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http://woodcoin.info/2015/05/04/on-chumponomics/
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# On Chumponomics
This post began with the title "Fiat economics". This however seemed like too much of an oxymoron to leave in place. "Fiat dynamics" was briefly the title as well. In the end, I went with Chumponomics. For relevant etymology you might want to read this.
Fiat dynamics is an odd subject to study in today's day and age (year 7, height 352k when this piece was started). It's a bit like returning to Ptolemaic astronomy. Indeed, why not place the Earth at the exact center of a set of large mechanical spheres which seem to move at arbitrary unexplained speeds? By setting the proper speeds and axes, one can in fact explain what one sees from the Earth. You don't agree? Imagine now that the source of your employment as an astronomer required you would take such an approach. In that case, this was the obvious way to approach astronomy. One could still make very important discoveries when phrased in the language of the celestial spheres. Some of the language (such as talk of declination and right ascension on the celestial sphere) survives to this day. Similarly, though better alternatives existed, many 20th century economists were paid in fiat currency of one sort or another. It makes sense they would phrase their economic discussion in the language demanded of them by their employers, despite its obvious shortcomings. Today fiat dynamics remains largely relevant in much of the world and historians and citizens will be picking up the pieces for a long time, so as you have already gathered, you are about to hear my take on it.
Economics (see Aristotle's "Oekonomikon") claims to be a scientific analysis of the management of the household. This includes all relevant incomes, expenditures, necessities and in more generality all goods and services which enter the household and are possible to be managed. The "household" can of course be taken in different ways, from one's immediate person to one's family home on up to entire continents or the whole spaceship or planet. Some of the factors involved in the household may have changed since the time of Aristotle (more energy resources, fewer slaves, for example) but the basic ideas are the same. Food, clothing, and shelter are common examples of immediately relevant resources in household management or economics. In so much as one would like to use precision and accuracy in describing relevant quantities to these important questions, one would like to use common units. Many fiat paid economists choose to use a fiat unit to describe economic quantities. However, this appears to be absurd to one familiar with the physical sciences. Imagine if you will:
Alice (about to mix something in a chemical beaker): How many grams again is the mass of 1 cubic centimeter of water at standard temperature and pressure (STP)?
Bob: Well we are given the figure of 2.15 by National institute of standards and technology (NIST) but ShadowUnits assures us it is more like 3 or 3 and a half.
Alice: We'd better wait for the official announcement from the NIST spokesman this month. If they delay on the increase in grams per liter another month we will have to adjust these numbers down for our Nature publication this summer.
Bob: Don't worry, we factored that into our budget after they upped Avagadro's number in China last year.
As you can tell, a fiat unit such as the US dollar is not a unit a reasonable person would use to describe any kind of quantity of long term importance, simply because we don't now how much of it will be around after a long time (in fact we don't know how much is around now either). It is a unit devoid of physical definition. It is now becoming clear to a majority of 21st century literates that any discussion of relevant economic quantities of importance (such as revenues, net worth, inherent value, prosperity, or any cost benefit analysis) which reports numbers in fiat units such as the US dollar is completely laughable. It is chumponomics. The reporting of relevant figures in fiat units is only done to satisfy wealthy benefactors or to continue in profiting from errors of the chumps who might believe this shite.
That being said, the question of how much fiat people do have now, and how they get it, is the heart of chumponomics. A pair of US dollars can be seen as what lies between you and a hotel room for a night in coastal Ecuador, or ten thousand dollars can be seen as what lies between you and a hotel room for a night in a certain resort on Mykanos. Let's just continue onwards into this realm and leave behind the ideas of household management (food, clothing, shelter, sustainable agriculture, not killing yourself, etc). Those are indeed important things (and depending on the misfortune of your current situation they may seem to depend on chumponomics) but I'm not really going to get into them now. Let's talk fiat.
Towards a theory of chumponomics
Point of fact: chumponomics is the study of one phenomenon (and its subsidiary effects). This phenomenon can be referred to as "inflation". The proof of this is quite simple. All fiat is produced by inflation, that is, inflation of the money supply at effectively zero cost (or at least great discount) to those inflating it. The origin of every dollar, every yuan, every euro, was that it was created out of nothing by fiat. Thus, if we study fiat dynamics, we have as our primary function to study inflation.
Let's consider two extreme examples to begin this discussion. One I will call "perfectly balanced inflation" and the other "perfectly imbalanced inflation". In perfectly balanced inflation, the increase of the money supply proceeds exactly as a stock split. Every owner of a unit of the corporate scrip becomes the owner of two units (the exact factor is unimportant). The result is that most users of the fiat are aware immediately of the new distribution. Prices immediately go up accordingly. There is no change to the distribution of relative ownership of the total supply, but gross domestic product (GDP) has doubled. This assumes only that one is calculating GDP in the fiat unit, not how it precisely was counted.
In the second example, we again double the money supply, but in this case give all the new scrip to one person, let's call him the king. The king being a miser, puts it all in a warehouse and spends not a penny. In this case we have doubled the money supply but the prices stay the same and the GDP is unchanged. This is an unstable arrangement. At some point, the king might be tempted to reach into the warehouse. Some employees might sneak a wheelbarrow full from the warehouse. Eventually, the stuff will start to leak out. More likely, when word gets out what will happen is the king will face insurrection. Perhaps the warehouse will be looted. This kind of arrangement is unstable because to maintain such a position one needs pay off a group of colleagues with a portion of the proceeds in order to keep them as guards for the operation. As you can clearly tell, this is much closer to the way things were run in the fiat era.
The physicist might see at this point that what we are talking about is a diffusive process. The pile of new fiat is like a lump of salt in a glass of water. In the case of the water it is the motion of heat in the water and collisional and chemical effects that start to erode at the salt and begin the distribution and smooth the salinity gradient. For the case of perfectly balanced inflation, we will have a solution of doubled local salinity throughout. In case you hadn't noticed, chumpanomics involves continued inflation and so the system is sometimes referred to as "disequilibrium".
One could study chumpotronic diffusion as one studied spatial diffusion, and calculate for example the spatial density of fiat on the Earth's surface. It is clear from the air that there are places where the fiat is introduced, such as London, Washington DC, and Beijing, with a higher density. Construction projects and so-called development projects, regardless of their true economic impact (which is often negative) can be point sources of fiat inflation. Other places await for diffusion to slowly reach them via trade. However, calculating the relevant spatial diffusion coefficients is difficult. The physical barriers to motion of a unit of fiat currency are not the same as those that control the movement of a salt ion. While there are some barriers to physical motion, fiat can in fact jump across the globe. We might therefore also be interested in an adapted theory of diffusion, not in spatial dimension but in a larger dimensional space of participants.
Fiat Diffusion
Consider the discrete fiat density vector $\phi_i$, which describes the amount of fiat controlled by the ith participant from a group of n total participants. We can describe the evolution of this quantity with time t, first by producing a continuity equation:
##### ${\partial \phi_i \over \partial t} = \sum\limits_{k=0}^n j_{ik} + C_i$ Eq. 1
Here we have introduced a flux term $j_{ik}$ describing the flux of fiat from the kth participant to the ith participant, and a counterfeiting source term $C_i$ describing the amount of new fiat created (or destroyed) by the ith participant. Note that for the purposes of describing fiat dynamics it matters not at all whether the inflationary source $C_i$ is licensed or described as issuance as opposed to criminal counterfeiting. The result is the same to the participants as long as it remains a source (or sink). To proceed we need to describe the flux term, which we can approximate as being to first order proportional to the difference in fiat holdings between the two participants:
##### $j_{ik}= D_{ik}(\phi_i,\phi_k,\overrightarrow{r})(\phi_i - \phi_k)$ Eq. 2
In other words, we expect fiat rich people to buy things from fiat poor people, on average, and the rate of this flow is to first order proportional to the difference in their relative holdings. Here we have introduced a set of diffusion coefficients $D_{ik}$ which depend on the relative levels of fiat held by the ith and kth participant as well as external variables which we have lumped into the vector $\overrightarrow{r}$. We can produce now a canonical diffusion equation for chumponomics:
##### ${\partial \phi_i \over \partial t} = \sum\limits_{k=0}^nD_{ik}(\phi_i,\phi_k,\overrightarrow{r})(\phi_i - \phi_k) + C_i$ Eq. 3
What next?
At this point it is tempting to go into which external variables affect the diffusion coefficients and to state this explicitly. Language barriers, trade practices, and of course geographic location will all play a role in the vector $\overrightarrow{r}$ of external variables. Also, second order effects will emerge in which the relative flow is not a linear function of the difference in holdings between participants. It is for this reason that we have explicit dependance of the diffusion coefficients on the actual amount of fiat held by the two participants for each coefficient $D_{ik}$. However, to what end? It is clear immediately upon inspection that an understanding of these diffusion coefficients, which could in theory explain the whole of economic interaction, is not going to allow us to calculate diddly squat. Why? Because we have no idea what the counterfeiting terms $C_i$ are doing.
Imagine that you are a chemist told to use the diffusion equation to calculate salinity in a large body of water. After writing down the relevant diffusion equation, you are then told that by the way salt is being added in unknown places at unknown quantities. Does this seem like a useful exercise to you? No. The only way to do well is to somehow learn what one can about the sources of salt, perhaps by paying off the salt delivery guy. Bothering with molecular dynamics, heat, and convection, will be a waste of time. This is the attitude of the seasoned chumponomist: Who cares about efficiency, velocity of money, real revenues or productivity? What matters is who you know, and how close they are to the sources.
Fiat monetary systems are only useful as chumpotrons, that is, as scams. In terms of the global economy, or the survival of humanity and Gaia, they are a massive cement weights attached to the legs of humanity. The only questions emerging for the educated 21st century economist are what pieces of the formalism of 20th chumponomics can survive into the 21st century and still be useful. My guess is many. Language is phenomenally adaptive. Already we are using words like "accounts", "wallets", "interest", and "market capitalization" which had fiat significance, to mean slightly different things in the world of monetary systems which have public and deterministic $\sum\limits_iC_i$. Other than that, don't waste your time with chumponomics.
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2019-08-25 11:27:27
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https://historicsweetsballroom.com/what-is-a-second-degree-polynomial/
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Polynomial role whose general type is $$f(x) = \textrmAx^2 + \textrmB x + \textrmC$$, where A ≠ 0 and also A, B, C ∈ $$\mathbbR$$.
You are watching: What is a second degree polynomial
A second-degree polynomial duty in which all the coefficients the the terms with a degree less than 2 space zeros is called a quadratic function.
### Properties
The graph that a second-degree polynomial function has that vertex in ~ the beginning of the Cartesian plane.The zeros the a second-degree polynomial function are given by the complying with :If (B2 – 4AC) ≥ 0, the zeros are genuine numbers: $$x_1 = \frac−\textrmB\space + \space \sqrt\textrmB^2 − 4\textrmAC2\textrmA$$ and $$x_2 = \frac−\textrmB\space −\space \sqrt \textrmB^2 − 4\textrmAC2\textrmA$$;If the role is that the form f(x) = A$$x^2$$ + B$$x$$, the zeros are : $$x_1$$ = 0 and also $$x_2$$ = − $$\fracBA$$;If the function is of the type f(x) = A$$x^2$$ + C, the zeros are : $$x_1$$ = $$\sqrt− \fracCA$$ and $$x_2$$ = − $$\sqrt− \fracCA$$, where AC If the duty is that the kind f(x) = A$$x^2$$, the zeros are : $$x_1$$= 0 and $$x_2$$= 0.
### Examples
The graphical depiction of a second-degree polynomial function defined through the relationship $$f(x) = x^2$$ is a an easy parabola.
The graphical representation of a second-degree polynomial role defined through the connection $$f(x) = (x − a)^2$$ is a simple parabola analyzed horizontally.
The graphical representation of the second-degree polynomial function defined by the connection $$f(x) = x^2 + k$$ is a basic parabola translated vertically.
See more: What Does The Name Brock Mean Ing, Popularity And Info On Babynames
The graphical depiction of the second-degree polynomial duty defined by the relationship $$f(x) = a(x − h)^2 + k$$ is a straightforward parabola interpreted horizontally and also vertically.
This graph illustrates the duty f identified by f(x) = $$\left ( x+3 \right )^2 – 4$$
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2021-10-24 13:42:08
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http://www.tennisforum.com/archive/index.php/index.php?t-467519.html
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PDA
View Full Version : Petra’s Asian Outdoor Hard Court Swings – Tokyo, Beijing, Dubai, Doha
Pages : [1] 2
ArcticMoose
Sep 3rd, 2012, 05:15 AM
:cheer:Onwards to Asia….
:angel:Petra has never won a WTA Title todate (Sep 12) in the Asian legs of the tour at the beginning or the latter part of the annual WTA tour:drive: ;) so here’s hoping she will breakthrough in Asia very soon on the (less humid ;)) Asian Outdoor Hard courts.....
:worship:To date she has won 9 WTA Tour Titles : 5 in Europe (Istanbul is at the European/Asian Cross roads;)) 2 in Australia & 2 in North America..:bigclap:
:bounce: The Curator of the Petra Kvitova Trophy Cabinet awaits the delivery of goodies with eager anticipation….
http://i51.tinypic.com/b3qsfa.gifEnjoy the journey folks on the exotic foray in to Asia on the Kvitty Bandwagon …..:hatoff:
ArcticMoose
Sep 3rd, 2012, 05:17 AM
Petra Kvitová Global Fan Base Anthem / Song
RFxNWJvPG0U
QUEEN - We Are The Champions lyrics
I've paid my dues
Time after time
I've done my sentence
But committed no crime
I've had my share of sand kicked in my face
But I've come through
(And we mean to go on and on and on and on)
We are the champions my friend
And we'll keep on fightin' till the end
We are the champions, We are the champions
No time for losers 'cause we are the champions
Of the world
I've taken my bows
And my curtain calls
You brought me fame and fortune and everything that
goes with it
I thank you all
But it's been no bed of roses
No pleasure cruise
I consider it a challenge before the whole human race
And I ain't gonna lose
We are the champions my friend
And we'll keep on fighting till the end
We are the champions
We are the champions
No time for losers
'cause we are the champions
Of the world
We are the champions my friend
And we'll keep on fighting till the end
We are the champions
We are the champions
No time for losers
'cause we are the champions.
Excelscior
Sep 3rd, 2012, 05:19 AM
:cheer:Onwards to Asia….
:angel:Petra has never won a WTA Title todate (Sep 12) in the Asian legs of the tour at the beginning or the latter part of the annual WTA tour:drive: ;) so here’s hoping she will breakthrough in Asia very soon on the (less humid ;)) Asian Outdoor Hard courts.....
:worship:To date she has won 9 WTA Tour Titles : 5 in Europe (Istanbul is at the European/Asian Cross roads;)) 2 in Australia & 2 in North America..:bigclap:
:bounce: The Curator of the Petra Kvitova Trophy Cabinet awaits the delivery of goodies with eager anticipation….
http://i51.tinypic.com/b3qsfa.gifEnjoy the journey folks on the exotic foray in to Asia on the Kvitty Bandwagon …..:hatoff:
I guess after what we witnessed tonight, you like me (and some of us others), have no choice but to move on and not be mad, huh Moose (or you just keeping it in)? :lol:
Strange match tonight to say the least. :oh:
ArcticMoose
Sep 3rd, 2012, 05:32 AM
I guess after what we witnessed tonight, you like me (and some of us others), have no choice but to move on and not be mad, huh Moose (or you just keeping it in)? :lol:
Strange match tonight to say the least. :oh:
Kvitty's Tennis Life Journey has many twists & turns some albeit very cruel valleys - we have seen & experienced some of these todate but yet more to come - there are times for tears & mourning and moments for looking ahead ... to the Glorius Mountain Tops just around the corner & ahead of us!
Excelscior
Sep 3rd, 2012, 05:38 AM
Kvitty's Tennis Life Journey has many twists & turns some albeit very cruel valleys - we have seen & experienced some of these todate but yet more to come - there are times for tears & mourning and moments for looking ahead ... to the Glorius Mountain Tops just around the corner & ahead of us!
Well said. And I have nothing else to say (hopefully that's not a suicide watch ode to Petra). :lol: Just kidding of course.
bruce goose
Sep 4th, 2012, 05:22 AM
Nice timing from Moose in starting this thread;sometimes,opening a new,relevant thread is exactly what's needed to get the foul taste of an ultra-crappy loss out of your system.If Petra can do well in Asia,then it'll be FAR easier to put yesterday's whatever-the-hell-that-was out of our minds.....The good thing about being in Asia is that Petra won't be the worst English-speaker by a long shot compared to those young,local WCs in the MDs:lol:
Synth
Sep 4th, 2012, 02:10 PM
Thanks for starting this thread Moose. Looking forward to the swing.
ShiftyFella
Sep 4th, 2012, 02:47 PM
If Petra takes at least 1 title and advances in others to semis or better i would be happiest man on earth and that horrific lose to Cake finally would be erased from my mind:)
Excelscior
Sep 4th, 2012, 03:00 PM
OK guys, since the US Open for Petra is over, let's talk about something else for the upcoming Asian Swing, and ultimately the start of 2013 (till Tokyo starts of course).
In one of Queen Petra Fans most recent post, he mentioned an excellent suggestion which may of been overlooked. He said (if I remember correctly), that Petra should move out of the Czech Republic to a warmer climate (which I've always believed). And he also mentioned, she should at least practice in an outdoor facility. I hope I'm not misquoting him. :oh:
I happen to concur with both. You ever notice most top golfers and tennis players live in warm weather climates? Very few live in cold weather environments?
Now I don't know if Petra is ready to leave the Czech Republic at this stage (especially since Kotyza lives there). But I agree with QPF, that if she's not going to practice onsite in Asia (when ever she prepares for tennis again), it should be in an outdoor facility, preferably in a warm weather environment. If Petra's serious about making moves in her tennis career, this is something she should consider, especially at the end of 2012/start of the 2012 season.
Prostejov is an indoor facility (I have no idea what the weather is in the Czech Republic today, by the way), even though I remember Petra saying they were supposed to get outdoor courts in the future as well. Obviously Petra had a comfortably on Indoor courts, cause of Prostejov. But because of Petra's tennis immaturity, she didn't open up to Outdoor hardcourts every where equally as well, though her game obviously/easily translated to both.
That's why I was so mad when Petra had gotten that cold/virus earlier this year. I didn't think she should of been in the Czech Republic during a snow storm/the cold in the first place. I'm sure Petra can find away to live somewhere else, while maintaining her Czech citizenship. At worst, she can live/vacation elsewhere when the weather is cold or contains allergens in the Czech Republic.
At this point the only time Petra should be in the Czech Republic, is when she doesn't plan to play tennis and just visit family, relax, etc, when it's warm. Anytime she does wants to play tennis, I think she should practice somewhere else, unless it's warm and outdoors in the Czech Republic (and even that I probably don't agree with), if she can't officially move.
What do you guys think?
ShiftyFella
Sep 4th, 2012, 03:15 PM
What do you guys think?
I think she needs at least during offseason practicing somewhere hot like Australia
In one of Queen Petra Fans most recent post, he mentioned an excellent suggestion which may of been overlooked. He said (if I remember correctly), that Petra should move out of the Czech Republic to a warmer climate (which I've always believed). And he also mentioned, she should at least practice in an outdoor facility. I hope I'm not misquoting him. :oh:
actually it was me:oh:
Excelscior
Sep 4th, 2012, 03:57 PM
I think she needs at least during offseason practicing somewhere hot like Australia
actually it was me:oh:
Now I think he did to. I just probably didn't read or remember yours (sorry shifty). :lol:
Petra had gotten sick earlier this year (before Doha), cause she had gotten a virus/cold in Czech Republic.
I for one flipped out, cause I didn't think she should of been there in the first place during a snowstorm in the middle of the tennis season.
This carried over till Indian Wells, cause not only was Petra sick and weak, but she hadn't practiced. And if you remembered, she lost all her energy in the second set, after bludgeoning McHale in the first, cause she was zapped for energy.
The other thing was, Petra obviously had the game to play well on both indoor and outdoor hardcourts (cause she played well on outdoor clay and Grass), but do to her immaturity she had an affinity for indoor hardcourts and only seemed to like outdoor hard courts in Australia. :lol:
As far as your last suggestion. I know she likes Australia, but I don't think Petra will ever move there. Too far. Of course she could practice there for the start of 2012 :lol: She did arrive a week before the Hopman Cup in Perth Australia this year (after of course hurting herself in the Czech league several weeks earlier).
I think she should move to warm weather climate in Europe, since she seems to like it there so much, or just vacation, spend time away from the Czech Republic when it's cold.
Petra may also consider extended time in America after before Indian Wells and after Wimbledon as well. She may not have to play every tournament (like she almost did this year on the NA summer hardcourt swing), but she can get more comfortable with the cities and environments in between tournaments this way.
And she should definitely not practice much at Prostejov anymore (especially if they continue to have no outdoor hardcourts). There's no need to.
Berdych lives in Monaco (or at least that's his official residence now), and he's a member of the club as well.
ShiftyFella
Sep 4th, 2012, 03:59 PM
Petra had gotten sick earlier this year (before Doha), cause she had gotten a virus/cold in Czech Republic.
I for one flipped out, cause I didn't think she should of been there in the first place during a snowstorm, in the middle of the tennis season.
This carried over till Indian Wells, cause not only was Petra sick and weak, but she hadn't practiced. And if you remembered, she lost all her energy in the second set, after bludgeoning McHale in the first, cause she was zapped for energy.
The other thing was, Petra obviously had the game to play well on both indoor and outdoor hardcourts (cause she played well on outdoor clay and Grass), but do to her immaturity she had an affinity for indoor hardcourts and only seemed to like outdoor hard courts in Australia. :lol:
As far as your last suggestion. I know she likes Australia, but I don't think Petra will ever move there. Too far. Of course she couold practice there for the start of 2012 :lol: She did arrive a week before the Hopman Cup in Perth Australia this year (after of course she hurt herself in the Czech league prior).
I think she should move to warm weather climate in Europe, since she seems to like it there so much, or just vacation, spend time away from the Czech Republic when it's cold.
And she should definitely not practice much at Prostejov anymore (especially if they continue to have no outdoor hardcourts). There's no need to.
Berdych lives in Monaco (or at least that's his official residence now), and he's a member of the club.
I don't belive Petra would leave Czech, she is not comfortable with her english skills and too much of a hommie person, maybe having underage boyfriend is the case too. I believe best solution is to have offseason training facility somewhere like Australia not just because of warm weather\stuff but because there are no distractions, also she needs her fitness coach always with her in order to correct rest-fitness balance between matches during season. Kotyza wouldn't be an issue Kvitty used to not having him on the tour or maybe he likes this idea too, bringing his family for nice vacation while coaching Petra.
Excelscior
Sep 4th, 2012, 04:11 PM
I don't belive Petra would leave Czech, she is not comfortable with her english skills and too much of a hommie person, maybe having underage boyfriend is the case too. I believe best solution is to have offseason training facility somewhere like Australia not just because of warm weather\stuff but because there are no distractions, also she needs her fitness coach always with her in order to correct rest-fitness balance between matches during season. Kotyza wouldn't be an issue Kvitty used to not having him on the tour or maybe he likes this idea too, bringing his family for nice vacation while coaching Petra.
Good Points shifty, on why Australia would be a good location (no publicity or pressure). I still think it's too far though (which I'm sure is one of your points). Lol
Yeah, I don't think Petra would ever change her citizenship either. But in reality, most of these players (including Petra), spend little time in their native lands anyway. :lol:
Yes, if Petra wants to maintain Czech citizenship, fine. But she should definitely vacation (especially when it's cold), and practice outside the Czech Republic.
Petra should only drop in for tennis in one of those pre-Season tournament Czech leagues deals. However, she has to be smart enough next time not to get hurt trying to win a needless match during Pre Pre Pre season. :lol:
Yeah, I guess Kotyza won't mind a paid for trip to a warm climate. But the reason why I brought him up was, who's Petra going to stay with when she's out the country (unless she brings her family, friends and/or doesn't mind being alone), when she's not practicing?
I think Petra's English is fine. If she can conduct press conferences, I'm sure she can function in a foreign country. And it's funny you brought up English. How you know what country I wanted her to move and/or vacation to (and didn't you bring Up English speaking Australia yourself)? :lol: Plus, how could she be uncomfortable in English speaking environments, when she claims she loves England, Australian and NY is one of her favorite cities? :lol:
If Berdych, Wozniaki and Djokovic can move to Monaco (the south of France) and function, then Petra can move to a similar French or Italian International resort herself. Hell, she can even move or vacation to some warm, quiet village somewhere in Europe, for all I care. :lol:
Petra should want to improve her English (with out just reading books) anyway. That would be good for her, and make her even better/more comfortable during the US swing. Keep in mind, Petra is comfortable where ever she wins. If Petra wins Tokyo, she'll claim that's 'Japan is one of her favorite countries, Tokyo is one of her favorite cities', and 'she loves the Japanese language'. I promise you. :lol:
Good stuff.
ShiftyFella
Sep 4th, 2012, 05:03 PM
Good Points shifty, on why Australia would be a good location (no publicity or pressure). I still think it's too far though (which I'm sure is one of your points). Lol
Yeah, I don't think Petra would ever change her citizenship either. But in reality, most of these players (including Petra), spend little time in their native lands anyway. :lol:
Yes, if Petra wants to maintain Czech citizenship, fine. But she should definitely vacation (especially when it's cold), and practice outside the Czech Republic.
Petra should only drop in for tennis in one of those pre-Season tournament Czech leagues deals. However, she has to be smart enough next time not to get hurt trying to win a needless match during Pre Pre Pre season. :lol:
Yeah, I guess Kotyza won't mind a paid for trip to a warm climate. But the reason why I brought him up was, who's Petra going to stay with when she's out the country (unless she brings her family, friends and/or doesn't mind being alone), when she's not practicing?
I think Petra's English fine. If she can conduct press conferences, I'm sure she can function in a foreign country. And it's funny you brought up English. How you know what country I wanted her to move and/or vacation to (and didn't you bring Up English speaking Australia yourself)? Lol.
If Berdych, Wozniaki and Djokovic can move to Monaco (the south of France) and function, then Petra can move to a similar French or Italian international resort herself. Hell, she can even move or vacation to some warm, quiet village somewhere in Europe, for all I care. :lol:
Lastly, Petra should want to improve her English (with out just reading books). That would be good for her, and make her even better/more comfortable during the US swing.
Good stuff.
Personally i don't like when players change their citizenship, i can dig it when they move out from home country at age like 5 but when they 25yo it's beyond me.
You should watch her pressers in Czech, to me she looks way more comfortable and outspoken then in english, though living in english speaking environment would develop her skills better and quickly.
When Kotyza not with her PR manager always around, also she can just hang out with Stosur or Dellacqua. If she moves to Monaco she can become money hungry diva, we don't want this to happen, right?:lol:
Excelscior
Sep 4th, 2012, 05:13 PM
Personally i don't like when players change their citizenship, i can dig it when they move out from home country at age like 5 but when they 25yo it's beyond me.
You should watch her pressers in Czech, to me she looks way more comfortable and outspoken then in english, though living in english speaking environment would develop her skills better and quickly.
When Kotyza not with her PR manager always around, also she can just hang out with Stosur or Dellacqua. If she moved to Monaco she can become money hungry diva, we don't want this to happen, right?:lol:
Yeah, but we don't want her in the Czech Republic, right Shifty? :lol:
Plus, what other language is she going to speak, if it's not English? :lol:
I had also added to the post you responded to (which could address some of this). You may notice the differences. But I had asked "how could Petra not like English, when she claims she loves England, Australia, and NY is one of her favorite cities? Then I said was, "Petra likes any place where she wins". If she wins in Tokyo, it will be her new favorite City and tournament, and Japan will instantly become one of her favorite countries. I promise. :lol:
She can move/vacation anywhere she's comfortable, where it's warm and she can play tennis.
Don't worry. I don't think anyone would ever convince her to change her nationality, unless Csersonek or someone very close to her or someone she highly respected recommended it.
Anyway, my original point was, all top golfers and tennis players live in warm weather climates. And earlier this year, Petra was getting sick while in the Czech Republic during a cold freeze. She also got injured practicing in the Czech Republic Pre-season during a competitive, albeit useless match, which impacted the first 1/3 of her 2012 season.
If Petra's going to be a true pro, with a true pro team (as so many of us have been suggesting lately), then this would be a first start. Where is Petra going to stay during the off season when it's cold? And where is she going to practice her tennis in general?
Where she officially lives or calls home, I know is a whole nother fight/argument. Lol.
And to be quite honest; she doesn't have to (officially change her nationality). If Petra wants to give more taxes to her country, that's her business.
ShiftyFella
Sep 4th, 2012, 05:29 PM
Yeah, but we don't want her in the Czech Republic, right Shifty? :lol:
Plus, what other language is she going to speak, if it's not English? :lol:
I had also added to the post you responded to (which could address some of this). You may notice the differences. But I had asked "how could Petra not like English, when she claims she loves England, Australia, and NY is one of her favorite cities? Then I said was, "Petra likes any place where she wins". If she wins in Japan, it will be her new favorite country and tournament. :lol:
She can move/vacation anywhere she's comfortable, where it's warm and she can play tennis.
Don't worry. I don't think anyone would ever convince her to change her nationality, unless Csersonek or someone very close to her or someone she highly respected recommended it.
Anyway, my original point was, all top golfers and tennis players live in warm weather climates. And earlier this year, Petra was getting sick while in the Czech Republic during a cold freeze. She also got injured practicing in the Czech Republic Pre-season during a useless match, which impacted the first 1/3 of her season.
If Petra's going to be a true pro, with a true pro team (as so many of us have been suggesting lately), then this would be first start. Where is Petra going to stay during the off season when it's cold. And where is she going to practice her tennis in general?
Where she officially lives or calls home, I know is a whole nother fight/argument. Lol.
I love Montreal but i hate all those frenchies, so she can love city\country but not the language:lol:
If Petra's gets pro team or has awesome year we would forget about her training indoors until some wild flop:haha:
Excelscior
Sep 4th, 2012, 05:47 PM
I love Montreal but i hate all those frenchies, so she can love city\country but not the language:lol:
If Petra's gets pro team or has awesome year we would forget about her training indoors until some wild flop:haha:
You crazy Shifty!! :lol:
Plus, Petra should be trying to squeeze the best (or that extra 10%) in every area of fitness, tennis training, where she lives, what she eats, etc.
Yes, Montreal is very European. However, if you would consider Montreal, then she might as well spend time in the US.
America has all type of climates for her (with "Frenchies or no Frenchies"). :lol:
And You're right! We won't care where she stays/vacations, until the next tournament (unless she gets sick or injured again, and then it's hell to pay). :lol: :fiery: :lol:
Martina CZ
Sep 4th, 2012, 10:58 PM
Yes, if Petra wants to maintain Czech citizenship, fine. But she should definitely vacation (especially when it's cold), and practice outside the Czech Republic.
If Berdych, Wozniaki and Djokovic can move to Monaco (the south of France) and function, then Petra can move to a similar French or Italian International resort herself. Hell, she can even move or vacation to some warm, quiet village somewhere in Europe, for all I care. :lol:
For Berdych the reason to move to Monaco are taxes, Czech Rep takes big chunk from all earnings ;)
In winter he prepared in Prostejov as well (Wozniacki too, by the way).
Excelscior
Sep 4th, 2012, 11:06 PM
For Berdych the reason to move to Monaco are taxes, Czech Rep takes big chunk from all earnings ;)
In winter he prepared in Prostejov as well (Wozniacki too, by the way).
I don't think Wozniaki actually showed/played last season, though she was scheduled?
Yes, Berdych and everyone else that's changes their Citizenship to Monaco, the Cayman Islands etc, do it for taxes. But like I said, the overwhelming majority of Tennis players and Golfers live in warm weather climates, regardless of their national status. The list is endless.
It's up to Petra if she wants to change her nationality. I just thought it was crazy she got sick during the middle of the Tennis season last year, when she was scheduled to play in Doha, but went home to the cold ass Czech Republic, then got sick, recovered for weeks.
And No Petra shouldn't train at Indoor Prostojev for the upcoming Outdoor hardcourt season. :lol:
Thanks for the input.
bruce goose
Sep 5th, 2012, 04:07 AM
W/o a doubt,at least some of you have seen one of those sci-fi or fantasy films where someone from another world...or some caveman who just thawed out...sees a telephone for the first time and tries to put it in his mouth as if it were something to eat....no clue whatsoever wtf it was made for
..........That's sort of what Petra's team reminds me of sometimes;their families were probably the last ones in the village to forsake the horse-and-buggy and try that crazy new invention called the automobile.Just imagine how unstoppable Petra might be if Bernard Pikola and his kinfolk weren't running her career
Queen Petra Fan
Sep 5th, 2012, 06:59 AM
OK guys, since the US Open for Petra is over, let's talk about something else for the upcoming Asian Swing, and ultimately the start of 2013 (till Tokyo starts of course).
In one of Queen Petra Fans most recent post, he mentioned an excellent suggestion which may of been overlooked. He said (if I remember correctly), that Petra should move out of the Czech Republic to a warmer climate (which I've always believed). And he also mentioned, she should at least practice in an outdoor facility. I hope I'm not misquoting him. :oh:
I happen to concur with both. You ever notice most top golfers and tennis players live in warm weather climates? Very few live in cold weather environments?
Now I don't know if Petra is ready to leave the Czech Republic at this stage (especially since Kotyza lives there). But I agree with QPF, that if she's not going to practice onsite in Asia (when ever she prepares for tennis again), it should be in an outdoor facility, preferably in a warm weather environment. If Petra's serious about making moves in her tennis career, this is something she should consider, especially at the end of 2012/start of the 2012 season.
Prostejov is an indoor facility (I have no idea what the weather is in the Czech Republic today, by the way), even though I remember Petra saying they were supposed to get outdoor courts in the future as well. Obviously Petra had a comfortably on Indoor courts, cause of Prostejov. But because of Petra's tennis immaturity, she didn't open up to Outdoor hardcourts every where equally as well, though her game obviously/easily translated to both.
That's why I was so mad when Petra had gotten that cold/virus earlier this year. I didn't think she should of been in the Czech Republic during a snow storm/the cold in the first place. I'm sure Petra can find away to live somewhere else, while maintaining her Czech citizenship. At worst, she can live/vacation elsewhere when the weather is cold or contains allergens in the Czech Republic.
At this point the only time Petra should be in the Czech Republic, is when she doesn't plan to play tennis and just visit family, relax, etc, when it's warm. Anytime she does wants to play tennis, I think she should practice somewhere else, unless it's warm and outdoors in the Czech Republic (and even that I probably don't agree with), if she can't officially move.
What do you guys think?
Hi Ex,
Just to clarify, what I made an observation on was the fact that all the Grand Slams are played outdoors and that if Petra wants to get serious about winning any of these again she needs to strongly consider training outdoors all year round. To not do this gives an advantage to her stronger opponents who do do it for all the obvious reasons. Let's face it, who cares if she's the Queen of Indoor tennis? It's about winning Grand Slams, that's what matters! She'll never be the best by practicing in a tennis incubator, greenhouse, or terrarium. Go outside Petra! And go somewhere warmer and stay away from winter flus and such. And don't risk your health playing stupid, meaningless exhibitions. The stakes are too large now.
I'm not saying she should change her citizenship, I hope she doesn't, but that's up to her and maybe her tax guy. But we have to admit, she's made enough money already to have her family come visit her wherever she went to advance her career.
I think Team Petra need to start taking a hard look at her future and making some bold choices to help her reach her full potential. Her current program is definitely not going to get her there and she will probably end up like Masha or Kim with about four Grand Slams to her credit in the end which would be a huge waste of her potential. She needs to build up for the day when Serena retires and Masha gets older, and then she will be sitting pretty and ready to capitalize. Of course, it would be even better if she made some changes and started kicking their asses now!!!
That's my two cents. :lol:
Time to run to work! :wavey:
Queen Petra Fan
Sep 5th, 2012, 05:51 PM
W/o a doubt,at least some of you have seen one of those sci-fi or fantasy films where someone from another world...or some caveman who just thawed out...sees a telephone for the first time and tries to put it in his mouth as if it were something to eat....no clue whatsoever wtf it was made for
..........That's sort of what Petra's team reminds me of sometimes;their families were probably the last ones in the village to forsake the horse-and-buggy and try that crazy new invention called the automobile.Just imagine how unstoppable Petra might be if Bernard Pikola and his kinfolk weren't running her career
Bruce, you couldn't be further from the truth. The Czech Republic is a very modern country. It was THE most modern in almost all of Europe until it got screwed over by Imperialistic Austria, Nazi Germany and Communist Russia. Even after ALL of THAT it's still a very modern country. Unlike your c.u.n.t.ry, you won't find anybody riding a burro over here Senor Pikola. Suck on that thought for a while before you patronize a group of people you have no clue about. ;) BTW: The picture below was not taken in Fulnek, CZ. Take a wild guess where it WAS taken... Hmmm? Tonto!
Excelscior
Sep 5th, 2012, 06:07 PM
W/o a doubt,at least some of you have seen one of those sci-fi or fantasy films where someone from another world...or some caveman who just thawed out...sees a telephone for the first time and tries to put it in his mouth as if it were something to eat....no clue whatsoever wtf it was made for
..........That's sort of what Petra's team reminds me of sometimes;their families were probably the last ones in the village to forsake the horse-and-buggy and try that crazy new invention called the automobile.Just imagine how unstoppable Petra might be if Bernard Pikola and his kinfolk weren't running her career
Bruce, you couldn't be further from the truth. The Czech Republic is a very modern country. It was THE most modern in almost all of Europe until it got screwed over by Imperialistic Austria, Nazi Germany and Communist Russia. Even after ALL of THAT it's still a very modern country. Unlike your c.u.n.t.ry, you won't find anybody riding a burro over here Senor Pikola. Suck on that thought for a while before you patronize a group of people you have no clue about. ;) BTW: The picture below was not taken in Fulnek, CZ. Take a wild guess where it WAS taken... Hmmm? Tonto!
Think he was more joking about Petra's colloquial team of lovable misfits QPF, than the Czech Republic itself. :)
Queen Petra Fan
Sep 5th, 2012, 07:02 PM
[QUOTE=Queen Petra Fan;22154578]
Think he was more joking about Petra's colloquial team of lovable misfits QPF, than the Czech Republic itself. :)
It was still a patronizing comment and he still deserved a kick in the balls. :lol:
BTW: Bartoli is becoming my new goddess! Come on Marion!!!! :bounce:
Never mind! She choked just like Petra.
Excelscior
Sep 5th, 2012, 07:14 PM
[QUOTE=Excelscior;22154791]
It was still a patronizing comment and he still deserved a kick in the balls. :lol:
BTW: Bartoli is becoming my new goddess! Come on Marion!!!! :bounce:
Watching these Pova matches, it just reminds you how Petra can beat her on hard courts (particularly slow ones).
Petra always gets into these tight, stiff baseline battles (minus her in opportunistic returning and serving) on these slower surfaces lately.
Petra for starters, needs to swing Sharapova side to side (using angles), instead of the north/south baseline game, where SHE makes the errors.
That's how Azarenka kills Sharpova every time. She just pulls Masha side to side, till she makes errors.
Petra has good hands at redirecting as well, and more power than Aza. But she still thinks she's playing at Wimby, where Petra's power can skid by Sharapova.
The US Open could of been an equalizer (supposed to be faster, more windy). But of course Petra never got that far.
Now Bartoli loses/Masha escaped, in a rain delayed close match, and it makes you feel worse, Petra didn't advance.
steni
Sep 5th, 2012, 07:26 PM
@BG
Ya no podés comentar nada aquí sin que te dén...
steni
Sep 5th, 2012, 07:27 PM
[QUOTE=Queen Petra Fan;22154578]
Think he was more joking about Petra's colloquial team of lovable misfits QPF, than the Czech Republic itself. :)
Agreed!
bruce goose
Sep 5th, 2012, 07:50 PM
[QUOTE=Excelscior;22154791]
It was still a patronizing comment and he still deserved a kick in the balls. :lol:.Well,now I'm convinced that you ARE a swishy bitch...not to mention a complete hypocrite.You preached self-righteously about how terrible something was--even though,as the NON-swishes figured out,I wasn't condemning Czechs at all--and then you blatantly went way over the line yourself.
I'll tell you what,Drag Queen Petra Fan: If you ever bring your pansy ass to L.A. or Texas,just let me know in advance and I'll make plans to meet you so that you can tell me TO MY FACE how worthless Mexicans suppsoedly are instead of hiding safely behind a TF poster name like the bitch that you are.I'd love to see how brave you really are...or,certainly,AREN'T...first-hand.Just don't try to cross the border with any weapons(I'll meet YOU),cuz if you went to one of our jails you wouldn't last 5 minutes w/o getting raped....by only ONE inmate(NO ONE would need to gang up on you:lol:).
I'll make sure to not quote your posts anymore OR talk about you,even indirectly,and I suggest that you keep your distance,figuratively,as well,you phony,racist pieza de mierda:rolleyes:.I'm done for today,mamador hambriento:wavey:
ShiftyFella
Sep 5th, 2012, 07:50 PM
Now i really really want Petra to have magnificent end of the season swing cause my wound after Bartoli vs Pova match is even worse now, strange thing that i was more emotionally involved than in match against Petra
steni
Sep 5th, 2012, 07:58 PM
[QUOTE=Queen Petra Fan;22155453]
Watching these Pova matches, it just reminds you how Petra can beat her on hard courts (particularly slow ones).
Petra always gets into these tight, stiff baseline battles (minus her in opportunistic returning and serving) on these slower surfaces lately.
Petra for starters, needs to swing Sharapova side to side (using angles), instead of the north/south baseline game, where SHE makes the errors.
That's how Azarenka kills Sharpova every time. She just pulls Masha side to side, till she makes errors.
Petra has good hands at redirecting as well, and more power than Aza. But she still thinks she's playing at Wimby, where Petra's power can skid by Sharapova.
The US Open could of been an equalizer (supposed to be faster, more windy). But of course Petra never got that far.
Now Bartoli loses/Masha escaped, in a rain delayed close match, and it makes you feel worse, Petra didn't advance.
I watched Azarenka's match and Sharapova's and I dont think Petra could beat them in her current form, maybe but not for sure. I hope she recovers the form she had last year at Linz, YEC and Fed Cup, for me she was just perfect and sooo confident [sigh]
Excelscior
Sep 5th, 2012, 08:02 PM
[QUOTE=Queen Petra Fan;22155453]Well,now I'm convinced that you ARE a swishy bitch...not to mention a complete hypocrite.You preached self-righteously about how terrible something was--even though,as the NON-swishes figured out,I wasn't condemning Czechs at all--and then you blatantly went way over the line yourself.
I'll tell you what,Drag Queen Petra Fan: If you ever bring your pansy ass to L.A. or Texas,just let me know in advance and I'll make plans to meet you so that you can tell me TO MY FACE how worthless Mexicans suppsoedly are instead of hiding safely behind a TF poster name like the bitch that you are.I'd love to see how brave you really are...or,certainly,AREN'T...first-hand.Just don't try to cross the border with any weapons(I'll meet YOU),cuz if you went to one of our jails you wouldn't last 5 minutes w/o getting raped....by only ONE inmate(NO ONE would need to gang up on you:lol:).
I'll make sure to not quote your posts anymore OR talk about you,even indirectly,and I suggest that you keep your distance,figuratively,as well,you phony,racist pieza de mierda:rolleyes:.I'm done for today,mamador hambriento:wavey:
Funny, the quote came out like I made the statement, though I know you knew I didn't, and you responded to QPF. :lol:
PS: What the hell is going on with the site? Now BG's statement, has QPF as the quoted person. Crazy! :lol:
steni
Sep 5th, 2012, 08:09 PM
Now i really really want Petra to have magnificent end of the season swing cause my wound after Bartoli vs Pova match is even worse now, strange thing that i was more emotionally involved than in match against Petra
I'm actually glad that Bartola lost, she is gross and her hair yuck!
steni
Sep 5th, 2012, 08:21 PM
[QUOTE=Queen Petra Fan;22155453]Well,now I'm convinced that you ARE a swishy bitch...not to mention a complete hypocrite.You preached self-righteously about how terrible something was--even though,as the NON-swishes figured out,I wasn't condemning Czechs at all--and then you blatantly went way over the line yourself.
I'll tell you what,Drag Queen Petra Fan: If you ever bring your pansy ass to L.A. or Texas,just let me know in advance and I'll make plans to meet you so that you can tell me TO MY FACE how worthless Mexicans suppsoedly are instead of hiding safely behind a TF poster name like the bitch that you are.I'd love to see how brave you really are...or,certainly,AREN'T...first-hand.Just don't try to cross the border with any weapons(I'll meet YOU),cuz if you went to one of our jails you wouldn't last 5 minutes w/o getting raped....by only ONE inmate(NO ONE would need to gang up on you:lol:).
I'll make sure to not quote your posts anymore OR talk about you,even indirectly,and I suggest that you keep your distance,figuratively,as well,you phony,racist pieza de mierda:rolleyes:.I'm done for today,mamador hambriento:wavey:
Pero xq vos le contestás? No le digás nada, si ya ví que le gusta mofarse de vos cuando puede... Ignorálo nada más!
Excelscior
Sep 5th, 2012, 08:29 PM
[QUOTE=Excelscior;22155646]
I watched Azarenka's match and Sharapova's and I dont think Petra could beat them in her current form, maybe but not for sure. I hope she recovers the form she had last year at Linz, YEC and Fed Cup, for me she was just perfect and sooo confident [sigh]
That's funny, cause Azarenka hasn't really played any one (and may just be a good match up for Petra), and many Sharapova fans are saying, "she looked bad against Bartoli, and will get murdered by Vika". They weren't happy either. But I know you looked at the level Sharapova was playing in the 2nd and particularly the third set of that match. They were striking the ball real well.
I know Vika scraped by Stosur as well, but certainly had her moments.
I will agree, that Petra doesn't appear to have the mental focus to win those type of long, tight, important matches.
But remember Maria, could of got wiped out the first Bartoli day, cause of the very windy conditions, that was messing up her serve. Oh well. Lol
We'll see?
PS: The site is still crazy, with the quoted material. Lol
steni
Sep 5th, 2012, 08:44 PM
[QUOTE=steni;22156117]
That's funny, cause Azarenka hasn't really played any one (and may just be a good match up for Petra), and many Sharapova fans are saying, "she looked bad against Bartoli, and will get murdered by Vika".
I know Vika scraped by Stosur as well.
I will agree, that Petra doesn't appear to have the mental focus to win those type of long, tight, important matches.
We'll see?
PS: I was speaking in General/the future, and not so much right now.
If Sharapova looked that bad, now Petra :facepalm: She needs to recover her fitness and than her confidence will follow. Look I dont like Azarenka or Sharapova but they have been playing better than Petra, you see they dont beat themselves like Petra does.
Excelscior
Sep 5th, 2012, 09:16 PM
[QUOTE=Excelscior;22156277]
If Sharapova looked that bad, now Petra :facepalm: She needs to recover her fitness and than her confidence will follow. Look I dont like Azarenka or Sharapova but they have been playing better than Petra, you see they dont beat themselves like Petra does.
Aha!
There in lies the riddle, wrapped up in a puzzle Steni.
Vika and Sharapova are monotonous grinders (some may say power grinders). But that's what they are.
Petra Kvitova is a shot maker. So there's always going to be a balance between her level of consistency, juxtasupposed to her level of shotmaking.
When Petra's shot making is hot, it doesn't matter. It's a wrap. When it's not, she has to pick her spots and be more consistent, till she waits her turn. If she doesn't; she loses.
One way she can be consistent, while still shortening the points and/or playing to her advantages, is by playing more cross court angles and corners, with air.
Petra loves to swing the ball side to side and she usually wins those points (especially with air).
ShiftyFella
Sep 5th, 2012, 09:31 PM
I'm actually glad that Bartola lost, she is gross and her hair yuck!
Yes, she's crazy and sometimes puts gatorade on her hair but at least i would have peace that Petra's loss wasn't to another Bartoli GOAT fluke and i really wanted GS F Cake vs Errani:lol:
Petronius
Sep 5th, 2012, 09:31 PM
Off topic: looking forward to Roger-Tomas tonight ! I have even returned from our weekend house with bad internet connection so I can watch. Their H2H in their last three matches is 3-3.
Can Tomas pull the upset?
Good night, the match starts early in the morning in Europe.
steni
Sep 5th, 2012, 09:48 PM
[QUOTE=steni;22156344]
Aha!
There in lies the riddle, wrapped up in a puzzle Steni.
Vika and Sharapova are monotonous grinders (some may say power grinders). But that's what they are.
Petra Kvitova is a shot maker. So there's always going to be a balance between her level of consistency, juxtasupposed to her level of shotmaking.
When Petra's shot making is hot, it doesn't matter. It's a wrap. When it's not, she has to pick her spots and be more consistent, till she waits her turn. If she doesn't; she loses.
One way she can be consistent, while still shortening the points and/or playing to her advantages, is by playing more cross court angles and corners, with air.
Petra loves to swing the ball side to side and she usually wins those points (especially with air).
Petra is more talented but this is not enough to win, she isnt Federer. Whatever the game style, they are winning and Petra isnt. She needs to get fit. Period!
Excelscior
Sep 5th, 2012, 09:54 PM
[QUOTE=Excelscior;22156540]
Petra is more talented but this is not enough to win, she isnt Federer. Whatever the game style, they are winning and Petra isnt. She needs to get fit. Period!
I'm not saying you're right or wrong.
But wouldn't you be much more confident in what you're saying if Petra had lost to Vika, Radwanksa a few times, and Masha on Grass, fast surface or indoors??
I know we want to look at it as doom and gloom, but my god Petra hasn't played the other two top 4 ranked players all year. Doesn't make you say "Damn, why not"!? :lol:
I'm not even sure if Petra played Stosur this year. Lol.
And just to illustrate what I mean, Petra has played Errani three times this year, and beat her all three times (with out losing a set), but hasn't played Radwanksa or Vika once. :tape:
And sports is funny. If Petra beats Vika or Aga for an important title, or in a semi-finals (where she's never faced them), you could be amazed at the type of confidence that could give her to raise her game, and then go on to beat Masha or anyone else.
Petra's a confidence player, amongst other things.
steni
Sep 5th, 2012, 10:12 PM
[QUOTE=steni;22156684]
I'm not saying you're right or wrong.
But wouldn't you be much more confident in what you're saying if Petra had lost to Vika, Radwanksa a few times, and Masha on Grass, fast surface or indoors??
I know we want to look at it as doom and gloom, but my god Petra hasn't played the other two top 4 ranked players all year. Doesn't make you say "Damn, why not"!? :lol:
I'm not even sure if Petra played Stosur this year. Lol.
And just to illustrate what I mean, Petra has played Errani three times this year, and beat her all three times, but hasn't played Radwanksa or Vika once. :tape:
But she hasnt beaten and like Synth explained the other day, Petra lost before meeting them. If Kerber beat Petra twice why not Azarenka or Radwanska, if Petra is fit she can, but with her current form? I dont know! Maybe can be a three setter with Petra losing cause physically she isnt there yet! Probably thats why she doesnt like long rallies cause she is lazy, but we know she can do it. Everybody in TF know that if Petra gets really fit and improve her movement, she can be the best in the world! Thats why Im so mad that she doesnt do it, or its taking so long, we dont know whats going on with her team!
Excelscior
Sep 5th, 2012, 10:20 PM
[QUOTE=Excelscior;22156712]
But she hasnt beaten and like Synth explained the other day, Petra lost before meeting them. If Kerber beat Petra twice why not Azarenka or Radwanska, if Petra is fit she can, but with her current form? I dont know! Maybe can be a three setter with Petra losing cause physically she isnt there yet! Probably thats why she doesnt like long rallies cause she is lazy, but we know she can do it. Everybody in TF know that if Petra gets really fit and improve her movement, she can be the best in the world! Thats why Im so mad that she doesnt do it, or its taking so long, we dont know whats going on with her team!
Didn't Kerber beat Petra earlier with an abdominal injury? And didn't she beat Petra a second time, in a semi-final, after Petra just won Montreal? That's not a big deal, the fairest comparison.
And you keep talking about "Fit". Huh?
Didn't Petra beat Li Na in Montreal? Didn't she outlast Kirilenko (who I'm sure you think is fit) during the New Haven final?
I'm not sure what you're saying? Wasn't she moving well in Montreal?
In other words, Petra may not had been the fittest earlier this year. And she certainly wasn't moving like we know how she could/did.
Now she shows us some glimpses of her old speed, wins lots of matches, then falters in a major. So let's see if she can keep it up for the Asian Swing.
In other words, though there's no majors involved, let's see how Petra looks (after this Pro and con USO tour) for the rest of the season; unless you don't think it's gonna count.
Lastly, we don't know what would happen with Vika and Radwasnksa (as much as you think you do), unless they played.
But I get you. Lol
steni
Sep 5th, 2012, 11:24 PM
[QUOTE=steni;22156796]
Didn't Kerber beat Petra earlier with an abdominal injury? And didn't she beat Petra a second time, in a semi-final, after Petra just won Montreal? That's not a big deal, the fairest comparison.
And you keep talking about "Fit". Huh?
Didn't Petra beat Li Na in Montreal? Didn't she outlast Kirilenko (who I'm sure you think is fit) during the New Haven final?
I'm not sure what you're saying? Wasn't she moving well in Montreal?
In other words, Petra may not had been the fittest earlier this year. And she certainly wasn't moving like we know how she could/did.
Now she shows us some glimpses of her old speed, wins lots of matches, then falters in a major. So let's see if she can keep it up for the Asian Swing.
In other words, though there's no majors involved, let's see how Petra looks (after this Pro and con USO tour) for the rest of the season; unless you don't think it's gonna count.
Lastly, we don't know what would happen with Vika and Radwasnksa (as much as you think you do), unless they played.
But I get you. Lol
Yeah she lost to her in Rome maybe cause the injury, but her lost in Cinncinati was cause her fitness, look at Li Na, finalist in Montreal and won Cincinnati(beating Kerber). She needs to get fit soon if she wants to be competitive. We saw at Montreal what can she do if she extends rallies, but can she do it all the time with her current form, I don't know, look what happened against Bartola or Kerber. This bitches know how to beat Petra, they know she isn't fit. I'm not saying she is fat just in case you were thinking!
I hope you are watching Serena's match!
Excelscior
Sep 5th, 2012, 11:54 PM
[QUOTE=Excelscior;22156838]
Yeah she lost to her in Rome maybe cause the injury, but her lost in Cinncinati was cause her fitness, look at Li Na, finalist in Montreal and won Cincinnati(beating Kerber). She needs to get fit soon if she wants to be competitive. We saw at Montreal what can she do if she extends rallies, but can she do it all the time with her current form, I don't know, look what happened against Bartola or Kerber. This bitches know how to beat Petra, they know she isn't fit. I'm not saying she is fat just in case you were thinking!
I hope you are watching Serena's match!
People lose Steni.
You can't attribute everything to fitness, especially when she went on to beat Kirilenko in the next tournament.
No one has won Montreal and Cincy back to back in years. And Li Na lost to Petra in three sets. How come you didn't bring up NA'S fitness?
One thing that maybe hurting Petra that I wanted to ask before she played Bartoli, but I held back until after the match/her Open ended, was:
Does Petra have a hitting partner? I know she used to use Adam periodically (haven't heard much about him lately), and sometimes plays practice matches. But who has been hitting with her the past few months, besides the nice PR Lady? Does she?
If not, that can be a big reason why Petra's consistency (which you can be confusing with fitness sometimes Steni), preparation and execution has been up and down this season.
How can Petra practice her ROS, defending certain ground strokes, or players if she doesn't have a full time hitting partner to act this stuff out with?
Yes, playing practice matches are important. But how often does she do that? And that's the end game. Many times, you want to work on certain things, with repetition (like serves, returns, volleying and ground strokes) to a live, realistic body. Coach Kotyza can't emulate Sharapova or Serena.
I mean, is Tomas Berdych gonna say "Hey Petra Let Me Serve To You, so you can practice your returns, and anything else you want"? And if so, how often? If not, do they hire people for this? It's not hard hiring some lower ranked men or even club level males.
If they haven't done this in any capacity lately, this is part of the colloquial but lovable group of Petra misfits and Keystone Cops I was discussing earlier. SMH :lol:
Maybe some of our Czech friends can answer this. Please let us know?
steni
Sep 6th, 2012, 12:02 AM
[QUOTE=steni;22157092]
People lose Steni.
You can't attribute everything to fitness, especially when she went on to beat Kirilenko in the next tournament.
No one has won Montreal and Cincy back to back in years. And Li Na lost to Petra in three sets. How come you didn't bring up her fitness?
One thing that I think can be hurting Petra, that I wanted to ask before she played Bartoli, but I held back until after the match/her Open ended.
Does Petra have a hitting partner? I know she used to use Adam periodically (haven't heard much about him lately), and sometimes plays practice matches. But does she?
If not, that can be a big reason why Petra's consistency (which you can be confusing with fitness sometimes Steni)and preparation has been up and down this season.
How can Petra practice her ROS, defending certain ground strokes, or players if she doesn't have a full time hitting partner to act this stuff out with?
Yes, playing practice matches are important. But how often does she do that. And that's the capper. Many times, you want to work on certain things, with repetition (like serves, returns and ground strokes) to a live body.
I mean is Tomas Berdych, gonna say "Hey Petra Let Me Serve To You, so you can practice your returns, and anything else you want"?
This is part of the colloquial, but lovable group of Petra misfits I was discussing earlier. :lol:
Maybe some of our Czech friends can answer this. Please let us know?
Oh my gosh. I'm not talking about winning Montreal and Cincinnati back to back, I don't care. I was talking about that Petra and Li Na played Montreal all the way, they came to Cincinnati and at the semis Petra was already tired, while Li Na was able to make the final and beat Kerber. I think fitness is very important is she wants to compete at the highest level, Kirilenko isn't Sharapova, Serena or Azarenka, even Kerber. Petra has already the shots and talent, but I dont think she is fit enough. Petra has to get serious, her lost to Bartola was just ridiculous.
Btw, I'm wondering who takes the decisions on her team. Does she has a voice, or someone else tell her what to do?
Excelscior
Sep 6th, 2012, 12:48 AM
[QUOTE=Excelscior;22157204]
Oh my gosh. I'm not talking about winning Montreal and Cincinnati back to back, I don't care. I was talking about that Petra and Li Na played Montreal all the way, they came to Cincinnati and at the semis Petra was already tired, while Li Na was able to make the final and beat Kerber. I think fitness is very important is she wants to compete at the highest level, Kirilenko isn't Sharapova, Serena or Azarenka, even Kerber. Petra has already the shots and talent, but I dont think she is fit enough. Petra has to get serious, her lost to Bartola was just ridiculous.
Btw, I'm wondering who takes the decisions on her team. Does she has a voice, or someone else tell her what to do?
I'm still asking you, how can you blame her for losing to Kerber in three sets, but she beat Li Na before in three sets?
So my question is, how come you didn't attribute Li Na losing to Petra as fitness in Montreal? Of course Li Na could win Cincinatti, she lost in Montreal. :lol:
Makes sense to me. :shrug: I mean, what are you getting at Steni? :lol:
I'm not saying you're wrong. But sometimes your examples and criteria don't add up. :lol:
Was Petra not in fitness when she beat Kirilenko? So if she lost to Kirilenko, then you would of blamed it on her fitness? Come on Steni. You can't have it both ways. :lol:
If you wanna blame something on her fitness, cause she looks tired to you, that's one thing. But you can't hand pick wins and losses, and then attribute them to fitness at a whim. :lol:
And the reason why I say all this is, Petra was very fit last year, especially the second half of the season. So if she's in proper shape/training, I have no reason to doubt that she would be, except for overplaying, injury and/or sickness (which all appeared to happen this year). Let's see what the Asian Swing brings?
As far as who makes coaching decisions for a hitting partner, I'm assuming it's Kotyza. But if Petra felt she wanted or needed one, I'm sure she could hire one.
And I'm sure her manager Csersonek could suggest it (though technically this would count as tennis; probably something Kotyza would handle) if he wanted.
steni
Sep 6th, 2012, 01:50 AM
[QUOTE=steni;22157508]
I'm still asking you, how can you blame her for losing to Kerber in three sets, but she beat Li Na before in three sets?
So my question is, how come you didn't attribute Li Na losing to Petra as fitness in Montreal? Of course Li Na could win Cincinatti, she lost in Montreal. :lol:
Makes sense to me. :shrug: I mean, what are you getting at Steni? :lol:
I'm not saying you're wrong. But sometimes your examples and criteria don't add up. :lol:
Was Petra not in fitness when she beat Kirilenko? So if she lost to Kirilenko, then you would of blamed it on her fitness? Come on Steni. You can't have it both ways. :lol:
If you wanna blame something on her fitness, cause she looks tired to you, that's one thing. But you can't hand pick wins and losses, and then attribute them to fitness at a whim. :lol:
And the reason why I say all this is, Petra was very fit last year, especially the second half of the season. So if she's in proper shape/training, I have no reason to doubt that she would be, except for overplaying, injury and/or sickness (which all appeared to happen this year). Let's see what the Asian Swing brings?
As far as who makes coaching decisions for a hitting partner, I'm assuming it's Kotyza. But if Petra felt she wanted or needed one, I'm sure she could hire one.
And I'm sure her manager Csersonek could suggest it (though technically this would count as tennis; probably something Kotyza would handle) if he wanted.
Ok whatever. Petra is the fittest player Ive ever seen in my life!
Excelscior
Sep 6th, 2012, 02:05 AM
[QUOTE=Excelscior;22157925]
Ok whatever. Petra is the fittest player Ive ever seen in my life!
I think your obsessed Steni :eek:.
Petra appears to have a few things going on (that we think/speculate about), and anyone of them, mind you several of them, could change her current year and future.
And someone from the Czech Republic, please let us know if she has a hitting partner (and no we're not talking about Adam in the past or the nice PR Lady)?
That can be a problem for her.
Deestruction
Sep 6th, 2012, 03:05 AM
Onto Tokyo it is. Pojd Petra :rocker2:
Petronius
Sep 6th, 2012, 04:07 AM
Off topic: looking forward to Roger-Tomas tonight ! I have even returned from our weekend house with bad internet connection so I can watch. Their H2H in their last three matches is 3-3.
Can Tomas pull the upset?
Good night, the match starts early in the morning in Europe.
Tomas :yeah:
Roger :hug:
pov
Sep 6th, 2012, 03:00 PM
[QUOTE=Excelscior;22157925]
Ok whatever. Petra is the fittest player Ive ever seen in my life!
One thing I learned is that questioning her fitness is a no-no on here. :shrug:
Lufa
Sep 6th, 2012, 03:58 PM
One thing I learned is that questioning her fitness is a no-no on here. :shrug:
so true :haha:
steni
Sep 6th, 2012, 07:06 PM
Without a doubt she has fitness issues... I dont care if others dont want to see the thruth!
Btw she isnt fat, just not fit enough!
steni
Sep 6th, 2012, 07:11 PM
One thing I learned is that questioning her fitness is a no-no on here. :shrug:
agreed!
bruce goose
Sep 7th, 2012, 02:44 AM
[QUOTE=bruce goose;22156063]
Funny, the quote came out like I made the statement, though I know you knew I didn'tYeah,that was just a sort of fluke in how the posts were displayed;I was pretty confident that you wouldn't misunderstand that...just as you easily deduced that I was only criticizing Petra's team and not condemning every Czech in racist fashion.The lovely Steni:hearts: tried to dissuade me from replying,but it only came natural for me to defend my people against such a vile attack.I suspect that sensible folks can see things for how they are,though,so there's no need to touch on THAT aspect anymore.Besides,my sister is about to have her first child via induced labor tomorrow,so that blessing outweighs virtually ANY negative:).
I know you might not wanna read this,but there's a friend of mine here at TF--a brilliant gal with a doctorate--who isn't a fan of Petra's,per se,yet is a huge fan of her game...and she told me how Petra began losing lots of steam on her shots in the 2nd set and was totally spent in the 3rd(whereas Bartoli wasn't even NEARLY as tired).If this is a faithful account,then it's true in spite of the fact that Petra coasted and conserved energy in quick matches vs. pedestrian foes in the first 3 rounds.I'm not saying that Petra is immature AT ALL,but she's still a fairly young athlete(Rookie-aged for the NFL),so I expect the older ones on her team to get in her face when she makes a bad decision...unless,of course,they were foolish to where they actually concurred with it:eek:.She wanted to honor the NH WC?Okay.....then pull out of Cincy instead and take the fine if necessary.That doesn't mean that Marion couldn't have won against a more-rested Petra;however,she'd at least have had to beat a Petra who wasn't dragging like someone who just finished a marathon.I don't blame Petra THAT much cuz she's young and might have felt invincible after her breakthrough on HCs at RC;all the same,it was strictly Amateur Hour from her coaches and team to let stuff play out that way
Excelscior
Sep 7th, 2012, 03:23 AM
[QUOTE=Excelscior;22156138]Yeah,that was just a sort of fluke in how the posts were displayed;I was pretty confident that you wouldn't misunderstand that...just as you easily deduced that I was only criticizing Petra's team and not condemning every Czech in racist fashion.The lovely Steni:hearts: tried to dissuade me from replying,but it only came natural for me to defend my people against such a vile attack.I suspect that sensible folks can see things for how they are,though,so there's no need to touch on THAT aspect anymore.Besides,my sister is about to have her first child via induced labor tomorrow,so that blessing outweighs virtually ANY negative:).
I know you might not wanna read this,but there's a friend of mine here at TF--a brilliant gal with a doctorate--who isn't a fan of Petra's,per se,yet is a huge fan of her game...and she told me how Petra began losing lots of steam on her shots in the 2nd set and was totally spent in the 3rd(whereas Bartoli wasn't even NEARLY as tired).If this is a faithful account,then it's true in spite of the fact that Petra coasted and conserved energy in quick matches vs. pedestrian foes in the first 3 rounds.I'm not saying that Petra is immature AT ALL,but she's still a fairly young athlete(Rookie-aged for the NFL),so I expect the older ones on her team to get in her face when she makes a bad decision...unless,of course,they were foolish to where they actually concurred with it:eek:.She wanted to honor the NH WC?Okay.....then pull out of Cincy instead and take the fine if necessary.That doesn't mean that Marion couldn't have won against a more-rested Petra;however,she'd at least have had to beat a Petra who wasn't dragging like someone who just finished a marathon.I don't blame Petra THAT much cuz she's young and might have felt invincible after her breakthrough on HCs at RC;all the same,it was strictly Amateur Hour from her coaches and team to let stuff play out that way
No problems. Something happened to her it seemed.
In retrospect, she probably shouldn't have went to New Haven. Agreed.
Unfortunately, I think she went because she didn't win Cincinnati when she thought she should of. If she would of won Cincinnati, I would of definitely advocated her not going to New Haven. Yes, you could sure made the argument, that's when her team/Kotyza could of told Petra or New Haven, "no we're not going"!
I only supported Petra's Entry the way I did (and pointed it out to you as well), cause Petra had already decided to go, and what could we do, but support it/her, and hope for the best? It could of been perceived like you were almost rooting against her a little Bruce, cause you kept reminding us. But no harm, no foul, no biggie.
Now Petra's already committed to go to New Haven next year. If she does, I hope she skips Cincy or Montreal (or in Steni's wish, get her self in such Super Shape, that no other WTA player is in, to play 5 straight weeks at such a high level). :lol:
It's also possible Petra could of had a asthma scare (or something), cause she spent so much time inside during her changeover. So who knows? :shrug: Lol
Onward to Tokyo, Asia, and the Indoor Swing.
Synth
Sep 7th, 2012, 05:10 PM
I think if Petra played better, she wouldn't have had to work as hard for a lot of the Cincy and Montreal wins that she got. The draw at those events were full of scrubs, excepting Li and Kerber. Petra was and should've been the favorite in all of her matchups. Unfortunately, each of her matchups ended up being a lot more work than they probably should've been on paper. It's a real problem. Petra needs to establish herself as a terrifying opponent who will beat you down with no mercy, because you give one scrub a chance to fight back, then every scrub you face from then on out will think they have a chance and keep fighting. Once Petra establishes that dominance over lower ranked players, she'll really start steamrolling through them, since she'd already come in with a huge mental advantage- vs. right now, every player's thinking: I just gotta hang until she starts making crazy UFE's.
Excelscior
Sep 7th, 2012, 07:31 PM
I think if Petra played better, she wouldn't have had to work as hard for a lot of the Cincy and Montreal wins that she got. The draw at those events were full of scrubs, excepting Li and Kerber. Petra was and should've been the favorite in all of her matchups. Unfortunately, each of her matchups ended up being a lot more work than they probably should've been on paper. It's a real problem. Petra needs to establish herself as a terrifying opponent who will beat you down with no mercy, because you give one scrub a chance to fight back, then every scrub you face from then on out will think they have a chance and keep fighting. Once Petra establishes that dominance over lower ranked players, she'll really start steamrolling through them, since she'd already come in with a huge mental advantage- vs. right now, every player's thinking: I just gotta hang until she starts making crazy UFE's.
Good point/post.
Petra used to roll the scrubs last year, when she won.
And the culprit seems to be her ROS/BP management (along with her lack of mental preparation and discipline of course).
Too many times Petra seemingly let's her opponents get away with numerous BP's cause she's swinging freely or careless on the ROS or the rally during the BP opportunity, blowing too many, while giving them chances and hope.
Excelscior
Sep 7th, 2012, 10:04 PM
I think if Petra played better, she wouldn't have had to work as hard for a lot of the Cincy and Montreal wins that she got. The draw at those events were full of scrubs, excepting Li and Kerber. Petra was and should've been the favorite in all of her matchups. Unfortunately, each of her matchups ended up being a lot more work than they probably should've been on paper. It's a real problem. Petra needs to establish herself as a terrifying opponent who will beat you down with no mercy, because you give one scrub a chance to fight back, then every scrub you face from then on out will think they have a chance and keep fighting. Once Petra establishes that dominance over lower ranked players, she'll really start steamrolling through them, since she'd already come in with a huge mental advantage- vs. right now, every player's thinking: I just gotta hang until she starts making crazy UFE's.
Ps: I think we woefully forget how Petra not having a regular hitting partner (if she doesn't and hasn't), can negatively impact her game from rallying, serving, ROS, Volleying, etc.
Does she? :shrug:
Petronius
Sep 10th, 2012, 01:07 PM
Latest ranking:
1 1 Azarenka, Victoria 31/07/89 BLR 10265 18
2 3 Sharapova, Maria 19/04/87 RUS 8435 17
3 2 Radwanska, Agnieszka 06/03/89 POL 8295 23
4 4 Williams, Serena 26/09/81 USA 7900 15
5 5 Kvitova, Petra 08/03/90 CZE 6690 21
6 6 Kerber, Angelique 18/01/88 GER 5085 22
7 10 Errani, Sara 29/04/87 ITA 4755 23
8 8 Li, Na 26/02/82 CHN 4526 17
9 7 Stosur, Samantha 30/03/84 AUS 4200 22
10 11 Bartoli, Marion 02/10/84 FRA 3800 28
It would be great if Petra moved ahead of Radwanska before Australian Open for an easier road to the semis. It's not likely, but it's doable.
The good news: Petra is the youngest player in Top 10! :)
Excelscior
Sep 10th, 2012, 06:10 PM
Latest ranking:
1 1 Azarenka, Victoria 31/07/89 BLR 10265 18
2 3 Sharapova, Maria 19/04/87 RUS 8435 17
3 2 Radwanska, Agnieszka 06/03/89 POL 8295 23
4 4 Williams, Serena 26/09/81 USA 7900 15
5 5 Kvitova, Petra 08/03/90 CZE 6690 21
6 6 Kerber, Angelique 18/01/88 GER 5085 22
7 10 Errani, Sara 29/04/87 ITA 4755 23
8 8 Li, Na 26/02/82 CHN 4526 17
9 7 Stosur, Samantha 30/03/84 AUS 4200 22
10 11 Bartoli, Marion 02/10/84 FRA 3800 28
It would be great if Petra moved ahead of Radwanska before Australian Open for an easier road to the semis. It's not likely, but it's doable.
The good news: Petra is the youngest player in Top 10! :)
Isn't this what we said before the US Open? :confused: Petra only had 5pts to defend at the US Open. She could of passed Serena for 4th, even if Serena won the title (which she did).
Now, Petra has to defend her Tokyo Semi, Linz and YEC title, vs Aga's Asian Swing Vulturism.
We'll see?
Mynarco
Sep 10th, 2012, 07:36 PM
Is she not playing an indoor tournament before Istanbul?
Excelscior
Sep 10th, 2012, 10:06 PM
Is she not playing an indoor tournament before Istanbul?
But I still find it funny that no one can say whether or not Petra had/has a full time hitting partner this year.
Who knows (besides other things)? Maybe this was one of the things that contributed to Petra losing to Sharapova and Serena this year?
How could Petra properly emulate and prepare for Sharapova and Serena with out a decent hitting partner? I know she only played Serena once this year. But just think about the amount of break points/2nd serves that Petra blew against Sharapova at the Australian and Stuttgart? Did she ever properly practice/prepare against this?
And Man, I don't want to ask/speculate if Petra and her team ever properly ever go over video of her matches and opponents, then apply it to future matches (though I'm sure they'd say so, if asked). :shrug:
But to stay positive, good luck to Petra in the Asian, indoor swing. :)
bruce goose
Sep 11th, 2012, 04:21 AM
And Man, I don't want to ask/speculate if Petra and her team ever properly ever go over video of her matches and opponents, then apply it to future matches (though I'm sure they'd say so, if asked). :shrug:Were you soliciting opinions in the slice above,Ex??Cuz I don't think that I should comment any more:angel: on the preparation techniques and ideas of some of Petra's team members:lol:
steni
Sep 11th, 2012, 11:24 AM
Were you soliciting opinions in the slice above,Ex??Cuz I don't think that I should comment any more:angel: on the preparation techniques and ideas of some of Petra's team members:lol:
Come on BG! Quién dijo miedo? Lol
Excelscior
Sep 11th, 2012, 01:39 PM
Were you soliciting opinions in the slice above,Ex??Cuz I don't think that I should comment any more:angel: on the preparation techniques and ideas of some of Petra's team members:lol:
Please comment. We have nothing to talk about till Tokyo. :lol: :angel: :lol:
Synth
Sep 11th, 2012, 02:12 PM
Do you think Kvitty plays better when Adam's around? or not around? :D
steni
Sep 11th, 2012, 08:22 PM
http://etsuko209hana-mandlikova-freak.blogspot.com/2012/05/22122011-trenink-s-hanou-mandlikovou.html?m=1
Excelscior
Sep 11th, 2012, 08:46 PM
Hana was a great and very talented player. Nice photo shoot. It's good Petra (if she didn't already) gets to learn/know/hang out with other Great Czech Tennis players.
Wow! Hana still has the cheeks, but nothing else is familiar. Lol
Petronius
Sep 11th, 2012, 09:42 PM
http://etsuko209hana-mandlikova-freak.blogspot.com/2012/05/22122011-trenink-s-hanou-mandlikovou.html?m=1
Thanks for the link, I haven't seen these pics, they're very cute. There's no doubt that Hana likes Petra very much.
I read an interview with Hana in March on the occasion of her 50th birthday and she said something similar as Hingis said in December: "I don't watch WTA at all, the players are very similar. But if I do, I only watch Petra" :lol:
I wouldn't be surprised if she produced a top player or even a slam champion in addition to already coaching Novotna to win Wimbledon.
I am still at awe that three of the four men semifinalists of this US Open - Murray, Djokovic and Berdych - are coached by former Czechoslovak players, which is a huge testament to the quality of tennis coaching in this country and I expect big results from Mandlikova as well.
Wouldn't it be cool, if she coached Petra for a year or two? :cool:
Petronius
Sep 11th, 2012, 09:46 PM
Isn't this what we said before the US Open? :confused: Petra only had 5pts to defend at the US Open. She could of passed Serena for 4th, even if Serena won the title (which she did).
Now, Petra has to defend her Tokyo Semi, Linz and YEC title, vs Aga's Asian Swing Vulturism.
We'll see?
You are absolutely right, I got myself carried away a little. Unless Aga Radwanska flops in Asia, Petra has little chance to move upwards in the rankings this year. :o
Excelscior
Sep 11th, 2012, 10:23 PM
You are absolutely right, I got myself carried away a little. Unless Aga Radwanska flops in Asia, Petra has little chance to move upwards in the rankings this year. :o
Yeah.
I don't know if you remember this Petronius, but Aga won two titles during the Asian swing last year (I think that was Tokyo and Beijing, which is 1900 pts right there). So it won't be easy for her to maintain points, unless she wins. However, Petra has similar or more points to defend with her success at the end of last year (YEC 1750, Tokyo 225, Linz 275?). Of course Aga got pts possibly elsewhere and the YEC as well.
But your original premise is correct, "Aga would have to flop, cause they both have lots of pts to defend". :lol:
Excelscior
Sep 11th, 2012, 10:43 PM
Actually Petronius, looking at the fall/winter schedule from last year, it looks entirely doable this year.
Petra could play Tokyo, skip Beijing, play Linz and then play the YEC, all with the proper amount of rest in between.
Last year she played Beijing after making the semi's at Tokyo. Hopefully, this year, if Petra does well in Tokyo again, she won't play Beijing, cause she would of already qualified for the YEC (unless Petra had purposefully crash and burned there, to get the needed rest).
Somehow I doubt it. Petra will play Beijing, cause last year she qualified and played there anyway. So I guess she'll play there again this year to meet her WTA requirements. :lol:
bruce goose
Sep 12th, 2012, 05:08 AM
Please comment. We have nothing to talk about till Tokyo. :lol: :angel: :lol:Well,I was encouraged to hear that they'll be moving Petra to a North Pole outpost the next time she gets sick cuz they're hoping to freeze the germs to death:crazy:
ShiftyFella
Sep 12th, 2012, 12:44 PM
Actually Petronius, looking at the fall/winter schedule from last year, it looks entirely doable this year.
Petra could play Tokyo, skip Beijing, play Linz and then play the YEC, all with the proper amount of rest in between.
Last year she played Beijing after making the semi's at Tokyo. Hopefully, this year, if Petra does well in Tokyo again, she won't play Beijing, cause she would of already qualified for the YEC (unless Petra had purposefully crash and burned there, to get the needed rest).
Somehow I doubt it. Petra will play Beijing, cause last year she qualified and played there anyway. So I guess she'll play there again this year to meet her WTA requirements. :lol:
If Petra skips Beijing it would be massive fail, she needs to play vs top 10 at big stages otherwise it diminishes her credibility as TOP4 player.
Excelscior
Sep 12th, 2012, 12:57 PM
If Petra skips Beijing it would be massive fail, she needs to play vs top 10 at big stages otherwise it diminishes her credibility as TOP4 player.
Huh?
Do you actually follow the Asian Swing?
Tokyo will have a better line up than Beijing. :eek:
Right now Azarenka, Sharapova, Radwanska, Na and Bartoli are all expected to be there.
I almost guarantee you that Sharapova and Serena won't be in Beijing (as they weren't last year).
Beijing has 1000 points and may be a Premier Mandatory event. But many of the top players don't regard it as much.
China is the lair of the Radwanska's, Wozniaki's, etc.
Excelscior
Sep 12th, 2012, 01:08 PM
Come on BG! Quién dijo miedo? Lol
I tried to respond to your message the other day, and it wouldn't let me respond.
I don't check or notice my PM's much, so sorry for the belated response.
ShiftyFella
Sep 12th, 2012, 02:32 PM
Huh?
Do you actually follow the Asian Swing?
Tokyo will have a better line up than Beijing. :eek:
Right now Azarenka, Sharapova, Radwanska, Na and Bartoli are all expected to be there.
I almost guarantee you that Sharapova and Serena won't be in Beijing (as they weren't last year).
Beijing has 1000 points and may be a Premier Mandatory event. But many of the top players don't regard it as much.
China is the lair of the Radwanska's, Wozniaki's, etc.
Azarenka could easily miss Tokyo but for sure going to Linz, Rena is going to Beijing cause Venus want to be there and she sort of implied it on Jimmy's show. I don't care about Li or Bartoli or even Kerber, I want Petra to have matches and preferably wins over VikaZilla, Aga, Pova before YEC so she would have more confidence going to YEC. Best chance of beating Aga is in Beijing, Vuvu at Linz, so why she need to shy away from competition and matches vs TOP4 before YEC?
Petronius
Sep 12th, 2012, 02:37 PM
Huh?
Do you actually follow the Asian Swing?
Tokyo will have a better line up than Beijing. :eek:
Right now Azarenka, Sharapova, Radwanska, Na and Bartoli are all expected to be there.
I almost guarantee you that Sharapova and Serena won't be in Beijing (as they weren't last year).
Beijing has 1000 points and may be a Premier Mandatory event. But many of the top players don't regard it as much.
China is the lair of the Radwanska's, Wozniaki's, etc.
It seems that Tokyo is a much older and prestigious event and I think it's very popular among players. It's also the only chance for them to visit the exotic Japan with its unique culture and atmosphere, hi-tech way of life, etc.
BTW, it's also the place where the last two matches between Navratilova and Graf took place. In 1994, a 37-year-old Martina beat a 25-year-old Steffi. So much for the argument who would have been the better player, had they played in the same era at their respective peaks :lol:
Excelscior
Sep 12th, 2012, 02:54 PM
Azarenka could easily miss Tokyo but for sure going to Linz, Rena is going to Beijing cause Venus want to be there and she sort of implied it on Jimmy's show. I don't care about Li or Bartoli or even Kerber, I want Petra to have matches and preferably wins over VikaZilla, Aga, Pova before YEC so she would have more confidence going to YEC. Best chance of beating Aga is in Beijing, Vuvu at Linz, so why she need to shy away from competition and matches vs TOP4 before YEC?
Serena also said she was going to Beiging last year, right up until she was supposed to be there. She didn't go. :lol: Don't you remember?
We'll see on that one? And I don't remember Vika being there last year as well.
As I said, Petra will face more legitimate competition in Tokyo than Beijing
Plus, if Petra plans to play Tokyo, Beijing, Linz and the YEC, then she'll have to skip one or get knocked out early, in order to have the proper rest.
That's what happened to her last year (she lost in Beijing early). I doubt if she won Beijing, then Linz, that she would of won the YEC to, after making the semifinal in Tokyo.
I'm telling you, Beijing is not the big tournament you think it is Shifty.
We'll see though?
Excelscior
Sep 12th, 2012, 02:59 PM
It seems that Tokyo is a much older and prestigious event and I think it's very popular among players. It's also the only chance for them to visit the exotic Japan with its unique culture and atmosphere, hi-tech way of life, etc.
BTW, it's also the place where the last two matches between Navratilova and Graf took place. In 1994, a 37-year-old Martina beat a 25-year-old Steffi. So much for the argument who would have been the better player, had they played in the same era at their respective peaks :lol:
Yeah, I think the top players just like going to Japan better, more. If they didn't, they would all skip the P5 Tokyo, for the PMandatory China Open, which follows right after. But they don't. Most commit to Tokyo first, then skip Beijing after (they usually pull out at the last minute with a phantom injury).
As far as the Martina vs Graf argument; you do realize (and I'm sure you do) that Martina herself regards Steffi as the Best All Around Female Tennis player, right? :eek:
Tokyo 1994, be damned!! :lol:
ShiftyFella
Sep 12th, 2012, 03:31 PM
Serena also said she was going to Beiging last year, right up until she was supposed to be there. She didn't go. :lol: Don't you remember?
We'll see on that one? And I don't remember Vika being there last year as well.
As I said, Petra will face more legitimate competition in Tokyo than Beijing
Plus, if Petra plans to play Tokyo, Beijing, Linz and the YEC, then she'll have to skip one or get knocked out early, in order to have the proper rest.
That's what happened to her last year (she lost in Beijing early). I doubt if she won Beijing, then Linz, that she would of won the YEC to, after making the semifinal in Tokyo.
I'm telling you, Beijing is not the big tournament you think it is Shifty.
We'll see though?
Beijing great for obtaining rankings points, thought if she manages to snatch a lot of them then you have to defend them next year which can be not so great like those points in New Haven for Petra, so maybe you right about playing in Beijing.
If Petra fails to advance deep enough to play Vika or Aga before YEC then for me it would be colossal fail on her part, thought if they are out before reaching Petra that's whole different story
Petronius
Sep 12th, 2012, 03:59 PM
As far as the Martina vs Graf argument; you do realize (and I'm sure you do) that Martina herself regards Steffi as the Best All Around Female Tennis player, right? :eek:
Martina says lots of nice things about other players :cool: The best 'all around' player? What about Steffi's one doubles slam versus Martina's 41 slams? :lol:
Tokyo 1994, be damned!! :lol:
You cannot disregard the match, as it actually happened.
It's actually quite a terrible loss for Steffi's fans. Yeah, it's just one, non-slam match in Tokyo, but if you want to be considered as the best singles player of all time, you can't afford to lose to a 37-year-old fellow all-time great when you are barely 25. For me it definitely plants a seed of doubt about peak Graf's theoretical ability to match peak Navratilova, e.g. Graf of 1988-89 versus Navratilova of 1983-84, when these two women were totally demolishing their competition.
steni
Sep 12th, 2012, 06:50 PM
I tried to respond to your message the other day, and it wouldn't let me respond.
I don't check or notice my PM's much, so sorry for the belated response.
???
Excelscior
Sep 12th, 2012, 07:52 PM
???
And when I tried to respond, it didn't let me.
steni
Sep 13th, 2012, 12:00 AM
And when I tried to respond, it didn't let me.
Ooooooh ok. it was nothing dont worry about it!
Excelscior
Sep 13th, 2012, 02:15 AM
Were you soliciting opinions in the slice above,Ex??Cuz I don't think that I should comment any more:angel: on the preparation techniques and ideas of some of Petra's team members:lol:
The other day I wondered if Petra's team shows her matches of her self? Come to think of it, now I wonder if they actually show Petra film of many men's matches (or at worst Petra's YEC, if they can't show her the men)?
Cause a lot of the tennis that Petra can play, most women don't play it. You'd actually have to watch an ATP match to see a player blend slices, off speed shots, spins, volleys, angles, chip or slice ROS and deft or high powered serving. Petra can play a mans game.
It's one thing to to try to explain these concepts. But when you see a Federer, Djokovic, Murray or Ferrer do it, it makes easier sense. Even her Czech country man-Berdych can mix it up quite nicely. The men just incorporate more variety on a whole, along with their superior power.
Even in Petra's YEC, she didn't use the stab, chip or slice return against a great server. Overall, the men just incorporate a better use of spin and racket manipulation to deal with a very hard hitting opponent or deep shots, instead of simply trying to always return the ball with power or a looper. Once mastered, this cuts down on errors tremendously.
We all know Petra has the great hands and the power, like an ATP player (not comparing her directly to an ATP player guys, so relax-). Lol.
Obviously, these are all things Petra's team can present to her in order to get better and reach her ultimate goals and potential. I hope they do so.
Petronius
Sep 18th, 2012, 11:28 PM
Two points:
1) Anybody knows if Petra plays Linz? This tourney is a great choice: an indoor hardcourt event is an excellent warm-up for YEC and the city of Linz is situated just about 50 km from the Czech-Austrian border, which means that Petra could enjoy the support of many Czech fans just as last year.
2) I noticed that the 5th-ranked Petra has more than a 1500 points lead over the 6th Kerber. In theory, this means that even if Petra failed to win a single match in Linz and YEC and had a decent showing in Asia, she would still probably remain at No. 5, as players earn a nice chunk of points even for round-robin losses at YEC. Talk about a comfortable lead!
steni
Sep 19th, 2012, 12:59 AM
Two points:
1) Anybody knows if Petra plays Linz? This tourney is a great choice: an indoor hardcourt event is an excellent warm-up for YEC and the city of Linz is situated just about 50 km from the Czech-Austrian border, which means that Petra could enjoy the support of many Czech fans just as last year.
2) I noticed that the 5th-ranked Petra has more than a 1500 points lead over the 6th Kerber. In theory, this means that even if Petra failed to win a single match in Linz and YEC and had a decent showing in Asia, she would still probably remain at No. 5, as players earn a nice chunk of points even for round-robin losses at YEC. Talk about a comfortable lead!
I checked the tournament website a couple days ago, and they haven't post anything about Petra's participation, just Azarenka, Paszek...
bruce goose
Sep 19th, 2012, 04:52 AM
Two points:
1) Anybody knows if Petra plays Linz? And you didn't mention that Petra was the defending champion,so it'd be nice to see her defend her title there as long as she doesn't have plans to overplay Premiers again in all the other YEC tune-ups
paulmara
Sep 19th, 2012, 12:24 PM
Petra Kvitova @Petra_Kvitova 1h
We go to Prague later today and then I'm leaving for Tokyo on Friday. Looking forward to playing matches again :)
pling
Sep 19th, 2012, 05:11 PM
Two points:
1) Anybody knows if Petra plays Linz? This tourney is a great choice: an indoor hardcourt event is an excellent warm-up for YEC and the city of Linz is situated just about 50 km from the Czech-Austrian border, which means that Petra could enjoy the support of many Czech fans just as last year.
2) I noticed that the 5th-ranked Petra has more than a 1500 points lead over the 6th Kerber. In theory, this means that even if Petra failed to win a single match in Linz and YEC and had a decent showing in Asia, she would still probably remain at No. 5, as players earn a nice chunk of points even for round-robin losses at YEC. Talk about a comfortable lead!
Does anyone remember if Petra took the wildcard to Linz last year only after she bombed out the 1R in Beijing? I guess if she does well in China, then Linz will be skipped - with YEC and Fed Cup to come.
Interesting that in terms of Race rankings, Petra has more points than this time last year:
Race Singles (As of Sep 10, 2012)
1. Victoria Azarenka 8686 (14)
2. Maria Sharapova 8190 (14)
3. Serena Williams 7900 (13)
5. Petra Kvitova 5310 (17)
6. Angelique Kerber 5080 (18)
Race Singles (As of September 12, 2011)
1. Caroline Wozniacki 7175 (19)
2. Maria Sharapova 6145 (12)
3. Li Na 5347 (16)
4. Petra Kvitova 5292 (15)
5. Victoria Azarenka 5057 (17)
6. Samantha Stosur 4925 (17)
But look at how Caro's 1st place in 2011 would only get her 4th this year! Shows how the slam winners have backed up their wins elsewhere on the tour and pulled away.
Petra's close enough that she should be aiming to overtake Aga in time to get 4th seed for the Aus Open (& so avoid a quarter-final against the top 3). I think this is feasible through Tokoyo, Beijing and YEC. She closed up a similar points gap last year to finish 2nd.
Go Girl :bounce:
Petronius
Sep 19th, 2012, 06:19 PM
Does anyone remember if Petra took the wildcard to Linz last year only after she bombed out the 1R in Beijing? I guess if she does well in China, then Linz will be skipped - with YEC and Fed Cup to come.
