, like a crepe, and not with the half of an Arabic bread like in Lyon.
• It's raining, A LOT. It's raining at least once a week, but usually way more than once a week.
• It's not that cold. I just came back from a week in Lyon and oh my god was it cold there, you can feel winter coming, but in Bordeaux ? Chill, you don't need that jacket.
• There are no Bordelais. Most people I run into come from other places in France. I actually only met one Bordelaise and it was during my first week here.
• The city is really not that big. In 30 minutes you feel like you've seen most of it.
• We have Velov' in Lyon, Velib' in Paris, here it's Vcub. Those free bikes you can rent pretty much anywhere.
# What is it like in Bordeaux?
## posted October 2013
So, I've been living here for a month and here is my list of what it is to live in Bordeaux.
• People say "chocolatine" instead of "pain au chocolat" and "poche" instead of "sac". It's kind of weird, especially when I have to say it, I'm always scared that they can tell I'm not from here, which is a stupid thing to be scared of, I had the same kind of feeling when I was living in Canada or China and didn't have the same accent as the locals, but it's weirder having that feeling in my own country.
• Streets are dirty, really dirty, you will always have to avoid dog poops when you go somewhere. Sidewalks are very small so you also always have to walk directly on the road.
• The city is pretty small. It's easy to get around. But when something is a bit far, it's annoying to get there since there is no subway.
• The public transportation system is horrendous, every morning I have to get squished by a thousand students taking the same tramway, most of the time I miss several trams because there are too many people inside, my personal record is seeing five tram passing without being able to enter them. Pretty annoying.
• Not so much accent here, but people say "gavé" a lot, it means "very". For example "c'était gavé bien hier soir".
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# SecureDrop
## posted October 2013
SecureDrop is an open-source whistleblower support system, originally written by Aaron Swartz and now run by the Freedom of the Press Foundation. The first instance of this system was named StrongBox and is being run by the New Yorker. To further add to the naming confusion, Aaron Swartz called the system DeadDrop when he wrote the code.
from Schneier's blog
You can find http://deaddrop.github.io/" target="_blank">the website here and if you have something important to submit and do not want to go through Wikileaks, I think this is the best alternative.
The security audit was done by Schneier himself, who is pretty popular in the cryptography community, the work was started by Aaron Swartz who is also extremly popular, especially since his suicide last year.
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# New effort to fully audit TrueCrypt raises \$16,000+ in a few short weeks
## posted October 2013
I just learned that TrueCrypt, the multi-OS solution to encrypt your personal data in a "very easy way" is coded and maintained by ... no one knows. Like bitcoin, the main creators are anonymous. http://www.truecrypt.org/downloads2" target="_blank">The source code is available here but no info about the coders can be found.
It seems like folks are getting a bit worried as TrueCrypt is wildly used, and money is being raised to conduct a security audit on them. http://arstechnica.com/security/2013/10/new-effort-to-fully-audit-truecrypt-raises-over-16000-in-a-few-short-weeks/" target="_blank">More info here.
Now I'm wondering, why is it that those huge cryptographic applications, that are polished and well maintained, are created by anonymous persons? Do they fear they would get pressure from governments? Mafia? Who knows...
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# Baidu now accepts bitcoins!
## posted October 2013
It's official, http://www.baidu.com" target="_blank">Baidu, the chinese google, now accepts bitcoins.
"As a cutting-edge IT guy and a professional webmaster, what else can showcase our difference? The answer is that we have Bitcoin! Bitcoin, as a new electronic and digital currency, is being accepted internationally. It's also used in daily lives. You can use Bitcoin buy a cup of coffee, or easily convert it to cash. But in China, Bitcoin is still a fairly new thing. Today, we have a good news: from today, we are starting to officially accept Bitcoin as a payment method. You can use Bitcoin to buy all Baidu Jiasule services. Baidu Jiasule as an innovator in the Internet industry, is now the first cloud service provider to accept Bitcoin and give everyone a better payment method and experience."
The bitcoin who has been remarkably stable these past weeks, even after the silk road shutdown, has increased a bit more since the announcement.
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# Elliptic Curve Cryptography (ECC)
## posted October 2013
a great video I bookmarked about ECC.
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# Silk Road caught, Tor compromised?
## posted October 2013
Silk Road and its owner have just http://www.reuters.com/article/2013/10/02/crime-silkroad-raid-idUSL1N0HS12C20131002" target="_blank">got caught by the FBI. If you didn't know, silk road (an illegal drug market) was hosted on the Tor network as an onion website, which was suppose to grant him total anonymity. Apparently the catch was made from a stupid human mistake :
1) Located the first reference to "silk road" on the internet. You can find this yourself on Google: "silk road" site:shroomery.org Date range: Jan 1,2011 - Jan 31,2011 * 2) The same username, "altoid", showed up on a bitcointalk days later. 3) Later in 2011 "altoid" made a post on bitcointalk with his email address, containing his real name, in it: https://bitcointalk.org/index.php?topic=47811.msg568744#msg5... If you search the name on Google it doesn't show up, but if you look at the user's page you can see it in his posts.
But some are skeptical, and many seems to think it could have been http://www.theguardian.com/world/2013/oct/04/tor-attacks-nsa-users-online-anonymity" target="_blank">the NSA getting into the Tor Network. What do you think?
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# RSA-210 has been factored!
## posted October 2013
The https://en.wikipedia.org/wiki/RSA_Factoring_Challenge" target="_blank">RSA Factoring Challenge has had one of its entry factored : RSA-210. More info here.
The RSA Factoring Challenge was a challenge put forward by RSA Laboratories on March 18, 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers and cracking RSA keys used in cryptography. They published a list of semiprimes (numbers with exactly two prime factors) known as the RSA numbers, with a cash prize for the successful factorization of some of them. The smallest of them, a 100 decimal digit number called RSA-100 was factored by April 1, 1991, but many of the bigger numbers have still not been factored and are expected to remain unfactored for quite some time.
The challenge is no longer active, this means no money for this brave Ryan P. And this doesn't mean RSA is less secure so no worries :)
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# Dread Pirate Roberts response to Atlantis' shutdown
## posted September 2013
For someone like me who has some money invested in bitcoins and other cryptocoins (especially litecoin), seeing Atlantis rising (a drug market using litecoin as the main currency) was a very good news. Sadly they had to shutdown months after not doing so much for the https://btc-e.com/exchange/ltc_usd" target="_blank">LTC value.