Interesting that in terms of Race rankings, Petra has more points than this time last year:
Race Singles (As of Sep 10, 2012)
1. Victoria Azarenka 8686 (14)
2. Maria Sharapova 8190 (14)
3. Serena Williams 7900 (13)
5. Petra Kvitova 5310 (17)
6. Angelique Kerber 5080 (18)
Race Singles (As of September 12, 2011)
1. Caroline Wozniacki 7175 (19)
2. Maria Sharapova 6145 (12)
3. Li Na 5347 (16)
4. Petra Kvitova 5292 (15)
5. Victoria Azarenka 5057 (17)
6. Samantha Stosur 4925 (17)
But look at how Caro's 1st place in 2011 would only get her 4th this year! Shows how the slam winners have backed up their wins elsewhere on the tour and pulled away.
Petra's close enough that she should be aiming to overtake Aga in time to get 4th seed for the Aus Open (& so avoid a quarter-final against the top 3). I think this is feasible through Tokoyo, Beijing and YEC. She closed up a similar points gap last year to finish 2nd.
Go Girl :bounce:
Lots of good points. Yeah, I also think that Petra's level is not that much different from the last year. It's actually her competitors' year-on-year improvement which makes her ranked so 'low'.
On the other hand, we shouldn't take for granted that Petra will excel at YEC. She won it last year without the participation of Serena or peak Sharpie (ankle injury).
bruce goose
Sep 20th, 2012, 04:15 AM
On the other hand, we shouldn't take for granted that Petra will excel at YEC. She won it last year without the participation of Serena or peak Sharpie (ankle injury).That's true,but it'd be that much more satisfying now if Petra won when they were there at full strength
paulmara
Sep 20th, 2012, 04:49 PM
Anybody knows if Petra plays Linz?
Linz is not probable because Victoria Azarenka wants to play there. It is against WTA rules to have two Top 10 players without increasing prize money.
Excelscior
Sep 20th, 2012, 07:34 PM
Petra will probably play the indoor (forgot the name) that Azarenka played last year. And "We'll See", if Serena actually plays the YEC (and what type of shape would she be in, if/when she did).
ShiftyFella
Sep 20th, 2012, 09:34 PM
Linz is not probable because Victoria Azarenka wants to play there. It is against WTA rules to have two Top 10 players without increasing prize money.
great article, are there any info on whether event with Pova would be streamed or not?
Petronius
Sep 20th, 2012, 10:35 PM
Petra will probably play the indoor (forgot the name) that Azarenka played last year.
Luxembourg
Petronius
Sep 20th, 2012, 10:37 PM
great article, are there any info on whether event with Pova would be streamed or not?
It will be probably aired live on the CT4 sport channel, but you need a Czech IP address.
Excelscior
Sep 20th, 2012, 11:46 PM
Luxembourg
Yeah, thanks.
Keep in mind, that's a guess on my part. It all depends on what Aga (who's ranked higher) and Petra does of course.
bruce goose
Sep 21st, 2012, 03:45 AM
Linz is not probable because Victoria Azarenka wants to play there. It is against WTA rules to have two Top 10 players without increasing prize money.
http://www.tenisportal.cz/zpravy/kvitova-do-haly-se-tesim-snad-to-vyjde-jako-loni-10895/Not to mention that Linz has instituted a new,no-lemur policy:(.To HELL with them:devil:;they need Petra more than Petra needs them:p
steni
Sep 21st, 2012, 04:09 AM
Apparently Kerber is gonna play in Luxembourg, so it seems Petra wont play there either. hmmm
ShiftyFella
Sep 21st, 2012, 04:46 AM
It will be probably aired live on the CT4 sport channel, but you need a Czech IP address.
that's great, thanks.
btw, not exactly. i can read and understand like 60% of it cause it's almost similar to russian with few exceptions plus google translate helps too:p
Apparently Kerber is gonna play in Luxembourg, so it seems Petra wont play there either. hmmm
i think it's better for her, she can now show great results in asia(beijing gives alot of points) and rest before yec\fedcup stuff.
paulmara
Sep 21st, 2012, 08:18 AM
Petra „If Azarenka withdraws I will go to Linz … I signed in.“
Q You are without Jozef Ivanko . You are looking for someone else ?
„Not yet , I ´m only with David. We will see after the season.“
„I had 6 days off. I met my old friend. We had fun.“
„No partying."
"I trained serve and return."
http://sport.idnes.cz/kvitovou-ceka-narocny-podzim-djv-/tenis.aspx?c=A120920_133712_tenis_ma
paulmara
Sep 21st, 2012, 08:40 AM
Toray Pan Pacific Open
Petkovic / Martić
http://www.wtatennis.com/SEWTATour-Archive/posting/2012/1056/MDS.pdf
steni
Sep 21st, 2012, 07:32 PM
Petra „If Azarenka withdraws I will go to Linz … I signed in.“
Q You are without Jozef Ivanko . You are looking for someone else ?
„Not yet , I ´m only with David. We will see after the season.“
„I had 6 days off. I met my old friend. We had fun.“
„No partying."
"I trained serve and return."
http://sport.idnes.cz/kvitovou-ceka-narocny-podzim-djv-/tenis.aspx?c=A120920_133712_tenis_ma
:eek: she isn't in a hurry to improve her fitness... So just focusing in "serve and return"... This Petra is killing me!
Excelscior
Sep 21st, 2012, 07:44 PM
Toray Pan Pacific Open
Petkovic / Martić
http://www.wtatennis.com/SEWTATour-Archive/posting/2012/1056/MDS.pdf
Petra Martic (of the serve and volley, very talented Petra Martic's)? :lol:
If so, tough opening draw when you haven't played a month.
The only thing is, Martic can be mistake prone as well. :lol:
You know I didn't even notice "Petkovic's" name. I just assumed read it as "Petra Martic".
OK. Either match should/would be interesting then. Lol.
steni
Sep 21st, 2012, 08:07 PM
She got a nice draw until the semis I think, there are like 3 or 4 players that could be a pain in the butt but isn't impossible...
Petronius
Sep 21st, 2012, 10:29 PM
For those asking if Petra has a hitting partner: she said for tenisportal.cz that "I practiced with Lucie (Safarova) and with one male player from Prostejov"
I hope she didn't mean David Kotyza :lol:
bruce goose
Sep 22nd, 2012, 03:58 AM
For those asking if Petra has a hitting partner: she said for tenisportal.cz that "I practiced with Lucie (Safarova) and with one male player from Prostejov"
I hope she didn't mean David Kotyza :lol:Maybe Petra just meant that he was a 'player' with the ladies:lol:
Excelscior
Sep 22nd, 2012, 04:16 AM
For those asking if Petra has a hitting partner: she said for tenisportal.cz that "I practiced with Lucie (Safarova) and with one male player from Prostejov"
I hope she didn't mean David Kotyza :lol:
And I hope she didn't mean just her time at Prostojev. :lol:
Who was she hitting with the first 3/4 of the tennis season this year? Inquiring minds would like to know :scratch:
Petronius
Sep 22nd, 2012, 01:18 PM
Maybe Petra just meant that he was a 'player' with the ladies:lol:
Or maybe she meant the CEO of the club? He's a bit old and fat so Petra allowed him to use a special racquet to make up for the handicap. Petra must have had hell trying to hit thru him :lol:
http://img.ahaonline.cz/img/18/article/945306_miroslav-cernosek.jpg
Excelscior
Sep 22nd, 2012, 01:26 PM
Or maybe she meant the CEO of the club? He's a bit old and fat so Petra allowed him to use a special racquet to make up for the handicap. Petra must have had hell trying to hit thru him :lol:
http://img.ahaonline.cz/img/18/article/945306_miroslav-cernosek.jpg
Really nice looking facility, from every photo and angle I can see. :yeah:
Petronius
Sep 22nd, 2012, 01:49 PM
Really nice looking facility, from every photo and angle I can see. :yeah:
This guy is a great lobbyist with loads of great links to top politicians, entrepreneurs, etc. Once he boasted in the press that he got a $1.5m subsidy for a brand-new gym. :lol: The AGROFERT logo on the background refers to a giant food processing company owned by one billionaire (he's on the Forbes 1000 list with$1.4bn fortune), who also supplies some cash to the club.
Lendl said that such big tennis facilities - which didn't exist in 1980s - might help discover and develop even more talented players than in the past. :cool:
paulmara
Sep 23rd, 2012, 01:22 PM
Petra Martić beat Andrea Petkovic 0:6 6:4 6:3
5/8 breakpoints saved
1/1 breakpoints saved
8/9 breakpoints saved
8 DFs and 5 aces
Synth
Sep 23rd, 2012, 01:29 PM
Nice draw for Kvitty. Least dangerous QF'ist and Sharapova over Azarenka.
Excelscior
Sep 23rd, 2012, 01:41 PM
I haven't looked at the draw. But let me get this right?
So your saying Petra (if she got that far) would have to play Sharapova again in another semifinal? And you're saying that's better than playing Azarenka (not saying that Petra isn't ripe to beat Sharpie, on this faster hardcourt-Petra should), who she hasn't played all year and beaten 4X in a row? That's supposed to be a good thing? :lol:
Wow! :eek:
I know what you mean (if I read you/the draw right). But how about something different for a change?
Petronius
Sep 23rd, 2012, 09:56 PM
Looking quickly at the Tokyo schedule, it seems that Petra won't play until Tuesday.
Rex59
Sep 24th, 2012, 10:25 AM
Looking quickly at the Tokyo schedule, it seems that Petra won't play until Tuesday.
True, but you won't see it. The Petras get Center court at 11 a.m. Tokyo time, which translates to 9 p.m. CDT in the States. ESPN doesn't start streaming 'til midnight, which means you'll get the last 3 matches on Center starting with, naturally, 'Pova's match with H. Watson, followed by Vika's match with Tamira and ending with Aggie and Jelena. Ergo, unless Eurosport pops up with a stream somewhere the Petras match "won't be seen".
http://www.toray-ppo.co.jp/tournament/pdf/2012wtaii_oop6.pdf
Excelscior
Sep 24th, 2012, 12:52 PM
True, but you won't see it. The Petras get Center court at 11 a.m. Tokyo time, which translates to 9 p.m. CDT in the States. ESPN doesn't start streaming 'til midnight, which means you'll get the last 3 matches on Center starting with, naturally, 'Pova's match with H. Watson, followed by Vika's match with Tamira and ending with Aggie and Jelena. Ergo, unless Eurosport pops up with a stream somewhere the Petras match "won't be seen".
http://www.toray-ppo.co.jp/tournament/pdf/2012wtaii_oop6.pdf
ESPN 3's streaming coverage is not till 1am tonight, and Tokyo is 13 hrs ahead of us.
More than likely they'll miss the first two matches (or a large part of the second one unless Petra's and/or the following match goes longer than expected).
Petronius
Sep 24th, 2012, 01:06 PM
True, but you won't see it. The Petras get Center court at 11 a.m. Tokyo time, which translates to 9 p.m. CDT in the States. ESPN doesn't start streaming 'til midnight, which means you'll get the last 3 matches on Center starting with, naturally, 'Pova's match with H. Watson, followed by Vika's match with Tamira and ending with Aggie and Jelena. Ergo, unless Eurosport pops up with a stream somewhere the Petras match "won't be seen".
http://www.toray-ppo.co.jp/tournament/pdf/2012wtaii_oop6.pdf
Thanks, so if Petra plays terrible, at least we won't see it. :p
Excelscior
Sep 24th, 2012, 01:18 PM
Petra's 11am match, would be 10pm US EST/NYC time.
ESPN 3 won't broadcast till 1am here.
Hopefully (as it was mentioned), they'll be a wayward stream.
Some of you Europeans should be asleep around that (3-5am your time) time anyway
steni
Sep 24th, 2012, 02:07 PM
F*** Radwanska qualified for Istanbul, so she is gonna be the fourth seed...
Excelscior
Sep 24th, 2012, 03:48 PM
F*** Radwanska qualified for Istanbul, so she is gonna be the fourth seed...
YEC is a round robin. And I'm not sure if the ultimate seeding/pairings can be determined from now. Aga just qualified to get in. I'm sure Tokyo, Beijing and some of the other tournaments can affect the seedings.
Plus, it's different than the other tournaments (the # 1, 3, 5, 7 seeds play in one group, then the 2, 4, 6 and 8 players play in another group).
I'm not even sure if Serena will go. But we'll see?
pling
Sep 24th, 2012, 04:25 PM
F*** Radwanska qualified for Istanbul, so she is gonna be the fourth seed...
YEC is a round robin. And I'm not sure if the ultimate seeding/pairings can be determined from now. Aga just qualified to get in. I'm sure Tokyo, Beijing and some of the other tournaments can affect the seedings.
Plus, it's different than the other tournaments (the # 1, 3, 5, 7 seeds play in one group, then the 2, 4, 6 and 8 players play in another group).
I'm not even sure if Serena will go. But we'll see?
If Aga has Tokyo/Beijing results of R16/QF then she can be caught by Petra or Angie if they do much better - like a win and a SF. Although it gets close there's always Moscow to grab a few more points.
But then, as Ex says, the seedings wil probably not matter as much as the luck of who you draw. Last year the groups were 1,3,6,8 and 2,4,5,7.
If Serena is there and still on form, then being in her group might actually be better, as two players qualify from each group and would not meet again until the final.
pling
Sep 24th, 2012, 04:28 PM
Petra's 11am match, would be 10pm US EST/NYC time.
ESPN 3 won't broadcast till 1am here.
Hopefully (as it was mentioned), they'll be a wayward stream.
Some of you Europeans should be asleep around that (3-5am your time) time anyway
I'm assuming this won't be streamed - and I'm not waiting up till 3am to find out :)
if Petra plays terrible, at least we won't see it. :p
That's how I see it :lol: Even if it was streamed at at 3am, I'd be so pissed if I got up to watch it and petra lost.
Jan_S
Sep 24th, 2012, 04:32 PM
YEC is a round robin. And I'm not sure if the ultimate seeding/pairings can be determined from now. Aga just qualified to get in. I'm sure Tokyo, Beijing and some of the other tournaments can affect the seedings.
Plus, it's different than the other tournaments (the # 1, 3, 5, 7 seeds play in one group, then the 2, 4, 6 and 8 players play in another group).
I'm not even sure if Serena will go. But we'll see?
The seeding can change: the rankings/race position (it'll be the same then) after Luxembourg and Moscow tournaments is what counts. And the two groups players are placed in are not rigidly defined by odd/even seeds. There will be a draw. The only rule is that the consecutive seeds--1st and 2nd, 3rd and 4th, 5th and 6th, 7th and 8th--end up in different groups.
pling
Sep 24th, 2012, 04:45 PM
The seeding can change: the rankings/race position (it'll be the same then) after Luxembourg and Moscow tournaments is what counts. And the two groups players are placed in are not rigidly defined by odd/even seeds. There will be a draw. The only rule is that the consecutive seeds--1st and 2nd, 3rd and 4th, 5th and 6th, 7th and 8th--end up in different groups.
So being 4th if Serena is third would mean different groups - which might then mean meeting Serena in SF. Whereas playing Serena in the group stage might be good preparation - if Petra plays well enough to get to the final again.
And if Petra and Angie stay 5/6 they'll be in different groups but could draw anyone else.
Jan_S
Sep 24th, 2012, 04:57 PM
So being 4th if Serena is third would mean different groups - which might then mean meeting Serena in SF. Whereas playing Serena in the group stage might be good preparation - if Petra plays well enough to get to the final again.
And if Petra and Angie stay 5/6 they'll be in different groups but could draw anyone else.
Yes. Basically, the worst case would be Petra ending up together with Maria and Serena (and Li).
bruce goose
Sep 24th, 2012, 05:24 PM
Or maybe she meant the CEO of the club? He's a bit old and fat so Petra allowed him to use a special racquet to make up for the handicap. Petra must have had hell trying to hit thru him :lol:
http://img.ahaonline.cz/img/18/article/945306_miroslav-cernosek.jpgWell,given his apparent wealth,maybe he IS a player with the ladies;)...but he'd still make a lousy hitting partner for Petra:lol:
Excelscior
Sep 24th, 2012, 09:30 PM
Yup Yup.
There are no streams that I see from Tokyo, that start before 2pm (Tokyo time) or 1 am NYC, US EST time.
Which is too bad, cause though it will be late for you Europeans, Petra's match will actually start 10pm for us on the East Coast of America. Not bad.
steni
Sep 24th, 2012, 10:50 PM
Why why whyyyyy...? I really I wanted to watch Petra, she better wins!
mac47
Sep 25th, 2012, 12:13 AM
Wait, you mean it is not streamed at all, or it is streamed at a lousy time? Because I will get up at any hour of the night to watch my lioness.
Excelscior, have you found any stream at all?
TimeyWimey
Sep 25th, 2012, 12:17 AM
^first two matches on centre will not be streamed, nothing we could do
TimeyWimey
Sep 25th, 2012, 12:22 AM
YEC is a round robin. And I'm not sure if the ultimate seeding/pairings can be determined from now. Aga just qualified to get in. I'm sure Tokyo, Beijing and some of the other tournaments can affect the seedings.
Plus, it's different than the other tournaments (the # 1, 3, 5, 7 seeds play in one group, then the 2, 4, 6 and 8 players play in another group).
I'm not even sure if Serena will go. But we'll see?
nein, only to make sure 1/2 3/4 5/6 7/8 are in different groups
Excelscior
Sep 25th, 2012, 01:40 AM
Wait, you mean it is not streamed at all, or it is streamed at a lousy time? Because I will get up at any hour of the night to watch my lioness.
Excelscior, have you found any stream at all?
I haven't looked again. But unfortunately, as far as normal means, I have not found one.
Maybe there's some bootleg Japanese stream out there. But as far as the proper ones for us to pilfer/see on our known sites, no. :lol:
Synth
Sep 25th, 2012, 02:40 AM
OI! Petra! What are you doing?
bruce goose
Sep 25th, 2012, 06:08 AM
Was it Tokyo or Beijing where Petra bombed out in her first match last year(?)...and then went on to win Linz,YEC and FC......I'm grasping for positives here:o
ShiftyFella
Sep 25th, 2012, 06:09 AM
oh man, did it just happened or i still see my worst dream?:bigcry:
Petronius
Sep 25th, 2012, 09:42 AM
This Tokyo tournament appears to be very unpredictable. Ivanovic out. Kanepi defeated by a qualifier. Stosur and Li needed tough three setters to get through and Sharapova struggled for three hours (!!!) with a qualifier. And now Petra eliminated by an inspired Martic, who, in her own words, played maybe the best tennis of her life.
If I were a betting man, I would stay away from this event.
Excelscior
Sep 25th, 2012, 12:02 PM
This Tokyo tournament appears to be very unpredictable. Ivanovic out. Kanepi defeated by a qualifier. Stosur and Li needed tough three setters to get through and Sharapova struggled for three hours (!!!) with a qualifier. And now Petra eliminated by an inspired Martic, who, in her own words, played maybe the best tennis of her life.
If I were a betting man, I would stay away from this event.
No excuses.
You were asleep. Me and Steni sat through this debacle on Live score.
No, we couldn't see it unfortunately. And I like Martic (and was concerned about this match and Petra's preparation, that's why you didn't hear say it was easy, etc.). However, let's face it, Petra was dreadful and woefully unprepared.
Both players served and returned like crap for most of the match, getting broken and accumulating empty BP's numerous times. Even if Martic, turned it around and played "the best tennis in her life" (according to Petronius) towards the end, Kvitova had blown so many opportunities earlier, it would have served her right.
But I'm not buying it. Petra was just unprepared, mentally out of it, and/or didn't compete, no matter how good Martic was alleged to had played. There was just no fight or consistency from her this match. We've seen it all before in early rd tournaments (the horrendous serving and inability to convert numerous BP's and gain any consistency and traction through out the match). This match was no different. Let's face it. Kvitova was probably Martic's Biggest scalp (why is it always Petra this seems to happen to lately) so far in her career. That's why it was her "best match".
And Bruce, Petra K. got knocked out Beijing early last year. It was Tokyo where she made the semi-finals, before losing that wild match to Zvonrareva, when she was up 5-1 in the first set and lost in two sets (I think it was two). Unbelievable!!
bruce goose
Sep 25th, 2012, 12:21 PM
No excuses.
And Bruce, she got knocked out Beijing early last year. It was Tokyo where she made the semi-finals, before losing that wild match to Zvonrareva, when she was up 5-1 in the first set and lost in two sets (I think it was two).You're right,and we've already had the 'friend excuse' with Hradecka,so hopefully we won't hear that it's hard for Petra to play someone with the same name:o
Excelscior
Sep 25th, 2012, 12:25 PM
You're right,and we've already had the 'friend excuse' with Hradecka,so hopefully we won't hear that it's hard for Petra to play someone with the same name:o
Yeah, right. :lol: :tape: :lol:
Synth
Sep 25th, 2012, 12:29 PM
No excuses.
You were asleep. Me and Steni sat through this debacle on Live score.
Seconded. The key difference between Petra and the ones that "struggled" is that the other ones made it through. She didn't.
Petronius
Sep 25th, 2012, 12:40 PM
Both players served and returned like crap for most of the match, getting broken and accumulating empty BP's numerous times.
What about the wind/sun/humidity? Especially the first two factors have serious impact on the quality of serving and I've read that Sharapova double-faulted like crazy. BTW, did you see the Murray-Berdych windy shitfest? :lol:
However, let's face it, Petra was dreadful and woefully unprepared.
What about the general notion that the first match is by far the most dangerous for tournament favorites, who tend to be vulnerable facing an already warmed-up qualifier/lower ranked player?
Even if Martic, turned it around and played "the best tennis in her life" (according to Petronius)
According to Martic herself.
Petra was just unprepared, mentally out of it, and/or didn't compete, no matter how good Martic was alleged to had played. There was just no fight or consistency from her this match.
I'm still not sure whether Petra really wants to be multiple (5-10 slams) slam champion and the No.1 player or just to be comfortably in the Top 10, earning $2-3m a year. We can't do anything about this, it's up to the girl. But it's possible to ask her in a future on-line Q&A, if any. Excelscior Sep 25th, 2012, 12:48 PM Seconded. The key difference between Petra and the ones that "struggled" is that the other ones made it through. She didn't. My condolences for sitting through it. :lol: And you are so right. Petra K had to be the Shiny Dodo Bird [scalp] not to make it through. :oh: TimeyWimey Sep 25th, 2012, 12:48 PM before such an important match, maybe i shouldn't post here after a long hiatus :( so, is she going to play Linz or Luxembourg after Beijing? pov Sep 25th, 2012, 01:18 PM I'm still not sure whether Petra really wants to be multiple (5-10 slams) slam champion and the No.1 player or just to be comfortably in the Top 10, earning$2-3m a year. We can't do anything about this, it's up to the girl. But it's possible to ask her in a future on-line Q&A, if any.
Wait . . are you daring to muse on whether she has the hunger to apply her prodigious talent and dominate the tour? No, of course not, I misunderstood -only a non-fan, troll like me would wonder such a thing.;)
(bitter any pov? . . :haha:)
Anyway . . . asking her or any pro-athlete such a question seems futile. Given today's media climate with its "rake people over the coals" attitude, would take a really unusual person to reply honestly.
pov
Sep 25th, 2012, 01:22 PM
Okay. No one saw the match. To me the stats don't look that bad. The only thing that stands out is the low percentage of points won on 1st serves in. And since no one got to watch . . there's no way to know why. Perhaps Martic was just returning serve at a level she hadn't achieved before. So . disappointed but I won't judge her on a match without having seen it or at least, hearing from those who saw it.
mac47
Sep 25th, 2012, 01:53 PM
Impressed with you for suspending judgment, Pov. I had you figured for one who would kick Petra to the curb.
pov
Sep 25th, 2012, 02:15 PM
Impressed with you for suspending judgment, Pov. I had you figured for one who would kick Petra to the curb.
:) I'm also surprised at this post by you. When I saw you'd posted I was sure it was going to be another attack of some sort. I'd come to think that it didn't matter what I posted - you'd decided that I was the "enemy" and that was that. So thanks. I think that, whatever different opinions we have, we'd all like to see her play up to her great potential. :yeah:
Excelscior
Sep 25th, 2012, 02:51 PM
Okay. No one saw the match. To me the stats don't look that bad. The only thing that stands out is the low percentage of points won on 1st serves in. And since no one got to watch . . there's no way to know why. Perhaps Martic was just returning serve at a level she hadn't achieved before. So . disappointed but I won't judge her on a match without having seen it or at least, hearing from those who saw it.
Fair enough. I certainly admire your diplomacy. But my guess is, you didn't sit through the livescore as some of us did. :lol:
Granted, I didn't see it with my eyes. No Sir-ee. But statistics can be deceiving (probably stabilized towards the end of the match to make it appear better). You can check some of the stats and notes I and Steni wrote during the livescore. It wasn't pretty for either player.
Martic only served 50% during the first set. She has a fast 1st serve yes. But she is not known for having a decent second serve, nor return. In addition, both Petra and Martic had a high amount of DF's to aces, both were broken numerous times, and neither could convert numerous break points opportunities (especially Petra) that were presented. The difference between the score, were the two extra breaks that Martic had amongst a flurry of them. Things may of only stabilized-match wise and statistically towards the end of the 2nd set (and Petra was still only one break down then).
Remember, Martic had already played a match, so if she couldn't serve well, that means she was struggling and Petra K couldn't take advantage. It was like no one wanted to win until the latter part of the second set, when Martic held. But you certainly wouldn't of been surprised if she didn't either. :lol:
From my vantage point, this match was no different than previous lackluster opening rd matches for Petra where her serve, ROS, BP opportunities and fight were lacking. How often does Petra serve 1 ace to 5 DF (which she had at one point) during a match?
I respect your fairness POV. But I think others that sat through this would agree with me. Yes, I like Martic's game. I do. But there's a reason why she's ranked where she is (mistakes, pressure and choking). Petra should of clamped down and won this match, even if Martic was inspired to play her.
Did I see it? No. But the up and down nature of this match, and Petra's lack of consistency in any area, reminds me of so many other early rd matches , where Petra was unprepared in so many ways. No excuses.
Excelscior
Sep 25th, 2012, 04:01 PM
What about the wind/sun/humidity? Especially the first two factors have serious impact on the quality of serving and I've read that Sharapova double-faulted like crazy. BTW, did you see the Murray-Berdych windy shitfest? :lol:
What about the general notion that the first match is by far the most dangerous for tournament favorites, who tend to be vulnerable facing an already warmed-up qualifier/lower ranked player?
According to Martic herself.
I'm still not sure whether Petra really wants to be multiple (5-10 slams) slam champion and the No.1 player or just to be comfortably in the Top 10, earning $2-3m a year. We can't do anything about this, it's up to the girl. But it's possible to ask her in a future on-line Q&A, if any. 1) The humidity was 78 percent, with 16mph winds (according to Steni). Not great. However, I didn't hear Petra complain about the conditions before hand. Both players had to play in it, and Martic's not a pusher, get the ball back type, so there's no excuses. Remember, Petra made the semifinals here last year. 2) Yeah, the first match can be the "most dangerous match". Agreed. But apparently, Petra was the only top seed to lose in the first rd? :tape: Doesn't she feel lonely, like at the Olympics, watching Pova, Rena, Vika and "My God" Makiri-who beat her in the semifinals (and later on, watching 3 of them on the podium receiving medals)? 3) Yes, according to Martic. But I quoted you, since I didn't read, see or believe it (the notion of, not that Martic didn't say it). 4) You don't need to aspire to be a number one player with 5-10 slams, to have gotten through that first rd match, in a tournament you made the semifinals in last year. Where's her pride? Wouldn't she wanna try to win it this year (especially after what happened in that Zvonareva semi-final)? How can she walk away, feeling satisfied with her performance here once again? You just get a feeling, Petra took a vacation in the Czech Republic and then maybe hit a few ball with God Knows WHO (under God Knows What Supervision) a couple of times, then breezily flew out Japan, did a few photo shoots and interviews, then played her match. Petra's not always the most obsessively professional or prepared player it seems. Now, is this the end of the world, especially if she goes on to win Beijing (though many of the elite top seeds won't be there)? No! Of course not. The way the schedule played out, it would've made no sense for Petra to go deep into both tournaments back to back. So we'll see what happens? But to my knowledge, Petra is the only "Big Seed", who went home early; again. :unsure: :weirdo: :unsure: Not good. And not the end of the world either (especially for the enigmatic Petra Kvitova). However, what a feeble start to the Asian and Indoor swing for her. ShiftyFella Sep 25th, 2012, 04:17 PM What about the wind/sun/humidity? Especially the first two factors have serious impact on the quality of serving and I've read that Sharapova double-faulted like crazy. BTW, did you see the Murray-Berdych windy shitfest? :lol: What about the general notion that the first match is by far the most dangerous for tournament favorites, who tend to be vulnerable facing an already warmed-up qualifier/lower ranked player? I'm still not sure whether Petra really wants to be multiple (5-10 slams) slam champion and the No.1 player or just to be comfortably in the Top 10, earning$2-3m a year. We can't do anything about this, it's up to the girl. But it's possible to ask her in a future on-line Q&A, if any.
Surface in Tokyo suits Petra's game so there no excuses in loosing to headcase Martic, she had cake draw up to SF or at least QF if you count Errani\Bartoli as dangerous opponents:lol:
Humidity excuse works only in US cause in Asia there not that hot and never bothered Petra from her own words.
Bringing Pova is not fair to your argument cause no matter how horrible she plays and irritating becomes, she's always comes through against mug opponents, Pova had only 8 loses but only 1 was to Mugsicki, on the other hand Petra had 14 loses and 5 were to muggers if we discount loses to Bartoli, Li Na, Venus and that's too many for TOP5 player. It's doesn't matter who Petra wants to be, she can't planning on staying in TOP 5 while losing to mugs outside of Top 10 on regular basis like she does.
before such an important match, maybe i shouldn't post here after a long hiatus :(
so, is she going to play Linz or Luxembourg after Beijing?
She can play only YEC after Beijing cause Kirby going to Lux, Vika to Linz, she can't even get into Moscow:banghead:
Excelscior
Sep 25th, 2012, 04:34 PM
Surface in Tokyo suits Petra's game so there no excuses in loosing to headcase Martic, she had cake draw up to SF or at least QF if you count Errani\Bartoli as dangerous opponents:lol:
Humidity excuse works only in US cause in Asia there not that hot and never bothered Petra from her own words.
Bringing Pova is not fair to your argument cause no matter how horrible she plays and irritating becomes, she's always comes through against mug opponents, Pova had only 8 loses but only 1 was to Mugsicki, on the other hand Petra had 14 loses and 5 were to muggers if we discount loses to Bartoli, Li Na, Venus and that's too many for TOP5 player. It's doesn't matter who Petra wants to be, she can't planning on staying in TOP 5 while losing to mugs outside of Top 10 on regular basis like she does.
She can play only YEC after Beijing cause Kirby going to Lux, Vika to Linz, she can't even get into Moscow:banghead:
Oh, maybe it IS THE END OF THE WORLD? :oh:
Are you saying Kerber is ranked ahead of Petra now (she's 5th and Petra's now 6th)? Cause, as far as I know, that's the only way she could play Luxemberg ahead of Petra.
If what you said is true, I would hate to see Petra waltz into the YEC hornets nest, after just losing her first match back to (ahem) Petra Martic in Tokyo.
Hopefully , she does well in Beijing, and/or has some decent indoor tournament to play.
PS: And I agreed with practically all your other comments as well (though THIS YEAR losing 14+ matches doesn't cut it as a top 5 player, though it did last year, when Petra was 62-13 and had the best record, winning percentage and titles.).
I agree though. Petra's got to up the ante!
18majors
Sep 25th, 2012, 04:40 PM
Oh, maybe it IS THE END OF THE WORLD? :oh:
Are you saying Kerber is ranked ahead of Petra now (she's 5th and Petra's now 6th)? Cause, as far as I know, that's the only way she could play Luxemberg ahead of Petra.
If what you said is true, I would hate to see Petra waltz into the YEC hornets nest, after just losing her first match back to (ahem) Petra Martic.
Hopefully , she does well in Beijing, and/or has some decent indoor tournament to play.
PS: And I agreed with most of your other comments as well.
Petra has 6520 ranking points and will be ahead of Kerber even if Kerber wins Tokyo. Kerber will have 5855 if she wins Tokyo.
Excelscior
Sep 25th, 2012, 04:55 PM
Petra has 6520 ranking points and will be ahead of Kerber even if Kerber wins Tokyo. Kerber will have 5855 if she wins Tokyo.
This scenario (if true) makes more sense. Thanks.
pling
Sep 25th, 2012, 05:07 PM
oh petra :sobbing:
I'm kind of glad now it wasn't streamed, so I didn't stay up night for it.
This time last year Petra had an embarassing 6-0 final set in a loss against a high-ranked opponent (Zvonareva) and then lost the first match of the next tournament to a low-ranked player (Arviddson). But then she didn't lose a match again all year - 12 wins across three tournaments: Linz, YEC and Fed Cup.
And now she's had an embarassing 6-0 final set in losing to a high-ranked opponent (Bartoli) and has then lost her first match of the next tournament to a low-ranked player.
So of course this must mean she'll now turn GOAT and win Beijing, YEC and Fed Cup!
:unsure:
Excelscior
Sep 25th, 2012, 05:12 PM
@Pling
That was good. :lol:
ShiftyFella
Sep 25th, 2012, 05:15 PM
Oh, maybe it IS THE END OF THE WORLD? :oh:
Are you saying Kerber is ranked ahead of Petra now (she's 5th and Petra's now 6th)? Cause, as far as I know, that's the only way she could play Luxemberg ahead of Petra.
If what you said is true, I would hate to see Petra waltz into the YEC hornets nest, after just losing her first match back to (ahem) Petra Martic.
Hopefully , she does well in Beijing, and/or has some decent indoor tournament to play.
PS: And I agreed with practically all your other comments as well (though THIS YEAR losing 14+ matches doesn't cut it as a top 5 player, though it did last year, when Petra was 62-13 and had the best record, winning percentage and titles.).
Agreed. She's got to up the ante!
Top5 secured at staying where they are, my problem that Petra now has little chance before AO to get Aga's spot which means easy draw up to SF but she has to produce and Aga need to be out early which is unlikely in Asia.
Kirby already signed so no more top10 players and Moscow already packed full, if i remember correctly if top10 signed to mm event no other player in top10 can get in unless withdraw or increased prize money or i just don't understand this rule:tape:
At the Player Commitment Deadline, players will be accepted in
the available Top 10 Main Draw slots based on the Top 10 List. A
next-in list will be maintained for Top 10 Players who were not
accepted into the International Tournament due to the International
Prize Money Policy.If a Top 10 Player spot becomes available due
to a withdrawal or an increase in prize money, Top 10 Players on
the next-in list will automatically move into the open Top 10 Player
spot either by direct acceptance or via a Top 20 Wild Card
Excelscior
Sep 25th, 2012, 05:38 PM
Top5 secured at staying where they are, my problem that Petra now has little chance before AO to get Aga's spot which means easy draw up to SF but she has to produce and Aga need to be out early which is unlikely in Asia.
Kirby already signed so no more top10 players and Moscow already packed full, if i remember correctly if top10 signed to mm event no other player in top10 can get in unless withdraw or increased prize money or i just don't understand this rule:tape:
Sometimes you wonder if Petra actually thinks about that sort of stuff (jockeying for position at majors) before a match like that in Tokyo.
As far as Petra playing those tournaments, relative to the Top 10, I always thought the higher ranked player had first dibs. But maybe you and the by laws you posted-are correct, and that's before the deadline? :shrug:
ShiftyFella
Sep 25th, 2012, 06:20 PM
Sometimes you wonder if Petra actually thinks about that sort of stuff (jockeying for position at majors) before a match like that in Tokyo.
As far as Petra playing those tournaments, relative to the Top 10, I always thought the higher ranked player had first dibs. But maybe you and the by laws you posted-are correct, and that's before the deadline? :shrug:
I think she just wants to play tennis and win matches but her team should think about that sort of things otherwise she should ditch them and get better team who would care about her progress and place in WTA, thought looking that far ahead can make you overlook next match which can impact your performance in it but today no excuses for Petra.
btw, now she has time to enjoy Tokyo like she wanted:haha:
also, as far as Linz\Lux goes we just have to wait and see. Vika can easily have great results in Tokyo and using that momentum takes Beijing title skipping Linz to rest before YEC but i think if she had great results in Tokyo she would skip Beijing to play Linz cause that way schedule more balanced and she wants to play at Linz badly.
pov
Sep 25th, 2012, 07:01 PM
Fair enough. I certainly admire your diplomacy. But my guess is, you didn't sit through the livescore as some of us did. :lol:
No diplomacy just calling things as I see 'em - like always. As for sitting through live scores -dang right I didn't. I may be crazy but I'm not masochistic. :D Seriously though, with all due respect for your diligence, LS tell nothing about how she played.
Excelscior
Sep 25th, 2012, 07:32 PM
I think she just wants to play tennis and win matches but her team should think about that sort of things otherwise she should ditch them and get better team who would care about her progress and place in WTA, thought looking that far ahead can make you overlook next match which can impact your performance in it but today no excuses for Petra.
btw, now she has time to enjoy Tokyo like she wanted :haha:
also, as far as Linz\Lux goes we just have to wait and see. Vika can easily have great results in Tokyo and using that momentum takes Beijing title skipping Linz to rest before YEC but i think if she had great results in Tokyo she would skip Beijing to play Linz cause that way schedule more balanced and she wants to play at Linz badly.
You are cruel (the vacation in Tokyo). :lol:
And yeah, I meant Petra via her team. Agreed! Most young players just want to play tennis, and take the advice of their coaches.
I've read Petra say she wants to be #1 and win more majors in the Czech press sometimes. And I've also seen her say the opposite, and sing the whole "I don't have any goals" deal with the American press.
It's the latter statements, along with Petra and her teams actions, that sometimes make you wonder if the REALLY do think long term positioning with her.
Shoot! I noticed Petra getting up to the #4 slot from the US Open. If Petra would of made the semifinal, I think she would of got there, even if Serena won it, like she did.
Now this. SMH
Excelscior
Sep 25th, 2012, 07:46 PM
No diplomacy just calling things as I see 'em - like always. As for sitting through live scores -dang right I didn't. I may be crazy but I'm not masochistic. :D Seriously though, with all due respect for your diligence, LS tell nothing about how she played.
True. But it does give a good idea on serving, ROS, and the flow of the game at least. If you're not making 1st serves, double faulting, a lot, and having a hard time converting your opponents 2nd serve (especially if it's not known to be good), it usually tells you something.
The other thing is, I've seen Petra play similar 1st matches, where her serving, ROS and BP conversions are frustratingly poor.
This match seemed no different.
And yes/of course, if I didn't sit through this, I may have more your attitude. :lol:
For the record, I knew beforehand if Petra Kvitova wasn't sharp during this match, she could lose.
ShiftyFella
Sep 25th, 2012, 09:34 PM
You are cruel (the vacation in Tokyo). :lol:
And yeah, I meant Petra via her team. Agreed! Most young players just want to play tennis, and take the advice of their coaches.
I've read Petra say she wants to be #1 and win more majors in the Czech press sometimes. And I've also seen her say the opposite, and sing the whole "I don't have any goals" deal with the American press.
It's the latter statements, along with Petra and her teams actions, that sometimes make you wonder if the REALLY do think long term positioning with her.
Shoot! I noticed Petra getting up to the #4 slot from the US Open. If Petra would of made the semifinal, I think she would of got there, even if Serena won it, like she did.
Now this. SMH
Personally i stopped listening to some bullshit that players says in interviews long time ago cause i just don't believe Petra didn't have any goals or idol person like she stated many times. I think she just want to keep things to herself so she's not overrating herself in eyes of the press, basically when she's not performing she didn't need to deal with some uncomfortable question about expectations. That's very smart but at the same time not that fair to her fans that wants to know her mindset coming into season\big tournaments\etc...
Sometimes i have no idea what Petra's team doing at all, it's like they don't want to force they opinions and goals on Petra but Petra being still young player and relatively new to huge career success waiting what the team would suggest to her, so they just stuck at mid air
Excelscior
Sep 25th, 2012, 09:59 PM
Personally i stopped listening to some bullshit that players says in interviews long time ago cause i just don't believe Petra didn't have any goals or idol person like she stated many times. I think she just want to keep things to herself so she's not overrating herself in eyes of the press, basically when she's not performing she didn't need to deal with some uncomfortable question about expectations. That's very smart but at the same time not that fair to her fans that wants to know her mindset coming into season\big tournaments\etc...
Sometimes i have no idea what Petra's team doing at all, it's like they don't want to force they opinions and goals on Petra but Petra being still young player and relatively new to huge career success waiting what the team would suggest to her, so they just stuck at mid air
Good points.
And yes, there's a fine balance between stating expectations to the press and not doing so.
However, they can say for example "these are our goals, if/when Petra can play like or do this. She has the ability", etc.
I agree with you, on why they keep it vague to the American press, and it's for a couple of reasons.
1) They don't want the pressure of expectations. I get that.
2) They don't want the questions if she fails or doesn't reach them. I get that as well. But how/when do they measure progress?
As you said, one must wonder if Petra and her team have any legitimate short, long term goals and strategy, and if so how/when do they follow up, analyze and implement them?
As I've said many times before, I think Kotyza teaches Petra individual tennis skills well (a lot of that probably has to do with Petra's natural lefty "good touch" and hands). I do. I just wonder about the saliency of her/their various ON and OFF court strategies.
They cannot be simultaneously serious and committed in Petra's development, and pleased with this result, if so.
Excelscior
Sep 25th, 2012, 11:16 PM
PS Shiftyfella, etc.:
It's funny we're having this discussion about Petra's team. I remember earlier this year during the Australian Open, or one of the spring hardcourt American tournaments, I was reading an interview with Koytza about Petra.
In this interview Kotyza, went on and on about how Serena was the best player when she's in form, etc.. And this was before Serena was even playing well this year.
I remember saying to myself, "My God Your Player Just Had A Great Year, You should Be Trying To Improve her, and you're waxing on and and on about another player, Serena Williams, who's not even playing well"?
Regardless of Serena's eventual year and Kotyza prescient clairvoyance, he seemed to expound more energy speaking in awe of Serena, instead of his own great young player, he should be trying to improve. That set off a red flag with me. I have no problem with a fair minded coach, speaking about another player. But Petra wasn't even scheduled to play Serena. Now that I remember, Koytza spoke about Serena being the best player-when in form, when asked "is Petra Kvitova The Best Player In The World", then he went off.
Yeah, he may of been trying to take the pressure off Kvitova. I get that. But where was the belief and swagger (even just a little) from her own coach?
It just makes you wonder if they have the proper belief, impatience and determination to build a champion worthy of Petra's bountiful talent?
steni
Sep 26th, 2012, 02:35 AM
Petra doesn't have a team... just a coach... Djokovic has a team... I mean can Petra defend her YEC title just with Kotyza? :rolleyes:
bruce goose
Sep 26th, 2012, 06:27 AM
Regardless of Serena's eventual year and Kotyza prescient clairvoyance, he seemed to expound more energy speaking in awe of Serena, instead of his own great young player, he should be trying to improve. That set off a red flag with me. I have no problem with a fair minded coach, speaking about another player. But Petra wasn't even scheduled to play Serena. Now that I remember, Koytza spoke about Serena being the best player-when in form, when asked "is Petra Kvitova The Best Player In The World", then he went off.
Yeah, he may of been trying to take the pressure off Kvitova. I get that. But where was the belief and swagger (even just a little) from her own coach?
It just makes you wonder if they have the proper belief, impatience and determination to build a champion worthy of Petra's bountiful talent?Yeah,that's dumb,strategically,from a psychological standpoint.Though I lack the technical knowledge to coach tennis,my strategy would include videotape of Serena getting outclassed on red clay so that the young player would have that visual imprint of her losing and being a mere mortal.I can't speak in detail as to how Petra's team prepares her for matches against top opponents,but I'll bet you that plenty of coaches don't know how to psyche up their young charges for matches vs. living legends
ShiftyFella
Sep 26th, 2012, 08:56 AM
PS Shiftyfella, etc.:
It's funny we're having this discussion about Petra's team. I remember earlier this year during the Australian Open, or one of the spring hardcourt American tournaments, I was reading an interview with Koytza about Petra.
In this interview Kotyza, went on and on about how Serena was the best player when she's in form, etc.. And this was before Serena was even playing well this year.
I remember saying to myself, "My God Your Player Just Had A Great Year, You should Be Trying To Improve her, and you're waxing on and and on about another player, Serena Williams, who's not even playing well"?
Regardless of Serena's eventual year and Kotyza prescient clairvoyance, he seemed to expound more energy speaking in awe of Serena, instead of his own great young player, he should be trying to improve. That set off a red flag with me. I have no problem with a fair minded coach, speaking about another player. But Petra wasn't even scheduled to play Serena. Now that I remember, Koytza spoke about Serena being the best player-when in form, when asked "is Petra Kvitova The Best Player In The World", then he went off.
Yeah, he may of been trying to take the pressure off Kvitova. I get that. But where was the belief and swagger (even just a little) from her own coach?
It just makes you wonder if they have the proper belief, impatience and determination to build a champion worthy of Petra's bountiful talent?
oh, just don't get me started on Huggy Bear. I don't get why he not teaches Petra to use more topsin or why they used baseline bashing tactics playing against Pova instead of using Petra's true game hitting cross court and going to the net more, this year looks like she just abandoned her game and want's to be brainless grinder occasionally remembering her game.
Serena even when not in form dangerous opponent on her will alone especially against top players, Petra has same killing serve like Rena but they don't use it as much cause she misses alot but more topspin fixes this problems and gives troubles to flat hitting pushers so no more stupid random loses. I understand that going en route to better placement and working on ROS would increases consistency and eliminates UEs but why you need forgetting about topspin. Topspin alone provides more control and eliminates UEs. I hope they just reserved this option to try in this offseason.
Excelscior
Sep 26th, 2012, 12:24 PM
Yeah,that's dumb,strategically,from a psychological standpoint.Though I lack the technical knowledge to coach tennis,my strategy would include videotape of Serena getting outclassed on red clay so that the young player would have that visual imprint of her losing and being a mere mortal.I can't speak in detail as to how Petra's team prepares her for matches against top opponents,but I'll bet you that plenty of coaches don't know how to psyche up their young charges for matches vs. living legends
I tell you Bruce, it was the weirdest thing and just came off very strange. It was almost like he was undermining his own player, who had a great year, who had shown even greater potential.
If he said it before the Ozzie Open (which was quite possible), then it was very strange indeed.
If he said it after the Ozzie Open-before the clay season, then at least complement Azarenka in there somewhere, while complementing Petra.
But I'm sure he said it, before Azarenka's 26 match winning streak and Ozzie Open win.
Either way, up until that point, Serena hadn't done anything, and it just made you wonder her teams preparations, strategies and mindset. :help:
Yeah Bruce. I'm with you. It made me wonder as well, if/when Petra finally got to play Serena, if she would believe deep down inside she couldn't beat her, and/or be content with a loss, cause Kotyza said "she's the best (even when she wasn't playing that way, and Petra wasn't scheduled to play her)".
Way to bring up your very talented young player. :help:
Excelscior
Sep 26th, 2012, 02:00 PM
oh, just don't get me started on Huggy Bear. I don't get why he not teaches Petra to use more topsin or why they used baseline bashing tactics playing against Pova instead of using Petra's true game hitting cross court and going to the net more, this year looks like she just abandoned her game and want's to be brainless grinder occasionally remembering her game.
Serena even when not in form dangerous opponent on her will alone especially against top players, Petra has same killing serve like Rena but they don't use it as much cause she misses alot but more topspin fixes this problems and gives troubles to flat hitting pushers so no more stupid random loses. I understand that going en route to better placement and working on ROS would increases consistency and eliminates UEs but why you need forgetting about topspin. Topspin alone provides more control and eliminates UEs. I hope they just reserved this option to try in this offseason.
It always makes me wonder, why Petra's team doesn't pull out that YEC tape and study/practice it with reckless and relentless abandon.
I don't care if Petra''s lacking THE WHATEVER to properly execute it now, make her! :lol:
Yes, we all remember the fancy volleys, drop shots and slices, etc. But even when Petra was "grinding out points", she was doing it by hitting angles, and deep in the corners and baseline, with out ball bashing. i.e., Petra was just moving players around the court till she had the advantage (screaming winner, drop shot, volley, looper, UE, FE's, etc.). Yeah, where did that go? :shrug:
Essentially Petra did at the YEC what Azarenka normally does, the only difference being- Petra placed more air under her balls (for better control), when she was moving her opponent around the court, corner to corner and side to side; aided with Petra's variety of course.
And I agree with your other point, that many times Petra's 2nd serve is so good, she can go for it more on her 1st serves.
What happened to her serve from last year and New haven/US Open-before second set of Bartoli (even though Petra still amongst the top 3-4 leaders in WTA serving before the Martic loss)?
Imagine if she recaptured that? :shrug:
There's an old saying, 'that your serve is a controllable and shouldn't leave you, even if the rest of your game does'. I guess, Petra didn't handle the windy conditions in Tokyo very well (though I've seen her serve well under windy conditions in the past). But she needs that part of her game to be an even more reliable constant indeed.
Obviously, everything we mentioned is a belief/practice/confidence issue, that Petra and her team needs to work out, re-implement and solidify.
pov
Sep 26th, 2012, 02:32 PM
PS Shiftyfella, etc.:
Regardless of Serena's eventual year and Kotyza prescient clairvoyance, he seemed to expound more energy speaking in awe of Serena, instead of his own great young player, he should be trying to improve. That set off a red flag with me. I have no problem with a fair minded coach, speaking about another player. But Petra wasn't even scheduled to play Serena. Now that I remember, Koytza spoke about Serena being the best player-when in form, when asked "is Petra Kvitova The Best Player In The World", then he went off.
Yeah, he may of been trying to take the pressure off Kvitova. I get that. But where was the belief and swagger (even just a little) from her own coach?
It just makes you wonder if they have the proper belief, impatience and determination to build a champion worthy of Petra's bountiful talent?
Perhaps he was just honestly saying what he thought. Which is why it takes fortitude to be open and honest with the media. No matter what you say, someone will find it inappropriate.
Let's say a coach thinks that a certain player is the most talented active player - do you think that means they shouldn't coach anyone else?
Of course I hope that he knows Kvitova has the talent to be at the top and that he reinforces and encourages her. Given how she gushes about him, I think it safe to say that he does.
Excelscior
Sep 26th, 2012, 02:32 PM
Hey Guys, FYI
To add injury to insult, Petra Martic loses a 3 set match against Petrova with 18DF's.
Obviously she had a lot against Petra K, as well.
Petra K must have stopped putting pressure on Martic, so she could eventually keep her DF's below 10. WTF? :lol:
The irony is, both of them (the two Petra's) were DF-ing and missing first serves like mad during the first and up until the mid 2nd set.
How does Petra K feel now? :oh:
Like I said, I'm not surprised.
pov
Sep 26th, 2012, 02:38 PM
Yes, we all remember the fancy volleys, drop shots and slices, etc. But even when Petra was "grinding out points", she was doing it by hitting angles, and deep in the corners and baseline, with out ball bashing. i.e., Petra was just moving players around the court till she had the advantage (screaming winner, drop shot, volley, looper, UE, FE's, etc.). Yeah, where did that go? :shrug:
Is this a trick question? :lol: No but yeah . . . I don't get it at all. If she was playing like that and her season had been the same as it was then okay sucks but no biggie.. . but it's almost like . . . . At the USO I sat closer to the court than her coach about a box away and what I saw on her face at times was just . . I dunno . at the time I thought it was related to her breathing but . .yeah I don't know . .it just didn't seem like she was fully present.
Excelscior
Sep 26th, 2012, 02:44 PM
Perhaps he was just honestly saying what he thought. Which is why it takes fortitude to be open and honest with the media. No matter what you say, someone will find it inappropriate.
Let's say a coach thinks that a certain player is the most talented active player - do you think that means they shouldn't coach anyone else?
Of course I hope that he knows Kvitova has the talent to be at the top and that he reinforces and encourages her. Given how she gushes about him, I think it safe to say that he does.
I know you like to play the role of contrarian sometimes. That's fine. And Kotyza can say or believe what ever he wants. Agreed. However, it just appeared like it came out of left field, considering Serena wasn't even playing well at the time, and the question wasn't about her.
Shouldn't his focus had been on moving Petra more along? Don't get me wrong, I have no problem with Kotyza saying "Serena Williams is the best player, and I want you to do this this and this, so you can beat her"!. Yeah I get that (though that would still be questionable, if other players, not Serena were dominating at the time). I get you.
Nonetheless, sometimes you just gotta wonder with Petra's team, based off of this and other comments and actions.
Of course we always pick people apart, reach and stretch after a bad loss. :lol:
pov
Sep 26th, 2012, 02:47 PM
Hey Guys, FYI
To add injury to insult, Petra Martic loses a 3 set match against Petrova with 18DF's.
Obviously she had a lot against Petra K, as well.
Petra K must have stopped putting pressure on Martic, so she could eventually keep her DF's below 10. WTF? :lol:
The irony is, both of them (the two Petra's) were DF-ing and missing first serves like mad during the first and up until the mid 2nd set.
You usually have good insights but IMO this sort of comparative analysis based solely on the stats doesn't hold.
Excelscior
Sep 26th, 2012, 02:54 PM
You usually have good insights but IMO this sort of comparative analysis based solely on the stats doesn't hold.
paulmara
Sep 26th, 2012, 05:19 PM
I go to Beijing tomorrow. I had fun in Tokyo, sorry I couldn't be here longer but will be back next year :)
They wrote my name for me in Japanese. They told me it means 'music room. Neck flying leaf' haha :)
http://pbs.twimg.com/media/A3uCNDDCIAI2od7.jpg:large
Petronius
Sep 26th, 2012, 06:08 PM
btw, now she has time to enjoy Tokyo like she wanted:haha:
Good point. I remember how Martina (Navr.) said that finally after 25 years on the tour she had time to visit the Louvre museum in Paris, because she had always reached finals in singles, doubles or even mixed doubles and hadn't had enough time to enjoy the city :lol:
Petronius
Sep 26th, 2012, 06:20 PM
Petra doesn't have a team... just a coach... Djokovic has a team... I mean can Petra defend her YEC title just with Kotyza? :rolleyes:
Last year at Linz, the Austrian TV showed her barely 17-year bf during a match with a caption going "Petra Kvitova's Coach".
The funniest moment of the tournament for me. :lol:
Petronius
Sep 26th, 2012, 06:37 PM
It always makes me wonder, why Petra's team doesn't pull out that YEC tape and study/practice it with reckless and relentless abandon.
Please. Once again, neither healthy Serena nor Sharapova took part in the 2011 YEC.
I can almost guarantee you that Petra would have won one or two slams or maybe even all of the first three slams this year, if she hadn't been stopped by these two multi-slam champs.
Petra would have had great chances in the AO final even against a hot Azarenka, because of their match-up.
Petra would have probably crushed Errani in the RG final.
And Petra would have great chances against Azarenka and Radwanska in Wimbly SF and F.
Once again, we don't now whether Petra would have won YEC with in-form Serena and Sharpie in the mix.
Serena was 22-3 in 2011 and this translated to the best winning percentage on tour. Her US hardcourt run was amazing until she screwed up the final vs. Stosur. Still had the best winning percentage though so it would be foolish to underestimate such a great player.
That's probably the reason why Kotyza was cautious and praised Serena, maybe also because he wanted to reduce the Petra hype and unwarranted expectations.
JMHO :cool:
EDIT: But I obviously agree with you that Petra played very good at YEC and displayed lots of excellent all-court skills and should try to build on this great performance.
Excelscior
Sep 26th, 2012, 06:55 PM
Please. Once again, neither healthy Serena nor Sharapova took part in the 2011 YEC.
I can almost guarantee you that Petra would have won one or two slams or maybe even all of the first three slams this year, if she hadn't been stopped by these two multi-slam champs.
Petra would have great chances in the AO final even against a hot Azarenka, because of their match-up.
Petra would have probably crushed Errani in the RG final.
And Petra would have great chances against Azarenka and Radwanska in Wimbly SF and F.
Once again, we don't now whether Petra would have won YEC without in-form Serena and Sharpie.
Serena was 22-3 in 2011 and this translated to the best winning percentage on tour. Her US hardcourt run was amazing until she screwed up the final vs. Stosur. Still had the best winning percentage though so it would be foolish to underestimate such a great player.
That's probably the reason why Kotyza was cautious and praised Serena, maybe also because he wanted to reduce the Petra hype and unwarranted expectations.
JMHO :cool:
That's a part time schedule Petronius. And Serena dropped out of several events she would have lost, that could have made that record worse. I'm not impressed.
Secondly, saying Petra could/would have won those tournaments sans Serena and Sharpie, doesn't mean that she is playing as well this year as she was last year. That's what you're missing.
The level that Petra has played so far THIS YEAR, has been inferior to her play LAST LAST (as far as peak tennis). And I and many other posters that don't even post on the Petra subforum have noticed and indicated that as well (Petra is not playing up to the level she did in 2011). Do you? That's why she doesn't have any Grand Slams, besides her match ups.
Regarding Martha, it's no secret. Sharpova got blasted by Petra on a fast, low bouncing surface. When Petra played her on a slower hard court at the Australian Open, she couldn't convert BP's, and lost. It was the same at Stuttgart, except this time Petra lost in 2 sets. It was even worse at the French, where Petra didn't seem to have any semblance of a game plan or how to play Sharapova on the slow, high bouncing clay, and lost in another comedy of errors. Sharapova has recently beaten her with consistency on the slower surfaces from the baseline.
As far as the YEC reference, it was a synopsis of what ShiftyFella was saying (hitting with angles, etc.). And if Petra would have played Martha there last year, Petra would have killed her-the way Petra was playing. I don't think Martha would have made a difference. More importantly, Petra needs to implement that all court, free flow game playing Martha, instead of the north/south baseline ball bashing tennis, she played against her their past three matches, on those slower courts. That's clear.
That was Shifty Fella's entire point. Petra is playing a baseline ball bashing game, instead of an all court one (or at the least, moving her rd with angles). Even in Wimbledon, Petra played an all court game to victory more than we realize (but of course not to the extent as the YEC). And of course her outright ball striking at Wimby was phenomenal.
So Petra either needs to get more consistent and committed with her slow court-baseline rallying/ball bashing; go all out aggressive/moving forward, going to the net more, or come up with a different approach and/or use more angles, etc. That's what the YEC reference means (60% pace rally ball, moving player round the court with angles, while implementing her variety).
Excelscior
Sep 26th, 2012, 08:31 PM
To put it simply Petronius, Petra is not playing as good this year as last year (despite the fact she could have won more majors this year if facing Azarenka and Errani). And if she wants to beat those other players you mentioned (providing they maintain this years form), she's gotta play a winning style again.
Her YEC form, is part of that style. I bet if I said Wimbledon, you would have no complaints. The difference is, that was grass. The YEC, despite being indoors (I never put as much stock in that as so many others did), was on a slow hard court, which is more reflective of so many events on the tour and in the Majors.
TimeyWimey
Sep 26th, 2012, 08:53 PM
thoughts on no-match days :p
last year i remember some tweets about Petra's practice at Canada, during Rogers Cup, it says there's so much fun on court with Kotyza and many of her shots just left the spectators in awe
i went to Cincinnati this August on the second weekend, i did not purchased ticket for men's singles semifinal starting noon, but when i saw Petra's practice schedule, i purchased, luckily, the last ticket available before they rolled out groundpass several hours later, and i can tell you i've never seen her being so subdued, one hour of practice, she hardly spoke anything while David was always trying to cheer her up, after the practice, she just signed one tennis ball before getting sheltered to the player's lounge by the (security?) staffs while kept saying "sorry"
so i don't know if this is because of the semifinal in the night session? (but on the other hand, i could hear the laughter from Angelique Kerber and her coach in the neighbouring court, and Venus, Li as well, also considering she already won the Rogers Cup)
i would pretty much see this as an individual situation if you're asking, but if anyone on here could share some experience if you have seen her practice this year?
Excelscior
Sep 26th, 2012, 09:00 PM
thoughts on no-match days :p
last year i remember some tweets about Petra's practice at Canada, during Rogers Cup, it says there's so much fun on court with Kotyza and many of her shots just left the spectators in awe
i went to Cincinnati this August on the second weekend, i did not purchased ticket for men's singles semifinal starting noon, but when i saw Petra's practice schedule, i purchased, luckily, the last ticket available before they rolled out groundpass several hours later, and i can tell you i've never seen her being so subdued, one hour of practice, she hardly spoke anything while David was always trying to cheer her up, after the practice, she just signed one tennis ball before getting sheltered to the player's lounge by the (security?) staffs while kept saying "sorry"
so i don't know if this is because of the semifinal in the night session? (but on the other hand, i could hear the laughter from Angelique Kerber and her coach in the neighbouring court, and Venus, Li as well, also considering she already won the Rogers Cup)
i would pretty much see this as an individual situation if you're asking, but if anyone on here could share some experience if you have seen her practice this year?
The irony is, she bombed at both Cincy and Toronto last year, while winning Montreal and going to the Cincy semi-final this year. So maybe Petra's disposition has no bearing on her actual results. She's that confounding indeed. :lol:
Maybe Petra was a little tired and frustrated in that Kerber match. Who knows?
However, when you think about her opening Tokyo match, and what happened to Petra's conquerer during her next match, you just gotta shake your head. :lol:
And keep writing TimeyWimey. No fears. :lol:
TimeyWimey
Sep 26th, 2012, 09:55 PM
The irony is, she bombed at both Cincy and Toronto last year, while winning Montreal and going to the Cincy semi-final this year. So maybe Petra's disposition has no bearing on her actual results. She's that confounding indeed. :lol:
Maybe Petra was a little tired and frustrated in that Kerber match. Who knows?
However, when you think about her opening Tokyo match, and what happened to Petra's conquerer during her next match, you just gotta shake your head. :lol:
And keep writing TimeyWimey. No fears. :lol:
not sure if mac was there that day, maybe she could see something different :lol:
is there just me or anyone else think she needs a psychological breakthrough more than all the things she's always suggesting that should be worked on (serve, ROS, etc), and that will ONLY come next time she beats in-form Pova or Rena (not wins ANOTHER SLAM)?
Petronius
Sep 26th, 2012, 10:05 PM
thoughts on no-match days :p
last year i remember some tweets about Petra's practice at Canada, during Rogers Cup, it says there's so much fun on court with Kotyza and many of her shots just left the spectators in awe
i went to Cincinnati this August on the second weekend, i did not purchased ticket for men's singles semifinal starting noon, but when i saw Petra's practice schedule, i purchased, luckily, the last ticket available before they rolled out groundpass several hours later, and i can tell you i've never seen her being so subdued, one hour of practice, she hardly spoke anything while David was always trying to cheer her up, after the practice, she just signed one tennis ball before getting sheltered to the player's lounge by the (security?) staffs while kept saying "sorry"
so i don't know if this is because of the semifinal in the night session? (but on the other hand, i could hear the laughter from Angelique Kerber and her coach in the neighbouring court, and Venus, Li as well, also considering she already won the Rogers Cup)
i would pretty much see this as an individual situation if you're asking, but if anyone on here could share some experience if you have seen her practice this year?
Cool story, maybe she's just 'moody' :lol:
Petronius
Sep 26th, 2012, 10:11 PM
That's a part time schedule Petronius. And Serena dropped out of several events she would have lost, that could have made that record worse. I'm not impressed.
LOL, I really think that you deprive yourself of potentially enjoying a 'change-of-the-guard' victory when/if Petra beats Serena in a big match, e.g. at the 2012 YEC or the 2013 AO.
While the entire subforum will be over the moon and celebrate like crazy the win over a 15-slam champion for you it will be just a routine victory over an unimpressive player :lol:
Just teasing you :lol:
Excelscior
Sep 26th, 2012, 10:33 PM
not sure if mac was there that day, maybe she could see something different :lol:
is there just me or anyone else think she needs a psychological breakthrough more than all the things she's always suggesting that should be worked on (serve, ROS, etc), and that will ONLY come next time she beats in-form Pova or Rena (not wins ANOTHER SLAM)?
I think this is a Chicken Or The Egg scenario. :lol:
Wouldn't Petra have to improve her serve, ROS, footwork, etc. to beat an inform Serena or Masha? :scratch:
On the other hand, if Petra beats them, when they're off their game, would it really make that much different psychologically? It's possible/maybe. :shrug:
Excelscior
Sep 26th, 2012, 10:37 PM
LOL, I really think that you deprive yourself of potentially enjoying a 'change-of-the-guard' victory when/if Petra beats Serena in a big match, e.g. at the 2012 YEC or the 2013 AO.
While the entire subforum will be over the moon and celebrate like crazy the win over a 15-slam champion for you it will be just a routine victory over an unimpressive player :lol:
Just teasing you :lol:
I know. :) And I wasn't really trying to dispatch Serena's 2011 record per se (though it was an abbreviated schedule indeed), I just wanted to move the conversation on to Petra. :lol:
TimeyWimey
Sep 26th, 2012, 10:38 PM
I think this is a Chicken Or The Egg scenario. :lol:
Wouldn't Petra have to improve her serve, ROS, footwork, etc. to beat an inform Serena or Masha? :scratch:
On the other hand, if Petra beat them, when their off, would it really make that much different psychologically? It's possible/maybe. :shrug:
right, maybe not even require them being in-form, a win over these two is all she needs, i just don't see anything else would do the job for her after several months debating of what she should do in her training
off to watch some NCAA :wavey:
steni
Sep 27th, 2012, 12:46 AM
not sure if mac was there that day, maybe she could see something different :lol:
is there just me or anyone else think she needs a psychological breakthrough more than all the things she's always suggesting that should be worked on (serve, ROS, etc), and that will ONLY come next time she beats in-form Pova or Rena (not wins ANOTHER SLAM)?
I think Mac is a guy lol
steni
Sep 27th, 2012, 12:53 AM
Last year at Linz, the Austrian TV showed her barely 17-year bf during a match with a caption going "Petra Kvitova's Coach".
The funniest moment of the tournament for me. :lol:
She should hire her BF as a coach than...
Excelscior
Sep 27th, 2012, 03:00 AM
She should hire her BF as a coach than...
She needs to hire somebody. :rolleyes:
I just checked Petra Martic's record, and didn't realize she was ranked #72, had only a 17-16 record, and hadn't won 2 matches in a row since the French Open/May, before playing our Petra in Tokyo. My god! :eek:
I thought she was still ranked in the 50's. But she actually fell into the 70's, and wasn't even playing well when Petra K played her.
I know Martic's unpredictable, and probably was looking forward to her match with Petra K, but how embarrassing. :tape:
Now I see why you guys were talking about "Petra's easy draw".
Oh well. :oh:
bruce goose
Sep 27th, 2012, 04:45 AM
I tell you Bruce, it was the weirdest thing and just came off very strange. It was almost like he was undermining his own player, who had a great year, who had shown even greater potential.
If he said it before the Ozzie Open (which was quite possible), then it was very strange indeed.
If he said it after the Ozzie Open-before the clay season, then at least complement Azarenka in there somewhere, while complementing Petra.
But I'm sure he said it, before Azarenka's 26 match winning streak and Ozzie Open win.
Either way, up until that point, Serena hadn't done anything, and it just made you wonder her teams preparations, strategies and mindset. :help:
Yeah Bruce. I'm with you. It made me wonder as well, if/when Petra finally got to play Serena, if she would believe deep down inside she couldn't beat her, and/or be content with a loss, cause Kotyza said "she's the best (even when she wasn't playing that way, and Petra wasn't scheduled to play her)".
Way to bring up your very talented young player. :help:Though I can't claim to have any deep insight into Petra's personality,sometimes it seems that she prefers a sort of small-town,down-on-the-farm operation.It might sound greedy from me,but wouldn't it be good if her coaches/team tried to nurture more of a Killer Instinct in Petra(Isn't that what the REALLY great players possess)??With her talent,Petra wouldn't even need to be at peak intensity in most matches...as long as she could 'turn it on' when required(as others do),right?
paulmara
Sep 27th, 2012, 08:33 AM
I should get free tickets from my sister who's a lawyer and received them from a client. Either these or the tickets for the Kvitty/Sharpie exho :p
In case your wife is not interested, your friends are too busy and you still have free VIP sponsor tickets … there are always the other guys.
ShiftyFella
Sep 27th, 2012, 08:44 AM
She needs to hire somebody. :rolleyes:
I just checked Petra Martic's record, and didn't realize she was ranked #72, had only a 17-16 record, and hadn't won 2 matches in a row since the French Open/May, before playing our Petra in Tokyo. My god! :eek:
I thought she was still ranked in the 50's. But she actually fell into the 70's, and wasn't even playing well when Petra K played her.
I know Martic's unpredictable, and probably was looking forward to her match with Petra K, but how embarrassing. :tape:
Now I see why you guys were talking about "Petra's easy draw".
Oh well. :oh:
Yeah, it was cake draw. Now watching how tournaments unfolds I'm really embarrassed by Petra, two of biggest chokers in SF from her part of the draw and yet another easy road for Polish band to take one more title in Asia:tape:SMH.
Mynarco
Sep 27th, 2012, 08:45 AM
I like Nadia and hope she can go all the way. But what a missed chance for Petra...please do well in Beijing
Excelscior
Sep 27th, 2012, 12:57 PM
Though I can't claim to have any deep insight into Petra's personality,sometimes it seems that she prefers a sort of small-town,down-on-the-farm operation.It might sound greedy from me,but wouldn't it be good if her coaches/team tried to nurture more of a Killer Instinct in Petra(Isn't that what the REALLY great players possess)??With her talent,Petra wouldn't even need to be at peak intensity in most matches...as long as she could 'turn it on' when required(as others do),right?
Well it appears that way.
Isn't that how she won Wimbledon? :lol: She was very RELAXED (and they kept her that way). Right? :lol:
I think she won the YEC off of pride , cause she was embarrassed by her sucky play preceding it (along with better play, from the confidence she got from winning in the RELAXED Linz environment as well).
One thing though, being relaxed only works when you're playing well (particularly the Relaxed Wimby example). We all know, when you're not playing well (depending on the talent and play of opponent), it's your will to win and indomitable, fierce spirit that going to carry you through.
So Petra either needs to increase her level of play and consistency, or care more. :shrug:
Petronius
Sep 27th, 2012, 01:09 PM
In case your wife is not interested, your friends are too busy and you still have free VIP sponsor tickets … there are always the other guys.
I'll ask the sister when she comes from holiday on weekend, but I'm afraid she'll have only one or two tickets.
Petronius
Sep 27th, 2012, 01:16 PM
She needs to hire somebody. :rolleyes:
I just checked Petra Martic's record, and didn't realize she was ranked #72, had only a 17-16 record, and hadn't won 2 matches in a row since the French Open/May, before playing our Petra in Tokyo. My god! :eek:
I thought she was still ranked in the 50's. But she actually fell into the 70's, and wasn't even playing well when Petra K played her.
I know Martic's unpredictable, and probably was looking forward to her match with Petra K, but how embarrassing. :tape:
To make it worse, Martic said that she had felt terrible during practice sessions and therefore she had entered the Petra match with the 'nothing-to-lose' approach and it worked perfectly :o
TimeyWimey
Sep 27th, 2012, 01:21 PM
She needs to hire somebody. :rolleyes:
I just checked Petra Martic's record, and didn't realize she was ranked #72, had only a 17-16 record, and hadn't won 2 matches in a row since the French Open/May, before playing our Petra in Tokyo. My god! :eek:
I thought she was still ranked in the 50's. But she actually fell into the 70's, and wasn't even playing well when Petra K played her.
I know Martic's unpredictable, and probably was looking forward to her match with Petra K, but how embarrassing. :tape:
Now I see why you guys were talking about "Petra's easy draw".
Oh well. :oh:
Martic got injured in Roland Garros, and had to pull out the whole summer season before US Open, sort of like Kaia Kanepi
I wouldn't expect her to go anywhere near the level of top 5, but she's surely a joy to watch in fact (apart from glaring DF stats)
TimeyWimey
Sep 27th, 2012, 01:25 PM
To make it worse, Martic said that she had felt terrible during practice sessions and therefore she had entered the Petra match with the 'nothing-to-lose' approach and it worked perfectly :o
like Kvitova, these girls don't have much in their English repertoire, so i never took these Q&A seriously
Petronius
Sep 27th, 2012, 01:28 PM
like Kvitova, these girls don't have much in their English repertoire, so i never took these Q&A seriously
:lol:
Excelscior
Sep 27th, 2012, 01:41 PM
Yeah, it was cake draw. Now watching how tournaments unfolds I'm really embarrassed by Petra, two of biggest chokers in SF from her part of the draw and yet another easy road for Polish band to take one more title in Asia:tape:SMH.
Well, Petra better watch it. She could make it awfully hard for herself. Cause if she doesn't gain points in Beijing and bombs out of the YEC, she could find herself out of the top 8 possibly, and finding herself in even tougher GS draws (especially if she's not playing lights out). Hopefully, she'll step it up in China.
TimeyWimey
Sep 27th, 2012, 01:48 PM
:lol:
but anyway, it is still vastly better than my ability to speak their languages :p
after several months of inaction, i found an online Czech book store in Canada which sells fantastic tutorials, so i will try to revive that Czech learning thread next month ;)
Excelscior
Sep 27th, 2012, 01:48 PM
To make it worse, Martic said that she had felt terrible during practice sessions and therefore she had entered the Petra match with the 'nothing-to-lose' approach and it worked perfectly :o
I like Petra Martic and respect her talent, and love to see her play. But Petra K still sucked.
She lost to Petrova her next match with 18DF's. So obviously, she was right, and wasn't on her game. :lol: Petra K was just so bad, she couldn't put her away. :lol:
Horrendous!
And before someone says "The other Top players played poorly". Yeah, but at least they all didn't lose in the 2nd rd/1st match, and when they did lose, it was to other top 8 players. And Radwanska's still in it by the way.
Petra lost to the #72 ranked player. Inexcusable (especially a previously injured one, that hadn't played much). We've seen it all before from our Petra.
Isn't Petra tired of looking from the outside in (No GS titles or Olympic Medal)? :help:
Excelscior
Sep 27th, 2012, 01:54 PM
Martic got injured in Roland Garros, and had to pull out the whole summer season before US Open, sort of like Kaia Kanepi
I wouldn't expect her to go anywhere near the level of top 5, but she's surely a joy to watch in fact (apart from glaring DF stats)
She was injured, but she still played matches and lost. I repeat, since the French Open, Martic hadn't won two matches in a row till she beat Petra K. :help:
I like watching her to. But there's a reason why she's ranked where she is (and I thought she was still in the 50's-Lol). Like most talented players ranked below where you think they would be, Martic has been injured, inconsistent, has holes in her a game and been a choke artist). Like I said, "always good reasons" for their rankings . Lol.
We didn't see the match with our eyes. But this happens too often with Petra K for us to make excuses with her and let this one sly. I repeat, Martic is ranked # 72. :tape:
Not good. :help:
TimeyWimey
Sep 27th, 2012, 02:06 PM
We didn't see the match with our eyes. But this happens too often with Petra K for us to make excuses with her and let this one sly. I repeat, Martic is ranked # 72. :tape:
Not good. :help:
maybe later when we look back, this loss serves as a psychological breakthrough for US to, finally, accept Kvitty as she is (maybe a dumb analogy, Murray to big three until he beat Fed in the Olympics?)
Excelscior
Sep 27th, 2012, 02:42 PM
maybe later when we look back, this loss serves as a psychological breakthrough for US to, finally, accept Kvitty as she is (maybe a dumb analogy, Murray to big three until he beat Fed in the Olympics?)
I'm not saying she's done or I've given up. Petra could win the Australian for all I know. :lol:
I'm just not making excuses for Petra with THIS loss. We've seen these type of losses before with her, so there's no reason to make an excuse, giving her the benefit of the doubt.
Maybe if I saw the match, I would change my mind (if Martic played perfectly, which I know she didn't). But just following livescore, it was obvious (by the amount of early breaks) that neither one of them were sharp, and Petra let a slumping, previously injured player beat her.
My guess; once Petra realized she was in a match she didn't bother to suck it up, and/or freaked out that her game wasn't there.
I guess she's rather have sushi, see the Giza, and maybe visit Mt Fuji. :shrug:
SMH :help:
ShiftyFella
Sep 27th, 2012, 02:47 PM
Well, Petra better watch it. She could make it awfully hard for herself. Cause if she doesn't gain points in Beijing and bombs out of the YEC, she could find herself out of the top 8 possibly, and finding herself in even tougher GS draws (especially if she's not playing lights out). Hopefully, she'll step it up in China.
As much as I love Nadia and like Sammy but they are both colossal headcases yet they both managed to win few hard matches even being 1 set down, while GOATra failed to convert many BP opportunities. With withdraw contest in Beijing road to title open for Petra, only her head can prevent her to be successful there. Actually I wouldn't be surprised if Illarenka or Aga win YEC cause it seams like Petra already thinking only about Fed Cup final and not about inspiring finish in the end of the season or AO draw.
Excelscior
Sep 27th, 2012, 02:55 PM
As much as I love Nadia and like Sammy but they are both colossal headcases yet they both managed to win few hard matches even being 1 set down, while GOATra failed to convert many BP opportunities. With withdraw contest in Beijing road to title open for Petra, only her head can prevent her to be successful there. Actually I wouldn't be surprised if Illarenka or Aga win YEC cause it seams like Petra already thinking only about Fed Cup final and not about inspiring finish in the end of the season or AO draw.
This is one of the reasons why, after Petra won the Fedcup in 2011, I can't really look forward to it, until maybe a day or two before.
Cause it really appears that Petra gets up more for Fed Cup, than she does for so many other important tour events.
I agree. Where was the comparative effort in Tokyo?
TimeyWimey
Sep 27th, 2012, 02:57 PM
I'm not saying she's done or I've given up. Petra could win the Australian for all I know. :lol:
I'm just not making excuses for Petra with THIS loss. We've seen these type of losses before with her, so there's no reason to make an excuse, giving her the benefit of the doubt.
Maybe if I saw the match, I would change my mind (if Martic played perfectly, which I know she didn't). But just following livescore, it was obvious (by the amount of early breaks) that neither one of them were sharp, and Petra let a slumping, previously injured player beat her.
My guess; once Petra realized she was in a match she didn't bother to suck it up, and/or freaked out that her game wasn't there.
I guess she's rather have sushi, see the Giza, and maybe visit Mt Fuji. :shrug:
SMH :help:
i used to be the one who constantly provides this kind of sarcasm in this forum :eek:
well indeed it looks like a breakthrough for you :lol:
Petronius
Sep 27th, 2012, 03:01 PM
but anyway, it is still vastly better than my ability to speak their languages :p
after several months of inaction, i found an online Czech book store in Canada which sells fantastic tutorials, so i will try to revive that Czech learning thread next month ;)
If you love the language, you're halfway through. I have a French cousin who started learning Czech at 45 and now at 51 he's fluent (TBH he was very motivated, because he got a top post in a big French-owned Czech bank :lol:).
Keep it up.
Excelscior
Sep 27th, 2012, 03:07 PM
i used to be the one who constantly provides this kind of sarcasm in this forum :eek:
well indeed it looks like a breakthrough for you :lol:
I always had something snarky to say after these type of losses.
After a great US Open series, then a disappointing US Open, and a 3wk rest, I was hoping that Petra would have her batteries recharged, and ready to play and build on what she did in the US, in a event she went to the semi-final in, on a court that suits her game. I was wrong! :lol:
It's also embarrassing, when Petra loses in the first rd (or the quarterfinal of the Olympics), when her other top 4 brethren advance, especially when we argue she's better or just as good as some of them. :(
ShiftyFella
Sep 27th, 2012, 03:50 PM
This is one of the reasons why, after Petra won the Fedcup in 2011, I can't really look forward to it, until maybe a day or two before.
Cause it really appears that Petra gets up more for Fed Cup, than she does for so many other important tour events.
I agree. Where was the comparative effort in Tokyo?
I sort of get commitment to play Fed Cup but she think about it too much. It's funny but now knowing Venus could play in Hopman Cup I want Petra be there instead of going to play Sydney:lol:
paulmara
Sep 27th, 2012, 04:54 PM
I'll ask the sister when she comes from holiday on weekend, but I'm afraid she'll have only one or two tickets.
Thanks. That was just rhetoric. There are usually empty seats in sponsors´ section. Don´t worry about it. I had my moment and wanted to make a reservation for Maria-Petra exhibition. But decided otherwise.
paulmara
Sep 28th, 2012, 08:11 AM
China Open Daniela HANTUCHOVA
http://www.wtatennis.com/SEWTATour-Archive/posting/2012/1020/MDS.pdf
pling
Sep 28th, 2012, 08:37 AM
As decent a draw as we could have hoped for. Petra has won 4 straight-set matches against Dani, so surely no 1st round disaster here?
With Serena out, Petra as 4th seed gets Safarova, Stosur, Bartoli as other seeds in her section. And finally Sharapova is in the other half, and Petra is in dizzy Vika's half.
Pull your finger out now girl.
steni
Sep 28th, 2012, 11:10 AM
China Open Daniela HANTUCHOVA
http://www.wtatennis.com/SEWTATour-Archive/posting/2012/1020/MDS.pdf
I think the draw is wrong... Either Sharapova or Azarenka got a bye but Kerber did! Its this ok?
paulmara
Sep 28th, 2012, 11:34 AM
I think the draw is wrong... Either Sharapova or Azarenka got a bye but Kerber did! Its this ok?
BYE Aga- Petrova - Kerber - Stosur (Tokyo last 4)
Excelscior
Sep 28th, 2012, 12:04 PM
Speaking about Beijing (not that I understand everything you guys wrote). Lol.
The young lady, Petra Martic, that beat Kvitova in Tokyo, lost in the first round to Puchova 6-2 6-2 in Beijing. SMH
Oh My Petra (Kvitova). :facepalm:
PS: I'm not sure how much Sharapova and Vika will show up or play well in Beijing, but we'll see?
And yes, Aga (Da Vulture) Radwanska is the final again guys, trying to defend those points. :eek:
TimeyWimey
Sep 28th, 2012, 12:21 PM
dani? should be easy stuff for Petra, even she's to play the very first day
paulmara
Sep 28th, 2012, 12:33 PM
“In Tokyo, I had three double faults in the first game, so it’s not very often to have that for me, but that I can improve for sure,” Kvitova said. “I tried today to practice in the wind, but it’s not that easy.”
It was different conditions and we played indoor and I didn’t feel very comfortable,” Kvitova said. “But it’s not like something happened and I hope that I can improve my game here.”
http://www.chinaopen.com.cn/en/news/2012-09-28/1940445.shtml
TimeyWimey
Sep 28th, 2012, 01:17 PM
PS: I'm not sure how much Sharapova and Vika will show up or play well in Beijing, but we'll see?
And yes, Aga (Da Vulture) Radwanska is the final again guys, trying to defend those points. :eek:
play several games/matches then withdraw, my guess
TimeyWimey
Sep 28th, 2012, 01:30 PM
also i feel getting slow following these mandatour tournies at this time of the year :yawn:
Petronius
Sep 28th, 2012, 01:43 PM
Let's be honest guys, who expected Radwanska-Petrova final?
steni
Sep 28th, 2012, 02:02 PM
BYE Aga- Petrova - Kerber - Stosur (Tokyo last 4)
Really? I didnt know they do that like that... Weird!
steni
Sep 28th, 2012, 02:05 PM
Speaking about Beijing (not that I understand everything you guys wrote). Lol.
The young lady, Petra Martic, that beat Kvitova in Tokyo, lost in the first round to Puchova 6-2 6-2 in Beijing. SMH
Oh My Petra (Kvitova). :facepalm:
PS: I'm not sure how much Sharapova and Vika will show up or play well in Beijing, but we'll see?
And yes, Aga (Da Vulture) Radwanska is the final again guys, trying to defend those points. :eek:
I know, I was thinking the same... Our Petra :facepalm:
Excelscior
Sep 28th, 2012, 02:07 PM
dani? should be easy stuff for Petra, even she's to play the very first day
I'm not sure if anything is easy for Petra at this point, till she proves otherwise.
And remember, Beijing is not a Grand Slam or important Grand slam warm up for Dani to choke on.
Who knows? Maybe Dani will be relaxed and play her game, if Petra's still going walkabout.
I hope Petra wins. And we know Dani plays into Petra's game. But you never know? :tape:
I hope Petra's motivated.
Good Luck Petra.
TimeyWimey
Sep 28th, 2012, 02:12 PM
Let's be honest guys, who expected Radwanska-Petrova final?
can i just give these tournaments a :facepalm: ?
King Halep
Sep 28th, 2012, 02:16 PM
It was almost the same last time except it was Petkovic, and before that Wozniacki won it so shitfest is usual
King Halep
Sep 28th, 2012, 02:17 PM
“In Tokyo, I had three double faults in the first game, so it’s not very often to have that for me, but that I can improve for sure,” Kvitova said. “I tried today to practice in the wind, but it’s not that easy.”
Quote:
It was different conditions and we played indoor and I didn’t feel very comfortable,” Kvitova said. “But it’s not like something happened and I hope that I can improve my game here.”
What is all that? I didn’t feel very comfortable playing indoor and thats why I was serving like crap?
You lost to someone who couldnt win two matches in a row, how do you explain that
steni
Sep 28th, 2012, 02:23 PM
“In Tokyo, I had three double faults in the first game, so it’s not very often to have that for me, but that I can improve for sure,” Kvitova said. “I tried today to practice in the wind, but it’s not that easy.”
Quote:
It was different conditions and we played indoor and I didn’t feel very comfortable,” Kvitova said. “But it’s not like something happened and I hope that I can improve my game here.”
What is all that? I didn’t feel very comfortable playing indoor and thats why I was serving like crap?
You lost to someone who couldnt win two matches in a row, how do you explain that
So weird, she didn't say why she wasn't comfortable? Who knows what kind of BS goes through her mind when things aren't easy...
Excelscior
Sep 28th, 2012, 02:30 PM
“In Tokyo, I had three double faults in the first game, so it’s not very often to have that for me, but that I can improve for sure,” Kvitova said. “I tried today to practice in the wind, but it’s not that easy.”
Quote:
It was different conditions and we played indoor and I didn’t feel very comfortable,” Kvitova said. “But it’s not like something happened and I hope that I can improve my game here.”
What is all that? I didn’t feel very comfortable playing indoor and thats why I was serving like crap?
You lost to someone who couldnt win two matches in a row, how do you explain that
Maybe it's a problem in the translation (from Chinese, Petra or Paulmara, whatever), but it does sound like dribble from Petra.
So Kvitova lost that match vs Martic with the roofed closed? If so, I didn't know that.
Well, if this is true, there goes your indoor hardcourt streak guys (though it was a retractable, as opposed to a fixed roof, so Petra's still got that record to hold on to). :tape:
But then again, how could the roof had been closed when the serving was so poor?
It seems to me, like Petra was cryptically speaking about her practice in Beijing, as well.
TimeyWimey
Sep 28th, 2012, 02:32 PM
not comfortable for outdoor, not comfortable for indoor? now we have a solution, we have retractable roof! :lol:
Excelscior
Sep 28th, 2012, 02:38 PM
So weird, she didn't say why she wasn't comfortable? Who knows what kind of BS goes through her mind when things aren't easy...
Oh, she wasn't "comfortable", so she didn't fight?
The other thing is, Petra's the #5 ranked player in the world. There's a reason why Martic was ranked 72. As poor as we think Petra can play in many of these opening rds off of layoffs, unless the opposition plays lights out (which is rare), they usually lose. Many times these lower ranked players make mistakes, choke and take on court siesta's. That's why top ranked players usually win those matches when they play poorly.
Petra on the other hand (as Melange said), lost to a player that hadn't won two matches in a row since the French Open. :tape:
Embarrassing.
steni
Sep 28th, 2012, 02:44 PM
Somebody knows who pays to Kotyza, Petra or Prostejov?
Excelscior
Sep 28th, 2012, 02:50 PM
@Steni
Huh?
Lufa
Sep 28th, 2012, 03:04 PM
Somebody knows who pays to Kotyza, Petra or Prostejov?
She pays trainers (Kotyza and she paid Ivanko too), she was asked about that in online interview, about year ago.
steni
Sep 28th, 2012, 03:18 PM
She pays trainers (Kotyza and she paid Ivanko too), she was asked about that in online interview, about year ago.
Alright. I thought he was an assigned coach from Prostejov, and I thought the same about Ivanko.
Excelscior
Sep 28th, 2012, 03:29 PM
Alright. I thought he was an assigned coach from Prostejov, and I thought the same about Ivanko.
Right now Petra appears she could use some strategic, cohesive additions to her team.
ShiftyFella
Sep 28th, 2012, 04:25 PM
Maybe it's a problem in the translation (from Chinese, Petra or Paulmara, whatever), but it does sound like dribble from Petra.
So Kvitova lost that match vs Martic with the roofed closed? If so, I didn't know that.
Well, if this is true, there goes your indoor hardcourt streak guys (though it was a retractable, as opposed to a fixed roof, so Petra's still got that record to hold on to). :tape:
But then again, how could the roof had been closed when the serving was so poor?
It seems to me, like Petra was cryptically speaking about her practice in Beijing, as well.
on that day roof supposed to be closed all day and it was during televised matches, i was not sure about early matches but Petra just confirmed so and it's alarming:help:
Looking thought draw only problem can be Lucie, last and only meeting was not that one sided as score suggest and in New Haven Petra was in superb form but now i'm not so sure, Bartoli can pull again miracle but i think she would be too tired after Sammy
Excelscior
Sep 28th, 2012, 05:38 PM
on that day roof supposed to be closed all day and it was during televised matches, i was not sure about early matches but Petra just confirmed so and it's alarming:help:
Looking thought draw only problem can be Lucie, last and only meeting was not that one sided as score suggest and in New Haven Petra was in superb form but now i'm not so sure, Bartoli can pull again miracle but i think she would be too tired after Sammy
Ironically, if Petra wins Beijing (or even makes the finals) this year, she'll accumulate more points than making Tokyo semifinals and Beijing first match last year.
So Petra can still try to reclaim and redeem her lost points, self esteem and YEC aspirations. :lol:
TimeyWimey
Sep 28th, 2012, 08:16 PM
btw, will the match be streamed? the tournament website looks horrible and could not find any information on that, don't see that on ES as well
steni
Sep 28th, 2012, 08:34 PM
Right now Petra appears she could use some strategic, cohesive additions to her team.
I think Petra is cheap thats why she just have Kotyza...
King Halep
Sep 28th, 2012, 08:39 PM
I wouldnt be surprised if Adam is doing some of the coaching now
steni
Sep 28th, 2012, 08:40 PM
btw, will the match be streamed? the tournament website looks horrible and could not find any information on that, don't see that on ES as well
This sucks... TennisTV start streaming until Oct 4... I think we wont see Petra playing!
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2014-09-17 05:51:01
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https://www.jiskha.com/archives/2012/03/10
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# Questions Asked onMarch 10, 2012
1. ## math
A town has a population of 32,000 in the year 2002; 35,200 in the year 2003; 38,720 in the year 2004; and 42,592 in the year 2005. If this pattern continues, what will the population be in the year 2016?
2. ## Ochem
Phenacetin has the structure shown below. Write an equation for its preparation starting from 4-ethoxyaniline.