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# Start of the school year
## posted September 2013
time table imported to google cal thanks to hackjack's fabulous application
I have at the moment 5 classes which are all taught in french (I guess because there are not enough foreigners this year), but some of them use english for their slides.
### Programmation
Nothing really new to me, some people coming from the same bachelor as I (mathematics) have difficulties getting to know Linux and programming as a whole for the first time. I'm used to coding so I'm pretty confident (I shouldn't relax too much though). We started on a fast-course on C, GCC, Emacs, SVN... and will move on later with Java. It's taught by Emmanuel Fleury who is a very chill professor, good vibe, very easy to talk to. And the best part is that everything he talks about is online here so if you're interested in the course I'm taking you can have a look there. PS: we're learning a bit of LaTeX AND will have to submit final reports in LaTeX. This is great as I have sought a good occasion to learn it for a while. PS2: I'm using LearnXinYminutes.com to get back into C (haven't coded in C for more than 4 years). It's a great website and I recommend it to you if you want to learn something about any language and already have knowledge in programming.
### Théorie de l'information
Taught by the head of the Cryptology Master, Gilles Zemor, the course seems like an introduction to some of the concepts around Cryptography. Our first classes were about Entropy (which I talked about a bit in the previous post) and easy notions of probability. Here are the professor's notes about the course.
### Arithmétique
The only "real" Math course we have, and I'm a bit surprised since this is a "Mathematics" Master". It's essentially about rings, it's about stuff I already learned. Nothing really captivating at the moment.
### Automates et Complexité
This is one of the most intriguing course, people coming from an IT bachelor seem to have no problem with it. I don't really understand the point of learning this but I like it, it's a lot like Regular Expressions and is about logic more than learning concepts by heart. As a programmer it just seems like funny games to me :) (it might get more difficult very quickly). Note : it's taught by Anca Muscholl.
### Réseaux
The only course I had to choose, but we didn't have much choice since they removed half of the available courses including the one I wanted to take (Probability). The course is taught by... it's a rapid introduction about network concept. I'm not really into it, it speaks too briefly about many things, some are interesting, some are not. I was supposed to have an application class but apparently our professor fell asleep on his way (he's narcoleptic). Overall I was surprised by the absence of real "cryptology courses". But the professors told us they would come very quickly in the second semester, so nothing to worry about. comment on this story
# Moving to Bordeaux !
## posted September 2013
I successfully found a new place after less than two weeks of exhausting research. It's a pain looking for a place in Bordeaux, a real pain, and fortunately I'm french (I've seen lots of places that wouldn't take foreigners). But I found a place! After squatting at Amandine's place and at a very cool German guy I met here, I finally found my new home. It's a cozy place in St Michel, the Arab district, it's a very lively area only a few minutes away from the center. The city has been a wonderful experience to me, it's like a miniature Lyon. I'm just minutes away from the bars, from my friends, from the stores AND above all, I don't have to take the subway, which is the worse part of living in a city (or so I think). Classes have started as well but waking up at 8 am everyday is pretty hard (and next to impossible with all the people I'm meeting who want to party every nights). Fortunately, the campus is way cozier than the one of Lyon 1 (which I strongly disliked) and classes never exceed 2 hours (still not the 50 minutes classes of McMaster (Hamilton) but still better than the 3 hours classes of Lyon 1). It's just been two weeks but it feels like I've already spent an eternity here. It's kinda scary knowing that I'll never live again in Lyon, but it's exciting to know that I now have a new home, a new life. comment on this story
# Encryption is less secure than we thought
## posted August 2013
A group of researchers at MIT just http://www.mit.edu/newsoffice/2013/encryption-is-less-secure-than-we-thought-0814.html" target="_blank">released a paper reconsidering a common mathematical assumption in Cryptography. This means, as the title implies, than most encryption systems are less secure than we thought, but not to worry, nowhere is it written the word "insecure" and it might really be negligible.
The problem here seems to be the definition of Entropy used.
In computing, entropy is the randomness collected by an operating system or application for use in cryptography or other uses that require random data. This randomness is often collected from hardware sources, either pre-existing ones such as mouse movements or specially provided randomness generators. The Famous Wikipedia
In information theory, entropy is a measure of the uncertainty in a random variable.[1] In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message.[2] Entropy is typically measured in bits, nats, or bans.[3] Shannon entropy is the average unpredictability in a random variable, which is equivalent to its information content. Shannon entropy provides an absolute limit on the best possible lossless encoding or compression of any communication, assuming that[4] the communication may be represented as a sequence of independent and identically distributed random variables. The Famous Wikipedia
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https://math.stackexchange.com/questions/704585/alias-alibi-in-permutation-groups | # Alias/alibi in permutation groups
This question came up in teaching a course on basic group theory to high school students.
I gave the class the task of enumerating as many subgroups as they could find in $S_4$ and in the group $O$ of rotations of the cube. The students became suspicious that the groups were isomorphic, and came up with the idea of considering the rotations' actions on the cube's long diagonals to get a map $f:O\rightarrow S_4$, which they (rightly) suspected was an isomorphism.
The conversation stalled out when they tried to prove that it was an isomorphism. I directed them first to the question of whether $f(xy)=f(x)f(y)$, figuring that this would make it easier to deduce injectivity or surjectivity, e.g. by finding generators in the image. However, they were already stuck on whether $f(xy)=f(x)f(y)$, although when they actually calculated $f(xy)$ and $f(x)f(y)$ for two or three pairs of rotations $x,y$ (which involved some intense visualizing work to compose the rotations in 3-space, since they do not know about matrices), the answers did match. As I listened to them talk about it, I realized that there were some subtleties here having to do with the way we labeled the group elements that made me realize there was something fundamental I wanted to understand better here too.
I want to get to the bottom of this. Here's the setup:
We were looking at rotations of the cube in terms of a fixed coordinate system; you could see them as alibi transformations. Thus, for example, although we didn't do this, you could see the cube as the one with vertices $\{\pm 1,\pm 1,\pm 1\}$ in $\mathbb{R}^3$, and $O$ as the group generated by matrices
$$x=\begin{pmatrix} & &1\\1& & \\ &1& \end{pmatrix},\; y=\begin{pmatrix}1& & \\ & &-1\\ &1& \end{pmatrix}$$
The point is that we imagine that the coordinate system is fixed, the group elements are fixed alibi transformations in the coordinate system, and the cube is being moved around.
Meanwhile, we were writing down the permutations as functions from the index set $\{1,2,3,4\}$ to itself, and composing them accordingly, using the right-to-left convention of function composition. $(123)$ applied to $1$ equals $2$, etc.
The map $f$ was given by choosing some labeling on the long diagonals of the cube in its initial position, for example $\overline{(-1,-1,-1)(1,1,1)} = 1$, $\overline{(1,-1,1)(-1,1,-1)} = 2$, $\overline{(1,-1,-1)(-1,1,1)} = 3$, and $\overline{(1,1,-1)(-1,-1,1)} = 4$. Then for a given rotation $\rho$, defining $f(\rho)$ as the permutation that describes where $\rho$ sends each index when the cube is in its original position.
To illustrate, in the present example, this means $y\mapsto (1234)$, for example, and $x\mapsto (243)$. We have
$$xy = \begin{pmatrix} & &1\\1& & \\ &1& \end{pmatrix}\begin{pmatrix}1& & \\ & &-1\\ &1& \end{pmatrix} = \begin{pmatrix} &1& \\1& & \\ & &-1\end{pmatrix}$$
and $f(xy) = (14)$. Meanwhile, $f(x)f(y) = (243)(1234) = (14)$ (remember that we are composing permutations right to left).
Thinking about both the permutations and the rotations as functions, in the former case on the set of indices and in the latter case on the cube, and the action can be restricted to the long diagonals, it is clear (obvious) to me why $f$ is a homomorphism. All $f$ does is it records what a rotation $\rho$ does to the diagonals. So $f(\rho\eta)$ is what $\eta$, followed by $\rho$, does to the diagonals, and $f(\rho)f(\eta)$ is what $\eta$ does to the diagonals followed by what $\rho$ does to the diagonals. These are obviously the same.
But there is another way of thinking about it that I can engage in that confuses me about this, and I can't quite sort through where the problem is. Furthermore, this (clearly wrong) way of thinking deals with some issues that the above doesn't engage at all. So my question is:
(A) What is wrong with the following train of thought? (B) Can you explain in terms that engage with this train of thought why $f$ is a homomorphism?
As above, think of the group $O$ as acting on the cube by rotations in a fixed coordinate system. $\rho\in O$ refers to a rotation with reference to the fixed coordinate system; changes in orientation of the cube do not affect the meaning of $\rho$.
Choose an initial orientation of the cube, and a labeling of the long diagonals, as above. For each $\rho\in O$, write down the permutation $f(\rho)$ that describes the action of $\rho$ on the long diagonals in this initial orientation.
Now consider $f(\rho\eta)$. $\eta$ moves the diagonals somewhere, $\rho$ moves them again, and $f$ writes down what the composition did, in terms of the original orientation of the cube.
On the other hand, consider $f(\rho)f(\eta)$. $f(\eta)$ is unproblematic; it writes down what $\eta$ did to the diagonals, which is the same as before. But now the diagonals are in new spots, so when $\rho$ acts on them, it will not do the same thing it did when it acted on the cube in its original orientation. Thus what $\rho$ does to the diagonals after $\eta$ has been applied will not be the same as $f(\rho)$, which is trying to describe what $\rho$ did to the diagonals in their original orientation. Thus $f(\rho)f(\eta)$ should come out to something different.
Empirically, this logic is wrong, and furthermore it contradicts the above logic explaining why $f$ is (obviously) a homomorphism. I assume there is some kind of alias/alibi confusion in it. Be that as it may, I can't shake it completely. Can you help? An ideal answer would both explain where the fallacy is and also give a correct explanation of what's going on that engages with the alias/alibi issues in the fallacious logic.
• I suspect this is the same sort of confusion that happens when dealing with the "Fifteen puzzle" with numbered tiles. The tiles are numbered 1-15 (and a 16th empty space is blank, but maybe it is a good idea to label it 16). The moves involving moving adjacent tiles into the blank spot, so every move is a transposition of the form $(n,16)$ where $n$ is some tile next to the blank. -- How do you describe this in terms of a group, since the moves available change as the blank moves around? – Jack Schmidt May 16 '14 at 18:00
• "But now the diagonals are in new spots, so when $\rho$ acts on them, it will not do the same thing it did when it acted on the cube in its original orientation. Thus what $\rho$ does to the diagonals after $\eta$ has been applied will not be the same as $f(\rho)$, which is trying to describe what $\rho$ did to the diagonals in their original orientation." .... This reads like gibberish to me, I have no idea what you're talking about. With $S_4$ acting on $\{1,2,3,4\}$, when considering what $\rho\sigma$ does, is it worrisome that nothing is in "its original position" after applying $\sigma$? – blue May 21 '14 at 2:43
• I think a key point of evidence is missing. How exactly did you work it out "empirically"? – marshal craft Dec 4 '15 at 5:53
• @marshalcraft - see the paragraph that begins "To illustrate..." The calculation in $O$ is done with standard matrix multiplication and the calculation in $S_4$ is done with standard permutation composition, adopting the right-to-left composition convention. – Ben Blum-Smith Dec 9 '15 at 5:24
• If you have two linear transformations $A$ and $B$, then consider the composition of them $AB$, the inverse of the coordinate change is $B^{-1}A^{-1}$ but what is $A^{-1}B^{-1}$? – marshal craft Dec 10 '15 at 8:05
Answer to (A) It is ambiguous and confusing to say that $f(\rho)$ “records what $\rho$ does to the diagonals” without distinguishing between diagonals as fixed positions in space and diagonals as movable objects in space, see below.
Answer to (B) Distinguish between a “geographical”, “unmovable”, “absolute” cube made of four “absolute” diagonals $AD_1,AD_2,AD_3,AD_4$ and a moving cube made of four “physical”, “movable” diagonals (we will call them rods) $MD_1,MD_2,MD_3,MD_4$. In every “reachable” position, each rod $MD_j$ has a unique location among the $AD_i$.
What does $f(\rho)$ express in this context ? If $f(\eta)$ sends $i$ to $j$, $\eta$ is to move the rod located in $AD_i$ (let us call it $r$) and put it at $AD_j$. In turn, if $f(\rho)$ sends $j$ to $k$, $\rho$ is to move again this same $r$ from $AD_j$ to $AD_k$. This succession of two moves, $\eta$ followed by $\rho$, is equivalent to simply move $r$ from $AD_i$ to $AD_k$. This should make it clear that $f(\rho\eta)=f(\rho)f(\eta)$. | 2019-10-17 18:16:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7999899983406067, "perplexity": 267.89931145199523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986675598.53/warc/CC-MAIN-20191017172920-20191017200420-00367.warc.gz"} |
https://projecteuclid.org/euclid.dmj/1077297295 | ## Duke Mathematical Journal
### On explicit integral formulas for $GL(n,\mathbb{R})$-Whittaker functions
#### Article information
Source
Duke Math. J., Volume 60, Number 2 (1990), 313-362.