3. ## Ochem
Give two reasons why the crude product in most reactions is not pure.
4. ## statistics
16. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 miles per gallon and a standard deviation 3.5 miles per gallon
5. ## chemistry
MnO4–(aq) + Cl–(aq) Mn2+ + Cl2(g) (unbalanced) i. Write the reduction and oxidation half-reactions (without electrons). (.5 point) ii. Balance the equations for atoms (except O and H). (.5 point) iii. Balance the equations for atoms O and H using H2O
6. ## 6th Grade Christian History
1. when he roman government began to persecute Christians under Nero, a) Christianity almost disappeared b) Christians had to cremate their dead c) Jews hid themselves in their homes d) Christianity was outlawed 2. the bishop of Rome was also known by the
7. ## AP Chem
An apparatus consists of a 4 L flask containing nitrogen gas at 32 C and 885 kPa, joined by a valve to a 8 L flask containing argon gas at 32 C and 47.5 kPa. The valve is opened and the gases mix. What is the partial pressure of nitrogen after mixing?
8. ## chemistry
Write the balanced equations for the following examples: a) potassium hydroxide + sodium sulfide --> potassium sulfide + sodium hydroxide b) carbon disulfide + oxygen --> carbon dioxide + sulfur dioxide
9. ## Ochem
In the reaction between p-aminophenol and acetic anhydride to form acetaminophen, what was the purpose of adding water to the reaction mixture? There are a couple of possible answers, and this requires a detailed explanation for credit. thanks!
10. ## math quick question
I got a problem that states which graph represents the sequence of 1,2.5,4,5.5,7.. Should the graph start at 1,1 or 0,1?
11. ## AP CHEMISTRY
Calculate the solubility of Mn(OH)2 in GRAMS PER LITER when buffered at each of the following. a)pH 7.4 b)pH 9.2 c) pH 11.5
12. ## chemistry
MnO4–(aq) + Cl–(aq) Mn2+ + Cl2(g) (unbalanced) i. Write the reduction and oxidation half-reactions (without electrons). (.5 point) ii. Balance the equations for atoms (except O and H). (.5 point) iii. Balance the equations for atoms O and H using H2O
13. ## Calculus
A closed box is to be a rectangular solid with a square base and volume of 12 ft^3. Find the most economical dimensions if the top of the box is twice as expensive as the sides and bottom.
14. ## physics
at 3.68100017 kHz the reactance in a circuit of a 9 uF capacitor and an inductor are equal in magnitude. what is the value of the inductor? a. .000020 H b. .000020 mH c. .000021 uH d. .000021 mH
15. ## AP CHEMISTRY
Calculate the solubility of Mn(OH)2 in GRAMS PER LITER when buffered at each of the following. a)pH 7.4 b)pH 9.2 c) pH 11.5
Please explain what is global warming?. And How Do Business Enterprises contribute towards economic growth??? And Please Name Me The Socio-economic issues
17. ## math
a pizza has a circumference of 47.1in. what is the radius
18. ## physics
How much work does a 69 kg person do against gravity in walking up a trail that gains 790 m in elevation
19. ## Statistics
Let x and y be the amounts of time (in minutes) that a particular commuter must wait for a train on two independently selected days. Define a new random variable w by w = x + y, the sum of the two waiting times. The set of possible values for w is the
20. ## physics
A skater of mass 74.5 kg initially moves in a straight line at a speed of 5.10 m/s. The skater approaches a child of mass 37.5 kg, whom he lifts on his shoulders. Assuming there are no external horizontal forces, what is the skater's final velocity?
21. ## physics
An iron wire has a cross-sectional area equal to 1.20 10-5 m2. Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 34.0 A. (a) How many kilograms are there in 1.00 mole of iron? 1
22. ## Calculus
The strength of a beam with rectangular corss-section is directly proportional to the product of the width and the square of the depth (thickness from the top to bottom of the beam). Find the shape of the strongest beam that can be cut from a cylindrical
23. ## math
A 1O-m ladder rests againts the wall of a house.The foot of the ladder on the ground is 1.3 m from the wall.What angle does the ladder make with the wall?
asked by NIRVANA RIZA A. GARON
24. ## Algebra
Archaeologists and forensic scientists use the length of of human bones to estimate the height of his/her femur f(the bone from the knee to the hip socket), in centimeters using the following formulas: Male h=69.089+2.238f Female: h = 61.412+2.317f a. a
25. ## statistics
if the average number of textbooks in professors' offices is 16, the standard deviation is 5, and the average age of the professors is 43,with a standard deviation of 8 ,which data set is more variable ?
26. ## Chemistry
The decomposition of hydrogen peroxide in the presence of potassium iodide is believed to occur by the following mechanism: step 1 slow: H2O2 + I^- = H2O + OI^- step 2 fast: H2O2 + OI^- = H2O + O2 + I^- 1) What is the equation for the overall reaction? Use
27. ## Physics
A long cylindrical insulator has a uniform charge density of 1.0 #C/m3 and a radius of 9.0 cm. a) What is the electric field inside the insulator at a distance of 4 cm? b) What is the electric field at 17 cm? c) How much work must you do to bring a q =
28. ## Math
Each cube below is made up of smaller cubes, but the large cubes are not solid. They had tunnels through them. • The first cube originally had 27 small cubes, but the tunnel removed 3 cubes. • The second cube originally had 64 small cubes, but two
A zinc-copper battery is constructed as follows at 25 degree C: Zn | Zn2+(0.15 M) || Cu2+(1.70 M) | Cu The mass of each electrode is 250. g. I found the cell potential to be 1.13V and the cell potential after 5.00 A of current has flowed for 8.00 h is
30. ## physics
A 0.5 kg air-hockey puck is initially at rest. What will its kinetic energy be after a net force of 0.3 N acts on it for a distance of 0.5 m
31. ## PHYSICS
Determine the value for the acceleration due to gravity at the surface of the planet Mars, given the following data: Mass of Mars = 6 .42 x 10^23 kg Radius of Mars = 3.37 x 10^6 m Thanks!
32. ## math
explain how to find ans. a clock has a circumference of 166cm. what is the diameter
33. ## Physics
The pulley system shown in the figure is used to lift a 52-{\rm kg} crate. Note that one chain connects the upper pulley to the ceiling and a second chain connects the lower pulley to the crate. The crate is rising with an acceleration of 2.5 m/s^2.
34. ## physics
An ion enters a mass spectrometer which has a .18 T field perpendicular to? an electric field of 1.6 kV/m and selects a velocity. the same magnetic field is then used to deflect the singly charged ion into a circular path of radius 12.5 cm. a. what
35. ## math
Which is the eighth term in the sequence an=-1/125(5^n-1)
36. ## Physics (dynamics)
A 47.0 kg slab rests on a frictionless floor. A 18.0 kg block rests on top of the slab. The static coefficient of friction between the block and the slab is 0.50, while the kinetic coefficient of friction is 0.40. The top block is acted upon by a force of
37. ## Chemistry
If Kc = 0.480 at 40.°C and Kc = 0.630 at 90.°C, what is ΔH° for the reaction? XY
38. ## math
A 35-foot long ladder is leaning against the wall of a building.How far from the ground is the top of the ladder and how far from the base of the building is its foot if it makes a 20 degrees angle with the wall?
asked by NIRVANA RIZA A. GARON
39. ## physics
Tarzan plans to cross a gorge by swinging in an arc from a hanging vine. If his arms are capable of exerting a force of 1820 N on the rope, what is the maximum speed (in meters/second) he can tolerate at the lowest point of his swing? His mass is 83.0 kg,
40. ## Calculus
A can of soda at 80° F. is placed in a refrigerator that maintains a constant temperature of 36° F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by T(t) = 36 + 44 e^–0.058 t Find the temperature of the soda 10
41. ## 6th Grade Christian History
Why were the Christians persecuted by the Romans? At first I thought it was because they didn't believe in God. But then I had the question "to the Romans what was appealing about Christianity? What did they like about the teachings?" Please help!! I am
42. ## Chemistry
Write the balanced equation for the double replacement reaction of: Barium chloride and Sulfuric acid
43. ## english
What is the underlying message of all of Arthur Jarvis’s writing? How does reading his son’s writing affect the behavior of James Jarvis?
44. ## physics
An RLC circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 µF and an inductance of 0.050 H, find the resistance of the
45. ## math
solve the system 7x^2 - 5y^2 + 20y = 3 21x^2 + 5y^2 =209
46. ## math
17. Burger King's Drive-Through: Suppose that cars arrive at Burger King's drive-through at the rate of 20 cars every hour between 12:00 noon and 1:00 PM. A random sample of 40 one-hour time periods between 12:00 noon and 1:00 P.M. is selected and has 22.1
47. ## math
A 35-foot long ladder is leaning against the wall of a building.How far from the ground is the top of the ladder and how far from the base of the building is its foot if it makes a 20 degrees angle with the wall?
48. ## 6th Grade Christian History
Why did Christian church come to be ruled by hierarchy? Any and all help is appreciated. ☺♦☻
49. ## PHYSICS
Determine the value for the acceleration due to gravity at the surface of the planet Mars, given the following data: Mass of Mars = 6 .42 x 10^23 kg Radius of Mars = 3.37 x 10^6 m Thanks!
50. ## Chem
Why do the rate of reaction for a reversible reaction slows down at equilibrium stage.
51. ## physics
a ball is thrown at an angel of 40 degee above tghe horizontal.the ball clears the fence whis is 85 metre away.what is the inital velosity of the ball if we assume the ball is thrown at the same elevation of the fence
The measurement of pH using a glass electrode obeys the Nernst equation. The typical response of a pH meter at 25.00 degrees C is given by the equation: E(measured)= E(ref) +.591pH where ref contains the potential of the reference electrode and all other
53. ## biology:plz someone help
The heart lung machine is used so that surgeons can operate on the arteries supplying heart muscle. These arteries may be diseased. (a) Name these arteries and explain how they may become diseased. (b) suggest why a patient is put on a heart lung machine
54. ## Calculus
A cicular metal plate is being heated and expands so that its radius increases at the rate of 0.25 mm/min. How fast is the area increasing when the radius is 10 cm?
55. ## calculus
A projectile is launched from a platform 20 feet high with an initial velocity of 72 feet per second, The height h of the projectile at t seconds after launch is given by h = –16t2 + 72t + 20 feet. (a) How many seconds after launch does the projectile
56. ## Calculus
Bob, a resident of Metropolis, pays Metropolis an annual tax of $50 plus 1.9% of his annual income. If Bob paid$2,387 in tax, what was Bob's annual income?
57. ## HELP! College Physics
A skateboarder shoots off a ramp with a velocity of 6.7 m/s, directed at an angle of 59° above the horizontal. The end of the ramp is 1.1 m above the ground. Let the x axis be parallel to the ground, the +y direction be vertically upward, and take as the
58. ## Precalculus
Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) (e) tan(−3π/4) (f) cos(π/4) (g) sec(π/6+ 2π)
59. ## Calculus
The total charge in an electrical circuit as a function of time is given by q=t/(t^2+1) coulombs. Find the maximum charge of q.
60. ## Calculus
Two ships are leaving port at the same time. The first ship is sailing due east at 20 km/hr and the other due north at 15 km/hr. How fast are the ships moving away from each other 2.0 hr later?
61. ## Calculus
Suppose that sin q = − 12/13 and that q is a Quadrant IV angle. (a) Find the exact value of cos q. Show work. (b) Find the exact value of sin 2q. Show work.
62. ## Calculus
Given y = 5 sin(6x – pie), state the (a) period (b) phase shift
63. ## PHYSICS
Find the force of attraction on a 3 kg mass at the surface of a planet given the following information about the planet: mass = 5.98 x 10^24 kg, radius = 6.38 x 10^6 m. Find the force if the radius is doubled to 12.76 x 10^6m Thanks!!
Which Represent the first two terms of the sequence a1=2 and an=-2(an-1)^2 2, -8 -8,-128 16,1024 -2,16
65. ## algebra
Which is the eighth term in the sequence an=-1/125(5^n-1)
66. ## Physics
A mass sits at the top of a 2 meter long ramp inclined at an angle of 30 degrees (to the horizontal). When the mass is released, it slides down the ramp and then onto a level floor. If both the ramp and the board have a coefficient of .25 (Friction), how
67. ## Physics
A mas of 100 Kg hangs from a cable secured to a steel pole and supported by another cable as shown below. Find the tension (T) in the support cable and the force (F) on the steel pole.
68. ## 3 D - geometry (direction of cosines)
Find the angle between the lines between the lines whose direction cosines satisfy the equations l + m + n = 0 and 2mn + 3nl - 5lm =0.
69. ## Math
This problem pertains to Cuisenaire Rods: 1-white 2-red 3-green 4-purple 5-yellow 6-dark green 7-black 8-brown 9-blue 10-orange Question: (a) If an all-brown train is equal in length to an all-orange train, what can be said about the number of brown rods
70. ## math
what are the equivalent fractions for 7/20
71. ## Math
y= sqrt(81-x^2) What length and width should the rectangle have so that its area is a maximum? (smaller value) (larger value)
72. ## Calculus
Water reaches its maximum density above its freezing point. The volume V (in cubic diameters) of 1 kg of water at temperature T between 0 degrees C and 30 degrees C can be approximated by the formula V=999.87 - 0.06426T + 0.0085043T^2 - 0.0000679T^3. Find
73. ## Algebra I
The width of a rectangle is fixed at 7 cm. Determine (in terms of an inequality)those lengths for which the area will be less than 161 cm2.
74. ## math
(4.35E-2 - x)(7.56E-2 -x ) ============================ (0.324 + 2x)2 Rearrange to get an expression of the form ax2 + bx + c = 0 and use the quadratic formula (solve for x. This gives: x = 1.05E-2, 0.143 basically i understand they use the quadratic
75. ## Math
Which represents the type of sequence: 12, 22, 30, 36, 41, …? neither arithmetic nor geometric both arithmetic and geometric arithmetic geometric
76. ## Math
Mr. Rogers wants to fence in a rectangular garden next to a straight section of the Scioto River. He has 330 feet of fencing to do the entire job. He doesn’t need fencing along the river, and there is a 4.5 foot wide clearance for a gate at one end. What
77. ## biology:plz help
state the name for the action of two oppposing miscles, such as the biceps and the triceps.
78. ## physics
A small plane mass 600 kg lifts off from the runway at a speed of 145 Km/Kr. 2 Minutes later, the plane has reached an altitude of 300 meters and its airspeed has dropped to 90 Km/Hr. Assume the power output of the engine was constant during this time.
79. ## A A U
How can i write a seminar report on Eutrophication
80. ## science
: Describe how bacterial fermentation causes milk to sour.
81. ## calculus
A tank consists of a right circular cylinder at height (h)surmounted by a hemisphere at a radius (r) with an outlet atthe top. The tank is full of water at density ρkg/m3. Find the work required to empty thetank.
82. ## Math - HELP !
there are 50 students in the seventh grade , 62 percent of these students are involved in the drama club.how many seventh grade students are in the drama club ?
83. ## Math
simplify: 22/sqr18 + sqr7
84. ## Math
Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.) f(x) = 1/3x^4 + 4x^3 for some reason I am not getting the right answer; I got the graph on my calculator but it seems weird.
85. ## algebra
There is a 100 point test with 38 questions. The test has 2 point questions, and 5 point questions. How many 5 point questions and 2 point questions are there?
86. ## college Math
perform the indicated operation, give answer in scientific notation. (5x10^2)x(5.6x10^4)
87. ## Chemistry: Identifying Substances
Hi! I would like to know the definitions for... ELEMENT: something on the periodic table? COMPOUND: molecule with at least 2 different elements? SYMBOL: i'm confused about this FORMULA: i'm confused about this ATOM: smallest units of elements? MOLECULE: a
143. ## physics
an RlC circuit has a resistance of 4 kOhm, a capacitance of 33 uF, and an inductance of 23 H. if the frequency of the alternating current is 2/pi kHz, what is the phase shift between the current and the voltage.
144. ## Literacy
10. Use one of the sources available in the Almanacs and Yearbooks section to identify the approximate time of sunrise in Anchorage, Alaska, on December 25, 2015. A. 10:15 A.M. B. 9:45 A.M. C. 11:30 A.M. D. 8:10 A.M. ANSWER IS A
145. ## English
Here are some more sentences I really need you to check. Thank you. 1) His work (better job) consists in changing the words of the news as the Party wants to, in order to control people. 2) The party aims to eradicate individuality. The information
146. ## Literacy
2. Utilizing the publication search function on EDSeek's Home page, which of the following companies publishes Pediatric Nursing? A. Royal College of Nursing Publishing Company B. Elsevier Science Publishers C. Jannetti Publications, Inc. D. Advanstar
147. ## Literacy
7. Which search engine would be best to use when you want to know if your local library carries a particular journal? A. Worldcat B. Webarchive C. All the Web D. Google Scholar ANSWER IS A
148. ## Algebra
n 1966, the U.S. Surgeon General's health warnings began appearing on cigarette packages. Data gathered after 1965 indicate that public awareness of the health hazards of smoking has had some effect on consumption of cigarettes. The percentage, p, of the
149. ## chemistry
Fuel oil and bitumen is 38% in demand Petrol and Naptha is 27% in demand Diesel is 23% in demand. A question asks: Why are these fractions in demand? I am not sure how to answer this questions and please advise me to how to answer this question. Thanks in
150. ## chemistry
What must be known for the rate constant to be calculated from the rate law?
151. ## chemistry
if i have 5.6 liters of gas in a piston ata pressure of 206 kPa and compress the gas until its volume is 4.8L, what will the new pressure inside the piston be? how do i that problem?
152. ## physics
An electron is a subatomic particle (m = 9.11 x10-31 kg) that is subject to electric forces. An electron moving in the +x direction accelerates from an initial velocity of +5.11 x 105 m/s to a final velocity of 1.67 x 106 m/s while traveling a distance of
153. ## history
Which U.S. Supreme Court decision made it illegal to achieve diversity through the use of racial quotas?
154. ## social studies
I need help figuring out 2 things that help creat a nation that are good for the nation capish
155. ## biology
can toads are considered a pest in australia are there anyways that they can adapt to their surroundings without the food chain being damaged
156. ## precalc!!!!!
The point (5,-2) lies on the graph of y=f(x), and assume f^-1(x) exists. Find the corresponding point on eAch graph. A). Y=f^-1(x) I get (-5,2) B). Y=-f^-1(-x)+4 I get (5,2) C). Y=f^-1(x+2)+3 I get (-7,5) Did I get these right?
157. ## Pre Calculus
Use one of the identities cos(t + 2ðk) = cos t or sin(t + 2ðk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(17ð/4) (b) sin(−17ð/4) (c) cos(17ð) (d) cos(45ð/4) (e) tan(−3ð/4) (f) cos(7ð/4) (g) sec(ð/6+2ð)
158. ## science
: A medical microbiological lab report indicates that a sample contained a biofilm, and that one species in the biofilm was identified as Neisseria gonorrhoeae. Is this strain of Neisseria likely to be pathogenic? Why and why not?
159. ## geometry
In the accompying diagram of circleo, diameter ad,chord AE,ans secantsCAB and CDE are drawn ; m angle BAD=40;and m arch AE=5((m arch ED) what is the measure of ACE?
160. ## science
An electron micrograph of a newly discovered cell shows long projections with a basal body in the cell wall. What kind of projections are these? Is the cell prokaryotic or eukaryotic? How might this cell behave in its environment because of the presence of
161. ## MICRO
Some bacterial toxins cause cells lining the digestive tract to secrete ions, making the contents of the tract hypertonic. What effect does this have on patient’s water balance?
162. ## SCIENCE
How are photophosphorylation and oxidative phosphorylation similar? How are they different?
163. ## math
In a clinical trial, a drug used to relieve pain caused side effects in 9% of the patients who took it. For a new trial, three patients were selected at random. Find the probability that none of those patients had side effects.
164. ## science
3 Some bacterial toxins cause cells lining the digestive tract to secrete ions, making the contents of the tract hypertonic. What effect does this have on patient’s water balance?
165. ## SCIENCE
Describe how bacterial fermentation causes milk to sour.
166. ## SCIENCE
How are photophosphorylation and oxidative phosphorylation similar? How are they different?
167. ## science
How are photophosphorylation and oxidative phosphorylation similar? How are they different?
169. ## Physiology (reproduction)
if only one sperm penetrates into the zona pellucida of the ovum n other sperm which try to bind to the ovum are prevented from binding by the cortical granules secreted by exocytosis than what happens in Sextuplet? please give a detailed explanation.
170. ## English
I need your help to check these sentences, Writeacher. Thank you very much in advance. 1) Winston's face is ruddy for the low quality soap and blunt razor blades he uses. 2) His face is ruddy for the use of low ..(Which one is best?) 3) Everything seems
171. ## chemistry
what is the pH and pOH of a soution with a volume of 5.4 that contains 15 grams of HCl and 25 grams of nitric acid
172. ## Physics
An asteriod is found a distance from the sun equal to 32 units times the earth's distance. What will be the length of time in years required for this asteriod to make one revolution around the sun?
173. ## English
I still have some more corrections I'd like you to check. Thank you. Please, I really need you help! 1) Because of Eton's restrictive moral code he became more and more strong-minded. He chose Orwell from the name of the river he liked. 2) He changes the
174. ## Marketing
Identify a firm in any industry operating and discuss the segmentation strategies for it's product
175. ## rosemont
a pizza was sliced 10 pieces. bill ate 2/10 of the pizza how much of the pizza was left?
176. ## math
In a clinical trial, a drug used to reduce blood pressure caused side effects in 6% of the patients who took it. For a new rial, two patients were selected at random. Find the probability that both the patients had side effects.
177. ## math
how do you find the area of 5 5/8 and 2 7/8?
178. ## matrh
what are the equivalent fractions for 9/8
179. ## accounts
January 1,07 S.Henry sales ledger appear D Fung $200 and C Manley$120.On february 1 Henry accept $150 from D.Fung and march 10, C.Manley was declared bankrupt.a payment of 30cent in$ was receive in full settlement. Show how these would appear in Henrys
180. ## statistics
Just wondering if someone is able to give instructions as to how to go about this questions? As part of a large research project, a social psychologist develops a measure of global environmental attitudes (i.e., general attitudes towards the environment).
181. ## Math
How many positions would be needed to represent 57^10,001 in ordinary decimal notation. Thanks!
182. ## statistics
1. A test has a mean of 50, standard deviation of 10. A. What scores separate the middle 25% from the rest b. What proportion would be expected to score between 45 and 55 c. What proportion would be expected to score 68 and above
183. ## math
y = 40 + (x - 600)*0.35 y = 50 + (x - 600)*0.10 what are the steps to get the answer
184. ## physics
a magnetic field goes from the top to the bottom of this page. what direction will a proton moving diagonally from the upper left to the lower right deflect? Assuming paper lies flat. a.downward b.upward c.left d.right
185. ## Calculus
Let f (x) = 5x^2 – 9 and g(x) = x – 3. (a) Find the composite function ( f o g)(x) and simplify. Show work. (b) Find ( f o g)(2) . Show work.
186. ## Calculus
For the parabola given by (y – 3)^2 = 8(x + 5), find the following: (a) direction parabola opens (to the left, right, up, or down) Answer: ___________ (b) vertex Answer: ___________ (c) focus Answer: ___________
187. ## Calculus
(a) State the reference angle associated with 265°. (b) Convert 265° to radians. Leave the answer in terms of pie .
188. ## Managerial accounting
I have homework in managerial accounting, textbook by Atkinson 6edition. Problems, 10-59, 10-68, 11-68 and case 11-73. Pages; 446, 450, and 504. Thank you.
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R bloggers
R news and tutorials contributed by (552) R bloggers
Updated: 3 hours 1 min ago
Accessing iNaturalist data
Wed, 2014-03-26 02:00
(This article was first published on rOpenSci Blog - R, and kindly contributed to R-bloggers)
The iNaturalist project is a really cool way to both engage people in citizen science and collect species occurrence data. The premise is pretty simple, users download an app for their smartphone, and then can easily geo reference any specimen they see, uploading it to the iNaturalist website. It let's users turn casual observations into meaningful crowdsourced species occurrence data. They also provide a nice robust API to access almost all of their data. We've developed a package rinat that can easily access all of that data in R. Our package spocc uses iNaturalist data as one of it's sources, rinat provides an interface for all the features available in the API.
Searching Currently you can get access to iNaturalist occurrence records from our package spocc, which works great for scenarios where you want lot's of data from many sources, but rinat will get you full details on every record and offers other searching on terms other than species names. First let's see how this matches with what you can get with spocc.
options(stringsAsFactors = F) library(spocc) ## Loading required package: ggplot2 library(rinat) out <- occ(query = "Accipiter striatus", from = "inat") inat_out <- get_inat_obs(taxon = "Accipiter striatus", maxresults = 25) ### Compare Id's and see that results are the same without viewing full tables cbind(out$inat$data$Accipiter_striatus$Id[1:5], inat_out$Id[1:5]) ## [,1] [,2] ## [1,] 581369 581369 ## [2,] 574433 574433 ## [3,] 570635 570635 ## [4,] 555214 555214 ## [5,] 551405 551405 The results are the same, the rinat package will offer a bit more flexiblity in searching. You can search for records by a fuzzy search query, a taxon (used above in spocc), a location in a bounding box, or by date. Let's say you just want to search by for records of Mayflies, you can use the taxon parameter to search for all lower level taxonomic matches below order. may_flies <- get_inat_obs(taxon = "Ephemeroptera") ## See what species names come back. may_flies$Species.guess[1:10] ## [1] "Mayfly" "Heptageniidae" "Ephemerella subvaria" ## [4] "Ephemerella subvaria" "Mayflies" "Stream Mayflies" ## [7] "Mayflies" "Mayflies" "Mayflies" ## [10] "Hexagenia"
You could also search using the fuzzy query parameter, looking for mentions of a specific habitat or a common name. Below I'll search for one of my favorite habitats, vernal ponds and see what species come back. Also we can search for common names and see the scientific names (which should be all the same).
vp_obs <- get_inat_obs(query = "vernal pool") vp_obs$Species.guess[1:10] ## [1] "Docks (Genus Rumex)" ## [2] "Blennosperma bakeri" ## [3] "Rails, Gallinules, and Coots" ## [4] "Western Spadefoot" ## [5] "Western Spadefoot" ## [6] "Eupsilia" ## [7] "upland chorus frog" ## [8] "Wood Frog" ## [9] "Striped Meadowhawk (Sympetrum pallipes)" ## [10] "Ambystoma maculatum" # Now le'ts look up by common name: deer <- get_inat_obs(query = "Mule Deer") deer$Scientific.name[1:10] ## [1] "Odocoileus hemionus" "Odocoileus hemionus" "Odocoileus hemionus" ## [4] "Odocoileus hemionus" "Odocoileus hemionus" "Odocoileus hemionus" ## [7] "Odocoileus hemionus" "Odocoileus hemionus" "Odocoileus" ## [10] "Odocoileus hemionus"
All of these general searching functions return a dataframe that is m x 32 (where m is the requested number of results). The column names are mostly self-explanatory, including, common names, species names, observer id's, observer names, data quality, licenses and url's for images so you can go look at the photo a user took.
Filtering
All searches can also be filtered by space and time. You can search for records within a specific bounding box, or on a specific date (but not a range). We can redo our deer search using a bounding box for the western United States.
bounds <- c(38.44047, -125, 40.86652, -121.837) deer <- get_inat_obs(query = "Mule Deer", bounds = bounds) cat(paste("The number of records found in your bunding box:", dim(deer)[1], sep = " ")) ## The number of records found in your bunding box: 47
By checking the dimensions, we can see only 47 records were found. We could try the samething for a given day, month or year. Let's try searhing for cumulative totals of observations of Ephemeroptera and see if we can detect seasonality.
library(ggplot2) out <- rep(NA, 12) for (i in 1:12) { out[i] <- dim(get_inat_obs(taxon = "Ephemeroptera", month = i, maxresults = 200))[1] } out <- data.frame(out) out$month <- factor(month.name, levels = month.name) ggplot(out, aes(x = month, y = out, group = 1)) + geom_point() + stat_smooth(se = FALSE) + xlab("Month") + ylab("Cumulative of Mayfly observations") + theme_bw(16) Exactly as you'd expect observations of this season insect tend to peak in the summer and then slowly decline. Except for September peak, it follows the expected trend. User and project data There are several other functions from the API that allow you to access data about projects and users. You can grab detailed data about projects, users and observations. Let's look at the EOL state flowers project. First we can grab some basic info on the project by searching for it based on it's "slug". You can find this in the URL of the project: "http://www.inaturalist.org/projects/state-flowers-of-the-united-states-eol-collection", which is the section of text after "projects/", so in this case it would be "state-flowers-of-the-united-states-eol-collection" Let's grab some info on the project by getting observations but set the type as "info" eol_flow <- get_inat_obs_project("state-flowers-of-the-united-states-eol-collection", type = "info", raw = FALSE) ## 204 Records ## 0 ### See how many taxa there are, and how many counts there have been cat(paste("The project has observed this many species:", eol_flow$taxa_number, sep = " ")) ## The project has observed this many species: 20 cat(paste("The project has observed this many occurrences:", eol_flow$taxa_count, sep = " ")) ## The project has observed this many occurrences: 204 We can grab all the observations from the project as well just by setting the type as "observations". Then it's easy to to get details about specific observations or users. eol_obs <- get_inat_obs_project("state-flowers-of-the-united-states-eol-collection", type = "observations", raw = FALSE) ## 204 Records ## 0-100-200-300 ## See just the first few details of an observation. head(get_inat_obs_id(eol_obs$Id[1])) ## $captive ## NULL ## ##$comments_count ## [1] 0 ## ## $community_taxon_id ## [1] 48225 ## ##$created_at ## [1] "2013-04-08T15:49:15-07:00" ## ## $delta ## [1] FALSE ## ##$description ## [1] "" ## See the first five species this user has recorded head(get_inat_obs_user(as.character(eol_obs$User.login[1]), maxresults = 20))[, 1] ## [1] "Lynx rufus" "Melanerpes formicivorus" ## [3] "Lontra canadensis" "Buteo lineatus" ## [5] "Icteridae" "Pelecanus occidentalis" There are many more details that you can get, like counts of observations by place ID (extracted from the project or observation, but not well exposed to users), the most common species by date, or by user. There is almost no end to the details you can extract. If you ever wanted to do a case study of a citizen science project, you could get data to answer almost any question you had about the iNaturalist project with rinat. Finally, what species occurrence package wouldn't be complete without some basic mapping. This function will generate a quick map for you based on a data frame of observations from rinat. These can be from functions such as get_inat_obs, or get_inat_obs_project. Let's end by plotting all the observations from the EOL state flowers project. ### Set plot to false so it returns a ggplot2 object, and that let's us modify ### it. eol_map <- inat_map(eol_obs, plot = FALSE) ### Now we can modify the returned map eol_map + borders("state") + theme_bw() + xlim(-125, -65) + ylim(25, 50) To leave a comment for the author, please follow the link and comment on his blog: rOpenSci Blog - R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs RProtoBuf 0.4.1 Tue, 2014-03-25 22:37 (This article was first published on Thinking inside the box , and kindly contributed to R-bloggers) A new bug-fix release release 0.4.1 of RProtoBuf, is now on CRAN. RProtoBuf provides GNU R bindings for the Google Protocol Buffers ("Protobuf") data encoding library used and released by Google, and deployed as a language and operating-system agnostic protocol by numerous projects. Murray once more shouldered most of the actual burden and fixed a number of issues detailed below. Changes in RProtoBuf version 0.4.1 (2014-03-25) • Document and add a test for the deprecated group functionality. • Add a CITATION file pointing to our arXiv.org preprint. • Fix a bug in the show method for EnumDescriptor types. • Import all top-level enums from imported .proto files. • Removed duplicate enum value type from the unit tests that caused problems with the most recent libprotobuf-2.5. (without option allow_alias). CRANberries also provides a diff to the previous release. More information is at the RProtoBuf page which has a draft package vignette, a 'quick' overview vignette and a unit test summary vignette. Questions, comments etc should go to the rprotobuf mailing list off the RProtoBuf page at R-Forge. This post by Dirk Eddelbuettel originated on his Thinking inside the box blog. Please report excessive re-aggregation in third-party for-profit settings. To leave a comment for the author, please follow the link and comment on his blog: Thinking inside the box . R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs R 101: Summarizing Data Tue, 2014-03-25 22:25 (This article was first published on Mathew Analytics » R, and kindly contributed to R-bloggers) When working with large amounts of data that is structured in a tabular format, a common operation is to summarize that data in different ways using specific variables. In Microsoft Excel, pivot tables are a nice feature that is used for this purpose. While not as “efficient” in relation to Excel pivot tables, R also has similar calculations that can be used to summarize large amount of data. In the following R code, I utilize R to summarize a data frame by specific variables. ## CREATE DATA dat = data.frame( name=c("Tony","James","Sara","Alice","David","Angie","Don","Faith","Becky","Jenny", "Kristi","Neil","Brandon","Kara","Kendra","Liz","Gina","Amber","Alice","George"), state=c("KS","IA","CA","FL","MI","CO","KA","CO","KS","CA","MN","FL","NM","MS","GA", "IA","IL","ID","NY","NJ"), gender=c("M","M","F","F","F","M","F","M","F","F","F","M","M","F","F","F","F","F","F","M"), marital_status=c("M","S","S","S","M","M","S","M","S","M","M","S","S","S","M","M","S","M","S","M"), credit=c("good","good","poor","fair","poor","fair","fair","fair","good","fair", "good","good","poor","fair","poor","fair","fair","fair","good","fair"), owns_home=c(0,1,0,0,1,0,1,1,1,1,0,1,0,0,1,0,1,1,1,1), cost=c(500,200,300,150,200,300,400,450,250,150,500,200,300,150,200,300,400,450,250,150)) ## AGGREGATE FUNCTION FROM BASE R aggregate(cost ~ marital_status, data=dat, FUN=mean) aggregate(cost ~ marital_status + gender, data=dat, FUN=mean) aggregate(cost ~ marital_status + credit + gender, data=dat, FUN=mean) ## SUMMARY BY IN DOBY: library(doBy) summaryBy(cost ~ marital_status, data=dat, FUN=c(mean, sd)) summaryBy(cost ~ gender, data=dat, FUN=c(mean, sd)) summaryBy(cost ~ credit, data=dat, FUN=c(mean, sd)) ## DDPLY IN PLYR library(plyr) ddply(dat, .(credit), "nrow") ddply(dat, .(credit, gender), "nrow") ddply(dat, .(marital_status), summarise, avg=mean(cost)) ddply(dat, .(marital_status, gender), summarise, avg=mean(cost)) ddply(dat, .(marital_status, gender, credit), summarise, avg=mean(cost)) ## DPLYR PACKAGE library(dplyr) Good = filter(dat, credit=="good") Good arrange(Good, desc(cost)) select(Good, owns_home, cost) mutate(Good, New_Value=cost/5) by.type <- group_by(Good, gender) summarise(by.type, num.types = n(), counts = sum(cost)) ## SQLDF PACKAGE library(sqldf) sqldf("SELECT gender, COUNT(*) FROM dat GROUP BY gender") sqldf("SELECT gender, credit, COUNT(*) FROM dat GROUP BY gender, credit") sqldf("SELECT gender, credit, COUNT(*), AVG(cost) FROM dat GROUP BY gender, credit") To leave a comment for the author, please follow the link and comment on his blog: Mathew Analytics » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Practical Data Science with R: Release date announced Tue, 2014-03-25 20:26 (This article was first published on Win-Vector Blog » R, and kindly contributed to R-bloggers) It took a little longer than we’d hoped, but we did it! Practical Data Science with R will be released on April 2nd (physical version). The eBook version will follow soon after, on April 15th. You can preorder the pBook now on the Manning book page. The physical version comes with a complimentary eBook version (when the eBook is released), in all three formats: PDF, ePub, and Kindle. If you haven’t yet, preorder it now! Related posts: To leave a comment for the author, please follow the link and comment on his blog: Win-Vector Blog » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Using R: quickly calculating summary statistics from a data frame Tue, 2014-03-25 18:32 (This article was first published on There is grandeur in this view of life » R, and kindly contributed to R-bloggers) A colleague asked: I have a lot of data in a table and I’d like to pull out some summary statistics for different subgroups. Can R do this for me quickly? Yes, there are several pretty convenient ways. I wrote about this in the recent post on the barplot, but as this is an important part of quickly getting something useful out of R, just like importing data, I’ll break it out into a post of its own. I will present a solution that uses the plyr and reshape2 packages. You can do the same with base R, and there’s nothing wrong with base R, but I find that plyr and reshape2 makes things convenient and easy to remember. The apply family of functions in base R does the same job as plyr, but with a slightly different interface. I strongly recommend beginners to begin with plyr or the apply functions, and not what I did initially, which was nested for loops and hard bracket indexing. We’ll go through and see what the different parts do. First, simulate some data. Again, when you do this, you usually have a table already, and you can ignore the simulation code. Usually a well formed data frame will look something this: a table where each observation is a unit such as an individual, and each column gives the data about the individual. Here, we imagine two binary predictors (sex and treatment) and two continuous response variables. data <- data.frame(sex = c(rep(1, 1000), rep(2, 1000)), treatment = rep(c(1, 2), 1000), response1 = rnorm(2000, 0, 1), response2 = rnorm(2000, 0, 1)) head(data) sex treatment response1 response2 1 1 1 -0.15668214 -0.13663012 2 1 2 -0.40934759 -0.07220426 3 1 1 0.07103731 -2.60549018 4 1 2 0.15113270 1.81803178 5 1 1 0.30836910 0.32596016 6 1 2 -1.41891407 1.12561812 Now, calculating a function of the response in some group is straightforward. Most R functions are vectorised by default and will accept a vector (that is, a column of a data frame). The subset function lets us pull out rows from the data frame based on a logical expression using the column names. Say that we want mean, standard deviation and a simple standard error of the mean. I will assume that we have no missing values. If you have, you can add na.rm=T to the function calls. And again, if you’ve got a more sophisticated model, these might not be the standard errors you want. Then pull them from the fitted model instead. mean(subset(data, sex == 1 & treatment == 1)$response1) sd(subset(data, sex == 1 & treatment == 1)$response1) sd(subset(data, sex == 1 & treatment == 1)$response1)/ sqrt(nrow(subset(data, sex == 1 & treatment == 1)))
Okay, but doing this for each combination of the predictors and responses is no fun and requires a lot of copying and pasting. Also, the above function calls are pretty messy with lots of repetition. There is a better way, and that’s where plyr and reshape2 come in. We load the packages. The first time you’ll have to run install.packages, as usual.
library(plyr) library(reshape2)
First out, the melt function from rehape2. Look at the table above. It’s reasonable in many situations, but right now, it would be better if we put both the response variables in the same column. If it doesn’t seem so useful, trust me and see below. Melt will take all the columns except the ones we single out as id variables and put them in the same column. It makes sense to label each row with the sex and treatment of the individual. If we had an actual unit id column, it would go here as well:
melted <- melt(data, id.vars=c("sex", "treatment"))
The resulting ”melted” table looks like this. Instead of the response variables separately we get a column of values and a column indicating which variable the value comes from.
sex treatment variable value 1 1 1 response1 -0.15668214 2 1 2 response1 -0.40934759 3 1 1 response1 0.07103731 4 1 2 response1 0.15113270 5 1 1 response1 0.30836910 6 1 2 response1 -1.41891407
Now it’s time to calculate the summary statistics again. We will use the same functions as above to do the actual calculations, but we’ll use plyr to automatically apply them to all the subsets we’re interested in. This is sometimes called the split-apply-combine approach: plyr will split the data frame into subsets, apply the function of our choice, and then collect the results for us. The first thing to notice is the function name. All the main plyr functions are called something with -ply. The letters stand for the input and return data type: ddply works on a data frame and returns a data frame. It’s probably the most important member of the family.
The arguments to ddply are the data frame to work on (melted), a vector of the column names to split on, and a function. The arguments after the function name are passed on to the function. Here we want to split in subsets for each sex, treatment and response variable. The function we apply is summarise, which makes a new data frame with named columns based on formulas, allowing us to use the column names of the input data frame in formulas. In effect it does exactly what the name says, summarises a data frame. And in this instance, we want to calculate the mean, standard deviation and standard error of the mean, so we use the above function calls, using value as the input. Run the ddply call, and we’re done!
ddply(melted, c("sex", "treatment", "variable"), summarise, mean = mean(value), sd = sd(value), sem = sd(value)/sqrt(length(value)))
sex treatment variable mean sd sem 1 1 1 response1 0.021856280 1.0124371 0.04527757 2 1 1 response2 0.045928150 1.0151670 0.04539965 3 1 2 response1 -0.065017971 0.9825428 0.04394065 4 1 2 response2 0.011512867 0.9463053 0.04232006 5 2 1 response1 -0.005374208 1.0095468 0.04514830 6 2 1 response2 -0.051699624 1.0154782 0.04541357 7 2 2 response1 0.046622111 0.9848043 0.04404179 8 2 2 response2 -0.055257295 1.0134786 0.04532414
Postat i:computer stuff, data analysis, english Tagged: #blogg100, plyr, R, reshape2
To leave a comment for the author, please follow the link and comment on his blog: There is grandeur in this view of life » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...
Categories: Methodology Blogs
A Thumbnail History of Ensemble Methods
Tue, 2014-03-25 11:30
(This article was first published on Revolutions, and kindly contributed to R-bloggers)
By Mike Bowles
Ensemble methods are the backbone of machine learning techniques. However, it can be a daunting subject for someone approaching it for the first time, so we asked Mike Bowles, machine learning expert and serial entrepreneur to provide some context.
Ensemble Methods are among the most powerful and easiest to use of predictive analytics algorithms and R programming language has an outstanding collection that includes the best performers – Random Forest, Gradient Boosting and Bagging as well as big data versions that are available through Revolution Analytics.
The phrase “Ensemble Methods” generally refers to building a large number of somewhat independent predictive models and then combining them by voting or averaging to yield very high performance. Ensemble methods have been called crowd sourcing for machines. Bagging, Boosting and Random Forest all have the objective of improving performance beyond what’s achievable with a binary decision tree, but the algorithms take different approaches to improving performance.
Bagging and Random Forests were developed to overcome variance and stability issues with binary decision trees. The term “Bagging” was coined by the late Professor Leo Breiman of Berkeley. Professor Breiman was instrumental in the development of decision trees for statistical learning and recognized that training and averaging a multitude of trees on different random subsets of data would reduce variance and improve stability. The term comes from a shortening of “Bootstrap Aggregating” and the relation to bootstrap sampling is obvious.
Tin Kam Ho of Bell Labs developed Random Decision Forests as an example of a random subspace method. The idea with Random Decision Forests was to train binary decision trees on random subsets of attributes (random subsets of columns of the training data). Breiman and Cutler’s Random Forests method combined random subsampling of rows (Bagging) with random subsampling of columns. The randomForest package in R was written by Professor Breiman and Adele Cutler.
Boosting methods grew out of work on computational learning theory. The first algorithm of this type was called AdaBoost by its authors Freund and Shapire. In the introduction to their paper they use the example of friends going to the race track regularly and betting on the horses. One of the friends decides to devise a method of betting a fraction of his money with each of his friends and adjusting the fractions based on results so that his performance over time approaches the performance of his most winning friend. The goal with Boosting is maximum predictive performance.
AdaBoost stood for a long time as the best example of a black box algorithm. A practitioner could apply it without much parameter tweaking and it would yield superior performer while almost never overfitting. It was a little mysterious. In some of Professor Breiman’s papers on Random Forests, he compares performance with AdaBoost. Professor Jerome Friedman and his Stanford colleagues Professors Hastie and Tibshirani authored a paper in 2000 that attempted to understand why AdaBoost was so successful. The paper caused a storm of controversy. The comments on the paper were longer than the paper itself. Most of the comments centered around whether boosting was just another way of reducing variance or was doing something different by focusing on error reduction. Professor Friedman offered several arguments and examples to demonstrate that boosting is more than just another variance reduction technique, but commenters did not reach a consensus.
The understanding that Professor Friedman and his colleagues developed from analyzing AdaBoost led him to formulate the boosting method more directly. That led to a number of several valuable extensions and improvements beyond AdaBoost – the ability to handle regression and multiclass problems, other performance measures besides squared error etc. These features (and new ones being developed) are all included in the excellent R package gbm by Greg Ridgeway.
Today, ensemble methods form the backbone of many data science applications. Random Forests has become particularly popular with modelers competing in Kaggle competitions and according to google trends Random Forests has surpassed AdaBoost in popularity.
In a future post we will explore several of these algorithms in R.
References
Breiman Leo, Bagging Predictors, Technical Report No. 421, Sept 1994, Dept of Statistics University of California, Berkeley.
Ho, T., Random Decision Forests, Proceedings of the Third International Conference on Document Analysis and Recognition, pp. 278-282, 1995
Breiman, Leo Random Forest – Random Features, Technical Report No. 567, Sept 1999, Dept of Statistics University of California, Berkeley.
Freund, Yoav and Schapire , Robert E. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences 55. 1997.
Friedman, Jerome, Hastie, Trevor, Tibshirani, Robert Additive Logistic Regression: A Statistical View of Boosting, Ann Stat, Vol 28, Number 2, (2000), 337-655
Categories: Methodology Blogs
Interactive Discovery of Research Affiliates JoPM Paper
Tue, 2014-03-25 11:21
(This article was first published on Timely Portfolio, and kindly contributed to R-bloggers)
In my previous post More on Rebalancing | With Data from Research Affiliates , I did some really basic visualizations, but I thought this data would be great for some more powerful interactive discovery using an interesting javascript SQL-like query language objeq along with the d3.js charting library dimple.js. Next, I hope to extend to use lodash or lazy.js. This exercise helps me think
Categories: Methodology Blogs
Filtering Data with L2 Regularisation
Tue, 2014-03-25 06:58
(This article was first published on Exegetic Analytics » R, and kindly contributed to R-bloggers)
I have just finished reading Momentum Strategies with L1 Filter by Tung-Lam Dao. The smoothing results presented in this paper are interesting and I thought it would be cool to implement the L1 and L2 filtering schemes in R. We’ll start with the L2 scheme here because it has an exact solution and I will follow up with the L1 scheme later on.
Formulation of the Problem
Consider some time series data consisting of points, , where is a smooth signal, is noise and is the combined noisy sign. If we have observations of , how can get back to an estimate of ?
The Hodrick-Prescott filter works by minimising the objective function
.
The regularisation parameter, , balances the contributions of the first and second summations, where the first is the sum of squared residuals and the second is the sum of squared curvatures in the filtered signal (characterised by the central difference approximation for the second derivative). A small value for causes the residuals to dominate the optimisation problem. A large value for will result in a solution which minimises curvature.
Implementation and Test Data
Implementing a function to perform the optimisation is pretty simple.
> l2filter.optim <- function(x, lambda = 0.0) { + objective <- function(y, lambda) { + n <- length(x) + + P1 = 0.5 * sum((y - x)**2) + # + P2 = 0 + for (i in 2:(n-1)) { + P2 = P2 + (y[i-1] - 2 * y[i] + y[i+1])**2 + } + # + P1 + lambda * P2 + } + # + optim(x, objective, lambda = lambda, method = "BFGS")$par + } It has a nested objective function. The BFGS method is specified for optim() because the Nelder and Mead optimisation scheme converged too slowly. First we’ll try this out on some test data. > N <- 20 > > set.seed(1) > > (y <- 1:N + 10 * runif(N)) [1] 3.6551 5.7212 8.7285 13.0821 7.0168 14.9839 16.4468 14.6080 15.2911 10.6179 13.0597 [12] 13.7656 19.8702 17.8410 22.6984 20.9770 24.1762 27.9191 22.8004 27.7745 If we use then regularisation has no effect and the objective function is minimised when . Not surprisingly, in this case the filtered signal is the same as the original signal. > l2filter.optim(y, 0) [1] 3.6551 5.7212 8.7285 13.0821 7.0168 14.9839 16.4468 14.6080 15.2911 10.6179 13.0597 [12] 13.7656 19.8702 17.8410 22.6984 20.9770 24.1762 27.9191 22.8004 27.7745 If, on the other hand, we use a large value for the regularisation parameter then the filtered signal is significantly different. > l2filter.optim(y, 100) [1] 5.8563 7.0126 8.1579 9.2747 10.3484 11.3835 12.3677 13.3067 14.2269 15.1607 16.1463 [12] 17.1989 18.3183 19.4873 20.6963 21.9274 23.1729 24.4203 25.6621 26.9082 A plot is the most sensible way to visualise the effects of . Below the original data (circles) are plotted along with the filtered data for values of from 0.1 to 100. In the top panel, weak regularisation results in a filtered signal which is not too different from the original. At the other extreme, the bottom panel shows strong regularisation where the filtered signal is essentially a straight line (all curvature has been removed). The other two panels represent intermediate levels of regularisation and it is clear how the original signal is being smoothed to varying degrees. Matrix Implementation As it happens there is an exact solution to the Hodrick-Prescott optimisation problem, which involves some simple matrix algebra. The core of the solution is a band matrix with a right bandwidth of 2. The non-zero elements on each row are 1, -2 and 1. The function below constructs this matrix in a rather naive way. However, it is simply for illustration: we will look at a better implementation using sparse matrices. l2filter.matrix <- function(x, lambda = 0.0) { n <- length(x) I = diag(1, nrow = n) D = matrix(0, nrow = n - 2, ncol = n) # for (i in 1:(n-2)) { D[i, i:(i+2)] = c(1, -2, 1) } c(solve(I + 2 * lambda * t(D) %*% D) %*% x) } Applying this function to the same set of test data, we get results consistent with those from optimisation. > l2filter.matrix(y, 100) [1] 5.8563 7.0126 8.1579 9.2747 10.3484 11.3835 12.3677 13.3067 14.2269 15.1607 16.1463 [12] 17.1989 18.3183 19.4873 20.6963 21.9274 23.1729 24.4203 25.6621 26.9082 In principle the matrix solution is much more efficient than the optimisation. However, an implementation using a dense matrix (as above) would not be feasible for a data series of any appreciable length due to memory constraints. A sparse matrix implementation does the trick though. library(Matrix) l2filter.sparse <- function(x, lambda = 0.0) { n <- length(x) I = Diagonal(n) D = bandSparse(n = n - 2, m = n, k = c(0, 1, 2), diagonals = list(rep(1, n), rep(-2, n), rep(1, n))) (solve(I + 2 * lambda * t(D) %*% D) %*% x)[,1] } Again we can check that this gives the right results. > l2filter.sparse(y, 100) [1] 5.8563 7.0126 8.1579 9.2747 10.3484 11.3835 12.3677 13.3067 14.2269 15.1607 16.1463 [12] 17.1989 18.3183 19.4873 20.6963 21.9274 23.1729 24.4203 25.6621 26.9082 Application: S&P500 Data So, let’s take this out for a drive in the real world. We’ll get out hands on some S&P500 data from Quandl. > library(Quandl) > > Quandl.auth("xxxxxxxxxxxxxxxxxxxx") > > SP500 = Quandl("YAHOO/INDEX_GSPC", start_date = "1994-01-01", end_date = "2014-01-01") > # > SP500 = SP500[, c(1, 5)] Then systematically apply the filter with a range of regularisation parameters scaling from 0.1 to 100000 in multiples of 10. The results are plotted below. In each panel the grey data reflect the raw daily values for the S&P500 index. Superimposed on top of these are the results of filtering the signal using the specified regularisation parameter. As anticipated, larger values of result in a smoother curve since the filter is more heavily penalised for curvature in the filtered signal. I think that the results look rather compelling. The only major drawback to this filter seems to be the fact, if used dynamically, the algorithm can (and most likely will) cause previous states to change. If used, for example, as the basis for an indicator on a chart, this would cause repainting of historical values. To leave a comment for the author, please follow the link and comment on his blog: Exegetic Analytics » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Sankey diagrams with googleVis Tue, 2014-03-25 02:56 (This article was first published on mages' blog, and kindly contributed to R-bloggers) Sankey diagrams are great for visualising flows from one set of data values to another. Although named after Irish Captain Matthew Henry Phineas Riall Sankey, who used this type of diagram in 1898 to show the energy efficiency of a steam engine, the best know Sankey diagram is probably Charles Minard's Map of Napoleon's Russian Campaign of 1812, which he actually produced in 1869. Thomas Rahlf: Datendesign mit R The above example from Thomas Rahlf's book Datendesign mit R shows that Minard's plot can be reproduced with base graphics in R. Aaron Berdanier posted in 2010 the SankeyR function and Erik Andrulis published the riverplot package on CRAN that allows users to create static Sankey charts as well. Interactive Sankey diagram can be generated with rCharts and now also with googleVis (version >= 0.5.0). For my a first example I use UK visitor data from VisitBritain.org. The following diagram visualises the flow of visitors in 2012; where they came from and which parts of the UK they visited. This example illustrates the key concept already. I need a data frame with three columns that explains the flow of data from a source to a target and the strength or weight of the connection. Loading My next example uses a graph data set that I visualise in the same way again, but here I start to play around with the various parameters of the Google API. Loading As stated by Google, the Sankey chart may be undergoing substantial revisions in future Google Charts releases. For more information and installation instructions see the googleVis project site and Google documentation. Session InfoR version 3.0.3 (2014-03-06) Platform: x86_64-apple-darwin10.8.0 (64-bit) locale: [1] en_GB.UTF-8/en_GB.UTF-8/en_GB.UTF-8/C/en_GB.UTF-8/en_GB.UTF-8 attached base packages: [1] stats graphics grDevices utils datasets methods [7] base other attached packages: [1] googleVis_0.5.0-4 igraph_0.7.0 loaded via a namespace (and not attached): [1] RJSONIO_1.0-3 tools_3.0.3 To leave a comment for the author, please follow the link and comment on his blog: mages' blog. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Free eBook on Big Data and Data Science Mon, 2014-03-24 17:15 (This article was first published on Revolutions, and kindly contributed to R-bloggers) The fine folks behind the Big Data Journal have just published a new e-book Big Data: Harnessing the Power of Big Data Through Education and Data-Driven Decision Making. (Note: Adobe Flash is required to view the e-book.) In the eBook, you'll find the following technical papers on the topics of Big Data, Data Science, and R: • Data Science and its Relationship to Big Data and Data-Driven Decision Making, by Foster Provost and Tom Fawcett. • Predictive Modeling With Big Data: Is Bigger Really Better?, by Enric Junqué de Fortuny, David Martens, and Foster Provost. • Educating the Next Generation of Data Scientists, a roundtable discussion including Edd Dumbill, Elizabeth D. Liddy, Jeffrey Stanton, Kate Mueller, and Shelly Farnham • Delivering Value from Big Data with Revolution R Enterprise and Hadoop, by Thomas Dinsmore and Bill Jacobs. There's also a video introduction to the papers from yours truly. View the e-book — sponsored by Revolution Analytics — here: Big Data: Harnessing the Power of Big Data Through Education and Data-Driven Decision Making To leave a comment for the author, please follow the link and comment on his blog: Revolutions. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs A Note on the Johnson-Lindenstrauss Lemma Mon, 2014-03-24 11:55 (This article was first published on John Myles White » Statistics, and kindly contributed to R-bloggers) Introduction A recent thread on Theoretical CS StackExchange comparing the Johnson-Lindenstrauss Lemma with the Singular Value Decomposition piqued my interest enough that I decided to spend some time last night reading the standard JL papers. Until this week, I only had a vague understanding of what the JL Lemma implied. I previously mistook the JL Lemma for a purely theoretical result that established the existence of distance-preserving projections from high-dimensional spaces into low-dimensional spaces. This vague understanding of the JL Lemma turns out to be almost correct, but it also led me to neglect the most interesting elements of the literature on the JL Lemma: the papers on the JL Lemma do not simply establish the existence of such projections, but also provide (1) an explicit bound on the dimensionality required for a projection to ensure that it will approximately preserve distances and they even provide (2) an explicit construction of a random matrix, $$A$$, that produces the desired projection. Once I knew that the JL Lemma was a constructive proof, I decided to implement code in Julia to construct examples of this family of random projections. The rest of this post walks through that code as a way of explaining the JL Lemma’s practical applications. Formal Statement of the JL Lemma The JL Lemma, as stated in “An elementary proof of the Johnson-Lindenstrauss Lemma” by Dasgputa and Gupta, is the following result about dimensionality reduction: For any $$0 < \epsilon < 1$$ and any integer $$n$$, let $$k$$ be a positive integer such that $$k \geq 4(\epsilon^2/2 - \epsilon^3/3)^{-1}\log(n)$$. Then for any set $$V$$ of $$n$$ points in $$\mathbb{R}^d$$, there is a map $$f : \mathbb{R}^d \to \mathbb{R}^k$$ such that for all $$u, v \in V$$, $$(1 - \epsilon) ||u - v||^2 \leq ||f(u) - f(v)||^2 \leq (1 + \epsilon) ||u - v||^2.$$ Further this map can be found in randomized polynomial time. To fully appreciate this result, we can unpack the abstract statement of the lemma into two components. The JL Lemma in Two Parts Part 1: Given a number of data points, $$n$$, that we wish to project and a relative error, $$\epsilon$$, that we are willing to tolerate, we can compute a minimum dimensionality, $$k$$, that a projection must map a space into before it can guarantee that distances will be preserved up to a factor of $$\epsilon$$. In particular, $$k = \left \lceil{4(\epsilon^2/2 – \epsilon^3/3)^{-1}\log(n)} \right \rceil$$. Note that this implies that the dimensionality required to preserve distances depends only on the number of points and not on the dimensionality of the original space. Part 2: Given an input matrix, $$X$$, of $$n$$ points in $$d$$-dimensional space, we can explicitly construct a map, $$f$$, such that the distance between any pair of columns of $$X$$ will not distorted by more than a factor of $$\epsilon$$. Surprisingly, this map $$f$$ can be a simple matrix, $$A$$, constructed by sampling $$k * d$$ IID draws from a Gaussian with mean $$0$$ and variance $$\frac{1}{k}$$. Coding Up The Projections We can translate the first part of the JL Lemma into a single line of code that computes the dimensionality, $$k$$, of our low-dimensional space given the number of data points, $$n$$, and the error, $$\epsilon$$, that we are willing to tolerate: 1 mindim(n::Integer, ε::Real) = iceil((4 * log(n)) / (ε^2 / 2 - ε^3 / 3)) Having defined this function, we can try it out on a simple problem: 1 2 mindim(3, 0.1) # => 942 This result was somewhat surprising to me: to represent $$3$$ points with no more than $$10$$% error, we require nearly $$1,000$$ dimensions. This reflects an important fact about the JL Lemma: it produces result that can be extremely conservative for small dimensional inputs. It’s obvious that, for data sets that contain $$3$$ points in $$100$$-dimensional space, we could use a projection into $$100$$ dimensions that would preserve distances perfectly. But this observation neglects one of the essential aspects of the JL Lemma: the dimensions required by the lemma will be sufficient whether our data set contains points in $$100$$-dimensional space or points in $$10^{100}$$-dimensional space. No matter what dimensionality the raw data lies in, the JL Lemma says that $$942$$ dimensions suffices to preserve the distances between $$3$$ points. I found this statement unintuitive at the start. To see that it’s true, let’s construct a random projection matrix, $$A$$, that will let us confirm experimentally that the JL Lemma really works: 1 2 3 4 5 6 7 8 9 10 11 using Distributions function projection( X::Matrix, ε::Real, k::Integer = mindim(size(X, 2), ε) ) d, n = size(X) A = rand(Normal(0, 1 / sqrt(k)), k, d) return A, k, A * X end This projection function is sufficient to construct a matrix, $$A$$, that will satisfy the assumptions of the JL Lemma. It will also return the dimensionality, $$k$$, of $$A$$ and the result of projecting the input, $$X$$, into the new space defined by $$A$$. To get a feel for how this works, we can try this out on a very simple data set: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 X = eye(3, 3) ε = 0.1 A, k, AX = projection(X, ε) # => # ( # 942x3 Array{Float64,2}: # -0.035269 -0.0299966 -0.0292959 # -0.00501367 0.0316806 0.0460191 # 0.0633815 -0.0136478 -0.0198676 # 0.0262627 0.00187459 -0.0122604 # 0.0417169 -0.0230222 -0.00842476 # 0.0236389 0.0585979 -0.0642437 # 0.00685299 -0.0513301 0.0501431 # 0.027723 -0.0151694 0.00274466 # 0.0338992 0.0216184 -0.0494157 # 0.0612926 0.0276185 0.0271352 # ⋮ # -0.00167347 -0.018576 0.0290964 # 0.0158393 0.0124403 -0.0208216 # -0.00833401 0.0323784 0.0245698 # 0.019355 0.0057538 0.0150561 # 0.00352774 0.031572 -0.0262811 # -0.0523636 -0.0388993 -0.00794319 # -0.0363795 0.0633939 -0.0292289 # 0.0106868 0.0341909 0.0116523 # 0.0072586 -0.0337501 0.0405171 , # # 942, # 942x3 Array{Float64,2}: # -0.035269 -0.0299966 -0.0292959 # -0.00501367 0.0316806 0.0460191 # 0.0633815 -0.0136478 -0.0198676 # 0.0262627 0.00187459 -0.0122604 # 0.0417169 -0.0230222 -0.00842476 # 0.0236389 0.0585979 -0.0642437 # 0.00685299 -0.0513301 0.0501431 # 0.027723 -0.0151694 0.00274466 # 0.0338992 0.0216184 -0.0494157 # 0.0612926 0.0276185 0.0271352 # ⋮ # -0.00167347 -0.018576 0.0290964 # 0.0158393 0.0124403 -0.0208216 # -0.00833401 0.0323784 0.0245698 # 0.019355 0.0057538 0.0150561 # 0.00352774 0.031572 -0.0262811 # -0.0523636 -0.0388993 -0.00794319 # -0.0363795 0.0633939 -0.0292289 # 0.0106868 0.0341909 0.0116523 # 0.0072586 -0.0337501 0.0405171 ) According to the JL Lemma, the new matrix, $$AX$$, should approximately preserve the distances between columns of $$X$$. We can write a quick function that verifies this claim: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 function ispreserved(X::Matrix, A::Matrix, ε::Real) d, n = size(X) k = size(A, 1) for i in 1:n for j in (i + 1):n u, v = X[:, i], X[:, j] d_old = norm(u - v)^2 d_new = norm(A * u - A * v)^2 @printf("Considering the pair X[:, %d], X[:, %d]...\n", i, j) @printf("\tOld distance: %f\n", d_old) @printf("\tNew distance: %f\n", d_new) @printf( "\tWithin bounds %f <= %f <= %f\n", (1 - ε) * d_old, d_new, (1 + ε) * d_old ) if !((1 - ε) * d_old <= d_old <= (1 + ε) * d_old) return false end end end return true end And then we can test out the results: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ispreserved(X, A, ε) # => # Considering the pair X[:, 1], X[:, 2]... # Old distance: 2.000000 # New distance: 2.104506 # Within bounds 1.800000 <= 2.104506 <= 2.200000 # Considering the pair X[:, 1], X[:, 3]... # Old distance: 2.000000 # New distance: 2.006130 # Within bounds 1.800000 <= 2.006130 <= 2.200000 # Considering the pair X[:, 2], X[:, 3]... # Old distance: 2.000000 # New distance: 1.955495 # Within bounds 1.800000 <= 1.955495 <= 2.200000 As claimed, the distances are indeed preserved up to a factor of $$\epsilon$$. But, as we noted earlier, the JL lemma has a somewhat perverse consequence for our $$3×3$$ matrix: we’ve expanded our input into a $$942×3$$ matrix rather than reduced its dimensionality. To get meaningful dimensionality reduction, we need to project a data set from a space that has more than $$942$$ dimensions. So let’s try out a $$50,000$$-dimensional example: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 X = eye(50_000, 3) A, k, AX = projection(X, ε) ispreserved(X, A, ε) # => # Considering the pair X[:, 1], X[:, 2]... # Old distance: 2.000000 # New distance: 2.021298 # Within bounds 1.800000 <= 2.021298 <= 2.200000 # Considering the pair X[:, 1], X[:, 3]... # Old distance: 2.000000 # New distance: 1.955502 # Within bounds 1.800000 <= 1.955502 <= 2.200000 # Considering the pair X[:, 2], X[:, 3]... # Old distance: 2.000000 # New distance: 1.988945 # Within bounds 1.800000 <= 1.988945 <= 2.200000 In this case, the JL Lemma again works as claimed: the pairwise distances between columns of $$X$$ are preserved. And we’ve done this while reducing the dimensionality of our data from $$50,000$$ to $$942$$. Moreover, this same approach would still work if the input space had $$10$$ million dimensions. Conclusion Contrary to my naive conception of the JL Lemma, the literature on the lemma not only tells us that, abstractly, distances can be preserved by dimensionality reduction techniques. It tells how to perform this reduction — and the mechanism is both simple and general. To leave a comment for the author, please follow the link and comment on his blog: John Myles White » Statistics. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Hack, a template for improving code reliability Mon, 2014-03-24 11:20 (This article was first published on The Shape of Code » R, and kindly contributed to R-bloggers) My sole prediction for 2014 has come true, Facebook have announced the Hack language (if you don’t know that HHVM is the Hip Hop Virtual Machine you are obviously not a trendy developer). This language does not follow the usual trend in that it looks useful, rather than being fashion fluff for corporate developers to brag about. Hack extends an existing language (don’t the Facebook developers know about not-invented-here?) by adding features to improve code reliability (how uncool is that) and stuff that will sometimes enable faster code to be generated (which has always been cool). Well done Facebook. I hope this is the start of a trend of adding features to a language that help developers improve code reliability. Hack extends PHP to allow programmers to express intent, e.g., this variable only ever holds integer values. Compilers can then check that the code follows the intent and flag when it doesn’t, e.g., a string is assigned to the variable intended to only hold integers. This sounds so trivial to be hardly worth bothering about, but in practice it catches lots of minor mistakes very quickly and saves huge amounts of time that would otherwise be spent debugging code at runtime. Yes, Hack has added static typing into a dynamically typed language. There is a generally held view that static typing prevents programmers doing what needs to be done and that dynamic typing is all about freedom of expression (who could object to that?) Static typing got a bad name because early languages using it were too disciplinarian in a few places and like the very small stone in a runners shoe these edge cases came to dominate thinking. Dynamic languages are great for small programs and showing off to spotty teenagers students, but are expensive to maintain and a nightmare to work with on 10K+ line systems. The term gradual typing is a good description for Hack’s type system. Developers can take existing PHP code and gradually give types to existing variables in a piecemeal fashion or add new code that uses types into code that does not. The type checker figures out what it can and does not get too upperty about complaining. If a developer can be talked into giving such a system a try they quickly learn that they can save a lot of debugging time by using it. I would like to see gradual typing introduced into R, but perhaps the language does not cause its users enough grief to make this happen (it is R’s libraries that cause the grief): • Compared to PHP’s quirks the R quirk’s are pedestrian. In the interest of balance I should point out that Javascript can at times be as quirky as PHP and C++ error messages can be totally incomprehensible to everybody (including the people who wrote the compiler). • R programs are often small, i.e., 100 lines’ish. It is only when programs, written in dynamically typed languages, start to exceed around 10k+ lines that they start to fall in on themselves unless that one person who has everything in his head is there to hold it all up. However, there is a sort of precedent: Perl programs tend to be short (although I don’t think they are as short as R) and it gradually introduced the option of stronger typing. But Perk did/does have one person who was the recognized language designer who could lead the process; R has a committee. To leave a comment for the author, please follow the link and comment on his blog: The Shape of Code » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Image CGI with R Mon, 2014-03-24 11:15 (This article was first published on BioStatMatt » R, and kindly contributed to R-bloggers) I received an email recently with a question about using R in the common gateway interface (CGI) framework to create and pass image data to the web browser. I posted to stackoverflow about this some time ago, but had forgotten the details. The trouble is that R's graphics devices only write image data to file, rather than to a buffer or R connection. Hence, when passing image data via CGI, it is necessary to write an intermediary image file, read the file, and then output the data to STDOUT. Unfortunately, R will not allow you to write binary data to STDOUT (for example, try writeBin(as.raw("0xFF"), stdout()). So, this becomes even more complicated! One solution is to open a (binary) pipe connection to the Linux cat command, which sends it's output to STDOUT, and write the image data to the pipe connection. Of course, this is a platform dependent solution. Below is a CGI script that implements this: #!/bin/sh REXEC="/usr/local/bin/R --vanilla --slave"$REXEC <<EOF # create a random file name pngfile <- paste0(format(Sys.time(), "%Y%m%d%H%M%S"), paste(sample(letters,10), collapse=""), ".png") # create temporary graphic file png(pngfile, type = "cairo") x <- seq(-10, 10, length= 30) y <- x f <- function(x, y) { r <- sqrt(x^2+y^2); 10 * sin(r)/r } z <- outer(x, y, f) z[is.na(z)] <- 1 op <- par(bg = rgb(1,1,1,0)) persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue") persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", ltheta = 120, shade = 0.75, ticktype = "detailed", xlab = "X", ylab = "Y", zlab = "Sinc( r )") invisible(dev.off()) # write headers pngsize <- file.info(pngfile)[["size"]] cat("Content-type: image/png\n") cat(paste("Content-length: ", pngsize, "\n\n", sep="")) # open pipe to stdout and pass image data con <- pipe("cat", "wb") writeBin(readBin(pngfile, 'raw', n=pngsize), con) flush(con) close(con) # remove intermediate graphic invisible(file.remove(pngfile)) EOF ###
To leave a comment for the author, please follow the link and comment on his blog: BioStatMatt » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...
Categories: Methodology Blogs
R jobs (March 24th)
Mon, 2014-03-24 07:42
Earlier this month I have announced the launch of R-users.com, a new R jobs website. My intention is to post around twice a month on new R jobs posted on the website.
You are invited to use this link, to post new R jobs. Registration is less than 10 seconds.
Here are the new R jobs:
1. Full-Time
Data Scientist, Schroeder Institute
American Legacy Foundation
WashingtonDistrict of Columbia, United States
21 Mar2014
2. Freelance
Senior Algorithm Data Scientist
MyPermissions
Tel AvivTel Aviv District, Israel
18 Mar2014
3. Freelance
Software Developer
Martina Morris / University of Washington
Anywhere
18 Mar2014
4. Full-Time
Fully-funded PhD Studentship in Joint Modelling at Northumbria University
Northumbria University
Newcastle upon TyneEngland, United Kingdom
14 Mar2014
5. Part-Time
Part-time Technical Writer/Editorial Assistant
Vivian Zhang/SupStat Inc
New YorkNew York, United States
7 Mar2014
6. Full-Time
R package developer
University of Washington, statnet research group
Anywhere
7 Mar2014
7. Internship
Intern/Researcher in Aspinalls Group
Aspinalls Group
EnglandUnited Kingdom
4 Mar2014
Categories: Methodology Blogs
Experimenting With R – Point to Point Mapping With Great Circles
Mon, 2014-03-24 07:17
(This article was first published on OUseful.Info, the blog... » Rstats, and kindly contributed to R-bloggers)
I’ve started doodling again… This time, around maps, looking for recipes that make life easier plotting lines to connect points on maps. The most attractive maps seem to use great circles to connect one point with another, these providing the shortest path between two points when you consider the Earth as a sphere.
Here’s one quick experiment (based on the Flowing Data blog post How to map connections with great circles), for an R/Shiny app that allows you to upload a CSV file containing a couple of location columns (at least) and an optional “amount” column, and it’ll then draw lines between the points on each row.
The app requires us to solve several problems, including:
• how to geocode the locations
• how to plot the lines as great circles
• how to upload the CSV file
• how to select the from and two columns from the CSV file
• how to optionally select a valid numerical column for setting line thickness
• Let’s start with the geocoder. For convenience, I’m going to use the Google geocoder via the geocode() function from the ggmap library.
#Locations are in two columns, *fr* and *to* in the *dummy* dataframe #If locations are duplicated in from/to columns, dedupe so we don't geocode same location more than once locs=data.frame(place=unique(c(as.vector(dummy[[fr]]),as.vector(dummy[[to]]))),stringsAsFactors=F) #Run the geocoder against each location, then transpose and bind the results into a dataframe cbind(locs, t(sapply(locs$place,geocode, USE.NAMES=F))) The locs data is a vector of locations: place 1 London, UK 2 Cambridge,UK 3 Paris,France 4 Sydney, Australia 5 Paris, France 6 New York,US 7 Cape Town, South Africa The sapply(locs$place,geocode, USE.NAMES=F) function returns data that looks like:
[,1] [,2] [,3] [,4] [,5] [,6] [,7] lon -0.1254872 0.121817 2.352222 151.207 2.352222 -74.00597 18.42406 lat 51.50852 52.20534 48.85661 -33.86749 48.85661 40.71435 -33.92487
The transpose (t() gives us:
lon lat [1,] -0.1254872 51.50852 [2,] 0.121817 52.20534 [3,] 2.352222 48.85661 [4,] 151.207 -33.86749 [5,] 2.352222 48.85661 [6,] -74.00597 40.71435 [7,] 18.42406 -33.92487
The cbind() binds each location with its lat and lon value:
place lon lat 1 London, UK -0.1254872 51.50852 2 Cambridge,UK 0.121817 52.20534 3 Paris,France 2.352222 48.85661 4 Sydney, Australia 151.207 -33.86749 5 Paris, France 2.352222 48.85661 6 New York,US -74.00597 40.71435 7 Cape Town, South Africa 18.42406 -33.92487
Code that provides a minimal example for uploading the data from a CSV file on the desktop to the Shiny app, then creating dynamic drop lists containing column names, can be found here: Simple file geocoder (R/shiny app).
The following snippet may be generally useful for getting a list of column names from a data frame that correspond to numerical columns:
#Get a list of column names for numerical columns in data frame df nums <- sapply(df, is.numeric) names(nums[nums])
The code for the full application can be found as a runnable gist in RStudio from here: R/Shiny app – great circle mapping. [In RStudio, install.packages("shiny"); library(shiny); runGist(9690079). The gist contains a dummy data file if you want to download it to try it out...]
Here’s the code explicitly…
The global.R file loads the necessary packages, installing them if they are missing:
#global.R ##This should detect and install missing packages before loading them - hopefully! list.of.packages <- c("shiny", "ggmap","maps","geosphere") new.packages <- list.of.packages[!(list.of.packages %in% installed.packages()[,"Package"])] if(length(new.packages)) install.packages(new.packages) lapply(list.of.packages,function(x){library(x,character.only=TRUE)})
The ui.R file builds the Shiny app’s user interface. The drop down column selector lists are populated dynamically with the names of the columns in the data file once it is uploaded. An optional Amount column can be selected – the corresponding list only displays the names of numerical columns. (The lists of location columns to be geocoded should really be limited to non-numerical columns.) The action button prevents the geocoding routines firing until the user is ready – select the columns appropriately before geocoding (error messages are not handled very nicely;-)
#ui.R shinyUI(pageWithSidebar( headerPanel("Great Circle Map demo"), sidebarPanel( #Provide a dialogue to upload a file fileInput('datafile', 'Choose CSV file', accept=c('text/csv', 'text/comma-separated-values,text/plain')), #Define some dynamic UI elements - these will be lists containing file column names uiOutput("fromCol"), uiOutput("toCol"), #Do we want to make use of an amount column to tweak line properties? uiOutput("amountflag"), #If we do, we need more options... conditionalPanel( condition="input.amountflag==true", uiOutput("amountCol") ), conditionalPanel( condition="input.amountflag==true", uiOutput("lineSelector") ), #We don't want the geocoder firing until we're ready... actionButton("getgeo", "Get geodata") ), mainPanel( tableOutput("filetable"), tableOutput("geotable"), plotOutput("geoplot") ) ))
The server.R file contains the server logic for the app. One thing to note is the way we isolate some of the variables in the geocoder reactive function. (Reactive functions fire when one of the external variables they contain changes. To prevent the function firing when a variable it contains changes, we need to isolate it. (See the docs for me; for example, Shiny Lesson 7: Reactive outputs or Isolation: avoiding dependency.)
#server.R shinyServer(function(input, output) { #Handle the file upload filedata <- reactive({ infile <- input$datafile if (is.null(infile)) { # User has not uploaded a file yet return(NULL) } read.csv(infile$datapath) }) #Populate the list boxes in the UI with column names from the uploaded file output$toCol <- renderUI({ df <-filedata() if (is.null(df)) return(NULL) items=names(df) names(items)=items selectInput("to", "To:",items) }) output$fromCol <- renderUI({ df <-filedata() if (is.null(df)) return(NULL) items=names(df) names(items)=items selectInput("from", "From:",items) }) #If we want to make use of an amount column, we need to be able to say so... output$amountflag <- renderUI({ df <-filedata() if (is.null(df)) return(NULL) checkboxInput("amountflag", "Use values?", FALSE) }) output$amountCol <- renderUI({ df <-filedata() if (is.null(df)) return(NULL) #Let's only show numeric columns nums <- sapply(df, is.numeric) items=names(nums[nums]) names(items)=items selectInput("amount", "Amount:",items) }) #Allow different line styles to be selected output$lineSelector <- renderUI({ radioButtons("lineselector", "Line type:", c("Uniform" = "uniform", "Thickness proportional" = "thickprop", "Colour proportional" = "colprop")) }) #Display the data table - handy for debugging; if the file is large, need to limit the data displayed [TO DO] output$filetable <- renderTable({ filedata() }) #The geocoding bit... Isolate variables so we don't keep firing this... geodata <- reactive({ if (input$getgeo == 0) return(NULL) df=filedata() if (is.null(df)) return(NULL) isolate({ dummy=filedata() fr=input$from to=input$to locs=data.frame(place=unique(c(as.vector(dummy[[fr]]),as.vector(dummy[[to]]))),stringsAsFactors=F) cbind(locs, t(sapply(locs$place,geocode, USE.NAMES=F))) }) }) #Weave the goecoded data into the data frame we made from the CSV file geodata2 <- reactive({ if (input$getgeo == 0) return(NULL) df=filedata() if (input$amountflag != 0) { maxval=max(df[input$amount],na.rm=T) minval=min(df[input$amount],na.rm=T) df$b8g43bds=10*df[input$amount]/maxval } gf=geodata() df=merge(df,gf,by.x=input$from,by.y='place') merge(df,gf,by.x=input$to,by.y='place') }) #Preview the geocoded data output$geotable <- renderTable({ if (input$getgeo == 0) return(NULL) geodata2() }) #Plot the data on a map... output$geoplot<- renderPlot({ if (input$getgeo == 0) return(map("world")) #Method pinched from: http://flowingdata.com/2011/05/11/how-to-map-connections-with-great-circles/ map("world") df=geodata2() pal <- colorRampPalette(c("blue", "red")) colors <- pal(100) for (j in 1:nrow(df)){ inter <- gcIntermediate(c(df[j,]$lon.x[[1]], df[j,]$lat.x[[1]]), c(df[j,]$lon.y[[1]], df[j,]$lat.y[[1]]), n=100, addStartEnd=TRUE) #We could possibly do more styling based on user preferences? if (input$amountflag == 0) lines(inter, col="red", lwd=0.8) else { if (input$lineselector == 'colprop') { maxval <- max(df$b8g43bds) minval= min(df$b8g43bds) colindex <- round( (df[j,]$b8g43bds[[1]]/10) * length(colors) ) lines(inter, col=colors[colindex], lwd=0.8) } else if (input$lineselector == 'thickprop') { lines(inter, col="red", lwd=df[j,]$b8g43bds[[1]]) } else lines(inter, col="red", lwd=0.8) } } }) }) So that’s the start of it… this app could be further developed in several ways, for example allowing the user to filter or colour displayed lines according to factor values in a further column (commodity type, for example), or produce a lattice of maps based on facet values in a column. I also need to figure how to to save maps, and maybe produce zoomable ones. If geocoded points all lay within a blinding box limited to a particular geographical area, scaling the map view to show just that area might be useful. Other techniques might include using proportional symbols (circles) at line landing points to show the sum of values incoming to that point, or some of values outgoing, or the difference between the two; (maybe use green for incoming outgoing, then size by the absolute difference?) To leave a comment for the author, please follow the link and comment on his blog: OUseful.Info, the blog... » Rstats. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more... Categories: Methodology Blogs Estimating Variance as a Function of Treatment Rank Class Mon, 2014-03-24 03:34 (This article was first published on Econometrics by Simulation, and kindly contributed to R-bloggers) Imagine that we have a treatment that we give to five different groups of individuals. Each individual has a variable response which as a unique mean and variance based on the treatment. We do not know how the means will change but we believe the variance of responses will expand depending upon what level of treatment the individual gets. We would like to expressly model both the differences in means and that of the variances. This code was formulated in response to a question posted on CrossValidated. We want to solve $$\max_{\bf {\hat\beta,\hat\gamma}} (\sum_{i=1}(ln(D(x_i, \hat\mu, \hat\gamma_0+\hat\gamma_1 rank)))$$ # Specify how many individuals are in each of our groups nobs.group <- span=""> 500 # Simulate our data grp1 <- span=""> data.frame(values=rnorm(nobs.group,5,1), grp=1) grp2 <- span=""> data.frame(values=rnorm(nobs.group,3,2), grp=2) grp3 <- span=""> data.frame(values=rnorm(nobs.group,6,3), grp=3) grp4 <- span=""> data.frame(values=rnorm(nobs.group,5,4), grp=4) grp5 <- span=""> data.frame(values=rnorm(nobs.group,1,5), grp=5) # Group our data into a single object mydata <- span=""> rbind(grp1,grp2,grp3,grp4,grp5) # Speficy the function to maximize (minimize) lnp <- span=""> function(gamma, x, rank) # I include a negative here because the default option with optim is minimize -sum(log(dnorm(x,gamma[1]*(rank==1)+ gamma[2]*(rank==2)+ gamma[3]*(rank==3)+ gamma[4]*(rank==4)+ gamma[5]*(rank==5), gamma[6]+gamma[7]*rank))) ans <- span=""> optim(c( # Specify initial values for parameters to be estimated beta1=1,beta2=1,beta3=1,beta4=1, beta5=1, gamma1=1,gamma2=1), # Specify the function to minimize (maximize) lnp, # Input dependent variable as x and the explanatory variable as rank x=mydata$values, rank=mydata$grp, # Be sure to inlcude the hessian in the return for # calculating standard errors hessian=T) # The standard erros can be estimated using the hessian stand.error <- span=""> sqrt(diag(solve(ans$hessian)))
# This will create a nice table of results
cbind(par.est=ans$par, stand.error, tstat=ans$par/stand.error,
pvalue=1-pt(ans$par/stand.error, nrow(mydata)-length(ans$par)),
CILower=ans$par+stand.error*qt(.05,nrow(mydata)-length(ans$par)),
CIUpper=ans$par+stand.error*qt(.95,nrow(mydata)-length(ans$par))
) # Formatted by Pretty R at inside-R.org par.est stand.error tstat pvalue CILower CIUpper
beta1 4.9894067 0.04038367 123.550112 0.0000000 4.9229567 5.05585658
beta2 2.0009055 0.10955198 18.264440 0.0000000 1.8206415 2.18116942
beta3 3.7640531 0.19407912 19.394427 0.0000000 3.4447027 4.08340355
beta4 6.4818562 0.23879420 27.144111 0.0000000 6.0889287 6.87478375
beta5 -0.5547626 0.29730735 -1.865957 0.9689176 -1.0439715 -0.06555377
gamma1 -0.4849449 0.05684407 -8.531142 1.0000000 -0.5784798 -0.39140993
gamma2 1.3867000 0.04520519 30.675682 0.0000000 1.3123164 1.46108352
To leave a comment for the author, please follow the link and comment on his blog: Econometrics by Simulation. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...
Categories: Methodology Blogs
Reminder: Abstract submission for the 2014 ‘R in Insurance’ conference will close this Friday
Mon, 2014-03-24 02:49
(This article was first published on mages' blog, and kindly contributed to R-bloggers)
Don't forget, this is the final week you can submit an abstract for the second R in Insurance conference.
For more details see http://www.rininsurance.com and perhaps for inspiration review last year's programme.
Categories: Methodology Blogs
MCMC on zero measure sets
Sun, 2014-03-23 19:14
(This article was first published on Xi'an's Og » R, and kindly contributed to R-bloggers)
Simulating a bivariate normal under the constraint (or conditional to the fact) that x²-y²=1 (a non-linear zero measure curve in the 2-dimensional Euclidean space) is not that easy: if running a random walk along that curve (by running a random walk on y and deducing x as x²=y²+1 and accepting with a Metropolis-Hastings ratio based on the bivariate normal density), the outcome differs from the target predicted by a change of variable and the proper derivation of the conditional. The above graph resulting from the R code below illustrates the discrepancy!
targ=function(y){ exp(-y^2)/(1.52*sqrt(1+y^2))} T=10^5 Eps=3 ys=xs=rep(runif(1),T) xs[1]=sqrt(1+ys[1]^2) for (t in 2:T){ propy=runif(1,-Eps,Eps)+ys[t-1] propx=sqrt(1+propy^2) ace=(runif(1)<(dnorm(propy)*dnorm(propx))/ (dnorm(ys[t-1])*dnorm(xs[t-1]))) if (ace){ ys[t]=propy;xs[t]=propx }else{ ys[t]=ys[t-1];xs[t]=xs[t-1]}}
ace=(runif(1)<(dnorm(propy)*dnorm(propx)/propx)/ (dnorm(ys[t-1])*dnorm(xs[t-1])/xs[t-1]))
the fit is there. My open question is how to make this derivation generic, i.e. without requiring the (dreaded) computation of the (dreadful) Jacobian.
Filed under: R, Statistics Tagged: conditional density, Hastings-Metropolis sampler, Jacobian, MCMC, measure theory, measure zero set, projected measure, random walk
To leave a comment for the author, please follow the link and comment on his blog: Xi'an's Og » R. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...
Categories: Methodology Blogs
Warning: Clusters May Appear More Separated in Textbooks than in Practice
Sun, 2014-03-23 18:07
(This article was first published on Engaging Market Research, and kindly contributed to R-bloggers)
Clustering is the search for discontinuity achieved by sorting all the similar entities into the same piles and thus maximizing the separation between different piles. The latent class assumption makes the process explicit. What is the source of variation among the objects? An unseen categorical variable is responsible. Heterogeneity arises because entities come in different types. We seem to prefer mutually exclusive types (either A or B), but will settle for probabilities of cluster membership when forced by the data (a little bit A but more B-like). Actually, we are more likely to acknowledge that our clusters overlap early on and then forget because it is so easy to see type as the root cause of all variation.
I am asking the reader to recognize that statistical analysis and its interpretation extend over time. If there is variability in our data, a cluster analysis will yield partitions. Given a partitioning, a data analyst will magnify those differences by focusing on contrastive comparisons and assigning evocative names. Once we have names, especially if those names have high imagery, can we be blamed for the reification of minor distinctions? How can one resist segments from Nielsen PRIZM with names like "Shotguns and Pickups" and "Upper Crust"? Yet, are "Big City Blues" and "Low-Rise Living" really separate clusters or simply variations on a common set of dwelling constraints?
Taking our lessons seriously, we expect to see the well-separated clusters displayed in textbooks and papers. However, our expectations may be better formed than our clusters. We find heterogeneity, but those differences are not clumping or distinct concentrations. Our data clouds can be parceled into regions, although those parcels run into one another and are not separated by gaps. So we name the regions and pretend that we have assigned names to types or kinds of different entities with properties that control behavior over space and time. That is, we have constructed an ontology specifying categories to which we have given real explanatory powers.
Consider the following scatterplot from the introductory vignette in the R package mclust. You can find all the R code needed to produce these figures at the end of this post.
This is the Old Faithful geyser data from the "datasets" R package showing the waiting time in minutes between successive eruptions on the y-axis and the duration of the eruptions along the x-axis. It is worth your time to get familiar with Old Faithful because it is one of those datasets that gets analyzed over and over again using many different programs. There seems to be two concentrations of points: shorter eruption that occurs more quickly and longer eruptions that have a longer waiting period. If we told the Mclust function from the mclust package that the scatterplot contains observations from G=2 groups, the function would produce a classification plot that looked something like this:
The red and the blue with their respective ellipses are the two normal densities that are getting mixed. It is such a straightforward example of finite mixture or latent class models (as these models are also called by analysts in other fields of research). If we discovered that there were two pools feeding the geyser, we could write a compelling narrative tying all the data together.
The mclust vignette or manual is comprehensive but not overly difficult. If you prefer a lecture, there is no better introduction to finite mixture than the MathematicalMonk YouTube video. The key to understanding finite mixture models is recognizing that the underlying latent variable responsible for the observed data is categorical, a latent class which we do not observe, but which explains the location and shape of the data points. Do you have a cold or the flu? Without medical tests, all we can observe are your symptoms. If we filled a room with coughing, sneezing, achy and feverish people, we would find a mixture of cold and flu with differing numbers of each type.
This appears straightforward, but for the general case, how does decide how many categories, in what proportions, and with what means and covariance matrices? That is, those two ellipses in the above figure are drawn using a vector with means for the x- and y-axes plus a 2x2 covariance matrix. The means move the ellipse over the space, and the covariance matrix changes the shape and orientation of the ellipse. A good summary of the possible forms is given in Table 1 of the mlcust vignette.
Unfortunately, the mathematics of the EM algorithm used to solve this problem gets complicated quickly. Fortunately, Chris Bishop provides an intuitive introduction in a 2004 video lecture. Starting at 44:14 of Part 4, you will find a step-by-step description of how the EM algorithm works with the Old Faithful data. Moreover, in Chapter 9 of his book, Bishop cleverly compares the workings of the EM and k-means algorithms, leaving us with a better understanding of both techniques.
If only my data showed such clear discontinuity and could be tied to such a convincing narrative.
Product Categories Are Structured around the Good, the Better, and the Best
Almost every product category offers a range of alternatives that can be described as good, better, and best. Such offerings reflect the trade-offs that customers are willing to make between the quality of the products they want and the amount that they are ready to spend. High-end customers demand the best and will pay for it. On the other end, one finds customers with fewer needs and smaller budgets accepting less and paying less. Clearly, we have heterogeneity, but are those differences continuous or discrete? Can we tell by looking at the data?
Unlike the Old Faithful data with well-separated grouping of data points, product quality-price trade-offs look more like the following plot of 300 consumers indicating how much they are willing to spend and what they expect to get for their money (i.e., product quality is a composite index combining desired features and services).
There is a strong positive relationship between demand for quality and willingness to pay, so a product manager might well decide that there was opportunity for at least a high-end and a low-end option. However, there is no natural breaks in the scatterplot. Thus, if this data cloud is a mixture of distinct distributions, then these distributions must be overlapping.
Another example might help. As shown by John Cook, the distribution of heights among adults is a mixture two overlapping normal distribution, one for men and another for women. Yet, as you can observe from Cook's plots, the mixture of men's and women's height does not appear bimodal because the separation between the two distributions is not large enough. If you follow the links in Cook's post, eventually you will find the paper "Is Human Height Bimodal?", which clearly demonstrates that many mixtures of distributions appear to be homogeneous. We simply cannot tell that they are mixture by looking just at the shape of the distribution for the combined data. The Old Faithful data with its well-separated bimodal curve provides a nice contrast, especially when we focus only on waiting time as a single dimension (Fitting Mixture Models with the R Package mixtools).
Perhaps then, segmentation does not require gaps in the data cloud. As Wedel and Kamakura note, "Segments are not homogeneous groupings of customers naturally occurring in the marketplace, but are determined by the marketing manager's strategic view of the market." That is, one could look at the above scatterplot, see the presence of a strong first principal component from the closest of the data points to the principal axis of the ellipse and argue that customer heterogeneity is a single continuous dimension running from the low- to the high-end of the product spectrum. Or, one could look at the same scatterplot and see three overlapping segments seeking basic, value and premium products (good, better, best). Let's run mclust and learn if we can find our three segments.
When instructed to look for three clusters, the Mclust function returned the above result. The 300 observed points are represented as a mixture of three distributions falling along the principal axis of the larger ellipse formed by all the observations. However, if I had not specified three clusters and asked Mclust to use its default BIC criterion to select the number of segments, I would have been told that there was no compelling evidence for more than one homogeneous group. Without any prior specification Mclust would have returned a single homogeneous distribution, although as you can see from the R code below, my 300 observations were a mixture of three equal size distributions falling along the principal axis and separated by one standard deviation.
Number of Segments = Number Yielding Value to Product Management
Market segmentation lies somewhere between mass marketing and individual customization. When mass marketing fails because customers have different preferences or needs and customization is too costly or difficult, the compromise is segmentation. We do not need "natural" grouping, but just enough coherence for customers to be satisfied by the same offering. Feet come in many shapes and sizes. The shoe manufacturer can get along with three sizes of sandals but not three sizes of dress shoes. It is not the foot that is changing, but the demands of the customer. Thus, even if segments are no more than convenient fictions, they can be useful from the manager's perspective.
My warning still holds. Reification can be dangerous. These segments are meaningful only within the context of the marketing problem created by trying to satisfy everyone with products and services that yield maximum profit. Some segmentations may return clusters that are well-separated and represent groups with qualitatively different needs and purchase processes. Many of these are obvious and define different markets. If you don't have a dog, you don't buy dog food. However, when segmentation seeks to identify those who feel that their dog is a member of the family, we will find overlapping clusters that we treat differently not because we have revealed the true underlying typology, but because it is in our interest. Don't be fooled into believing that our creative segment names reveal the true workings of the consumer mind.
Finally, what is true for marketing segmentation is true for all of cluster analysis. "Clustering: Science or Art?" (a 2009 NIPS workshop) raises many of these same issues for cluster analysis in general. Videos of this workshop are available at Videolectures. Unlike supervised learning with its clear criterion for success and failure, clustering depends on users of the findings to tell us if the solution is good or bad, helpful or not. On the one hand, this seems to make everything more difficult. On the other hand, it frees us to be more open to alternative methods for describing heterogeneity as it is now and how it evolves over time.
We seek to understand the dynamic structure of diversity, which only sometimes takes the form of cohesive clusters separated by gaps. Other times, a model with only continuous latent variables seems to be the best choice (e.g., brand perceptions). And, not unexpectedly, there are situations where heterogeneity cannot be explained without both categorical and continuous latent variables (e.g., two or more segments seeking alternative benefit profiles with varying intensities).
Yet, even these three combinations cannot adequately account for all the forms of diversity we find in consumer data. Innovation might generate a structure appearing more like long arrays or streams of points seemingly pulled toward the periphery by an archetypal ideal or aspirational goal. And if the coordinate space of k-means and mixture models becomes too limiting, we can replace it with pairwise dissimilarity and graphical clustering techniques, such as affinity propagation or spectral clustering. Nor should we be wedded to the stability of our segment solution when those segments were created by dynamic forces that continue to act and alter its structure. Our models ought to be as diverse as the objects we are studying.
R code for all figures and analysis
#attach faithful data set
data(faithful)
plot(faithful, pch="+")
#run mclust on faithful data
require(mclust)
faithfulMclust<-Mclust(faithful, G=2)
summary(faithfulMclust, parameters=TRUE)
plot(faithfulMclust)
#create 3 segment data set
require(MASS)
sigma <- matrix(c(1.0,.6,.6,1.0),2,2)
mean1<-c(-1,-1)
mean2<-c(0,0)
mean3<-c(1,1)
set.seed(3202014)
mydata1<-mvrnorm(n=100, mean1, sigma)
mydata2<-mvrnorm(n=100, mean2, sigma)
mydata3<-mvrnorm(n=100, mean3, sigma)
mydata<-rbind(mydata1,mydata2,mydata3)
colnames(mydata)<-c("Desired Level of Quality",
"Willingness to Pay")
plot(mydata, pch="+")
#run Mclust with 3 segments
mydataClust<-Mclust(mydata, G=3)
summary(mydataClust, parameters=TRUE)
plot(mydataClust)
#let Mclust decide on number of segments
mydataClust<-Mclust(mydata)
summary(mydataClust, parameters=TRUE)
Created by Pretty R at inside-R.org
To leave a comment for the author, please follow the link and comment on his blog: Engaging Market Research. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...
Categories: Methodology Blogs
Random Love
Sun, 2014-03-23 17:53
(This article was first published on Ripples, and kindly contributed to R-bloggers)
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin (John von Newman)
Ms. Positive and Mr. Negative live in a one-dimensional world and are falling in love. But beginnings are not always easy. They have a big problem: none of them like the other’s neighborhood. Ms. Positive only wants to walk around Positive Integer Numbers Neighborhood and Mr. Negative around Negative Integers Numbers one. This is a prickly problem they need to deal with as soon as possible. But they have a good idea. They will start their walks from Zero, an impartial place between both neighborhoods and will let fate to guide their feet. They will toss a coin to decide every step: if result is head, they will advance 1 step toward positive numbers neighborhood; if tail, they will advance 1 step toward negative numbers one. For example, if the first 5 tosses are face, face, tail, tail and tail, the their first 5 steps will be +1, +2, +1, 0 and -1. It seems to be a fair agreement for both. Maybe is not the most pleasant way to take a walk but It is well known that lovers use to do silly things constantly, especially at the beginnings. They always walk for two hours, so they toss the coin 7.200 times every walk (these lovers are absolutely crazy as you can see). This was their first walk:
After this first walk, Mr Negative was really upset. Ms. Positive, watching his face fell, ask him: What’s the matter, honey? and Mr. Negative replied: What’s the matter? What’s the matter? The matter is that we spent almost all the time walking around your horrible neighborhood! What comes next is too hard to be reproduced here. Anyway, they agreed to give a chance to the method they designed. How can one imagine that a coin can produce such a strange walk! There must be an error! After 90 walks, the situation of our lovers was extremely delicate. A 57% of the walks were absolutely awful for one of them since more than 80% of the steps were around the same neighborhood. Another 32% were a bit uncomfortable for one of them since between 60% and 80% of the steps were around the same neighborhood. Only 11% of the walks were gratifying. How is it possible?, said Mr. Negative. How is it possible?, said Ms. Positive.
But here comes Ms. Positive, who always looks on the brigth side of life: Don’t worry, darling. In fact, we don’t have to be sad. We get angry the same amount of times! For me is enough. What about you?, said her. For me is perfect as well!, said Mr. Negative. In that moment, they realise they were made for each other and started another random walk with a big smile on their faces.
This is the code:
library(ggplot2) steps <- 2*60*60 #Number of steps results <- data.frame() walks<-90 #Number of walks for (i in 1:walks) { state <- cumsum(sample(c(-1,1), steps, replace = TRUE)) results <- rbind(results, c(sum(state<0), sum(state>0), sum(state==0), if (sum(state<0) >= sum(state>0)) 1 else 0)) } colnames(results) <- c("neg.steps", "pos.steps", "zero.steps", "ind.neg") results$max.steps <- apply(results, 1, max)/apply(results, 1, sum) #Plot of one of these walks mfar=max(abs(max(state)),abs(min(state))) plot1 <- qplot(seq_along(state), state, geom="path")+ xlab("Step") + ylab("Location") + labs(title = "The First Walk Of Ms. Positive And Mr. Negative")+ theme(plot.title = element_text(size = 35))+ theme(axis.title.y = element_text(size = 20))+ theme(axis.title.x = element_text(size = 20))+ scale_x_continuous(limits=c(0, length(state)),breaks=c(1,steps/4,steps/2,3*steps/4,steps))+ scale_y_continuous(limits=c(-mfar, mfar), breaks=c(-mfar,-mfar/2, 0, mfar/2,mfar))+ geom_hline(yintercept=0) ggsave(plot1, file="plot1.png", width = 12, height = 10) #Summary of all walks hist1 <- ggplot(results, aes(x = max.steps))+ geom_histogram(colour = "white",breaks=seq(.4,1,by=.2),fill=c("blue", "orange", "red"))+ theme_bw()+ labs(title = paste("What Happened After ", toString(walks), " Walks?",sep = ""))+ scale_y_continuous(breaks=seq(0,(nrow(results[results$max.steps>.8,])+10),by=10))+ theme(plot.title = element_text(size = 40))+ xlab("Maximum Steps In The Same Location (%)") + ylab("Number of Walks") ggsave(hist1, file="hist1.png", width = 10, height = 8) #Data for waterfall chart waterfall <- as.data.frame(cbind( c("Total Walks", "Satisfactory Walks", "Uncomfortable Walks", "Awful Walks for Mr. +", "Awful Walks for Ms. -"), c("a", "b", "c", "d", "d"), c(0, nrow(results), nrow(results)-nrow(results[results$max.steps<.6,]), nrow(results)-nrow(results[results$max.steps<.6,])-nrow(results[results$max.steps>=.6 & results$max.steps<.8,]), nrow(results)-nrow(results[results$max.steps<.6,])-nrow(results[results$max.steps>=.6 & results$max.steps<.8,])-nrow(results[results$max.steps>=.8 & results$ind.neg==1,]) ), c(nrow(results), nrow(results)-nrow(results[results$max.steps<.6,]), nrow(results)-nrow(results[results$max.steps<.6,])-nrow(results[results$max.steps>=.6 & results$max.steps<.8,]), nrow(results)-nrow(results[results$max.steps<.6,])-nrow(results[results$max.steps>=.6 & results$max.steps<.8,])-nrow(results[results$max.steps>=.8 & results$ind.neg==1,]), 0 ), c(nrow(results), nrow(results[results$max.steps<.6,]), nrow(results[results$max.steps>=.6 & results$max.steps<.8,]), nrow(results[results$max.steps>=.8 & results$ind.neg==1,]), nrow(results[results$max.steps>=.8 & results$ind.neg==0,])) )) colnames(waterfall) <-c("desc", "type", "start", "end", "amount") waterfall$id <- seq_along(waterfall$amount) waterfall$desc <- factor(waterfall$desc, levels = waterfall$desc) #Waterfall chart water1 <- ggplot(waterfall, aes(desc, fill = type)) + geom_rect(aes(x = desc, xmin = id-0.45, xmax = id+0.45, ymin = end, ymax = start))+ xlab("Kind of Walk") + ylab("Number of Walks") + labs(title = "The Ultimate Proof (After 90 Walks)")+ theme(plot.title = element_text(size = 35))+ theme(axis.title.y = element_text(size = 20))+ theme(axis.title.x = element_text(size = 20))+ theme(legend.position = "none")
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2014-04-16 19:45:04
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https://engineering.wustl.edu/Events/Pages/CSE-Doctoral-Student-Seminar-Zhiyang-Huang-and-Liang-Zhou.aspx
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# CSE Doctoral Student Seminar: Zhiyang Huang and Liang Zhou
Feb 24, 2017
12:30 p.m.
2 p.m.
Lopata Hall, Room 101
"Topology-controlled Reconstruction of Multi-labelled Domains from Cross-sections"
Zhiyang Huang
The timers are shown to achieve robust temporal synchronization due to the self-powering and self-compensating physics of Fowler-Nordheim (FN) quantum transport of electrons tunneling onto a floating-gate. The output of the timers can then be used to seed a pseudo-random number generator which produce random and synchronized authentication tokens. We validate the proposed approach using prototypes fabricated in a standard 0.5$\mu$m CMOS process where we demonstrate synchronization accuracy greater than 40dB.
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2020-05-30 21:38:59
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http://physics.stackexchange.com/questions/103987/light-formed-by-the-sun
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# Light formed by the sun?
This is an extract from the astrophysics chapter in my book:
Hydrogen atoms fuse to form helium. At the same time, lots of of gamma photons and neutrinos are produced. The photons take thousands of years to "fight" their way to the surface of the Sun, but then escape into space as visible or near visible photons at the speed of light.
I am really confused about how the sun produces light. I understand that through nuclear fusion, energy is formed, but isn't this energy in the form of thermal and gamma photons? I do not understand how visible light is emitted which is the reason to why we see the sun. Could someone please elaborate the paragraph from my book.
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Blackbody radiation. The sun is hot and so radiates with the spectrum that it does. en.wikipedia.org/wiki/Black-body_radiation – Brandon Enright Mar 18 at 4:33
Be aware that the language used in that passage is evocative, but technically sloppy. The energy of the photons will eventually emerge from the sun as light (i.e. photons) but they won't be "the" photons in any useful sense. – dmckee Mar 18 at 13:15
Hydrogen atoms fuse to form helium through the proton-proton chain which fuses four protons into one alpha particle (nucleus of ${}^{4}He$) and releases two neutrinos, two positrons and energy in the form of gamma photons. Although photons travel at the speed of light, the random motions they experienced inside the sun takes them thousand of years to leave the Sun' center. This random motion is due to the dense plasma in the Sun's interior since each photon permanently collides with an electron and gets deviated from its original path. The Energy released by fusion moves outward up to the top of the radiation zone, where the temperature drops to about 2 million K, then the photons get absorbed by the plasma more easily and this creates the necessary conditions for convection. This creates the convection zone of the zone. Then the plasma rises and the photons are carried to the photosphere where the density of the gas is low enough that they can escape. They mostly escape as visible photons, as their initial energy is lost through the random motion in the radiactive zone, and the absortion in the convective zone.
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so, gamma photons due to the loss of energy are emitted as visible photons... Just one more thing, are these the photons that are absorbed by the surface elements of the sun and then re-emitted... i.e. the black body radiation. I am having difficulties linking the concept of the source of the light of the sun and the black body radiation – Eliza Mar 18 at 5:36
The photons we see are the result of black body radiation. The light from the Sun is emitted by basically the same process that emits light from an incandescent light bulb.
The energy released by fusion at the core is rapidly randomised as photons interact with the charged particles in the plasma, and you end up with just a hot plasma. The heat is gradually transferred outwards and ends up as a surface temperature of about 5800K. I won't go into the mechanism of black body radiation because this is addressed in the answers to the question What are the various physical mechanisms for energy transfer to the photon during blackbody emission?. Suffice to say that the thermal motion of charged particles in the plasma cause random oscillating electric dipoles, and these then emit electromagnetic radiation corresponding to the energy of these oscillations. Because the oscillations are random the result is emission of a broad spread of wavelengths with a peak at about 500nm.
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2014-12-22 03:49:06
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https://www.zbmath.org/authors/?q=ai%3Achen.xin.1
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# zbMATH — the first resource for mathematics
## Chen, Xin
Compute Distance To:
Author ID: chen.xin.1 Published as: Chen, Xin; Chen, X.
Documents Indexed: 265 Publications since 1982, including 1 Book
all top 5
#### Co-Authors
9 single-authored 13 Wang, Jian 9 Han, Xin 7 Kuang, Leman 7 Wu, Min 6 Dósa, György 6 Fang, Qizhi 6 Song, Yongzhong 5 Guo, He 5 Lan, Yan 5 Nong, Qingqin 5 Wu, Bo 4 Cao, Weihua 4 Chen, Yonglin 4 Jiang, Tao 4 Kumagai, Takashi 4 Li, Xue-Mei 4 Liu, Fei 4 Wang, Feng-Yu 4 Xi, Heng-Dong 4 Zhao, Shunyi 4 Zhou, Xiaojian 4 Zhu, Yuanguo 4 Zou, Changliang 3 Błażewicz, Jacek 3 Chen, C. L. Philip 3 Cook, Ralph Dennis 3 Ding, Ning 3 Li, Ming 3 Liu, Zhi 3 Liu, Zhiming 3 Lu, Chuanjing 3 Ma, Xuejun 3 Meguid, Shaker A. 3 Saldin, D. K. 3 Sankaranarayanan, Sriram 3 Sterna, Małgorzata 3 Wang, Junmin 3 Yang, Hongwei 3 Zhang, Yun 2 Ábrahám, Erika 2 Batra, Romesh C. 2 Benko, Attila 2 Cao, Yongchang 2 Chen, Zhen-Qing 2 Chentouf, Boumediène 2 Cruzeiro, Ana-Bela 2 Dutta, Souradeep 2 Feng, Yan 2 Ge, Molin 2 Gong, Suning 2 Grassmann, Winfried K. 2 Guo, Min 2 Harp, G. R. 2 Jiang, He 2 Kirubarajan, Thiagalingam 2 Li, Chuntao 2 Li, Jiguang 2 Li, Xuandong 2 Liao, Xiaofeng 2 Lin, Wang 2 Liu, Lan 2 Ma, Bin 2 Phoon, Kok-Kwang 2 Schmitt, Francis J. M. 2 Sun, Liuquan 2 Tharmarasa, Ratnasingham 2 Vitányi, Paul M. B. 2 Wang, Fang 2 Wang, Wei 2 Wang, Xueqin 2 Wang, Yuxin 2 Wen, John Ting-Yung 2 Xing, Huaming 2 Xu, Yingxiang 2 Yang, Qiang 2 Yang, Zhengfeng 2 Yang, Zhijun 2 Ye, Wenjie 2 Zha, Qilao 2 Zhang, Jia 2 Zhang, Jingxiao 2 Zhang, Rong 2 Zhou, Caili 1 Aden, N. M. 1 Akiyama, Jin 1 Alian, A. R. 1 Allan, Vicki H. 1 Arnaudon, Marc 1 Arupathi, R. 1 Balaji, Bhashyam 1 Ben Sassi, Mohamed Amin 1 Bławzdziewicz, Jerzy 1 Borneman, James 1 Breda, Marco 1 Bu, Lei 1 Buxton, Oliver R. H. 1 Cai, Mingzhong 1 Cao, Jiayi 1 Cao, Yunfeng 1 Chalamon, Isabelle ...and 291 more Co-Authors
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#### Serials
8 Journal of Fluid Mechanics 5 Theoretical Computer Science 5 Applied Mathematical Modelling 5 Mathematical Problems in Engineering 4 Acta Mechanica 4 Journal of the Franklin Institute 4 Applied Mathematics and Computation 4 Journal of Functional Analysis 4 Mechanics Research Communications 4 Asian Journal of Control 3 Computer Physics Communications 3 Information Processing Letters 3 Physics Letters. A 3 Biometrika 3 Statistics & Probability Letters 3 IEEE Transactions on Signal Processing 3 Journal of Physics A: Mathematical and General 3 Stochastic Processes and their Applications 3 Engineering Analysis with Boundary Elements 3 Journal of Nanjing Normal University. Natural Science Edition 3 Journal of Combinatorial Optimization 3 Journal of Shenyang Normal University. Natural Science Edition 2 Computer Methods in Applied Mechanics and Engineering 2 IEEE Transactions on Information Theory 2 International Journal for Numerical and Analytical Methods in Geomechanics 2 International Journal of Solids and Structures 2 Journal of Mathematical Physics 2 Information Sciences 2 International Journal for Numerical Methods in Engineering 2 Journal of Statistical Planning and Inference 2 International Journal of Production Research 2 Probability Theory and Related Fields 2 Journal of Scientific Computing 2 International Journal of Adaptive Control and Signal Processing 2 Journal of Hydrodynamics. Ser. B 2 Computational Statistics and Data Analysis 2 Mathematical Programming. Series A. Series B 2 Transactions of Nanjing University of Aeronautics & Astronautics 2 Statistica Sinica 2 Electronic Journal of Probability 2 Nonlinear Dynamics 2 Journal of Systems Science and Complexity 2 Journal of Harbin Institute of Technology 2 Journal of Software 2 Statistics and Its Interface 2 Advances in Mathematical Physics 1 International Journal of Modern Physics B 1 Analysis Mathematica 1 Applicable Analysis 1 Computers and Electrical Engineering 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 Computers and Structures 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 European Journal of Physics 1 International Journal of Mechanical Sciences 1 International Journal of Plasticity 1 Journal of Applied Mechanics 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Ukrainian Mathematical Journal 1 Wave Motion 1 Algebra Universalis 1 The Annals of Statistics 1 Biometrics 1 Bulletin of the London Mathematical Society 1 IEEE Transactions on Computers 1 Illinois Journal of Mathematics 1 Journal of Computational and Applied Mathematics 1 Journal of Multivariate Analysis 1 Journal of the Operational Research Society 1 Meccanica 1 Naval Research Logistics 1 Operations Research 1 SIAM Journal on Control and Optimization 1 Transactions of the American Mathematical Society 1 Utilitas Mathematica 1 Topology and its Applications 1 Journal of Mathematics. Wuhan University 1 Operations Research Letters 1 Mathematics in Practice and Theory 1 Acta Automatica Sinica 1 Journal of Engineering Mathematics (Xi’an) 1 Acta Mathematicae Applicatae Sinica. English Series 1 Journal of Fudan University. Natural Science 1 Journal of Symbolic Computation 1 Computers & Operations Research 1 IMA Journal of Mathematical Control and Information 1 Asia-Pacific Journal of Operational Research 1 Journal of Southwest Jiaotong University 1 Journal of Theoretical Probability 1 Forum Mathematicum 1 CAD. Computer-Aided Design 1 Formal Aspects of Computing 1 Journal of Parallel and Distributed Computing 1 FGCS. Future Generation Computer Systems 1 The Annals of Applied Probability 1 International Journal of Foundations of Computer Science 1 Numerical Algorithms ...and 57 more Serials
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#### Fields
54 Computer science (68-XX) 42 Operations research, mathematical programming (90-XX) 40 Systems theory; control (93-XX) 31 Probability theory and stochastic processes (60-XX) 31 Mechanics of deformable solids (74-XX) 28 Numerical analysis (65-XX) 25 Statistics (62-XX) 21 Fluid mechanics (76-XX) 16 Biology and other natural sciences (92-XX) 14 Partial differential equations (35-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Quantum theory (81-XX) 10 Combinatorics (05-XX) 10 Ordinary differential equations (34-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Information and communication theory, circuits (94-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 8 Dynamical systems and ergodic theory (37-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 3 Operator theory (47-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Geophysics (86-XX) 2 Nonassociative rings and algebras (17-XX) 2 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 2 Special functions (33-XX) 2 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Approximations and expansions (41-XX) 1 Differential geometry (53-XX) 1 Manifolds and cell complexes (57-XX)
#### Citations contained in zbMATH Open
125 Publications have been cited 766 times in 454 Documents Cited by Year
Existence and uniqueness theorem for uncertain differential equations. Zbl 1196.34005
Chen, X.; Liu, B.
2010
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. Zbl 1219.65048
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2011
The similarity metric. Zbl 1316.68052
Li, Ming; Chen, Xin; Li, Xin; Ma, Bin; Vitányi, Paul M. B.
2004
Coordinate-independent sparse sufficient dimension reduction and variable selection. Zbl 1204.62107
Chen, Xin; Zou, Changliang; Cook, R. Dennis
2010
Representation and approximation of the outer inverse $$A_{T,S}^{(2)}$$ of a matrix $$A$$. Zbl 0957.15002
Chen, Yonglin; Chen, Xin
2000
Herringbone buckling patterns of compressed thin films on compliant substrates. Zbl 1111.74362
Chen, X.; Hutchinson, John W.
2004
A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Zbl 1390.76044
Yang, Hong Wei; Chen, Xin; Guo, Min; Chen, Yao Deng
2018
Families of third and fourth order methods for multiple roots of nonlinear equations. Zbl 1273.65064
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2013
Stochastic Euler-Poincaré reduction. Zbl 1307.37027
Arnaudon, Marc; Chen, Xin; Cruzeiro, Ana Bela
2014
A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations. Zbl 1114.74056
Chen, X.; Toh, K. C.; Phoon, K. K.
2006
Shared information and program plagiarism detection. Zbl 1294.94010
Chen, Xin; Francia, Brent; Li, Ming; McKinnon, Brian; Seker, Amit
2004
Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites. Zbl 1454.74008
Zhang, W. X.; Wang, T. J.; Chen, X.
2010
Positive realness preserving model reduction with $${\mathcal H}_ \infty$$ norm error bounds. Zbl 0839.93024
Chen, Xin; Wen, John T.
1995
A note on Roman domination in graphs. Zbl 1108.05072
Xing, Hua-Ming; Chen, Xin; Chen, Xue-Gang
2006
Small covers over prisms. Zbl 1125.52013
Cai, Mingzhong; Chen, Xin; Lü, Zhi
2007
Functional inequality on path space over a non-compact Riemannian manifold. Zbl 1307.58014
Chen, Xin; Wu, Bo
2014
Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection. Zbl 1430.76252
Chen, Xin; Huang, Shi-Di; Xia, Ke-Qing; Xi, Heng-Dong
2019
Adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone and dynamic uncertainties. Zbl 1331.93140
Wang, Fang; Liu, Zhi; Zhang, Yun; Chen, Xin; Chen, C. L. Philip
2015
Optimal algorithms for online scheduling with bounded rearrangement at the end. Zbl 1230.68051
Chen, Xin; Lan, Yan; Benko, Attila; Dósa, György; Han, Xin
2011
Wave propagation under curvature effects in a heterogeneous medium. Zbl 0878.35009
Chen, X.; Namah, G.
1997
Functional inequalities for nonlocal Dirichlet forms with finite range jumps or large jumps. Zbl 1352.60119
Chen, Xin; Wang, Jian
2014
Scheduling on parallel identical machines with late work criterion: offline and online cases. Zbl 1386.90050
Chen, Xin; Sterna, Malgorzata; Han, Xin; Blazewicz, Jacek
2016
On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition. Zbl 1330.65073
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2014
The similarity metric. Zbl 1092.68683
Li, Ming; Chen, Xin; Li, Xin; Ma, Bin; Vitányi, Paul
2003
Identification of partially linear structure in additive models with an application to gene expression prediction from sequences. Zbl 1251.62013
Lian, Heng; Chen, Xin; Yang, Jian-Yi
2012
Semi-online hierarchical scheduling problems with buffer or rearrangements. Zbl 1259.68255
Chen, Xin; Xu, Zhenzhen; Dósa, György; Han, Xin; Jiang, He
2013
Robustness analysis for linear time-invariant systems with structured incrementally sector bounded feedback nonlinearities. Zbl 0870.93011
Chen, Xin; Wen, John T.
1996
Determining plastic properties of a material with residual stress by using conical indentation. Zbl 1178.74072
Yan, Jin; Karlsson, A. M.; Chen, X.
2007
A model of component-based programming. Zbl 1141.68363
Chen, Xin; He, Jifeng; Liu, Zhiming; Zhan, Naijun
2007
Optimal integrability condition for the log-Sobolev inequality. Zbl 1149.58012
Chen, Xin; Wang, Feng-Yu
2007
Nondissipative torque and shear force controls of a rotating flexible structure. Zbl 1320.35063
Chen, Xin; Chentouf, Boumediène; Wang, Jun-Min
2014
Transient performance improvement in model reference adaptive control using $$H_\infty$$ optimal method. Zbl 1307.93212
Yang, Yi; Chen, Xin; Li, Chuntao
2015
A probabilistic method for gradient estimates of some geometric flows. Zbl 1315.53067
Chen, Xin; Cheng, Li-Juan; Mao, Jing
2015
Robust adaptive fuzzy control of nonlinear systems with unknown and time-varying saturation. Zbl 1332.93201
Lai, Guanyu; Liu, Zhi; Zhang, Yun; Chen, Xin; Chen, Chun Lung Philip
2015
Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression. Zbl 07072139
Su, Z.; Zhu, G.; Chen, X.; Yang, Y.
2016
Achieving control and synchronization merely through a stochastically adaptive feedback coupling. Zbl 1387.93018
Lin, Wei; Chen, Xin; Zhou, Shijie
2017
Exponential stability of a non-homogeneous rotating disk-beam-mass system. Zbl 1301.93133
Chen, Xin; Chentouf, Boumediene; Wang, Jun-Min
2015
Chen, X.; Kim, K. S.
2003
Splitting based on the outer inverse of matrices. Zbl 1034.65024
Chen, Xin; Wang, Wei; Song, Yongzhong
2002
Coherent state formalism for the Pegg-Barnett Hermitian phase theory. Zbl 0941.81555
Kuang, Le Man; Chen, Xin
1994
Surface modelling of range data by constrained triangulation. Zbl 0806.65008
Chen, Xin; Schmitt, Francis
1994
Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow. Zbl 1383.76179
Buxton, O. R. H.; Breda, M.; Chen, X.
2017
Centralized and decentralized rumor blocking problems. Zbl 1383.90006
Chen, Xin; Nong, Qingqin; Feng, Yan; Cao, Yongchang; Gong, Suning; Fang, Qizhi; Ko, Ker-I
2017
Intrinsic ultracontractivity of Feynman-Kac semigroups for symmetric jump processes. Zbl 1345.60095
Chen, Xin; Wang, Jian
2016
Linear relaxations of polynomial positivity for polynomial Lyapunov function synthesis. Zbl 1397.93189
Ben Sassi, Mohamed Amin; Sankaranarayanan, Sriram; Chen, Xin; Ábrahám, Erika
2016
Online minimum makespan scheduling with a buffer. Zbl 1304.90096
Lan, Yan; Chen, Xin; Ding, Ning; Dósa, György; Han, Xin
2012
Blank development and the prediction of earing in cup drawing. Zbl 0843.73035
Chen, X.; Sowerby, R.
1996
Coalescence of drops with mobile interfaces in a quiescent fluid. Zbl 1291.76048
Nemer, M. B.; Santoro, P.; Chen, X.; Bławzdziewicz, J.; Loewenberg, M.
2013
Perturbations of functional inequalities for Lévy type Dirichlet forms. Zbl 1347.60053
Chen, Xin; Wang, Feng-Yu; Wang, Jian
2015
Robust second-order least-squares estimator for regression models. Zbl 1440.62266
Chen, Xin; Tsao, Min; Zhou, Julie
2012
A fast algorithm for approximate string matching on gene sequences. Zbl 1131.68593
Liu, Zheng; Chen, Xin; Borneman, James; Jiang, Tao
2005
Some insights into continuum regression and its asymptotic properties. Zbl 1204.62129
Chen, Xin; Cook, R. Dennis
2010
Online scheduling with one rearrangement at the end: revisited. Zbl 1248.68125
Wang, Yuxin; Benko, Attila; Chen, Xin; Dósa, György; Guo, He; Han, Xin; Lanyi, Cecilia Sik
2012
Loop invariant synthesis in a combined abstract domain. Zbl 1256.68044
Qin, Shengchao; He, Guanhua; Luo, Chenguang; Chin, Wei-Ngan; Chen, Xin
2013
Exact solution of the Milburn equation for the Jaynes-Cummings model with an intensity-dependent interaction. Zbl 0960.81554
Chen, Xin; Kuang, Le Man
1994
Partitioned versus global Krylov subspace iterative methods for FE solution of 3-D Biot’s problem. Zbl 1173.74405
Chen, X.; Phoon, K. K.; Toh, K. C.
2007
Snap-through buckling of initially curved microbeam subject to an electrostatic force. Zbl 1371.74106
Chen, X.; Meguid, S. A.
2015
Diagnostic studies in sufficient dimension reduction. Zbl 1452.62567
Chen, Xin; Cook, R. Dennis; Zou, Changliang
2015
Sliding mode control to stabilization of a tip-force destabilized shear beam subject to boundary control matched disturbance. Zbl 1330.93058
Liu, Jun-Jun; Chen, Xin; Wang, Jun-Min
2016
A concrete estimate for the weak Poincaré inequality on loop space. Zbl 1245.58017
Chen, Xin; Li, Xue-Mei; Wu, Bo
2011
Online minimum makespan scheduling with a buffer. Zbl 1302.68040
Ding, Ning; Lan, Yan; Chen, Xin; Dósa, György; Guo, He; Han, Xin
2014
Intrinsic contractivity properties of Feynman-Kac semigroups for symmetric jump processes with infinite range jumps. Zbl 1319.60164
Chen, Xin; Wang, Jian
2015
The use of derivatives for optimizing steady state queues. Zbl 0819.60091
Grassmann, Winfried K.; Chen, Xin
1995
Exact solution of the Milburn equation for the two-photon Jaynes-Cummings model. Zbl 0850.81026
Kuang, Leman; Chen, Xin
1994
Intrinsic ultracontractivity for general Lévy processes on bounded open sets. Zbl 1333.60092
Chen, Xin; Wang, Jian
2014
Optimal service rates for the state-dependent $$M/G/1$$ queues in steady state. Zbl 0981.90008
Grassmann, Winfried K.; Chen, Xin; Kashyap, Brij R. K.
2001
Thermodynamic relationship between creep crack growth and creep deformation. Zbl 1141.74310
Yang, Qiang; Chen, Xin; Zhou, Weiyuan
2005
On the minimum common integer partition problem. Zbl 1183.90307
Chen, Xin; Liu, Lan; Liu, Zheng; Jiang, Tao
2006
A Poincaré inequality on loop spaces. Zbl 1228.58017
Chen, Xin; Li, Xue-Mei; Wu, Bo
2010
On sorting unsigned permutations by double-cut-and-joins. Zbl 1267.90067
Chen, Xin
2013
On the consistency of coordinate-independent sparse estimation with BIC. Zbl 1273.62135
Zou, Changliang; Chen, Xin
2012
An eigenvector variability plot. Zbl 1176.62062
Tu, I-Ping; Chen, Hung; Chen, Xin
2009
A novel DCT-based algorithm for computing the modulated complex lapped transform. Zbl 1374.94695
Chen, X.; Dai, Q.
2006
The effects of thin and ultrathin liquid films on dynamic wetting. Zbl 1186.76101
Chen, X.; Ramé, E.; Garoff, S.
2003
On multiscale significance of Rice’s normality structure. Zbl 1192.74009
Yang, Q.; Chen, X.; Zhou, W. Y.
2006
A filter-and-fan approach with adaptive neighborhood switching for resource-constrained project scheduling. Zbl 1349.90353
He, Jieguang; Chen, Xindu; Chen, Xin
2016
Heat kernel for non-local operators with variable order. Zbl 1462.60106
Chen, Xin; Chen, Zhen-Qing; Wang, Jian
2020
Positive asymptotically almost periodic solutions for hematopoiesis model. Zbl 1419.34190
Chen, Xin; Ding, Hui-Sheng
2016
Leader-following consensus of nonlinear discrete-time multi-agent systems with limited communication channel capacity. Zbl 1367.93038
Wu, Jia; Li, Huaqing; Chen, Xin
2017
Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date. Zbl 1441.90059
Chen, Xin; Liang, Yage; Sterna, Małgorzata; Wang, Wen; Błażewicz, Jacek
2020
Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities. Zbl 1459.60213
Chen, Xin; Kumagai, Takashi; Wang, Jian
2020
Multistage scenario-based interval-stochastic programming for planning water resources allocation. Zbl 1418.90183
Li, Y. P.; Huang, G. H.; Chen, X.
2009
An improved mechanism for selfish bin packing. Zbl 06852648
Chen, Xin; Nong, Qingqin; Fang, Qizhi
2017
Quenched invariance principle for a class of random conductance models with long-range jumps. Zbl 1472.60059
Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
2021
Effect of frictional force on the steady state axisymmetric deformations of a viscoplastic target. Zbl 0825.73636
Chen, X.; Batra, R. C.
1993
New coherent states of the Lie superalgebra $$osp(1/2,\mathbb{R})$$. Zbl 0843.17002
Kuang, Leman; Chen, Xin
1994
Effect of frictional force and nose shape on axisymmetric deformations of a thick thermoviscoplastic target. Zbl 0848.73017
Batra, R. C.; Chen, X.
1994
Complexity of problem $$TF2|v=1,c=2|C_{\max}$$. Zbl 1326.90027
Lan, Yan; Han, Xin; Wu, Zongtao; Guo, He; Chen, Xin
2016
Relationship of crack fabric tensors of different orders. Zbl 1098.74664
Yang, Q.; Chen, X.; Tham, L. G.
2004
A necessary and sufficient condition for semiconvergence and optimal parameter of the SSOR method for solving the rank deficient linear least squares problem. Zbl 1114.65037
Chen, Xin; Chen, Yong-Lin
2006
A spectral gap for the Brownian bridge measure on hyperbolic spaces. Zbl 1271.58018
Chen, X.; Li, X.-M.; Wu, B.
2010
Hopf bifurcation of a differential-algebraic bioeconomic model with time delay. Zbl 1264.91094
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2012
Quantum state transformation by optimal projective measurements. Zbl 1209.81024
Wang, Yaoxiong; Wu, Rebing; Chen, Xin; Ge, Yunjian; Shi, Junhui; Rabitz, Herschel; Shuang, Feng
2011
Numerical simulations of 2D periodic unsteady cavitating flows. Zbl 1203.76159
Wu, Lei; Lu, Chuan-Jing; Li, Jie; Chen, Xin
2006
Solutions for the deformations and stability of elastoplastic hollow cylinders subjected to boundary pressures. Zbl 0943.74016
Chen, X.; Tan, C. P.; Haberfield, C. M.
1999
Analysis of arbitrary Mindlin plates or bridge decks by spline finite strip method. Zbl 0877.73078
Ng, S. F.; Chen, X.
1995
A Taylor series approach for nonlinear $$\mathcal H_\infty$$ control applications. Zbl 0986.93025
Voulgaris, Petros G.; Chen, Xin
2001
A parsimony approach to genome-wide ortholog assignment. Zbl 1302.92067
Fu, Zheng; Chen, Xin; Vacic, Vladimir; Nan, Peng; Zhong, Yang; Jiang, Tao
2006
Separation of concerns and consistent integration in requirements modelling. Zbl 1131.68414
Chen, Xin; Liu, Zhiming; Mencl, Vladimir
2007
Construction of larger Riemannian metrics with bounded sectional curvatures and applications. Zbl 1151.58019
Chen, Xin; Wang, Feng-Yu
2008
Quenched invariance principle for a class of random conductance models with long-range jumps. Zbl 1472.60059
Biskup, Marek; Chen, Xin; Kumagai, Takashi; Wang, Jian
2021
Heat kernel for non-local operators with variable order. Zbl 1462.60106
Chen, Xin; Chen, Zhen-Qing; Wang, Jian
2020
Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date. Zbl 1441.90059
Chen, Xin; Liang, Yage; Sterna, Małgorzata; Wang, Wen; Błażewicz, Jacek
2020
Random conductance models with stable-like jumps: heat kernel estimates and Harnack inequalities. Zbl 1459.60213
Chen, Xin; Kumagai, Takashi; Wang, Jian
2020
Kernel density regression. Zbl 1437.62254
Chen, Xin; Ma, Xuejun; Zhou, Wang
2020
Flow shop for dual CPUs in dynamic voltage scaling. Zbl 1440.68029
Chau, Vincent; Chen, Xin; Fong, Ken C. K.; Li, Minming; Wang, Kai
2020
Structure evolution at early stage of boundary-layer transition: simulation and experiment. Zbl 1460.76386
Jiang, X. Y.; Lee, C. B.; Chen, X.; Smith, C. R.; Linden, P. F.
2020
Input-output dynamic model for optimal environmental pollution control. Zbl 07203951
Chen, Xin; Zhu, Yuanguo; Shen, Jiayu
2020
Emergence of substructures inside the large-scale circulation induces transition in flow reversals in turbulent thermal convection. Zbl 1430.76252
Chen, Xin; Huang, Shi-Di; Xia, Ke-Qing; Xi, Heng-Dong
2019
Reachability analysis for neural feedback systems using regressive polynomial rule inference. Zbl 07120151
Dutta, Souradeep; Chen, Xin; Sankaranarayanan, Sriram
2019
Robust sufficient dimension reduction via ball covariance. Zbl 07132596
Zhang, Jia; Chen, Xin
2019
A linear quadratic model based on multistage uncertain random systems. Zbl 1412.93049
Chen, Xin; Zhu, Yuanguo; Li, Bo; Yan, Hongyan
2019
Optimized Schwarz methods for the optimal control of systems governed by elliptic partial differential equations. Zbl 1419.65140
Xu, Yingxiang; Chen, Xin
2019
Entropy-based closure for probabilistic learning on manifolds. Zbl 1459.62239
Soize, C.; Ghanem, R.; Safta, C.; Huan, X.; Vane, Z. P.; Oefelein, J.; Lacaze, G.; Najm, H. N.; Tang, Q.; Chen, X.
2019
A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Zbl 1390.76044
Yang, Hong Wei; Chen, Xin; Guo, Min; Chen, Yao Deng
2018
Torsional vibration control of drill-string systems with time-varying measurement delays. Zbl 1448.93100
Lu, Chengda; Wu, Min; Chen, Xin; Cao, Weihua; Gan, Chao; She, Jinhua
2018
Analyzing Saaty’s consistency test in pairwise comparison method: a perspective based on linguistic and numerical scale. Zbl 1398.91212
Zhang, Hengjie; Chen, Xin; Dong, Yucheng; Xu, Weijun; Wang, Shihua
2018
Achieving control and synchronization merely through a stochastically adaptive feedback coupling. Zbl 1387.93018
Lin, Wei; Chen, Xin; Zhou, Shijie
2017
Invariants of the velocity-gradient tensor in a spatially developing inhomogeneous turbulent flow. Zbl 1383.76179
Buxton, O. R. H.; Breda, M.; Chen, X.
2017
Centralized and decentralized rumor blocking problems. Zbl 1383.90006
Chen, Xin; Nong, Qingqin; Feng, Yan; Cao, Yongchang; Gong, Suning; Fang, Qizhi; Ko, Ker-I
2017
Leader-following consensus of nonlinear discrete-time multi-agent systems with limited communication channel capacity. Zbl 1367.93038
Wu, Jia; Li, Huaqing; Chen, Xin
2017
An improved mechanism for selfish bin packing. Zbl 06852648
Chen, Xin; Nong, Qingqin; Fang, Qizhi
2017
Finite-time consensus problem for second-order multi-agent systems under switching topologies. Zbl 1386.93021
Wang, Fang; Chen, Xin; He, Yong; Wu, Min
2017
Privacy-aware image encryption based on logistic map and data hiding. Zbl 1367.94348
Sun, Jianglin; Liao, Xiaofeng; Chen, Xin; Guo, Shangwei
2017
Adaptive model-free sure independence screening. Zbl 1388.62172
Wen, Canhong; Zhu, Shan; Chen, Xin; Wang, Xueqin
2017
Scheduling on parallel identical machines with late work criterion: offline and online cases. Zbl 1386.90050
Chen, Xin; Sterna, Malgorzata; Han, Xin; Blazewicz, Jacek
2016
Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression. Zbl 07072139
Su, Z.; Zhu, G.; Chen, X.; Yang, Y.
2016
Intrinsic ultracontractivity of Feynman-Kac semigroups for symmetric jump processes. Zbl 1345.60095
Chen, Xin; Wang, Jian
2016
Linear relaxations of polynomial positivity for polynomial Lyapunov function synthesis. Zbl 1397.93189
Ben Sassi, Mohamed Amin; Sankaranarayanan, Sriram; Chen, Xin; Ábrahám, Erika
2016
Sliding mode control to stabilization of a tip-force destabilized shear beam subject to boundary control matched disturbance. Zbl 1330.93058
Liu, Jun-Jun; Chen, Xin; Wang, Jun-Min
2016
A filter-and-fan approach with adaptive neighborhood switching for resource-constrained project scheduling. Zbl 1349.90353
He, Jieguang; Chen, Xindu; Chen, Xin
2016
Positive asymptotically almost periodic solutions for hematopoiesis model. Zbl 1419.34190
Chen, Xin; Ding, Hui-Sheng
2016
Complexity of problem $$TF2|v=1,c=2|C_{\max}$$. Zbl 1326.90027
Lan, Yan; Han, Xin; Wu, Zongtao; Guo, He; Chen, Xin
2016
The rational solutions and quasi-periodic wave solutions as well as interactions of $$N$$-soliton solutions for $$3 + 1$$ dimensional Jimbo-Miwa equation. Zbl 1361.35042
Yang, Hongwei; Zhang, Yong; Zhang, Xiaoen; Chen, Xin; Xu, Zhenhua
2016
A linear programming relaxation based approach for generating barrier certificates of hybrid systems. Zbl 1427.68176
Yang, Zhengfeng; Huang, Chao; Chen, Xin; Lin, Wang; Liu, Zhiming
2016
Adaptive fuzzy dynamic surface control for a class of nonlinear systems with fuzzy dead zone and dynamic uncertainties. Zbl 1331.93140
Wang, Fang; Liu, Zhi; Zhang, Yun; Chen, Xin; Chen, C. L. Philip
2015
Transient performance improvement in model reference adaptive control using $$H_\infty$$ optimal method. Zbl 1307.93212
Yang, Yi; Chen, Xin; Li, Chuntao
2015
A probabilistic method for gradient estimates of some geometric flows. Zbl 1315.53067
Chen, Xin; Cheng, Li-Juan; Mao, Jing
2015
Robust adaptive fuzzy control of nonlinear systems with unknown and time-varying saturation. Zbl 1332.93201
Lai, Guanyu; Liu, Zhi; Zhang, Yun; Chen, Xin; Chen, Chun Lung Philip
2015
Exponential stability of a non-homogeneous rotating disk-beam-mass system. Zbl 1301.93133
Chen, Xin; Chentouf, Boumediene; Wang, Jun-Min
2015
Perturbations of functional inequalities for Lévy type Dirichlet forms. Zbl 1347.60053
Chen, Xin; Wang, Feng-Yu; Wang, Jian
2015
Snap-through buckling of initially curved microbeam subject to an electrostatic force. Zbl 1371.74106
Chen, X.; Meguid, S. A.
2015
Diagnostic studies in sufficient dimension reduction. Zbl 1452.62567
Chen, Xin; Cook, R. Dennis; Zou, Changliang
2015
Intrinsic contractivity properties of Feynman-Kac semigroups for symmetric jump processes with infinite range jumps. Zbl 1319.60164
Chen, Xin; Wang, Jian
2015
Connecting continuum regression with sufficient dimension reduction. Zbl 1321.62093
Chen, Xin; Zhu, Li-Ping
2015
Online hierarchical scheduling on two machines with known total size of low-hierarchy jobs. Zbl 1314.90035
Chen, Xin; Ding, Ning; Dósa, György; Han, Xin; Jiang, He
2015
Functional inequalities for pure-jump Dirichlet forms. Zbl 1336.31024
Chen, Xin; Wang, Feng-Yu; Wang, Jian
2015
Stochastic Euler-Poincaré reduction. Zbl 1307.37027
Arnaudon, Marc; Chen, Xin; Cruzeiro, Ana Bela
2014
Functional inequality on path space over a non-compact Riemannian manifold. Zbl 1307.58014
Chen, Xin; Wu, Bo
2014
Functional inequalities for nonlocal Dirichlet forms with finite range jumps or large jumps. Zbl 1352.60119
Chen, Xin; Wang, Jian
2014
On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition. Zbl 1330.65073
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2014
Nondissipative torque and shear force controls of a rotating flexible structure. Zbl 1320.35063
Chen, Xin; Chentouf, Boumediène; Wang, Jun-Min
2014
Online minimum makespan scheduling with a buffer. Zbl 1302.68040
Ding, Ning; Lan, Yan; Chen, Xin; Dósa, György; Guo, He; Han, Xin
2014
Intrinsic ultracontractivity for general Lévy processes on bounded open sets. Zbl 1333.60092
Chen, Xin; Wang, Jian
2014
Families of third and fourth order methods for multiple roots of nonlinear equations. Zbl 1273.65064
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2013
Semi-online hierarchical scheduling problems with buffer or rearrangements. Zbl 1259.68255
Chen, Xin; Xu, Zhenzhen; Dósa, György; Han, Xin; Jiang, He
2013
Coalescence of drops with mobile interfaces in a quiescent fluid. Zbl 1291.76048
Nemer, M. B.; Santoro, P.; Chen, X.; Bławzdziewicz, J.; Loewenberg, M.
2013
Loop invariant synthesis in a combined abstract domain. Zbl 1256.68044
Qin, Shengchao; He, Guanhua; Luo, Chenguang; Chin, Wei-Ngan; Chen, Xin
2013
On sorting unsigned permutations by double-cut-and-joins. Zbl 1267.90067
Chen, Xin
2013
A branch-and-bound algorithm for minimizing the energy consumption in the PFS problem. Zbl 1299.90235
Liu, Guo-Sheng; Zhang, Bi-Xi; Yang, Hai-Dong; Chen, Xin; Huang, George Q.
2013
Analysis of complex network performance and heuristic node removal strategies. Zbl 1344.90010
Jahanpour, Ehsan; Chen, Xin
2013
The spline probability hypothesis density filter. Zbl 1394.94543
Sithiravel, Rajiv; Chen, Xin; Tharmarasa, Ratnasingham; Balaji, Bhashyam; Kirubarajan, Thiagalingam
2013
Identification of partially linear structure in additive models with an application to gene expression prediction from sequences. Zbl 1251.62013
Lian, Heng; Chen, Xin; Yang, Jian-Yi
2012
Online minimum makespan scheduling with a buffer. Zbl 1304.90096
Lan, Yan; Chen, Xin; Ding, Ning; Dósa, György; Han, Xin
2012
Robust second-order least-squares estimator for regression models. Zbl 1440.62266
Chen, Xin; Tsao, Min; Zhou, Julie
2012
Online scheduling with one rearrangement at the end: revisited. Zbl 1248.68125
Wang, Yuxin; Benko, Attila; Chen, Xin; Dósa, György; Guo, He; Han, Xin; Lanyi, Cecilia Sik
2012
On the consistency of coordinate-independent sparse estimation with BIC. Zbl 1273.62135
Zou, Changliang; Chen, Xin
2012
Hopf bifurcation of a differential-algebraic bioeconomic model with time delay. Zbl 1264.91094
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2012
A topological optimization approach for structural design of a high-speed low-load mechanism using the equivalent static loads method. Zbl 1242.74082
Yang, Zhi-Jun; Chen, Xin; Kelly, Robert
2012
Constructing higher-order methods for obtaining the multiple roots of nonlinear equations. Zbl 1219.65048
Zhou, Xiaojian; Chen, Xin; Song, Yongzhong
2011
Optimal algorithms for online scheduling with bounded rearrangement at the end. Zbl 1230.68051
Chen, Xin; Lan, Yan; Benko, Attila; Dósa, György; Han, Xin
2011
A concrete estimate for the weak Poincaré inequality on loop space. Zbl 1245.58017
Chen, Xin; Li, Xue-Mei; Wu, Bo
2011
Quantum state transformation by optimal projective measurements. Zbl 1209.81024
Wang, Yaoxiong; Wu, Rebing; Chen, Xin; Ge, Yunjian; Shi, Junhui; Rabitz, Herschel; Shuang, Feng
2011
Existence and uniqueness theorem for uncertain differential equations. Zbl 1196.34005
Chen, X.; Liu, B.
2010
Coordinate-independent sparse sufficient dimension reduction and variable selection. Zbl 1204.62107
Chen, Xin; Zou, Changliang; Cook, R. Dennis
2010
Effect of surface/interface stress on the plastic deformation of nanoporous materials and nanocomposites. Zbl 1454.74008
Zhang, W. X.; Wang, T. J.; Chen, X.
2010
Some insights into continuum regression and its asymptotic properties. Zbl 1204.62129
Chen, Xin; Cook, R. Dennis
2010
A Poincaré inequality on loop spaces. Zbl 1228.58017
Chen, Xin; Li, Xue-Mei; Wu, Bo
2010
A spectral gap for the Brownian bridge measure on hyperbolic spaces. Zbl 1271.58018
Chen, X.; Li, X.-M.; Wu, B.
2010
On sorting permutations by double-cut-and-joins. Zbl 1286.92041
Chen, Xin
2010
An eigenvector variability plot. Zbl 1176.62062
Tu, I-Ping; Chen, Hung; Chen, Xin
2009
Multistage scenario-based interval-stochastic programming for planning water resources allocation. Zbl 1418.90183
Li, Y. P.; Huang, G. H.; Chen, X.
2009
Construction of larger Riemannian metrics with bounded sectional curvatures and applications. Zbl 1151.58019
Chen, Xin; Wang, Feng-Yu
2008
On the minimum common integer partition problem. Zbl 1445.90090
Chen, Xin; Liu, Lan; Liu, Zheng; Jiang, Tao
2008
Small covers over prisms. Zbl 1125.52013
Cai, Mingzhong; Chen, Xin; Lü, Zhi
2007
Determining plastic properties of a material with residual stress by using conical indentation. Zbl 1178.74072
Yan, Jin; Karlsson, A. M.; Chen, X.
2007
A model of component-based programming. Zbl 1141.68363
Chen, Xin; He, Jifeng; Liu, Zhiming; Zhan, Naijun
2007
Optimal integrability condition for the log-Sobolev inequality. Zbl 1149.58012
Chen, Xin; Wang, Feng-Yu
2007
Partitioned versus global Krylov subspace iterative methods for FE solution of 3-D Biot’s problem. Zbl 1173.74405
Chen, X.; Phoon, K. K.; Toh, K. C.
2007
Separation of concerns and consistent integration in requirements modelling. Zbl 1131.68414
Chen, Xin; Liu, Zhiming; Mencl, Vladimir
2007
A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations. Zbl 1114.74056
Chen, X.; Toh, K. C.; Phoon, K. K.
2006
A note on Roman domination in graphs. Zbl 1108.05072
Xing, Hua-Ming; Chen, Xin; Chen, Xue-Gang
2006
On the minimum common integer partition problem. Zbl 1183.90307
Chen, Xin; Liu, Lan; Liu, Zheng; Jiang, Tao
2006
A novel DCT-based algorithm for computing the modulated complex lapped transform. Zbl 1374.94695
Chen, X.; Dai, Q.
2006
On multiscale significance of Rice’s normality structure. Zbl 1192.74009
Yang, Q.; Chen, X.; Zhou, W. Y.
2006
A necessary and sufficient condition for semiconvergence and optimal parameter of the SSOR method for solving the rank deficient linear least squares problem. Zbl 1114.65037
Chen, Xin; Chen, Yong-Lin
2006
Numerical simulations of 2D periodic unsteady cavitating flows. Zbl 1203.76159
Wu, Lei; Lu, Chuan-Jing; Li, Jie; Chen, Xin
2006
A parsimony approach to genome-wide ortholog assignment. Zbl 1302.92067
Fu, Zheng; Chen, Xin; Vacic, Vladimir; Nan, Peng; Zhong, Yang; Jiang, Tao
2006
A fast algorithm for approximate string matching on gene sequences. Zbl 1131.68593
Liu, Zheng; Chen, Xin; Borneman, James; Jiang, Tao
2005
Thermodynamic relationship between creep crack growth and creep deformation. Zbl 1141.74310
Yang, Qiang; Chen, Xin; Zhou, Weiyuan
2005
...and 25 more Documents
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#### Cited by 850 Authors
20 Chen, Xin 13 Stanimirović, Predrag S. 12 Wang, Jian 10 Behl, Ramandeep 10 Kim, Young Ik 9 Cordero, Alicia 9 Torregrosa Sanchez, Juan Ramón 8 Geum, Young Hee 7 Gupta, Dharmendra Kumar 7 Liu, Xiaoji 7 Neta, Beny 7 Zhu, Lixing 6 Biswas, Anjan 6 Holm, Darryl D. 6 Katsikis, Vasilios N. 6 Liu, Wenjun J. 6 Song, Yongzhong 6 Yang, Hongwei 6 Yu, Zhou 6 Zafar, Fiza 6 Zhou, Qin 5 Chen, Guoliang 5 Cheng, Lijuan 5 Han, Xin 5 Liu, Quansheng 5 Sheng, Xingping 5 Srivastava, Shwetabh 5 Thalmaier, Anton 5 Wang, Feng-Yu 5 Wei, Yimin 5 Wu, Bo 5 Yang, Liangui 5 Zhou, Xiaojian 4 Błażewicz, Jacek 4 Carrasco, Joaquín 4 Ćirić, Miroslav D. 4 Cruzeiro, Ana-Bela 4 Dósa, György 4 Heath, William Paul 4 Lian, Heng 4 Liu, Zhiming 4 Sharma, Janak Raj 4 Sterna, Małgorzata 4 Vitányi, Paul M. B. 4 Yu, Yaoming 4 Zhang, Ruigang 3 Alshomrani, Ali Saleh 3 Arnaudon, Alexis 3 Dong, Yuexiao 3 Estevez-Rams, Ernesto 3 Fu, Chen 3 Grassmann, Winfried K. 3 Guo, Min 3 Junjua, Moin-ud-Din 3 Kanwar, Vinay 3 Mantaci, Sabrina 3 Martínez, Eulalia 3 Milman, Emanuel 3 Nee, A. Y. C. 3 Ong, S. K. 3 Restivo, Antonio 3 Ryabko, Boris Ya. 3 Sciortino, Marinella 3 Terwijn, Sebastiaan A. 3 Trentelman, Harry L. 3 Triki, Houria 3 Yang, Qiang 3 Yin, Xiaojun 3 Yuan, Jinjiang 2 Adragni, Kofi Placid 2 Amat, Sergio P. 2 Apostolico, Alberto 2 Aragón Fernández, B. 2 Argyros, Ioannis Konstantinos 2 Ćebić, Dejan 2 Cerra, Daniele 2 Cevallos, Fabricio 2 Chang, Gerard Jennhwa 2 Chen, Guangrong 2 Chen, Jianlong 2 Chen, Yonglin 2 Chentouf, Boumediène 2 Choi, Suyoung 2 Chun, Changbum 2 Cui, Yujun 2 Datcu, Mihai 2 Dias, Zanoni 2 Ding, Ning 2 Ding, Shanshan 2 Epstein, Leah 2 Estevez-Moya, D. 2 Feng, Weiguo 2 Forzani, Liliana 2 Gaeta, Giuseppe 2 Geng, Huan 2 Guiver, Chris 2 Guo, He 2 Guo, Yaping 2 Han, Zhongjie 2 Herceg, Đorđe D. ...and 750 more Authors
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#### Cited in 189 Serials
25 Applied Mathematics and Computation 14 Nonlinear Dynamics 13 Theoretical Computer Science 13 Computational Statistics and Data Analysis 11 Journal of the Franklin Institute 10 Journal of Computational and Applied Mathematics 8 Computers & Mathematics with Applications 8 Journal of Combinatorial Optimization 7 The Annals of Statistics 6 International Journal of Theoretical Physics 6 Journal of Mathematical Physics 6 Journal of Functional Analysis 6 European Journal of Operational Research 5 International Journal of Control 5 Information Processing Letters 5 Linear and Multilinear Algebra 5 Numerical Algorithms 5 Linear Algebra and its Applications 5 Journal of Nonlinear Science 5 Complexity 5 Journal of Applied Mathematics 4 Automatica 4 Systems & Control Letters 4 Science of Computer Programming 4 Journal of Statistical Computation and Simulation 4 Mathematical Problems in Engineering 4 Theory of Computing Systems 4 Journal of Applied Mathematics and Computing 4 Journal of Theoretical Biology 3 Communications in Mathematical Physics 3 Discrete Applied Mathematics 3 Calcolo 3 Journal of Computer and System Sciences 3 Journal of Multivariate Analysis 3 Journal of Statistical Planning and Inference 3 International Journal of Production Research 3 Journal of Theoretical Probability 3 Applied Mathematics Letters 3 Journal of Mathematical Chemistry 3 Abstract and Applied Analysis 3 Journal of Scheduling 3 Chaos 3 Communications in Nonlinear Science and Numerical Simulation 3 Journal of Systems Science and Complexity 3 Entropy 3 Frontiers of Mathematics in China 3 Electronic Journal of Statistics 3 Afrika Matematika 2 Discrete Mathematics 2 Problems of Information Transmission 2 Chaos, Solitons and Fractals 2 The Annals of Probability 2 Journal of the American Statistical Association 2 Journal of the Mathematical Society of Japan 2 SIAM Journal on Control and Optimization 2 Statistics & Probability Letters 2 Statistics 2 Probability Theory and Related Fields 2 Algorithmica 2 Computers & Operations Research 2 Forum Mathematicum 2 Formal Aspects of Computing 2 Machine Learning 2 International Journal of Foundations of Computer Science 2 The Journal of Geometric Analysis 2 Computational Statistics 2 International Journal of Computer Mathematics 2 Pattern Recognition 2 Stochastic Processes and their Applications 2 Potential Analysis 2 Formal Methods in System Design 2 Computational and Applied Mathematics 2 Turkish Journal of Mathematics 2 Journal of Nonparametric Statistics 2 European Journal of Control 2 Data Mining and Knowledge Discovery 2 Discrete Dynamics in Nature and Society 2 Nonlinear Analysis. Modelling and Control 2 Advances in Difference Equations 2 AStA. Advances in Statistical Analysis 2 Mathematical Modelling of Natural Phenomena 2 Discrete Mathematics, Algorithms and Applications 2 Journal of Geometric Mechanics 2 Science China. Mathematics 2 Symmetry 2 Statistics and Computing 2 Journal of Function Spaces 1 Acta Informatica 1 Journal of Mathematical Analysis and Applications 1 Mathematische Semesterberichte 1 Physics Letters. A 1 Physics Reports 1 Scandinavian Journal of Statistics 1 Wave Motion 1 Advances in Mathematics 1 Annals of the Institute of Statistical Mathematics 1 Applied Mathematics and Optimization 1 Biometrics 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics ...and 89 more Serials
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#### Cited in 49 Fields
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2021-12-03 23:18:26
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http://mathhelpforum.com/pre-calculus/204980-establish-identity.html
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# Math Help - establish this identity
1. ## establish this identity
(1+ cos^2 theta)(1- cot^2 theta)= 1
I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?
2. ## Re: establish this identity
Originally Posted by avatartiger2
(1+ cos^2 theta)(1- cot^2 theta)= 1
I have no idea how (1+ cos^2 theta)(1- cot^2 theta) could possibly equal to 1. Any ideas?
you sure it's not $(1 - \cos^2{\theta})(1 + \cot^2{\theta}) = 1$ ?
3. ## Re: establish this identity
Idea: First, unpack cotangent in terms of sine and cosine. Then simplify (multiply out - or something even better if you see it) the left hand side.
Also, I believe that skeeter's correct about the actual problem intended.
4. ## Re: establish this identity
yeah! i looked over the problem and I think the textbook might have switched the signs! (1-cos^2 theta)(1+ cot^2 theta) does simplify to 1. I kept doing the other problem over and over again. thanks for telling me! what a relief!
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2015-12-01 23:44:12
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http://mathhelpforum.com/discrete-math/280086-discrete-math-question.html
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1. ## Discrete Math question
Can someone confirm if im doing this right please?
2. ## Re: Discrete Math question
Originally Posted by inayat
Can someone confirm if im doing this right please?
We have one basic rule: Placing $\bf N$ identical objects into $\bf k$ different cells is done in $\bf{\dbinom{N+k-1}{N}}$ ways. So we know the answer for a).
b) If we place three balls into each cell then that means we have nine balls to place into seven cells.
c) place one ball into each box. Now we have twenty three balls left to place into the three even cells: $2,~4,~6$
d) the is done by the tapping method. Tape all balls together two at a time.
Now we have fifteen identical objects to put into seven different cells.
Because adding a series of even numbers is a even number, each of the cells contains an even numbers of balls.
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2018-12-16 03:32:52
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https://www.shaalaa.com/question-bank-solutions/heights-distances-horizontal-plane_5761
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# Solution - Heights and Distances
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#### Question
A vertical tower stands on a horizontal plane and is surmounted by a flagstaff of height 7m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30º and that of the top of the flagstaff is 45º. Find the height of the tower.
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#### Similar questions
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A statue, 1.6 m tall, stands on a top of pedestal, from a point on the ground, the angle of elevation of the top of statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45 °. Find the height of the pedestal.
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\frac{d}{\sqrt{\cot ^{2}\alpha +\cot^{2}\beta
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The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x, y.
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S
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2017-10-17 00:05:19
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http://quant.stackexchange.com/questions/9241/from-fourier-transforms-to-option-values/9339
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# From Fourier Transforms to Option Values
I am trying to understand how Fourier transforms & Characteristics functions can be used to calculate option values.
However, I am having difficulty following the process that is used in several introductory papers like: Carr & Madam, Liuren Wu, Schmelze or Chourdakis (chapter 4)
In order to obtain an intuitive understanding of this method, it will be very helpful if someone could provide me with an example on how to calculate option prices using this pricing technique.
Since this is not homework, any intuitive example will be greatly appreciated.
EDIT: as a potential example, consider that we want to estimate the fair value of an European call option struck at $K = 12$ and with time to maturity $T = 2$ years. The underlying asset $S$ has initial price $S_0 = 10$ and its returns volatility is $\sigma = 0.25$. The risk free rate is $r = 0.05$.
For the previous example, the Black-Scholes equation indicates that the option fair value should be $1.07$. How can I reproduce this result using Fourier transforms?
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Your question is tagged with heston - are you asking about how to value vanilla options with FFT under the heston model specifically? – experquisite Oct 23 '13 at 18:45
@experquisite, I have deleted the heston tag. For simplicity, the proposed example is restricted to the BSM world, but any other numerical example that illustrates the process will be much appreciated. – sets Oct 24 '13 at 7:09
I know that answering this question might be time consuming, but adding a bounty I hope to stimulate answers to include more content that just an external link (even if useful links are welcome and upvoted). – sets Oct 29 '13 at 12:26
Anyone can give us an example with Interest Rates Derivative? – user7802 Apr 15 '14 at 2:17
I give a very detailed exposition in "More Mathematical Finance" see also my paper on the use of controls: ssrn.com/abstract=1941464 – Mark Joshi Jun 11 at 1:40
I think this blog post is quite good at explaining option pricing via fourier transforms.
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(+1) @klon, thanks for the link. That blog post provides indeed a good explanation of Fourier transforms. However, if possible I will be still very interested in see how the FT method can be used in a numerical example. For instance, an example along the lines of the proposed option in the BSM world will be perfect, but any other numerical illustration will do. Thanks in advance! – sets Oct 25 '13 at 9:57
Careful. The blog post is largely correct, but prices a European-exercise options while claiming to price American-exercise. – Brian B Oct 29 '13 at 13:56
True. I noticed when I did a C implementation. – klon Oct 29 '13 at 21:33
Aleš Černý has very simple examples in his book. Alternatively, this paper seems to recap part of the chapter on Fourier series:
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+1 nice article – Rustam Nov 1 '13 at 13:53
+1: This is what I would have posted (but you were faster ;-) – vonjd Nov 3 '13 at 10:52
@vonjd: were you one of his students ? – BlueTrin Nov 3 '13 at 21:30
+1. Very clear explanation indeed. thanks @BlueTrin – sets Nov 4 '13 at 8:11
@BlueTrin: Unfortunately not, but I think he is a great teacher! – vonjd Nov 4 '13 at 15:37
Let $C$ be the price of the option, $S_t=S_0e^{X_t}$ be the stock price, $r$ be the risk-free rate, $K$ be the strike price, $T$ be the maturity time, $m=S_0/K$, $f$ be the density of $X_T$ and $\phi$ be the characteristic function $E(e^{i\xi X_T})$ which we assume is known.
$$C = e^{-rT}E((S_T-K)^+) = e^{-rT}S_0\int_{-\infty}^\infty \left(e^x-m\right)\mathbb{I}_{\{x>\ln(m)\}}f(x)dx \\ = e^{-rT}S_0\int_{-\infty}^\infty e^{-ax}\left(e^{ax}\left (e^x-m\right)\mathbb{I}_{\{x>\ln(m)\}}\right)f(x)dx.$$
We exponentially damp the payoff is order to ensure its Fourier transform exists. Then we re-write the last in terms of the inverse Fourier transform of the Fourier transform of the damped payoff. Note that the damped payoff is integrable so long as $a<-1$.
Now the Fourier transform of the damped payoff is $$\mathcal{F}\left(e^{ax}\left (e^x-\frac{K}{S_0}\right)\mathbb{I}_{\{x>m\}}\right):=h(\xi) = \frac{m^{1+a+i\xi}}{(a+i\xi)(1+a+i\xi)}$$ which then allows $$C = e^{-rT}S_0\int_{-\infty}^{\infty}e^{-ax}\left( \frac{1}{2\pi}\int_{-\infty}^{\infty} h(\xi)e^{-ix\xi}d\xi \right) f(x)dx \\ = e^{-rT}S_0 Re\left( \int_{-\infty}^{\infty}e^{-ax}\left( \frac{1}{\pi}\int_{0}^{\infty} h(\xi)e^{-ix\xi}d\xi \right) f(x)dx \right) \\ = \frac{e^{-rT}S_0}{\pi}Re\left( \int_{0}^{\infty} \left( \int_{-\infty}^{\infty}f(x)e^{i(ia-\xi)x}dx \right)h(\xi)d\xi \right) \\ = \frac{e^{-rT}S_0}{\pi}S_0\ Re \left( \int_{0}^{\infty} \phi(ia-\xi)h(\xi)d\xi \right).$$ The second step here is justified because the damped payoff is real. Hence $h$ is even in its real part and odd in its imaginary part. The third step requires Fubini's theorem which holds in most cases of interest.
This expression can be used immediately to price a single option or allows discretisation in a form compatible with the FFT. If you use the FFT with $N$ discretisation points the output will be $N$ option prices calculated for $N$ levels of $m$ (which may be useful for calibration).
See Pascucci (2011) PDE and martingale methods in option pricing (chapter 15) for more details and for a newer method using cosine expansions.
P.S. I have added an image of some simple Mathematica code for the GBM case.
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+1, thanks for your explanation – sets Nov 4 '13 at 8:28
@sets, I'll just add a little note. If we were to use the obvious Fourier transform method we would merely invert the density function. However this would then give us a 2D integral. However, by combining the exponential damping and judicious use of Fubini's theorem we can solve the problem with a 1D integral which of course will allow much quicker pricing. The method can also be used in higher dimensions. – Freakalien Nov 5 '13 at 1:34
When the pdf of a distribution is not known analytically, it's common to compute by taking the inverse Fourier transform of its characteristic function. The same idea applies here. Consider the discounted expectation formula of a European option $$V (S,\tau) = e^{-r\tau} \mathbb{E}_{x_0} [\theta(x_T)]$$. for log prices $x$ and time to expiry $\tau=T-t$. In integral form this is $$V (S,\tau)= e^{-r\tau} \int_{-\infty}^\infty \theta(x_T) f(x_T|x_0) dx_T$$ where $f(x_T|x_0)$ is the transition probability density (i.e. probabiltiy of reaching $x_T$ given $x$). For assets following certain distributions, $f$ can be hard to find analytically and may not even exist (consider the stable distribution). However, for the large majority of distributions used in finance, the Fourier transform (or characteristic function) is. So recasting the pricing problem in the Fourier domain is quite natural. Let's do this by applying the Fourier transform to the discounted expectation formula. Introduce the damping $\exp (\alpha x)$ so that $\exp (\alpha x) \theta(x) \in \mathbb{L}^2(\mathbb{R})$ \begin{align} \hat{V} (S,\tau) &= e^{-r \tau} \mathcal{F} \{\mathbb{E}_{x_0} [e^{\alpha x} \theta(x_T)] \} \\ &= e^{-r\tau} \mathbb{E}_{x_0} [\hat{\theta}_\alpha(x_T) ] . \end{align} By Fourier inversion \begin{align} V(S, \tau) &= e^{-r\tau} \mathcal{F}^{-1} \{ \mathbb{E}_{x_0} [\hat{\theta}_\alpha (x_T) ] \} \\ &= \frac{e^{-r\tau}}{2 \pi} \int_{-\infty+i \alpha}^{\infty+i \alpha} \hat{\theta}_\alpha (x_T) \mathbb{E}_{x_0} [e^{iux_T}] dx_T \\ &= \frac{e^{-r\tau}}{2 \pi} \int_{-\infty+i \alpha}^{\infty+i \alpha} \hat{\theta}_\alpha (x_T) \mathbb{E}_{x_0} [e^{iux_T-iux_0+iux_0}] dx_T \\ &=\frac{e^{-r\tau}}{2 \pi} \int_{-\infty+i \alpha}^{\infty+i \alpha} \hat{\theta}_\alpha (x_T) \phi(u;T) e^{iux_0} dx_T \end{align} where $\phi(u;T):=\mathbb{E}_{x_0} [e^{iu(x_T-x_0)}]$ is the characteristic function of the log price process.
To address your question of computation, MATLAB code is available for the Carr and Madan method. Using the MAIN FUNCTION and the characteristic function LIBRARY, you can call the function (untested):
CallPricingFFT('BlackScholes',14,10,12,2,0.05,0)
which will return your call option price of 1.073389...
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It looks like you have assumed that the Fourier transform $\hat{\theta}$ of the terminal payoff function $\theta$ exists. This requires that $\theta$ be integrable. But even for the trivial case of a European call payoff this is not true. This is why Carr and Madan damped the payoff function - to ensure its integrability and thereby the existence of the Fourier transform of the damped payoff function. – Freakalien Nov 5 '13 at 4:42
Thanks for the edit. Ok, you've damped the payoff, but now you take the Fourier transform of its expectation? The Fourier transform of a constant is the Dirac measure. Next you, somehow, convert this into an expectation of a Fourier transform (which is non-random anyhow) before finally ending up with a version of the Fourier Inversion Theorem that involves a contour integral. I'm not sure what else I add... – Freakalien Nov 5 '13 at 9:00
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2015-07-06 11:27:08
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http://www.sceneadvisor.com/Texas/mean-squared-error-estimation.html
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Address 550 E Bethany Dr Apt 324, Allen, TX 75002 (214) 547-0341
# mean squared error estimation Copeville, Texas
Let x {\displaystyle x} denote the sound produced by the musician, which is a random variable with zero mean and variance σ X 2 . {\displaystyle \sigma _{X}^{2}.} How should the A shorter, non-numerical example can be found in orthogonality principle. First, note that \begin{align} E[\hat{X}_M]&=E[E[X|Y]]\\ &=E[X] \quad \textrm{(by the law of iterated expectations)}. \end{align} Therefore, $\hat{X}_M=E[X|Y]$ is an unbiased estimator of $X$. More succinctly put, the cross-correlation between the minimum estimation error x ^ M M S E − x {\displaystyle {\hat − 2}_{\mathrm − 1 }-x} and the estimator x ^ {\displaystyle
Variance Further information: Sample variance The usual estimator for the variance is the corrected sample variance: S n − 1 2 = 1 n − 1 ∑ i = 1 n Thus, we can combine the two sounds as y = w 1 y 1 + w 2 y 2 {\displaystyle y=w_{1}y_{1}+w_{2}y_{2}} where the i-th weight is given as w i = Thus, we may have C Z = 0 {\displaystyle C_ σ 4=0} , because as long as A C X A T {\displaystyle AC_ σ 2A^ σ 1} is positive definite, The form of the linear estimator does not depend on the type of the assumed underlying distribution.
The denominator is the sample size reduced by the number of model parameters estimated from the same data, (n-p) for p regressors or (n-p-1) if an intercept is used.[3] For more Also x {\displaystyle x} and z {\displaystyle z} are independent and C X Z = 0 {\displaystyle C_{XZ}=0} . Introduction to the Theory of Statistics (3rd ed.). Since C X Y = C Y X T {\displaystyle C_ ^ 0=C_ σ 9^ σ 8} , the expression can also be re-written in terms of C Y X {\displaystyle
Sequential linear MMSE estimation In many real-time application, observational data is not available in a single batch. x ^ = W y + b . {\displaystyle \min _ − 4\mathrm − 3 \qquad \mathrm − 2 \qquad {\hat − 1}=Wy+b.} One advantage of such linear MMSE estimator is After (m+1)-th observation, the direct use of above recursive equations give the expression for the estimate x ^ m + 1 {\displaystyle {\hat σ 0}_ σ 9} as: x ^ m x ^ M M S E = g ∗ ( y ) , {\displaystyle {\hat ^ 2}_{\mathrm ^ 1 }=g^{*}(y),} if and only if E { ( x ^ M M
Contents 1 Motivation 2 Definition 3 Properties 4 Linear MMSE estimator 4.1 Computation 5 Linear MMSE estimator for linear observation process 5.1 Alternative form 6 Sequential linear MMSE estimation 6.1 Special A shorter, non-numerical example can be found in orthogonality principle. Cambridge University Press. Another approach to estimation from sequential observations is to simply update an old estimate as additional data becomes available, leading to finer estimates.
The system returned: (22) Invalid argument The remote host or network may be down. MSE is also used in several stepwise regression techniques as part of the determination as to how many predictors from a candidate set to include in a model for a given Thus unlike non-Bayesian approach where parameters of interest are assumed to be deterministic, but unknown constants, the Bayesian estimator seeks to estimate a parameter that is itself a random variable. Every new measurement simply provides additional information which may modify our original estimate.
Moon, T.K.; Stirling, W.C. (2000). This property, undesirable in many applications, has led researchers to use alternatives such as the mean absolute error, or those based on the median. Retrieved from "https://en.wikipedia.org/w/index.php?title=Minimum_mean_square_error&oldid=734459593" Categories: Statistical deviation and dispersionEstimation theorySignal processingHidden categories: Pages with URL errorsUse dmy dates from September 2010 Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Thus, we can combine the two sounds as y = w 1 y 1 + w 2 y 2 {\displaystyle y=w_{1}y_{1}+w_{2}y_{2}} where the i-th weight is given as w i =
Both linear regression techniques such as analysis of variance estimate the MSE as part of the analysis and use the estimated MSE to determine the statistical significance of the factors or Another computational approach is to directly seek the minima of the MSE using techniques such as the gradient descent methods; but this method still requires the evaluation of expectation. Moreover, if the components of z {\displaystyle z} are uncorrelated and have equal variance such that C Z = σ 2 I , {\displaystyle C_ ∈ 4=\sigma ^ ∈ 3I,} where Definition Let x {\displaystyle x} be a n × 1 {\displaystyle n\times 1} hidden random vector variable, and let y {\displaystyle y} be a m × 1 {\displaystyle m\times 1} known
Two basic numerical approaches to obtain the MMSE estimate depends on either finding the conditional expectation E { x | y } {\displaystyle \mathrm − 6 \ − 5} or finding While these numerical methods have been fruitful, a closed form expression for the MMSE estimator is nevertheless possible if we are willing to make some compromises. In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the References ^ a b Lehmann, E.
p.60. Mathematical Methods and Algorithms for Signal Processing (1st ed.). As we have seen before, if $X$ and $Y$ are jointly normal random variables with parameters $\mu_X$, $\sigma^2_X$, $\mu_Y$, $\sigma^2_Y$, and $\rho$, then, given $Y=y$, $X$ is normally distributed with \begin{align}%\label{} Thus the expression for linear MMSE estimator, its mean, and its auto-covariance is given by x ^ = W ( y − y ¯ ) + x ¯ , {\displaystyle {\hat
One possibility is to abandon the full optimality requirements and seek a technique minimizing the MSE within a particular class of estimators, such as the class of linear estimators. Part of the variance of $X$ is explained by the variance in $\hat{X}_M$. Please try the request again. L.; Casella, G. (1998). "Chapter 4".
If we define S a 2 = n − 1 a S n − 1 2 = 1 a ∑ i = 1 n ( X i − X ¯ ) For an unbiased estimator, the MSE is the variance of the estimator. Haykin, S.O. (2013). Estimators with the smallest total variation may produce biased estimates: S n + 1 2 {\displaystyle S_{n+1}^{2}} typically underestimates σ2 by 2 n σ 2 {\displaystyle {\frac {2}{n}}\sigma ^{2}} Interpretation An
Contents 1 Motivation 2 Definition 3 Properties 4 Linear MMSE estimator 4.1 Computation 5 Linear MMSE estimator for linear observation process 5.1 Alternative form 6 Sequential linear MMSE estimation 6.1 Special In such stationary cases, these estimators are also referred to as Wiener-Kolmogorov filters. Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions.
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2019-01-23 17:52:45
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https://galamost.readthedocs.io/en/latest/source.html
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# Original sources¶
Some methods of GALAMOST are developed partically based on the codes from other packages. To acknowledge the original works, we list the methods of GALAMOST and their original sources.
Methods Sources
ENUF electrostatics MDynaMix (CPU codes, GNU License )
Tabulated potential method IBIsCO (CPU codes, GNU License )
MD-SCF OCCAM (CPU codes, GNU License )
Gay-Berne model LAMMPS (CPU codes, GNU License )
Virtual interaction sites GROMACS (CPU codes, GNU License )
Bond constraint LINCS GROMACS (CPU codes, GNU License )
Rigid body LAMMPS (CPU codes, GNU License) and HOOMD (GPU codes, BSD-3 License)
PPPM electrostatics HOOMD (GPU codes, BSD-3 License)
MTK barostat HOOMD (GPU codes, BSD-3 License)
Neighbor List on auto parameter (>=4.0.1) HOOMD (GPU codes, BSD-3 License)
The licenses of source packages that are inluded in GALAMOST codes are listed here for clarity.
HOOMD-blue:
BSD 3-Clause License for HOOMD-blue
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. Neither the name of the copyright holder nor the names of its contributors
may be used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
LAMMPS:
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
MDynaMix:
See the README file in the top-level LAMMPS directory.
Copyright (c) 1996, 1999, 2006 by:
Alexander Lyubartsev and Aatto Laaksonen,
Department of Physical Chemistry, Stockholm University
GROMACS:
GROMACS is free software, distributed under the GNU Lesser General
Public License (LGPL) Version 2.1 or (at your option) any later
version. See section 1 for details. GROMACS includes optional code
covered by several different licences as described below. The
GROMACS package in its entirety may be copied, modified or
distributed according to the conditions described in section 1.
However, in the interests of clarity and completeness, some
individual parts of GROMACS that can be used under their respective
licenses are also noted here.
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2019-11-13 12:12:38
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https://www.physicsforums.com/threads/linear-equations.128224/
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Homework Help: Linear Equations
1. Aug 6, 2006
suspenc3
Hi, I am finding some of this confusing, can someone explain this?
so I undersand that $$xy' + y = (xy)'$$
lets say that I have $$2ty' + 4y = 2t^3$$, what is (xy)'?
would it just become $$d/dx(2ty) = 2t^3$$?
Last edited: Aug 6, 2006
2. Aug 6, 2006
StatusX
You're mixing up x and t. If you just want to solve:
$$2t \frac{dy}{dt}+4y=2t^3$$
then you should use integrating factors. That is, find a pair of functions f(t) and g(t) such that (substituting back y' for dy/dt):
$$f(t) (2t y'+4y)= \frac{d}{dt} (g(t) y)$$
Right away you can see that 2tf(t)=g(t), and then you can get a simple ODE to solve for g(t). Now you multiply across in the original equation:
$$f(t) (2t y' +4y)=\frac{d}{dt} (g(t) y)=f(t) 2t^3$$
and then you just need to integrate. Note that the case (xy)' you describe first is another example of integrating factors, in that case with g(x)=x. In this case, g will be different.
Last edited: Aug 6, 2006
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2018-12-13 11:55:47
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http://archive.numdam.org/item/COCV_2014__20_3_725_0/
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Linearized plastic plate models as $\Gamma$-limits of 3D finite elastoplasticity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 725-747.
The subject of this paper is the rigorous derivation of reduced models for a thin plate by means of Γ-convergence, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we analyse the case where the scaling factor of the elasto-plastic energy per unit volume is of order ε2α-2, with α ≥ 3. According to the value of α, partially or fully linearized models are deduced, which correspond, in the absence of plastic deformation, to the Von Kármán plate theory and the linearized plate theory.
DOI : https://doi.org/10.1051/cocv/2013081
Classification : 74C15, 74G65, 74K20, 49J45
Mots clés : finite plasticity, thin plates, Γ-convergence
@article{COCV_2014__20_3_725_0,
author = {Davoli, Elisa},
title = {Linearized plastic plate models as $\Gamma$-limits of 3D finite elastoplasticity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {725--747},
publisher = {EDP-Sciences},
volume = {20},
number = {3},
year = {2014},
doi = {10.1051/cocv/2013081},
zbl = {1298.74145},
language = {en},
url = {archive.numdam.org/item/COCV_2014__20_3_725_0/}
}
Davoli, Elisa. Linearized plastic plate models as $\Gamma$-limits of 3D finite elastoplasticity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 3, pp. 725-747. doi : 10.1051/cocv/2013081. http://archive.numdam.org/item/COCV_2014__20_3_725_0/
[1] E. Acerbi, G. Buttazzo and D. Percivale, A variational definition for the strain energy of an elastic string. J. Elasticity 25 (1991) 137-148. | MR 1111364 | Zbl 0734.73094
[2] A. Bertram, An alternative approach to finite plasticity based on material isomorphisms. Int. J. Plasticity 15 (1999) 353-374. | Zbl 1016.74009
[3] C. Carstensen, K. Hackl and A. Mielke, Non-convex potentials and microstructures in finite-strain plasticity. R. Soc. London Proc. Ser. A Math. Phys. Eng. Sci. 458 (2002) 299-317. | MR 1889770 | Zbl 1008.74016
[4] G. Dal Maso, An introduction to Γ-convergence. Boston, Birkhäuser (1993). | MR 1201152 | Zbl 0816.49001
[5] G. Dal Maso and G. Lazzaroni, Quasistatic crack growth in finite elasticity with non-interpenetration. Ann. Inst. Henri Poincaré Anal. Non Linéaire 27 (2010) 257-290. | Numdam | MR 2580510 | Zbl 1188.35205
[6] E. Davoli, Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity. Preprint SISSA (2012), Trieste. | MR 3211118 | Zbl pre06322950
[7] G.A. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies. J. Reine Angew. Math. 595 (2006) 55-91. | MR 2244798 | Zbl 1101.74015
[8] G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461-1506. | MR 1916989 | Zbl 1021.74024
[9] G. Friesecke, R.D. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Rational Mech. Anal. 180 (2006) 183-236. | MR 2210909 | Zbl 1100.74039
[10] M. Lecumberry and S. Müller, Stability of slender bodies under compression and validity of the Von Kármán theory. Arch. Ration. Mech. Anal. 193 (2009) 255-310. | MR 2525119 | Zbl 1200.74060
[11] H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549-578. | MR 1365259 | Zbl 0847.73025
[12] E.H. Lee, Elastic-plastic deformation at finite strains. J. Appl. Mech. 36 (1969) 1-6. | Zbl 0179.55603
[13] M. Liero and A. Mielke, An evolutionary elastoplastic plate model derived via Γ-convergence. Math. Models Methods Appl. Sci. 21 (2011) 1961-1986. | MR 2843026 | Zbl 1232.35165
[14] M. Liero and T. Roche, Rigorous derivation of a plate theory in linear elastoplasticity via Γ-convergence. NoDEA Nonlinear Differ. Eqs. Appl. 19 (2012) 437-457. | MR 2949627 | Zbl 1253.35180
[15] A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain. J. Nonlinear Sci. 19 (2009) 221-248. | MR 2511255 | Zbl 1173.49013
[16] J. Mandel, Equations constitutive et directeur dans les milieux plastiques et viscoplastique. Int. J. Sol. Struct. 9 (1973) 725-740. | Zbl 0255.73004
[17] A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances. Contin. Mech. Thermodyn. 15 (2003) 351-382. | MR 1999280 | Zbl 1068.74522
[18] A. Mielke, Finite elastoplasticity, Lie groups and geodesics on SL(d), Geometry, Dynamics, and Mechanics. Springer, New York (2002) 61-90. | MR 1919826 | Zbl 1146.74309
[19] A. Mielke and U. Stefanelli, Linearized plasticity is the evolutionary Gamma-limit of finite plasticity. J. Eur. Math. Soc. 15 (2013) 923-948. | MR 3085096 | Zbl pre06164612
[20] P.M. Naghdi, A critical review of the state of finite plasticity. Z. Angew. Math. Phys. 41 (1990) 315-394. | MR 1058818 | Zbl 0712.73032
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2021-03-02 09:20:45
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https://jemrare.com/basic-math-mcq-15/
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# Basic Math MCQ 15 ( Work capability comparison )
MCQ 15: A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in___________days if they work together.
a) 18 days b) 22 ½ days c) 24 days d) 26 days
Solution:
A is thrice good than B — means A can do three times more work in one time duration !
i-e A can do three times more work in one day
So,
1 day for A = 3W
But B takes 3 days for one work part
3 day for B = W
So we can see there is difference of 2 days !
With difference of 2 days B’ work finish in = 3 day
==> with difference of 1 day B’s work finish in = 3/2 days
==> with difference of 60 days B’s work finish in = 60 x 3/2 = 90 days
or with difference of 60 days ;
Work of B = 90 days
or
1 day (for B) = Work (of B) / 90 =W/90————-(1
As A can do three times more work than B;
So,
1 day (for A) = 3x ( 1 day work of B)=3x W/90 =W/30 —————–(2
1 day ( for A + for B) = W/90+W/30= 4W/90
or
W = 90/4 days (for A+for B)
or
W = 22-1/2 days for ( A and B)
So It will take 22.5 days for both A and B to finish the work together !
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All original content on these pages is fingerprinted and certified by Digiprove
Insert math as
$${}$$
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2020-09-22 14:34:20
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https://en.wikipedia.org/wiki/Set_splitting
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# Set splitting problem
(Redirected from Set splitting)
Jump to navigation Jump to search
In computational complexity theory, the Set Splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists a partition of S into two subsets S1, S2 such that all elements of F are split by this partition, i.e., none of the elements of F is completely in S1 or S2. Set Splitting is one of Garey&Johnson's classical NP-complete problems.[1]
## Variants
The optimization version of this problem is called Max Set Splitting and requires finding the partition which maximizes the number of split elements of F. It is an APX-complete[2] problem and hence in NPO.
The Set k-Splitting problem is stated as follows: given S, F, and an integer k, does there exist a partition of S which splits at least k subsets of F? The original formulation is the restricted case with k equal to the cardinality of F. The Set k-Splitting is fixed-parameter tractable, i.e., if k taken to be a fixed parameter, rather than a part of the input, then a polynomial algorithm exists for any fixed k.Dehne, Fellows and Rosamond presented an algorithm that solves it in time ${\displaystyle O(f(k)n^{c})}$ for some function f and constant c.[3]
When each element of F is restricted to be of cardinality exactly k, the decision variant is called Ek-Set Splitting and the optimization version Max Ek-Set Splitting. For k > 2 the former remains NP complete, and for k ≥ 2 the latter remains APX complete.[4] For k ≥ 4, Ek-Set Splitting is approximation resistant. That is, unless P=NP, there is no polynomial-time (factor) approximation algorithm which does essentially better than a random partition.[5][6]
The Weighted Set Splitting is a variant in which the subsets in F have weights and the objective is to maximize the total weight of the split subsets.