Dates
First available in Project Euclid: 20 February 2004
https://projecteuclid.org/euclid.dmj/1077297295
Digital Object Identifier
doi:10.1215/S0012-7094-90-06013-2
Mathematical Reviews number (MathSciNet)
MR1047756
Zentralblatt MATH identifier
0731.11027
#### Citation
Stade, Eric. On explicit integral formulas for $GL(n,\mathbb{R})$ -Whittaker functions. Duke Math. J. 60 (1990), no. 2, 313--362. doi:10.1215/S0012-7094-90-06013-2. https://projecteuclid.org/euclid.dmj/1077297295
#### References
• [1] D. Bump, Automorphic Forms on $\mathrm GL(3,\mathbbR)$, Springer Lecture Notes in Mathematics, vol. 1083, Springer-Verlag, Berlin, 1984.
• [2] D. Bump, The Rankin-Selberg method: A survey, to appear in the proceedings of the Selberg Symposium, Oslo, 1987.
• [3] D. Bump, Barnes' second lemma and its application to Rankin-Selberg convolutions, to appear in Amer. J. Math.
• [4] D. Bump and S. Friedberg, The exterior square automorphic $L$-functions on $GL(n)$, to appear.
• [5] D. Bump and J. Huntley, in preparation.
• [6] I. Gradshteyn and I. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980, corrected and enlarged edition.
• [7] H. Jacquet, Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. France 95 (1967), 243–309.
• [8] B. Kostant, On Whittaker vectors and representation theory, Invent. Math. 48 (1978), no. 2, 101–184.
• [9] I. I. Pjateckij-Šapiro, Euler subgroups, Lie Groups and their Representations (Proc. Summer School, Bolyai János Math. Soc., Budapest, 1971), Halsted, New York, 1975, pp. 597–620.
• [10] A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47–87.
• [11] J. Shalika, The multiplicity one theorem for $\rm GL\sbn$, Ann. of Math. (2) 100 (1974), 171–193.
• [12] E. Stade, Poincaré series for $\rm GL(3,\bf R)$-Whittaker functions, Duke Math. J. 58 (1989), no. 3, 695–729.
• [13] I. Vinogradov and L. Takhtadzhyan, Theory of Eisenstein Series for the group $\mathrmSL(3,\mathbbR)$ and its application to a binary problem, J. Soviet Math. 18 (1982), 293–324. | 2019-11-21 15:52:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 1, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.672835648059845, "perplexity": 1884.2036732835124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670921.20/warc/CC-MAIN-20191121153204-20191121181204-00249.warc.gz"} |
https://faq.gutenberg.eu.org/2_composition/illustrations/dessiner_avec_tex2?do= | # In-line source for graphics applications
Some of the free-standing graphics applications may also be used (effectively) in-line in LaTeX documents; examples are
• The package asymptote (provided in the asymptote distribution) defines an environment asy which arranges that its contents are available for processing, and will therefore be typeset (after “enough” runs, in the “usual” LaTeX way).
Basically, you write
\begin{asy}
<asymptote code>
\end{asy}
and then run the commands
latex document
asy document-*.asy
latex document
• egplot allows you to incorporate GNUplot instructions in your document, for processing outside of LaTeX. The package provides commands that enable the user to do calculation in GNUplot, feeding the results into the diagram to be drawn.
• gmp allows you to include the source of MetaPost diagrams, with parameters of the diagram passed from the environment call.
• emp is an earlier package providing facilities similar to those of gmp's author hopes that his package will support the facilities emp, which he believes is in need of update.)
• mpgraphics allows you again to program parameters of MetaPost diagrams from your LaTeX document, including the preamble details of the LaTeX code in any recursive call from MetaPost.
In all cases (other than asymptote), these packages require that you can run external programs from within your document.
Source:
2_composition/illustrations/dessiner_avec_tex2.txt · Dernière modification: 2020/12/16 00:34 par jejust | 2021-03-01 01:41:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9117345809936523, "perplexity": 6114.04955779199}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361808.18/warc/CC-MAIN-20210228235852-20210301025852-00118.warc.gz"} |
http://mathhelpforum.com/algebra/105843-logarithms.html | # Math Help - Logarithms
1. ## Logarithms
I have this problem but I'm having a little trouble figuring it out
Log10 (322.039)
2. Put it into your calculator. I get 2.51 (3sf) | 2015-01-26 05:11:22 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8430426716804504, "perplexity": 2257.2398689903243}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115858171.97/warc/CC-MAIN-20150124161058-00149-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://hackage-origin.haskell.org/package/aeson-1.4.4.0/candidate/changelog | ## Changelog for aeson-1.4.4.0
### 1.4.4.0
New features:
• Adds a parameterized parser jsonWith that can be used to choose how to handle duplicate keys in objects, thanks to Xia Li-Yao.
• Add generic implementations of FromJSONKey and ToJSONKey, thanks to Xia Li-Yao. Example:
data Foo = Bar
deriving Generic
opts :: JSONKeyOptions
opts = defaultJSONKeyOptions { keyModifier = toLower }
instance ToJSONKey Foo where
toJSONKey = genericToJSONKey opts
instance FromJSONKey Foo where
fromJSONKey = genericFromJSONKey opts
Minor:
• aeson now uses time-compat instead of time-locale-compat, thanks to Oleg Grenrus.
• Prepare for MonadFail breakages in GHC 8.8, thanks to Oleg Grenrus.
• Require bytestring >= 0.10.8.1 for newer GHCs to avoid build failures, thanks to Oleg Grenrus.
• Support primitive 0.7.*, thanks to Adam Bergmark.
• Allow semigroups 0.19.* and hashable 1.3.*, thanks to Oleg Grenrus.
• Fix a typo in the error message when parsing NonEmpty, thanks to Colin Woodbury.
• Document surprising behavior when using omitNothingFields with type variables, thanks to Xia Li-Yao.
Internal changes:
• Code cleanup by Oleg Grenrus
• Fix dependencies of the benchmarks on older GHC's, thanks to Xia Li-Yao.
### 1.4.3.0
• Improve error messages for FromJSON in existing instances and GHC Generic implementation. Thanks to Xia Li-Yao & Igor Pashev.
• Tweak error-reporting combinators and their documentation. Thanks to Xia Li-Yao.
• typeMismatch is now about comparing JSON types (i.e., the expected and actual names of the Value constructor).