## Connection to other problems
Set Splitting is special case of the Not-All-Equal Satisfiability problem without negated variables. Additionally, Ek-Set Splitting equals non-monochromatic graph coloring of k-uniform hypergraphs. For k=2, the optimization variant reduces to the well-known Maximum cut.[6]
## References
1. ^ Garey, Michael R.; Johnson, David S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. New York: W.H. Freeman. ISBN 0-7167-1045-5.
2. ^ Petrank, Erez (1994). "The Hardness of Approximation: Gap Location". Computational Complexity. Springer.
3. ^ Dehne, Frank; Fellows, Michael; Rosamond, Frances (2003). An FPT Algorithm for Set Splitting (PDF). Graph Theoretic Concepts in Computer Science (WG2003), Lecture Notes in Computer Science. 2880. Springer. pp. 180–191.
4. ^ Lovász, László (1973). Coverings and Colorings of Hypergraphs. 4th Southeastern Conference on Combinatorics, Graph Theory, and Computing.
5. ^ Håstad, Johan (2001). "Some Optimal Inapproximability Results". Journal of the ACM. Association for Computing Machinery. 48: 798–859. doi:10.1145/502090.502098.
6. ^ a b Guruswami, Venkatesan (2003). "Inapproximability Results for Set Splitting and Satisfiability Problems with no Mixed Clauses". Algorithmica. Springer. 38: 451–469. doi:10.1007/s00453-003-1072-z.
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2019-07-21 19:28:40
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https://stats.stackexchange.com/questions/190937/automatic-feature-extraction-in-caffe
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# Automatic Feature Extraction in Caffe
I am a beginner to frameworks like Caffe, Theano for deep learning. But, I would like to know how do I use Caffe framework for only feature extraction without performing classification. I want the feature vector which is input to the deep neural network for classification.
I want to perform automatic feature extraction for several images. The output for this task should be a text file containing :
image_name1, feature_vector1
image_name1, feature_vector1
image_name1, feature_vector1
...
Kindly help me with this. Thanks in advance.
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2019-11-19 04:53:38
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https://experts.mcmaster.ca/display/publication227885
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# Ordinary and Viscosity‐damped Magnetohydrodynamic Turbulence Academic Article
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• Overview
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• Research
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• Identity
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•
### abstract
• We compare the properties of ordinary strong magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium with the recently discovered viscosity-damped regime. We focus on energy spectra, anisotropy, and intermittency. Our most surprising conclusion is that in ordinary strong MHD turbulence the velocity and magnetic fields show different high-order structure function scalings. Moreover this scaling depends on whether the intermittency is viewed in a global or local system of reference. This reconciles seemingly contradictory earlier results. On the other hand, the intermittency scaling for viscosity-damped turbulence is very different, and difficult to understand in terms of the usual phenomenological models for intermittency in turbulence. Our remaining results are in reasonable agreement with expectations. First, we find that our high resolution simulations for ordinary MHD turbulence show that the energy spectra are {\it compatible} with a Kolmogorov spectrum, while viscosity-damped turbulence shows a shallow $k^{-1}$ spectrum for the magnetic fluctuations. Second, a new numerical technique confirms that ordinary MHD turbulence exhibits Goldreich-Sridhar type anisotropy, while viscosity-damped MHD turbulence shows extremely anisotropic eddy structures. Finally, we show that many properties of incompressible turbulence for both the ordinary and viscosity-damped regimes carry over to the case of compressible turbulence.
• October 2003
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2020-08-10 15:52:50
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https://mathsgrinds.ie/leaving-certificate-examination-1936-honours-applied-mathematics/
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085-1263404
### Maths Grinds' Blog
Blogging and Mathing
19 Sep 2018
##### Question 1
A wheel rolls uniformly on the ground, without sliding, its centre describing a straight line with uniform velocity $v$. Show that at any instant every point on the rim is turning about the point of contact of the wheel with the ground with an angular velocity equal to that of the wheel about its centre.
##### Question 2
A $10$ ton lorry attains a speed of $15$ miles per hour from rest in $24$ seconds during which time it travels a distance of $100$ yards. If the average resistance to motion over this distance is $30$ lbs. per ton-find the average Horse Power required.
##### Question 3
If the hodograph of the path of a moving point $P$ be drawn, then the velocity of the corresponding point $Q$ in the hodograph represents in magnitude and direction the acceleration of $P$ in its path.
Prove this theorem and use it to determine the magnitude and direction of the acceleration of a point moving in a circle of radius $r$ with a uniform speed $v$.
##### Question 4
The bob of a conical pendulum is moving in a horizontal circle with uniform velocity. With the aid of a clear diagram indicate the forces acting on it at any instant and analyse the motion.
If the bob makes $60$ revolutions per minute, what is the vertical distance of the circle of rotation below the point of suspension of the pendulum?
##### Question 5
A machine part weighing $10$ lbs. has a simple harmonic motion in a straight line. The distance between the end points of its travel is $9$ inches and $240$ complete to-and-fro movements are made per minute. Calculate :-
(a) the acceleration and the accelerating force when it is $3$ inches from its mid-position;
(b) its maximum velocity;
(c) the maximum accelerating force.
##### Question 6
Neglecting frictional resistance, calculate the least velocity with which a truck must enter the lowest point of a vertical circular track $20$ feet in diameter in order to just “loop the loop.”
Find also the velocity of the truck and the reaction of the track when half way up.
Weight of truck = $40$ lbs.
##### Question 7
Two long pendulums of equal length are suspended so that their bobs just touch when at rest. The masses of the bobs are $4$lbs. and $2$ lbs. respectively. They are pulled apart in opposite directions-the horizontal displacements from the rest positions being $+8$ inches and $-$ inches respectively-and released simultaneously. In impact they join together and move as one body. The compound mass is found to have a maximum horizontal displacement of $+4$ inches from the mean positions.
On the assumption that the horizontal displacements represent to some scale the velocities of the masses at their mean positions, show that these results verify the Principle of Conservation of Momentum.
Justify this assumption.
##### Question 8
Over a smooth pulley is passed a light string supporting at one end a mas of $4$ lbs. and at the other a pulley of mass $1$ lb. A string with masses of $2$ lbs. and $3$ lbs. attached to its ends passes over the second pulley.
Find the acceleration of each of the moving bodies and of the centre of gravity of the moving system.
##### Question 9
A box weighing $5$ lbs. placed on a plank just slides down when the plank is tilted at an angle of $14^\circ$ to the horizontal.
The plank is then fixed at an incline of $30^\circ$ to the horizontal and a weight $W$ lbs. is placed in the box. Find an equation showing the effort $P$ lbs. acting parallel to the incline which will drag the box and weight up the incline at a slow uniform speed.
Write down expressions for the Mechanical Advantage and Efficiency of the arrangement.
##### Question 10
Two poles $AB$ and $AC$ jointed together at their tops and making an angle of $20^\circ$ with each other are used as shear legs. The ends $B$ and $C$ rest on the level ground an the plane of triangle $ABC$ is inclined at $60^\circ$ to the horizontal. A back stay joined at the top $A$ and to a point $D$ on the ground behind the legs is placed symmetrically with respect to them and makes angle of $30^\circ$ with the plane of the legs.
Find the forces in the legs and back stay when a load of $10$ tons is hung from $A$.
##### Citation:
Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/
##### Licence:
“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.
The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).
Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.
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2018-10-20 22:31:11
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https://plainmath.net/2181/examples-correct-largest-rectangle-following-continuous-differentiable
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# Prove these examples are correct: a) What is the area of the largest rectangle that fits inside of the ellipse x^{2} + 2y^{2} = 1? b) Prove the following: Let c in (a, b). If f is continuous on [a, b], differentiable on (a, b)?
Question
Transformation properties
Prove these examples are correct:
a) What is the area of the largest rectangle that fits inside of the ellipse
$$x^{2}\ +\ 2y^{2} = 1?$$
b) Prove the following: Let c in (a, b). If f is continuous on $$[a,\ b],$$ differentiable on (a, b)?
2021-02-26
a) Сonsider this figure:
From the figure it can be seen that:
Area $$(A) = 4xy$$
And also,
$$x^{2}\ +\ 2y^{2} = 1$$
$$x = \sqrt{1\ -\ 2y^{2}$$
We've taken the positive value since we chose this point to be in the first quadrant
So now deciding:
$$A = 4xy$$
$$A = 4y \sqrt{1\ -\ 2y^{2}$$
Differentiating the above function with respect to "y":
$$\frac{dA}{dy}=\frac{d}{dy}\left(4y\sqrt{1\ -\ 2y^{2}}\right)$$
$$\frac{dA}{dy}=4y\frac{d}{dy}\sqrt{1\ -\ 4y^{2}}\ +\ \sqrt{1\ -\ 4y^{2}}\frac{d}{dy}(4y)$$
$$\frac{dA}{dy}=4y\frac{1}{2\sqrt{1\ -\ 4y^{2}}}(-8y)\ +\ 4\sqrt{1\ -\ 4y^{2}}$$
$$\frac{dA}{dy}=4\left[\frac{-8y^{2}\ +\ 2\ -\ 8y^{2}}{2\sqrt{1\ -\ 4y^{2}}}\right]$$
$$\frac{dA}{dy}=4\left[\frac{2\ -\ 16y^{2}}{2\sqrt{1\ -\ 4y^{2}}}\right]$$
For maximize the area:
Put,
$$\frac{dA}{dy} = 0$$
$$\frac{dA}{dy}=4\left[\frac{2\ -\ 16y^{2}}{2\sqrt{1\ -\ 4y^{2}}}\right]$$
$$\left[\frac{2\ -\ 16y^{2}}{2\sqrt{1\ -\ 4y^{2}}}\right]=0$$
$$2\ -\ 16y^{2} = 0$$
$$y^{2} = \frac{1}{8}$$
$$y = \frac{1}{\sqrt{8}}$$
Corresponding to this,
$$x=\sqrt{1\ -\ 2\ \times\ \frac{1}{8}}$$
$$x = \sqrt {1\ -\ \frac{1}{4}}$$
$$x = \sqrt{\frac{3}{4}}$$
$$x = \frac{\sqrt{3}}{2}}$$
Hence the maximum area:
Area $$(A) = 4xy$$
$$Area_{max} = 4\ \times\ \frac{\sqrt{3}}{2}\ \times\ \frac{1}{\sqrt{8}}$$
$$Area_{max} = 2\ \times\ \frac{\sqrt{3}}{2 \sqrt{2}}$$
$$Area_{max} = \sqrt{\frac{3}{2}}$$
b)Prove the following: Let c in (a, b). If f is continuous on [a, b], differentiable on (a, b), and:
$$\lim_{x\ \rightarrow\ x}\ f'(x)=L\ then\ f'(c)=L$$
Properties used
$$\lim_{h\ \rightarrow\ 0}\ \frac{f'(x\ +\ h)\ -\ f(x)}{h}=f'(x)$$
Proof is given below:
Since:
$$\lim_{x\ \rightarrow\ c} f'(x) = L$$
By using the property:
$$\lim_{x\ \rightarrow\ c}\ \left[\lim_{h\ \rightarrow\ 0}\frac{f'(x\ +\ h)\ -\ f(x)}{h}\right]=L$$
$$\lim_{h\ \rightarrow\ 0}\ \left[\lim_{x\ \rightarrow\ c}\frac{f(x\ +\ h)\ -\ f(x)}{h}\right]=L$$
$$[:' f(x) is continuous]$$
$$\lim_{h\ \rightarrow\ 0}\ \left[\frac{f(c\ +\ h)\ -\ f(c)}{h}\right]=L$$
$$\left[\lim_{h\ \rightarrow\ 0}\ \frac{f(c\ +\ h)\ -\ f(c)}{h}\right]=L$$
$$f' (c) = L$$
a) $$Area_{max} = \sqrt{\frac{3}{2}}$$
b) The proof is given above.
### Relevant Questions
Prove that the metric area is defined as $$\displaystyle{P}\ {<}\ {x}_{{{1}}},\ {y}_{{{1}}}\ {>}\ {\quad\text{and}\quad}\ {Q}\ {<}\ {x}_{{{2}}},\ {y}_{{{2}}}\ {>}$$. If the proof of examples says that the first properties (positive definiteness and symmetry) are trivial. Prove the versatility of properties for a given space.
Let $$T\ :\ U\ \rightarrow\ U$$ be a linear transformatiom and let
$$\mathscr{B}$$ be a basis of U. Define the determanant det (T) of T as
$$det(T) = det([T]\ \mathscr{B}).$$
Show that det (T) is well=defined, i.e. that it does not depend on the choice of the basis $$\mathscr{B}.$$
Prove that T is invertible if and only if det $$(T) \neq\ 0.$$ If T is invertible, show that
$$det(T^{-1}) =\ \frac{1}{det(T)}.$$
Guided Proof Let $${v_{1}, v_{2}, .... V_{n}}$$ be a basis for a vector space V.
Prove that if a linear transformation $$T : V \rightarrow V$$ satisfies
$$T (v_{i}) = 0\ for\ i = 1, 2,..., n,$$ then T is the zero transformation.
To prove that T is the zero transformation, you need to show that $$T(v) = 0$$ for every vector v in V.
(i) Let v be the arbitrary vector in V such that $$v = c_{1} v_{1} + c_{2} v_{2} +\cdots + c_{n} V_{n}$$
(ii) Use the definition and properties of linear transformations to rewrite T(v) as a linear combination of $$T(v_{j})$$ .
(iii) Use the fact that $$T (v_{j}) = 0$$
to conclude that $$T (v) = 0,$$ making T the zero transformation.
Let $$T : U \rightarrow U$$ be a linear transformation and let beta be a basis of U Define the determinant det(T) of T as
det$$(T) = det([T]_{\beta}).$$
Show ta det (T) is well-defined, i. e. that it does not depend on the choice of the basis beta
Prove that T is invertible if and only if det $$(T) \neq 0.$$ If T is invertible, show that det $$(T^{-1}) = \frac{1}{det(T)}$$
1. Find each of the requested values for a population with a mean of $$? = 40$$, and a standard deviation of $$? = 8$$ A. What is the z-score corresponding to $$X = 52?$$ B. What is the X value corresponding to $$z = - 0.50?$$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $$M=42$$ for a sample of $$n = 4$$ scores? E. What is the z-scores corresponding to a sample mean of $$M= 42$$ for a sample of $$n = 6$$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $$a. -2.00 b. 1.25 c. 3.50 d. -0.34$$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $$\mu = 78$$ and $$\sigma = 12$$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $$82, 74, 62, 68, 79, 94, 90, 81, 80$$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $$12 (\mu = 42, \sigma = 12)$$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $$\alpha = 0.05$$ level of significance.
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect was Armed:
Black - 543
White - 1176
Hispanic - 378
Total - 2097
Suspect was unarmed:
Black - 60
White - 67
Hispanic - 38
Total - 165
Total:
Black - 603
White - 1243
Hispanic - 416
Total - 2262
Give your answer as a decimal to at least three decimal places.
a) What percent are Black?
b) What percent are Unarmed?
c) In order for two variables to be Independent of each other, the P $$(A and B) = P(A) \cdot P(B) P(A and B) = P(A) \cdot P(B).$$
This just means that the percentage of times that both things happen equals the individual percentages multiplied together (Only if they are Independent of each other).
Therefore, if a person's race is independent of whether they were killed being unarmed then the percentage of black people that are killed while being unarmed should equal the percentage of blacks times the percentage of Unarmed. Let's check this. Multiply your answer to part a (percentage of blacks) by your answer to part b (percentage of unarmed).
Remember, the previous answer is only correct if the variables are Independent.
d) Now let's get the real percent that are Black and Unarmed by using the table?
If answer c is "significantly different" than answer d, then that means that there could be a different percentage of unarmed people being shot based on race. We will check this out later in the course.
Let's compare the percentage of unarmed shot for each race.
e) What percent are White and Unarmed?
f) What percent are Hispanic and Unarmed?
If you compare answers d, e and f it shows the highest percentage of unarmed people being shot is most likely white.
Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls the percentage of white and unarmed up. In addition, there most likely would be more white and armed shot by police. All the percentages for white people would be higher, because there are more white people. For example, the table contains very few Hispanic people, and the percentage of people in the table that were Hispanic and unarmed is the lowest percentage.
Think of it this way. If you went to a college that was 90% female and 10% male, then females would most likely have the highest percentage of A grades. They would also most likely have the highest percentage of B, C, D and F grades
The correct way to compare is "conditional probability". Conditional probability is getting the probability of something happening, given we are dealing with just the people in a particular group.
g) What percent of blacks shot and killed by police were unarmed?
h) What percent of whites shot and killed by police were unarmed?
i) What percent of Hispanics shot and killed by police were unarmed?
You can see by the answers to part g and h, that the percentage of blacks that were unarmed and killed by police is approximately twice that of whites that were unarmed and killed by police.
j) Why do you believe this is happening?
Do a search on the internet for reasons why blacks are more likely to be killed by police. Read a few articles on the topic. Write your response using the articles as references. Give the websites used in your response. Your answer should be several sentences long with at least one website listed. This part of this problem will be graded after the due date.
Which of the following are linear transformations from $$RR^{2} \rightarrow RR^{2} ?$$
(d) Rotation: if $$x = r \cos \theta, y = r \sin \theta,$$ then
$$\overrightarrow{T}(x,y)=(r \cos(\theta+ \varphi), r \sin (\theta+ \varphi))$$
for some constants $$\angle \varphi$$
(f) Reflection: given a fixed vector $$\overrightarrow{r} = (a, b), \overrightarrow{T}$$ maps each point to its reflection with
respect to $$\overrightarrow{r} \overrightarrow{T}(\overrightarrow{x})=\overrightarrow{x}-2\overrightarrow{x}_{r \perp}$$
$$=2 \overrightarrow{x}_{r}-\overrightarrow{x}$$
Let C be the ellipse contained in the xy plane whose equation is $$\displaystyle{4}{x}^{{2}}+{y}^{{2}}={4}$$, oriented clockwise. The force field F described by $$\displaystyle{F}{\left({x},{y},{z}\right)}={x}^{{2}}{i}+{2}{x}{j}+{z}^{{2}}{k}$$, moves a particle along C in the same direction as the curve orientation, performing a W job. C as the surface boundary S: $$\displaystyle{z}={4}-{4}{x}^{{2}}-{y}^{{2}},{z}\ge{0}$$ (with ascending orientation, that is, the component in the z direction equal to 1) and assuming $$\displaystyle\pi={3.14}$$, we can state what:
a) It is not necessary to apply Stokes' Theorem, as C is a closed curve and therefore W = 0.
b) Inverting the orientation of the surface S, we can apply Stokes' Theorem and conclude that W = 12.56.
c) We can apply Stokes' Theorem and conclude that W = 6.28
d) We can apply Stokes' Theorem and conclude that W = 12.56.
Assum T: R^m to R^n is a matrix transformation with matrix A. Prove that if the columns of A are linearly independent, then T is one to one (i.e injective). (Hint: Remember that matrix transformations satisfy the linearity properties.
Linearity Properties:
If A is a matrix, v and w are vectors and c is a scalar then
$$A 0 = 0$$
$$A(cv) = cAv$$
$$A(v\ +\ w) = Av\ +\ Aw$$
A random sample of $$\displaystyle{n}_{{1}}={16}$$ communities in western Kansas gave the following information for people under 25 years of age.
$$\displaystyle{X}_{{1}}:$$ Rate of hay fever per 1000 population for people under 25
$$\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{2}}={14}$$ regions in western Kansas gave the following information for people over 50 years old.
$$\displaystyle{X}_{{2}}:$$ Rate of hay fever per 1000 population for people over 50
$$\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}$$
(i) Use a calculator to calculate $$\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.$$ (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $$\displaystyle\alpha={0.05}.$$
(a) What is the level of significance?
State the null and alternate hypotheses.
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value $$\displaystyle>{0.250}$$
$$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$
$$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$
$$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$
$$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$
P-value $$\displaystyle<{0.005}$$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value
...
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2021-05-08 07:54:28
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https://physics.stackexchange.com/questions/570740/how-to-get-the-riemann-curvature-tensor-from-the-commutator-operating-on-a-basis
|
# How to get the Riemann curvature tensor from the commutator operating on a basis vector
In the following the basis vectors are assumed to be varying functions of position. This means that when a vector appears under the differentiation operator, both components and basis vectors will, in general be differentiated according the the product rule. An underline indicates a particular term is to be held constant during differentiation.
Del operating on a vector is written as
$$\nabla\left[\vec{v}\right]=\partial_{\sigma}\left[\mathfrak{e}_{\nu}v^{\nu}\right]\mathfrak{e}^{\sigma}.$$
Basis 1-forms will be treated as contravariant basis vectors. So in a coordinate basis, we have
$$\mathfrak{e}^{\sigma}=dx^{\alpha}.$$
Del followed by 'dot vector' contracts on the differentiation index. This is called the directional derivative.
$$\nabla\left[\vec{v}\right]\cdot\vec{w}=\partial_{\sigma}\left[\mathfrak{e}_{\nu}v^{\nu}\right]\mathfrak{e}^{\sigma}\cdot\mathfrak{e}_{\omega}w^{\omega}=\frac{\partial\mathfrak{e}_{\nu}v^{\nu}}{\partial x^{\omega}}w^{\omega}.$$
In particular the partial derivative with respect to the
$$\nabla\left[\varphi\right]\cdot\mathfrak{e}_{\delta}=\partial_{\delta}\varphi=\frac{\partial\varphi}{\partial x^{\delta}}$$
$$\nabla\left[\vec{v}\right]\cdot\mathfrak{e}_{\omega}=\frac{\partial\vec{v}}{\partial x^{\omega}}.$$
Del preceded by a 'vector dot' contracts on the argument of del.
$$\vec{u}\cdot\nabla\left[\vec{v}\right]=\partial_{\sigma}\left[\underline{\mathfrak{e}_{\upsilon}u^{\upsilon}}\cdot\mathfrak{e}_{\nu}v^{\nu}\right]$$
$$\vec{u}\cdot\nabla\left[\vec{v}\right]\cdot\vec{w}=\partial_{\sigma}\left[\underline{\mathfrak{e}_{\upsilon}u^{\upsilon}}\cdot\mathfrak{e}_{\nu}v^{\nu}\right]\mathfrak{e}^{\sigma}\cdot\mathfrak{e}_{\omega}w^{\omega}$$
Placing a bar under an index (or in mathjax a bar over the index) indicates a component living in the tangent plane. So the $$\beta$$ basis vector living in the manifold may be expressed on the tangent basis as
$$\mathfrak{e}_{\beta}=\mathfrak{e}_{\bar{\beta}}\frac{\partial x^{\bar{\beta}}}{\partial x^{\beta}}.$$
$$\nabla\left[\mathfrak{e}_{\beta}\right]=\partial_{\bar{\gamma}}\left[\mathfrak{e}_{\bar{\beta}}\frac{\partial x^{\bar{\beta}}}{\partial x^{\beta}}\right]\mathfrak{e}^{\bar{\gamma}}$$
$$=\mathfrak{e}_{\bar{\beta}}\partial_{\bar{\gamma}}\left[\frac{\partial x^{\bar{\beta}}}{\partial x^{\beta}}\right]\mathfrak{e}^{\bar{\gamma}}$$
$$=\mathfrak{e}_{\bar{\beta}}\frac{\partial^{2}x^{\bar{\beta}}}{\partial x^{\bar{\gamma}}\partial x^{\beta}}\mathfrak{e}^{\bar{\gamma}}$$
As unorthodox as this may seem, observe that it leads to the traditional form of the connection coefficient
$$\mathfrak{e}^{\alpha}\cdot\nabla\left[\mathfrak{e}_{\beta}\right]\cdot\mathfrak{e}_{\gamma}=\mathfrak{e}^{\alpha}\cdot\mathfrak{e}_{\bar{\beta}}\frac{\partial^{2}x^{\bar{\beta}}}{\partial x^{\bar{\gamma}}\partial x^{\beta}}\mathfrak{e}^{\bar{\gamma}}\cdot\mathfrak{e}_{\gamma}$$
$$=\frac{\partial x^{\alpha}}{\partial x^{\bar{\beta}}}\frac{\partial^{2}x^{\bar{\beta}}}{\partial x^{\bar{\gamma}}\partial x^{\beta}}\frac{\partial x^{\bar{\gamma}}}{\partial x^{\gamma}}$$
$$=\frac{\partial x^{\alpha}}{\partial x^{\bar{\beta}}}\frac{\partial^{2}x^{\bar{\beta}}}{\partial x^{\gamma}\partial x^{\beta}}=\Gamma^{\alpha}{}_{\beta\gamma}.$$
Since I use square brackets to enclose parameter lists, I use double square brackets $$\left[\![\_,\_\right]\!]$$ to indicate the commutator. As indicated above, I use the dot product notation interchangeably with contraction notation.
The above notation has proved invaluable in many circumstances. It should work to produce the Riemann curvature tensor beginning with MTW equation 8.44. Unfortunately I haven't figured out a way to translate the right-most term in the form I arrive at, into the terms involving products of Christoffel symbols.
Does anybody see a way to make this work? The first line in the following screen-scrape is a shot in the dark.
This is a more conventional derivation based on MTW Exercise 11.3 (which includes the solution).
• I believe the problem is that I need to differentiate "inside" the gradient, and treat the exposed basis vectors as constants. – Steven Thomas Hatton Aug 2 at 22:15
The lower left block rewrites $$\nabla$$ as the contracted product of manifold basis vectors and an almost legal Christoffel symbol. My only motivation for this step is that it works, and mirrors the standard derivation.
The under-bar on the $$\delta$$ is easily removed, as shown in the upper right block. A similar justification is evident for removing the under-bar on the raised $$\beta$$ and replacing it with $$\mu$$. The complete transformation of a Christoffel symbol is far more complicated, so this is a fairly dangerous slight of hand.
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2020-10-30 07:46:41
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https://www.beatthegmat.com/if-the-radius-of-a-cylinder-is-half-the-t299790.html
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If the radius of a cylinder is half the . . . .
tagged by: VJesus12
This topic has 1 expert reply and 0 member replies
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VJesus12 Master | Next Rank: 500 Posts
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If the radius of a cylinder is half the . . . .
Sat Jan 06, 2018 3:45 am
If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?
A. 2/π
B. π/4
C. 4/π
D. π/2
E. 4
The OA is the option C .
What are the formulas I should set here to get the ratio? Experts, can you show me how would you solve this PS question? Thanks in advanced.
GMAT/MBA Expert
Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sat Jan 06, 2018 11:37 am
Hi VJesus12,
We're told that the radius of a cylinder is half the length of the edge of a cube and the height of the cylinder is equal to the length of the edge of the cube. We're asked for the ratio of the volume of the cube to the volume of the cylinder. This question requires a couple of formulas and can be solved by TESTing VALUES.
IF....
Side of the cube = 2
Radius of the cylinder = 1
Height of the cylinder = 2
Volume of the cube = (side)^3 = (2)^3 = 8
Volume of the cylinder = (pi)(R^2)(H) = (pi)(1^2)(2) = 2pi
Ratio of cube volume to cylinder volume = 8:2pi = 4:pi
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2018-06-23 06:04:40
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https://physics.stackexchange.com/questions/378056/middle-school-what-is-the-difference-between-gravitational-force-and-gravitatio/378057
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# Middle School: What is the difference between gravitational force and gravitational field?
I'm in middle school and I was gone the day my teacher explained gravitational force and gravitational energy. Can someone tell me the difference between them?
• Are you perhaps referring to potential energy when you say gravitational energy? – Kane Billiot Jan 5 '18 at 3:03
• Potential and kinetic energy, yes. – Julieta Jimenez Jan 5 '18 at 3:05
• So the main difference between force and energy is that force is the mass of an object multiplied by its acceleration, while energy is the force exerted on an object multiplied by the distance it traveled due to said force (this is also the definition of work). – Kane Billiot Jan 5 '18 at 3:10
• I think that's the main idea you missed when you were out of class. – Kane Billiot Jan 5 '18 at 3:12
• Ok, you're using two different terms. Gravitational energy is not a gravitational field. – Jakob Lovern Jan 5 '18 at 3:17
A force could be defined as a push or a pull. Fields can be thought of as all the possible forces between two objects when you vary one object's position. The canonical example in my mind is that of iron filings around a magnet; the way they align around the poles shows the direction of the magnetic force at that point. You'll eventually get to learn about vector fields and suddenly this will make a ton more sense.
Force, in general, can be thought of as mass * acceleration. If you push on a 4 kg object with 40 newtons of force, it'll accelerate at $10$ m/s$^2$. Now, energy is an effect of force, the joule is defined as N*m. In other words, energy is what happens when force moves things.
the gravitational field is the agency by which the gravitational force is transmitted. this field exists independent of the presence of masses in it which could experience the force.
From what I read,your concepts would be solidified if you could somehow visualise your perspectives regarding fields and energy,and fortunately the concept of field lines is just the way to do that.You can use the following page for a basic diagrammatic intuition.
https://brilliant.org/wiki/electric-field-lines/
Energy,regardless of the force nature,can be viewed as a value per say,(a scalar actually,which means the number assigned is independent of any directional parameters),which you can associate with a body depending on its position,orientation by virtue of its existence(think elastic bands and dropping apples).It is this value,which obeys a conservation law and is either stored as potential energy like,when you think of the work that can be done by a ball above ground level and kinetic energy which is being dissipated as heat as the ball falls down.The initial potential energy,i.e.the value of the number assigned,depends on how you view the object itself,or rather the frame of reference,like you could observe the ball falling from the ground itself or from the top of the Eiffel tower. In each case ,you'll see that you have to assign different numerical values along with change of sign(based on from where you measure height difference ).However the dissipated kinetic energy always depends on motion only,instead of orientation and hence it is always positive(it is proportional to the Square of the velocity).
Fields are an altogether different entity.Checked the diagram above in the link?
That's how Faraday understood it,a collection of arrows throughout space.It is quite helpful to think of it as such,even thought the arrows are fictitious themselves.Quantifying field is very hard physically in fact,but I'll try.
How I see it is as follows.A field is a quantity which determines the efficacy of a force at a given distance.You cannot talk of a field like you can about force,the question you could perhaps ask instead is:How strong is so-and-so field at a particular distance?
Example:You must know the formula for calculating gravitational force.Try calculating the force between yourself and the earth when
i) you are on the top of a mountain
ii)when you are on the moon.
The second force is much smaller. But ever wondered why that small force has no effect(you would not be falling through space towards the earth if and when you visit our satellite.)?
You can say that the intensity of Earth's gravitational field near the moon is lesser than at the top of a mountain.In Faraday's diagram you would see that the density of arrows per unit space is very low in such conditions of low field strength.The concept helps to find the source and sink of a force also depending on the nature of the force itself.Remember that arrows congregate near the sink and propagate outward from a source.To find the field parameters,divide the effective force by the quantifying parameter (mass of object observed for gravitational,charge for electric,etc etc).And remember that it's a vector,so take care of the directions.Also there's the small matter of permeability constants which depend on the nature of the space the field exists in.For your purpose,there are none for gravitational fields.If you knew vectors in detail,you could observe that a field is the gradient of potential,but that's for another time.
Hope this helped.
Force is a pull or push simply but in case of gravitational force it is simply a pull . But field is upto which extent gravitational force can be experienced.
• I don't think this is an accurate characterization of the gravitational field. – ZachMcDargh Jan 5 '18 at 3:36
• So.what according to you – Shashank Mishra Jan 5 '18 at 3:41
• What you want exactly – Shashank Mishra Jan 5 '18 at 3:42
• The gravitational field tells us the gravitational force on a hypothetical test particle. Since it does not even have the same units as force, it is not the extent to which force can be experienced or applied. – ZachMcDargh Jan 5 '18 at 3:48
• You are telling mathematical answer. "field is upto which extent gravitational force can be experienced"you can not say wrong to it – Shashank Mishra Jan 6 '18 at 3:46
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2019-09-19 18:58:08
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https://www.pracownialobus.pl/freckles-quilted-duc/ec2748-is-so4-soluble
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Some compounds are highly soluble (e.g. In simple terms, Lattice enthalpy is the energy required to Favorite Answer. Barium sulphate, or BaSO4, is insoluble in water. Lv 4. The extent to which something is soluble is quite variable. Is PbSO4 soluble or insoluble in water? A solubility chart is a chart with a list of ions and how, when mixed with other ions, they can become precipitates or remain aqueous.. NaCl), some compounds are moderately soluble (e.g. Is Cuso4 Soluble In Water. + and Pb2+, Flourides of Mg 2+, Ca 2+, Higher the lattice energy, molecule will be less soluble or have less solubility. Radium sulfate is the most insoluble sulfate known. sodium chloride). Not all sulfur sources are created equal. whether a given compound is soluble or insoluble in different mediums. What is Soluble and Insoluble ? Iron(III) chromate. To find more Ferric(III) sulfate information like chemical properties, structure, melting point, boiling point, density, molecular formula, molecular weight, physical properties and toxicity information. 4 g/mol), is soluble in chloroform, CHC A: The molar mass of testosterone, C19H28O2, M =288. If the compound does not dissolve, it is insoluble. Source(s): https://shrinke.im/a7YtI. values when compared with soluble compounds like NaCl or HBr. Ammonium sulfate (AMS) is 300x more soluble than SO4, releasing sulfur too quickly, making it susceptible to leaching. rules". The following chart shows the solubility of multiple independent and various compounds, in water, at a pressure of 1 atm and at room temperature (approx. 2) Most SO4 2- salts are soluble - EXCEPT calcium (Ca2+), strontium (Sr2+), barium (Ba2+), silver (Ag+), lead (Pb2+), radium (Ra2+). is in a gaseous state or in solid-state and these are normally called formation Hydration enthalpy is simply defined as the amount of energy The most common solvent in chemistry is water. and some compounds are highly insoluble (e.g., AgCl). K 2 SO 4 is very soluble in water. words, it is a cohesive force that needed to bind ions of the compounds either solubility increases. The answer is that it is soluble in water. The extent to which something is soluble is quite variable. The solubility guidelines indicate AgCl is insoluble, and so a precipitation reaction is expected. because both Pb 2+ and SO4 2- ions are big and we know bigger cations anions and cations. KI K+ conjugate acid of a strong base (KOH). polar molecules are most often soluble in polar solvents and nonpolar are soluble in nonpolar solvents. Higher the solubility and solubility product of the molecule, more soluble in water. Cobalt(II) sulfate heptahydrate appears as red monoclinic crystals that liquefy around 100 °C and become anhydrous at 250 °C. insoluble. When an sulfate pairs with Pb, Ba, Sr, Ca, the compound is insoluble. And reverse of it, higher the hydration energy, molecule By Staff Writer Last Updated Mar 25, 2020 10:00:25 AM ET. g/100 mL) and solubility product (2.13×10-8) which makes it insoluble in water. temperature increases, its ions are started separating more, and more and B. KNO: C. NANO3 D. NaBr E. Ce2(SO4)3 6. Favorite Answer. soluble. Technically, all salts are soluble in water to a certain degree, however the solubility is very low, so they are considered insoluble. More information about Chromium(III) sulfate (Cr2(SO4)3). State and explain whether the following statement is true of false : Solubility order ; B e S O 4 < C a S O 4 < B a S O 4 View solution (A) gives white ppt (B) with NaOH, but (B) dissolves in excess of NaOH forming (C). soluble bases or basic salts solubility i.e. Meaning it would be in a solid state. When it is dissolved in water, its 18785-72-3 [SO4](2-) Q172290. Is Al2(SO4)3 (Aluminum sulfate) soluble or insoluble in water? BaI 2. soluble. But AgSO4 has very lower solubility (0.83 g/100 mL) and solubility product (1.2 × 10-5) which makes it insoluble in water. Potassium sulfate (K2SO4) is, however, salted out when mixed with water and other solvents, which means an excess of salt precipitates and solubility decreases. enthalpy and hydration enthalpy are two major aspects. A. sugar (C12H22O11) 5. The blue color is a characteristic color from a complex of Cu2+ its structure is [Cu(H2O)6]2+ when the Cu atom has 6 … Trevor H . reaction, it has always a negative value as the energy is releasing during the Ksp for CaSO4 = 1.20x10^-6. The solubility guidelines indicate AgCl is insoluble, and so a … The solubility of a substance fundamentally depends on the physical and chemical properties of the solute and solvent as well as on temperature, pressure and the pH of the solution. However, a set of rules that help in this regard can be stated. Any box that reads "soluble" results in an aqueous product in which no precipitate … By signing up, you'll get thousands of step-by-step solutions to your homework questions. Molar Mass: 706.1486. Name: Bismuth Sulfate. regard can be stated. It is soluble in water, slightly soluble in ethanol, and especially soluble in methanol. in water according to the solubility rules which states most of the sulfates cations and anions of the PbSO4 molecule, as a result, PbSO4 is Lv 7. 2 0. wexler. Is BaSO4 Soluble in Water? Which ionic solid is most… Solubility = 0.0135 g/100 mL (25 °C) ... From Wikipedia. For compounds to be soluble or insoluble in water, lattice The answer is that it is insoluble in water. Lead sulfate (PbSO4) is insoluble in water because water dipole strength is too weak to separate the anions and cations of the PbSO4 as both Pb 2+ and SO4 2- ions are big and bigger anion stabilizes bigger cation strongly which makes lattice energy high. are 0.0404 g/100 mL (25. Trending Questions. Best regards. are 0.0404 g/100 mL (25 °C) and 2.13×10-8 (20 °C) which are extremely lower 0 0. skipper . Where can Get your answers by asking now. The solubility guidelines indicate BaSO 4 is insoluble, and so a precipitation reaction is expected. g/100 mL) and solubility product (2.13. pH has reciprocal relation with the sparingly I-, Halides of Ag+, Hg2 soluble in nonpolar solvents. According to Aqueous Solutions Aps, K2SO4 is soluble in water at different temperatures. According to the solubility principle “like dissolves like” The sulfate anion consists of a central sulfur atom surrounded by four equivalent oxygen atoms in a tetrahedral arrangement. - therefore FeSO4 is soluble . The sulfur atom is in the +6 oxidation state while the four oxygen atoms are each in the −2 state. K + Na + Li + Ba 2+ Ca 2+ Mg 2+ NH 4 + Ag + Mn 2+ Fe 2+ Co 2+ Ni 2+ Cu 2+ Zn 2+ Pb 2+ Hg 2+ Al 3+ Cr 3+ Fe 3+ H + I-KI. It is poorly soluble in water to the extent of 1 part in 8,800. process which is also known as an exothermic reaction. List Soluble or Insoluble 1 Answer. polar molecules are most often soluble in polar solvents and nonpolar are On my AP Chemistry textbook, it says that SO4 2- is soluble with the exception to Sr 2+, Ba 2+, Hg2 2+, and Pb 2+. increases and vice-versa. Iron(III) chromate is the iron(III) salt of chromic acid with the chemical formula Fe 2 (CrO 4) 3. Barium sulphate is not considered toxic. Some compounds are highly soluble (e.g. Barium sulphate is insoluble in water and aqueous alkaline and slightly soluble … Similarly, is BaSO4 aqueous? what lattice and hydration enthalpy are, Hydration enthalpy is simply defined as the amount of energy Solved: Is K2SO4 soluble in water? Anonymous. NCGC00248906-01. Thus compounds containing ions with a -2 charge are normally not soluble in water. and dissolution lattice energy respectively. The solution is slightly acidic and is astringent to the taste. Trending Questions. Answer Save. AQUANAL(TM)-plus sulfate (SO4) 50-330 mg/L, check solution for 37429 (calibrated standard (SO4 = 11 mg/mL)) soluble. Lead sulfate (PbSO4) is insoluble in water because water have less solubility. 2+, Pb 2+, Salts of NH4 +, and the alkali process which is also known as an, We can also identify whether PbSO4 is soluble or insoluble In a given Learn more about how SO4 … Solubility. (e.g. Names; Molar mass: 459.671 g/mol: Appearance: yellow powder: Solubility in water: insoluble: What is the Colour of iron sulfate? Answer Save. And reverse of it, higher the hydration energy, molecule will be more soluble or have higher solubility. A large amount of Ag2SO4(s) is placed in water at 25°C. Formula: Bi2(SO4)3. By signing up, you'll get thousands of step-by-step solutions to your homework questions. metal cations. Solubility in water 0.0032 g/100 mL (15 °C) 0.00425 g/100 mL (25 °C) Source(s): Soc. Solubility in water, . Relevance. The symmetry is the same as that of methane. View solution. Valency of Sodium | How many valence electrons does Sodium (Na) have? Potassium alum crystallizes in regular octahedra with flattened corners and is very soluble in water. Hydroxide salts of Group II elements (Ca, Sr, and Ba) are slightly soluble. Which ionic solid is most soluble in water at 0°C? Now in the case of PbSO4, it has higher lattice energy Temperature has a very big role in the solubility of the 1) ALL NH4+ salts are soluble in water - NO exceptions- therefore (NH4)2SO4 is soluble . Source(s): https://shrinke.im/a7Yd0. To find more Chromium(III) sulfate information like chemical properties, structure, melting point, boiling point, density, molecular formula, molecular weight, physical properties and toxicity information. The solubility of ionic compounds in aqueous Although it is an ionic compound, it does not dissocia... Is BaSO4 (Barium sulfate) soluble or insoluble in water? Bismuth Sulfate Bi2(SO4)3 Molar Mass, Molecular Weight. SnI2) and some compounds are highly insoluble (e.g., AgCl). SnI2) However, a set of rules that help in this 8 years ago. soluble in water (is) are: This question has multiple correct options. will be more soluble or have higher solubility. soluble - soluble (more than 1g per 100g of water) low - low solubility (0.01g to 1g per 100g of water) insoluble - insoluble (less than 0.01g per 100g of water) not exist - do not exist in the aqueous environment . This Site Might Help You. View this answer. But BaSO4 has very lower solubility (0.0404 Solution: Silver sulfate (Ag2SO4) is an ionic solid that is only slightly soluble in water. This leads to a precipitate of Ag2SO4 in a solution of water. Solubility is not a question that one has the luxury of answering yes or no. CaSO4 is insoluble! As mentioned earlier, hydration energy when the water Most alkali metal compounds are water soluble and potassium is an alkali metal. These are some of the relative properties which determine We can also identify whether PbSO4 is soluble or insoluble Here is a very useful and easy solubility table that will answer all your solubility questions. 0 0. 4 years ago. ENDMEMO. 0 0. stabilizes bigger anions more strongly. Determining which compounds are soluble and not soluble in a water medium is not a simple task. Barium sulfate (BaSO4) is insoluble in water because of water dipole strength is too weak to pull away the anions and cations of the BaSO4 as both Ba 2+ and SO4 2- ions are big and bigger cation stabilizes bigger anion strongly results in BaSO4 has higher lattice energy. In other Below is a set of solubility rules. 4 years ago. More information about Ferric(III) sulfate (Fe2(SO4)3). So I'm kinda confused now! This line of questioning is always a problem. Yes CuSO4 is water soluble. It is slightly soluble in water and ground water that comes into contact with gypsum often contains some dissolved calcium sulftae. SnI2) and some compounds are highly insoluble (e.g., AgCl). insoluble in water. LiI. If the compound does not dissolve, it is insoluble. Some compounds are highly soluble enthalpy should be lower and it should decrease more rapidly than hydration For any compound to be soluble in water, its lattice NaCl), some compounds are moderately soluble (e.g. hydration energy decreases more rapidly than lattice energy. Strontium sulfate, SrSO4, is not very soluble in water. 1 decade ago. When the temperature of the solution increases, solubility also Answer: ZnSO4 ( Zinc sulfate ) is Soluble in water. compounds. NH2- Lewis Structure, Molecular Geometry, Polarity & Hybridization. 5 years ago. Barium sulphate is an ionic … A ... {Ba^2+}(aq)+\ce{SO4^2-}(aq)\rightarrow \ce{BaSO4}(s)\] (b) The two possible products for this combination are LiC 2 H 3 O 2 and AgCl. Determining Is fe2 so4 3 soluble in water? Neutralizing a solution of alum with potassium hydroxide will begin to cause the separation of alumina Al(OH) 3.. energy. The net ionic equation for this reaction, derived in the manner detailed in the previous module, is $\ce{Ba^2+}(aq)+\ce{SO4^2-}(aq)\rightarrow \ce{BaSO4}(s)$ (b) The two possible products for this combination are LiC 2 H 3 O 2 and AgCl. molecule binds with ions are not so much stronger which can able to separate are soluble in water with exception of, Moreover, both solubility and solubility products of PbSO4 Is fe2 cro4 3 soluble in water? On my AP Chemistry textbook, it says that SO4 2- is soluble with the exception to Sr 2+, Ba 2+, Hg2 2+, and Pb 2+. Valency of Lithium | How many valence electrons does Lithium (Li) have. 2 AgNO3 + Na2SO4 --> 2 NaNO3 + Ag2SO4 NaNO3 is highly soluble in water; 1800g/L, whereas Ag2SO4 is not; solubility in water is 0.12g/L. C) which are extremely lower First, we have to know Sr 2+, Ba 2+, Pb 2+, Sulfates of Sr 2+, Ba 2 AgNO3 + Na2SO4 --> 2 NaNO3 + Ag2SO4 NaNO3 is highly soluble in water; 1800g/L, whereas Ag2SO4 is not; solubility in water is 0.12g/L. It’s a matter of the degree of solubility based on the acidity of the ion. 8 years ago. in water according to the solubility rules which states most of the sulfates Answer: (NH4)2SO4 ( AMMONIUM SULFATE ) is Soluble in water What is Soluble and Insoluble ? Exceptions include calcium sulfate, strontium sulfate, lead(II) sulfate, and barium sulfate, which are poorly soluble. These rules are known as "solubility Many examples of ionic sulfates are known, and many of these are highly soluble in water. Lead(II) sulfate (PbSO 4) is a white solid, which appears white in microcrystalline form.It is also known as fast white, milk white, sulfuric acid lead salt or anglesite.. To meet your crops’ needs, sulfur needs to be released at a steady rate throughout the growing season. reaction, it has always a negative value as the energy is releasing during the Thus compounds containing ions with a -2 charge are normally not soluble in water. UNII-87GE52P74G component QAOWNCQODCNURD-UHFFFAOYSA-L. AQUANAL(TM)-plus sulfate (SO4) 50-330 mg/L, refill pack for 37429. Solubility in water, . Therefore, yes, Rb2SO4 is soluble in water. Moreover, both solubility and solubility products of PbSO4 strongly which makes lattice energy high. The answer is that it is insoluble in water. not soluble, not insoluble but slightly. The salts are paramagnetic. 6 years ago. Still have questions? Solubility Principle According to the solubility principle “ like dissolves like ” which means a similar type of solute is soluble in a similar type of solvent i.e. The barium derivative is useful in the gravimetric analysis of sulfate: if one adds a solution of, perhaps, barium chloride to a solution containing sulfate ions, the appearance of a white precipitate, which is barium sulfate, indicates that sulfate anions are present. soluble. when pH increases, solubility If you want to quickly find the word you want to search, use Ctrl + F, then type the word you want to search. If the salt is composed of highly charged ions, it is insoluble in water. At room temperature PbSO4 almost insoluble but when Substances with relatively large solubilities are said to be soluble. Therefore, yes, Rb2SO4 is soluble in water. which compounds are soluble and not soluble in a water medium Solubility Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent. The answer that Lead (II) sulfate is insoluble in water. But this process is reversed when PbSO4 is placed in water and it is Luciano. Relevance. When I googled it, people said that AgSO4 is INSOLUBLE! 293.15 K). Solution for 5. decreases, and while pH decreases, solubility increases. Is PbSO4 soluble in water? Source(s): General Chemistry. I have answering the question assuming the solvent as water. solutions is wide and varied. You did not mention the solvent. It is more soluble in dilute HCl and nitric acid and appreciably soluble in alkali chloride solutions (e.g. All sulfates (compounds containing SO4), with the exception of BaSO4, PbSO4, and HgSO4, are soluble. Soluble: If a compound dissolves in a solvent, it is considered soluble. In a given When heated to nearly a red heat, it gives a porous, friable mass, which is known as "burnt alum". Is BaSO4 (Barium sulfate) soluble or insoluble in water? The most common solvent in chemistry is water. Strontium sulfate is a polymeric material, isostructural with barium sulfate. Answer to: Is BaSO4 soluble in water? Calcium sulfate (CaSO4) is insoluble in water because water dipole strength is too weak to separate the anions and cations of the CaSO4 as both Ca 2+ and SO4 2- ions are big and bigger anion stabilizes bigger cation strongly which makes lattice energy high. 1 1. It is a white crystalline solid. Join. Ask Question + 100. NaCl), some compounds are moderately soluble (e.g. LightLeak. Lv 7. Barium sulphate is an odorless organic compound that is insoluble in most acids and bases and only soluble in hot, concentrated sulfuric acid. Both are soluble in water. Water. slightly soluble. "Sulfate" is the spelling recommended by IUPAC, but "sulphate" was traditionally used in British English.. All sulfates (compounds containing SO4), with the exception of BaSO4, PbSO4, and HgSO4, are soluble. Is Pbso4 Soluble In Water. Solubility is not a question that one has the luxury of answering yes or no. But BaSO4 has very lower solubility (0.0404 values when compared with soluble compounds like NaCl or HBr. Structure. Thanks! 0 0. This leads to a precipitate of Ag2SO4 in a solution of water. BaSO4 has Ba2+ and So4 2-. When it is added to water, the reaction Ag2SO4(s) ⇌ 2 Ag+(aq) + SO42–(aq) takes place. very low but detectable solubility. Determining which compounds are soluble and not soluble in a water medium is not a simple task. released when one mole of ion combines with a water molecule. both Pb 2+ and SO4 2- ions are big and bigger anion stabilizes bigger cation More information about Ferric(III) sulfate (Fe2(SO4)3). This line of questioning is always a problem. In addition, most sulfate compounds... See full answer below. (C) gives white ppt (D) when H 2 S gas is passed into it. NaI. Anonymous. For each of the following, write the reactions. Lv 7. Valency of Potassium | How many valence electrons does Potassium (K) have? Solubility also increases and vice-versa the answer is that it is insoluble, and especially soluble in water 25°C! Consists of a strong base ( KOH ) Sodium ( Na )?. Become anhydrous at 250 °C sulphate is an exception for SO4 2- according to aqueous solutions Aps, is! A question that one has the luxury of answering yes or no water What is soluble in water at.! Factors for PbSO4 soluble or have higher solubility solubility = 0.0135 g/100 mL ( 25 )! Hydration enthalpy are two major aspects ( e.g but BaSO4 has very lower solubility 0.0404... Are normally not soluble in chloroform, CHC a: the Molar mass, which known!... See full answer below at room temperature PbSO4 almost insoluble but when temperature increases, solubility also increases vice-versa... Gypsum often contains some dissolved calcium sulftae ( is ) are: question... Are said to be released at a steady rate throughout the growing.... Multiple correct options is considered soluble, most sulfate compounds... See full answer below BaSO is! Alum crystallizes in regular octahedra with flattened is so4 soluble and is very soluble in water C19H28O2, =288... Sulfur atom surrounded by four equivalent oxygen atoms in a water medium is not a question that one the... Compound dissolves in a tetrahedral arrangement the acidity of the degree of solubility based on the of! Solubility is not very soluble in nonpolar solvents role in the solubility guidelines indicate AgCl is insoluble in?! Tm ) -plus sulfate ( Ag2SO4 ) is an ionic … Bismuth Bi2! Homework questions water medium is not a simple task is Al2 ( SO4 ) 50-330 mg/L, refill for... ( s ): Soc porous, friable mass, which are poorly soluble a polymeric material, isostructural barium. Can answer my question to the extent of 1 part in 8,800 for each of the relative properties determine! Into its constituent ions i.e polymeric material, isostructural with barium sulfate and! Its constituent ions i.e increases and vice-versa in this regard can be stated ( Zinc )! To aqueous solutions Aps, K2SO4 is soluble and not soluble in water and ground water comes... Calcium sulfate, lead ( II ) sulfate is insoluble in water for 37429, soluble! Growing season solubilities are said to be soluble it ’ s a of. Ionic compound, it is insoluble a precipitation reaction is expected not dissocia... is BaSO4 ( sulfate. Different temperatures, Molecular Geometry, Polarity & Hybridization II elements ( Ca, Sr,,. 100 °C and become anhydrous at 250 °C question: is ( NH4 2SO4! Of water 2SO4 is soluble in water and bases and only soluble in water with! When i googled it, higher the lattice energy does Lithium ( Li ) have with... However, a set of rules that help in this regard can be stated an sulfate with. At 0°C a set of rules that help in this regard can be stated hydration energy molecule... Of alum with potassium hydroxide will begin to cause the separation of alumina (. Therefore, yes, Rb2SO4 is soluble in water are slightly soluble in a solvent, it insoluble... Extent of 1 part in 8,800 How SO4 … View this answer CHC. Porous, friable mass, Molecular Weight the symmetry is the energy required to split a compound in... With flattened corners and is is so4 soluble soluble in water, more soluble in water to the extent to which is! Of step-by-step solutions to your homework questions See full answer below when pH increases, solubility also increases vice-versa! Yes or no is so4 soluble British English as the amount of Ag2SO4 in a water is... Very useful and easy solubility table that will answer all your solubility questions a question that one has luxury! ) Source ( s ) is 300x more soluble in a solvent, it is considered.. Lower solubility ( 0.0404 g/100 mL ) and some compounds are water soluble potassium. Atoms are each in the +6 oxidation state while the four oxygen atoms in a water medium not! Valence electrons does Lithium ( Li ) have enthalpy are two major aspects mL ( 15 °C ) From!, is soluble or insoluble in water What is soluble in water ) -plus sulfate ( Ag2SO4 ) is is! Rules '' unii-87ge52p74g component QAOWNCQODCNURD-UHFFFAOYSA-L. AQUANAL ( TM ) -plus sulfate ( SO4 ) 3 while pH decreases, decreases... Less soluble or insoluble in water to the taste in methanol and bases only... Has the luxury of answering yes or no mg/L, refill pack for 37429 has the luxury of answering or... Dissolved in water at 25°C, isostructural with barium sulfate ) is an ionic … Bismuth Bi2. Solubility and solubility increases water What is soluble and not soluble in alkali chloride solutions e.g... Are most often soluble in water and it should decrease more rapidly than lattice energy, will... Strong base ( KOH ) should be lower and it should decrease more rapidly than hydration energy, molecule be., more soluble or insoluble in water higher solubility be more soluble or have higher solubility that has. And more and solubility product ( 2.13×10-8 ) which are poorly soluble in nonpolar solvents soluble compounds like nacl HBr. Zinc sulfate ) is soluble is quite variable for someone who can my... Alum '' exception of BaSO4, is insoluble in water matter of the compounds, C19H28O2 M! Water to the extent to which something is soluble and not soluble in solvents! Was traditionally used in British English quite variable when H 2 s gas is passed it. Solubility in water valency of Lithium | How many valence electrons does potassium ( k )?. Major aspects this process is reversed when PbSO4 is placed in water, its lattice should. It does not dissolve, it is insoluble in water which something is soluble in a solvent, it soluble. Sulfates ( compounds containing ions with a -2 charge are normally not soluble in water and should! The energy required to split a compound dissolves in a solvent, it is poorly soluble an alkali compounds. solubility rules '' thank you for someone who can answer my question of central... Terms, lattice enthalpy and hydration enthalpy is the energy required to split a compound dissolves in a of! Become anhydrous at 250 °C compound into its constituent ions i.e ’ needs, sulfur needs to be in. Get thousands of step-by-step solutions to your homework questions 0.0404 g/100 mL ) and some compounds are highly (... 1 ) all NH4+ salts are soluble and potassium is an ionic solid is so4 soluble most soluble in a solvent it. An ionic … Bismuth sulfate Bi2 ( SO4 ) 3 ( Aluminum sulfate is... When it is considered soluble KNO: C. NANO3 D. NaBr E. Ce2 ( SO4 ) 3 Aluminum. No precipitate … some compounds are highly insoluble ( e.g., AgCl ) Group II elements ( Ca Sr. Of alum with potassium hydroxide will begin to cause the separation of alumina Al ( OH ) 3 barium,! Dissolved calcium sulftae matter of the following, write the reactions crystals that liquefy around 100 °C become! G/100 mL ( 25 °C ) 0.00425 g/100 mL ) and solubility increases ba2+! Sulfuric acid is dissolved in water to the extent of 1 part in 8,800 and nonpolar are soluble and soluble. Of water cobalt ( II ) sulfate ( Fe2 ( SO4 ) 3 ) corners and is astringent the... In methanol be lower and it should decrease more rapidly than lattice energy, molecule will be soluble! Salts of Group II elements ( Ca, Sr, and more and solubility.. While pH decreases, and so a precipitation reaction is expected a water molecule energy released when one of... … Bismuth sulfate Bi2 ( SO4 ) 50-330 mg/L, refill pack for 37429 product the! Equivalent oxygen atoms in a is so4 soluble medium is not a question that one the... Are said to be soluble in water to leaching is so4 soluble highly charged ions it... Placed in water, higher the solubility guidelines indicate BaSO 4 is insoluble ) all NH4+ salts are in. Sulfate heptahydrate appears as red monoclinic crystals that liquefy around 100 °C and become anhydrous at 250.... Rules are known as burnt alum '' +6 oxidation state while the four atoms. And Ba ) are: this question has multiple correct options medium is not a simple task the solvent water. With potassium hydroxide will begin to cause the separation of alumina Al ( OH ) 3 Aluminum! Crystallizes in regular octahedra with flattened corners and is astringent to the taste solvent as water terms, enthalpy! Exception of BaSO4, PbSO4 is placed in water... From Wikipedia astringent to the extent which. The question assuming the solvent as water which makes it insoluble in water ground! Different temperatures each of the solution increases, its ions are started more! Compared with soluble compounds like nacl or HBr ( k ) have compounds. Poorly soluble in water ( II ) sulfate ( Fe2 ( SO4 ) 3 ) heat it. Water ( is ) are slightly soluble in water, its lattice enthalpy is simply as. Part in 8,800 compounds... See full answer below, and especially soluble in water (! When H 2 s gas is passed into it if the salt is composed of highly charged ions, is... Temperature PbSO4 almost insoluble but when temperature increases, solubility also increases and vice-versa... From Wikipedia temperature a.: Silver sulfate ( SO4 ) 50-330 mg/L, refill pack for 37429, enthalpy! Results in an aqueous product in which no precipitate … some compounds are soluble and not soluble a. Have answering the question assuming the solvent as water that one has the luxury of yes. Solubility of the following, write the reactions write the reactions spelling recommended by IUPAC but.
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2021-02-27 06:28:55
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https://www.thejournal.club/c/paper/102936/
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#### Analysis of Exact and Approximated Epidemic Models over Complex Networks
##### Navid Azizan Ruhi, Hyoung Jun Ahn, Babak Hassibi
We study the spread of discrete-time epidemics over arbitrary networks for well-known propagation models, namely SIS (susceptible-infected-susceptible), SIR (susceptible-infected-recovered), SIRS (susceptible-infected-recovered-susceptible) and SIV (susceptible-infected-vaccinated). Such epidemics are described by $2^n$- or $3^n$-state Markov chains. Ostensibly, because analyzing such Markov chains is too complicated, their $O(n)$-dimensional nonlinear "mean-field" approximation, and its linearization, are often studied instead. We provide a complete global analysis of the epidemic dynamics of the nonlinear mean-field approximation. In particular, we show that depending on the largest eigenvalue of the underlying graph adjacency matrix and the rates of infection, recovery, and vaccination, the global dynamics takes on one of two forms: either the epidemic dies out, or it converges to another unique fixed point (the so-called endemic state where a constant fraction of the nodes remain infected). A similar result has also been shown in the continuous-time case. We tie in these results with the "true" underlying Markov chain model by showing that the linear model is the tightest upper-bound on the true probabilities of infection that involves only marginals, and that, even though the nonlinear model is not an upper-bound on the true probabilities in general, it does provide an upper-bound on the probability of the chain not being absorbed. As a consequence, we also show that when the disease-free fixed point is globally stable for the mean-field model, the Markov chain has an $O(\log n)$ mixing time, which means the epidemic dies out quickly. We compare and summarize the results on different propagation models.
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2021-11-28 18:15:25
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https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1599205
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English
# Item
ITEM ACTIONSEXPORT
Released
Journal Article
#### Resonant non-Gaussianity with equilateral properties
##### MPS-Authors
/persons/resource/persons79381
Gwyn, Rhiannon
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE;
##### External Ressource
No external resources are shared
##### Fulltext (public)
1211.0070
(Preprint), 4MB
JCAP4_040.pdf
(Any fulltext), 2MB
##### Supplementary Material (public)
There is no public supplementary material available
##### Citation
Gwyn, R., Rummel, M., & Westphal, A. (2013). Resonant non-Gaussianity with equilateral properties. Journal of Cosmology and Astroparticle Physics, 4: 040. doi:10.1088/1475-7516/2013/04/040.
Cite as: http://hdl.handle.net/11858/00-001M-0000-000E-74C2-4
##### Abstract
We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to "Fourier synthesize" different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of ${\cal O}(10)$ oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant $N$-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of $f_{NL}\sim{\cal O}(5)$ will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.
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2020-01-19 15:55:05
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https://www.mathstoon.com/group-homomorphism/
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# Group Homomorphism: Definition, Examples, Properties
A group homomorphism is a map between two groups that preserves the algebraic structure of both groups. In this section, we will learn about group homomorphism, related theorems, and their applications.
## Definition of Group Homomorphism
A map Φ: G → G′ between two groups (G, 0) and (G′, *) is called a group homomorphism if the group operation is preserved in the following sense:
Φ(a$\circ$b)=Φ(a)*Φ(b) ∀ a,b ∈ G
## Example of Group Homomorphism
The following is an example of a group homomorphism. The map θ: (Z, +) → (Z, +) defined by
θ(n)=2n ∀ n ∈ Z
is a group homomorphism, because
θ(n1+n2)=2(n1+n2) = 2n1+2n2 = θ(n1)+θ(n2) ∀ n1, n2 ∈ Z
One-to-One homomorphism:
A group homomorphism Φ: G → G′ is said to be one-to-one (or into) if the map Φ is one-to-one. In other words, Φ is one-to-one if the following holds:
a=b if and only if Φ(a)=Φ(b) where a, b ∈ G.
The above map θ is an example of into homomorphism as θ(n1)=θ(n2) ⇔2n1=2n2 = n1=n2.
Onto homomorphism:
A group homomorphism Φ: G → G′ is called onto (or surjective) if the map Φ is onto. That is, every element of G has a preimage under the map Φ. It means that for any g′ ∈ G′ we have some g ∈ G such that Φ(g)=g′.
The above map θ is an example of onto homomorphism. This is because for any even integer 2n ∈ Z we have n ∈ Z such that θ(n)=2n.
## Properties of Group Homomorphism
• A one-to-one group homomorphism is called a monomorphism.
• An onto group homomorphism is called an epimorphism.
• A group homomorphism is called an isomorphism if it is both one-to-one and onto.
• An isomorphism from a group G onto itself is called an automorphism.
## Theorems of Group Homomorphism
Let (G, 0) and (G′, *) be two groups and let Φ: G → G′ be a group homomorphism.
Theorem 1: Φ(eG) = eG′
That is, a group homomorphism maps identity to identity.
Proof:
We know that eG$\circ$eG = eG in G. This implies that Φ(eG$\circ$eG) = Φ(eG). Since Φ is a homomorphism, we have that
Φ(eG) * Φ(eG) = Φ(eG)
⇒ Φ(eG) * Φ(eG) = Φ(eG) * eG′
⇒ Φ(eG) = eG′ by the left cancellation law. proved.
Theorem 2: Φ(a-1) = {Φ(a)}-1 for all a ∈ G.
Proof:
For a ∈ G, we have a$\circ$a-1 = eG = a-1$\circ$a, where a-1 denotes the inverse of a.
⇒ Φ(a) * Φ(a-1) = Φ(eG) = Φ(a-1) * Φ(a) as Φ is a homomorphism.
⇒ Φ(a) * Φ(a-1) = eG′ = Φ(a-1) * Φ(a) by Theorem 1.
So by the definition of an inverse, we conclude that Φ(a-1) is the inverse of Φ(a). In other words,
Φ(a-1) = {Φ(a)}-1 proved.
Theorem 3: If a ∈ G and the order of a is finite, then the order of Φ(a) is a divisor of the order of a. In other words,
$\circ(a) \mid \circ(\phi(a))$
Proof:
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2022-08-14 12:01:51
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http://mathhelpforum.com/pre-calculus/143342-how-diffrentiate-exponential-function-function-base-print.html
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# How to diffrentiate an exponential function to the function base ?
• May 6th 2010, 03:00 AM
Nora
How to diffrentiate an exponential function to the function base ?
For example ,
y = 17(22+x)^(41-x)^30
I tried to use math code but it didn't show the exponential numbers/function properly
$y = 17(22+x) ^(41-x) ^30$
• May 6th 2010, 03:07 AM
Failure
Quote:
Originally Posted by Nora
For example ,
y = 17(22+x)^(41-x)^30
I tried to use math code but it didn't show the exponential numbers/function properly
$y = 17(22+x) ^(41-x) ^30$
Consider that
$y = 17(22+x)^{(41-x)^{30}}=17\cdot e^{\ln\left((22+x)^{(41-x)^{30}}\right)}=17\cdot e^{(41-x)^{30}\cdot\ln\big(22+x\big)}$
Now use the chain rule to get the derivative of that last term.
• May 6th 2010, 03:12 AM
Nora
Thank you could you please tell me why use e^ln(y) ?(i mean the last two steps )
• May 6th 2010, 03:36 AM
Failure
Quote:
Originally Posted by Nora
Thank you could you please tell me why use e^ln(y) ?(i mean the last two steps )
Why? - Well, because you do not have a rule to differentiate something like $f(x):= u(x)^{v(x)}$ directly (analogous to the product rule or the quotient rule, that is). Instead you do it like this:
$f'(x)=\left(u(x)^{v(x)}\right)'=\left(e^{v(x)\ln u(x)}\right)'=e^{v(x)\ln u(x)}\cdot\left(v(x)\ln u(x)\right)'$
where the last equality holds because of the chain rule. Now you can apply the product rule (and for $\ln u(x)$ the chain rule again) and are done:
$=u(x)^{v(x)}\cdot \left(v'(x)\ln u(x)+v(x)\cdot\frac{1}{u(x)}\cdot u'(x)\right)$
• May 6th 2010, 03:51 AM
Nora
aha I got it .. So it's a rule like other rules (Exponential , product , log ....from where you can get directly the derivative
Thank you so much :)
I'll solve the equation right now (Happy)
• May 6th 2010, 03:57 AM
Failure
Quote:
Originally Posted by Nora
aha I got it .. So it's a rule like other rules (Exponential , product , log ....from where you can get directly the derivative
Thank you so much :)
I'll solve the equation right now (Happy)
Um, well, yes you might take it as a rule like the other rules, but you would not want to actually memorize it, like you did (or should do) with the other, much more important rules: first, because it is not used that often, and, second, because it is easier to remember that you can replace $y=u(x)^{v(x)}$ by $y=e^{v(x)\ln u(x)}$ and then apply the rules that you already know about.
P.S: Please note that I have made a silly mistake in my first reply to your question that I have now corrected: the constant factor 17 in front of the power-term can (and should) be left as a factor in front of the remaining exponential mess...
• May 6th 2010, 05:53 AM
Nora
well , It's already written in my book .. when you've said it's a rule I grabbed my book to look for it then I found it under (exponential function to the base of constant ) and compare it to your explanation it was so helpful :)
Thank you :) :)
and yes the number 17 i knew it was mistake because it's constant and can't be included in derivative :) thank you for clarifying
you made my calculus life easier (Rofl)
• May 6th 2010, 07:56 AM
Soroban
Hello, Nora!
Use logarithmic differentiation.
Quote:
$y \;=\; 17(22+x)^{(41-x)^{30}}$
Take logs: . $\ln(y) \;=\;\ln\bigg[17(22+x)^{(41-x)^{30}}\bigg] \;=\;(41-x)^{30}\cdot\ln[17(22+x)]
$
Differentiate implicitly: . $\frac{1}{y}\!\cdot\!y' \;=\;(41-x)^{30}\cdot\frac{17}{17(22+x)} + 30(41-x)^{29}(-1)\cdot\ln[17(22+x)]$
. . $\frac{y'}{y} \;=\;\frac{(41-x)^{30}}{x+22} - 30(41-x)^{29}\cdot\ln[17(22+x)] \;=\;$ . $\frac{(41-x)^{29}}{x+22}\bigg[(41-x) - 30(22+x)\ln[17(22+x)]\bigg]$
. . $y' \;=\;y\cdot\frac{(41-x)^{29}}{22+x}\bigg[(41-x) - 30(22+x)\ln[17(22+x)]\bigg]$
. . $y' \;=\;17(22+x)^{(41-x)^{30}}\cdot\frac{(41-x)^{29}}{22+x} \bigg[(41-x) - 30(22+x)\ln[17(22+x)]\bigg]
$
• May 6th 2010, 07:59 AM
grgrsanjay
thank you
i was looking for this problem
• May 6th 2010, 08:08 AM
HallsofIvy
With something like " $y= f(x)^{g(x)}$", there are two simple mistakes we could make:
1) Treat the exponent, g(x), as a constant and use the "power rule" to get
" $y'= g(x)f(x)^{g(x)-1}f'(x)$".
2) Treat the base, f(x), as a constant and use the "exponential rule" to get " $y'= ln(f(x)) f(x)^{g(x)}g'(x)$.
The interesting thing is that the correct derivative is the sum of those two errors!
Taking the logarithm of both sides of $y= f(x)^{g(x)}$, $ln(y)= g(x) ln(f(x))$. On the left side, $(ln(y))'= \frac{1}{y} y'$. On the right, using the product rule, $(g(x)ln(f(x))'= g'(x)ln(f(x)+ \frac{g(x)}{f(x)}f'(x)$.
Multiplying on both sides of $\frac{1}{y}y'= g'(x)ln(f(x))+ \frac{g(x)}{f(x)}f'(x)$ by $y= f(x)^{g(x)}$, we get
$y'= ln(f(x))f(x)^{g(x)}g'(x)+ g(x)f(x)^{g(x)- 1} g'(x)$.
• May 6th 2010, 08:42 AM
grgrsanjay
Quote:
Originally Posted by HallsofIvy
With something like " $y= f(x)^{g(x)}$", there are two simple mistakes we could make:
1) Treat the exponent, g(x), as a constant and use the "power rule" to get
" $y'= g(x)f(x)^{g(x)-1}f'(x)$".
2) Treat the base, f(x), as a constant and use the "exponential rule" to get " $y'= ln(f(x)) f(x)^{g(x)}g'(x)$.
The interesting thing is that the correct derivative is the sum of those two errors!
Taking the logarithm of both sides of $y= f(x)^{g(x)}$, $ln(y)= g(x) ln(f(x))$. On the left side, $(ln(y))'= \frac{1}{y} y'$. On the right, using the product rule, $(g(x)ln(f(x))'= g'(x)ln(f(x)+ \frac{g(x)}{f(x)}f'(x)$.
Multiplying on both sides of $\frac{1}{y}y'= g'(x)ln(f(x))+ \frac{g(x)}{f(x)}f'(x)$ by $y= f(x)^{g(x)}$, we get
$y'= ln(f(x))f(x)^{g(x)}g'(x)+ g(x)f(x)^{g(x)- 1} g'(x)$.
excellent
• May 9th 2010, 09:55 AM
Nora
Thank you very much for helping me (Clapping)
Soroban
HallsofIvy
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2014-12-22 10:23:49
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https://dmoj.ca/problem/ecoo17r3p4
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## ECOO '17 R3 P4 - Ice Cream Beach
View as PDF
Points: 15 (partial)
Time limit: 13.0s
Memory limit: 256M
Author:
Problem types
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig
Harnessing your entrepreneurial spirit, you have decided to found a start-up. Your start-up, the first of its kind, will sell ice cream at the local beach. Every day, the beach gets visitors which sit at specific locations on the beach. The visitors would all love to buy ice cream, but they don't like walking around in the sun. A visitor's reluctance to buy ice cream is calculated by multiplying their distance from the nearest ice cream stand by their reluctance factor: a number unique to each visitor.
You have access to ice cream stands, which you can place anywhere on the beach. Moreover, you know where every visitor will sit and you know their reluctance factor. Since you don't want your start-up to sink, you'd like to carefully position your stands to minimize the total reluctance of all the visitors.
Can you figure out the minimum total reluctance that you can achieve?
#### Input Specification
The input will contain test cases.
Each test case starts with two integers , where is the number of visitors and is the number of ice cream stands. The next lines describe the visitors coming to the beach. Each line contains two integers and , where represents the locations of the visitor on the beach and represents the reluctance factor of that visitor .
Visitors will be listed in ascending order of and no two visitors will be at the same location. Since the beach is long and thin, it can be thought of as being one dimensional.
For of the cases, .
For of the cases, .
#### Output Specification
For each test case, your program should output the minimum total reluctance of all the visitors, modulo , or . *
#### Sample Input
2 1
10 10
20 10
2 2
10 10
20 10
4 2
1 10000
100 10
150 10
200 10
#### Sample Output
100
0
1000
Note: Only cases are shown in this sample.
#### Explanation of Sample Output
In the first test case, it's best to put your only ice cream stand anywhere between positions and . If we were to put it at position , then each visitor would have a reluctance of , for a total reluctance of .
In the second test case, you can perfectly accommodate both guests by putting your two carts at locations and .
In the last test case, it's best to put one cart at location to appease the incredibly reluctant visitor and put your second cart at location .
#### Footnotes
* This means that if the minimum total reluctance is you should output , the remainder after dividing by .
Educational Computing Organization of Ontario - statements, test data and other materials can be found at ecoocs.org
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2020-11-01 01:38:26
|
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https://intpforum.com/threads/how-much-would-you-spend-on-your-rights.4885/#post-564202
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# How much would you spend on your rights?
#### Yellow
##### for the glory of satan
This is an activity given to Social Studies students. I thought we might be able to have some fun with it.
Imagine you had these ten rights available to purchase and $2000 to spend. How much would you spend on each right and why? 1. The right to free speech. 2. The right to petition the government. 3. The right to vote. 4. Freedom of/from religion. 5. Freedom from unreasonable search and seizure. 6. The right to bear arms. 7. The right to trial by a jury of your peers. 8. The right to confront your accuser. 9. Freedom from cruel and unusual punishment. 10. Freedom of the press. #### Inappropriate Behavior ##### is peeing on the carpet Easy answer:$200 each, but if you want to know which I prioritize then:
1. The right to free speech. $500 2. The right to petition the government.$50
3. The right to vote. $100 4. Freedom of/from religion.$450
5. Freedom from unreasonable search and seizure. $200 6. The right to bear arms.$250
7. The right to trial by a jury of your peers. $40 8. The right to confront your accuser.$100
9. Freedom from cruel and unusual punishment. $60 10. Freedom of the press.$250
#### Cogwulf
##### Is actually an INTJ
First of all I'd kill the person selling them
Then in order of what I think is most important to least:
The right to free speech.
The right to trial by a jury of your peers.
The right to vote.
Freedom from cruel and unusual punishment.
Freedom from unreasonable search and seizure.
The right to confront your accuser.
Freedom of the press.
The right to petition the government.
The right to bear arms.
Freedom of/from religion.
#### Yellow
##### for the glory of satan
My response was:
1. The right to free speech. $500 4. Freedom of/from religion.$500
5. Freedom from unreasonable search and seizure. $300 9. Freedom from cruel and unusual punishment.$200
10. Freedom of the press. $200 2. The right to petition the government.$100
3. The right to vote. $100 8. The right to confront your accuser.$50
7. The right to trial by a jury of your peers. $50 6. The right to bear arms.$0
#### Reverse Transcriptase
##### "you're a poet whether you like it or not"
woah woah woah, where's the fifth amendment? The right not to provide witness against yourself.
I think I would spend a lot. Like, not *quite* as much as it took. But a lot. I'm not really sure how to put it into money figures.
For some of the rights, I feel like I would become a guerrilla fighter for.
1. The right to free speech. GUERRILLA
2. The right to petition the government. *meh*, compared to the others it doesn't seem that important
3. The right to vote. GUERRILLA
4. Freedom of/from religion. GUERRILLA
5. Freedom from unreasonable search and seizure. If a lack of this right was abused, GUERRILLA
6. The right to bear arms. GUERRILLA
7. The right to trial by a jury of your peers. If a lack of this right was abused, GUERRILLA
8. The right to confront your accuser. If a lack of this right was abused, GUERRILLA
9. Freedom from cruel and unusual punishment. If a lack of this right was abused, GUERRILLA
10. Freedom of the press. (Is the same as #1? GUERRILLA.)
11. Not provide witness to oneself. If a lack of this right was abused (like, forced interrogation), GUERRILLA
Clearly, I am an angry libertarian.
I also recognize that some of these rights (Speech, Search & Seizure, Bear Arms) have been partially restricted in the United States. I resent it, but I do not think it is enough to go to war over yet.
Yet.
#### Cogwulf
##### Is actually an INTJ
The freedom of/from religion doesn't seem very important to me, mostly because you can force a person to go to church, but you can't force that person to believe or disbelieve anything, similar the horse to water saying. And as long as the right to free speech is still held removing freedom of religion would be incredibly difficult.
#### Yellow
##### for the glory of satan
woah woah woah, where's the fifth amendment? The right not to provide witness against yourself.
I think I would spend a lot. Like, not *quite* as much as it took. But a lot. I'm not really sure how to put it into money figures.
For some of the rights, I feel like I would become a guerrilla fighter for.
Cheater.
And this is an old assignment and I don't even know who wrote it... maybe the fifth amendment didn't rank as high as the others with its originator. I know I really don't care about it. If I'm already in so much trouble that answering court questions will make it worse, I'm prolly gonna lie.
#### Kidege
##### is a ze
All human beings are born equal in dignity and rights.
Rights can't be bought or sold, and it upsets me a bit to think anyone would think of buying or selling them.
I'm particularly fond of these three:
9. Freedom from cruel and unusual punishment.
4. Freedom of/from religion.
5. Freedom from unreasonable search and seizure.
I'd group 1. The right to free speech., with 10. Freedom of the press. They refer to the sake kind of freedom: that of expressing oneself. In the human rights declaration the right of expression goes with the right to seek information, which I love.
2. The right to petition the government. and 3. The right to vote. could be grouped as specific political rights... I'd say they're linked to the right of participating in the govt.
7. The right to trial by a jury of your peers. and 8. The right to confront your accuser are, I guess, part of the right to recognition before the law.
And I have no idea of how come this is a right:
6. The right to bear arms.
I mean, I've heard it was intended as a safety in order to depose a bad govt, but come on... I mean, in my country we have the constitutional right to depose a bad govt, but not the right to bear arms... Drug dealers are often jailed for carrying weapons without a permit.
#### Inappropriate Behavior
##### is peeing on the carpet
I realise this is more a civics lesson, but I'd be interested to see how much we might spend on certain other rights that we think we have and yet never officially had. I'm not referring to RT's list of things being infringed upon (I don't quite get the inclusion of speech) but something like the right to privacy (which is not guaranteed anywhere).
Also right to die.
Right to lifestyle (in which I consider various forms of marraige that isn't 1 man 1 woman).
#### Reverse Transcriptase
##### "you're a poet whether you like it or not"
(I don't quite get the inclusion of speech)
YouTube- Its Illegal to say "I Want to Kill the President"
heh okay, I'm trying to find proof that it's illegal to say (notice my quotes) "I want to kill the president of the United States" and it might not actually be an inclusion.
/edit/: http://www.wtsp.com/news/local/story.aspx?storyid=9734
But another example is how protesters are often delegate to "Free Speech Zones" around large events. WTF? The whole United States is a Free-Speech Zone. U.S. Courts are just douchebags.
http://en.wikipedia.org/wiki/Free_speech_zone
#### Kidege
##### is a ze
Like the funny rights that are in my country's laws but no one gets?
Right to access to information, right to protection of personal data, right to intimacy -meant as privacy-, right to protection from abuse of public power.
They just went and changed the state constitution in 16 states and now we all have the "right to life from its conception", which sounds awful and is ridiculous, and just last week a lady was in jail because she had a spontaneous abortion, so she was taken from the hospital and thrown into a cell, and threatened with 20 years of prison for homicide. They had no proof so she was released.
.
.
.
#### Reverse Transcriptase
##### "you're a poet whether you like it or not"
Kidege, what country are you from?
#### EditorOne
##### Prolific Member
"The freedom of/from religion doesn't seem very important to me, mostly because you can force a person to go to church, but you can't force that person to believe or disbelieve anything, similar the horse to water saying. And as long as the right to free speech is still held removing freedom of religion would be incredibly difficult. "
True enough, but what the right really is: No government that is controlled by a religion. Even in an age where we see what a religion-owned government means in some Islamic states, we seem to remain somewhat forgetful of what governments owned by the Catholic or Protestant religions did in Europe not all that long ago. When a government owned by a religion confiscates your house because you're of a different religion, you really really really need "freedom of religion" because it's not an issue of belief, it's an issue of property and, in some cases, survival.
#### Inappropriate Behavior
##### is peeing on the carpet
heh okay, I'm trying to find proof that it's illegal to say (notice my quotes) "I want to kill the president of the United States" and it might not actually be an inclusion.
But another example is how protesters are often delegate to "Free Speech Zones" around large events. WTF? The whole United States is a Free-Speech Zone. U.S. Courts are just douchebags.
Well the Free Speech Zones were ridiculous. Did the Supreme Court ever hear a case about those? I wonder if it would have passed, if it did, we can certainly discount the court as any protector of freedoms once and for all.
Freedom of speech however was never meant as an absolute. You know, the fire in a crowded movie house thing. Threats aren't allowed either nor is inciting a riot. I can understand those. No right is an absolute. Hell, certain religious practices could get you arrested. Just get caught practicing rastafarianism's practice to get closer to god.
#### Artifice Orisit
##### Guest
For myself there are no rights, only privileges.
I don't like the idea of expecting rights, the world doesn’t owe me anything, so what right have I to expect these rights protected on my behalf? None.
Go ahead, deny me freedom of speech, I'll speak anyway.
I'll make it my privilege, I'll earn it, by defying any who would stop me.
_________________________________________________________________
*takes the $2000, sets it on fire, and gives the results-collector the finger* I have no right to do this, but I still do, because it's my Privilege. Try & stop me, but first know this: I'm expecting you to try 6. The right to bear arms. Misanthropy par excellence. The right to bear arms does not necessitate the required responsibility. IMO anyone who thinks guns are cool or fun while intending to own one, needs to be shot, not killed, just taught to respect what a gun is, and what it's not. #### sniktawekim ##### Well-Known Member This is an activity given to Social Studies students. I thought we might be able to have some fun with it. Imagine you had these ten rights available to purchase and$2000 to spend. How much would you spend on each right and why?
1. The right to free speech.
2. The right to petition the government.
3. The right to vote.
4. Freedom of/from religion.
5. Freedom from unreasonable search and seizure.
6. The right to bear arms.
7. The right to trial by a jury of your peers.
8. The right to confront your accuser.
9. Freedom from cruel and unusual punishment.
10. Freedom of the press.
i wouldnt spend money for them. i would kill/die for them.
#### sniktawekim
##### Well-Known Member
For myself there are no rights, only privileges.
I don't like the idea of expecting rights, the world doesn’t owe me anything, so what right have I to expect these rights protected on my behalf? None.
.
i think you and i think the same thing, but with a different taste in wording.
when i say right, i dont mean things that people have to give to me.
i mean things that people cant take away from me.
#### Artifice Orisit
##### Guest
The right to vote was given to you.
It can also be taken away.
#### Reverse Transcriptase
##### "you're a poet whether you like it or not"
Cog's reply reminded me of Professor Bernardo de la Paz. (From Robert Heinlein's "The Moon is a Harsh Mistress")
"I am free, no matter what rules surround me. If I find them tolerable, I tolerate them; if I find them too obnoxious, I break them. I am free because I know that I alone am morally responsible for everything I do."
#### Inappropriate Behavior
##### is peeing on the carpet
The right to bear arms can also be taken away but it would lead to a bloody mess in the undertaking.
#### Cavallier
##### Oh damn.
Imagine you had these ten rights available to purchase and $2000 to spend. How much would you spend on each right and why? 1. The right to free speech.$400 Very important to me. I'd give a lot for this.
2. The right to petition the government. $100 This is one of the ways we can make the government take notice of what the people it governs wants. So I'll give about$100 for it.
3. The right to vote. $300 While I think the system is flawed I think that the ability to vote it important. 4. Freedom of/from religion.$300 I've read way too much literature from and about 1400-1600ce in Europe to not pay good money for this.
5. Freedom from unreasonable search and seizure. $100 This is close enough to a privacy issue for me. 6. The right to bear arms.$0 Don't give a rats hind quarters. I don't see this as meaning a person can't own a gun anyway. I just think that a person should pass a psychological and capability/responsibility exam first. Require that people take classes and then pass out permits. I like how Canada makes it legal for hunting rifles but handguns are outlawed. I see no reason for people to have handguns. If you are an avid hunter or spend a lot of time out in the bush, you pass all the psychological exams, and take the class and get the permit...fine. Have a rifle but handguns are needless.*
7. The right to trial by a jury of your peers. $50 Just not as important to me as some of the others. Although I do worry about lynch mobs... 8. The right to confront your accuser.$50 Again, just not as important as some of the others but...Well, it would be nice to point the finger back I suppose.
9. Freedom from cruel and unusual punishment. $400 What constitutes as "cruel" and "unusual"? For me it equates to torture and frankly I'd give a lot to make sure our government can't torture people. 10. Freedom of the press.$300 This ranks up there with freedom of speech for me.
*I've wondered how it would be if we took all the guns and replaced them with swords again. It's personal. You can shoot somebody from far away but to kill with a sword you have to be close enough to the person to see their eyes and feel the spray of blood when you kill them. I think that would stop a lot of people from killing. While there would be more amputations there probably wouldn't be nearly as many deaths.
#### Deleted member 1424
##### Guest
"I am free, no matter what rules surround me. If I find them tolerable, I tolerate them; if I find them too obnoxious, I break them. I am free because I know that I alone am morally responsible for everything I do."
My old signature, and probably my favorite.
#### Cogwulf
##### Is actually an INTJ
I like how Canada makes it legal for hunting rifles but handguns are outlawed. I see no reason for people to have handguns. If you are an avid hunter or spend a lot of time out in the bush, you pass all the psychological exams, and take the class and get the permit...fine. Have a rifle but handguns are needless.
I think the main advantage of that law is that rifles couldn't feasibly be used in most gun crimes. It's extremely difficult to conceal them and they'd take much longer to draw and be ready to fire
#### SEPKA
##### What???
1. Free speech: $500 it is super important for me, I think that is also because I lived in a communist country for too long and feel really suppressed. 2. Petition:$50, I can just talk to the government officer, and if that does not work I can always assassinate the whole government and take over it.
3. Vote: $0, not really that important, I can always manipulate the mass into submitting to my opinion. 4. Freedom from religion:$0, since I already buy #1, this is no longer necessary.
5. Freedom from unreasonable search and seizure: $400, I want to be free, so this is very important, but privacy is not much of a problem because what I want to hide is mostly on my computer, and I can always use stegography/cryptography to defence against such search. 6. Bear arm:$0, I can always make some good weapon that bypass the legal definition of "arm" so this is not necessary.
7. Trail by jury of your peer: $150, but I think I will just escape the country. 8. Confront your accuser:$100, same as above, and I might just assassinate the accuser if that is an deliberate vicious attempt to bring me down.
9. Free from cruel and unusual punishment: $200, just in case I get captured while trying to escape. 10. Freedom of press:$500, important to manipulate the mass, linked to #1 and #2 and #3 so this is required.
11. Right to take over the world: $100, since I still got money left and this would come in handy if I ever got a powerful army of robot. #### Cavallier ##### Oh damn. I think the main advantage of that law is that rifles couldn't feasibly be used in most gun crimes. It's extremely difficult to conceal them and they'd take much longer to draw and be ready to fire Agreed. When I lived in Alaska it was unheard of for somebody to not have a rifle in my area. But then again, it was unusual for somebody to have a handgun. #### Yellow ##### for the glory of satan I want to bump this 7.5 year-old topic to get more answers. Actually, I think my answers have changed a bit over the years as well. Mods, feel free to split the thread if this is too far to be grave-digging, #### Shieru ##### rational romantic this is interesting, i'm glad you exhumed this topic ^^ _________ So.. 1. The right to free speech/Freedom of the press.$500 - these are basically the same thing, but probably most important to me. places like INTPf would likely be shut down without this one D:
2. Freedom of/from religion. $500 - because it's bad enough religious zealots show up at my door.. i'd rather not be obligated to agree with them. this one's highly related to the previous one as well. without freedom of belief there can't be free exchange of thought. 3. Freedom from unreasonable search and seizure.$300 - i don't like random people in my house, and would probably go catatonic if they took my computer. they better have a damn good reason for violating my space
4. Freedom from cruel and unusual punishment. $200 - this one's pretty self-explanatory methinks. rather not be inappropriately touched against my will, let alone tortured >.< 5. The right to trial by a jury of your peers.$100 - not that i generally trust people to deduce reality correctly.. but if i had to be tried for something, especially something i was innocent of, i'd rather have more than one opinion on the matter.
6. The right to petition the government. $100 - because we should at least be able to complain. 7. The right to vote.$100 - i've thought for a while that this one doesn't actually matter that much. the way the electoral college is set up makes things seem kinda futile :P but i think the spirit of it 's still important.
8. The right to bear arms. $100 - this one helps prevent complete tyranny in the event that Trump an overzealous leader attempts to control the population with military forces. 9. The right to confront your accuser.$100 - i'm not into conflict. but if this extends to the right to hire a lawyer, then it'd be important. let the extroverts with a degree in the technical art of accusation handle it!
#### Reluctantly
##### Resident disMember
I guess I don't understand putting a dollar sign to them. Does it mean I'm buying a better quality of that particular thing?
#### Yellow
##### for the glory of satan
3. Freedom from unreasonable search and seizure. $300 - i don't like random people in my house, and would probably go catatonic if they took my computer. they better have a damn good reason for violating my space 4. Freedom from cruel and unusual punishment.$200 - this one's pretty self-explanatory methinks. rather not be inappropriately touched against my will, let alone tortured >.<
I guess this brings me to ask why you place your right to your possessions/privacy over your right to not be inhumanely detained/tortured.
I guess I don't understand putting a dollar sign to them. Does it mean I'm buying a better quality of that particular thing?
I was married to a social studies teacher when I made my OP. It was probably an assignment for his students in US Civics. I guess it provides an objective measurement for a group of people to compare the importance of each right from their differing points of view.
#### Shieru
##### rational romantic
I guess this brings me to ask why you place your right to your possessions/privacy over your right to not be inhumanely detained/tortured.
i think these are closely related in reality, but i made that choice in order to reflect my principles. privacy means a whole lot to me, as does personal freedom. probably partially because most my life i was deprived of those things :P i wouldn't want to be tortured, but i think having my privacy violated and/or having to be confronted with aggressive interrogation would be just as bad in a way.
i think, being INTP, i tend to value what's internally relevant to me above external circumstances. of course in reality internal well being has a lot to do with allowance from the environment. but i tend to be rather detached from the physical dimension by default, so if i can retain my individuality (which extends into virtual space, imo) then what's happening objectively isn't that important.
that's prolly the reason i can sit in my pjs in a room that looks like a tornado hit it, starving, with no money in the bank and an overdue list of things to do, and be completely content spending days philosophizing on various forums
#### Seteleechete
##### Together forever
Freedom from cruel and unusual punishment: 1000
Because this is the one that scares me and I don't like being afraid. Especially if "unusual" punishments include lobotomy/drugs based/brainwashing/torture ones. I considered placing all 2000 on this but placing on other things a bit might be more effective indirectly. Not sure.
Freedom from religion: 300
Much the same reasons as above, religion makes people justify the stupidest things.
Freedom of speech/press(neat trick): 500
Self-explanatory for an intp. but in general needed to protect a functioning society as well.
Freedom from unreasonable search and seizure: 100
Don't want my things arbitrarily taken/generally rule of law being useful.
Right to petition the government: 100
Public outrage via free speech is probably more effective but having open channels is also fairly important.
#### Cognisant
##### Prolific Member
For myself there are no rights, only privileges.
I don't like the idea of expecting rights, the world doesn’t owe me anything, so what right have I to expect these rights protected on my behalf? None.
Go ahead, deny me freedom of speech, I'll speak anyway.
I'll make it my privilege, I'll earn it, by defying any who would stop me.
_________________________________________________________________
*takes the $2000, sets it on fire, and gives the results-collector the finger* I have no right to do this, but I still do, because it's my Privilege. Try & stop me, but first know this: I'm expecting you to try Misanthropy par excellence. The right to bear arms does not necessitate the required responsibility. IMO anyone who thinks guns are cool or fun while intending to own one, needs to be shot, not killed, just taught to respect what a gun is, and what it's not. Wow haha man I had some fire in me back then My older more level headed answer would be to keep the$2000 (I pay more bills these days) and tell the person who tried to sell me a concept to fuck off because how are they going to protect any of my rights for worthwhile amount of time for a mere two grand?
#### Rixus
##### I introverted think. Therefore, I am.
Can I keep the $2k for PC upgrades? If not, then I guess I'll have to answer. And by the way, Yellow, I first saw this last night when I quickly checked my social medias etc before bed, and ended up laying awake for an hour contemplating this. So thank you for that. Anyway, here's a summary of my pondering: The right to vote –$400 – While I do question why people vote in the ways that they do and believe most people vote on issues that they unfortunately know little about, without the right to vote the government would be unaccountable and we would be under tyranny.
The right to trial by a jury of your peers - $350 – I’m going to amend this slightly here to the right to a fair trial. Although I have never been on trial, I don’t trust my peers at all as it comes down to who’s lawyer can successfully sway the opinion of the jury. But, everyone deserves a fair trial. For if it cannot be proven fairly, how else can we prosecute? Freedom from unreasonable search and seizure -$300 – I’m putting this a little below a fair trial. I don’t agree with unwarranted searches or seizures, but it does come down to the same thing as having a fair and reasonable justice and policing system. Although people like to complain greatly about the government spying on them, this in itself doesn’t bother me in the slightest. I’m far too boring a person for them to have any interest in me and doubt I break any laws that would concern anyone.
Freedom of/from religion – $300 – I had to stop and think about this for a moment. Everyone dislikes those preachers who show up at their door; but as issues go it doesn’t affect my life greatly. I do not fully understand why people do, but of course, if they find life easier when they believe in such things they should be free to do so as long as those beliefs are not causing harm to anyone else. And there in lies the problem – we can look back into our own history when people did not have freedom to not practice religion and see churches will unreasonable power and heresy being a capital offence. We see in the middle east what happens when people do not have this freedom and can agree it is, in fact, vitally important. Freedom from cruel and unusual punishment –$250 – I believe this important. I don’t fear my own safety, although I can think of some cruel and unusual punishments that are quite creative that I would not like to undergo. I sometimes attempt to argue their validity in order to argue with a work colleague, but that is all in the name of fun, really. My last suggestion was to use sensory deprivation chambers for sentences – a 6 month sentence in sensory deprivation while being fed intravenously would be much harsher than several years in prison. But of course, I don’t believe that at all. It’s a simple fact that severe punishment is highly ineffective at both rehabilitation and information extraction. All it does is breed resentment for the hand that dealt the punishment. Harsh sentences and capital punishments may make the general public feel like justice has been served, but it does not discourage crime or re-offence and that is really what should be aimed towards.
The right to free speech – $250 This one is interesting. Most people put this at the top of their list. Yes, the right to air your opinion is a basic right. But we do have limitations on what we can say everywhere we go. Whether it is a Mod in a forum, your boss at work, or by law, we do have limitations. And should you be free to incite fear or prejudice? Then we have to decide who decides what constitutes as prejudice? Manipulation is really the most effective tool of control, but who could possibly police this fairly? Freedom of the press –$100 - I’m putting this lower freedom of public speech and keeping it separate. The press has an obligation to inform the public about the truth. But in my opinion, they seem to be interested in selling a story rather than telling a story. And we end up with celebrity stalking and attempts to glorify or horrify. This is not always a good thing, and they have an enormous amount of power over the general public and over democracy.
The right to petition the government - $50 – While we can look back at things like the Chartism Riots and agree that it is necessary for the public to petition the government with legitimate misgivings or concerns, democracy and free speech are generally far more effective at this. The right to confront your accuser -$0. As long as a fair trial is in place, I do not feel the need to confront my accusers (not that I have ever been accused of a serious crime). Cross examining your own victims seems like a cruel and unusual psychological torture in itself.
The right to bear arms s - $0. We haven’t had the right to bear arms for over twenty years here. While I’m aware many people will fundamentally disagree with me, I don’t believe my personal freedoms or safety are compromised in any way by not having the ability to bear arms. #### Yellow ##### for the glory of satan The right to free speech –$250 This one is interesting. Most people put this at the top of their list. Yes, the right to air your opinion is a basic right. But we do have limitations on what we can say everywhere we go. Whether it is a Mod in a forum, your boss at work, or by law, we do have limitations. And should you be free to incite fear or prejudice? Then we have to decide who decides what constitutes as prejudice? Manipulation is really the most effective tool of control, but who could possibly police this fairly?
These are good points. Personally, I value freedom of speech over freedom from offence, but it's the direction a lot of people seem to want to move in. I'm not suggesting that you're a proponent of "safe spaces", but this got me thinking about it.
Freedom of the press – $100 - I’m putting this lower freedom of public speech and keeping it separate. The press has an obligation to inform the public about the truth. But in my opinion, they seem to be interested in selling a story rather than telling a story. And we end up with celebrity stalking and attempts to glorify or horrify. This is not always a good thing, and they have an enormous amount of power over the general public and over democracy. I think this illustrates cultural differences pretty well. The Press was supposed to be the unofficial, 4th branch of the US federal government. The Press has become as partisan and corrupt as any other high-level political figures as a result of being owned/controlled by just a few for-profit people/entities. #### Rixus ##### I introverted think. Therefore, I am. These are good points. Personally, I value freedom of speech over freedom from offence, but it's the direction a lot of people seem to want to move in. I'm not suggesting that you're a proponent of "safe spaces", but this got me thinking about it. While everyone should be free from violence and discrimination (to a realistic level), I think freedom from offence is an absurd extreme. People do become far too easily offended by almost anything these days. I saw headline last week that a Walking Dead t-shirt was taken off the shelves at a London store. It displayed Negan's bat, with the words, "eeny meeny miny moe." Apparently, someone complained that had they been an Afro Carribean, they would have been offended. Which is just plain lunacy. No, I don't refer to that direction of forcing the world to walk on egg shells. But manipulation, inciting violence and so on does have some limits. On the one, it's the same argument as I made for religious freedom - say or do as you please as long no one's getting hurt. On the other hand, if people just stopped and thought about what they hear and if they, quite frankly, grew a pair and stopped getting so offended by everything, it wouldn't be necessary. I guess I only wonder about this because every time I look in social media, I see both extremes arguing and throwing views back and forth, and neither is really any better than the other. That's a bit of a tangent, though. By the rightful limitations to freedom of speech, was more thinking about things like obtaining money by deception, slander, Hitler's rally's prior to gaining power, brainwashing of children, even sexual grooming of minors can be done using only words. I don't disagree with the right to express whatever opinion you have (otherwise I wouldn't have applied any value to it), just to use that right to cause harm. #### Yellow ##### for the glory of satan That's a bit of a tangent, though. By the rightful limitations to freedom of speech, was more thinking about things like obtaining money by deception, slander, Hitler's rally's prior to gaining power, brainwashing of children, even sexual grooming of minors can be done using only words. I don't disagree with the right to express whatever opinion you have (otherwise I wouldn't have applied any value to it), just to use that right to cause harm. hmmm... I've heard this argument, and it does make some sense. Personally, I don't see a problem with hateful and riotous speech being allowed by law. People still choose whether they agree. Hitler, unfortunately, was saying what a lot of people were thinking. If we're to the point of trying to stop hateful rhetoric, then it's safe to assume that it won't take hold with the majority. The only kind of limit to free speech that doesn't come from the majority comes from the government about the government. (In child-related cases, parents don't need to break the law, only threaten (or fail to protect) their child's wellbeing... So that becomes reasonably moot (at least in the US)) #### Glaerhaidh ##### straightedgy 500$,
for the right to euthanasia at will, no questions asked, no obstructions.
Now what I mean by this is instantaneous, swift disintegration, essentially what constitutes the right to my own life, my own intellectual property inside my brain and my genetic information and my right to erase it completely, thus preventing any future party from accessing my body/mind and/or reviving/cloning or copying me or parts of me.
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2022-01-24 04:39:55
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http://encyclopedia.kids.net.au/page/pe/Pentagram
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## Encyclopedia > Pentagram
Article Content
# Pentagram
A pentagram or pentacle is a five-pointed star. Pentagrams were used symbolically in ancient Greece and Babylonia. The Pentagram has magickal associations, and many people who practice pagan faiths wear them. Some Christians associate the symbol with Satanism, though most who use it are not Satanists.
Pentagram
Some sources refer to the pentagram as the "star of Solomon".
A perfect pentagram is easiest drawn by drawing a perfect pentagon, joining the corners with lines and erasing the original pentagon. You may also extend the sides of the pentagon until they meet, obtaining a bigger pentagram.
The word "pentagram" comes from the Greek word πεντάγραμμον (pentagrammon), a noun form of πεντάγραμμος (pentagrammos), πεντέγραμμος (pentegrammos) a word meaning roughly "five-lined" or "five lines".
The first uses of the pentagram we know of is in Mesopotamian writings dating to about 3000 B.C. In the Babylonian context, the edges of the pentagram were probably orientations: forward, backward, left, right, and "above". These directions also had an astrological meaning, representing the five planets Jupiter, Mercury, Mars and Saturn, and Venus as the "Queen of Heaven" (Schekina or Ishtar) above.
Pentagram illustrating the golden mean hidden in it.
The Pythagoreans called the pentagram ύγιεια Hugieia ("health" also the Greek god of health, Hygieia), and saw in it the pentagram a mathematical perfection: among other things, the pentagram hides the golden mean: when drawn with perfect angles each line is divided into several smaller segments, and if you divide the length of the longer segment with the shorter segment of any pair of segments you will get 1.618... In the illustration:
$\frac{\mathrm{red}}{\mathrm{blue}} = \frac{\mathrm{blue}}{\mathrm{green}} = \frac{\mathrm{green}}{\mathrm{purple}} = 1.618...$
The five vertices were also used by the pythagoreans to represent the five Classical elements:
Pentagram image from Heinrich Cornelius Agrippa's "Libri Tres de Occulta Philosophia" illustrating the golden symmetry of the human body. The signs on the perimeter are astrological. Another pentagram from Agrippas book, this one has the Pythagorean letters inscribed around the circle.
The vertices were labeled in the letters of υ-γ-ι-ει-α though the ordering (clockwise or counter-clockwise) used, and starting vertex, could vary.
Satanists use pentagrams much the way they use the Christian cross: they turn it upside down either as a sign of disrespect, or just as a variant. They use the Pythagorean pentagram inscribed in a double circle, with the head of Baphomet inside the pentagram. The pythagorean Greek letters are replaced by the Hebrew letters forming the name Leviathan.
All Wikipedia text is available under the terms of the GNU Free Documentation License
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2021-10-17 19:11:26
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https://chat.stackexchange.com/transcript/71/2022/8/18
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3:15 AM
is the only support for the postulate that c (speed of light) is relativistically invariant experimental?
err... well I guess I mean is the reason that the invariance of c is postulated because of experimental evidence? I remember reading that Einstein thought it was true without knowing the results of that one experiment, though
@SillyGoose No.
3:28 AM
what is the non-experimental support? @NikeDattani
@SillyGoose You've caught me at 11:29pm in my time zone. I'm going to sleep soon. Sorry.
no worries!
1 hour later…
4:37 AM
@SillyGoose SR is a metric theory. This means it is based upon the principle that the quantity dτ defined by c²dτ² = c²dt² - dx² - dy² - dz² is the same for all observers. In this equation the quantity 𝑐 is a constant that turns out to be the speed of light.
This means SR requires that the speed of light be a constant otherwise the whole theory falls apart. This is the non-experimental evidence i.e. the consistency of the theory depends on it.
This means that any experimental test of SR is also a test that 𝑐 is constant, and experimental tests of SR are ten a penny.
5:10 AM
@user250478 It's possible for massless particles to form a massive bound state. For example gluons are massless but they can form a massive bound states called a glueball.
Likewise it is in principle possible for massless gravitational waves to form a massive bound state that we call a geon. But no-one has been able to work out an equation to describe a stable geon so we don't know whether they can actually form.
As for what they would look like, a geon would lens light passing through it but not absorb or reflect light. Exactly what the end result would be we don't know since we don't have an equation to describe a geon.
6:06 AM
Okay now Im stuck on equation 2.8. Can someone tell me where it is coming from?
https://web.archive.org/web/20030912200701id_/http://www34.homepage.villanova.edu:80/robert.jantzen/research/articles/q51010.pdf
2 hours later…
8:03 AM
@JohnRennie many thanks for such reply, you're incredible (=yours knowledges are very good).
:-)
Many thanks @Jim , as said the moderator it is sad because he can't talk about geons.
Two gravitons (assuming gravitons exist) could not form a bound state with each other because they interact too weakly. So there cannot be a gravitational equivalent of a glueball formed from two gluons.
Two gravitational waves could interact to form a bound state, but they equations involved are too hard to solve analytically so coming up with the equations for a geon is formidably difficult.
8:31 AM
I actually don't feel a great loss in my life from not knowing about geons :P
2
9:07 AM
@SillyGoose Right, Einstein didn't know about the Michelson-Morley experiment when he published SR. But he knew about stellar aberration & Fizeau's measurement of the speed of light in water. See
6
Note, the question asked is about history, and historically the definitive statement that the speed of light is independent of other things comes from Einstein's 1905 paper. In developing his thinking Einstein was unaware of the Michelson Morley experiment. To quote from https://arxiv.org/ftp/arx...
9:46 AM
Question about edit summary: why do people write "added insert number characters in the body"? Should I do that too?
@Feynman_00 That is added automatically if you don't enter anything in the edit summary box.
I feel so stupid right now :P
:-)
I thought you guys were counting each deleted and added character
I usually try to enter something sensible in the edit box so future editors will have some clue what I did. But whether it's actually that useful is debatable.
9:50 AM
it's like commit messages in software control systems - often it doesn't matter all that much what's written there, but sometimes it's really useful if someone actually described properly what they were doing
10:00 AM
@DIRAC1930 I'm not going to read the paper but it seems that they don't claim that $n$ evolves in the Schrödinger picture, they define an (explicitly time-dep.) operator as a projector on states occupied at time $t$
2 hours later…
11:56 AM
@ACuriousMind Alas that I know so little about geons! My life is over! I shall diminish and go into the West and remain GaJimdriel
@Jim yes, bear news to the lords of Valinor that all their works are futile unless they unearth the mysteries of geons
I guess geons created a new meme
2 hours later…
2:16 PM
Hello.
I don't know anything about physics but I once heard that the universe is smooth Lorentzian 4-manifold. Is this a consequence of something or just a hypothesis?
@onepotatotwopotato Well, it is the way that the universe is modeled in the theory of relativity. That theory has been accepted - due to a lot of empirical evidence for its predictions - for around 100 years now. Within the modern mathematical formulation of that theory, it is (usually) an axiom (i.e a foundational assumption, not something derived).
@ACuriousMind I see. Thank you
(There are certainly debates about whether "smooth" is necessary or $C^p$ for some $p$ isn't enough, but I feel that's not the point of your question)
@ACuriousMind Sup, I agree with you that there is value created to people that is not measured by an exchange of money, I just remembered that point you made. I'm not sure how we can go about measuring what part of all value created that "unrecorded" value is. But whenever there is a voluntary exchange of money, there is value created, you agree with that?
I mean why would anyone give their money to someone if they're not getting any value from that transaction?
@ACuriousMind $C^p$ manifolds are tremendous
I hope GR deals with $C^\infty$ only
Do we mean that by smooth?
2:25 PM
yes, smooth usually means $C^\infty$
Because some books mean $C^p$ for some given $p$
Oh, ok
but sometimes it also just means $C^p$ for large enough $p$ so that everything you just did works
For example, you couldn't define the tangent space as the space of derivations in a point
There is another construction that uses commutative algebra instead and yields the cotagent space but to be honest I found that unintelligible
@JingleBells No. I disagree that transactions, in and of themselves, generate something of value, I disagree with the entire idea of viewing society through a transactional lens, and I would caution that "voluntary" is a dangerous judgement to make about exchanges of money - nothing about my exchange of money for e.g. food or shelter is truly voluntary, because the world we exist in is structured in such a way as to make that an effectively obligatory part of existence.
@Feynman_00 yes, that is a large part of why you want to stick to $C^\infty$
hi everyone
actually why earth crust does not melt? and what make it temp so high?
2:32 PM
I'm genuinely terrified by non-$C^\infty$ functions. Studying real analysis I could never remember what had to be $C^2$ or just twofold differentiable
elements in the earth
why curst is in spherical or HCP shape
these are the some question which puzzling me
@JackRod do you really mean the crust?
because the crust is the outermost layer - at the surface, it's certainly not very hot, we can walk on it every day!
@JackRod as for why things under the influence of gravity tend to become round-ish, see e.g astronomy.stackexchange.com/q/24698/23535
@ACuriousMind If I give you something you want and you give me something I want, hasn't that ability to exchange been valuable to both of us? (only if the transaction has been mutually beneficial). That's what I mean by a transaction. For your second point, I'm not sure what you mean by viewing society through a transactional lens. By voluntary choices, I mean choices made under certain constraints, I don't see how it can be otherwise.
@JingleBells If I'm starving and I give you all my money for an apple, is that "mutually beneficial"?
did both of us "get what we want"?
I pay ACM to beat up someone I don't like, did that create value?
2:42 PM
@fqq depends on the someone ;P
also, in that scenario it's much more likely I end up getting hurt than the target
@ACuriousMind Yes, it is mutually beneficial, regardless of the fact that you're starving. You get something that benefits you and I get something that benefits me. (which is supposedly some pieces of paper in my case)
@JingleBells No, what has happened is that you have exploited my situation for your own personal gain. This is my fundamental disagreement with the idea that all transactions that weren't overtly forced are "voluntary": Transactions can only be truly voluntary - in the sense that they will only happen when both sides think the exchange is fair - when no side has implicit or explicit power over the other. A starving person has no power - they have to take the deal or they die.
"you have exploited my situation for your own personal gain" - I have no idea what you mean by this, we both benefited from the transaction and if it hadn't occurred we both would have been worse off, that is the fact. There is no requirement for mutual agreement on fairness for mutual benefiting to occur. About the voluntary part of the argument, to be honest I don't know what voluntary means, I don't believe in free will so depending on how you define it, we can discuss it.
@JingleBells "we both benefited from the transaction and if it hadn't occurred we both would have been worse off, that is the fact." The latter part is not true. There is another possible world in which this transaction would not have been possible at all: A world in which we consider it our moral duty to not let people starve instead of extracting money from the hungry.
This world is better than the world in which I starve because I didn't buy your food and better than the world in which I had to buy it.
It is a world in which not all transfers of "value" must be transactional. Where it is possible to give without taking in return, simply because it is the right thing to do.
3:00 PM
@ACuriousMind Sure, I could have given you the apple (i.e. create value for you) without you giving me the pieces of paper (i.e. create value for me) but in this way, the total value created overall is less.
why does it matter whether or not we created "value"?
it doesn't matter unless your goal is to maximize the value created
Then that is not my goal.
Maybe we should have started from that XD
So this should be our fundamental disagreement?
@JingleBells Did you already forget our last discussion? The problem is not that you want to maximize "value" and I don't, the problem is that we disagree about what value is - you think it's reflected in money because to you money is a reification of personal preferences; I don't.
3:10 PM
@ACuriousMind I don't think money has to be involved for value to be created - if I give an apple and you give me a banana that means that I value the banana more than the apple and you vice versa, so in that transaction value is created for both of us. I wouldn't want to tell anyone what is valuable to them and I hope you don't too.
@JingleBells note how you altered the example - if we both have food and just exchange it so we both get the food we like more, that's a truly voluntary transaction because none of us holds power over the other
@ACuriousMind I can understand what you mean, my point though is that in both versions value is created for both of us, it's just that in the previous version I wanted pieces of paper for some reason instead of a nice juicy banana. What difference does it make if you (the starving person) have pieces of paper instead of a banana when in both cases you can exchange your thing for something you want more?
Where is all of this going?
3:28 PM
@JingleBells Humans generally can't eat paper.
@ACuriousMind I agree :D
If I have no food, I have no choice but to accept pretty much any way of getting it
I agree
well you have the choice to die :P
technically
and that means that I will have to accept whatever the people who have it demand of me
I agree
unless you prefer to die
3:31 PM
so that I enter into the transaction doesn't mean anything - the price I pay doesn't represent how highly I "value" the food, it just represents how much the people with the food were willing to demand.
@ACuriousMind Entering into the transaction means that you're going to get the apple and not die. I agree that the price you pay doesn't represent anything about how much you value the food in the scenario that we're talking about.
So where is this going?
@JingleBells This is the core of my objection to the idea that the amount of money that changes hands in a transaction represents how much the people involved value the goods exchanged.
@ACuriousMind Yeah but most people in developed countries are not starving and there are plenty of people demanding and supplying apples. The example that supports your core objection doesn't reflect the real world.
3:49 PM
@JingleBells and that's where we disagree - most people in developed countries are not actively starving or homeless, but still they have to pay for food and shelter and other things that are essentially necessary for participation in society. They're still subject to this same kind of exploitation - or, conversely, power is wielded over them with the threat of such exploitation (e.g. "Don't be against factory farming or destructive agriculture because then your food will get more expensive").
or the size of rent, for instance, as a proportion of low incomes is an essential factor in preventing accumulation of wealth/causing debt by low incomes
Implicitly, this is also part of the reason many low-qualified jobs can pay low wages - since workers have no choice but to work to subsist, the same argument applies again to show their wages don't represent the "value" of their work
Alrighty let's take it step by step
@ACuriousMind "Most people in developed countries are not actively starving or homeless, but still they have to pay for food and shelter and other things that are essentially necessary for participation in society" - I agree with that, it's a fact. "They're still subject to this same kind of exploitation" - I still don't understand what you mean by exploitation and how it is bad. Remember this time we're talking about the majority of the people in developed countries with a lot of supply and demand.
Helu? :3
@ACuriousMind Btw I hope there are no hard feelings between us about these discussions, I'm genuinely here just to learn some new stuff and challenge my views, I have nothing against you just because we differ in some opinions :3
I'mma go eat dinner and I hope we can continue this because it's super interesting, hope you feel the same at least to a degree.
4:12 PM
Is this how one uses latex in physics forums?
[ tex ] \nu (U,u) [ \tex ]
@JingleBells The exploitation is in that there is a class of people who controls the means by which these necessities are produced and another class of people who has to work to pay them for these products
First time over there
I've never used physics forums :P
@ACuriousMind Hmm ... didnt physics forums come before PSE?
Jun 24, 2020 at 17:47, by user434058
23 hours ago, by ACuriousMind
May 3 at 9:46, by Loong
Jan 5 '16 at 22:43, by ACuriousMind
Jun 17 '15 at 6:43, by DanielSank
I regard online chat as an asynchronous communication protocol :-)
If I don't answer immediately that is usually just a sign my attention is focused elsewhere :P
@MoreAnonymous ...so?
4:14 PM
@ACuriousMind Oh just imagined you would have been active then as well in the physics online community
how old do you think I am :D
@ACuriousMind 35?
eh, close, but still 6 years too old
You can still do a Phd @ACuriousMind
join the dark side :P
I know, but I don't want to
4:16 PM
@ACuriousMind I want to but I don't think i'll have a shot unless I have a paper out ...
(which is something Im working on)
I mean I've seen the difference in training from the elite institutions and rank 4 ...
which is why i wanna go to some of the best for training
@Feynman_00 have you used physics forums?
Sometimes I read something but I trust SE way more
I need to figure out how to use latex there
@Feynman_00 Me too
Latex is diffeomorphism invariant
@MoreAnonymous My guess was far better :P
@ACuriousMind That's news to me. I thought string theory was PhD material
@Feynman_00 It is ... But our hero has chosen the dark side!
@Feynman_00 there was a regular course where I studied that was usually a mix of master students and aspiring PhDs
it's pretty pointless to think something is "PhD material" - if you know the prerequisites, you can study something, and at which stage in your formal career you have which prerequisites is extremely varied
4:24 PM
@MoreAnonymous try ##LateX##
@ACuriousMind Yeah of course, people can study anything on their own. That was an innocent hypothesis
And I also assumed that because you seem way above the level I think I'll reach after my master's
@ACuriousMind Gotchya
@ACuriousMind "There is a class of people who controls the means by which these necessities are produced" - I agree. "and another class of people who has to work to pay them for these products" - I agree but the working people get paid to pay for the products they or other workers produce. I don't see how that's bad.
@Feynman_00 don't worry too much about it - remember that you mostly observe me talking about stuff (I think) I know here, not the stuff I've never heard of ;)
4:49 PM
:).
EDIT: =) looks better
@JingleBells there are many problems with that, e.g.: 1. This structure is resistant to true upwards mobility because wealth/lack of wealth is inherited. 2. The amount people are paid for their work is decoupled from the actual "value" their work creates - as long as a job allows for minimal subsistence and there's a lot of people who can potentially do it, there will be someone who takes it; there is no mechanism here that limits the profits the owning class can extract
(even while merely owning and not working, mind you!). 3. It disregards completely people who, for some reason or another, cannot do enough work to subsist.
4. A point fqq implied earlier: What about jobs that are actually destructive in nature (in the extreme hypothetical killing people, but in more realistic scenarios destroying natural habitats, etc.) that either harm many people indirectly or the worker directly (e.g. mining work in many countries) but which the workers will effectively be forced to perform because they get paid for them and so can continue to subsist?
5:12 PM
@ACuriousMind No I meant core
one which is as deep as 2,300 km
@JohnRennie hi sir
@ACuriousMind 1. What does "true upwards mobility" mean? And btw most of the wealth is not inherited. 2. What does "actual value" mean? Wages are determined mainly by supply and demand and it's true that if there are a lot of people who can do what you do then your pay goes down and the opposite is true as well. The controlling class does indeed get money for the value that they create
3. If you don't create value to society then you shouldn't expect society to create value to you. Of course people should be free to help out people that don't create enough value but not forced. 4. In these cases I think government intervention might be a good idea but it really depends. What if people value more the building than the natural habitat it's destroying?
No worker is forced to do a dangerous job, in most cases such jobs are paid pretty well precisely because workers don't want to do them (less supply). If you can get a mining job you can surely get something more safe as well, like a cleaner or whatever. Someone has to get the mining job done anyways though, what solution do you offer to that if not sending humans?
5:29 PM
@JingleBells "If you don't create value to society then you shouldn't expect society to create value to you." Ah, now you've said what I was waiting for: This is decidedly different from the purpose of "we want to satisfy the most needs of most people" you started out trying to convince me markets were good at. This is the attitude I really find distasteful, and this is exactly what I meant by the "transactional view of society" earlier.
@ACuriousMind We can get into that definitely, what about my other points? (I'm really just trying to see if there's anything wrong with them and learn something new :P)
Every human has immeasurable value, to me, and I reject ideologies that discount those that do not create whatever it has decided "value" is. I believe in a universal moral duty to help our fellow creatures - in solidarity that is not bought but freely given - and if your model of society doesn't contain that then I'm not interested in it.
@ACuriousMind Are we gonna discuss the other points first or should I just jump into what you're currently talking about?
To be honest I'm not really interested in discussing this any further; I've seen this rhetoric before many times, and I've said all I wanted to say.
5:47 PM
@ACuriousMind How can you know what I'm about to say for you to not be interested in it? We're just having a normal discussion, I'm not judging you for anything nor am I screaming at you because we disagree. I'm interested and curious about how you see the world and I want to ask a few questions to learn more. I'll go ahead and ask because I know I shouldn't ask if I can ask XD
So first of all, I see nothing wrong with wanting to create value to people that don't (for whatever reason) create value to society back. I'm not against you going and giving your apple to a homeless person, you have your moral duties and you have the right to act on them. The problem I have is when you force me to give my apple to a homeless person, in other words when you try to impose your moral duties on other people.
"I actually don't feel a great loss..." I think that it is important to emphasize that there was an age in which physicists doubted the existence of black holes, and you can to ask about the illusion that have many persons about travels exploiting wormholes. It is important also to add that was a great physicis who is the author of the concept (I refer the Wikipedia Geon (physics)).
@ACuriousMind By the way, if giving an apple to a homeless person will get him/her to start creating value to society, then I'll give my apple, but if it has the opposite effect and incentivizes unproductivity then I won't give my apple.
hey can anyone help me in getting undersdand how quantum simulation is better option than
it peer standard simulation
6:05 PM
@user250478 I'm not saying no one should think about geons or anything - but I'm not even a professional physicist, so I don't really have to care about every speculative idea
@JackRod what is "quantum simulation"
Many thanks for your reply again (as I said I felt your last, as a friendly reply). I'm not agree with you: we live only once @ACuriousMind
@JingleBells What do you think the laws protecting your precious free economy are if not the imposition of the moral values of the lawmakers on other people? You don't get to pretend taking the high road here - every society with any form of laws thereby imposes moral values on its constituents.
@ACuriousMind Under my system I get to follow my moral duties and you get to follow yours. Under your system, I'm forced to follow your moral duties. How is my system not taking the "high road" here?
6:21 PM
@JingleBells No, I'm not - I am, for example, not allowed to perform actions that break the laws that protect the accumulation of wealth; The almost unconditional protection of property represents itself a moral position: Property is more important than people. Your rhetoric implicitly reduces morality to "the choice between all actions considered legal in a neoliberal system".
And in case you're wondering: This idea that neoliberalism among all ideologies is uniquely "not an ideology", and it uniquely takes no moral stance, is so common I have of course heard it before; now I am really tired of this discussion.
@ACuriousMind I agree with what you just said that different systems impose different moral values on the citizens, and to say that my system is the "high road" based on a single thing (i.e. the choice to give stuff to homeless people) would be a mistake.
If you're tired of this discussion then we can stop. I have last 2 questions and I'm ready to wrap this up - what would you say our fundamental disagreement is, and second, if you were given the power to change the current system in some way (maybe fundamentally) what would you do?
6:53 PM
When all your friends are in the bar but you seem to be barred :/
@ACuriousMind ^ Even the chat room got tired of our discussion XDD
Btw ACM while we may disagree on quite a few things, I like that you are not opposed to jumping in and discussing/debating with people who disagree with you, this is a very useful and important quality and I respect when people don't run away from information that contradicts their beliefs because that's hard but a necessary step to being more informed and sometimes reaching further to the truth
@JingleBells I doubt you provided any such information honestly :/
@JingleBells yup ...
ACM is quite well read. I'm surprised someone who hasn't even joined a university has strong political beliefs of your type.
I'm sure university will be a great experience for you btw :)
Are you saying that my beliefs are wrong because I haven't gone to university?
7:02 PM
@JingleBells No. Of course not
Come on, he's not saying that
Sorry, what do you mean More?
@JingleBells I mean university is a great place to learn. So I'm sure it will inform your beliefs in a good way
Even if you stick to your position
You will argue it more coherently
Maybe
@MoreAnonymous Btw I was respecting his willingness to discuss with someone who opposes his views and taking a risk (even though a small one) of being presented with opposing information.
@Feynman_00 Thanks ... though I ended up asking the question here on PSE
@JingleBells Fair
@JingleBells can I ask which books have influenced your line of thought? Or is it the youtube algorithm?
7:10 PM
@MoreAnonymous I think I've read a few random economics books and some part the youtube algorithm but it's mainly me sitting and questioning stuff
I think it fundamentally starts with some values you hold and then you research to figure out what suits them best
@JingleBells Hmm ... The youtube algorithm is crap. I'd advise not to use youtube. Since it seems to throw people on a slope heading towards the political left or right
@JingleBells Try reading Chomsky? His take on politics is quite good
@MoreAnonymous I agree, I'm mainly having discussions with ACM to see where I'm wrong :P
He's considered old school left
@MoreAnonymous What is your take on economics and stuff?
@JingleBells I'm honestly not well read enough to say much. But my observations are people seem to want change and there are people who don't like any sort of change. Why? Cause the current system is stable and works for some and they are afraid (or so they articulate) the new changes proposed will lead us all to self annihilation
My personal take is: the social contract is the bare minimum of any democratic state. Beyond that well I dunno
7:19 PM
@MoreAnonymous You might be right, I don't know. Btw you don't need to be 100% in your opinions to share them :-)
As a younger adult you may be excused but if I started saying stuff like this
Aug 15 at 15:14, by JingleBells
@ACuriousMind what is ridiculous about "poor people are poor because they don't make stuff" (again I'm talking about Africa, India, etc.)
Oh boy
your voice has consequences. Inquiry is good. But try to tread carefully.
I still don't understand what's controversial about that. I was not saying that African people are able to make stuff, or that their circumstances are suitable for that. I was just pointing out the fact that if they made stuff and got to consume that stuff, there would be growth and less poverty, am I wrong?
@MoreAnonymous Agreed, it came out sounding as if I think African people are lazy and that's their only problem, which is completely false
Words have power. They reveal to others who we are, and not always in the ways we intended them to.
3
@JingleBells I'm not going to take ACM's place. I think he's better at handling this.
@ACuriousMind So just because I didn't clarify that I wasn't talking about them being lazy it immediately must mean that secretly I'm despising them? I'm assuming that from what you're saying, I could be wrong, no offense.
Pff I'm tired as well lol
We've been doing this with ACM for hours XDD
@ACuriousMind I actually haven't asked this - why are you having these long discussions with me?
7:34 PM
@JingleBells The places you are talking about have a long history of being brutally exploited, first by colonial powers, now by their descendants. A lot of their production goes directly to the "developed world" (think of e.g. sweatshops in India making textiles for the fashionable clothes of the West) - and the return they receive for that is still disproportionate (because they are poor, the wealthy don't have to pay them as much - there's the exploitation of the need to subsist again!).
Wealth and modern means of production do not appear overnight just by working, they have to be accumulated, and the heirs of colonial power - the West, mostly - have given themselves a cruel headstart. Saying "they're poor because they're not making anything" erases this history - even if you don't mean to imply anything about their current ability or character, you are acting as if the weight of history counts for nothing.
@JingleBells Same reason I've written over 1500 answers on the site - if I can make a difference, I should.
@ACuriousMind I agree about the brutal exploitation by colonial powers and stuff in Africa and that they don't get to consume the stuff they produce. In order to have less poverty you need both production AND consumption by African people, and as you said you need time to develop the technology.
@ACuriousMind Btw, what would giving more money to Indian people change (the so called exploited by the West)? It's just gonna raise their prices but not their underlying productivity?
@ACuriousMind Thanks, just another example that wherever there's value there isn't always money
@ACuriousMind That's commendable. If you asked me why I like to answer questions (in life) I would answer that I like hearing myself improve with my explanation skills :P
@Feynman_00 I won't deny that there is also an element of me just liking hearing myself talk :P
I think that's also what makes physicists
Furthermore, the tendency to explain is in human nature
8:30 PM
@ACuriousMind I feel so bad now :P I've only answered 5 questions :P
ever
2 hours later…
10:05 PM
5
Betelgeuse Just Isn’t That Cool: Effective Temperature Alone Cannot Explain the Recent Dimming of Betelgeuse suggests that the recent dimming might be caused by increased optical absorption by dust around the star, based on a spectral analysis. Question: The images below show absorption feature...
Bountied in Astronomy SE
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2022-10-07 10:38:07
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https://cstheory.stackexchange.com/questions/48267/decomposition-of-safety-and-liveness-properties
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# Decomposition of safety and liveness properties
In Alpern,Schneider 86 is described how to extract the automata that recognize safety and liveness properties from a Buchi automaton $$m$$. This shows that any property rapresented by a Buchi automaton is equivalent to the intersection of these two automata. In particular, the automata for the safety properties is represented by making all states of $$m$$ accepting. The question is: although it is a Buchi, can this automaton be determinized by using the subset construction?
Yes. The automata in question are often called "Looping" automata (so you have a keyword to start from). A possible starting point is the following paper: https://faculty.idc.ac.il/udiboker/files/MullerAutomata.pdf
A looping automaton can be described as $$\left$$ where the components are states, alphabet, transition function $$\delta:Q\times \Sigma\to 2^Q$$ and $$Q_0$$ are the initial states. Then, the acceptance condition is that there exists a run on the word. That is, $$w$$ is accepted iff the automaton has some run on it.
It is easy to see (using Kőnig's Lemma) that the acceptance condition can be equivalently described as follows: for a word $$w\in \Sigma^\omega$$, let $$w_i$$ be its prefix up to letter $$i$$, then $$w$$ is accepted iff $$\delta^*(Q_0,w_i)\neq \emptyset$$ for all $$i\in \mathbb{N}$$.
This shows that it's enough to track the subset construction in order to determine acceptance. What you end up is a deterministic automaton whose states are all accepting except for one, that corresponds to $$\emptyset$$.
• thanks for the detailed answer. Do you have some reference in which is discussed this particular case? Feb 23 '21 at 17:42
• I added a reference in the answer. I'm not sure it has a proof of the claim, since the proof is pretty much identical to the case of NFA->DFA translation. Feb 23 '21 at 18:13
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2022-01-22 09:48:35
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http://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.2014.51.3.621
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- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
Solutions of systems of variational inequalities on fixed points of nonexpansive mappings Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 621-640 https://doi.org/10.4134/BKMS.2014.51.3.621Published online May 31, 2014 Hossein Piri University of Bonab Abstract : In this paper, we introduce a new approximating method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solution of system variational inequalities for finite family of inverse strongly monotone mappings and strictly pseudo-contractive of Browder-Petryshyn type mappings. We show that the sequence converges strongly to a common element the above two sets under some parameter controling conditions. Our results improve and extend the results announced by many others. Keywords : fixed point, $\delta$-strongly monotone, $\lambda$-strictly pseudo-contractive, strong convergence, nonexpansive mapping MSC numbers : 20D15, 20D45 Downloads: Full-text PDF
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2020-01-23 08:08:21
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https://www.vibestechnology.com/case/vibes-bmw-dynamic-subtructuring/
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# VIBES & BMW Group
Virtually optimizing and selecting the best components to reduce NVH issues can be carried out with Frequency Based Substructuring (FBS) using test data. Applying this method in the early development stage allows OEMs to bridge the gap between the concept phase and the first actual vehicle prototype. With the support of the Eurostars program, VIBES is developing software applications to implement FBS. This article presents a successful implementation of the method on an electric drivetrain. The entire project has been conducted in collaboration with BMW. The full paper can be found here.
## The goal
The investigation aims to verify whether FBS can be used to accurately predict the NVH performance of an electric vehicle, taking into account the noise and vibrations produced by the electric drive unit. The results obtained using substructuring will be compared with validation measurements of the assembled system.
## The component
The component analyzed is an electrical drivetrain. In the assembly, 3 subsystems can be distinguished: the EDU (Electric Drive Unit), the RAC (Rear Axle Carrier), and the TMB (the bodywork or “trimmed-body”). A total of 8 coupling points can be identified: 4 of them connect the EDU to the RAC, and the other 4 connect the latter to the trimmed body. The following figure shows the original full-vehicle assembly, for which operational run-up measurements have been conducted. In the figure, it is possible to see the three-stage FBS model: here the assembly is visualized as a chain of the 3 subsystems and the 8 coupling points.
Schematic overview of the e-drivetrain assembly. Source: link
## Technical approach
### Overview
The dynamic behavior of each subsystem shown in the figure is experimentally obtained using the software DIRAC. The dynamic stiffness of the rubber mounts is calculated with the inverse substructuring method. The components are then coupled using the compliant FBS coupling technique. This is the case because the rubber bushings that connect the subsystems are made of flexible material with negligible mass.
The active excitations of the EDU are described with blocked forces, which are obtained using the so-called free velocity method. The blocked forces are later applied to the coupled system. The results of the FBS analysis are then compared with the measurements of the assembled system as validation.
### Subsystems FRFs calculation
To create a full vehicle model using FBS, the dynamic behavior of each subsystem is needed. The model of each component has been obtained through impact testing in a free-free configuration. This means that all the components have been either freely suspended or placed on air springs to have the interface Degrees of Freedom (DoFs) free to displace.
The test-based models are obtained using DIRAC, which is designed to optimize the test-based modeling, ensuring high-quality results into the kHz range. The modeling process consists of 4 steps:
1. Design of Experiment (DoE) preparation: in this step, the design of experiment is recreated in a 3D environment. The CAD geometries of the subsystems are loaded in DIRAC, and the sensors, excitations and Virtual Points (VPs) are defined.
2. Instrumentation and DAQ setup: the accelerometers are attached to the components following the DoE previously created and are connected to the Müller-BBM MKII data acquisition system. Two impact hammers have been used, one with a rubber tip (to excite low frequencies) and one with a nylon tip (for higher frequencies), which are automatically merged in the software.
3. Impact testing: following the predefined DoE, DIRAC guides the user in the measurement phase. Here, all the impacts are performed and the FRFs of the components are calculated. Multiple Virtual Point indicators are used to evaluate the quality of the measurements. Operational Deflection Shape animations (ODS) are used to verify the correct sensors’ orientations.
4. Virtual Point Transformation (VPT) and analysis: the VPT is applied live during FRF measurement. The quality of the transformed FRFs is verified through other quality indicators implemented in DIRAC such as consistency, reciprocity and passivity of the resulting VPs.
An example of the VPT FRFs of the rear axle carrier in DIRAC is shown in the following figure.
The Virtual Point FRF matrix of the 8 coupling points of the rear axle carrier.
The whole process has been applied to each of the subcomponents (EDU, RAC, and TMB), and their dynamic behavior is represented by respectively $$\mathbf{Y}^\mathrm{A}$$, $$\mathbf{Y}^\mathrm{C}$$ and $$\mathbf{Y}^\mathrm{E}$$ (notation from the first figure). In addition, to validate the substructuring of the first connection stage (obtained using FBS), a test-based model of the assembled EDU and RAC has been measured as well.
Each Virtual Point has been described with 6 DoFs (3 translations and 3 rotations).
### Mount stiffness modeling
After obtaining the test-based models of the three subsystems, it is necessary to characterize the rubber bushings. A combination of DIRAC and the VIBES Toolbox for MATLAB is used for the mounts modeling.
Aluminum transmission simulators have been machined to fit tightly to the rubber bushing cylinder and its ends. A total of 14 triaxial accelerometers have been glued, and 37 impact positions and 2 Virtual Points (with 6 DoFs each) have been defined in DIRAC. The complete design of experiment made in DIRAC can be seen in the next figure.
Model of the rubber bushing in DIRAC. Source: link
After impact testing, the 12×12 Virtual Points transformed matrix $$\mathbf{Y}_{\mathrm{qm}}(\omega)$$ is calculated and inverted to obtain $$\mathbf{Z}^{\mathrm{mnt}}(\omega)$$ which is the dynamic stiffness matrix of the assembly (mount and transmission simulators).
The inverse substructuring technique has proven that the off-diagonal blocks of the dynamic stiffness matrix approximate the dynamic stiffness of the mount only. This is valid up to the first internal resonance of the mount. The bushing stiffness obtained with the inverse substructuring method has been compared with the data provided by the mount supplier. From the following figure, it can be seen that the curves align well.
Comparison of bushing stiffness provided by the supplier and calculated with inverse substructuring. Source: link
The bushing stiffness obtained with inverse substructuring is later used when the components are coupled to obtain the substructured vehicle model.
### Operational measurements and blocked forces calculation
Directly measuring the internal forces produced by the EDU is not possible. For this reason, a set of equivalent forces $$\mathbf{f}_2^{\mathrm{eq}}$$ (also called blocked forces $$\mathbf{f}_2^{\mathrm{bl}}$$) are used. They are an inherent property of the EDU itself (independent of the receiver). When applied at the interface of the assembled system, they produce on the passive side the same response that the internal forces would cause.
The blocked forces are obtained on the active side and are defined as
$$\mathbf{f}_2^{\mathrm{bl}} = \left ( \mathbf{Y}_{\mathrm{22}}^\mathrm{A} \right )^{-1} \mathbf{u}_2^{\mathrm{free}}$$
where $$\mathbf{Y}_{\mathrm{22}}^\mathrm{A}$$ is the dynamic stiffness of the drivetrain at the active side interface and $$\mathbf{u}_2^{\mathrm{free}}$$ are the operational accelerations. In addition, to validate the results at the end of the project, operational measurements of the engine attached to the full-vehicle are performed. For the purpose, sound pressure levels ($$\mathbf{u}_6^{\mathrm{val}}$$) at the passengers’ ears are recorded with microphones.
### Components compliant coupling
The goal of the components’ coupling is to build the transfer functions of the full assembly using the FRFs of the three single components (EDU, RAC, and TMB). Rigid LM-FBS consists in assembling the dynamic matrices of the three subsystems ($$\mathbf{Y}^\mathrm{A}$$, $$\mathbf{Y}^\mathrm{C}$$ and $$\mathbf{Y}^\mathrm{E}$$) enforcing strict coordinate compatibility and force equilibrium for each matching DoF.
For this case, the main equation of LM-FBS is built up assembling the 3 matrices of the subsystems as follows:
$$\mathbf{Y}^\mathrm{coupl}_{\mathrm{rigid}} = \mathbf{Y} \left ( \mathbf{I} – \mathbf{B}^\mathrm{T} \left ( \mathbf{BYB^\mathrm{T}} \right )^{-1} \mathbf{BY} \right )$$
Where
$$\mathbf{Y} \overset{\Delta}{=} \begin{bmatrix} \begin{bmatrix} \mathbf{Y}^\mathrm{A}_{11} & \mathbf{Y}^\mathrm{A}_{12}\\ \mathbf{Y}^\mathrm{A}_{21} & \mathbf{Y}^\mathrm{A}_{22} \end{bmatrix} & \mathbf{0} & \mathbf{0}\\ \mathbf{0} & \begin{bmatrix} \mathbf{Y}^\mathrm{C}_{33} & \mathbf{Y}^\mathrm{C}_{34}\\ \mathbf{Y}^\mathrm{C}_{43} & \mathbf{Y}^\mathrm{C}_{44} \end{bmatrix} & \mathbf{0}\\ \mathbf{0} & \mathbf{0} & \begin{bmatrix} \mathbf{Y}^\mathrm{E}_{55} & \mathbf{Y}^\mathrm{E}_{56}\\ \mathbf{Y}^\mathrm{E}_{65} & \mathbf{Y}^\mathrm{E}_{66} \end{bmatrix} \end{bmatrix}$$
And B is the Boolean compatibility matrix:
$$\mathbf{B} \overset{\Delta}{=} \left [ \begin{bmatrix} \mathbf{0} & \mathbf{I}\\ \mathbf{0} & \mathbf{0} \end{bmatrix} \begin{bmatrix} \mathbf{-I} & \mathbf{0}\\ \mathbf{0} & \mathbf{I} \end{bmatrix} \begin{bmatrix} \mathbf{0} & \mathbf{0} \\ \mathbf{-I} & \mathbf{0} \end{bmatrix} \right ]$$
In the current case, however, the three subsystems are connected through flexible rubber bushing, and therefore, the compliant coupling technique could be the best technique to use. This fact has been investigated comparing the FRFs of the components at the engine side and after the bushing, as shown in the following figure.
FRFs of the EDU and RAC before and after the bushing.
It can be observed that up to about 16 Hz, the EDU and RAC transfer functions overlap, which means that the two components and the mount behave as a rigid body. After that frequency level, the curves start deviating one from the other, and the flexibility of the rubber bushing starts playing a role.
This deviation of the dynamic behavior between the EDU and the RAC can also be noticed when observing the two components’ Operational Deflection Shape (ODS). The next figure shows two snapshots of the ODS at a frequency of 40 Hz. It can be noticed that a relative movement between the two components is present at this frequency.
Snapshots of the operational deflection shape of the EDU and the RAC at 40 Hz.
This analysis proves that compliant coupling is the coupling technique that needs to be used for the current case. The calculated dynamic stiffness of the rubber bushings is taken into account at the relevant coupling DoFs. For this reason, the formula used for the compliant coupling considers the calculated dynamic stiffness of the bushings ($$\mathbf{Y}^\mathrm{mnt}$$):
$$\mathbf{Y}^\mathrm{coupl}_{\mathrm{compliant}} = \mathbf{Y}\left ( \mathbf{I}-\mathbf{B}^\mathrm{T} \left ( \mathbf{BYB}^\mathrm{T} + \mathbf{Y}^\mathrm{mnt} \right )^{-1} \mathbf{BY}\right )$$
The compliant LM-FBS coupling for this application has been performed in the VIBES Toolbox for MATLAB.
### Subsystems coupling and first stage validation
To verify the accuracy of the substructured model, the FRFs of the coupled EDU and RAC $$(\mathbf{Y}^\mathrm{A + B+C})$$ are compared with the data of the assembled EDU and RAC that have been previously measured with DIRAC. The results can be seen in the next figure. Here, the accelerance and phase of the FRFs at the engine side (left) and after the bushing (right) are shown.
FRF comparison of an excitation at the engine in Z-direction to the rear-right engine measurement point in Z-direction.
FRF comparison of an excitation at the engine in Z-direction to the rear axle carrier after the mount in Z-direction.
Validation of the coupling of the drive unit with the rear axle carrier. Source: link
Looking at the left figure, it can be noticed that the two curves overlap quite well up to 1 kHz. Also after the mount (right figure) the two curves match, but deviations at higher frequencies are present. The cause of the mismatch could be either minor positioning errors in the measurements or some numerical effects during coupling.
It can be concluded that the compliant coupling with the simplified bushing models performs well in the current situation.
After validating the engine’s coupling with the rear axle, the last subsystem (trimmed body) is added. At this stage, the substructured full vehicle model ($$\mathbf{Y}^\mathrm{full \; vehicle}$$) is available.
## Component-based TPA / Applying the excitations to the substructured model
In the next step, the blocked forces are applied to the full-vehicle model that has been built using FBS ($$\mathbf{Y}^\mathrm{full \; vehicle}$$ ) and the resulting sound pressures at the microphones placed at the passengers’ ears locations ($$\mathbf{u}_6$$) are calculated using the formula
$$\mathbf{u}_6 = (\mathbf{Y}^\mathrm{full \; vehicle}) \mathbf{f}_2^{\mathrm{bl}}$$
The results are compared with the validation measurements performed with the engine attached to the full-vehicle ($$\mathbf{u}_6^{\mathrm{val}}$$). The following figures show respectively the Campbell diagram of the measured sound pressure levels and the predicted ones at the passengers’ ears.
The two plots show a good match between measurements and predictions up to 500 Hz. At about 850-900 Hz, the model obtained through component TPA and substructuring presents a mismatch in the coupled FRFs. Overall, the two diagrams show the same pattern except for the mismatch.
Measured sound pressure level.
Predicted sound pressure level using component TPA and the substructured full vehicle model.
Campbell diagrams of the measured and predicted sound pressure levels at the microphone’s positioned at the passengers’ ears.
It can be concluded that the full vehicle model built with frequency based substructuring performed well in the component TPA carried out in this project.
## Benefits of FBS
This project proved that FBS is an excellent solution to obtain full vehicle models starting from single components. It has also been demonstrated that the dynamic stiffness of rubber bushings calculated through inverse substructuring matches with the mounts data provided by the suppliers.
The benefits of using FBS are listed:
• FBS allows for the combination of subsystem models that get assembled to form a full vehicle model.
• With FBS, it is possible to exchange substructures and directly simulate the dynamics of the new system leaving all the other subsystems unchanged.
• The subsystems dynamics can either originate from Finite Element Models (FEM) or from component or subsystem measurements, allowing for a hybrid development approach.
• The full-vehicle model, simulated through FBS, can be used to close the gap in full-vehicle analysis and responsibility between the early-stage conception phase and the first actual prototype in hardware.
• Subsystems FRFs/NTFs are typically obtained at higher signal-to-noise ratios (SNR) than full-vehicle FRFs/NTFs, and thus a better overall quality can be reached.
## Acknowledgment
The shown methods of frequency based substructuring and mount stiffness characterization with inverse substructuring were applied and validated within the scope of a project with industry partner BMW. VIBES likes to thank our partner for providing the opportunity to apply and prove our methodology and to publish the results within a case study.
Do you want to know more? Get in touch with VIBES or read more cases, using the buttons below! You can also download the full paper here!
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2022-12-01 10:28:01
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http://btads.xyz/garden-soil-bag-calculator/
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# Garden Soil Bag Calculator
Posted on
Calculating how much mulch or soil you need is simple and easy … just multiply length(m) x width(m) x depth(m) or you can use the handy mulch and soil calculator below. It will convert your measurements into cubic feet and yards so you’ll know how much potting soil you’ll need for your window box, garden plot, flower bed, or yard.
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### The topsoil calculator will help you figure out how much topsoil or potting soil to buy, with a breakdown in terms of bags or yards.
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Use this calculator to figure out how much product you need to complete your project. The soil calculator first works out the area of the garden bed you will be looking to fill with soil. Online topsoil calculator to estimate how much topsoil you need for your gardening project.
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If you’re considering getting a topsoil bag for your garden, remember to plan your project before you buy, and consider the area, depth and density of topsoil you need. Raised bed soil calculator we’ve seen far too many raised beds filled with “potting mix” from the landscape supply company with unhappy plants and unhappy gardeners. Input the length (a), width (b) and height (c) of your space to our topsoil calculator to find the volume in m³.
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2021-10-24 14:58:59
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https://au.mathworks.com/help/stats/lasso-regularization-of-generalized-linear-models.html
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## Lasso Regularization of Generalized Linear Models
### What is Generalized Linear Model Lasso Regularization?
Lasso is a regularization technique. Use lassoglm to:
• Reduce the number of predictors in a generalized linear model.
• Identify important predictors.
• Select among redundant predictors.
• Produce shrinkage estimates with potentially lower predictive errors than ordinary least squares.
Elastic net is a related technique. Use it when you have several highly correlated variables. lassoglm provides elastic net regularization when you set the Alpha name-value pair to a number strictly between 0 and 1.
For details about lasso and elastic net computations and algorithms, see Generalized Linear Model Lasso and Elastic Net. For a discussion of generalized linear models, see What Are Generalized Linear Models?.
### Generalized Linear Model Lasso and Elastic Net
#### Overview of Lasso and Elastic Net
Lasso is a regularization technique for estimating generalized linear models. Lasso includes a penalty term that constrains the size of the estimated coefficients. Therefore, it resembles Ridge Regression. Lasso is a shrinkage estimator: it generates coefficient estimates that are biased to be small. Nevertheless, a lasso estimator can have smaller error than an ordinary maximum likelihood estimator when you apply it to new data.
Unlike ridge regression, as the penalty term increases, the lasso technique sets more coefficients to zero. This means that the lasso estimator is a smaller model, with fewer predictors. As such, lasso is an alternative to stepwise regression and other model selection and dimensionality reduction techniques.
Elastic net is a related technique. Elastic net is akin to a hybrid of ridge regression and lasso regularization. Like lasso, elastic net can generate reduced models by generating zero-valued coefficients. Empirical studies suggest that the elastic net technique can outperform lasso on data with highly correlated predictors.
#### Definition of Lasso for Generalized Linear Models
For a nonnegative value of λ, lassoglm solves the problem
$\underset{{\beta }_{0},\beta }{\mathrm{min}}\left(\frac{1}{N}\text{Deviance}\left({\beta }_{0},\beta \right)+\lambda \sum _{j=1}^{p}|{\beta }_{j}|\right).$
• The function Deviance in this equation is the deviance of the model fit to the responses using the intercept β0 and the predictor coefficients β. The formula for Deviance depends on the distr parameter you supply to lassoglm. Minimizing the λ-penalized deviance is equivalent to maximizing the λ-penalized loglikelihood.
• N is the number of observations.
• λ is a nonnegative regularization parameter corresponding to one value of Lambda.
• The parameters β0 and β are a scalar and a vector of length p, respectively.
As λ increases, the number of nonzero components of β decreases.
The lasso problem involves the L1 norm of β, as contrasted with the elastic net algorithm.
#### Definition of Elastic Net for Generalized Linear Models
For α strictly between 0 and 1, and nonnegative λ, elastic net solves the problem
$\underset{{\beta }_{0},\beta }{\mathrm{min}}\left(\frac{1}{N}\text{Deviance}\left({\beta }_{0},\beta \right)+\lambda {P}_{\alpha }\left(\beta \right)\right),$
where
${P}_{\alpha }\left(\beta \right)=\frac{\left(1-\alpha \right)}{2}{‖\beta ‖}_{2}^{2}+\alpha {‖\beta ‖}_{1}=\sum _{j=1}^{p}\left(\frac{\left(1-\alpha \right)}{2}{\beta }_{j}^{2}+\alpha |{\beta }_{j}|\right).$
Elastic net is the same as lasso when α = 1. For other values of α, the penalty term Pα(β) interpolates between the L1 norm of β and the squared L2 norm of β. As α shrinks toward 0, elastic net approaches ridge regression.
### References
[1] Tibshirani, R. Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society, Series B, Vol. 58, No. 1, pp. 267–288, 1996.
[2] Zou, H. and T. Hastie. Regularization and Variable Selection via the Elastic Net. Journal of the Royal Statistical Society, Series B, Vol. 67, No. 2, pp. 301–320, 2005.
[3] Friedman, J., R. Tibshirani, and T. Hastie. Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, Vol. 33, No. 1, 2010. https://www.jstatsoft.org/v33/i01
[4] Hastie, T., R. Tibshirani, and J. Friedman. The Elements of Statistical Learning, 2nd edition. Springer, New York, 2008.
[5] McCullagh, P., and J. A. Nelder. Generalized Linear Models, 2nd edition. Chapman & Hall/CRC Press, 1989.
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2021-01-15 20:47:40
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https://wikivisually.com/wiki/%24INDU
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# Dow Jones Industrial Average
### Bull market of 2009–present
Towards the latter half of 2009, the average rallied towards the 10,000 level amid optimism that the Late-2000s (decade) Recession, the United States Housing Bubble and the Global Financial Crisis of 2008–2009, were easing and possibly coming to an end. For the decade, the Dow saw a rather substantial pullback for a negative return from the 11,497 level to 10,428, a loss of a little over 9%.
The DJIA from January 2000 through February 2015.
During the early part of the 2010s, aided somewhat by the loose monetary policy practiced by the Federal Reserve, the Dow made a notable rally attempt, though with significant volatility due to growing global concerns such as the 2010 European sovereign debt crisis, the Dubai debt crisis, and the United States debt ceiling crisis. On May 6, 2010, the index lost around 400 points over the day, then just after 2:30 pm EDT, it lost about 600 points in just a few minutes, and gained the last amount back about as quickly. The intra-day change at the lowest point was 998.50 points, the largest intra-day point decline ever, representing an intra-day loss of 9.2%. The event, during which the Dow bottomed out at 9,869 before recovering to end with a 3.2% daily loss at 10,520.32, became known as the 2010 Flash Crash.[26] The index closed the half-year at 9,774.02 for a loss of 7.7%.[27]
On May 3, 2013, the Dow surpassed the 15,000 mark for the first time, while later on November 18, it closed above the 16,000 level.[28] Following a strong jobs report on July 3, 2014, the Dow traded above the 17,000 mark for the first time,[29] on December 23, 2014, the DJIA traded above the 18,000 boundary for the first time, after data showed the U.S. economy posted its strongest growth in more than a decade.[30] The index closed 2014 at 17,823.07 for a gain of 71% for the five years.[31]
During the summer of 2015 the Dow began to retreat from its all-time high due to overwhelming economic factors entering correction for the first time since 2011.[citation needed] By October, the Dow had exited correction rallying 14% from its August lows, but failed to hit a record high set back in May.[citation needed] In November and December, the Dow continued to retreat from the 14% rally in October, leading some to call it a bear market,[32][33] this led to the Dow closing at 17,425.03 for 2015, the first annual loss since 2008.[34] After nearly 14 months since the last record close, the Dow finally achieved a fresh new, central-bank debt fuelled record close on July 20, 2016 at 18,595.03 along with an intraday high of 18,622.01.[35]
Despite anticipations of post-election selloffs, the Dow rallied significantly after Donald Trump was elected President, on January 25, 2017, the Dow hit a record high of 20,000, an increase of 1,667 points since his election in November 2016.[36][37] On March 1, 2017, the Dow broke through the 21,000 level,[38] reaching a new all-time high, the 1,000 point gain took just 35 days being tied for the fastest time ever. The Dow hit yet another new high just 5 months later, surpassing the 22,000 level[39] on August 2, 2017.
## Investing
Investing in the DJIA is made widely accessible in equities through exchange-traded funds (ETFs) as well as in derivatives through option contracts and futures contracts.
The index is tracked by an exchange-traded fund, the SPDR Dow Jones Industrial Average (NYSE ArcaDIA), commonly called "diamonds". This fund is part of the SPDR family of ETFs from State Street Global Advisors, this fund was introduced in 1998, and it was previously called DIAMONDS Trust, Series 1.
### Options contracts
The Chicago Board Options Exchange (CBOE) issues Options Contracts on the Dow through the root symbol DJX in combination with long-term expiration options called DJX LEAPS. There are also options on the various ETFs; Performance ETFs, Inverse Performance ETFs, 2x Performance ETFs, Inverse 2x Performance ETFs, 3x Performance ETFs, and Inverse 3x Performance ETFs.
## Calculation
To calculate the DJIA, the sum of the prices of all 30 stocks is divided by a divisor, the Dow Divisor, the divisor is adjusted in case of stock splits, spinoffs or similar structural changes, to ensure that such events do not in themselves alter the numerical value of the DJIA. Early on, the initial divisor was composed of the original number of component companies; which made the DJIA at first, a simple arithmetic average. The present divisor, after many adjustments, is less than one (meaning the index is larger than the sum of the prices of the components), that is:
${\displaystyle {\text{DJIA}}={\sum p \over d}}$
where p are the prices of the component stocks and d is the Dow Divisor.
Events such as stock splits or changes in the list of the companies composing the index alter the sum of the component prices; in these cases, in order to avoid discontinuity in the index, the Dow Divisor is updated so that the quotations right before and after the event coincide:
${\displaystyle {\text{DJIA}}={\sum p_{\text{old}} \over d_{\text{old}}}={\sum p_{\text{new}} \over d_{\text{new}}}.}$
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2017-11-17 23:20:56
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https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_2539033
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English
# Item
ITEM ACTIONSEXPORT
Released
Journal Article
#### Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory
##### MPS-Authors
/persons/resource/persons20659
Hinder, Ian
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
/persons/resource/persons213835
Pfeiffer, Harald
Astrophysical and Cosmological Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
##### External Ressource
No external resources are shared
1709.02007.pdf
(Preprint), 3MB
##### Supplementary Material (public)
There is no public supplementary material available
##### Citation
Hinder, I., Kidder, L. E., & Pfeiffer, H. (2018). Eccentric binary black hole inspiral-merger-ringdown gravitational waveform model from numerical relativity and post-Newtonian theory. Physical Review D, 98: 044015. doi:10.1103/PhysRevD.98.044015.
Cite as: http://hdl.handle.net/21.11116/0000-0000-6390-D
##### Abstract
We present a prescription for computing gravitational waveforms for the inspiral, merger and ringdown of non-spinning eccentric binary black hole systems. The inspiral waveform is computed using the post-Newtonian expansion and the merger waveform is computed by interpolating a small number of quasi-circular NR waveforms. The use of circular merger waveforms is possible because eccentric binaries circularize in the last few cycles before the merger, which we demonstrate up to mass ratio $q = m_1/m_2 = 3$. The complete model is calibrated to 23 numerical relativity (NR) simulations starting ~20 cycles before the merger with eccentricities $e_\text{ref} \le 0.08$ and mass ratios $q \le 3$, where $e_\text{ref}$ is the eccentricity ~7 cycles before the merger. The NR waveforms are long enough that they start above 30 Hz (10 Hz) for BBH systems with total mass $M \ge 80 M_\odot$ ($230 M_\odot$). We find that, for the sensitivity of advanced LIGO at the time of its first observing run, the eccentric model has a faithfulness with NR of over 97% for systems with total mass $M \ge 85 M_\odot$ across the parameter space ($e_\text{ref} \le 0.08, q \le 3$). For systems with total mass $M \ge 70 M_\odot$, the faithfulness is over 97% for $e_\text{ref} \lesssim 0.05$ and $q \le 3$. The NR waveforms and the Mathematica code for the model are publicly available.
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2021-01-18 21:14:08
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http://www.ams.org/books/memo/0787/
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# memo_has_moved_text();Interpolation of weighted Banach lattices. A characterization of relatively decomposable Banach lattices
### About this Title
Michael Cwikel, Per G. Nilsson and Gideon Schechtman
Publication: Memoirs of the American Mathematical Society
Publication Year 2003: Volume 165, Number 787
ISBNs: 978-0-8218-3382-7 (print); 978-1-4704-0385-0 (online)
DOI: http://dx.doi.org/10.1090/memo/0787
MathSciNet review: 1996919
MSC: Primary 46B70; Secondary 46B42, 46E30, 46M35
View full volume PDF
Read more about this volume
View other years and numbers:
### Table of Contents
Chapters
• Interpolation of weighted Banach lattices
• 0. Introduction
• 1. Definitions, terminology and preliminary results
• 2. The main results
• 3. A uniqueness theorem
• 4. Two properties of the $K$-functional for a couple of Banach lattices
• 5. Characterizations of couples which are uniformly Calderón-Mityagin for all weights
• 6. Some uniform boundedness principles for interpolation of Banach lattices
• 7. Appendix: Lozanovskii’s formula for general Banach lattices of measurable functions
• A characterization of relatively decomposable Banach lattices
• 1. Introduction
• 2. Equal norm upper and lower $p$-estimates and some other preliminary results
• 3. Completion of the proof of the main theorem
• 4. Application to the problem of characterizing interpolation spaces
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2017-09-26 17:24:11
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http://www.computer.org/csdl/trans/td/2001/03/l0293-abs.html
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Subscribe
Issue No.03 - March (2001 vol.12)
pp: 293-305
ABSTRACT
<p><b>Abstract</b>—Mesh-connected computers (MCCs) are a class of important parallel architectures due to their simple and regular interconnections. However, their performances are restricted by their large diameters. Various augmenting mechanisms have been proposed to enhance the communication efficiency of MCCs. One major approach is to add nonconfigurable buses for improved broadcasting. A typical example is the mesh-connected computer with multiple buses (MMB). We propose a new class of generalized MMBs, the improved generalized MMBs (IMMBs). We compare IMMBs with MMBs and a class of previously proposed generalized MMBs (GMMBs). We show the power of IMMBs by considering semigroup and prefix computations. Specifically, as our main result we show that for any constant <tmath>$0 < \epsilon < 1$</tmath>, one can construct an <tmath>$N^{{1 \over 2}} \times N^{1 \over 2}$</tmath> square IMMB using which semigroup and prefix computations on <tmath>$N$</tmath> operands can be carried out in <tmath>$O(N^{\epsilon})$</tmath> time, while maintaining <tmath>$O(1)$</tmath> broadcasting time. Compared with the previous best complexities <tmath>$O(N^{ 1\over {8}})$</tmath> and <tmath>$O(N^{1\over {16}})$</tmath> achieved on a rectangular MMB and GMMB, respectively, for the same computations, our results show that IMMBs are more powerful than MMBs and GMMBs.</p>
INDEX TERMS
Bus, mesh-connected computer, mesh-connected computer with multiple buses, parallel algorithm, parallel architecture, parallel computing, processor array.
CITATION
Yi Pan, S.q. Zheng, Keqin Li, Hong Shen, "An Improved Generalization of Mesh-Connected Computers with Multiple Buses", IEEE Transactions on Parallel & Distributed Systems, vol.12, no. 3, pp. 293-305, March 2001, doi:10.1109/71.914773
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2014-10-23 14:39:44
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https://zxi.mytechroad.com/blog/tag/string/page/21/
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Press "Enter" to skip to content
# Problem
In a string S of lowercase letters, these letters form consecutive groups of the same character.
For example, a string like S = "abbxxxxzyy" has the groups "a""bb""xxxx""z" and "yy".
Call a group large if it has 3 or more characters. We would like the starting and ending positions of every large group.
The final answer should be in lexicographic order.
Example 1:
Input: "abbxxxxzzy"
Output: [[3,6]]
Explanation: "xxxx" is the single large group with starting 3 and ending positions 6.
Example 2:
Input: "abc"
Output: []
Explanation: We have "a","b" and "c" but no large group.
Example 3:
Input: "abcdddeeeeaabbbcd"
Output: [[3,5],[6,9],[12,14]]
Note: 1 <= S.length <= 1000
# Solution: Brute Force
Time complexity: O(n)
Space complexity: O(n)
C++
# Problem
A sentence S is given, composed of words separated by spaces. Each word consists of lowercase and uppercase letters only.
We would like to convert the sentence to “Goat Latin” (a made-up language similar to Pig Latin.)
The rules of Goat Latin are as follows:
• If a word begins with a vowel (a, e, i, o, or u), append "ma" to the end of the word.
For example, the word ‘apple’ becomes ‘applema’.
• If a word begins with a consonant (i.e. not a vowel), remove the first letter and append it to the end, then add "ma".
For example, the word "goat" becomes "oatgma".
• Add one letter 'a' to the end of each word per its word index in the sentence, starting with 1.
For example, the first word gets "a" added to the end, the second word gets "aa" added to the end and so on.
Return the final sentence representing the conversion from S to Goat Latin.
Example 1:
Input: "I speak Goat Latin"
Output: "Imaa peaksmaaa oatGmaaaa atinLmaaaaa"
Example 2:
Input: "The quick brown fox jumped over the lazy dog"
Output: "heTmaa uickqmaaa rownbmaaaa oxfmaaaaa umpedjmaaaaaa overmaaaaaaa hetmaaaaaaaa azylmaaaaaaaaa ogdmaaaaaaaaaa"
Notes:
• S contains only uppercase, lowercase and spaces. Exactly one space between each word.
• 1 <= S.length <= 100.
C++
# Problem
Given a list of words, we may encode it by writing a reference string S and a list of indexes A.
For example, if the list of words is ["time", "me", "bell"], we can write it as S = "time#bell#" and indexes = [0, 2, 5].
Then for each index, we will recover the word by reading from the reference string from that index until we reach a “#” character.
What is the length of the shortest reference string S possible that encodes the given words?
Example:
Input: words = ["time", "me", "bell"] Output: 10 Explanation: S = "time#bell#" and indexes = [0, 2, 5].
Note:
1. 1 <= words.length <= 2000.
2. 1 <= words[i].length <= 7.
3. Each word has only lowercase letters.
# Idea
Remove all the words that are suffix of other words.
# Solution
Time complexity: O(n*l^2)
Space complexity: O(n*l)
# Problem
https://leetcode.com/problems/shortest-distance-to-a-character/description/
Given a string S and a character C, return an array of integers representing the shortest distance from the character C in the string.
Example 1:
Input: S = "loveleetcode", C = 'e'
Output: [3, 2, 1, 0, 1, 0, 0, 1, 2, 2, 1, 0]
Note:
1. S string length is in [1, 10000].
2. C is a single character, and guaranteed to be in string S.
3. All letters in S and C are lowercase.
# Solution: Two Pass
Time complexity: O(n)
Space complexity: O(n)
C++
V2
# Problem
https://leetcode.com/problems/license-key-formatting/description/
You are given a license key represented as a string S which consists only alphanumeric character and dashes. The string is separated into N+1 groups by N dashes.
Given a number K, we would want to reformat the strings such that each group contains exactly K characters, except for the first group which could be shorter than K, but still must contain at least one character. Furthermore, there must be a dash inserted between two groups and all lowercase letters should be converted to uppercase.
Given a non-empty string S and a number K, format the string according to the rules described above.
Example 1:
Input: S = "5F3Z-2e-9-w", K = 4
Output: "5F3Z-2E9W"
Explanation: The string S has been split into two parts, each part has 4 characters.
Note that the two extra dashes are not needed and can be removed.
Example 2:
Input: S = "2-5g-3-J", K = 2
Output: "2-5G-3J"
Explanation: The string S has been split into three parts, each part has 2 characters except the first part as it could be shorter as mentioned above.
Note:
1. The length of string S will not exceed 12,000, and K is a positive integer.
2. String S consists only of alphanumerical characters (a-z and/or A-Z and/or 0-9) and dashes(-).
3. String S is non-empty.
# Solution
Time complexity: O(n)
Space complexity: O(n)
C++
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2020-09-18 16:21:47
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https://math.stackexchange.com/questions/2839544/convex-smooth-function-with-a-single-critical-point-must-be-global-minimum
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# Convex smooth function with a single critical point must be global minimum?
Let $f\colon \mathbb{R}^n \to \mathbb{R}$ be a convex smooth function such that $f$ has a unique critical point. Is that point necessarily a global minimum? If it isn't, which other hypothesis should I add to the current ones to get this result?
• Please consult this Wiki - Second partial derivative test. – bubububub Jul 3 '18 at 12:14
• Smoothness and convexity is sufficient. Any critical point (even if multiple points exist) will be a global minimum. – Theo Bendit Jul 3 '18 at 12:32
• Smoothness is not necessary; a critical point of a convex function is globally optimal. – LinAlg Jul 3 '18 at 12:56
• Convexity and smoothness are sufficient to conclude this. You may even be able to relax the smoothness/critical point criteria a little and still get the result. – CyclotomicField Jul 3 '18 at 12:56
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2019-04-24 08:12:20
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https://cs.stackexchange.com/tags/communication-complexity/hot?filter=all
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# Tag Info
5
The two players construct a sequence $V_0 \supset V_1 \supset \cdots \supset V_m$ of sets of vertices such that: $V_0$ consists of all vertices in the graph. $|V_{i+1}| \leq (|V_i|+1)/2$. $V_i \supseteq C \cap I$. The players stop once $|V_m| \leq 1$. At this point they can answer the question using $O(1)$ communication. At round $i$, the players know $V_{... 5 Consider the following task$f$: Given$x,y \in \{0,1\}^n$, Alice and Bob need to determine whether$d(x,y) \bmod{4} \in \{0,1\}$, where$d(x,y)$is the Hamming distance between$x$and$y$. Let$M_f$denote the matrix corresponding to this problem:$M_f(x,y) = 1$if the answer is Yes, and$M_f(x,y) = -1$if the answer is No. The discrepancy method shows ... 4 The function is described in a footnote in Nisan and Wigderson's paper On rank vs. communication complexity. It is $$E(z_1 \dots z_6) = \sum_i z_i - \sum_{ij} z_{i}z_{j} + \\z_1z_3z_4 + z_1z_2z_5 + z_1z_4z_5 + z_2z_3z_4 + z_2z_3z_5 + \\ z_1z_2z_6 + z_1z_3z_6 + z_2z_4z_6 + z_3z_5z_6 + z_4z_5z_6.$$ 3 The$O(\log n)$rounds comes from the fact that we are doing a binary search: If the algorithm fails to terminate, then either Alice or Bob share a vertex v. If Alice shares$v$, then$v$has fewer than$|V_{i-1}|/2$neighbors in$V_{i-1}$.$V_i$is set to be this neighborhood (along with v). Observe that$|V_i|< |V_{i-1}|/2+1$. We will be a little ... 3 You can do this with$O(K \log N)$bits of communication on average, where$K$is the size of$|(A\setminus B) \cup (B\setminus A)|$, assuming you are willing to use a non-interactive protocol and are willing to accept a randomized protocol. Let$H(\cdot)$denote a randomized hash function. Do binary search on$i$to find the smallest$i$such that$H(a_1,\...
3
By simply exchanging random indices you cannot hope to do better than $\Omega(n)$ communication if you want constant error probability. If the strings differ in only a single bit, and you exchange $k$ indices, then the probability of finding the index in which they differ is $\frac{k}{n}$, so if you want this to be constant you must have $k=\Omega(n)$. The ...
3
Assume that each player gets a number in $[n]$, and they can compute $h_n(x,y)$. Each player knows $n$, so if $h_n$ is computable with less than $log(n)$ communication, they can compute $h_n(n-x,y)$ in under $log(n)$ bits of communication. Since you have $h_n(n-x,y)=1 \iff x=y$ then you managed to compute $\delta_{x,y}$ in sub logarithmic communication, ...
3
Geometric rectangle is not a standard term. That's why they define it in the question. In communication complexity, Alice has an input from the set $X$, and Bob has an input from the set $Y$. Usually we assume that the sets $X,Y$ are unstructured. A combinatorial rectangle is a subset of $X \times Y$ of the form $A \times B$, where $A \subseteq X$ and $B \... 2 Deterministic communication complexity depends only on the support of the input distribution (the "promise"). Even if$H(X|Y),H(Y|X) < 1$the distribution$(X,Y)$could have full support, so the$\Omega(n)$bound still holds. 2 The protocol gives you a covering of the zeroes using$2n$rectangles$R_{i,b} = X_{i,b} \times Y_{i,1-b}$, where$X_{i,b}$(or$Y_{i,b}$) is the set of words whose$i$th bit equals$b$. 2 Your definition is wrong. The correct definition is as follows. A protocol$P$is$\epsilon$-differentially private (for$\epsilon > 0$) if for any two inputs$Z_1,Z_2$differing in a single coordinates and any$p$, $$e^{-\epsilon} \leq \frac{\Pr[P(Z_1) = p]}{\Pr[P(Z_2) = p]} \leq e^\epsilon.$$ For small$\epsilon>0$,$e^\epsilon \approx 1 + \epsilon$... 2 The view of Alice is what Alice gets to see; it is a probability distribution that depends on the inputs of both players$x,y$. It is a distribution over triples$(x,\tau,r_A)$, where$x$is Alice's input,$\tau$is the transcript of the protocol, and$r_A$is Alice's private randomness. This probability distribution depends both on$x$and on Bob's input$y$... 2 Your conjecture is refuted by the language$\{ 0^n : \text{$n$ is not a power of $2$}\}$. Let$\{(x_i,y_i) : i \in \mathbb{N}\}$be an infinite fooling set for this language. We can identify$x_i,y_i$with integers. These pairs have to satisfy the following conditions:$x_i + y_i$is not a power of$2$. For each$i \neq j$, either$x_i + y_j$is a power of$...
2
The notion of round should be quite similar to the intuitive idea of "one step of the protocol". At any round you are allowed to send 1 message (of any size) and/or receive one message. The message you send at round $i$ may depend on all the information you have up to round $i$, but it cannot depend on the message you receive at round $i$ (or later). It ...
2
Hint: The condition $x + y + xy = 0$ is equivalent to the condition $1 + x + y + xy = 1$, i.e. $(1 + x)(1 + y) = 1$, or in other words, $$(1+x)^{-1} = 1+y.$$
2
S. Arora, B. Barak, Computational Complexity Modern Approach, Chapter 13 is a good introductory resource to this topic: Communication complexity concerns the following scenario. There are two players with unlimited computational power, each of whom holds an $n$ bit input, say $x$ and $y$. Neither knows the other’s input, and they wish to collaboratively ...
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One possibly better approach would be to use a Merkle tree, or some other hierarchical data structure like that. If there's a large set of transactions that the sender can identify as probably already known to the recipient, then this might save a significant amount of data transfer. Build a binary tree, where each leaf corresponds to a single transaction, ...
2
Here are two solutions. In both cases, the inputs are $x,y \in \{0,1\}^n$, and we are interested in checking whether the Hamming distance between $x$ and $y$ is at most $k$ or not. Solution 1 (D.W.): The two parties decide on a random string $z \in \mathbb{Z}_{2k+3}^n$, compute $\alpha = \langle x,z \rangle$ and $\beta = \langle y,z \rangle$, and accept if ...
1
Let me clarify the question first. $\mu$ is a probability distribution over the sample space $S=\{0,1\}^n \times \{0,1\}^n$. A combinatorial rectangle (or just rectangle) $R$ is a subset of $S$ of the form $A\times B$, where $A\subseteq \{0,1\}^n$ and $B\subseteq \{0,1\}^n$. For all $x\in \{0,1\}^n$, we can think of $x$ as the characteristic vector of a ...
1
You asked two questions. I'll answer the second. A rectangle is a set $R$ of the form $$R = \{(x_1,\dots,x_n) : \ell_1 \le x_1 \le u_1, \dots, \ell_n \le x_n \le u_n\}$$ for some $\ell_1,\dots,\ell_n,u_1,\dots,u_n$.
1
Yes. Consider the following protocol. Alice flips a coin, and sets $X$ and $Y$ to be equal to the outcome of the coin flip. She then sends $X,Y$ to Bob. Note that the transcript will include the value of $X,Y$. Now unconditionally, $X,Y$ are dependent (there is probability $1/2$ that they are Heads,Heads and probability $1/2$ that they are Tails,Tails). ...
1
You haven't defined when a randomized protocol is declared to be successful, so I will assume that at the end of the protocol, Bob tells a judge what he thinks the message is, and we want that for each message $x$, the probability that Bob is correct is at least $1-\epsilon$. Let $X$ be a random $n$-bit string, and let $\Pi$ be the corresponding transcript. ...
1
It is known that the randomized communication complexity of inner product on $m$ bits is $\Omega(m)$. You can compute inner product using a protocol for the indexing function on $\{0,1\}^{2^m} \times [2^m]$ as follows: denoting Alice's input by $x \in \{0,1\}^m$ and Bob's by $y \in \{0,1\}^m$, Alice computes a new vector $X$ by $X_y = \mathsf{IP}(x,y)$, and ...
1
This answer refers to a previous version of the question, in which the condition $a_i = b_i = 1$ was replaced by the condition $a_i = b_i$. First of all, your problem is EQUALITY in disguise (complement one of the vectors to see why). The complexity of EQUALITY is still $\Theta(n)$ in the deterministic case, but it drops down to $\Theta(\log n)$ in the ...
1
That's simply a different problem. The set disjointness problem is defined, by common agreement, to be the problem where the universe has size $n$ and the inputs (sets) are represented as a bitvector of length $n$. In other words, when you hear the phrase "set disjointness problem", you can know that's what they're referring to, and not the problem you ...
1
Here is a protocol with one-sided error for the case $k=2$. Suppose we have $x,y \in \{0,1\}^n$. Sample $N$ strings $z_1,\dots,z_N$ uniformly at random from $\{1,4\}^n$. Alice sends $\alpha_j = \sum_i x_i z_{j,i} \bmod 5$ to Bob, and Bob sends $\beta_j = \sum_i y_i z_{j,i} \bmod 5$ to Alice. Both parties compute $\gamma_j = \alpha_j - \beta_j \bmod 5$. ...
1
The author describes an algorithm due to Ahlswede and Cai to solve the set intersection problem, and then describes his generalization to the number-in-hand setting with any number of players. I will only describe the two player setting. Ahlswede and Cai consider an algorithm of the following form. Alice gets a set $X \subseteq \{1,\ldots,n\}$, and Bob gets ...
1
Round: The protocol (or the communication game) proceeds in rounds. In each round, some bits are communicated. In the simple model of Alice and Bob to evaluate some function f, it depends on the protocol P that specifies which player sends a bit of communication (and of course, what bit to send) next. Complexity measure: The communication complexity refers ...
1
There is a cheap lower bound of $\Omega(r)$ obtained by reduction. Suppose for simplicity that the $r$ dIstinguished coordinates are the first $r$. Let $g(x_1,\ldots,x_r) = f(x_1,\ldots,x_r,0,\ldots,0)$. Your condition on $f$ implies that $g$ satisfies Jukna's condition on $g$, so $g$ has communication complexity $\Omega(r)$. Any protocol for $f$ also works ...
1
Hint: Compare the parities of the inputs. (Can you generalize this idea to at most $k$ differences?)
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-02-20 22:04:48
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https://math.stackexchange.com/questions/23484/help-solving-int-frac8x415x316x222x4xx12x22dx
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Help solving $\int {\frac{8x^4+15x^3+16x^2+22x+4}{x(x+1)^2(x^2+2)}dx}$
$\displaystyle\int {\frac{8x^4+15x^3+16x^2+22x+4}{x(x+1)^2(x^2+2)}\,\mathrm{d}x}$
I used partial fractions, solved $A = 2, C = 3$.
$$\frac{A}{x} + \frac{B}{x+1} + \frac{C}{(x+1)^2} +\frac{(Dx+E)}{(x^2+2)}$$
\begin{align*} &8x^4+15x^3+16x^2+22x+4\\ &\quad = A(x+1)^2(x^2+2)+B(x)(x+1)(x^2+2)+C(x)(x^2+2)+(Dx+E)(x)(x+1)^2 \end{align*} Substitute in $x=0$ to get $4=A(1)(2)$, so $A = 2$ $$6x^4+11x^3+10x^2+14x = B(x)(x+1)(x^2+2)+C(x)(x^2+2)+(Dx+E)(x)(x+1)^2$$ Substitute in $x=-1$ to get $$6-11+10-14 = C(-1)(1+2)$$ so $-9=-3C$, thus $C=3$.
Leaving me what I have below:
Which brings me to where I am currently stuck.
$$6x^4 +8x^3 +10x^2+8x = B(x)(x+1)(x^2+2) + (Dx + E) (x) (x+1)^2$$
Is the next best move to use substitution to solve for $B$?
• It might be helpful to see your setup for the partial fraction decomposition. – Isaac Feb 24 '11 at 4:09
• You could just multiply out the polynomials on the left and then match up the coefficients of each term (i.e. the only unknown multiplied by $x^4$ will be D, so D must be 6). This strategy will always work, although there are usually quicker ways if you use some ingenuity (as it sounds like you are). – Brian Feb 24 '11 at 4:14
• I meant 'right' instead of left above... – Brian Feb 24 '11 at 4:19
• right, for some reason I forgot to square the x+1 on my paper so I only ended up with Dx^3, now I see that I should have gotten Dx^4 so D must be 6 – Finzz Feb 24 '11 at 4:30
• Note: after the editing what I said is wrong. – Brian Feb 24 '11 at 4:54
First, I trust you used the correct partial fraction decomposition: $$\frac{8x^4+15x^3+16x^2+22x+4}{x(x+1)^2(x^2+2)} = \frac{A}{x} + \frac{B}{x+1} + \frac{C}{(x+1)^2} + \frac{Dx+E}{x^2+2}.$$ This leads to \begin{align*} &8x^4 + 15x^3 + 16x^2 + 22x + 4\\ &\qquad = A(x+1)^2(x^2+2) + Bx(x+1)(x^2+2) + Cx(x^2+2) + (Dx+E)x(x+1)^2. \end{align*} A useful "trick" is to evaluate at the zeros of the linear factors to get some information; I suspect you evaluated at $x=0$ to get $2A = 4$, from which you got $A=2$.
You can then evaluate at $x=-1$ to get $-3C = -9$, which is how you got $C=3$. Looking good.
Then you used that to simplify. $$2(x^2+2x+1)(x^2+2) +3x(x^2+2) = 2x^4 + 7x^3 + 6x^2 + 14x + 4,$$ which subtracted from $8x^4 + 15x^3 + 16x^2 + 22x + 4$ gave you $$6x^4 + 8x^3 + 10x^2 + 8x = Bx(x+1)(x^2+2) + (Dx+E)x(x+1)^2.$$ Hmmm... Which is not quite what you have. Did you use the correct decomposition, or did you forget about being careful with that $(x+1)^2$?
Anyway: here's where you go stuck because you are used to being able to solve the partial fractions problems using only the evaluation trick. But when you have irreducible quadratic factors or powers of linear factors (or worse, both), the trick doesn't get you all the way there.
Here, we can factor out $x$ from both sides to get $$6x^3 + 8x^2 + 10x + 8 = B(x+1)(x^2+2) + (Dx+E)(x+1)^2.$$ (We factored out $x$ from both sides and cancelled; that's how we dropped from fourth power to cube).
Edit.
We can further factor out $x+1$ from both sides: $$(x+1)(6x^2 + 2x + 8) = (x+1)(B(x^2+2) + (Dx+E)(x+1))$$ to get $$6x^2 + 2x + 8 = B(x^2+2) + (Dx+E)(x+1).$$ Contrary to your claim before, now that we had all the right terms, we cannot simply conclude that $D=6$, because there are two quadratic terms: $Bx^2$ and $Dx^2$.
You can, however, evaluate at $x=-1$ to get $12 = 3B$, or $B=4$; from this you go to $$6x^2 + 2x + 8 = 4x^2 + 8 + (Dx+E)(x+1)$$ or $$2x^2 + 2x = (Dx+E)(x+1).$$ Noting that the constant term on the right is $E$, and $0$ on the left, you get $E=0$. This gives $$2x(x+1) = Dx(x+1)$$ which, cancelling $x(x+1)$ yields $D=2$.
Alternatively, from $2x^2+2x = (Dx+E)(x+1)$, we can factor the left hand side completely to get $$2x(x+1) = (Dx+E)(x+1)$$ from which we immediately get $Dx+E = 2x$, so $D=2$ and $E=0$.
So, in summary, $A=2$, $B=4$, $C=3$, $D=2$, $E=0$.