• withObject and other with* combinators now also mention the JSON types they expect
• New unexpected and prependFailure combinators.
• Add Contravariant ToJSONKeyFunction instance. Thanks to Oleg Grenrus.
• Add KeyValue instance for Object. Thanks to Robert Hensing.
• Improve performance when parsing certain large numbers, thanks to Oleg Grenrus.
• Add Data.Aeson.QQ.Simple - A limited version of aeson-qq. Thanks to Oleg Grenrus.
• Exposes internal helper functions like <?>, JSONPath, and parseIndexedJSON from Data.Aeson module. Thanks to Abid Uzair.
• Better error messages when there are syntax errors parsing objects and arrays. Thanks to Fintan Halpenny.
• Support building with th-abstraction-0.3.0.0 or later. Thanks to Ryan Scott.
### 1.4.2.0
• Add Data.Aeson.QQ.Simple which is a simpler version of the aeson-qq package, it does not support interpolation, thanks to Oleg Grenrus.
• Add Contravariant ToJSONKeyFunction instance, thanks to Oleg Grenrus.
• Add KeyValue Object instance, thanks to Robert Hensing
• Improved performance when parsing large numbers, thanks to Oleg Grenrus.
### 1.4.1.0
• Optimizations of generics, thanks to Rémy Oudompheng, here are some numbers for GHC 8.4:
• Compilation time: G/BigProduct.hs is 25% faster, G/BigRecord.hs is 2x faster.
• Runtime performance: BigRecord/toJSON/generic and BigProduct/encode/generic are more than 2x faster.
• Added To/FromJSON instances for Void and Generics's V1, thanks to Will Yager
• Added To/FromJSON instances for primitive's Array, SmallArray, PrimArray and UnliftedArray, thanks to Andrew Thad.
• Fixes handling of UTCTime wrt. leap seconds , thanks to Adam Schønemann
• Warning and documentation fixes thanks to tom-bop, Gabor Greif, Ian Jeffries, and Mateusz Curyło.
## 1.4.0.0
This release introduces bounds on the size of Scientific numbers when they are converted to other arbitrary precision types that do not represent them efficiently in memory.
This means that trying to decode a number such as 1e1000000000 into an Integer will now fail instead of using a lot of memory. If you need to represent large numbers you can add a newtype (preferably over Scientific) and providing a parser using withScientific.
The following instances are affected by this:
• FromJSON Natural
• FromJSONKey Natural
• FromJSON Integer
• FromJSONKey Integer
• FromJSON NominalDiffTime
For the same reasons the following instances & functions have been removed:
• Remove FromJSON Data.Attoparsec.Number instance. Note that Data.Attoparsec.Number is deprecated.
• Remove deprecated withNumber, use withScientific instead.
Finally, encoding integral values with large exponents now uses scientific notation, this saves space for large numbers.
#### 1.3.1.1
• Catch 0 denominators when parsing Ratio
### 1.3.1.0
• Fix bug in generically derived FromJSON instances that are using unwrapUnaryRecords, thanks to Xia Li-yao
• Allow base-compat 0.10.*, thanks to Oleg Grenrus
## 1.3.0.0
Breaking changes:
• GKeyValue has been renamed to KeyValuePair, thanks to Xia Li-yao
• Removed unused FromJSON constraint in withEmbeddedJson, thanks to Tristan Seligmann
Other improvements:
• Optimizations of TH toEncoding, thanks to Xia Li-yao
• Optimizations of hex decoding when using the default/pure unescape implementation, thanks to Xia Li-yao
• Improved error message on Day parse failures, thanks to Gershom Bazerman
• Add encodeFile as well as decodeFile* variants, thanks to Markus Hauck
• Documentation fixes, thanks to Lennart Spitzner
• CPP cleanup, thanks to Ryan Scott
### 1.2.4.0
• Add Ord instance for JSONPathElement, thanks to Simon Hengel.
### 1.2.3.0
• Added withEmbeddedJSON to help parse JSON embedded inside a JSON string, thanks to Jesse Kempf.
• Memory usage improvements to the default (pure) parser, thanks to Jonathan Paugh. Also thanks to Neil Mitchell & Oleg Grenrus for contributing a benchmark.
• omitNothingFields now works for the Option newtype, thanks to Xia Li-yao.
• Some documentation fixes, thanks to Jonathan Paug & Philippe Crama.
### 1.2.2.0
• Add FromJSON and ToJSON instances for
• DiffTime, thanks to Víctor López Juan.
• CTime, thanks to Daniel Díaz.
• Fix handling of fractions when parsing Natural, thanks to Yuriy Syrovetskiy.
• Change text in error messages for Integral types to make them follow the common pattern, thanks to Yuriy Syrovetskiy.
• Add missing INCOHERENT pragma for RecordToPair, thanks to Xia Li-yao.
• Everything related to Options is now exported from Data.Aeson, thanks to Xia Li-yao.
• Optimizations to not escape text in clear cases, thanks to Oleg Grenrus.
• Some documentation fixes, thanks to Phil de Joux & Xia Li-yao.
### 1.2.1.0
• Add parserThrowError and parserCatchError combinators, thanks to Oleg Grenrus.
• Add Generic instance for Value, thanks to Xia Li-yao.
• Fix a mistake in the 1.2.0.0 changelog, the cffi flag is disabled by default! Thanks to dbaynard.
## 1.2.0.0
• tagSingleConstructors, an option to encode single-constructor types as tagged sums was added to Options. It is disabled by default for backward compatibility.
• The cffi flag is now turned off (False) by default, this means C FFI code is no longer used by default. You can flip the flag to get C implementation.
• The Options constructor is no longer exposed to prevent new options from being breaking changes, use defaultOptions instead.
• The contents of GToJSON and GToEncoding are no longer exposed.
• Some INLINE pragmas were removed to avoid GHC running out of simplifier ticks.
### 1.1.2.0
• Fix an accidental change in the format of deriveJSON. Thanks to Xia Li-yao!
• Documentation improvements regarding ToJSON, FromJSON, and SumEncoding. Thanks to Xia Li-yao and Lennart Spitzner!
### 1.1.1.0
• Added a pure implementation of the C FFI code, the C FFI code. If you wish to use the pure haskell version set the cffi flag to False. This should make aeson compile when C isn't available, such as for GHCJS. Thanks to James Parker & Marcin Tolysz!
• Using the fast flag can no longer cause a test case to fail. As far as we know this didn't affect any users of the library itself. Thanks to Xia Li-yao!