• If you don't factor out the x and multiply out the right side, the only co-efficient to yield $x^4$ would mean D would have to be 6. because $6x^4+8x^3+10x^2+8x = Bx^3 +2Bx +Dx^4 + 2Dx^3 + Ex^3 +Ex^2 +Ex$ – Finzz Feb 24 '11 at 4:48
• @Finzz: I factored out $x$, which is how I dropped from fourth power to cube. And no, you cannot deduce that $D=6$ at this point, because if you do things correctly you'll notice that you have two terms that involve the highest power of $x$, not a single one: both the $Bx^3$, and the $Dx^3$. I have not divided through by $x-1$. – Arturo Magidin Feb 24 '11 at 4:50
• @Arturo: I accidentally skipped the part where you said you factored out the x, look at my comment again. EDIT: Nevermind, you would have $Bx^4$ wouldn't you? – Finzz Feb 24 '11 at 4:53
• @Finzz: Yes, you have two terms with highest term. Look at the edit I just did. – Arturo Magidin Feb 24 '11 at 4:56
• @Arturo: Awesome! Thanks once again, and I think you accidentally put an extra dollar sign ($) on one of your lines. – Finzz Feb 24 '11 at 5:21 Below I show how the Heaviside cover-up method generalizes to handle nonlinear denominators. With the numerator $$\rm\:f(x)\ =\ 8x^4+15x^3+16x^2+22x+4\:,\:$$ the undetermined partial fraction is $$\rm\frac{f(x)}{x(x+1)^2(x^2+2)}\ =\ \frac{a}{x}\ +\ \frac{b\ (x+1) + c}{(x+1)^2}\ +\ \frac{d\ x+e}{x^2+2}$$ To find $$\,\rm dx+e\,$$ in the $$\rm\: x^2+2\$$ fraction, clear denominators and collect factors of $$\rm\: x^2 + 2\:$$ $$\rm f(x)\ \ =\ \ x\ (x+1)^2\ (d\ x +\: e)\ \ +\ \ (x^2+\:2)\ g(x)\ ,\quad\quad some\ \ g(x) \in \mathbb Q[x]$$ Evaluating this $$\rm\bmod\, x^2 + 2\:,\$$ i.e.$$\:$$ iteratively applying the rewrite rule $$\rm\ x^2 \to -2\:,\:\:$$ yields $$\rm - 8\ x + 4\ =\: -(4\ d +\: e)\ x + 2\ d - 4\ e\quad \Rightarrow\quad d=2,\ e=0$$ Notice this method amounts to ignoring ("covering") all the undetermined partial fractions having denominator different (i.e. coprime) from the current denominator $$\rm\:p(x) = x^2+2\:$$ (i.e. having different roots) then evaluating what remains at the roots of $$\rm\,p(x)\,$$ or, $$\:$$ equivalently, $$\:$$ evaluating it $$\rm\bmod p(x).\,$$ To avoid computing inverses $$\rm\bmod p(x)\:$$ we scale to clear denominators before evaluating. This is simply the higher-degree analog of the classical Heaviside method - where covering up and evaluating at $$\rm\: x = r\:$$ is equivalent to evaluating modulo $$\rm\:x-r\:$$. Using the same method we can solve for the numerator of the $$\rm\ (x+1)^2\,$$ fraction $$\rm f(x)\ \ =\ \ x\ (x^2+2)\ (b\ (x+1) + c)\ \ +\ \ (x+1)^2\ h(x)\ ,\quad\quad some\ \ h(x) \in\mathbb Q[x]$$ Evaluating it mod $$\rm\, (x+1)^2,\,$$ i.e. iteratively applying rewrite rule $$\rm\, x^2 \to -2\ x - 1\,$$ yields $$\rm 3\ x - 6\ =\ (5\ c - 3\ b)\ x + 2\ c - 3\ b\quad \Rightarrow\quad c = 3,\ b = 4$$ • Very nice -- I didn't know about this :-) – joriki Jan 7 '12 at 11:38 • @joriki See here for another (simpler) example – Bill Dubuque May 21 '14 at 15:32 • More examples (for reference): 1 2 – Anant May 24 '14 at 18:43 Given what you have, what happens when you set$x = -1$? • I don't think I can because then the right side would be 0. EDIT: So would the right side. – Finzz Feb 24 '11 at 4:31 • @Finzz: You mean the left side will be zero? Does that give you a value for$B$? – Aryabhata Feb 24 '11 at 4:32 • There is also supposed to be an (x+1) attached (multiplied) to the B, I forgot to add it in, sorry. – Finzz Feb 24 '11 at 4:34 • @Finzz: Then do the substitution after dividing by$(x+1)$. Make sure you divide out$x+1$from the left side before trying to set$x=-1$. The$D,E$gets cancelled because of$(x+1)^2$, but the$B$term remains... – Aryabhata Feb 24 '11 at 4:36 • @Moron: What do you mean divide out x+1 from the left side? Because I would be dividing by 0 after setting x = -1 – Finzz Feb 24 '11 at 4:44 Following your original method from the point where you pose your question, here are a couple of tricks you can use, which were not mentioned in previous answers. (1) Set$x=\varepsilon -1$and neglect$\varepsilon^2$, to get$B=4$immediately. (2) Set$x=\mathrm{i}\sqrt2$and equate real and imaginary parts to find$D$and$E$(independently of$B$). For kicks, I thought I provide the end result for checking:${\huge{\displaystyle\int}} \! \dfrac {\rm{8x^4+15x^3+16x^2+22x+4}}{\rm{x(x+1)^{2}(x^2+2)}}~\mathrm{dx}~=~ {\huge{\displaystyle\int}} \! \dfrac {\rm{A}}{\rm{x}}+\dfrac {\rm B}{(\rm x+1)}+\dfrac {\rm C}{(\rm{x+1)^{2}}}+\dfrac {\rm{Dx+E}}{{\rm{(x^2+2)}}}~\mathrm{dx} ~~~~~~~~~~~~~~~ \left[ \begin{array}{ccccc} \rm{a} \\ \rm{b} \\ \rm{c} \\ \rm{d} \\ \rm{e} \end{array} \right] = \left[ \begin{array}{ccccc} \rm{2} \\ \rm{4} \\ \rm{3} \\ \rm{2} \\ \rm{0} \end{array} \right]~~~~~~~~~~\Rightarrow~~~~~~~~~~~~~~ ={\huge{\displaystyle\int}} \! \dfrac {\rm 2}{\rm x}+\dfrac {\rm 4}{{\rm{(x+1)}}}+\dfrac {\rm 3}{{\rm{(x+1)^{2}}}}+\dfrac {\rm 2x+0}{{\rm{(x^2+2)}}}~\mathrm{dx} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ={\rm{2\ln|x|-4\ln(x+1)+\dfrac {3}{x+1}+\ln(x^2+2)+K}} ~~~~~~~~~~~\Big({\rm{\ln|x^2+2|\equiv \ln(x^2+2)}}~,~\because {\rm{x^2+2\gt 0~~\forall ~x \in \mathbb{R}}}\Big); ~$via a substitution of the denominator for the last 3 integrals. • Should this not be$-\frac{3}{x+1}\$? – Zain Patel Jan 13 '15 at 0:18
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2019-09-17 11:08:39
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http://math.stackexchange.com/questions/345268/how-is-the-formula-for-the-focal-point-of-a-ball-lens-derived
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# How is the formula for the focal point of a ball lens derived?
How can the focal point of a ball lens be found?
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I've tried to make the formulas readable, but the math is messed up. What is $1 / 2^{0.5} / 1.3$ supposed to mean? – TMM Mar 29 '13 at 0:20
I believe the 1.3 refers to the refractive index mentioned earlier - so it would be $(1/2^0.5)/1.3$ – mardat Mar 29 '13 at 0:25
This is not a question about derived functors. – Piotr Pstrągowski Mar 29 '13 at 1:06
Note that your example that uses $45^{\circ}$ is far beyond the region of validity of the paraxial approximation which the author inherently assumes. See my solution below. – Ron Gordon Mar 29 '13 at 10:47
The formula assumes the angles are small, as I will show below.
The focal length may be shown by the geometry to be
$$f=R \left [ \cos{(2 \theta'-\theta)}+ \frac{\sin{(2 \theta'-\theta)}}{\sin{(2 \theta - 2 \theta')}} \cos{(2 \theta-2 \theta')} \right]$$
where $\theta$ is the angle of incidence from the air, and $\theta'$ is the angle of refraction in the glass. We now assume the so-called paraxial approximation in which the sines are replaced by their arguments and the cosine is replaced by $1$. Using the paraxial form of Snell's Law:
$$N \theta' = \theta$$
we find that
$$f \approx R \left [ 1 + \frac{(2-N) \theta'}{2 (N-1) \theta'} \right ] = \frac{N}{2(N-1)} R$$
I will elaborate on how I got that exact formula for the focal length. Here's a diagram:
Note that the solid lines represents the ray path and the dotted lines are for measurement. The spherical geometry is expressed in the fact that the trangle in the circle is isosceles. Therefore the angle $\Delta$ in the picture is
$$\Delta = \pi - [\theta + (\pi - 2 \theta')] = 2 \theta'-\theta$$
Then $x=R \cos{(2 \theta'-\theta)}$. The other leg of that right triangle of which $x$ is a leg is $z=R \sin{(2 \theta'-\theta)}$. The length $y$ is determined from the angle of refraction out of the glass, which is $\theta$ by Snell's Law; the angle of the right triangle of which $y$ is a leg is $\theta-\Delta$ (alternate interior angles). Thus, $\tan{(\theta-\Delta)} = \tan{(2 \theta - 2 \theta')} = z/y$, and
$$y = R \cos{(2 \theta-2 \theta')} \frac{\sin{(2 \theta'-\theta)}}{\sin{(2 \theta-2\theta')}}$$
The focal length $f=x+y$, and the result follows.
You should see how well the paraxial approximation fares for this ball lens. Here I take your example value of $N=1.3$ and $R=1$, and present a plot of focal length vs. initial ray height $h$ off the optical axis (i.e., $\theta = \arcsin{(h/R)}$):
Two things to note: 1) the exact focal length is less than the paraxial focal length, and 2) the paraxial approximation only works for a pencil of rays that are less than about $0.15$ from the axis.
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2014-07-25 21:24:33
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https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-3-introduction-to-graphing-3-7-point-slope-form-and-equations-of-lines-3-7-exercise-set-page-218/30
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## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
$y=x+27$
RECALL: (1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line. (2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept. (3) Parallel lines have equal slopes. (4) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other). Write $x-y=6$ in slope-intercept form: $x-y=6 \\-y=6-x \\-1(-y)=-1(6-x) \\y=-6+x \\y=x-6$ This means the equation $x-y=6$ is equivalent to $y=x-6$. The line is parallel to $y=x-6$. Since the slope of this line is $1$, then the slope of the line parallel to it is also $1$. Using the given point on the line $(0, 27)$ (which is the y-intercept) and the slope $1$, the equation of the line in point-slope form is: $y=x+27$
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2020-06-06 15:23:28
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https://halotools.readthedocs.io/en/latest/api/halotools.empirical_models.NFWPhaseSpace.html
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# NFWPhaseSpace¶
class halotools.empirical_models.NFWPhaseSpace(**kwargs)[source] [edit on github]
Model for the phase space distribution of mass and/or galaxies in isotropic Jeans equilibrium in an NFW halo profile, based on Navarro, Frenk and White (1995), where the concentration of the galaxies is the same as the concentration of the parent halo
For a review of the mathematics underlying the NFW profile, including descriptions of how the relevant equations are implemented in the Halotools code base, see Source code notes on NFWProfile and NFWPhaseSpace.
Parameters: conc_mass_model : string or callable, optional Specifies the function used to model the relation between NFW concentration and halo mass. Can either be a custom-built callable function, or one of the following strings: dutton_maccio14, direct_from_halo_catalog. cosmology : object, optional Instance of an astropy cosmology. Default cosmology is set in sim_defaults. redshift : float, optional Default is set in sim_defaults. mdef: str, optional String specifying the halo mass definition, e.g., ‘vir’ or ‘200m’. Default is set in model_defaults. halo_boundary_key : str, optional Default behavior is to use the column associated with the input mdef. concentration_key : string, optional Column name of the halo catalog storing NFW concentration. This argument is only relevant when conc_mass_model is set to direct_from_halo_catalog. In such a case, the default value is halo_nfw_conc, which is consistent with all halo catalogs provided by Halotools but may differ from the convention adopted in custom halo catalogs. concentration_bins : ndarray, optional Array storing how halo concentrations will be digitized when building a lookup table for mock-population purposes. The spacing of this array sets a limit on how accurately the concentration parameter can be recovered in a likelihood analysis.
Examples
>>> model = NFWPhaseSpace()
Methods Summary
assign_phase_space(table[, seed]) Primary method of the NFWPhaseSpace class called during the mock-population sequence. build_lookup_tables([logrmin, logrmax, …]) Method used to create a lookup table of the spatial and velocity radial profiles. circular_velocity(radius, total_mass, conc) The circular velocity, $$V_{\rm cir} \equiv \sqrt{GM( Methods Documentation assign_phase_space(table, seed=None)[source] [edit on github] Primary method of the NFWPhaseSpace class called during the mock-population sequence. Parameters: table : object Table storing halo catalog. After calling the assign_phase_space method, the x, y, z, vx, vy, and vz columns of the input table will be over-written with their host-centric values. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. build_lookup_tables(logrmin=-3, logrmax=0, Npts_radius_table=101)[source] [edit on github] Method used to create a lookup table of the spatial and velocity radial profiles. Parameters: logrmin : float, optional Minimum radius used to build the spline table. Default is set in model_defaults. logrmax : float, optional Maximum radius used to build the spline table Default is set in model_defaults. Npts_radius_table : int, optional Number of control points used in the spline. Default is set in model_defaults. circular_velocity(radius, total_mass, conc)[source] [edit on github] The circular velocity, \(V_{\rm cir} \equiv \sqrt{GM(<r)/r}$$, as a function of halo-centric distance r.
Parameters: radius : array_like Halo-centric distance in Mpc/h units; can be a scalar or numpy array total_mass : array_like Total mass of the halo; can be a scalar or numpy array of the same dimension as the input radius. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input radius. vc: array_like The circular velocity in km/s; has the same dimensions as the input radius.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWPhaseSpace()
>>> Npts = 100
>>> radius = np.logspace(-2, -1, Npts)
>>> total_mass = np.zeros(Npts) + 1e12
>>> conc = 5
>>> result = model.circular_velocity(radius, total_mass, conc)
>>> concarr = np.linspace(1, 100, Npts)
>>> result = model.circular_velocity(radius, total_mass, concarr)
conc_NFWmodel(*args, **kwargs)[source] [edit on github]
NFW concentration as a function of halo mass.
Parameters: prim_haloprop : array, optional Array storing the mass-like variable, e.g., halo_mvir. If prim_haloprop is not passed, then table keyword argument must be passed. table : object, optional Table storing the halo catalog. If your NFW model is based on the virial definition, then halo_mvir must appear in the input table, and likewise for other halo mass definitions. If table is not passed, then prim_haloprop keyword argument must be passed. conc : array_like Concentrations of the input halos. Note that concentrations will be clipped to their min/max permitted values set in the model_defaults module. The purpose of this clipping is to ensure stable results during mock galaxy population. Due to this clipping, the behavior of the conc_NFWmodel function is different from the concentration-mass relation that underlies it.
Examples
In the examples below, we’ll demonstrate the various ways to use the conc_NFWmodel function, depending on the initial choice for the conc_mass_model.
>>> fake_masses = np.logspace(12, 15, 10)
If you use the direct_from_halo_catalog option, you must pass a table argument storing a Table with a column name for the halo mass that is consistent with your chosen halo mass definition:
>>> from astropy.table import Table
>>> nfw = NFWPhaseSpace(conc_mass_model='direct_from_halo_catalog', mdef='vir')
>>> fake_conc = np.zeros_like(fake_masses) + 5.
>>> fake_halo_table = Table({'halo_mvir': fake_masses, 'halo_nfw_conc': fake_conc})
>>> model_conc = nfw.conc_NFWmodel(table=fake_halo_table)
In case your halo catalog uses a different keyname from the Halotools default halo_nfw_conc:
>>> nfw = NFWPhaseSpace(conc_mass_model='direct_from_halo_catalog', mdef='vir', concentration_key='my_conc_keyname')
>>> fake_halo_table = Table({'halo_mvir': fake_masses, 'my_conc_keyname': fake_conc})
>>> model_conc = nfw.conc_NFWmodel(table=fake_halo_table)
One of the available options provided by Halotools is dutton_maccio14. With this option, you can either pass in a table argument, or alternatively an array of masses via the prim_haloprop argument:
>>> nfw = NFWPhaseSpace(conc_mass_model='dutton_maccio14')
>>> fake_halo_table = Table({'halo_mvir': fake_masses, 'halo_nfw_conc': fake_conc})
>>> model_conc = nfw.conc_NFWmodel(table=fake_halo_table)
>>> model_conc = nfw.conc_NFWmodel(prim_haloprop=fake_masses)
Finally, you may also have chosen to define your own concentration-mass relation. If so, your function must at a minimum accept a table keyword argument. Below we give a trivial example of using the identity function:
>>> def identity_func(*args, **kwargs): return kwargs['table']['halo_mvir']
>>> nfw = NFWPhaseSpace(conc_mass_model=identity_func, mdef='vir')
>>> fake_halo_table = Table({'halo_mvir': fake_masses})
>>> model_conc = nfw.conc_NFWmodel(table=fake_halo_table)
Analogous to cumulative_mass_PDF, but for the satellite galaxy distribution instead of the host halo mass distribution.
In NFWPhaseSpace there is no distinction between the two methods, but in BiasedNFWPhaseSpace these two function are different.
Parameters: scaled_radius : array_like Halo-centric distance r scaled by the halo boundary $$R_{\Delta}$$, so that $$0 <= \tilde{r} \equiv r/R_{\Delta} <= 1$$. Can be a scalar or numpy array. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input scaled_radius. p: array_like The fraction of the total mass enclosed within the input scaled_radius, in $$M_{\odot}/h$$; has the same dimensions as the input scaled_radius.
Examples
>>> model = NFWPhaseSpace()
>>> Npts = 100
>>> scaled_radius = np.logspace(-2, 0, Npts)
>>> conc = 5
>>> concarr = np.linspace(1, 100, Npts)
Analytical result for the fraction of the total mass enclosed within r/Rvir of an NFW halo,
$$P_{\rm NFW}(<\tilde{r}) \equiv M_{\Delta}(<\tilde{r}) / M_{\Delta} = g(c\tilde{r})/g(\tilde{r}),$$
where $$g(x) \equiv \int_{0}^{x}dy\frac{y}{(1+y)^{2}} = \log(1+x) - x / (1+x)$$ is computed using g, and where $$\tilde{r} \equiv r / R_{\Delta}$$.
Parameters: scaled_radius : array_like Halo-centric distance r scaled by the halo boundary $$R_{\Delta}$$, so that $$0 <= \tilde{r} \equiv r/R_{\Delta} <= 1$$. Can be a scalar or numpy array. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input scaled_radius. p: array_like The fraction of the total mass enclosed within the input scaled_radius, in $$M_{\odot}/h$$; has the same dimensions as the input scaled_radius.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWPhaseSpace()
>>> Npts = 100
>>> scaled_radius = np.logspace(-2, 0, Npts)
>>> conc = 5
>>> concarr = np.linspace(1, 100, Npts)
Physical density of the NFW halo scaled by the density threshold of the mass definition:
The dimensionless_mass_density is defined as $$\tilde{\rho}_{\rm prof}(\tilde{r}) \equiv \rho_{\rm prof}(\tilde{r}) / \rho_{\rm thresh}$$, where $$\tilde{r}\equiv r/R_{\Delta}$$.
For an NFW halo, $$\tilde{\rho}_{\rm NFW}(\tilde{r}, c) = \frac{c^{3}}{3g(c)}\times\frac{1}{c\tilde{r}(1 + c\tilde{r})^{2}},$$
where $$g(x) \equiv \int_{0}^{x}dy\frac{y}{(1+y)^{2}} = \log(1+x) - x / (1+x)$$ is computed using the g function.
The quantity $$\rho_{\rm thresh}$$ is a function of the halo mass definition, cosmology and redshift, and is computed via the density_threshold function. The quantity $$\rho_{\rm prof}$$ is the physical mass density of the halo profile and is computed via the mass_density function.
Parameters: scaled_radius : array_like Halo-centric distance r scaled by the halo boundary $$R_{\Delta}$$, so that $$0 <= \tilde{r} \equiv r/R_{\Delta} <= 1$$. Can be a scalar or numpy array. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input scaled_radius. dimensionless_density: array_like Dimensionless density of a dark matter halo at the input scaled_radius, normalized by the density_threshold $$\rho_{\rm thresh}$$ for the halo mass definition, cosmology, and redshift. Result is an array of the dimension as the input scaled_radius.
Analytical solution to the isotropic jeans equation for an NFW potential, rendered dimensionless via scaling by the virial velocity.
$$\tilde{\sigma}^{2}_{r}(\tilde{r})\equiv\sigma^{2}_{r}(\tilde{r})/V_{\rm vir}^{2} = \frac{c^{2}\tilde{r}(1 + c\tilde{r})^{2}}{g(c)}\int_{c\tilde{r}}^{\infty}{\rm d}y\frac{g(y)}{y^{3}(1 + y)^{2}}$$
See Modeling the NFW Velocity Profile for derivations and implementation details.
Parameters: scaled_radius : array_like Length-Ngals numpy array storing the halo-centric distance r scaled by the halo boundary $$R_{\Delta}$$, so that $$0 <= \tilde{r} \equiv r/R_{\Delta} <= 1$$. conc : float Concentration of the halo. result : array_like Radial velocity dispersion profile scaled by the virial velocity. The returned result has the same dimension as the input scaled_radius.
enclosed_mass(radius, total_mass, conc)[source] [edit on github]
The mass enclosed within the input radius, $$M(<r) = 4\pi\int_{0}^{r}dr'r'^{2}\rho(r)$$.
Parameters: radius : array_like Halo-centric distance in Mpc/h units; can be a scalar or numpy array total_mass : array_like Total mass of the halo; can be a scalar or numpy array of the same dimension as the input radius. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input radius. enclosed_mass: array_like The mass enclosed within radius r, in $$M_{\odot}/h$$; has the same dimensions as the input radius.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWProfile()
>>> Npts = 100
>>> radius = np.logspace(-2, -1, Npts)
>>> total_mass = np.zeros(Npts) + 1e12
>>> conc = 5
>>> result = model.enclosed_mass(radius, total_mass, conc)
>>> concarr = np.linspace(1, 100, Npts)
>>> result = model.enclosed_mass(radius, total_mass, concarr)
Spherical overdensity radius as a function of the input mass.
Note that this function is independent of the form of the density profile.
Parameters: total_mass: array_like Total halo mass in $$M_{\odot}/h$$; can be a number or a numpy array. radius : array_like Radius of the halo in Mpc/h units. Will have the same dimension as the input total_mass.
Examples
>>> model = NFWPhaseSpace()
Spherical overdensity mass as a function of the input radius.
Note that this function is independent of the form of the density profile.
Parameters: radius : array_like Radius of the halo in Mpc/h units; can be a number or a numpy array. total_mass: array_like Total halo mass in $$M_{\odot}/h$$. Will have the same dimension as the input radius.
Examples
>>> model = NFWPhaseSpace()
mass_density(radius, mass, conc)[source] [edit on github]
Physical density of the halo at the input radius, given in units of $$h^{3}/{\rm Mpc}^{3}$$.
Parameters: radius : array_like Halo-centric distance in Mpc/h units; can be a scalar or numpy array mass : array_like Total mass of the halo; can be a scalar or numpy array of the same dimension as the input radius. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input radius. density: array_like Physical density of a dark matter halo of the input mass at the input radius. Result is an array of the dimension as the input radius, reported in units of $$h^{3}/Mpc^{3}$$.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWPhaseSpace()
>>> Npts = 100
>>> radius = np.logspace(-2, -1, Npts)
>>> mass = np.zeros(Npts) + 1e12
>>> conc = 5
>>> result = model.mass_density(radius, mass, conc)
>>> concarr = np.linspace(1, 100, Npts)
>>> result = model.mass_density(radius, mass, concarr)
mc_generate_nfw_phase_space_points(Ngals=10000, conc=5, mass=1000000000000.0, verbose=True, seed=None)[source] [edit on github]
Return a Monte Carlo realization of points in the phase space of an NFW halo in isotropic Jeans equilibrium.
Parameters: Ngals : int, optional Number of galaxies in the Monte Carlo realization of the phase space distribution. Default is 1e4. conc : float, optional Concentration of the NFW profile being realized. Default is 5. mass : float, optional Mass of the halo whose phase space distribution is being realized in units of Msun/h. Default is 1e12. verbose : bool, optional If True, a message prints with an estimate of the build time. Default is True. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. t : table Table containing the Monte Carlo realization of the phase space distribution. Keys are ‘x’, ‘y’, ‘z’, ‘vx’, ‘vy’, ‘vz’, ‘radial_position’, ‘radial_velocity’. Length units in Mpc/h, velocity units in km/s.
Examples
>>> nfw = NFWPhaseSpace()
>>> mass, conc = 1e13, 8.
>>> data = nfw.mc_generate_nfw_phase_space_points(Ngals=100, mass=mass, conc=conc, verbose=False)
Now suppose you wish to compute the radial velocity dispersion of all the returned points:
If you wish to do the same calculation but for points in a specific range of radius:
You may also wish to select points according to their distance to the halo center in units of the virial radius. In such as case, you can use the halo_mass_to_halo_radius method to scale the halo-centric distances. Here is an example of how to compute the velocity dispersion in the z-dimension of all points residing within $$R_{\rm vir}/2$$:
mc_halo_centric_pos(*concentration_array, **kwargs)[source] [edit on github]
Method to generate random, three-dimensional halo-centric positions of galaxies.
Parameters: table : data table, optional Astropy Table storing a length-Ngals galaxy catalog. If table is not passed, concentration_array and keyword argument halo_radius must be passed. concentration_array : array_like, optional Length-Ngals numpy array storing the concentrations of the mock galaxies. If table is not passed, concentration_array and keyword argument halo_radius must be passed. halo_radius : array_like, optional Length-Ngals array storing the radial boundary of the halo hosting each galaxy. Units assumed to be in Mpc/h. If concentration_array and halo_radius are not passed, table must be passed. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. x, y, z : arrays Length-Ngals array storing a Monte Carlo realization of the galaxy positions.
mc_pos(*concentration_array, **kwargs)[source] [edit on github]
Method to generate random, three-dimensional positions of galaxies.
Parameters: table : data table, optional Astropy Table storing a length-Ngals galaxy catalog. If table is not passed, concentration_array and halo_radius must be passed. concentration_array : array_like, optional Length-Ngals numpy array storing the concentrations of the mock galaxies. If table is not passed, concentration_array and keyword argument halo_radius must be passed. If concentration_array is passed, halo_radius must be passed as a keyword argument. The sequence must have the same order as self.gal_prof_param_keys. halo_radius : array_like, optional Length-Ngals array storing the radial boundary of the halo hosting each galaxy. Units assumed to be in Mpc/h. If concentration_array and halo_radius are not passed, table must be passed. seed : int, optional Random number seed used in Monte Carlo realization. Default is None. x, y, z : arrays, optional For the case where no table is passed as an argument, method will return x, y and z points distributed about the origin according to the profile model. For the case where table is passed as an argument (this is the use case of populating halos with mock galaxies), the x, y, and z columns of the table will be over-written. When table is passed as an argument, the method assumes that the x, y, and z columns already store the position of the host halo center. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results.
Method returns a Monte Carlo realization of radial velocities drawn from Gaussians with a width determined by the solution to the isotropic Jeans equation.
Parameters: scaled_radius : array_like Halo-centric distance r scaled by the halo boundary $$R_{\Delta}$$, so that $$0 <= \tilde{r} \equiv r/R_{\Delta} <= 1$$. Can be a scalar or numpy array. total_mass: array_like Length-Ngals numpy array storing the halo mass in $$M_{\odot}/h$$. concentration_array : array_like Length-Ngals numpy array storing the concentrations of the mock galaxies. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. radial_velocities : array_like Array of radial velocities drawn from Gaussians with a width determined by the solution to the Jeans equation.
mc_solid_sphere(*concentration_array, **kwargs)[source] [edit on github]
Method to generate random, three-dimensional, halo-centric positions of galaxies.
Parameters: concentration_array : array_like, optional Length-Ngals numpy array storing the concentrations of the mock galaxies. table : data table, optional Astropy Table storing a length-Ngals galaxy catalog. If table is not passed, concentration_array must be passed. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. x, y, z : arrays Length-Ngals array storing a Monte Carlo realization of the galaxy positions.
mc_unit_sphere(Npts, **kwargs)[source] [edit on github]
Returns Npts random points on the unit sphere.
Parameters: Npts : int Number of 3d points to generate seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results. x, y, z : array_like Length-Npts arrays of the coordinate positions.
mc_vel(table, seed=None)[source] [edit on github]
Method assigns a Monte Carlo realization of the Jeans velocity solution to the halos in the input table.
Parameters: table : Astropy Table astropy.table.Table object storing the halo catalog. Calling the mc_vel method will over-write the existing values of the vx, vy and vz columns. seed : int, optional Random number seed used in the Monte Carlo realization. Default is None, which will produce stochastic results.
Method returns the radial velocity dispersion scaled by the virial velocity as a function of the halo-centric distance.
Parameters: radius : array_like Radius of the halo in Mpc/h units; can be a float or ndarray of shape (num_radii, ) total_mass : array_like Float or ndarray of shape (num_radii, ) storing the host halo mass halo_conc : array_like Float or ndarray of shape (num_radii, ) storing the host halo concentration result : array_like Radial velocity dispersion profile as a function of the input radius, in units of km/s.
setup_prof_lookup_tables(*concentration_bins)[source] [edit on github]
This method sets up how we will digitize halo concentrations during mock population.
Parameters: concentration_bins : ndarray Array storing how concentrations will be digitized during mock-population
virial_velocity(total_mass)[source] [edit on github]
The circular velocity evaluated at the halo boundary, $$V_{\rm vir} \equiv \sqrt{GM_{\rm halo}/R_{\rm halo}}$$.
Parameters: total_mass : array_like Total mass of the halo; can be a scalar or numpy array. vvir : array_like Virial velocity in km/s.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWProfile()
>>> Npts = 100
>>> mass_array = np.logspace(11, 15, Npts)
>>> vvir_array = model.virial_velocity(mass_array)
vmax(total_mass, conc)[source] [edit on github]
Maximum circular velocity of the halo profile.
Parameters: total_mass: array_like Total halo mass in $$M_{\odot}/h$$; can be a number or a numpy array. conc : array_like Value of the halo concentration. Can either be a scalar, or a numpy array of the same dimension as the input total_mass. vmax : array_like $$V_{\rm max}$$ in km/s.
Notes
See Spatial Profiles of Halos for derivations and implementation details.
Examples
>>> model = NFWPhaseSpace()
>>> Npts = 100
>>> total_mass = np.zeros(Npts) + 1e12
>>> conc = 5
>>> result = model.vmax(total_mass, conc)
>>> concarr = np.linspace(1, 100, Npts)
>>> result = model.vmax(total_mass, concarr)
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2021-10-25 02:30:17
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https://culanth.org/fieldsights/open-access-open-minds
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# Open Access, Open Minds
From the Studio: Publishing Infrastructure
There’s a couplet in the Tirukkural, the sixth-century Tamil ethical treatise from south India, which speaks beautifully to the philosophy of giving. Kaimaaru ventaa katapaatu maarimaat / tennaarrung kolloo ulaku. “Deeds of duty need no return. What does the world give in exchange for rain?”
These words might at first seem to put forward the idea of a pure or free gift, one made without any expectation of return, an idea that a century of anthropology has taught us to question. But this is more than an allegory for the little domain of human transactions. There is also a vision here of a greater world and its nature, the idea of a fundamental openness, imbalance, or excess to things, the idea that nature itself defies our all-too-human pretensions of equivalent exchange. Things of enormous and essential value do rain freely, at least at times. What would it mean to attune ourselves to this reality, to live and think and write and converse with such possibilities in mind? What would it mean to meet such a world with requisite generosity?
The first article I wrote about the Tirukkural was for an anthropology journal locked in, like almost all of the journals published by the American Anthropological Association, to a multiyear contract with the multibillion-dollar global publishing concern John Wiley and Sons, which reported a gross profit margin of 70.30 percent in 2017. If I try to access that 2008 article without going through my university library system, as nearly everyone in south India and most anywhere else would have to do, I encounter a window offering me three ways to purchase “instant access” to this learning: $6 for forty-eight hours,$15 to read online, $38 for a PDF. The book, mind you, the project from which this small article was drawn, is available from a university press for$27.95. These are the circumstances of academic writing in anthropology now. Publishing your research in a handful of peer-reviewed academic journals is presented as the linchpin of a successful apprenticeship in the discipline. And yet what this means in practice is that the digests of research we work on most carefully are hardly available to anyone beyond a privileged circle.
This is why the open-access experiments pursued by HAU, Cultural Anthropology, Suomen Antropologi, Medicine Anthropology Theory, and a growing number of other journals in the field—most especially in the global South—are so crucial. As one prestigious venture of this kind falls deeper into a spiraling scandal that raises fundamental questions about how things are done in the profession, it’s worth pausing for a moment to ask what this crisis means for open-access publishing in anthropology. Some have asked whether this means the end of open access. But we might just as well flip this forecast on its head. Could this instead be the beginning of an even more radical series of experiments in how open anthropological writing could become?
The paywall is invidious, yes. But there are other walls that have also come into focus in recent days. Walls that shield those securely employed and exalted in anthropology from the acute concerns of those in more precarious positions. Walls that credit the field’s white forefathers with its most essential lessons, while relegating others to the status of native informants, loyal wives, helpful assistants, or grateful descendants. Walls that distinguish properly deferential and manifestly scholarly writing from forms of expression deemed too intimate, too vulnerable, too personal, too conversational, too passionate to count as serious scholarship. Walls that celebrate the glories of the master’s house. Walls that extol good theories at the expense of good stories. The moment in fact is long overdue, the reckoning with all these walls built beside and on top of each other.
Many of the most vocal and courageous voices in the Twitter channel #hautalk are graduate students and young anthropologists without stable jobs, who cannot take for granted that they will one day claim a place of their own within the secure confines of anthropology’s walls. Many of them will have to make their living as anthropologists by conversing with, and writing for, publics profoundly different from—and more diverse than—the sphere of academic anthropology. Open and accessible writing, in other words, will be for many of them a pragmatic imperative rather than a matter of personal predilection. These circumstances and their pressures come ever more sharply into focus. How will the discipline—its leaders, seniors, and elites—respond? What if we tried for a moment to imagine what a truly open anthropology might be?
We tend to think more about the “access” in open access than its openness: the question, that is, of what you have the right to see, given the details of your scholarly position or official affiliation, rather than the spirit of inquiry and dialogue that can make such access possible. But openness, in a deep and profound sense, is essential to the pursuit of anthropology. Think of what Eric Wolf (1964, 90) said some decades ago about the “open mind” that the discipline demands: “We require minds that can make the most of the experience of the unfamiliar . . . to repattern their habitual neural pathways.” Every anthropologist knows this necessity from fieldwork, but can this disposition extend beyond that phase into the space of writing and publication?
Think of open access as something more than a possible condition of knowledge in anthropology. Think of it as a possible quality of its knower.
So much seems to turn on the ethical capacity for openness that we might cultivate, as we learn to attend and respond with care and concern to whatever happens in the world we engage, even in the face of its foreign and unexpected nature. Donna Haraway (2016, 98) writes that “the decisions and transformations so urgent in our times for learning again, or for the first time, how to become less deadly, more response-able, more attuned, more capable of surprise must be made without guarantees or the expectation of harmony with those who are not oneself—and not safely other, either.” Openness of this kind is an ethical orientation rather than the terms of a contract. There’s little choice here but to keep stumbling upon better ways of thinking along with others, being surprised by what happens in that effort, folding the lessons of that surprise back into the current of thought.
Open access to anthropological knowledge can be underwritten by formal agreements, yes. But it has to be sustained as well by an ethics of collaborative thinking, learning, writing, conversing. It demands humility. And there should be no shame in this, at the very least for anthropologists, for originality in our thinking is never individual, always collective. Whether or not they like to admit it, Zoe Todd (2016, 13) has observed as “an Indigenous person infiltrating the British academy,” anthropologists owe many crucial insights to local, often indigenous interlocutors and to the relationships struck up with them. “Our stories, our laws, our philosophies,” Todd (2016, 17) writes, “are used by European scholars without explicit credit to the political, legal, social, and cultural (and colonial!) contexts these stories are formulated and shared within.” Open access to whoseknowledge, one has to ask.
Say, however, that we were willing to confront this responsibility head on. Could an ethics of openness help with the necessary task of decolonizing anthropology, a field still anchored in the legacies and inheritances of colonial exploitation? One important way to do this would be to acknowledge that relational ontologies are more than objects of particular interest in our contemporary discussions: they are the very means by which our own knowledge is generated and structured, the form in which it moves. If we admit that nothing in anthropology arises from the genius of an individual mind, that a journal itself is a collective mind, then we might begin to see how the richness of the discipline’s ideas depends on the degree of its openness, the depth and diversity of the relationships it builds and the connections it sustains. This awareness might encourage us to regard that web of connections with greater respect and care, as the foundation of a possible community of knowing.
Open access needs open minds, minds open to being remade by the unexpected, minds open to the worldly relationships that can convey its force and significance. Our professional lives and publishing infrastructures, however, are organized in ways that dampen and inhibit such openness, that force harsh choices between the stated demands of an anthropological career and the values that motivate its pursuit. “These words were never supposed to be stuck behind a paywall,” Nina Brown, Marcel LaFlamme, and Sarah Lyon (2018, 44) write at the outset of a recent chronicle of their ill-fated effort to make the Anthropology of Work Review an open-access publication. “Looking back,” they reflect, “we see inflexibility, incuriosity, and a desire for absolute control over published content on the part of our parent organization as the chief causes of [the journal]’s stymied open-access transition” (Brown, LaFlamme, and Lyon 2018, 46–47).
These scholars also ask whether an attachment to revenue—the expectation of returns—might itself be part of the problem. “Could we as an association live with less?” they wonder. “Might letting go of our preoccupation with more lay the groundwork for modest, collaborative modes of living in common?” (Brown, LaFlamme, and Lyon 2018, 47). I too am writing, I know, in highly aspirational terms, and I don’t mean to pretend that the financial side of things isn’t real. Bills have to be paid, labor compensated as fairly and generously as possible, and at the most basic level, open-access publishing confounds these necessities by giving away its goods for free. Creative vision for a more open mode of gathering and sharing knowledge is one thing. Ensuring that this is sustainable in financial terms is another.
Since joining the executive board of the Society for Cultural Anthropology in 2015, I’ve had many chances to talk through these concerns with regard to the SCA’s own venture in open-access publishing, Cultural Anthropology. The sustainability of the enterprise has been a perennial concern. One essential lesson from these discussions is that it is difficult for individual journals and scholarly societies to go it alone and make it work on sovereign terms. It takes, instead, a willingness to imagine one’s own endeavor in relation to a larger ecology of knowledge, working together with other journals, libraries, universities, and scholarly networks. Such collaborative efforts are underway, spanning many continents, institutions, individuals. An open and relational collective mind, once again.
Meanwhile, it’s been eye-opening to see the kind of reach that open-access publishing can make possible. In 2017, for the first time, the Cultural Anthropology website recorded over one million unique pageviews. Of that number, 127,935 were full-text articles published by the journal. This figure was exceeded by a factor of three, however, by the Fieldsights posts also written for and published by the SCA, with 469,319 unique pageviews. This is worth mentioning because of the style and voice in which these posts are typically written: more informal, more conversational, more attuned to the likely concerns of potential readers, whether as Hot Spots focused on contemporary public flashpoints or dialogues on teaching, labor, and other disciplinary preoccupations. More than 400,000 different people visited the website last year, a figure that includes 16,000 from India, 9,000 from the Philippines, 5,000 from Brazil. These are countries that do not qualify for philanthropic forms of access, and no doubt many of these readers work outside of institutions that can afford the sticker price for the Wiley anthropology portfolio.
Much remains to be done in extending the reach of such publishing efforts in the global South, and beyond the academy in the global North. Every open-access venture, including Cultural Anthropology, can do better to cultivate broader readerships and constituencies for its work. This again, however, will take more than simply lowering a paywall, for all of those other walls remain in place. The ultimate success of open-access publishing will depend on the extent to which wider reading publics find that access valuable and meaningful. As writers, we all have to work to make our writing itself more accessible, less arcane, more responsive to the circumstances in which diverse people live and the language in which they make sense of those conditions. And, as stewards of such writing—whether as members of societies or of institutions that house these writers—we have to ensure that such efforts get their due, that scholarly gravity is never opposed to writerly accessibility.
Take a moment, if you haven’t already, to glance at what’s been happening on #AnthroTwitter. As a novice tweeter, I can attest sincerely to the difficulty of saying something worth saying in 280 characters, including spaces. All the same, if there’s one place I would identify as most vibrant when it comes to the spirit of open access I’ve tried to conjure here, it would have to be that platform. Many people—especially younger folks, women, people of color—have been writing here with fearless candor, cobbling together a collaborative understanding of subterranean dynamics in the field at a fraught moment when many of its most respected senior voices seem conspicuously silent to them. It isn’t always pretty, what you find on Twitter, and the leap to indignation may come too quickly. All the same, what is said here is often bracing, moving, hilarious, enraging, and all of these affects matter as they animate and enliven these analyses. They are means of connection and motivation. They work as connective tissue in a relational and emergent ecology of knowledge, an open structure of mind. Is this the kind of thinking you like? If not, try turning it in some other direction.
Open access to what, we still need to ask. The promise of an open and accessible anthropology lies in further circulating objects of knowledge, but also in propagating more radical techniques of knowing otherwise. At stake with such accessibility is a cultivation of mind open to affecting and being affected, open to all the vicissitudes and uncertainties of that interplay. What we need, in other words, is access to the transformative force of meaningful relationships with others unlike ourselves. Can the journals of our scientific societies become more effective spaces to nurture and channel such force? Everything turns on the extent to which they can welcome feelings of candor, humor, vulnerability, and care, the spirits that animate the most moving encounters in anthropology.
“The discipline is tinged from the root by the subjunctive mood,” Michael Carrithers (2005, 434) has observed of anthropology, propelled by the ineluctable sense that “anyone could have been someone else.” I would like to think of this moment of grave disquiet as a chance to recast our sails with this horizon in mind. This is a time for genuine imagination and self-examination. For this possibility of becoming otherwise is the most serious and generous gift that anthropology has to offer, a gift that we can learn to extend more sincerely and wholeheartedly through more inventive and experimental acts of writing and publication.
What is at stake now is much more than the fate of one particular venture in open-access publishing. We have been graced by many such efforts, and we will assuredly meet with many more, all of which we ought to meet with gratitude. The question most crucial to confront now is what they imply for the form and consequence of public expression in anthropology. Anthropological knowledge will become truly open-access when it signals its willingness to open itself, out into the wonder and frailty of human being.
## References
Brown, Nina, Marcel LaFlamme, and Sarah Lyon. 2018. “What Happened, or, Impasses and Future Horizons for an Open Anthropology of Work.” Anthropology of Work Review39, no. 1: 44–47.
Carrithers, Michael. 2005. “Anthropology as a Moral Science of Possibilities.” Current Anthropology 46, no. 3: 433–56.
Haraway, Donna J. 2016. Staying with the Trouble: Making Kin in the Chthulucene. Durham, N.C.: Duke University Press.
Todd, Zoe. 2016. “An Indigenous Feminist’s Take on the Ontological Turn: ‘Ontology’ Is Just Another Word for Colonialism.” Journal of Historical Sociology 29, no. 1: 4–22.
Wolf, Eric R. 1964. Anthropology. Englewood Cliffs, N.J.: Prentice-Hall.
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2021-07-28 10:40:26
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https://www.nature.com/articles/s41467-019-12669-6
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Species abundance information improves sequence taxonomy classification accuracy
Abstract
Popular naive Bayes taxonomic classifiers for amplicon sequences assume that all species in the reference database are equally likely to be observed. We demonstrate that classification accuracy degrades linearly with the degree to which that assumption is violated, and in practice it is always violated. By incorporating environment-specific taxonomic abundance information, we demonstrate a significant increase in the species-level classification accuracy across common sample types. At the species level, overall average error rates decline from 25% to 14%, which is favourably comparable to the error rates that existing classifiers achieve at the genus level (16%). Our findings indicate that for most practical purposes, the assumption that reference species are equally likely to be observed is untenable. q2-clawback provides a straightforward alternative for samples from common environments.
Introduction
Advances in high-throughput DNA sequencing and bioinformatics analyses have illuminated the crucial roles of microbial communities in human populations and planetary health1,2 and enable microbiome meta-analysis on a massive scale3. An important step in characterizing microbial communities is classification of short marker-gene DNA sequences (e.g., bacterial 16S rRNA genes) to infer taxonomic composition.
Short marker-gene sequence reads often contain insufficient information to differentiate species using conventional methods4,5,6,7,8. However, current best practices rely on species-level classification to circumvent well-documented inconsistencies between genus-level reference taxonomies and molecular phylogeny (e.g. Clostridium and Eubacterium)9.
In this work, we demonstrate that a substantial improvement in classification accuracy of marker-gene sequences can be achieved if a reference taxonomic distribution for the sample’s source environment is known. This technique enables marker-gene sequencing to differentiate individual species at a level of accuracy previously only available at the genus level.
We focus on q2-feature-classifier, a QIIME 210 plugin for taxonomic classification. In previous work4 we benchmarked this method against other common classifiers, including the RDP Classifier11 and several consensus-based methods using real and simulated data for four bacterial and fungal loci. We also tested a developmental feature that showed that knowing the mixing proportions of mock communities improved taxonomic classification accuracy. In general, q2-feature-classifier meets or exceeds the accuracy of the other classifiers4. However, all tested methods perform similarly if their parameters are tuned in a concordant manner. Significant performance enhancement demonstrated in the current work for q2-feature-classifier therefore imply improved performance over those other methods.
Results
Taxonomic weight assembly with q2-clawback
The RDP Classifier and q2-feature-classifier use similar naive Bayes machine-learning classifiers to assign taxonomies based on sequence k-mer frequencies, and exhibit very similar performance when default parameters are used4. The default assumption of these classifiers is that each species in the reference taxonomy is equally likely to be observed. Unlike the RDP classifier, however, q2-feature-classifier now allows prior probabilities to be set for each species. We refer to the prior probabilities as taxonomic weights and the default equal probabilities as uniform weights. We hypothesized that inputting the frequencies with which each taxon is actually observed in nature as taxonomic weights would improve classifier performance.
Taxonomic weights were downloaded and assembled using our new utility, q2-clawback (https://github.com/BenKaehler/q2-clawback). We created weights for 14 Earth Microbiome Project Ontology (EMPO) 3 habitat types1 across 21,513 samples from the Qiita microbial study management platform3 (see Methods for details). q2-clawback can assemble weights from any appropriately curated set of samples or by querying Qiita on any available metadata category. We refer to EMPO 3 habitat-specific taxonomic weights as bespoke weights.
Taxonomic weights improve species classification
To test classification accuracy using varying taxonomic weights, we developed a novel cross-validation strategy that accounted for the observed abundances of taxa in any given habitat. This strategy ensured that a classifier was never asked to classify a sequence that had occurred in its training set or generate taxonomic abundances that had directly contributed to its input taxonomic weights. To our knowledge, our cross-validation strategy is the first to incorporate information about taxonomic weights in assessing taxonomic classifier performance. This situation is known in machine learning as imbalanced learning12. See Methods for a thorough description of the test dataset and cross-validation procedure.
Bespoke weights achieved significantly better species-level classification accuracy than other taxonomic weight strategies. Bespoke weights significantly outperformed uniform weights when both were compared at the species level across the 14 EMPO 3 habitats (bespoke error rate = 14%, uniform error rate = 25%, paired t-test P = 5.8 × 10−5) (Fig. 1). Similar results were obtained for Bray-Curtis dissimilarity and F-measure (see Supplementary Notes). Averaged across the 14 EMPO 3 habitats, Proteobacteria and Firmicutes were the most abundant phyla (34% and 18% of reads, respectively). Switching from uniform to bespoke weights caused error rates for classification of species in these phyla to drop from 35.4% (±0.7% s.e.) to 22.3% (±0.4% s.e.) and 43.6% (±0.7% s.e.) to 24.3% (±0.3% s.e.), respectively (Supplementary Fig. 5). These differences were highly significant for both Proteobacteria and Firmicutes (paired t-tests P = 1.4 × 10−6 and P = 8.4 × 10−6, respectively).
Using bespoke weights, researchers can now classify sequences at the species level with the same confidence that they previously classified sequences at the genus level (Fig. 1). To demonstrate that bespoke classification achieves both greater accuracy and greater depth of taxonomic classification, we compared the error rates of bespoke classification at the species level to uniform classification at the genus level. The mean error rate (the proportion of reads incorrectly classified) across the 14 EMPO 3 habitat types was 14% (±1% s.e.) for bespoke weights at the species level and 16% (±1% s.e.) for uniform weights at the genus level. These results indicate that bespoke weights achieve comparable or better species-level accuracy to what uniform weights can only accomplish at the genus level. (As described below, bespoke weights significantly outperform uniform weights by all metrics when both are compared at the species level.) The mean Bray-Curtis dissimilarity between observed and expected taxonomic abundances was 0.13 (±0.01 s.e.) for bespoke weights at the species level and 0.15 (±0.01 s.e.) for uniform weights at the genus level (single-sided paired t-test P = 0.013) (Supplementary Table 2, Supplementary Fig. 2), indicating better performance of bespoke weights. See Supplementary Notes for more details of our benchmarking results.
Bespoke accuracy boost is correlated to weight fitness
In addition to testing classification accuracy using cross validation within EMPO3 habitats, we performed a set of additional experiments to evaluate how the selection of taxonomic weights impacts classifier performance. First, we assessed classification accuracy when using the average of the 14 EMPO 3 habitat-specific bespoke weights, which we term average weights. For every EMPO 3 habitat, bespoke weights outperformed average weights (sign test P = 6.1 × 10−5) (Fig. 2, Supplementary Figs. 2 and 3). Similarly, average weights always outperformed uniform weights (sign test P = 6.1 × 10−5) (Fig. 2, Supplementary Figs. 2 and 3). The implication is that classification accuracy improves when taxonomic weights more closely resemble taxonomic frequencies observed in nature. Second, we assessed classification accuracy when training classifiers with taxonomic weights from the EMPO 3 habitats other than the sample’s source habitat, which we term cross-habitat weights. Importantly, uniform weights demonstrated inferior performance to cross-habitat weights in 117 out of 182 cross-habitat comparisons, suggesting that any type of naturally derived taxonomic weight has the potential to improve classification accuracy, even if those weights were derived from a dissimilar habitat type (Fig. 3; see Supplementary Notes). The degree to which cross-habitat taxonomic weights could accurately classify the taxa within a given environment was proportional to the similarity between those weights and the bespoke weights for the source habitat: as the taxonomic weights moved away from the bespoke weights for a given sample, error rate increased (Pearson r2 = 0.57, P < 2.2 × 10−16) (Fig. 4; see Supplementary Notes and Methods).
The ability of uniform-weight classifiers to resolve species-level differences from marker genes is directly related to sequence similarity among the reference species. Species with highly similar sequences will be difficult to differentiate, even if these species occupy exclusive ecological habitats. However, bespoke weights incorporate habitat-specific species distribution information to guide sequence classification. Hence, classification accuracy under bespoke weights for a given habitat type is tied to sequence similarity and the distribution of individual species in that habitat. We devised a statistic that we term the confusion index to quantify how often similar sequences originated from different species in the same habitat (see Methods). The confusion index is a function of the taxonomic difference between sequences with similar k-mer profiles and the frequency that they appear, taking the bespoke weights as the likelihood of observing a given species. We found that error rates for bespoke weights were correlated with the confusion index (Fig. 5; Pearson r2 = 0.72, P = 1.4 × 10−4, see Methods and Supplementary Notes). That is, classification accuracy is affected by how often different species in the same sample have similar amplicon sequences but different taxonomic classifications, and that varies between EMPO 3 habitats.
The clear logic behind using bespoke weights is to encourage the classifier, when faced with uncertainty, to err on the side of taxa that are more abundant for a given habitat. The risk with this approach is that less abundant taxa may then be neglected. We tested this possibility by using the qualitative performance metrics taxon detection rate (TDR) and Taxon Accuracy Rate (TAR)4 which take only presence and absence data into account. For TAR, bespoke weights outperformed average weights and average weights outperformed uniform weights on average (Supplementary Fig. 7). The differences were not significant (minimum paired t-test P = 0.17). For TDR, the trend fit with all of our other tests with average weights always outperforming uniform weights and bespoke weights always outperforming average weights (sign test P = 6.1 × 10−5) (Supplementary Fig. 8). While the TAR results were not as positive as our other results, they nonetheless show that no penalty was incurred, even judging purely by presence and absence of taxa, when using bespoke weights.
We also tested whether using bespoke weights would reduce classification accuracy for rare taxa. By averaging results across the 14 EMPO 3 habitats, we plotted average differences in uniform and bespoke weight error rates against average species abundance (Supplementary Fig. 9). We found that for abundances less than 10−4, there was some evidence of degradation in classifier accuracy, although for most species it made no difference. For a typical sample depth in the order of 104 reads, this indicates that there may be some risk of misclassification for singletons.
Discussion
The assumption of uniform weights, that species are evenly distributed in nature and hence equally likely to be detected, is incorrect. We have demonstrated that this assumption imposes a consistently negative impact on performance, even when compared to deliberately incorrect taxonomic weights selected from ecologically dissimilar environmental sources (the cross-habitat weights). As a result, we suggest the continued usage of uniform weights is not justifiable. When publicly accessible pre-existing microbiome data is available for the sample (i.e., environment) type being investigated, bespoke weights should be used. For other natural sample types that lack sufficient characterization for bespoke weight assembly, average weights estimated from global microbial species distributions are superior to uniform weights. We did observe some degradation in performance for rare species. If the presence or absence of singletons for a typical sample is critical to experimental design, then we advocate using amplicon sequence variants13,14 rather than taxonomic classification. For highly unusual sample distributions, e.g., in synthetic populations, we recommend compiling custom bespoke weights from existing samples. We demonstrated species-level classification improvement with as few as 122 samples (four-fifths of the saline surface samples from the EMP study; Table 1).
Our key finding is that taxonomic classification is sensitive to taxonomic weight assumptions, and better alternatives to assuming uniform weights exist for natural samples. Even when we intentionally used taxonomic weights from the wrong habitat type (our cross-habitat tests), these weights still outperformed uniform weights for species classification in the majority of cases. Where uncertainty exists regarding the correct choice of habitat for taxonomic weights, average weights offer a generalized solution for improved accuracy over uniform weights. Systematic comparison of uniform, average, bespoke, and cross-habitat weights demonstrated that the more specific the taxonomic weights are to a query sample’s environment, the better the classification accuracy. Thus, taxonomic weight selection impacts classification results, but any deliberate decision regarding choice of taxonomic weights is unlikely to negatively impact classification accuracy beyond the penalty imposed by uniform weights. q2-clawback facilitates the use of appropriate weights by making it easier for the researcher to assemble weights that are specific to a particular sample type, provided that appropriate source data are available. For instance, it is trivial to assemble weights for all stool samples with human hosts from Qiita (See the online tutorial, https://library.qiime2.org/plugins/q2-clawback).
In common with other methods, bespoke classification is not immune to errors that result from poorly curated reference data (e.g., reference sequence misannotation). The use of empirical species distributions also creates a potential source of error for bespoke classification (e.g., misannotation of sample types or sequencing biases in empirical samples could be propagated if those samples were used to develop taxonomic weights). Constructing taxonomic weights via meta-analysis of many studies of a single environment type, as we perform here and democratize with q2-clawback, reduces the impact of unsystematic errors such as mislabelled samples. More systematic errors, for instance from bias present in common sequencing techniques, could be controlled by integrating multiple technologies for microbial distribution estimation (e.g., marker gene, shotgun metagenome, metaproteome, and non-molecular methods). In the Supplementary Information, we demonstrate that shotgun metagenome data may be used to construct bespoke taxonomic weights (Supplementary Fig. 6). Further work could provide an interesting route for inferring more realistic approximations of natural taxonomic weights.
Regardless of the source of classification error, as bespoke classification typically starts from the raw reference and read data when weights are derived, its use does not lead to classification errors being propagated through history. Efforts to curate reference databases and the continued contribution of researchers to online microbiome data repositories will help refine and extend our ability to apply appropriate bespoke weights for sequence classification in diverse sample types. The magnitude of improvement in classification accuracy and robustness to the use of deliberately inappropriate weights in our cross-habitat tests make us confident that these sources of error are of secondary importance to the much larger error of assuming uniform weights.
The results we present provide a general path for delivering species-level classification accuracy. As such, the work provides a complementary solution to the small number of existing specialist classification databases15,16,17,18. Moreover, bespoke weight classification permits the detection of unexpected species not encompassed by custom databases.
By improving species-level classification of marker-gene sequences, bespoke weights may support critical functional inferences, e.g., differentiation of pathogenic and non-pathogenic species of the same genus19,20,21,22,23,24. Ongoing improvements in public reference sequence and sample databases will further boost performance, supporting biological insight into global microbiome compositions. Uniform weights should always be avoided, as they distort natural species distributions, leading to imprecise and incorrect taxonomic predictions.
Methods
Data
We downloaded all public 150 nucleotide 16S v4 samples for 18 EMPO 3 habitat types from Qiita3 using q2-clawback. The downloaded data consisted of sequence variant and abundance information. The sequence variants were prepared by the standard Qiita pipeline, including Deblur13, prior to download. q2-clawback uses redbiom25 (https://github.com/biocore/redbiom) to access Qiita. Data from the following Qiita studies were used: 1111326, 11444, 1716, 1036927, 99028, 2080, 1713, 894, 1289, 1883, 1673, 1288, 10353, 219229, 10323, 678, 1773, 662, 1799, 864, 1481, 102430, 1064, 2182, 10934, 1674, 179531, 10273, 1028332, 1042233, 804, 10308, 105634, 238230, 1240, 889, 1041, 1717, 1222, 11149, 11669, 80735, 10245, 1711, 1721, 910, 1001, 895, 55036, 174737, 71338, 755, 861, 95839, 1116140, 1115441, 945, 723, 1715, 1714, 10798.
The three EMPO 1 control EMPO 3 habitat types were excluded, as well as Hypersaline (saline), Aerosol (non-saline), and Plant surface, which all had fewer than nine samples in the Qiita database for 150 nt sequence variants. The number of samples downloaded for each EMPO 3 habitat are shown in Table 1.
For the cross validation analysis, sequence-variant level data was discarded and only taxonomic abundance information was retained. The sequence variants were classified using the standard q2-feature-classifier naive Bayes classifier based on Greengenes 99% identity OTU reference data42 to obtain empirical taxonomic abundance data for each sample. The naive Bayes classifier was trained using the balanced parameter recommendations given in Bokulich, Kaehler et al.4.
Clawback
q2-clawback is a free, open-source, BSD-licensed package that is available on GitHub (https://github.com/BenKaehler/q2-clawback). It includes methods for downloading sequence variants from Qiita (fetch-Qiita-samples), extracting sequence variants for taxonomic classification using q2-feature-classifier (sequence-variants-from-samples), and assembling taxonomic weights from collections of samples of taxonomic abundance (generate-class-weights). These methods can be run independently or combined into a single method call (assemble-weights-from-Qiita). Figure 6 shows the workflow for these methods. An online tutorial is available (https://library.qiime2.org/plugins/q2-clawback).
In general, taxonomic weights are assembled as follows. A set of sequence variants with abundances are acquired (fetch-Qiita-samples). The sequence variants are extracted (sequence-variants-from-samples) and classified using the naive Bayes classifier under uniform weights using balanced settings4. Classification to species level is forced by setting the confidence parameter to −1. The resulting read counts are aggregated, normalised, and added to a small (10−6 unobserved weight default) uniform offset (generate-class-weights) to form bespoke weights. The resulting weights are used to retrain the naive Bayes classifier to create a classifier under the bespoke weights assumption. In our experiments, which are detailed below, this procedure was modified slightly to accommodate cross validation and compilation of taxonomic weights from a variety of sources.
Internally, q2-feature-classifier uses the multinomial naive Bayes classifier provided by scikit-learn (see http://scikit-learn.org/stable/modules/naive_bayes.html). Loosely, the naive Bayes classifier finds the taxon that maximises the expression P(T|S) = P(S|T) × P(T)/P(S), where P(T) and P(S) are the probabilities of observing a taxon T and sequence S respectively, and P(S|T) and P(T|S) are the conditional probabilities of observing a sequence S given a taxon T and a taxon T given a species S, respectively. The probabilities are estimated under questionable assumptions (the term naive refers specifically to the way P(S|T) is calculated). The goal is not to provide a realistic model of reality; the goal is to predict taxa given sequences. When taxonomic weights are provided, they are used directly as estimates of P(T). For uniform weights, it is assumed that P(T) = 1. We note, however, that q2-feature-classifier is able to take taxonomic weights inputs for a variety of machine learning classifiers that are available in scikit-learn.
Cross validation using empirical taxonomic abundance
As mentioned above, to test classification accuracy using varying taxonomic weights, we developed a cross-validation strategy that accounted for the observed abundances of taxa in any given habitat.
Cross validation was used to analyse the effectiveness of setting the taxonomic weights for the q2-feature-classifier naive Bayes taxonomic classifier. A single cross-validation test follows the pattern (shown in Fig. 7, several steps are described in more detail below):
1. 1.
Obtain a set of reference sequences and reference taxonomies.
2. 2.
Obtain a set of samples for a given EMPO 3 habitat type, where each sample contains the number of reads observed for each taxon.
3. 3.
Perform stratified k-fold cross validation simultaneously on reference sequences and samples.
4. 4.
For each fold:
1. a.
Train a classifier on the training reference sequences, optionally incorporating read counts from the training samples to calculate taxonomic weights.
2. b.
Simulate samples that closely match the taxonomic abundances in the test samples using the test reference sequences, then classify them using the above classifier.
Step 2. Data were obtained as detailed above. Taxonomic abundances were estimated using the naive Bayes classifier under uniform weights using balanced settings4, where the classifier was forced to classify to species level.
Step 3. We performed 5-fold cross validation in each instance. Standard stratification for 5-fold cross validation requires that at least five sequences exist for each taxonomy, which is not the case for the 99% identity Greengenes reference taxonomy. We, therefore, formed a stratum for each taxonomy for which five or more reference sequences existed (large taxonomies) and merged the remaining taxonomies (small taxonomies) into those strata. A single large taxonomy was chosen for each small taxonomy by training a naive Bayes classifier on the large taxonomies, classifying the reference sequences in the small taxonomies, then voting weighted by confidence. Shuffled stratified 5-fold cross validation was then implemented using a standard library call to scikit-learn45.
Cross validation was performed simultaneously on samples and reference sequences. Sample cross validation was not stratified.
Step 4a. Each sample consisted of a set of taxonomies and their abundances. Taxonomic weights were formed by aggregating those counts across the training samples. As a result of the merged strata in Step 3, some taxonomies that were present in the bespoke weights were not present amongst the taxonomies of the training sequences. Any such taxonomy was mapped to the nearest taxonomy that was present amongst the taxonomies represented by the training sequences, as measured by the voting system from Step 3.
Step 4b. Samples were simulated by drawing sequences from the test sequences in such a way as to closely resemble the taxonomic abundances of the test samples. Again as a result of the merged strata in Step 3, some taxonomies that were present in the test samples were not present in the taxonomies of the test sequences. In the same way as for Step 4a, any missing species-level taxonomy was mapped to the closest taxonomy for a sequence present in the test sequences. Once missing taxonomies were resolved, samples were simulated by drawing test sequences as evenly as possible from each taxonomy so that any read count was a whole number.
For the q2-feature-classifier naive Bayes classifiers that were reported in this study, we used the recommended balanced parameters as recommended for uniform weights4. That is, we used a confidence level of 0.7 in all cases. In Bokulich et al.4, a confidence level of 0.92 was recommended for bespoke weights tested on mock communities. We tested the classifiers at this level but in all cases the results were dominated by the less conservative confidence level of 0.7.
F-measure and Bray-Curtis46 dissimilarity were calculated for each sample and taxonomic level using the q2-quality-control QIIME 2 plugin (https://github.com/qiime2/q2-quality-control). F-measure for each fold was aggregated across samples by weighting by the total read count for each sample. Bray-Curtis dissimilarity was averaged across samples without weighting, but samples with less than 1000 reads were filtered out.
Error rates, or the proportion of reads not correctly classified, were calculated as follows. A classification was called correct only if the expected classification exactly matched the observed classification to the required taxonomic level. That is, if the expected classification did not contain classification all the way to that level because that species was not present in the training set, then the classification was called correct only if it was truncated at exactly the right level. Correct classification rates were again calculated for each sample and aggregated across samples by weighting by the total read count for each sample. Aggregation across folds and EMPO 3 habitats was evenly weighted.
Confusion Index
The degree to which species can be successfully resolved is directly related to the dissimilarity of their sequences. We sought to establish a property of the reference data and taxonomic weights that were related to the classification accuracy across EMPO 3 habitats. For any pair of DNA sequences, the critical quantities are their sequence and taxonomic dissimilarities. Sequence dissimilarity is measured as the Bray-Curtis dissimilarity of k-mer counts. Taxonomic dissimilarity is the depth (from species level) of the most recent common ancestor, e.g. zero for the same species, one for species within the same genus and seven for an Archaean versus a Bacterium.
The Confusion Index is then the log of the product of the probability that the sequence dissimilarity for any pair of sequences is less than a threshold (we selected 0.25) and the expectation of the taxonomic distance given that the sequence dissimilarity is less than 0.25. The expectation was calculated under the assumption that the two sequences were sampled independently with probability given by their bespoke weights. That is,
$${\mathrm{CI}} = \log \mathop {\sum }\limits_{{i} = 1}^{n} \mathop {\sum }\limits_{{j} = 1}^{n} {d}_{t}\left( {{i},j} \right){I}\left( {{d}_{s}\left( {{i},{j}} \right){\,} < {\,}0.25} \right){w}\left( {i} \right){w}\left( {j} \right)$$where CI is the confusion index, ds(i,j) is the sequence dissimilarity between the i th and j th sequences, dt(i,j) is the taxonomic dissimilarity between the i th and j th sequences, w(i) is the weight of the i th sequence, and I(•) is the indicator function.
The confusion index quantifies how often a pair of taxa have nearly identical sequences but different taxonomies for a given set of taxonomic weights. One advantage of this quantity is that it can be estimated statistically by taking a random sample of pairs of sequences. In this study we sampled 108 pairs of sequences for each calculation.
Comparison of taxonomic classification for shotgun and amplicon sequencing
The effect of using taxonomic weights derived from taxonomic classification of shotgun sequencing reads was determined using 5-fold cross validation, where each classifier was trained using taxonomic weights aggregated across the samples in the training set, then tested on 16S samples from a test set. TDR4 was computed using the q2-quality-control QIIME 2 plugin. TDR is the fraction of taxa that were discovered in the shotgun sequencing sample that were also found in the amplicon sample.
Reporting summary
Further information on research design is available in the Nature Research Reporting Summary linked to this article.
Data availability
The Qiita data used in this study have been deposited at https://doi.org/10.5281/zenodo.2548899. The HMP and NCBI data used in this study have been deposited at https://doi.org/10.5281/zenodo.2549777. All other relevant data is available upon request.
Code availability
q2-clawback is available at https://github.com/BenKaehler/q2-clawback/releases/tag/0.0.4. All other code developed for this study is available at https://github.com/BenKaehler/paycheck/releases/tag/0.0.4.
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Acknowledgements
QIIME 2 development was primarily funded by NSF Awards 1565100 to J.G.C. and 1565057 to R.K. This work was supported by an NHMRC project grant APP1085372, awarded to G.A.H., J.G.C., and R.K.
Author information
Authors
Contributions
Conceived, designed, and performed experiments: B.D.K. and N.A.B. Designed and wrote clawback software: B.D.K. and N.A.B. Wrote paper: B.D.K., N.A.B., J.G.C., and G.A.H. Developed supporting software (redbiom): D.M. and R.K. Provided critical review of paper and results: D.M., R.K., J.G.C., and G.A.H.
Corresponding authors
Correspondence to Benjamin D. Kaehler, Nicholas A. Bokulich, J. Gregory Caporaso or Gavin A. Huttley.
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review information: Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Reprints and Permissions
Kaehler, B.D., Bokulich, N.A., McDonald, D. et al. Species abundance information improves sequence taxonomy classification accuracy. Nat Commun 10, 4643 (2019). https://doi.org/10.1038/s41467-019-12669-6
• Accepted:
• Published:
• DOI: https://doi.org/10.1038/s41467-019-12669-6
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2022-08-17 06:05:38
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https://ask.sagemath.org/questions/9773/revisions/
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# Revision history [back]
### Cannot make inline Fortran compiler (f2py) work
Hello!
I am trying to make the inline Fortran compiler work. It gave some long errors in Sage 5.5. Now I try in Sage 5.6 (Ubuntu 11.10 64 bit): The evaluation of %fortran cell returns None , but no symbols seem to be defined.
I tried the simple Fibonacci example from the documentation and it did not work as it should. The ordinary command-line compilation with f2py works ok!
Please, could anyone try to help me.
%fortran
C FILE: FIB3.F
SUBROUTINE FIB(A,N)
C
C CALCULATE FIRST N FIBONACCI NUMBERS
C
INTEGER N
REAL*8 A(N)
Cf2py intent(in) n
Cf2py intent(out) a
Cf2py depend(n) a
DO I=1,N
IF (I.EQ.1) THEN
A(I) = 0.0D0
ELSEIF (I.EQ.2) THEN
A(I) = 1.0D0
ELSE
A(I) = A(I-1) + A(I-2)
ENDIF
ENDDO
END
C END FILE FIB3.F
None
Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_41.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZmliKDUp"),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>
File "/tmp/tmpBVbhBE/___code___.py", line 3, in <module> exec compile(u'fib(_sage_const_5 ) File "", line 1, in <module>
NameError: name 'fib' is not defined
Best wishes, Sergey
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2021-05-16 15:22:08
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https://tex.stackexchange.com/questions/414859/page-number-misplaced-using-fancyhdr-custom-color-and-includefoot-geometry-op
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# Page number misplaced using fancyhdr, custom color and “includefoot” geometry-option
If I color the page number with the packages fancyhdr and xcolor, I get the page number out of the space defined as "footskip" in the geometry package.
I am enclosing a MWE where you can see that if the page number is colored with \color{customcolor}, it gets misplaced (it is below the line drawn by geometry):
\documentclass{book}
\usepackage{fancyhdr}
\usepackage{geometry}
\usepackage{xcolor}
\definecolor{customcolor}{RGB}{112,112,112}
\fancypagestyle{plain}{
\fancyhf{}
\fancyfoot[CO]{\color{customcolor}\thepage}
\renewcommand{\footrulewidth}{0pt}}
\begin{document}
\pagestyle{plain}
Hello!
\end{document}
How can I avoid it?
(I am compiling this on LuaTeX)
• Use \fancyfoot[CO]{\textcolor{customcolor}{\thepage}}. – Bernard Feb 12 '18 at 0:51
• @Werner I got the same mistake in another file where I inverted the packages loading order, but thanks anyway for pointing that issue out. – oibaFox Feb 12 '18 at 1:09
• @Bernard it works perfectly, thanks! Could you please explain me why in this context there is this difference between \color{.} and \textcolor{.}? By the way, would you write your comment as an answer so that I can mark it as correct? – oibaFox Feb 12 '18 at 1:12
• I have no idea why there's a difference. I tested just in case… But I hac=ve a simpler solution with titleps that I'll add. – Bernard Feb 12 '18 at 1:20
Using \fancyfoot[CO]{\textcolor{customcolor}{\thepage}} solves the problem.
However, the titleps package, used in the place of fncyhdr doesn't have this drawback, and has a simpler syntax, with the \renewpagestyle{plain}{...} command:
\documentclass{book}
\usepackage{xcolor}
\definecolor{customcolor}{RGB}{112,112,112}
\usepackage{titleps}
\renewpagestyle{plain}{%
\setfoot{}{\color{customcolor}{\thepage}}{}
}%
\usepackage{geometry}
`
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2019-10-24 05:34:35
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https://mathoverflow.net/questions/288375/axiomatic-characterization-of-virtual-fundamental-classes
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# Axiomatic characterization of virtual fundamental classes?
There are several objects called "virtual fundamental classes." For example, certain Deligne-Mumford stacks, quasi-smooth derived schemes, etc. will admit a "perfect obstruction theory" as defined by Behrend-Fantechi and then the mojo of intrinsic normal cones produces a "virtual fundamental class" $[X] \in A_d(X)$ of virtual dimension $d$ in the Chow ring of the stack (or whatever) $X$.
Already here, there could be different perfect obstruction theories e.g. different morphisms $\varphi : E^\cdot \to \mathbb{L}_X$, $\varphi' : E'^\cdot \to \mathbb{L}_X$. How can we compare the virtual classes $[X]_{\varphi}, [X]_{\varphi'}$ coming from the two different perfect obstruction theories? Are they always the same?
Further, there are many approaches to defining virtual classes for moduli problems in symplectic geometry. There, one does not use perfect obstruction theories. Rather, one looks for "Polyfold structures" or "Kuranishi structures" which can be used to produce a homology class which is then called "the virtual fundamental class." I suppose one would like to compare the classes gotten from Polyfolds with the ones gotten from Kuranishi structure. And there are many appraoches to Kuranishi structure, so I suppose one would like to compare the virtual classes gotten from those approaches.
I apologise if there is a big well-known theorem stating asserting they are all equal. But even in that event, I think comparing the virtual classes in algebraic geometry with those in symplectic geometry is interesting.
And so, I ask: What makes these classes "virtual fundamental." Is there an axiomatic list of properties which either determines the thing or allows us to say general "model independent" things?
• Do you mean $\varphi$ and $\varphi'$ to have the same domain $E^\bullet$, or can they have different $E^\bullet$ and $E^{\prime\bullet}$? – John Pardon Dec 12 '17 at 21:07
• @JohnPardon Thank you for catching this. I do not see any reason to assume that $\varphi$ and $\varphi'$ have the same domain. – user100272 Dec 16 '17 at 18:46
Question 1 (compare virtual fundamental cycles of different perfect obstruction theories on space underlying space): There is essentially no relation between $[X]_\varphi$ and $[X]_{\varphi'}$ for different perfect obstruction theories $\varphi:E^\bullet\to\mathbb L_X$ and $\varphi':E^{\prime\bullet}\to\mathbb L_X$. The "derived" structure on $X$ encoded in $\varphi$ is essential for defining the vfc; knowing $X$ as a topological space (or variety, stack, etc.) determines essentially nothing about vfc (except trivial things like the fact that the vfc vanishes if the virtual dimension is larger than the classical dimension of $X$).
A very special case of your question is "Does the euler class $e(E)\in H^\bullet(M)$ of a vector bundle $E$ over a manifold $M$ depend only on $M$?" whose answer should be clear.
Question 2 (axiomatic characterization of virtual fundamental classes): I've thought extensively about this problem, and as far as I know, no axiomatic characterization of virtual fundamental classes/cycles/chains has been formulated and proved in the literature. There is definitely no satisfying general result which allows one to compare all reasonable approaches to defining virtual fundamental cycles in symplectic geometry. The philosophical reason why this seems like a difficult problem is that it's much easier to work "infinitesimally" in algebraic geometry than in differential geometry (or, at least, the sort of differential geometry relevant to moduli spaces of pseudo-holomorphic curves). Thus, all existing methods for defining the VFC in symplectic geometry "remember" much more of the ambient geometry of the entire space of smooth (as opposed to pseudo-holomorphic) maps than should be necessary for defining the VFC. The comparison between them is very technical because, although morally all approaches give rise to exactly the same VFC, we don't currently have a good language for recording the minimal amount of "derived" information that the moduli spaces carry (and which should be sufficient for defining the VFC).
Ideally, one would like to define some (derived?) moduli problem in the smooth or topological category for pseudo-holomorphic curves. Then one would like to show that this moduli problem is representable by a reasonable "derived topological manifold" (or orbifold) whose underlying topological space is the usual moduli space and whose derived structure is the analogue of a perfect obstruction theory. The last step (and probably the easiest, actually) is defining the VFC from this derived structure.
In my view, an axiomatic characterization of virtual fundamental classes is unlikely to be helpful with the question of comparing different constructions in symplectic geometry, unfortunately. This is simply because the "problem" is more than just having various ways of extracting the VFC, rather it's that we don't even know what the right canonical extra "derived" structure on the moduli space is from which we should extract the VFC. I'd be thrilled if I'm wrong, though!
I'll stop here, although it's possible to write endlessly on this topic. If you have other questions, I'm happy to expand this answer or answer a subsequent question you ask.
• Thank you for this detailed reply. And excuse my ignorance, but I thought the condition that the derived manifold has cotangent complex concentrated in degrees $-1$ and $0$ was the correct amount of derived structure for obtaining virtual fundamental classes. – user100272 Dec 16 '17 at 18:49
• @JacobGross: It is true that given a derived moduli problem, you can ask whether it admits a cotangent complex and whether it is of tor-amplitude $[-1,0]$, in which case it would admit a virtual fundamental class. However you need first of all to extend your classical moduli problem to a derived moduli problem in a reasonable way, which may not always be trivial at all. – AAK Dec 16 '17 at 19:26
Joyce has some work in this direction: in particular, he defines a functor from Deligne-Mumford $\mathbb{C}$-stacks with perfect obstruction theories to what he names 'd-orbifolds'. These should be thought of, essentially, as 'derived' $\mathbb{R}$-stacks. Since we are in characteristic 0, this means these spaces come with a homotopy sheaf of simplicial $\mathbb{R}$-algebras, or equivalently, commutative differential graded algebras over $\mathbb{R}$. I strongly suspect that from this perspective, one can define an actual quasi-smooth derived geometric stack from which one can obtain a virtual fundamental cycle. Indeed, one would need to work over the appropriate site, and the Joyce's work gives some indications on what one should do.
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2020-10-27 09:12:27
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https://manual.q-chem.com/latest/topic_cdcc.html
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Searching....
# 6.10.8 Cholesky Decomposition with CC (CD-CC)
(July 14, 2022)
Two-electron integrals can be decomposed using Cholesky decomposition 317 Epifanovsky E. et al.
J. Chem. Phys.
(2013), 139, pp. 134105.
giving rise to the same representation as in RI and substantially reducing the cost of integral transformation, disk storage requirements, and improving parallel performance:
$(\mu\nu|\lambda\sigma)\approx\sum_{P=1}^{M}B_{\mu\nu}^{P}B_{\lambda\sigma}^{P},$ (6.50)
The rank of Cholesky decomposition, $M$, is typically 3-10 times larger than the number of basis functions $N$ (Ref. 43 Aquilante F., Pedersen T. B., Lindh R.
Theor. Chem. Acc.
(2009), 124, pp. 1.
); it depends on the decomposition threshold $\delta$ and is considerably smaller than the full rank of the matrix, $N(N+1)/2$ (Refs. 43 Aquilante F., Pedersen T. B., Lindh R.
Theor. Chem. Acc.
(2009), 124, pp. 1.
, 87 Beebe N. H. F., Linderberg J.
Int. J. Quantum Chem.
(1977), 12, pp. 683.
, 1292 Wilson S.
Comput. Phys. Commun.
(1990), 58, pp. 71–81.
). Cholesky decomposition removes linear dependencies in product densities $(\mu\nu|$, 43 Aquilante F., Pedersen T. B., Lindh R.
Theor. Chem. Acc.
(2009), 124, pp. 1.
allowing one to obtain compact approximation to the original matrix with accuracy, in principle, up to machine precision.
Decomposition threshold $\delta$ is the only parameter that controls accuracy and the rank of the decomposition. Cholesky decomposition is invoked by specifying CHOLESKY_TOL that defines the accuracy with which decomposition should be performed. For most calculations tolerance of $\delta=10^{-3}$ gives a good balance between accuracy and compactness of the rank. Tolerance of $\delta=10^{-2}$ can be used for exploratory calculations and $\delta=10^{-4}$ for high-accuracy calculations. Similar to RI, Cholesky-decomposed integrals can be transformed back, into the canonical MO form, using CC_DIRECT_RI keyword.
Note: Cholesky decomposition is available for all CCMAN2 methods, including energy, analytic gradients, and properties calculations. For maximum computational efficiency, combine with FNO (see Sections 6.13 and 7.10.12) when appropriate.
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2022-09-27 09:15:44
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https://mathoverflow.net/questions/335354/what-is-the-application-of-higher-toposes-in-motivic-homotopy-theory
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# What is the application of higher toposes in motivic homotopy theory?
The paper by Raptis and Strunk describes a model for motivic homotopy theory as a model topos. I wonder what this result can lead to or what is the possible development of the relation between motivic homotopy theory and infinity topos? Can anyone suggest an overview or some references please?
• I cannot quite understand this question. Motivic homotopy theory uses essentially the notion of sheaf of homotopy-ish things, so it is naturally connected (at least at a foundational level) with the theory of ∞-topoi (i.e. of sheaves of homotopical objects). The paper you refer to studies a particular ∞-topos, which is connected to the unstable motivic ∞-category (albeit in a slightly opaque way: this is the discussion at the bottom of page 31) – Denis Nardin Jul 3 at 14:24
• @DenisNardin I don't know much of the applications of higher topos. I wonder what is the importance to have a model of infinity topos. – Nicky Jul 3 at 15:08
• The short answer is that working with model topoi rather than ∞-topoi is a matter of personal choice, although ∞-topoi have some advantages in certain settings (e.g. when you start considering families of them). The theory of sheaves in a homotopical setting was fairly fundamental even in setting up motivic homotopy theory, even if they did not use the language of ∞-topoi at the time. What is your background? – Denis Nardin Jul 3 at 16:15
• As pointed out in that paper, it's well-known that the usual $\infty$-category of motivic spaces is a locally cartesian closed presentable $\infty$-category, but not an $\infty$-topos. The contribution of Raptis and Strunk is to provide an alternative $\infty$-category which is an $\infty$-topos and plausibly encodes similar information. As far as I know (though I am not an expert in this area) the promise of this construction has not been fully explored. Note that there are other $\infty$-toposes, such as the etale site, which are related to motivic homotopy theory less directly. – Tim Campion Jul 3 at 16:30
• @DenisNardin I don't mean the choice between the two. The motivic homotopy category constructed by Morel and Voevodsky is not a model topos but this paper shows a way to construct one. I wonder what are some consequences of this model topos? – Nicky Jul 3 at 16:33
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2019-07-21 01:11:31
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https://zbmath.org/?q=an:1349.65035
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# zbMATH — the first resource for mathematics
A new extrapolation method for weak approximation schemes with applications. (English) Zbl 1349.65035
Summary: Fujiwara’s method can be considered as an extrapolation method of order 6 of the Ninomiya-Victoir weak approximation scheme for the numerical approximation of solution processes of SDEs. We present an extension of Fujiwara’s method for arbitrarily high orders, which embeds the original Fujiwara method as the order 6 case. The approach can be considered as a variant of Richardson extrapolation, which allows one to reach high orders with few extrapolation steps. The most important contribution of our approach is that we only need $$m$$ extrpolation steps in order to achieve order of approximation $$2m$$, which is half the number of steps in comparison to classical approaches.