## 1.1.0.0
• Added instances for UUID.
• The operators for parsing fields now have named aliases:
• .: => parseField
• .:? => parseFieldMaybe
• .:! => parseFieldMaybe'
• These functions now also have variants with explicit parser functions: explicitParseField, explicitParseFieldMaybe, "explicitParseFieldMaybe' Thanks to Oleg Grenrus.
• ToJSONKey (Identity a) and FromJSONKey (Identity a) no longer require the unnecessary FromJSON a constraint. Thanks to Oleg Grenrus.
• Added Data.Aeson.Encoding.pair' which is a more general version of Data.Aeson.Encoding.pair. Thanks to Andrew Martin.
• Days BCE are properly encoded and + is now a valid prefix for Days CE. Thanks to Matt Parsons.
• Some commonly used ToJSON instances are now specialized in order to improve compile time. Thanks to Bartosz Nitka.
JSONTestSuite cleanups, all motivated by tighter RFC 7159 compliance:
Over 90% of JSONTestSuite tests currently pass. The remainder can be categorised as follows:
• The string parser is strict with Unicode compliance where the RFC leaves room for implementation-defined behaviour (tests prefixed with "i_string_". (This is necessary because the text library cannot accommodate invalid Unicode.)
• The parser does not (and will not) support UTF-16, UTF-32, or byte order marks (BOM).
• The parser accepts unescaped control characters, even though the RFC states that control characters must be escaped. (This may change at some point, but doesn't seem important.)
#### 1.0.2.1
• Fixes a regression where a bunch of valid characters caused an "Invalid UTF8-Stream" error when decoding. Thanks to Vladimir Shabanov who investigated and fixed this.
### 1.0.2.0
• Fixes a regression where it was no longer possible to derive instances for types such as data T a = T { f1 :: a, f2 :: Maybe a }.
Thanks to Sean Leather for fixing this, and to Ryan Scott for helping out.
### 1.0.1.0
• Decoding performance has been significantly improved (see https://github.com/bos/aeson/pull/452). Thanks to @winterland1989.
• Add ToJSON/FromJSON instances for newtypes from Data.Semigroup: Min, Max, First, Last, WrappedMonoid, Option. Thanks to Lennart Spitzner.
• Make the documentation for .:! more accurate. Thanks to Ian Jeffries.
# 1.0.0.0
Major enhancements:
• Introduced new FromJSONKey and ToJSONKey type classes that are used to encode maps without going through HashMap. This also allows arbitrary serialization of keys where a string-like key will encode into an object and other keys will encode into an array of key-value tuples.
• Added higher rank classes: ToJSON1, ToJSON2, FromJSON1, and FromJSON2.
• Added Data.Aeson.Encoding with functions to safely write ToJSON instances using toEncoding.
Other enhancements:
• A Cabal fast flag was added to disable building with optimizations. This drastically speeds up compiling both aeson and libraries using aeson so it is recommended to enable it during development. With cabal-install you can cabal install aeson -ffast and with stack you can add a flag section to your stack.yaml:
flags:
aeson:
fast: true
• Added list specific members to ToJSON and FromJSON classes. In the same way Read and Show handle lists specifically. This removes need for overlapping instances to handle String.
• Added a new sumEncoding option UntaggedValue which prevents objects from being tagged with the constructor name.
• JSONPaths are now tracked in instances derived with template-haskell and generics.
• Get rid of redundancy of JSONPath error messages in nested records.
eitherDecode "{\"x\":{\"a\": [1,2,true]}}" :: Either String Y previously yielded Error in $.x.a[2]: failed to parse field" x: failed to parse field a: expected Int, encountered Boolean and now yields Error in$.x.a[2]: expected Int, encountered Boolean".
Some users might prefer to insert modifyFailure themselves to customize error messages, which previously prevented the use of (.:).
• Backwards compatibility with bytestring-0.9 using the bytestring-builder compatibility package.
• Export decodeWith, decodeStrictWith, eitherDecodeWith, and eitherDecodeStrictWith from Data.Aeson.Parser. This allows decoding using explicit parsers instead of using FromJSON instances.
• Un-orphan internal instances to render them in haddocks.
Other changes:
• Integral FromJSON instances now only accept integral values. E.g. parsing 3.14 to Int fails instead of succeeding with the value 3.
• Over/underflows are now caught for bounded numeric types.
• Remove the contents field encoding with allNullaryToStringTag = False, giving us { "tag" : "c1" } instead of { "tag" : "c1", contents : [] }. The contents field is optional when parsing so this is only a breaking change for ToJSON instances.
• Fix a bug where genericToEncoding with unwrapUnaryRecords = True would produce an invalid encoding: "unwrap\":"".
• ToJSON instances using genericToEncoding and omitNothingFields no longer produce invalid JSON.
• Added instances for DList, Compose, Product, Sum.
### 0.11.2.0
• Enable PolyKinds to generalize Proxy, Tagged, and Const instances.
• Add unsafeToEncoding in Data.Aeson.Types, use with care!
#### 0.11.1.4
• Fix build with base >= 4.8 and unordered-containers < 0.2.6.
#### 0.11.1.3
• Fix build on TH-less GHCs
#### 0.11.1.2
• Fix build with base < 4.8 and unordered-containers < 0.2.6.
• Add missing field in docs for defaultOptions.
#### 0.11.1.1
• Fixes a bug where the hashes of equal values could differ.
### 0.11.1.0
The only changes are added instances.
These are new:
• ToJSON a => ToJSON (NonEmpty a)
• FromJSON a => FromJSON (NonEmpty a)
• ToJSON (Proxy a)
• FromJSON (Proxy a)
• ToJSON b => ToJSON (Tagged a b)
• FromJSON b => FromJSON (Tagged a b)
• ToJSON a => ToJSON (Const a b)
• FromJSON a => FromJSON (Const a b)
These are now available for older GHCs:
• ToJSON Natural
• FromJSON Natural
# 0.11.0.0
This release should be close to backwards compatible with aeson 0.9.
If you are upgrading from aeson 0.10 it might be easier to go back in history to the point you were still using 0.9.
Breaking changes:
• Revert .:? to behave like it did in 0.9. If you want the 0.10 behavior use .:! instead.
• Revert JSON format of Either to 0.9, Left and Right are now serialized with an initial uppercase letter. If you want the names in lowercase you can add a newtype with an instance.
• All ToJSON and FromJSON instances except for [a] are no longer OVERLAPPABLE. Mark your instance as OVERLAPPING if it overlaps any of the other aeson instances.
• All ToJSON and FromJSON instances except for [Char] are no longer incoherent, this means you may need to replace your incoherent instances with a newtyped instance.
• Introduce .:! that behaves like .:? did in 0.10.
• Allow HH:MM format for ZonedTime and UTCTime. This is one of the formats allowed by ISO 8601.
• Added ToJSON and FromJSON instances for the Version, Ordering, and Natural types.
Bug fixes:
• JSONPath identifiers are now escaped if they contain invalid characters.
• Fixed JSONPath messages for Seq to include indices.
• Fixed JSONPath messages for Either to include left/right.
• Fix missing quotes surrounding time encodings.
• Fix #293: Type error in TH when using omitNothingFields = True.
Compatibility:
• Various updates to support GHC 8.
# 0.10.0.0
## Performance improvements
• Direct encoding via the new toEncoding method is over 2x faster than toJSON. (You must write or code-gen a toEncoding implementation to unlock this speedup. See below for details.)
• Improved string decoding gives a 12% speed win in parsing string-heavy JSON payloads (very common).
• Encoding and decoding of time-related types are 10x faster (!!) as a result of bypassing Data.Time.Format and the arbitrary-precision Integer type.
• When using toEncoding, [Char] can be encoded without a conversion to Text. This is fast and efficient.
• Parsing into an Object is now 5% faster and more allocation-efficient.
## SUBTLE API CHANGES, READ CAREFULLY
With the exception of long-deprecated code, the API changes below should be upwards compatible from older versions of aeson. If you run into upgrade problems, please file an issue with details.
• The ToJSON class has a new method, toEncoding, that allows direct encoding from a Haskell value to a lazy bytestring without construction of an intermediate Value.
The performance benefits of direct encoding are significant: more than 2x faster than before, with less than 1/3 the memory usage.
To preserve API compatibility across upgrades from older versions of this library, the default implementation of toEncoding uses toJSON. You will not see any performance improvement unless you write an implementation of toEncoding, which can be very simple:
instance ToJSON Coord where
toEncoding = genericToEncoding defaultOptions
(Behind the scenes, the encode function uses toEncoding now, so if you implement toEncoding for your types, you should see a speedup immediately.)
If you use Template Haskell or GHC Generics to auto-generate your ToJSON instances, you'll benefit from fast toEncoding implementations for free!
• When converting from a Value to a target Haskell type, FromJSON instances now provide much better error messages, including a complete JSON path from the root of the object to the offending element. This greatly eases debugging.
• It is now possible to use Template Haskell to generate FromJSON and ToJSON instances for types in data families.
• If you use Template Haskell or generics, and used to use the camelTo function to rename fields, the new camelTo2 function is smarter. For example, camelTo will rename CamelAPICase to camelapi_case (ugh!), while camelTo2 will map it to camel_api_case (yay!).
• New ToJSON and FromJSON instances for the following time-related types: Day, LocalTime.
• FromJSON UTCTime parser accepts the same values as for ZonedTime, but converts any time zone offset into a UTC time.
• The Result type is now an instance of Foldable and Traversable.
• The Data.Aeson.Generic module has been removed. It was deprecated in late 2013.
• GHC 7.2 and older are no longer supported.
• The instance of Monad for the Result type lacked an implementation of fail (oops). This has been corrected.
• Semantics of (.:?) operator are changed. It's doesn't anymore accept present Null value.
• Added (Foldable t, ToJSON a) => ToJSON (t a) overlappable instance. You might see No instance for (Foldable YourPolymorphicType) arising from a use of ‘.=’ -errors due this change.
# 0.9.0.1
• A stray export of encodeToBuilder got away!
# 0.9.0.0
• The json and json' parsers are now synonyms for value and value', in conformance with the looser semantics of RFC 7159.
• Renamed encodeToByteStringBuilder to the more compact encodeToBuilder.
# 0.8.1.1
• The dependency on the unordered-containers package was too lax, and has been corrected.
# 0.8.1.0
• Encoding a Scientific value with a huge exponent is now handled efficiently. (This would previously allocate a huge arbitrary-precision integer, potentially leading to a denial of service.)
• Handling of strings that contain backslash escape sequences is greatly improved. For a pathological string containing almost a megabyte of consecutive backslashes, the new implementation is 27x faster and uses 42x less memory.
• The ToJSON instance for UTCTime is rendered with higher (picosecond) resolution.
• The value parser now correctly handles leading whitespace.
• New instances of ToJSON and FromJSON for Data.Sequence and Data.Functor.Identity. The Value type now has a Read instance.
• ZonedTime parser ordering now favours the standard JSON format, increasing efficiency in the common case.
• Encoding to a Text.Builder now escapes '<' and '>' characters, to reduce XSS risk.
# 0.8.0.2
• Fix ToJSON instance for 15-tuples (see #223).
# 0.8.0.1
• Support time-1.5.
# 0.8.0.0
• Add ToJSON and FromJSON instances for tuples of up to 15 elements.
# 0.7.1.0
• Major compiler and library compatibility changes: we have dropped support for GHC older than 7.4, text older than 1.1, and bytestring older than 0.10.4.0. Supporting the older versions had become increasingly difficult, to the point where it was no longer worth it.
# 0.7.0.0
• The performance of encoding to and decoding of bytestrings have both improved by up to 2x, while also using less memory.
• New dependency: the scientific package lets us parse floating point numbers more quickly and accurately.
• eitherDecode, decodeStrictWith: fixed bugs.
• Added FromJSON and ToJSON instances for Tree and Scientific.
• Fixed the ToJSON instances for UTCTime and ZonedTime.
# 0.6 series
• Much improved documentation.
• Angle brackets are now escaped in JSON strings, to help avoid XSS attacks.
• Fixed up handling of nullary constructors when using generic encoding.
• Added ToJSON/FromJSON instances for:
• The Fixed class
• ISO-8601 dates: UTCTime, ZonedTime, and TimeZone
• Added accessor functions for inspecting Values.
• Added eitherDecode function that returns an error message if decoding fails.
# 0.5 to 0.6
• This release introduces a slightly obscure, but backwards-incompatible, change.
In the generic APIs of versions 0.4 and 0.5, fields whose names began with a "_" character would have this character removed. This no longer occurs, as it was both buggy and surprising (https://github.com/bos/aeson/issues/53).
• Fixed a bug in generic decoding of nullary constructors (https://github.com/bos/aeson/issues/62).
# 0.4 to 0.5
• When used with the UTF-8 encoding performance improvements introduced in version 0.11.1.12 of the text package, this release improves aeson's JSON encoding performance by 33% relative to aeson 0.4.
As part of achieving this improvement, an API change was necessary. The fromValue function in the Data.Aeson.Encode module now uses the text package's Builder type instead of the blaze-builder package's Builder type.
# 0.3 to 0.4
• The new decode function complements the longstanding encode function, and makes the API simpler.
• New examples make it easier to learn to use the package (https://github.com/bos/aeson/tree/master/examples).
• Generics support
aeson's support for data-type generic programming makes it possible to use JSON encodings of most data types without writing any boilerplate instances.
Thanks to Bas Van Dijk, aeson now supports the two major schemes for doing datatype-generic programming:
• the modern mechanism, built into GHC itself (http://www.haskell.org/ghc/docs/latest/html/users_guide/generic-programming.html)
• the older mechanism, based on SYB (aka "scrap your boilerplate")
The modern GHC-based generic mechanism is fast and terse: in fact, its performance is generally comparable in performance to hand-written and TH-derived ToJSON and FromJSON instances. To see how to use GHC generics, refer to examples/Generic.hs.
The SYB-based generics support lives in Data.Aeson.Generic and is provided mainly for users of GHC older than 7.2. SYB is far slower (by about 10x) than the more modern generic mechanism. To see how to use SYB generics, refer to examples/GenericSYB.hs.
• We switched the intermediate representation of JSON objects from Data.Map to Data.HashMap which has improved type conversion performance.
• Instances of ToJSON and FromJSON for tuples are between 45% and 70% faster than in 0.3.
• Evaluation control
This version of aeson makes explicit the decoupling between identifying an element of a JSON document and converting it to Haskell. See the Data.Aeson.Parser documentation for details.
The normal aeson decode function performs identification strictly, but defers conversion until needed. This can result in improved performance (e.g. if the results of some conversions are never needed), but at a cost in increased memory consumption.
The new decode'` function performs identification and conversion immediately. This incurs an up-front cost in CPU cycles, but reduces reduce memory consumption. | 2022-01-19 06:52:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3731255829334259, "perplexity": 14739.660039164026}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301264.36/warc/CC-MAIN-20220119064554-20220119094554-00226.warc.gz"} |
https://math.answers.com/Q/What_is_the_square_root_of_128 | 0
# What is the square root of 128?
Wiki User
2016-03-06 11:20:51
The square root of 128 is 8 times the square root of 2 because it's an irrational number. An estimate is 11.313708498984760390413509793678
Wiki User
2016-03-06 11:20:51
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See all cards | 2021-12-04 11:31:38 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8133525252342224, "perplexity": 4955.982331236603}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362969.51/warc/CC-MAIN-20211204094103-20211204124103-00077.warc.gz"} |
https://www.iacr.org/cryptodb/data/author.php?authorkey=11603 | ## CryptoDB
### Sihang Pu
#### Publications
Year
Venue
Title
2021
PKC
Threshold Private Set Intersection (PSI) allows multiple parties to compute the intersection of their input sets if and only if the intersection is larger than $n-t$, where $n$ is the size of the sets and $t$ is some threshold. The main appeal of this primitive is that, in contrast to standard PSI, known upper-bounds on the communication complexity only depend on the threshold $t$ and not on the sizes of the input sets. Current Threshold PSI protocols split themselves into two components: A Cardinality Testing phase, where parties decide if the intersection is larger than some threshold; and a PSI phase, where the intersection is computed. The main source of inefficiency of Threshold PSI is the former part. In this work, we present a new Cardinality Testing protocol that allows $N$ parties to check if the intersection of their input sets is larger than $n-t$. The protocol incurs in $\tilde{ \mathcal{O}} (Nt^2)$ communication complexity. We thus obtain a Threshold PSI scheme for $N$ parties with communication complexity $\tilde{ \mathcal{O}}(Nt^2)$.
2021
TCC
Consider a server with a \emph{large} set $S$ of strings $\{x_1,x_2\ldots,x_N\}$ that would like to publish a \emph{small} hash $h$ of its set $S$ such that any client with a string $y$ can send the server a \emph{short} message allowing it to learn $y$ if $y \in S$ and nothing otherwise. In this work, we study this problem of two-round private set intersection (PSI) with low (asymptotically optimal) communication cost, or what we call \emph{laconic} private set intersection ($\ell$PSI) and its extensions. This problem is inspired by the recent general frameworks for laconic cryptography [Cho et al. CRYPTO 2017, Quach et al. FOCS'18]. We start by showing the first feasibility result for realizing $\ell$PSI~ based on the CDH assumption, or LWE with polynomial noise-to-modulus ratio. However, these feasibility results use expensive non-black-box cryptographic techniques leading to significant inefficiency. Next, with the goal of avoiding these inefficient techniques, we give a construction of $\ell$PSI~schemes making only black-box use of cryptographic functions. Our construction is secure against semi-honest receivers, malicious senders and reusable in the sense that the receiver's message can be reused across any number of executions of the protocol. The scheme is secure under the $\phi$-hiding, decisional composite residuosity and subgroup decision assumptions. Finally, we show natural applications of $\ell$PSI~to realizing a semantically-secure encryption scheme that supports detection of encrypted messages belonging to a set of illegal'' messages (e.g., an illegal video) circulating online. Over the past few years, significant effort has gone into realizing laconic cryptographic protocols. Nonetheless, our work provides the first black-box constructions of such protocols for a natural application setting.
2020
ASIACRYPT
Quantum pseudorandom functions (QPRFs) extend the classical security of a PRF by allowing the adversary to issue queries on input superpositions. Zhandry [Zhandry, FOCS 2012] showed a separation between the two notions and proved that common construction paradigms are also quantum secure, albeit with a new ad-hoc analysis. In this work, we revisit the question of constructing QPRFs and propose a new method starting from small-domain (classical) PRFs: At the heart of our approach is a new domain-extension technique based on bipartite expanders. Interestingly, our analysis is almost entirely classical. As a corollary of our main theorem, we obtain the first (approximate) key-homomorphic quantum PRF based on the quantum intractability of the learning with errors problem.
#### Coauthors
Navid Alamati (1)
Pedro Branco (2)
Nico Döttling (3)
Sanjam Garg (1)
Mohammad Hajiabadi (1)
Giulio Malavolta (1) | 2021-10-22 15:58:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5097940564155579, "perplexity": 1321.7842481559578}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585516.51/warc/CC-MAIN-20211022145907-20211022175907-00230.warc.gz"} |