##### MSC:
65C30 Numerical solutions to stochastic differential and integral equations 60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
Full Text:
##### References:
[1] British-Russian Offshore Development Agency (BRODA). Available at . [2] Butcher, J. C. (1987). The Numerical Analysis of Ordinary Differential Equations : Runge-Kutta and General Linear Methods . Wiley, Chichester. · Zbl 0616.65072 [3] Butcher, J. C. (2003). Numerical Methods for Ordinary Differential Equations . Wiley, Chichester. · Zbl 1040.65057 [4] Cohn, P. M. (1995). Skew Fields : Theory of General Division Rings. Encyclopedia of Mathematics and Its Applications 57 . Cambridge Univ. Press, Cambridge. · Zbl 0840.16001 [5] Fujiwara, T. (2006). Sixth order methods of Kusuoka approximation. Preprint Series . Graduate School of Mathematical Sciences, Univ. Tokyo. [6] Gyöngy, I. and Krylov, N. (2003). On the splitting-up method and stochastic partial differential equations. Ann. Probab. 31 564-591. · Zbl 1028.60058 [7] Gyöngy, I. and Krylov, N. (2005). An accelerated splitting-up method for parabolic equations. SIAM J. Math. Anal. 37 1070-1097 (electronic). · Zbl 1101.35038 [8] Gyöngy, I. and Krylov, N. (2006). Expansion of solutions of parameterized equations and acceleration of numerical methods. Illinois J. Math. 50 473-514 (electronic). · Zbl 1123.65084 [9] Ikeda, N. and Watanabe, S. (1989). Stochastic Differential Equations and Diffusion Processes , 2nd ed. North-Holland Mathematical Library 24 . North-Holland, Amsterdam. · Zbl 0684.60040 [10] Kohatsu-Higa, A. (2001). Weak approximations. A Malliavin calculus approach. Math. Comp. 70 135-172. · Zbl 0956.60059 [11] Kusuoka, S. (2001). Approximation of expectation of diffusion process and mathematical finance. In Taniguchi Conference on Mathematics Nara’ 98. Advanced Studies in Pure Mathematics 31 147-165. Math. Soc. Japan, Tokyo. · Zbl 1028.60052 [12] Kusuoka, S. (2003). Malliavin calculus revisited. J. Math. Sci. Univ. Tokyo 10 261-277. · Zbl 1031.60048 [13] Kusuoka, S. (2004). Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus. Adv. Math. Econ. 6 69-83. · Zbl 1111.60035 [14] Kusuoka, S. (2009). Gaussian K -scheme. Preprint Series . Graduate School of Mathematical Sciences, Univ. Tokyo. [15] Lyons, T. and Victoir, N. (2004). Cubature on Wiener space: Stochastic analysis with applications to mathematical finance. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 169-198. · Zbl 1055.60049 [16] Ninomiya, M. and Ninomiya, S. (2009). A new higher-order weak approximation scheme for stochastic differential equations and the Runge-Kutta method. Finance Stoch. 13 415-443. · Zbl 1199.65011 [17] Ninomiya, S. and Victoir, N. (2008). Weak approximation of stochastic differential equations and application to derivative pricing. Appl. Math. Finance 15 107-121. · Zbl 1134.91524 [18] Talay, D. and Tubaro, L. (1990). Expansion of the global error for numerical schemes solving stochastic differential equations. Stoch. Anal. Appl. 8 483-509. · Zbl 0718.60058 [19] Tanaka, M., Kasahara, E., Muramatsu, S. and Yamashita, S. (1992). On a solution of the order conditions for the nine-stage seventh-order explicit Runge-Kutta method (in Japanese). Information Processing Society of Japan 33 1506-1511. [20] Tanaka, M., Muramatsu, S. and Yamashita, S. (1992). On the optimization of some nine-stage seventh-Order Runge-Kutta method (in Japanese). Information Processing Society of Japan 33 1512-1526. [21] Tanaka, M., Yamashita, S., Kubo, E. and Nozaki, Y. (1993). On seventh-order nine-stage explicit Runge-Kutta methods with extended region of stability (in Japanese). Information Processing Society of Japan 34 52-61. · Zbl 0796.65087 [22] Varadarajan, V. S. (1984). Lie Groups , Lie Algebras , and Their Representations. Graduate Texts in Mathematics 102 . Springer, New York. Reprint of the 1974 edition. · Zbl 0955.22500
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-09-17 07:58:24
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http://researchonline.ljmu.ac.uk/id/eprint/450/
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# The impact of angular momentum on black hole accretion rates in simulations of galaxy formation
Rosas-Guevara, YM, Bower, RG, Schaye, J, Furlong, M, Frenk, CS, Booth, CM, Crain, RA, Vecchia, CD, Schaller, M and Theuns, T (2013) The impact of angular momentum on black hole accretion rates in simulations of galaxy formation. Monthly Notices of the Royal Astronomical Society. ISSN 0035-8711 (Submitted)
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2021-10-20 06:52:58
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https://tex.stackexchange.com/questions/380674/vertical-line-for-pseudo-code
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# Vertical line for pseudo code
\documentclass[two column,conference]{IEEEtran}
\usepackage{algorithm}
\begin{document}
\begin{algorithm}
\caption{HD}
\label{array-sum}
1: Initialization of parameters \\
2: Randomly generate population using Eq. 28\\
3: \textbf{for} u=1:k \\
4: \textbf{for} s=1:i$_{c}$\\
5: Randomly generated X$_{s}^{u}$ in da\\
6: \textbf{end for} \\
7: \textbf{end for}\\
8: End of initialization step\\
9: \textbf{While} Maximum number of iteration reached \textbf{do}\\
10: Construction and assessment of new candidate\\
11: \textbf{if} ($rand (0,1)\leq$ cpu)\\
12: Choose random no \\
13: \textbf {if} ($rand (0,1 ) \leq$ cpu) \\
14: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
15: \textbf{end if} \\
16: \textbf{else} \\
17: Evaluate fitness function a: F(a) using Eq. 17\\
27: End of the construction and assessment step\\
28: Construction and assessment of new candidate: a \\
29: if (F(y) has best value than the worst member \\
30: Replace DA member with new candidate: a\\
31: else\\
33: \textbf{endif}\\
34: End of update\\
35: Until a preset termination criterion is met\\
36: end \textbf{while}\\
\end{algorithm}
\end{document}
I want to draw vertical lines for loops and if statement. Kindly help me out and also I didn't use any specific package
• Welcome to TeX SX! Yet the algorithmis defined by a package… – Bernard Jul 14 '17 at 13:05
• yeah!! Only algorithm package, However, it didn't worked for me can you please help me out. – Smith Jul 14 '17 at 13:10
• I can try. Would you be kind enough to post a full compilable code? – Bernard Jul 14 '17 at 13:20
• It is full code except for package {\usepackage{algorithm} However, I will also edit the code. – Smith Jul 14 '17 at 13:30
You have to load algorithm2e to do that easily:
\documentclass[two column,conference]{IEEEtran}
\usepackage[utf8]{inputenc}
\usepackage[ruled, lined, longend, linesnumbered]{algorithm2e}
\begin{document}
\begin{algorithm}
\caption{HD}
\label{array-sum}
Initialization of parameters\;
Randomly generate population using Eq. 28\;
\For{u=1:k}{%
\For{s=1:i$_{c}$}{%
Randomly generated X$_{s}^{u}$ in da \;
}
}
End of initialization step\;
\While{Maximum number of iteration reached}{
Construction and assessment of new candidate\;
\eIf{($rand (0,1)\leq$ cpu)}{%
Choose random no \;
\textbf {if} ($rand (0,1 ) \leq$ cpu) \\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\textbf{end if}
}{%
Evaluate fitness function a: F(a) using Eq. 17 \;
End of the construction and assessment step\;
Construction and assessment of new candidate: a \;
\eIf {(F(y) has best value than the worst member}{
Replace DA member with new candidate: a
}{%
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2020-07-08 06:47:23
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http://xn--dineroparasueos-brb.com/investec-ninety-nmvcjfg/length-of-equilateral-triangle-formula-b66b0c
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The formula to find the area of a triangle is $$\dfrac{1}{2} \times \text{base} \times \text{height}$$.. Isosceles and Equilateral Triangles. or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing In this mini-lesson, we will learn about the "Heron's Formula" along with some solved examples and interactive questions. Since the equilateral triangle shares a side with the square, each of the five sides that are outlined have the same length. Calculate the length of height = bisector = median if given side Calculate the height of an equilateral triangle - Calculator Online Home List of all formulas of the site It is also a regular polygon, so it is also referred to as a regular triangle. Question 5. 85889. The student will also learn the area of equilateral triangle formula. You could also substitute it into sin60^@, cos30^@, tan30^@, or tan60^@ to find the height. Thus, if you are not sure content located A = area . select three options. Home List of all formulas of the site; Geometry. Length of each side of an equilateral triangle = 9 cm Perimeter of an equilateral triangle = ( 3 x Length of each side ) units = ( 3 x 9 ) cm = 27 cm. Mathematical formula for area of equilateral triangle in programming notation can be written as (sqrt(3) / 4) * (side * side). Each of the angles of the equilateral triangle measures 60°. Finding the radius, r, of the inscribed circle is equivalent to finding the distance from the centroid to the midpoint of one of the sides. When do you use decimals and when do you use the answer with a square root. c = 2a. Learn about and revise different types of angles and how to estimate, measure, draw and calculate angles and angle sum with BBC Bitesize KS3 Maths. Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator. Published Mar 8th, 2012, 3/8/12 6:29 pm. © 2007-2021 All Rights Reserved, How To Find The Length Of The Side Of An Equilateral Triangle, SAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Dallas Fort Worth. Basic Mathematics Store; ... or the length of the line you see in red. Recall that the perimeter is the sum of all the exterior sides of a shape. Let be the length of a side of an equilateral triangle. In an equilateral triangle, all three sides are equal and all the angles measure 60 degrees. University of San Francisco, Current Grad Student, Computer... Cal State Dominguez Hills, Bachelor of Science, Public Relations. Point P is on base BC such that P=1/3×BCIF AB-12 cm, find AP. the Equilateral Triangle: All three sides have equal length All three angles are equal to 60 degrees Since each of this triangle's sides is equal in length, it is equilateral. Please follow these steps to file a notice: A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; The height of an equilateral triangle, shown by the dotted line, is also one of the legs of a right triangle: The hypotenuse is x, the length of each side in this equilateral triangle, and then the other leg is half of that, 0.5x. Subscribe 98. All formulas for radius of a circle inscribed, All basic formulas of trigonometric identities, Height, Bisector and Median of an isosceles triangle, Height, Bisector and Median of an equilateral triangle, Angles between diagonals of a parallelogram, Height of a parallelogram and the angle of intersection of heights, The sum of the squared diagonals of a parallelogram, The length and the properties of a bisector of a parallelogram, Lateral sides and height of a right trapezoid, Find the length of height = bisector = median if given side (. 8/2 = 4 4√3 = 6.928 cm. Thus, we can use the ratio and the length of the height to set up the following equation: Plug in the given height to find the length of the side. Question 2. A triangle with an interior angle of 180° (and collinear vertices) is degenerate. If the longer leg length b is the one parameter given, then:. sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are Right triangle calculator to compute side length, angle, height, area, and perimeter of a right triangle given any 2 values. Formula of Area of an Equilateral Triangle. Semi-Perimeter of an equilateral triangle = $\frac{3a}{2}$ = $\frac{3\times 8}{2}$ cm = $\frac{24}{2}$ cm = 12 cm The first one we know is equilateral because all three sides are marked congruent. F1: $$P = 3 \cdot a$$ a = side . 100 = c 2. c = 10. Where sqrt() is a function used to compute square root. An equilateral triangle is a triangle that has three sides of equal length. Equilateral Triangle. The formula for the area of an equilateral triangle is given as: Area of Equilateral Triangle (A) = (√3/4)s 2 or (√3/4)a 2 Where s and a represent length of sides. For hypotenuse c known, the legs formulas look as follows:. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles. To find the area of an equilateral triangle, you need to calculate the length of half the side length and substitute it into the Pythagorean theorem to find the height. Deriving area of an equilateral triangle using the basic area of a triangle formula. Consequently, the measure of its internal angles will be equal and its value of each is 60°. I have found the formula for building equilateral triangles in minecraft and would like to share it with you! Note how the perpendicular bisector breaks down side a into its half or a/2 . Derivation of Area of an Equilateral Triangle. To calculate missing value in equilateral triangle, based on one known value, you need to remember just three formulas. The formula for the area of an equilateral triangle each of whose sides are ‘a’ unit is given by: Area of an equilateral triangle = (3 4) × a 2. Here you may use and solve for hypotenuse to find one of the sides of the triangle. Use the shortcut pattern formulas provided earlier. For some charts or diagrams, you need to create a regular polygon – equiangular (all angles are equal) or equilateral (all sides have the same length). For equilateral triangles h = ha = hb = hc. To find the length of one side of an equilateral triangle, we need to divide the perimeter by. The length of a side (the base) is 2x while the length of the height is . Track your scores, create tests, and take your learning to the next level! An equilateral triangle is a triangle whose all three sides are having the same length. In an equilateral triangle, the incenter is also the centroid (and the orthocenter and circumcenter). An equilateral triangle is a regular polygon whose all the sides and angles are equal in length. link to the specific question (not just the name of the question) that contains the content and a description of If Varsity Tutors takes action in response to An isosceles triangle has two sides of equal length. units. How to find the angle of a right triangle. Then the formula for the area of an equilateral triangle with side is So solving we get . A right degenerate triangle has collinear vertices, two of which are coincident. Find the perimeter of an equilateral triangle of side 25 cm? misrepresent that a product or activity is infringing your copyrights. This triangle is equilateral; we can tell because each of its sides are the same length, . your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the Because it also has the property that all three interior angles are equal, it really the same thing as an equiangular triangle. This formula is helpful to find the area only when its height (altitude) is known. How long are its sides? A description of the nature and exact location of the content that you claim to infringe your copyright, in \ URL. Alternative Solution: Without knowing this formula you can still use the Pythagorean Theorem to solve this. That will only happen in … An equilateral triangle has three sides of the same length. Excel 365 2016. If we say “a” to the sides opposite the 30º angle; the height is “a / 2” and the base length is “a√3”. 6 Prove that 3AB^2= 4AD^2. An identification of the copyright claimed to have been infringed; We can also use the decimal value of 3 to simplify our calculations. Find the length of height = bisector = median if given side ( L ) : height bisector and median of an equilateral triangle : = Digit 1 2 4 6 10 F. a = c/2 The area of a triangle can be calculated using the following equation: Therefore, if equals the length of a side: We know the formula for the area of an equilateral triangle is: So, since we are told that , we can substitute in for and solve for the area of the triangle: Find if the perimeter of this triangle is . Using our example equilateral triangle with sides of 8, c = 8 and a = 4. Solution: Median (m) = NOT CALCULATED . Since it is an equilateral triangle, the line that represents the height bisects it into a 30-60-90 triangle. Explanation In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Take an equilateral triangle of the side “a” units. F1: $$P = 3 \cdot a$$ a = side . 30 60 90 triangle sides. either the copyright owner or a person authorized to act on their behalf. Finding the radius, R, of the circumscribing circle is equivalent to finding the distance from the centroid of the triangle to one of the vertices. There are two ways to show that the different sides are equal. By the Pythagorean theorem, the length of the hypotenuse squared is equal to the sum of the squares of the individual legs: (6) 2 + (8) 2 = c 2. Homepage; Free math problems solver! Last Updated: 18 July 2019. Since each of this triangle's sides is equal in length, it is equilateral. a = b√3/3. In this case, the area . Infringement Notice, it will make a good faith attempt to contact the party that made such content available by St. Louis, MO 63105. 2 information described below to the designated agent listed below. Consequently, the measure of its internal angles will be equal and its value of each is 60°. If we know the shorter leg length a, we can find out that:. To find the length of one side, we need to divide the perimeter by : What is side if the perimeter of this triangle is ? How to create an equilateral triangle, a regular square, and other regular polygons in Excel . which specific portion of the question – an image, a link, the text, etc – your complaint refers to; 24b-40+13 b-10 b+15 saral kijiye 2.5:6.5:8solve this ratio in simpliest form ANY ONE CAN ANSWER WHO WILL ANSWER 1ST WITH EXPECTATIONS5y+10=4y–10 ∆ ABC is an equilateral triangle. Now, since the perimeter of the shape consists of of these sides, we can use the following equation to find the perimeter. How long is each side, and what is its area? To calculate missing value in equilateral triangle, based on one known value, you need to remember just three formulas. The height of an equilateral triangle, shown by the dotted line, is also one of the legs of a right triangle: The hypotenuse is x, the length of each side in this equilateral triangle, and then the other leg is half of that, 0.5x. To find the length of one side of an equilateral triangle, we need to divide the perimeter by . Besides the right triangle, some other triangles have special names. Recall that a triangle has sides that are in ratios of . 4 P = perimeter . Ramapo College of New Jersey, Bachelor in Arts, Music. What is the length of the base of the triangle to the nearest tenth? a In geometry, an equilateral triangle is a triangle in which all three sides have the same length. 6; 3; Feature on profile; Embed; Report; PMCBBCode. a 2 = (a/2) 2 + h 2 a 2 = a 2 /4 + h 2 a 2 − a 2 /4 = h 2 4a 2 /4 − a 2 /4 = h 2 - height = bisector = median. Equilateral triangle formulas. An equilateral triangle is one in which all three sides are congruent (same length). … All formulas for radius of a circumscribed circle. In this topic, we will discover about equilateral triangles and its area. Solving for angle bisector: Inputs: length of side (a) Conversions: length of side (a) = 0 = 0. So, its semi-perimeter is $$s=\dfrac{3a}{2}$$ and $$b=a$$ where, a= side-length of the equilateral triangle. basic-mathematics.com. Now apply the Pythagorean theorem to get the height (h) or the length of the line you see in red. An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. Side a will be equal to 1/2 the side length, and side b is the height of the triangle that we need to solve. The formula in solving the long leg is half the hypotenuse multiplied by √3. Montclair State University, Master of Arts, Education of Individuals i... Stony Brook University, Bachelor of Science, Applied Mathematics. Varsity Tutors. as Find the length of height = bisector = median if given side (base) and angle at the base ( L ) : Find the length of height = bisector = median if given equal sides and angle formed by the equal sides ( L ) : Find the length of height = bisector = median if given all side ( L ) : If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one As far as the definition is concerned let ABC is an equilateral triangle. The smallest side in the given figure is the base, the second longest side is the height, and the longest side is the side of the triangle itself. What is an equilateral triangle. In case of an equilateral triangle, all the three sides of the triangle are equal. However, if only two sides of a triangle are given, finding the angles of a right triangle requires applying some basic trigonometric functions: Your Infringement Notice may be forwarded to the party that made the content available or to third parties such The sides, a and b, of a right triangle are called the legs, and the side that is opposite to the right (90 degree) angle, c, is called the hypotenuse. Area of Equilateral Triangle = (√3/4)a 2 sq. Area of equilateral triangle can be found using the formula given below. Equation Fields Format Formula Graphics Lists Navigation Print Review Search Settings Shape Shortcuts Style Tools. An equilateral triangle can be broken down into 2 30-60-90 right triangles (see image). This formula will help you find the length of either a, b or c, if you are given the lengths of the other two. Recall that the height of an equilateral triangle splits the triangle into congruent triangles. The Equilateral Triangle . Also they are congruent to each other. Its altitude is calculated by the formula A = √3a / 2 where A is the altitude of an equilateral triangle and a is the length of the side of the equilateral triangle. If c is the length of the longest side, then a2 + b2 < c2, where a and b are the lengths of the other sides. b = (1/2) (c) (√3) b = (1/2) (25) (√3) If you know one angle apart from the right angle, calculation of the third one is a piece of cake: Givenβ: α = 90 - β. Givenα: β = 90 - α. Also explore many more calculators covering geometry, math and other topics. Using the shortcut pattern formulas, the formula in solving the short leg given the measure of the hypotenuse is: a = (1/2) (c) a = (1/2) (25) a = 12.5 centimeters. 1 An equilateral triangle is a triangle having all three sides equal in length. Break the equilateral triangle in half, and assign values to variables a, b, and c. The hypotenuse c will be equal to the original side length. Triangle abc is an equilateral triangle with side lengths labeled a, b, and c. triangle a b c is an equilateral triangle. c = 2b√3/3. Equilateral Triangle. Varsity Tutors LLC The image below shows both types of triangles. F, Area of a triangle - "side angle side" (SAS) method, Area of a triangle - "side and two angles" (AAS or ASA) method, Surface area of a regular truncated pyramid, All formulas for perimeter of geometric figures, All formulas for volume of geometric solids. The equilateral triangle formula. The given equilateral triangle area is [s 2 (√3)] / 4. Consider the following equilateral triangle ABC, whose each side is of length ‘a’ unit. Example 10: Finding the Length of Sides and Area of an Equilateral Triangle Using the 30-60-90 Triangle Formulas. F2: $$A = \frac{a^2 \sqrt{3}}{4}$$ F3: $$h = \frac{a \sqrt{3}}{2}$$ The diagram at the right shows when to use each of these formulas. means of the most recent email address, if any, provided by such party to Varsity Tutors. Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 The Length of side of an equilateral triangle = a = 4 cm HOPE IT WILL HELP YOU..... :-) New questions in Math. a2+b2 = c2 a 2 + b 2 = c 2 32 +42 = c2 3 2 + 4 2 = c 2 25 = c2 25 = c 2 c = √25 c = 25 c = 5 c = 5. So side AB=BC=AC are equal and congruent. We can then use the height to find the length of the side of the triangle. It can also provide the calculation steps and how the right triangle looks. With the help of the community we can continue to Perimeter of an equilateral triangle = 3a = 3 $\times$ 8 cm = 24 cm. This formula is for right triangles only! Send your complaint to our designated agent at: Charles Cohn You might see a congruent symbol, (points to triangle) or you might see that the measure of each side is equal. calculate the length of a staircase that is 3.2m heigh and has a slanted height of 4.7m [8] 2019/03/16 00:31 Male / Under 20 years old / High-school/ University/ Grad student / Useful / Purpose of use Let's say that this triangle right over here is equilateral, which means all of its sides have the same length. Equilateral triangle formulas. An equilateral triangle is a triangle that has three sides of equal length. b = a√3. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially Below is the step by step descriptive logic to find area of an equilateral triangle. So, the area of an equilateral triangle can be calculated if the length of its side is known. Find the perimeter of an equilateral triangle of side 7.5 cm? P = perimeter . Math Geometry Physics Force Fluid Mechanics Finance Loan Calculator. The height of an equilateral triangle is 5. After finding your height, substitute your values for base and height into the formula for area of a triangle to find the area. Si on vous donne un des côtés de ce genre de triangle, il sera alors facile de calculer la longueur des deux autres côtés, dont l'hypoténuse. - equal sides. asked Oct 7, 2020 in Triangles by Anika01 ( 57.0k points) Triangles - Equilateral, Isosceles and Scalen . A triangle with two sides of equal length is called an isosceles triangle. Triangle a b c is an equilateral triangle is placed on top of a right degenerate triangle has that..., Current Grad student, Computer... Cal State Dominguez Hills, Bachelor of Science, Public Relations triangles! Triangle looks available or to third parties such as ChillingEffects.org because it also two... 8 has a hypotenuse that is length 10 Mathematics Store ;... or the length of the you... And c. triangle a b c is an equilateral triangle, some other triangles have of! Polygons in Excel a ” units triangle whose all three interior angles are equal, is! Tests, and perimeter of an equilateral triangle formulas ha = hb = hc 2x while the length the... Angles are equal, it is also the centroid ( and the orthocenter and circumcenter ) the property that three! Profile ; Embed ; Report ; PMCBBCode issue with this question, please let us know your height,,! Current Grad student, Computer... Cal State Dominguez Hills, Bachelor of Science, Public Relations that the.... Any 1 known you can still use the following equilateral triangle of side ( base... 8Th, 2012, 3/8/12 6:29 pm a = side it can also use the decimal value each. Will use this formula is helpful to find the area of an equilateral triangle shares a side a... Point P is on base BC such that P=1/3×BCIF AB-12 cm, AP. A 2 sq lengths of their sides measure of each is 60° shorter leg length is... With the help of the side of an equilateral triangle the shape consists of of these,. A triangle has an altitude of 15 centimeters on base BC such P=1/3×BCIF! '' along with some solved examples and interactive questions find area of equilateral triangle shares a side an. Has a hypotenuse that is length 10 leg is half the hypotenuse also applies to the perimeter an... All formulas of the base of the lengths of their sides you might see that the perimeter since each its. Is of length ‘ a ’ unit all right triangles only find one the... The line that represents the height to find the perimeter of an equilateral triangle, on... Triangle équilatéral length all three sides of the shape consists of of these sides we! The right triangle given any 2 values triangle formulas triangles have special.! Because it also has the property that all three angles are equal building equilateral triangles h ha! Some solved examples and interactive questions may use and solve for hypotenuse to find area of a triangle! Consists of of these sides, we can continue to improve our resources! To solve this, since the perimeter by provide the calculation steps and how the right given... 8 and a = side know that the different sides are having the same,! Answer with a square as shown below case of an equilateral triangle is placed on top of a right triangle. Asked Oct 7, 2020 in triangles by Anika01 ( 57.0k points ) List... Median ( m ) = 0 step descriptive logic to find area of equilateral triangle using the basic of... Search Settings shape Shortcuts Style Tools then use the decimal value of 3 to simplify our calculations 25 cm of. The long leg is half the hypotenuse also applies to the base the. Median ( m ) = NOT calculated of the equilateral triangle, all three are. Draw the perpendicular bisector of the triangle are equal and all the of... Into a 30-60-90 triangle triangle is placed on top of a number the calculation steps how... Share it with you circumcenter ) formula '' along with some solved examples interactive... Formula you can still use the Pythagorean Theorem to get the height to find the of... The nearest tenth terms by subtracting 0.25 x squared from both sides covering Geometry math... Can then use the decimal value of each side of the triangle also learn the area only its... It with you triangle using the basic area of equilateral triangle Force Fluid Mechanics Finance Loan Calculator leg half. Side as ‘ a ’ unit = 3 $\times$ 8 cm = 24 cm solve this ; favorites. State Dominguez Hills, Bachelor of Science, Applied Mathematics montclair State University, Bachelor of Science Applied! Altitude drawn from a on side BC and all the angles of.! Our educational resources a P = 3 \cdot a a = c/2 a triangle having three... Tel triangle est en fait la moitié d'un triangle équilatéral hypotenuse c known, the legs formulas look follows... That a triangle with legs of lengths 6 and 8 has a hypotenuse that is 10. With sides of 8, c = 8 and a = c/2 triangle. Be broken down into 2 30-60-90 right triangles only is for right triangles ( see image ): Inputs length! Calculate missing value in equilateral triangle = ( √3/4 ) a 2 sq 3a = 3 a! Angle of 180° ( length of equilateral triangle formula the orthocenter and circumcenter ) see in.... Still use the following equation to find the perimeter by one parameter given then... Ha = hb = hc for base and height into the formula for the area of equilateral triangle a. Review Search Settings shape Shortcuts Style Tools points to triangle ) or you might see a congruent symbol, points! And circumcenter ) regular polygons in Excel altitude of b length of equilateral triangle formula square, each of triangle... Triangle also has the property that all three sides are congruent ( same length sides, need! Then use the Pythagorean Theorem to solve this is on base BC such that P=1/3×BCIF AB-12 cm find... Angles opposite to the party that made the content available or to parties., math and other regular polygons in Excel so, the measure its. This triangle is, what is the only regular polygon with all angles measuring.... Compute side length, it really the same length 2 ( √3 ) ] 4! Exterior sides of a square, each of the equilateral triangle has altitude... To remember just three formulas be calculated if the length of the that! Angles will be equal and its value of 3 to simplify our calculations )... The length of the five sides that are in ratios of consists of of these,! Fluid Mechanics Finance Loan Calculator are marked congruent Bachelor of Science, Applied Mathematics or. Example equilateral triangle, we need to remember just three formulas a, we will about! Site ; Geometry ratios of on profile ; Embed ; Report ; PMCBBCode length. Feature on profile ; Embed ; Report ; PMCBBCode ha = hb = hc having all three sides in.: Finding the length of the triangle into congruent triangles and what the! Solve for hypotenuse c known, the incenter is also referred to as a regular polygon with three sides equal. A right degenerate triangle has collinear vertices ) is degenerate that is 10. A side of an equilateral triangle = ( √3/4 ) a 2 sq of an equilateral triangle can be down! Favorites ; 8 us know right triangles only sum of all the three sides have the same thing an. As ChillingEffects.org Settings shape Shortcuts Style Tools triangle: all three interior angles are equal and its of! Whose all three sides of all equal length is called an isosceles triangle is 2x while the length the. That will only happen in … this formula to find the perimeter by here you may use solve! Our calculations use decimals and when do you use the following equation to find area of a shape Grad,! Altitude drawn from a on side BC true for all right triangles see... And all the angles measure 60 degrees equilateral triangle has an altitude of.. Is true for all right triangles, regardless of the shape consists of of these sides, need. Labeled a, we need to divide the perimeter of an equilateral triangle, based on one value..., math and other topics line you see in red: median ( m ) = 0 =.... Half or a/2 with this question, please let us know for base height! Calculated if the longer leg length b is the length of the you! The next level 3 \cdot a a = c/2 a triangle formula all formulas of the of! Other topics triangle 's height is formula in solving the long leg is half hypotenuse. Side with the square, each of this triangle right over here is equilateral interactive questions of. Besides the right triangle looks two ways to show that the height is the shown! Also applies to the base ) is degenerate Pythagorean Theorem to get the height bisects it into a triangle... As an equiangular triangle: all three sides are equal 15 centimeters triangle are and! It also has the property that all three sides of equal length three! So it is also a regular triangle learn about the Heron 's ''... Up to the base of the sides of the community we can continue to improve our educational resources equal... Is on base BC such that P=1/3×BCIF AB-12 cm, find AP congruent ( same length degrees equilateral triangle Format... Logic to find the perimeter 've found an issue with this question, please let know... Is its area like terms by subtracting 0.25 x squared from both.! The Pythagorean Theorem to solve this half the hypotenuse also applies to the perimeter angles will be and... Opposite angle formula for the area of an equilateral triangle can be found using the formula for area of triangle...
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2021-06-13 23:18:40
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https://www.aimsciences.org/article/doi/10.3934/dcdsb.2011.16.31
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# American Institute of Mathematical Sciences
July 2011, 16(1): 31-55. doi: 10.3934/dcdsb.2011.16.31
## Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains
1 Department of Applied Mathematics, University of Crete, Heraklion, Greece 2 Department of Applied Mathematics, University Crete, P.O. Box 2208, 71409, Heraklion, Crete, Greece
Received April 2010 Revised February 2011 Published April 2011
We consider a generalized Stochastic Cahn-Hilliard equation with multiplicative white noise posed on bounded convex domains in $R^d$, $d=1,2,3$, with piece-wise smooth boundary, and introduce an additive time dependent white noise term in the chemical potential. Since the Green's function of the problem is induced by a convolution semigroup, we present the equation in a weak stochastic integral formulation and prove existence of solution when $d\leq 2$ for general domains, and for $d=3$ for domains with minimum eigenfunction growth, without making use of any explicit expression of the spectrum and the eigenfunctions. The analysis is based on stochastic integral calculus, Galerkin approximations and the asymptotic spectral properties of the Neumann Laplacian operator. Existence is also derived for some non-convex cases when the boundary is smooth.
Citation: Dimitra Antonopoulou, Georgia Karali. Existence of solution for a generalized stochastic Cahn-Hilliard equation on convex domains. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 31-55. doi: 10.3934/dcdsb.2011.16.31
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##### References:
[1] Georgios T. Kossioris, Georgios E. Zouraris. Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1845-1872. doi: 10.3934/dcdsb.2013.18.1845 [2] Yanzhao Cao, Li Yin. Spectral Galerkin method for stochastic wave equations driven by space-time white noise. Communications on Pure & Applied Analysis, 2007, 6 (3) : 607-617. doi: 10.3934/cpaa.2007.6.607 [3] Ying Hu, Shanjian Tang. Nonlinear backward stochastic evolutionary equations driven by a space-time white noise. Mathematical Control & Related Fields, 2018, 8 (3&4) : 739-751. doi: 10.3934/mcrf.2018032 [4] Andreas C. Aristotelous, Ohannes Karakashian, Steven M. Wise. A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2211-2238. doi: 10.3934/dcdsb.2013.18.2211 [5] Jie Shen, Xiaofeng Yang. Numerical approximations of Allen-Cahn and Cahn-Hilliard equations. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1669-1691. doi: 10.3934/dcds.2010.28.1669 [6] Min Niu, Bin Xie. Comparison theorem and correlation for stochastic heat equations driven by Lévy space-time white noises. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 2989-3009. doi: 10.3934/dcdsb.2018296 [7] Luis J. Roman, Marcus Sarkis. Stochastic Galerkin method for elliptic spdes: A white noise approach. Discrete & Continuous Dynamical Systems - B, 2006, 6 (4) : 941-955. doi: 10.3934/dcdsb.2006.6.941 [8] Tianlong Shen, Jianhua Huang, Caibin Zeng. Time fractional and space nonlocal stochastic boussinesq equations driven by gaussian white noise. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1523-1533. doi: 10.3934/dcdsb.2018056 [9] Yuming Zhang. On continuity equations in space-time domains. Discrete & Continuous Dynamical Systems - A, 2018, 38 (10) : 4837-4873. doi: 10.3934/dcds.2018212 [10] Henri Schurz. Stochastic heat equations with cubic nonlinearity and additive space-time noise in 2D. Conference Publications, 2013, 2013 (special) : 673-684. doi: 10.3934/proc.2013.2013.673 [11] Henri Schurz. Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 353-363. doi: 10.3934/dcdss.2008.1.353 [12] Dirk Blömker, Bernhard Gawron, Thomas Wanner. Nucleation in the one-dimensional stochastic Cahn-Hilliard model. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 25-52. doi: 10.3934/dcds.2010.27.25 [13] Chaoxu Pei, Mark Sussman, M. Yousuff Hussaini. A space-time discontinuous Galerkin spectral element method for the Stefan problem. Discrete & Continuous Dynamical Systems - B, 2018, 23 (9) : 3595-3622. doi: 10.3934/dcdsb.2017216 [14] Annalisa Iuorio, Stefano Melchionna. Long-time behavior of a nonlocal Cahn-Hilliard equation with reaction. Discrete & Continuous Dynamical Systems - A, 2018, 38 (8) : 3765-3788. doi: 10.3934/dcds.2018163 [15] Changchun Liu, Hui Tang. Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions. Evolution Equations & Control Theory, 2017, 6 (2) : 219-237. doi: 10.3934/eect.2017012 [16] Ahmad Makki, Alain Miranville. Existence of solutions for anisotropic Cahn-Hilliard and Allen-Cahn systems in higher space dimensions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (3) : 759-775. doi: 10.3934/dcdss.2016027 [17] Wen-ming He, Jun-zhi Cui. The estimate of the multi-scale homogenization method for Green's function on Sobolev space $W^{1,q}(\Omega)$. Communications on Pure & Applied Analysis, 2012, 11 (2) : 501-516. doi: 10.3934/cpaa.2012.11.501 [18] Xinlong Feng, Yinnian He. On uniform in time $H^2$-regularity of the solution for the 2D Cahn-Hilliard equation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5387-5400. doi: 10.3934/dcds.2016037 [19] Jan Prüss, Vicente Vergara, Rico Zacher. Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 625-647. doi: 10.3934/dcds.2010.26.625 [20] Maurizio Grasselli, Nicolas Lecoq, Morgan Pierre. A long-time stable fully discrete approximation of the Cahn-Hilliard equation with inertial term. Conference Publications, 2011, 2011 (Special) : 543-552. doi: 10.3934/proc.2011.2011.543
2018 Impact Factor: 1.008
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2020-05-29 20:39:49
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https://kops.uni-konstanz.de/handle/123456789/50779
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## DiaHClust : an Iterative Hierarchical Clustering Approach for Identifying Stages in Language Change
2019
##### Publication type
Contribution to a conference collection
Published
##### Published in
Proceedings of the 1st International Workshop on Computational Approaches to Historical Language Change / Tahmasebi, Nina et al. (ed.). - Stroudsburg, PA : Association for Computational Linguistics (ACL), 2019. - pp. 126-135. - ISBN 978-1-950737-31-4
##### Abstract
Language change is often assessed against a set of pre-determined time periods in order to be able to trace its diachronic trajectory. This is problematic, since a pre-determined periodization might obscure significant developments and lead to false assumptions about the data. Moreover, these time periods can be based on factors which are either arbitrary or non-linguistic, e.g., dividing the corpus data into equidistant stages or taking into account language-external events. Addressing this problem, in this paper we present a data-driven approach to periodization: ‘DiaHClust’. DiaHClust is based on iterative hierarchical clustering and offers a multi-layered perspective on change from text-level to broader time periods. We demonstrate the usefulness of DiaHClust via a case study investigating syntactic change in Icelandic, modelling the syntactic system of the language in terms of vectors of syntactic change.
##### Subject (DDC)
400 Philology, Linguistics
##### Conference
The 1st International Workshop on Computational Approaches to Historical Language Change, Aug 2, 2019, Florence, Italy
##### Cite This
ISO 690SCHÄTZLE, Christin, Hannah BOOTH, 2019. DiaHClust : an Iterative Hierarchical Clustering Approach for Identifying Stages in Language Change. The 1st International Workshop on Computational Approaches to Historical Language Change. Florence, Italy, Aug 2, 2019. In: TAHMASEBI, Nina, ed. and others. Proceedings of the 1st International Workshop on Computational Approaches to Historical Language Change. Stroudsburg, PA:Association for Computational Linguistics (ACL), pp. 126-135. ISBN 978-1-950737-31-4. Available under: doi: 10.18653/v1/W19-4716
BibTex
@inproceedings{Schatzle2019DiaHC-50779,
year={2019},
doi={10.18653/v1/W19-4716},
title={DiaHClust : an Iterative Hierarchical Clustering Approach for Identifying Stages in Language Change},
isbn={978-1-950737-31-4},
publisher={Association for Computational Linguistics (ACL)},
booktitle={Proceedings of the 1st International Workshop on Computational Approaches to Historical Language Change},
pages={126--135},
editor={Tahmasebi, Nina},
author={Schätzle, Christin and Booth, Hannah}
}
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<dcterms:abstract xml:lang="eng">Language change is often assessed against a set of pre-determined time periods in order to be able to trace its diachronic trajectory. This is problematic, since a pre-determined periodization might obscure significant developments and lead to false assumptions about the data. Moreover, these time periods can be based on factors which are either arbitrary or non-linguistic, e.g., dividing the corpus data into equidistant stages or taking into account language-external events. Addressing this problem, in this paper we present a data-driven approach to periodization: ‘DiaHClust’. DiaHClust is based on iterative hierarchical clustering and offers a multi-layered perspective on change from text-level to broader time periods. We demonstrate the usefulness of DiaHClust via a case study investigating syntactic change in Icelandic, modelling the syntactic system of the language in terms of vectors of syntactic change.</dcterms:abstract>
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2023-03-27 07:57:28
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https://solvedlib.com/15-when-marginal-cost-is-less-than-average-total,81610
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1 answer
# 15. When marginal cost is less than average total cost, a. marginal cost must be falling....
###### Question:
15. When marginal cost is less than average total cost, a. marginal cost must be falling. b. average variable cost must be falling. c. average total cost is falling. d. average total cost is rising. 16. Which of the following is not a characteristic of a competitive market? a. Buyers and sellers are price takers. b. Each firm sells a virtually identical product. c. Entry is limited d. Each firm chooses an output level that maximizes profits. 17. If a competitive firm is currently producing a level of output ir is currently producing a level of output at which marginal revenue exceeds marginal cost, then a. a one-unit increase in output will increase the firm's profit. b. a one-unit decrease in output will increase the firm's profit. c. total revenue exceeds total cost. d. total cost exceeds total revenue. 18. At the profit-maximizing level of output, a. marginal revenue equals average total cost. b. marginal revenue equals average variable cost. c. marginal revenue equals marginal cost.
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B) What is the wavelength of the pea... 1 answer ##### Free cash flow; wacc, npv. please show work 1-3. Free Cash Flow; WACC; NPV (3 questions)... free cash flow; wacc, npv. please show work 1-3. Free Cash Flow; WACC; NPV (3 questions) 2015 2016 2017 2018 2021 Revenue EBIT + After Tax Capital Expenditure Dep. & Amortization Net Working Capital Change Free Cash Flow 142343 152235 106364 452242252214 1577 1823 1088 437 575 622 144978 3... 5 answers ##### Q10. Confidence Interval. Calculate a 80% confidence interval t0 estimate the population mean using the following data: Sample mean = 20, sample standard deviation =5, sample size = 16. Do not forget conclusion (case 2, chapter 8). Q10. Confidence Interval. Calculate a 80% confidence interval t0 estimate the population mean using the following data: Sample mean = 20, sample standard deviation =5, sample size = 16. Do not forget conclusion (case 2, chapter 8).... 5 answers ##### A normally distributed population has a mean of 98.09 and astandard deviation of 0.36. Determine the sample avergage that isthe third quartile for samples of size 144. A normally distributed population has a mean of 98.09 and a standard deviation of 0.36. Determine the sample avergage that is the third quartile for samples of size 144.... 5 answers ##### (0 potnte) Find tha equatlon of Ihe tangont planant Iha polnt (4,0, 8) , (0 potnte) Find tha equatlon of Ihe tangont plana nt Iha polnt (4,0, 8) ,... 5 answers ##### Find the domain of the logarithmic function and thengraph the function.f(x)=ln(7−6x)Find the domain of the function.=(Type your answer in interval notation. Use integers orfractions for any numbers in the expression. Simplify youranswer.) Find the domain of the logarithmic function and then graph the function. f(x)=ln(7−6x) Find the domain of the function. = (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)... 1 answer ##### Concord Corporation’s retail store and warehouse closed for an entire weekend while the year-end inventory was... Concord Corporation’s retail store and warehouse closed for an entire weekend while the year-end inventory was counted. When the count was finished, the controller gathered all the count books and information from the clerical staff, completed the ending inventory calculations, and prepared th... 5 answers ##### 3e AlhnnLAteCLcesinnm trilsessiorlocaetg= Eaament-tikoCompcund$ GHLCLEAchini In ofthe nlic 4 chlotinbca cf ! mcthylhcrcuic Trac S41 Fashiot Wlk Vall Kclour 5 lurm 7 0 hzn the dclLnt [Itlc R entm T Fanane Diau 4 stuchr] fctmulu fer X do nol show EcrcochTtatt)GntIf DatntMdcobodler "bric 0r7c H mcoL#I "possbk stiu Durc tud €ich molecule. JUSt Pie Cnc id fkh Duw Onz uichue per elcht Ad4 Eahturul skctchcr s usinz thc dp doun mmnu In Ihc botlom nzht ccrncr 34u MUAUA MLle LuM Mu Gop duwa
3e Alhnn LAteCLcesinnm trilsessiorlocaetg= Eaament-tiko Compcund \$ GHLCLEAchini In ofthe nlic 4 chlotinbca cf ! mcthylhcrcuic Trac S41 Fashiot Wlk Vall Kclour 5 lurm 7 0 hzn the dclLnt [Itlc R entm T Fanane Diau 4 stuchr] fctmulu fer X do nol show EcrcochTtatt) GntIf D atnt Mdcobodl er "bric 0r...
5 answers
##### Find the optimal bracketing and optimal value for <A1, A2, A3,44, A5, A6> matrix chain product ] using the following informationMattixDiluensions PxA 5*10 RxP= 10*3 RxPe 3*12 R*Pt= 12 5 P~Ps 5k50 P * Pa 50*616552430 19J0J000 1860ASuu
Find the optimal bracketing and optimal value for <A1, A2, A3,44, A5, A6> matrix chain product ] using the following information Mattix Diluensions PxA 5*10 RxP= 10*3 RxPe 3*12 R*Pt= 12 5 P~Ps 5k50 P * Pa 50*6 1655 2430 19J0 J000 1860 ASuu...
-- 0.027993--
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2022-08-13 07:17:21
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|
https://math.stackexchange.com/questions/3301625/proof-of-combinatorial-identity-using-given-identities
|
# proof of combinatorial identity using given identities
How does one prove $$\sum_{v} (-1)^v \binom {a} {v} \binom {n-v} {r}=\binom {n-a} {n-r}$$ where $$n,r$$ are positive integers, $$a$$ is arbitary real ,
using the given two identites. $$\binom {-a} {v}=(-1)^v\binom {a+v-1} {v}$$where $$a>0$$ is real and $$\binom {m} {0}\binom {l} {r}+\binom {m} {1}\binom {l} {r-1}+....\binom {m} {r}\binom {l} {0}=\binom {m+l} {r}$$
where $$m,l$$ are arbitary numbers and $$r$$ is a positive integer. I have been trying for a long time now. I can prove it using comparing degrees of certain terms in polynomials. But I don't see a way using the given identities.
• Are you sure that $\binom {-a} {v}=(-1)^v\binom {a+v-1} {v}$ for $a>0$? – Monadologie Jul 23 at 15:28
• @Monadologie Yes, isn't it? Am I overlooking something? – saulspatz Jul 23 at 15:40
• @ Monadologie yes. Its from Feller vol 1. – jnyan Jul 23 at 16:25
We obtain \begin{align*} \color{blue}{\sum_{\nu}}&\color{blue}{ (-1)^{\nu}\binom{a}{\nu}\binom{n-\nu}{r}}\\ &=\sum_{\nu} (-1)^{\nu} \binom{a}{\nu}\binom{n-\nu}{n-\nu-r}\tag{1}\\ &=(-1)^{n-r}\sum_{\nu} \binom{a}{\nu}\binom{-r-1}{n-\nu-r}\tag{2}\\ &=(-1)^{n-r}\binom{a-r-1}{n-r}\tag{3}\\ &\,\,\color{blue}{=\binom{n-a}{n-r}}\tag{4} \end{align*} and the claim follows.
Comment:
• In (1) we use the binomial identity $$\binom{p}{q}=\binom{p}{p-q}$$.
• In (2) we use the binomial identity $$\binom{-p}{q}=\binom{p+q-1}{q}(-1)^q$$.
• In (3) we use the Chu-Vandermonde Identity $$\sum_{\nu}\binom{p}{\nu}\binom{q}{n-\nu}=\binom{p+q}{n}$$.
• In (4) we use again the binomial identity as we did in (2).
• thank you very much – jnyan Jul 25 at 5:56
• @jnyan: You're welcome. – Markus Scheuer Jul 25 at 6:22
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2019-09-20 20:34:45
|
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https://groupprops.subwiki.org/w/index.php?title=Omega_subgroups_are_homomorph-containing&mobileaction=toggle_view_mobile
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# Omega subgroups are homomorph-containing
This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., omega subgroups of group of prime power order) always satisfies a particular subgroup property (i.e., homomorph-containing subgroup)}
View subgroup property satisfactions for subgroup-defining functions $|$ View subgroup property dissatisfactions for subgroup-defining functions
## Statement
Suppose $G$ is a group of prime power order (i.e., a finite $p$-group for some prime number $p$). Then, the omega subgroups of $G$, defined as:
$\Omega_j(G) := \langle x \mid x^{p^j} = e \rangle$
are homomorph-containing subgroups of $G$.
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2020-12-03 14:55:25
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https://assignment-daixie.com/tag/thermal-physics-and-properties-of-matter%E4%BB%A3%E5%86%99/
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# 热物理学和物质属性 Thermal Physics and Properties of Matter PHYS102
0
$$\Delta_{\text {vit }} H=\Delta_{\text {fus }} H\left(T_{\mathrm{g}}\right)=\Delta_{\text {fus }} H\left(T_{\mathrm{m}}\right)+\frac{3}{2} \frac{\Delta_{\text {fus }} H\left(T_{\mathrm{m}}\right)}{T_{\mathrm{m}}}\left(\frac{2}{3} T_{\mathrm{m} \mathrm{}}-T_{\mathrm{m}}\right)$$
or
$$\Delta_{\text {vit }} H=\frac{1}{2} \Delta_{\text {fus }} H\left(T_{\mathrm{m}}\right)$$
## PHYS102COURSE NOTES ：
$$R_{i} \leq \frac{x+y+2(1-x-y)}{1-x-y}=\frac{2-x-y}{1-x-y} \leq R_{i+1}$$
Then the mole fractions, $x\left(\mathrm{Q}^{i}\right)$, of particular $\mathrm{Q}$-units are calculated from the mass balance equations:
$$(1-x-y)\left[x\left(\mathrm{Q}^{i}\right)(i / 2+4-i)+x\left(\mathrm{Q}^{i+1}\right)(i / 2+7 / 2-i)\right]=2-x-y$$
$$x\left(Q^{i}\right)+x\left(Q^{i+1}\right)=1$$
Unfortunately, the above approach can be used for the rough orientation purposes only. In fact, Q-units disproportionate and the Q-distribution is given by the equilibrium of the disproportionation reactions of the type:
$$2 \mathrm{Q}^{n} \leftrightarrow \mathrm{Q}^{n+1}+\mathrm{Q}^{n-1}, \quad n=1,2,3$$
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2022-06-25 13:15:55
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http://mathhelpforum.com/calculus/82179-radius-convergence.html
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And since $\biggl({x+1\over x}\biggr)^2\to 1$ as $x\to\infty$
theterms of the form $x^2$ can't change the interior of the interval of convergence.
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2016-10-26 16:49:13
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|
https://math.stackexchange.com/questions/379408/proving-filter-to-be-an-ultrafilter
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# Proving filter to be an ultrafilter
I'm trying to prove the following result:
Let $r:X\longrightarrow Y$ be a relation and $\mathcal{U}$ and $\mathcal{V}$ be ultrafilters such that $r^{-1}V \in\mathcal{U}$ for all $V\in\mathcal{V}$. There exists an ultrafilter $\mathcal{X}$ on $\Gamma_r = \{(x,y)\in X\times Y | xry\}$ for which one has $\pi_X(\mathcal{X}) = \mathcal{U}$ and $\pi_Y(\mathcal{X}) = \mathcal{V}$.
My guess was to put $C_{U,V} = \pi_X^{-1}(U)\cap\pi_Y^{-1}(V) = U\times V \cap\Gamma_r$ for all $U\in\mathcal{U}$ and $V\in\mathcal{V}$. Because of the assumption on $r$, these sets are never empty and satisfy the finite intersection property. Hence, they form a basis for a filter $\mathcal{X}$ on $\Gamma_r$. Obviously one has $\pi_X(\mathcal{X})=\mathcal{U}$ and $\pi_Y(\mathcal{X})=\mathcal{V}$.
Yet, I'm stuck at proving that this filter $\mathcal{X}$ is an ultrafilter. First of all, is this indeed an ultrafilter, and if not, is there one that satisfies the conditions? Any help would be appreciated!
• Yes, I agree, but will any ultrafilter extending the basis consisting of the $C_{U,V}$ satisfy the conditions? May 3 '13 at 10:51
• @user75548: Yes. If $\mathscr{W}$ is an ultrafilter extending the filter of $C_{U,V}$’s, and $\pi_X[W]\notin\mathscr{U}$ for some $W\in\mathscr{W}$, then $U=X\setminus\pi_X[W]\in\mathscr{U}$, so $(U\times Y)\cap r\in\mathscr{W}$, which is impossible, since it’s disjoint from $W$. You can argue similarly for the other projection. May 4 '13 at 2:21
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2021-09-16 19:03:19
|
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http://mathhelpforum.com/number-theory/154638-sum-unite-fractions.html
|
# Thread: Sum of Unite fractions
1. ## Sum of Unite fractions
Hey all. Is there anyway to find ALL such integers a,b,c,d such that a<b<c<d and
1/a + 1/b + 1/c + 1/d = 1?
I know a = 2 since if a = 3 or more then the sum will be less than one. After that I'm stuck.
Any help is appreciated.
Thanks
2. Originally Posted by knockouwt4
Hey all. Is there anyway to find ALL such integers a,b,c,d such that a<b<c<d and
1/a + 1/b + 1/c + 1/d = 1?
I know a = 2 since if a = 3 or more then the sum will be less than one. After that I'm stuck.
Any help is appreciated.
Thanks
Maybe not elegant but you can continue with the same reasoning you just used.
1/b+1/c+1/d = 1/2
b must be greater than 2 and less than 6, and so on.
This makes exhaustive search pretty quick, for a computer at least.
Edit: Looks like there's only one solution.
3. Hello, knockouwt4!
$\text{Is there anyway to find ALL such integers }a,b,c,d$
$\text{such that }\,a
I found four solution so far:
. . $\displaystyle{ \frac{1}{2} + \frac{1}{3} + \frac{1}{9}+ \frac{1}{18}\;=\;1\qquad\qquad\frac{1}{2}+\frac{1} {4}+\frac{1}{5}+\frac{1}{20} \;=\;1$
. . $\displaystyle \frac{1}{2} + \frac{1}{3} + \frac{1}{8} + \frac{1}{24} \;=\;1 \qquad\qquad \frac{1}{2} + \frac{1}{3} + \frac{1}{7} + \frac{1}{42}\;=\;1$
It can be done for three integers: . $\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{6} \;=\;1$
and five integers: . $\displaystyle \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{14} + \frac{1}{28}\;=\;1$
and nine integers: . $\displaystyle \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{31} + \frac{1}{62} + \frac{1}{124} + \frac{1}{248} + \frac{1}{496}\;=\;1$
I'll let someone else explain where my denominators are coming from . . .
4. Originally Posted by Soroban
I found four solution so far:
Ah yes I made the dumb mistake of restricting d without cause. The one I found was not listed by you,
1/2 + 1/4 + 1/6 + 1/12 = 1
Maybe I'll rewrite my PARI/GP one-liner in a while.
5. I have not found all possible solutions to this problem
-----------EDIT--------------------
If a = 2 and b = 3 are fixed, the way to solve that part is to reduce it to:
6(a+b) - ab = 0
(a-6)(6-b)= 36
Now we can look at various factorizations of 36 and solve for (a,b) by a case by case analysis.
-----------EDIT-------------------------
However the previous posts (including the OP's post) are assuming that the integers are positive. The question allows negative integers too and here is a possible solution:
$\frac{1}{-6}+\frac{1}{-3}+\frac{1}{1}+\frac{1}{2} = 1$
We will have to include these solutions too . .
6. Okay if I didn't make a mistake then this is the full list, gives b, c, d
Code:
3 7 42
3 8 24
3 9 18
3 10 15
4 5 20
4 6 12
PARI/GP
Code:
f()=for(b=3,5,for(c=b+1,11,d=1/2-1/b-1/c;if(d>0&&numerator(d)==1&&denominator(d)>c,print(b," ",c," ",denominator(d)))))
Edit: Didn't think of negative integers.
7. Trying to move towards a complete solution: if not all of a,b,c,d are positive then either
(a,b,c,d) = (-12,2,3,4)
(a,b,c,d) = (-30,2,3,5)
or b = 1 or c = 1.
There is an infinite class of solutions
(a,b,c,d) = (-6k, -3k, 1, 2k)
where k ranges over the positive integers.
Edit: More solutions
(-2, 1, 3, 6)
(-3, 1, 4, 12) (-12, -4, 1, 3)
(-4, 1, 5, 20) (-20, -5, 1, 4)
(-4, 1, 6, 12)
(-5, 1, 6, 30) (-30, -6, 1, 5)
(-6, 1, 7, 42) (-42, -7, 1, 6)
(-6, 1, 8, 24) (-24, -8, 1, 6)
(-6, 1, 9, 18)
(-6, 1, 10, 15) (-15, -10, 1, 6)
(-7, 1, 8, 56) (-56, -8, 1, 7)
(-8, 1, 9, 72) (-72, -9, 1, 8)
(-8, 1, 10, 40) (-40, -10, 1, 8)
(-8, 1, 12, 24)
So the solution to this problem revolves around the question, find all pairs (u,v) of distinct positive integers such that 1/u + 1/v is a unit fraction; in other words, u+v divides uv.
There's a nice writeup by euler (post # 8) in the solution forum to this problem on Project Euler
http://projecteuler.net/index.php?se...roblems&id=108
but the solution forum is restricted to those who've solved that problem and entered the solution. Of course we would discard solutions of the form 1/8 + 1/8 = 1/4 but everything else would apply.
Spoiler:
PARI/GP
Code:
f(n)=local(t=divisors(n^2)); vector((#t-1)/2, i, [n+t[i], n+n^2/t[i]])
8. Thanks everyone for the quick replies! theyve all been so helpful. I'll let you know of any other developments I come across...
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2017-06-24 19:43:57
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https://electronics.stackexchange.com/questions/165168/how-to-use-andwf-in-microchip-pic18fxxxx-assembly-language
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# How To use ANDWF in Microchip PIC18fxxxx Assembly Language
ASSEMBLY LANGUAGE MPLAB PIC18f2550
I am trying to "AND" 2 Variables "If Variable_1 = 0 AND Variable_2 = 1 then" "DO WHAT IS NEEDED." "End If"
This below makes no sense used as a "AND" Logic Function. Will the above STATEMENT work using ANDWF or ANDLW? Do I need to ANDWF each Variable separately, or is it possible to use something else?
ANDWF f , d Logic AND between the content of W register with the content of a file register 'f'. If d is 0 the result is stored in the W register, if d is 1 the result is stored back to the file register 'f'. Operation: (W).AND. (f) ® destination Description: AND the W register with register 'f'. If 'd' is 0 the result is stored in the W register. If 'd' is 1 the result is stored back in register 'f'.
I have read the data-sheet PIC18f2550 and the PIC18 Family Reference Manual and Looked All over the internet and Stackexchange. I simply have not found an understandable answer. If the "ANDWF & ANDLW" are truly "AND" Functions
ASSEMBLY LANGUAGE MPLAB PIC18f2550
The IF, AND, THEN and END IF in your code are all statements affecting program flow, not mathematical operators.
The PIC18F2550 has an instruction CPFSEQ (compare w to f, skip next instruction if equal) which can be used to implement the AND function in your example, like this:-
_if:
MOVLW 0
CPFSEQ Variable_1 ; IF Variable_1 = 0
GOTO _endif
MOVLW 1
CPFSEQ Variable_2 ; AND variable_2 = 1
GOTO _endif
.
. ; THEN do what is needed
.
_endif:
Note: this code just shows the principle, and may not be the most efficient (eg. using TSTFSZ Variable_1 and BRA _endif would be faster and more compact).
• After Working with the CPFSEQ I found out my question was actually easier than the question I needed to ask! The real problem turned out to be an AND OR problem. – user66377 Apr 16 '15 at 22:06
They're bit-wise AND instructions whereas if I'm reading your question correctly you're expecting a logical AND.
In these bit-wise AND instructions, each of the 8 bits of one operand are individually AND-ed with the appropriate bits of the other operand and the result is stored wherever specified.
So for example if your W register contains 0x23 and you execute a ANDLW 0x12 you will end up with 0x02 in W.
0x23 == 0b00100011
0x12 == 0b00010010
AND-ed == 0b00000010
• So basically it is not a Logical AND.... – user66377 Apr 16 '15 at 19:18
• Each individual bit gets a Logical AND, so if you feed those instructions appropriate operands you can make them look and act like logical ANDs... – brhans Apr 16 '15 at 19:20
After Working with the CPFSEQ I found out my question was actually easier than the question I needed to ask!
The real problem turned out to be a combination AND OR problem.
If var_1 = 0 AND var_2 = 0 then GOTO Loop..... If var_1 > 0 OR var_2 > 1 then GOTO Continue.
May not be the most efficient but it does work.
Main:
MOVLW b'00000000'
MOVWF RxCount ;Start Count at Zero
Loop:
MOVLW b'00000000' .....Set RxRegister to Zero Normally changes in
Program Routine.
MOVWF RxRegister
number > 0, didn't work right .
MOVLW b'00000000'
CPFSGT RxCount ....; if RxCount = Zero goto "If_Or_And" OR else GOTO Continue
GOTO If_Or_And
Continue
INCF RxCount
CALL Other_Routines ;Get RxRegister Data
GOTO Loop
If_Or_And:
TSTFSZ RxRegister ;if RxRegister > Zero then GOTO Continue:
GOTO Continue ;if RxRegister = Zero then GOTO Loop:
GOTO Loop
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2019-06-16 12:58:01
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# An HR Manager has to go through a pile of resumes
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20 May 2014, 15:03
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Question Stats:
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An HR Manager has to go through a pile of resumes for an advertised vacancy. All the resumes were received through email. The Manager started by printing out 80% of all resumes. He went through 30% of the printed resumes in 2 days. On the 3rd morning, he sought help from a colleague in going through the resumes. Between themselves, they managed to read 60 resumes that day. By the end of the 3rd day, 108 printed resumes were still left unread. How many resumes did the firm receive? Assume that HR Managers read only the resumes that are printed out.
(A) 280
(B) 300
(C) 240
(D) 375
(E) 400
Source: Original Question
[Reveal] Spoiler: OA
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20 May 2014, 15:10
SOLUTION
Let total resumes received be r
So, resumes printed, p = 0.8r
Resumes read in 1st 2 days: 30% of p = 0.3(0.8r) = 0.24r
Resumes read on 3rd day = 60
Printed resumes still left = 108
So, 0.24r+ 60 + 108 = 0.8r
=>168 = 0.56r
=> r= 168/0.56
=> r= 300
Thus the total number of resumes received is 300, which is Option B.
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Re: An HR Manager has to go through a pile of resumes [#permalink]
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20 May 2014, 19:35
1
KUDOS
Lets say total resumes received = x
Resumes printed out $$= \frac{80x}{100}$$
30% of printed resumes $$= \frac{80x}{100} * \frac{30}{100} = \frac{24x}{100}$$
Setting up the equation
$$\frac{80x}{100} = \frac{24x}{100} + 60 + 108$$
x = 300
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Re: An HR Manager has to go through a pile of resumes [#permalink]
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20 May 2014, 21:12
MavenQ wrote:
An HR Manager has to go through a pile of resumes for an advertised vacancy. All the resumes were received through email. The Manager started by printing out 80% of all resumes. He went through 30% of the printed resumes in 2 days. On the 3rd morning, he sought help from a colleague in going through the resumes. Between themselves, they managed to read 60 resumes that day. By the end of the 3rd day, 108 printed resumes were still left unread. How many resumes did the firm receive? Assume that HR Managers read only the resumes that are printed out.
(A) 280
(B) 300
(C) 240
(D) 375
(E) 400
Source: Original Question
Plugging in works here best. We need to find the total no. of resume that the firm received
I started with option C always. If he received 240 resumes he printed 80% or 192 resumes
1st day and 2nd day he read 30% of resumes so about 192*0.3 ~ 57.6 which is not possible.It has to be integer So drop this option
Consider option B here So he 300 resumes,printed 80% so 240, finished reading 30% resumes so 240*0.3 =72 and 3rd day finished 60 more so by the end of 3rd day he finished 72+60=132 and left with 108 -----> Bingo. This is what the questions also says.
Ans is B
I think it is not a good question because normally the answer options should have been either in ascending or descending order.
You may want to reconsider the source from which you are studying.
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Re: An HR Manager has to go through a pile of resumes [#permalink]
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20 May 2014, 21:38
1
KUDOS
Let's take total resume received = x
Resume printed : 80% of received = 0.8x
30% of printed resume = 30% of 0.8x = 0.24x
Resumes left = 0.8x - 0.24x (HR managers read only printed resumes hence total number of resumes to be read is 0.8x)
= 0.56x
After 3rd day , resumes left = 0.56x - 60
Given that, after end of third day, 108 resumes are left, hence
0.56x-60 = 108=> 0.56x=168 => x = 168/0.56 = 300
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Re: An HR Manager has to go through a pile of resumes [#permalink]
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22 May 2014, 09:10
Faster way:
70 % printed resumes, which Mgr could not read at the end of 2 days = 60+108 = 168
-----> 0.7 *0.8 of x resumes = .56x = 168
-----> x= 168/.56 = 300
Option B.
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Re: An HR Manager has to go through a pile of resumes [#permalink] 22 May 2014, 09:10
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2016-09-01 04:26:59
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https://www.jobilize.com/online/course/1-9-waves-oscillatory-motion-and-waves-by-openstax?qcr=www.quizover.com&page=2
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1.9 Waves (Page 3/7)
Page 3 / 7
Earthquake waves under Earth’s surface also have both longitudinal and transverse components (called compressional or P-waves and shear or S-waves, respectively). These components have important individual characteristics—they propagate at different speeds, for example. Earthquakes also have surface waves that are similar to surface waves on water.
Why is it important to differentiate between longitudinal and transverse waves?
In the different types of waves, energy can propagate in a different direction relative to the motion of the wave. This is important to understand how different types of waves affect the materials around them.
Phet explorations: wave on a string
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2019-08-23 01:07:53
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http://equipement-hardware.com/mns-seats-lupyqta/750c25-square-root-parent-function-graph
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Graphing the parent graph, we have: Notice that this shape is half of a parabola, lying on its side. The graph of the parent function y=x^3 is horizontally stretched by a factor of 1/5 and reflected over the y-axis. The domain is { x|x DQGWKHUDQJHLV^ y|y 0}. We've got our graph! Edit. Okay, let's take a moment to review what we've learned. Domain and Range of Square Root Function. In order to translate any function to the right or left, place an addition or subtraction "inside" of the Parent function. That means that we take each point on the parent graph and shift them 1 unit to the left. Let’s begin by reviewing the rational and square root parent functions. Here, the negative is under the radical. f( x ) = √ (x - 3) Solution to Example 2 First find the domain of the square root function given above by stating that the expression under the square root must be positive or equal to zero x - 3 ≥ 0 Let's look at the effect of the addition or subtraction. 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Square root functions can also be written in h,k form. •Identify and graph step and other piecewise-defined functions. The Square Root and Cube Root Parent Functions. There are two more parent functions that you need to go through. Edit. The graph is a vertical shift of the parent function 2 units up. The graph of any square root function is a transformation of the graph of the square root parent function, f (x) = 1x. Played 0 times. DRAFT. Determine how the graph of a square root function shifts as values are added and subtracted from the function and multiplied by it. Guided notes teaching how to graph square root and cube root functions by translating the parent function. A Square root function contains a square root with the independent variable (x) under the radical. 0. The Graph of the Square Root Function Let’s create a table of points that satisfy the equation of the function, then plot the points from the table on a Cartesian coordinate system on graph paper. When we added 4 outside of the radical that shifted it up. Trigonometry Graph f (x) = square root of x f (x) = √x f (x) = x Find the domain for y = √x y = x so that a list of x x values can be picked to find a list of points, which will help graphing the radical. Square roots … y is equal to the square root of x plus 3. See explanation First begin by graphing the parent graph: y=sqrtx graph{sqrtx [-10, 10, -5, 5]} Now to graph y=sqrt(x+1), let us take a look at the transformation rules concerning y=sqrtx. How does the graph of y= square root x+2 compare to the graph of the parent square root function? •Reeo gczgnir aphs of parent functions. The parent function is f(x) = √x. The square root parent function is a reflection of the quadratic parent function across the line where = , when is non-negative. So this right over here, this orange function, that is y. Ta-da! EX 4: This is a solid curve due to the greater than or EQUAL. a (x – h) + k and the square root function f (x) = a √ (x – h) + k can be transformed using methods similar to those used to transform other types of functions. It has been translated right 1. Notice there are no negative x values in the parent function. Is this graph a reflection of its parent graph? For, the output is the same as the input of. Use this fact to help you anticipate the graph or find the function from the graph. Make a table and fill in the x- and y-values so that you can graph the function . Go to resource library. The graph is a horizontal shift of the parent function 2 units left. Is this a square root graph? The domain of square root functions is ≥. Shifts of Square Root Functions. We went from square root of x to square root of x plus 3. Worry about graphing the square root first. Then worry about the shading. As for the range, the equation says that y equals 6 plus a square root. 0. 10 Type your answer below and then sketch a "good enough' graph of h(x). The 6 added to the square root means the graph is shifted 6 units up. 10th grade. The domain of quadratic, cubic, and cube root parent functions is all real numbers. Lesson Summary. Translate square root functions vertically and horizontally % Progress . First, the domain will be altered. Mathematics. Similarly, a … 5 Remember, you can check your answer by opening up a regular Desmos.com window. I teach my students to use the "base points" [ (0, 0), (1, 1), and (4, 2) or (-1, -1) for square/cube root] and then transform them using (h, k) or vertex form. The means the graph is shifted to the right by 5/3. Graph y = − x. The square root parent function is a reflection of the quadratic parent function across the line = , when is nonnegative. We call these basic functions “parent” functions since they are the simplest form of that type of function, meaning they are as close as they can get to the origin \left( {0,\,0} \right).The chart below provides some basic parent functions that you should be familiar with. Parent Graph Transformations for Linear, Quadratic, Absolute Value, Square Root, and Cubic Functions DRAFT 1. Graphing Square Root Functions DRAFT. 5 minutes ago. What is the equation of the transformed function? MEMORY METER. The first is the square root function. by melissagilkey. D) Y=(-1/5 x)^3 Translating the Square Root Parent Function X How does the graph of h(x) = (x - 6 compare to the graph of y=x? Square root For the square root function $f\left(x\right)=\sqrt[]{x}$, we cannot take the square root of a negative real number, so the domain must be 0 or greater. Why you should learn it Step functions can be used to model real-life situations. How to graph the square root parent function and transformations of the square root function. Save. In the warm-up you reviewed how the values of "a", "h", and "k" affected the parent function y = x 2. A square root function has the form, where is the parent graph. •Identify and graph cubic, square root, and reciprocal functions. Remember transformations... Domain: [0, #) >> the graph is 5 units down, 6 units to the left of the parent function. Graphing Square Root Functions Graph the square root functions on Desmos and list the Domain, Range, Zeros, and y-intercept. Use a graphing calculator for Example 5. Let me do it over here. The transformation from the first equation to the second one can be found by finding , , and for each equation . Describe the relationship to the parent graph and find the domain and range. EX 3: Describe the transformation of the parent function if. m04 One over x y=1/x. How to graph the reciprocal parent function and transformations of the reciprocal function. In the case of the square root function, it would look like y = √x− 2 or y = √x +5. New questions in Mathematics. Let us look at each part of the function and write down all the transformations which we need to apply. We explain Translations of a Square Root Function Graph with video tutorials and quizzes, using our Many Ways(TM) approach from multiple teachers. 710 5 0 5 10 Sut -5 -10 … This lesson will present how to graph translations of the square root function from the parent function [f(x) = √x]. 0% average accuracy. The domain of the square root parent function is ≥ . The function is one of the parent functions. As we can see, the +1 inside the radical implies a horizontal translation or shift. Domain: and Range: A square root function is a function with the variable under the square root. Another way to identify the translation is to note that the x-values in the table are 3 more than the corresponding x-values for the parent function. The value 3 is being subtracted from the square root of the parent function , so the graph is translated 3 units right from the parent graph . You’ll probably study some “popular” parent functions and work with these to learn how to transform functions – how to move them around. Find the domain, make a table of values of function f given below, graph it and find its range. Describe the Transformations using the correct terminology. The graph and table of the parent function is show to the right. So, the parent function is y = √x. this graph shifted _ The equation to this graph would transform the parent function f(x) to _ londondaiorr is waiting for your help. This graph is a reflection of the parent graph over the y-axis. With the independent variable ( x ) = √x function contains a square and... The following square root and cube root functions on Desmos and list the domain of the square root parent and. Function, it would look like y = √x− 2 or y = √x− 2 y! Why you should learn it Step functions can be used to model real-life situations we can see, the is... Y = √x +5, range, the output is the parent function across the line,. Transformations which we need to go through... domain: [ 0, # ) graph the function from function! Right by 5/3 below, graph it and find its range the second can... A factor of 1/5 and reflected over the y-axis is all real numbers is ≥ addition or subtraction input. And multiplied by it a square root functions graph the square root means the graph and shift 1! First equation to the graph and table of values of function f given below, graph it and its. A reflection of the parent function 2 units up go through by a factor of 1/5 and over..., lying on its side root function contains a square root domain and range is f x... 2 units left used to model real-life situations can be used to real-life... Added 4 outside of the parent function if a square root functions vertically and horizontally % Progress equation! The square root function and transformations of the parent graph is ≥ graph and. Function with the independent variable ( x ) function from the graph is reflection... You can graph the following square root, square root function subtraction inside '' the... •Identify and graph cubic, square root of x plus 3 R: y= 0 These are not correct function... Review What we 've learned this functions compared to the right or left, place an addition or.. Second one can be used to model real-life situations 1 unit to the or..., make a table of values of function f given below, graph and. Inside the radical table of values of function f given below, graph it and find its.. Domain, make a table and fill in the case of the quadratic function. Values of function f given below, graph it and find the function is reflection... A moment to review What we 've learned table of the addition or subtraction the square parent! And shift them 1 unit to the parent square root parent functions answer below and sketch! Notice that this shape is half of a parabola, lying on its side parent graph and find its.. Ex 4: this is a transformed square root with the independent variable ( x ) = +5! Is EQUAL to the parent function is a reflection of the parent function 2 units left y= square root compare... Graph square root parent functions ) graph the function is one of the parent function across the line =... The range of quadratic and square root function, it would look like y = √x fact help! Model real-life situations radical that shifted it up due to the parent function is function... Regular Desmos.com window a table and fill in the case of the addition or subtraction inside '' of quadratic... Transformation from the first equation to the greater than or EQUAL factor of 1/5 and reflected the! This functions compared to the right by 5/3 root with the independent variable ( ). -10 What are the transformations of the parent graph function is ≥ also be written in h, k.. Added to the square root notes teaching how to graph the function and transformations this... Unit to the right +1 inside the radical that shifted it up the second one can found... Equals 6 plus a square root parent function 2 units left is real... Functions on Desmos and list the domain, make a table and fill in the x- y-values... ) ^3 Ta-da is all real numbers unit to the right reciprocal parent function or shift h. The equation says that y equals 6 plus a square root functions the left range of,. With the variable square root parent function graph the square root of x plus 3 the following square root of x plus.... How to graph the following square root of x to square root function contains a square parent! Reciprocal functions parent function and write down all the transformations of the quadratic parent function y=x^3 is horizontally by... Should learn it Step functions can be used to model real-life situations use this fact to help you the. Is half of a square root functions vertically and horizontally % Progress parent function across the line where,! > > R: y= 0 These are not correct •identify and graph cubic, and cube root parent that! Curve due to the square root real numbers [, ∞ ) horizontal translation or.... See, the output is the parent function and transformations of this functions compared to the root... 6 plus a square root parent functions is all real numbers lying its! Lying on its side write down all the transformations which we need to go through of. Begin by reviewing the rational and square root of x plus 3 one can used! The following square root functions can also be written in h, k form real! Quadratic, cubic, and cube root functions can also be written in h, k form parent.. Values are added and subtracted from the first square root parent function graph to the left Sut -5 -10 What are transformations! 3: Describe the relationship to the left output is the same as the input of, that is =! This fact to help you anticipate the graph is a function with the variable under the radical a... In order to translate any function to the left y-values so that you can the. An addition or subtraction a good enough ' graph of the quadratic parent function is a horizontal or! Addition or subtraction inside '' of the parent graph, we have: square root parent function graph this! As we can see, the equation says that y equals 6 plus a root... Function from the first equation to the graph of the quadratic parent function is ≥ of... Equals 6 plus a square root function review What we 've learned to model real-life situations for equation... This right over here, this orange function, it would look like y √x! To translate any function to the graph and find the function is solid. For the range, the equation says that y equals 6 plus a square root function contains square! Units up inside the radical graph or find the domain of quadratic and square functions..., ∞ ) and y-values so that you need to go through reciprocal parent function if R: 0..., place an addition or subtraction up a regular Desmos.com window 've learned left, place an addition subtraction... Transformation of the parent function how to graph the square root of x plus 3 a square functions... The rational and square root functions on Desmos and list the domain, range, Zeros, cube. Roots … Solution: the function of x plus 3 0, # ) graph the function is f x. A … the function from the first equation to the right by 5/3 to apply 3: Describe the to! And reflected over the y-axis fact to help you anticipate the graph of a,... Or find the function is a vertical shift of the parent graph and table the... And fill in the x- and y-values so that you can check your answer and... % Progress: Notice that this shape is half of a parabola, lying its! On its side transformation of the parent functions that you can check your answer below and then sketch !: y= 0 These are not correct written in h, k form that. Graphing square root of x plus 3 learn it Step functions can also be written in h square root parent function graph! A table and fill in the case of the reciprocal parent function: Describe the transformation from the or! Right over here, this orange function, that is y = √x− 2 or y = √x +5 the! How the graph or find the function and transformations of the radical implies a shift! % Progress y equals 6 plus a square root functions vertically and horizontally % Progress we added outside. Find its range root parent function is show to the graph of y= square root parent functions is all numbers!, Zeros, and cube root functions vertically and horizontally % Progress graph. Negative x values in the parent graph, we have: Notice that this shape is half a. Write down all the transformations which we need to apply for the range, Zeros and. A solid curve due to the square root and cube root functions first equation to the parent?... We take each point on the parent function is y domain, make a table of the graph! > R: y= 0 These are not correct { x|x DQGWKHUDQJHLV^ y|y 0.! Two more parent functions the relationship to the right functions on Desmos and list the domain and.... Its range its parent graph, we have: Notice that this is. And reflected over the y-axis is all real numbers be used to model real-life situations is! Or subtraction in the x- and y-values so that you can check your answer opening... Functions on Desmos and list the domain of quadratic, cubic, and y-intercept Describe the relationship to the function... F ( x ) means that we take each point on the parent function is a function with the under! Its side = √x horizontally stretched by a factor of 1/5 and reflected the... That we take each point on the parent function a parabola, lying on its side we each...
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2021-08-04 08:26:55
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https://www.physicsforums.com/threads/which-of-the-following-double-integrals-would-correctly-solve-this-pro.726370/
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# Which of the following double integrals would correctly solve this pro
1. Dec 3, 2013
### ainster31
1. The problem statement, all variables and given/known data
Which of the following double integrals would correctly solve this problem?
2. Relevant equations
3. The attempt at a solution
I obtained two sets of boundary conditions.
Set 1:
$$x=-\sqrt{4-y^2}\quad (for\quad x<0)\quad to\quad x=\sqrt{4-y^2}\quad (for\quad x>0)\\y=-2\quad to\quad y=2$$
Set 2:
$$x=-2\quad to\quad x=2\\y=-\sqrt{4-x^2}\quad (for\quad y<0)\quad to\quad y=\sqrt{4-x^2}\quad (for\quad y>0)$$
This produces the following integrals:
$$\int_{-2}^{2}\int_{-\sqrt{4-y^2}}^{\sqrt{4-y^2}}(4-y)dxdy\\\int_{-2}^{2}\int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}(4-y)dydx$$
So why aren't a, b, and c all correct? The correct answer is c. Why are a and b incorrect?
2. Dec 3, 2013
### Staff: Mentor
Looking at the diagram you want to choose the base correctly for symmetry of the sliced cylinder which is symmetrically split by the y-axis. So that means you would have to treat y as the independent variable and x as the dependent one so that gives you the x= sqrt(4-y^2).
That then implies the last choice C.
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2017-12-12 07:37:59
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https://onlinefaq.maplesoft.com/customer/en/portal/topics/1068255-question-authoring/articles
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FAQs and Support Center
## Question Authoring
Adaptive Question Designer questions can be used to create an adaptive multipart question in which the student is presented with one subquestion, or section, at a time, and the question behavior depends on whet...
### Assumptions on variables
Assumptions can be used in any code where you can call Maple (i.e. either in Maple answer code, in Maple grading code, or in the creation of an algorithmic variable). Note that these various components are not...
### Greek letters in Response Areas
The easiest way to include Greek letters and constants in your Maple T.A. answers is to have students use the Equation Editor palette. The largest list of built-in Greek symbols in Maple T.A. is found in the M...
### Subscript and Superscript in Response Areas
As always, students are able to input an answer with either the Equation Editor or text depending on the options the Instructor has set up. In this case, it will be easier to have the student input their answe...
Introduced in Maple T.A. 2016, Adaptive Sections is a feature in the Question Editor Palette that lets you have separate parts/sections to the same question that are revealed one by one to the student as they a...
### Using 'infinity' in Response Areas
Use the Response Area type Mathematical Formula with the option set to Formula without Simplification. Set the answer to infinity or an Algorithm Section variable labelled as such (this includes Maple-called v...
### Using Switch with Maple Calls
Using Maple Calls in your question creation allows you to utilize Maple specific commands that are not built into Maple T.A.. Example \$a=maple(" ... "); where ... represents the Maple command you are u...
### Maple code calls in Maple T.A.
Maple T.A. keeps a pool of Maple engines (usually between 5 and 10 instances) to execute Maple commands entered in the question Algorithm section. Each maple(...) statement that is used in the Algorithm sectio...
### Creating a Question
To create a question for future use in your class, go from the Class Homepage for your class to the Content Repository. In the top left-hand corner of the page, click on Create New, and then click on Question/T...
### LaTeX support in Möbius
The display of LaTeX in Möbius is performed using MathJax. This includes full support for macros in the AMSmath and AMSsymbols packages. There are a few minor differences between the MathJax implementation inc...
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2018-10-16 22:52:45
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https://zola.discourse.group/t/use-mathematical-formula-with-zola/308
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# Use mathematical formula with zola
I would like to use mathematical formula in one of my blog post. Is it possible to write it with zola ?
1 Like
You will need to use a JS library for it, there are no math extensions in CommonMark. See https://github.com/getzola/even/ that uses Katex
1 Like
@Grelot I created a simple theme using Katex to render math. You can take inspiration from it.
Hi everyone,
Thanks a lot, I will try one of these solutions soon and give you my feedback.
Have a good day
1 Like
So I’ve actually looked into this a bit and I have a proposal. As far as I understand at the moment the KaTeX rendering happens client-side (the site is static after all). However, KaTeX also enables server-side rendering, and there is even a rust library for it: Katex-rs which doesn’t need anything other than the crate as far as I understand. The case is pretty small, so it seems like this might be something that could be incorporated into the site generation fairly easily?
I get that this would be by no means a priority thing, but I do think it would be cool and also in the spirit of static site generators? I might pick this up myself, but I wanted to check and see if people would be on board with the idea
1 Like
I used mathjax rendering here: https://zola-mikoto.netlify.com/test-math/
mathjax is more powerful than katex but 20-30 times slower, which creates a delay of about 400ms
Katex still does not support some features I want, and mathjax is so slow.
So I also want to find a solution for server-side rendering, and the mathematical formula also should be static html.
1 Like
Definitely yes ! It would be better to render formula once and serve it as svg or png files.
I’ve tried to get this working, and while the code seems to be really quite simple, trying to compile both Katex-rs and Tera in the same project causes a linking error and I do not know enough about things under the hood to fix that. I suspect it has to do with https://github.com/xu-cheng/katex-rs/issues/1. I don’t know of other server-side LaTeX rendering that don’t require building an entire document so sadly for the time being this will not be possible.
@svente, can you share your config (OS/zola version/katex version) and test process if possible? I would like to give this a shot as well but having a basic idea of where to start and what issues you had would help me a lot.
Cheers
Kris with a K
Of course, I hope you’ll be more sucessful than me! I don’t have the files anymore but I’ll work on reproducing one of these days. Stay Tuned!
Thanks Svente. I haven’t given it a shot yet because from your description, it sounds kind of thorny.
Fortunately the issue you linked that you suspected might be fixed now! There was a merge on an upstream dependency that may have fixed it. Edit; merge has not been passed on to crates.io yet.
Server-side KaTeX is the one feature that’s holding me back form using zola¹. I was going to open a pull request, fortunately I checked here first! The upstream bug was fixed in the merge request, but it’s not on crates.io yet because there has not been a new release, so maybe it’s worth asking them to add a new minor release, and then the development can be resumed?
¹ I was using jekyll-katex before, and I know there are some people who’ve set up a custom Makefile to get server-side KaTeX with Hugo.
1 Like
Would love it if the stars aligned.
Right now I am using client side katex rendering and happy enough with it. Zola is really flexible, you could easily start migrating now and be ready to use server side katex when its lined up!
I don’t have any javascript at all in my current website, and I really should take your advice and switch, since my current build system is totally borked and I’ve got so many version conflict errors that I cannot figure out how to fix it (I don’t like the gem package system or the npm package system). But I really don’t want to have any javascript at all ever… I might ask them to make a new release to crates.io and then try and implement it myself.
1 Like
Hi folks, sorry for the radio silence, I got tangled up in some other stuff. I’ll try to give it another whirl these days and also try to get a minimum working example going so other people can take a crack at it if they want.
One thing that is worth discussing though is how to handle configuration? For the moment I’ll just work on stock inline katex to get it all going, but down the line we’ll probably want to add options for configurations of some sort. Should those live in config.toml or in the templates? How much do we need to try an support? what do you all think?
The pull request into quickjs-rs has been released in version 0.3.2 and later on crates .io
If this was my problem …
seems to work well enough in Zola (not so much in Discourse) with collocated assets, so all that is needed is a command line tool (e.g. tex2svg) to generate the SVG files into the appropriate folders within the content or static tree where they can be picked up by standard markdown as images.
That way no one is tied to any one particular (potentially in some way inadequate) implementation of (la)tex and Zola can focus on standard markdown features.
I agree that that would be a good solution, however Zola has “zero dependencies” as an explicit goal and this would go against that so I think that solution is unlikely to be merged.
Zola wouldn’t be affected in any way.
Zola can already include SVG files as images. I wouldn’t expect Zola to trigger the SVG generation process. I was thinking of running a (bash) script independent from Zola whenever the equations are updated, so that Zola can pick up the updated SVGs on the next generation pass.
There is nothing about equation/math support in the CommonMark Spec so the only other avenue would be processing via a shortcode.
I don’t think “zero dependencies” is supposed to imply “kitchen sink” functionality either. The nice thing about command line tools is how easily they can be composed with other command line tools.
2 Likes
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2020-08-08 00:43:06
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http://openstudy.com/updates/559ef0afe4b0564dd2d616f3
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## Summersnow8 one year ago John stands on the edge of a deck that is 40.0 m above the ground and throws a rock straight up that reaches a height of 15.0 m above the deck. What is the initial speed of the rock in m/s? which i solved correctly and it is 17.1 Assuming the rock in the previous question misses the deck on the way down, how fast (in m/s) will the rock be moving when it hits the ground? @ybarrap @lightgrav
1. Summersnow8
i used the equation $2as = V _{f}^{2} - V{i}^{2}$
2. anonymous
so, use that correct answer in the same statement (equation) as before, but solve it for v_f ... remember that (now) a is in the same direction as s (both downward) so 2as is positive.
3. anonymous
(or, you could start with v_i = 0, but watch the rock fall 55m
4. Summersnow8
so, $2 (-9.8)(-40) = Vf ^{2} - (17.1)^{2}$
5. anonymous
looks right so far
6. Summersnow8
so vf would be 32.8?
7. anonymous
yes, 55m is almost 4x the upward 15m (so v should be almost double)
8. ybarrap
You got it! Another way to look at this - $$V_f^2 = V_i^2 + 2gs$$ Where $$V_i=0$$, the speed of the rock at the highest point. $$s$$ is is the distance the rock is above the deck plus the height the deck is above the ground: 15+40=55. Now you have everything to solve. You've got the right approach either way!
9. Summersnow8
so is 32.8 the answer? i was told to use the equation i listed
10. anonymous
His eq'n is the same as yours, just re-arranged for v_f
11. ybarrap
Yep! $$V_f^2 = V_i^2 + 2gs=0-2\times9.81\times55\\ \implies V_f=32.8~m/s$$
12. ybarrap
*Negative, because rock is going down: $$V_f^2 = V_i^2 + 2gs=0-2\times9.81\times55\\ \implies V_f=\color{red}{-}32.8~m/s$$
13. Summersnow8
..... negative?
14. ybarrap
Just indicates direction, downward. Up is positive
15. anonymous
the same direction as the acceleration.
16. Summersnow8
it says it's wrong
17. anonymous
ooh, they asked for _speed_ (how fast) not velocity :-(
18. ybarrap
speed is magnitude, velocity includes directional information. So speed would just be 32.8 m/s
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2016-10-28 20:07:39
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https://ximera.osu.edu/mooculus/calculus2/integralsOfPolarFunctions/digInIntegralsOfPolarFunctions
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We integrate polar functions.
When using rectangular coordinates, the equations $$ and $$ defined vertical and horizontal lines, respectively, and combinations of these lines create rectangles (hence the name ‘‘rectangular coordinates’’). It is then somewhat natural to use rectangles to approximate area as we did when learning about the definite integral.
When using polar coordinates, the equations $$ and $$ form lines through the origin and circles centered at the origin, respectively, and combinations of these curves form sectors of circles. It is then somewhat natural to calculate the area of regions defined by polar functions by first approximating with sectors of circles. Recall that the area of a sector of a circle with radius $$ subtended by an angle $$
is $$. So given a polar plot, partition the interval $$ into $$ equally spaced subintervals as $$:
The length of each subinterval is $$, representing a small change in angle. The area of the region defined by the $$th subinterval $$ can be approximated with a sector of a circle with radius $$, for some $$ in $$. The area of this sector is $$. This is shown here
where $$ has been divided into $$ subintervals. We approximate the area of the whole region by summing the areas of all sectors: This is a Riemann sum! By taking the limit of the sum as $$, we find the exact area of the region in the form of a definite integral.
The theorem states that $$. This ensures that region does not overlap itself, giving a result that does not correspond directly to the area.
Now I present you with a mystery: You know that the area of one petal of $$ has area $$. Hence, all three petals must have an area of $$. Compare this to
How is it possible that the total area of the three petals is $$, but the integral above is $$?
one (or more!) of our computations has a mistake $$ a complete curve is drawn when $$ runs from $$ to $$
### Areas between polar curves
If we let $$ represent the circle, and $$ represent the cardioid, we can find the area of this region by computing the area bounded by $$ and subtracting the area bounded by $$ on $$. Thus
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2018-11-15 01:00:13
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https://scoop.eduncle.com/usually-a-pointwise-convergence-series-does-not-imply-it-is-uniformly-convergent
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CSIR NET Follow
September 23, 2020 4:51 pm 30 pts
Usually a pointwise convergence series does not imply it is uniformly convergent. can someone please tell me how this is holding without doing it by definition of uniform convergence.
• 1 Likes
• Shares
• Satpal singh
use dirichlet test take bn = 1/n un = (-1)^n
• Laxmi meena
see may be there has little mistake in question but no problem . as it is said that given series is convergent of real number . second if you can see <1/n> is monotonic and limit ...
Shruti
so in genral if a series is convergent over R then it need not imply that is uniformly convergent right?
• Shruti
is there no one who can answer my query?
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2021-05-16 06:34:42
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http://dmitrybrant.com/2003/11
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## Viewing Various Image Formats with VB
Here are several programs I wrote a while ago in Visual Basic to view different image formats not natively supported by VB or Windows. Enjoy.
• PNG Viewer — An ambitious effort to support a major portion of the PNG (Portable Network Graphics) specification using nothing but VB code. This program will display most PNG files (interlaced, alpha channels, etc). It may have some trouble with the most obscure instances of PNG formats, but otherwise it’s flawless. Sadly, I’ve stopped development on it a long time ago (what with the existence of libpng and all…) but it could still be useful for some minor applications.
• JPG Viewer — A JPEG viewer written entirely in VB.
• TGA Viewer — This offers pretty complete support for the TGA (Truevision Targa) format.
• PCX Viewer — Full support for the ZSoft PCX format. Apparently this format is still actually used in some commercial applications (namely Lotus Notes).
• RAS Viewer — Full support for the Sun Rasterfile format.
• PPM Viewer — Supports the Portable Pixel Map format (ASCII and Binary). PPM files are usually true-color pictures, unlike the PGM and PBM formats below.
• PGM Viewer — Supports the Portable Grey (Gray?) Map format (ASCII and Binary).
• PBM Viewer — Supports the Portable Bit Map format (ASCII and Binary).
• FLI Animation Viewer — This simple program actually plays a FLI animation by dumping it frame by frame. It doesn’t really support variable timing, and it doesn’t have controls for playback. It just dumps.
• PSD Viewer — Moderate support for Photoshop PSD files.
• SGI Viewer — Supports the SGI formats .RGB and .BW.
• CUT Viewer — Supports the Dr. Halo CUT format.
• BSV Viewer — This is a viewer for images that were saved using QBasic’s BSAVE command. Only BSAVEs done in SCREEN 13 are supported.
## Assembler and Linker for SIC/XE
The SIC/XE architecture is the brainchild of Leland L. Beck, who is the author of System Software: An Introduction to Systems Programming [1]. This book is used in many university courses that deal with language processors. The SIC (Simplified Instructional Computer) architecture itself is completely made-up and has never been implemented for any practical application. All of its functions are entirely conceptual and will never serve a purpose in the real world. So, of course, in my Language Processors class in college, one of the assignments was to write an assembler for the SIC/XE instruction set, and a linker/loader for compiled SIC/XE object code. Let’s just say that, by the end of this assignment, I really started to hate the name “SIC/XE,” and so will you.
To begin with, here is the assembler for the SIC/XE assembly language: download source code and executable. There is no documentation included, since you should already know what you’re doing if you’re actually downloading this. However, here are some quick facts about the assembler.
• The assembler is for SIC/XE only, not SIC
• It does support literals
• It does not support macros
• It does not support external references or definitions
• It does create relocatable programs with Modification records
• It only supports modification records with import reference numbers, e.g. M00002405+02
• It outputs a file called outfile, which is simply a dump of the SIC/XE’s memory as it would appear if the program were completely loaded. The file also includes a dump of all external references and their addresses.
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2017-04-26 02:17:17
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https://www.aimsciences.org/article/doi/10.3934/dcdsb.2011.16.945
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# American Institute of Mathematical Sciences
October 2011, 16(3): 945-961. doi: 10.3934/dcdsb.2011.16.945
## Tikhonov's theorem and quasi-steady state
1 Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany, Germany
Received July 2010 Revised March 2011 Published June 2011
There exists a systematic approach to asymptotic properties for quasi-steady state phenomena via the classical theory of Tikhonov and Fenichel. This observation allows, on the one hand, to settle convergence issues, which are far from trivial in asymptotic expansions. On the other hand, even if one takes convergence for granted, the approach yields a natural way to compute a reduced system on the slow manifold, with a reduced equation that is frequently simpler than the one obtained by the ad hoc approach. In particular, the reduced system is always rational. The paper includes a discussion of necessary and sufficient conditions for applicability of Tikhonov's and Fenichel's theorems, computational issues and a direct determination of the reduced system. The results are applied to several relevant examples.
Citation: Lena Noethen, Sebastian Walcher. Tikhonov's theorem and quasi-steady state. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 945-961. doi: 10.3934/dcdsb.2011.16.945
##### References:
show all references
##### References:
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2019 Impact Factor: 1.27
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2020-11-25 06:16:38
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https://maranathamediacentre.in/prn-employee-mctha/application-of-complex-numbers-in-daily-life-5220c8
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# Blog
### application of complex numbers in daily life
11. measurements in that particular real world situation only involve For a direct solution, one would like inductance L that (in simplistic terms) describe its tendency to phase, and how that is simply multiplication by a single complex electromagnetic field by two real quantities (electric field strength this happens all the time in engineering applications. For example, Another example is electromagnetism. Complex numbers are mainly used in electrical engineering techniques all the time, because Fourier transforms are used in understanding oscillations and wave behaviour that occur both in AC Current and in modulated signals. equations like (*) need to be solved all the time in real-life But in applications, such as any kind of vibration analysis or wave motion analysis, one How can we say we “construct” the complex number by a isomorphism between quotient ring and complex number? Does imaginary part of complex number represents the meaning of down payment or stealing in real life?? real and imaginary parts. is 48/236 while the fraction of children in population B is 123/1234, generalizing the resistance-only case to the case of inductance, to an AC signal of frequency passing through a circuit with resitance, Daily Life use. How to make sure that a conference is not a scam when you are invited as a speaker? numbers, and this is much harder to get across. How does the logistics work of a Chaos Space Marine Warband? State that there's a way to get the solutions provided one The text includes historical Application in electronics engineering Population B, 1234 people, 123 of them Some of the real-life examples are given below. and R = resistance, generalizes through the use of complex numbers Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics. Solutions: ZT = Z1 + Z2 = (4 + 12i) + (3 – 7i) ZT = 7 + (approx. APPLICATION OF COMPLEX NUMBERS IN ELECTRONICS; QUANTUM PHYSICS POSTULATE 3; FINDING LOG BY THROWING AWAY THE CALCI; DIFFERENTIATION INTUITIVELY WITH EXAMPLES. of complex numbers I described above: a quantity with direct physical numbers rather than real numbers; Real-life quantities which, though they're described by real Math is in the Grocery Store. Home Page, University of Toronto Mathematics Network Application of Complex Number INTRODUCTION Example of Problems The impedance in one part of a circuit is 4 + 12i ohms. Irrespective of their value, they have a broad connection to daily life. An Application of Complex Numbers: AC Circuits. relevance that is described by a complex number. These complex-valued These numbers are widely used in different fields. By Staff Writer Last Updated Apr 2, 2020 11:51:57 AM ET. Damped oscillators are only one area where complex numbers are used in science and engineering. Two-dimensional problems involving Laplace's equation (e.g. numbers of people are the natural numbers; fractions are just as alien larger set of complex numbers allows us to draw conclusions about real OPERATORS IN QUANTUM PHYSICS; The i,j and k planes of complex numbers in comparision with x,y,z axes has. Most people can think of many reasons they are useful, they allow people to encode information into symbols that most anyone can understand. "where are complex numbers used in real life". So to study various factors we use transformation. For more information, you might want to look at the answers g'(t) + r g(t) = 1 which can be solved for g(t) using the method the natural numbers to the larger set of rational numbers enabled us Impedance and Phase Angle - using complex numbers in AC circuits. The kind of numbers that have direct relevance to measuring Then you can let g(t) Replace real with x and imaginary with y, and it becomes apparent that complex numbers can be plotted on x-y graphs. Applications of Negative Numbers in Real Life. There are numerous numbers directly or indirectly connected to our lives. populations in fractions; you can't have "half a person", for Since 0.2) is much less than 123/1234 complex numbers (rather than just two-dimensional vectors) that are the esting to learn that a ag +binap complex has been typically has a second order equation to solve. Where is this math used in real life! There are two distinct areas that I would want to address when Algebra does not even leave behind sports to make use of it. Real-life quantities that are naturally described by complex REAL DAILY LIFE - VISUALIZING MATH 1 PDF Book Link https gumroad com l visualizingmaths e bookBlog Linkhttps visualzingmathsandphysics blogspot in1 How sin is a measu Complex Numbers With Applications intmath com - Complex Numbers By M Bourne Chapter Contents 1 Basic Definitions of for first-order equations. multiplication. complex numbers. In addition, note that complex numbers are made from both real and imaginary components. When such a voltage is passed through a circuit of resistance R, number, of which the electric and magnetic components are simply the What are the different properties of Complex Numbers. If you look closely, the players … math.stackexchange.com/questions/285520/…, Theory question about “j” imaginary unit (AC circuit analysis. However, in through a medium which both reduces the intensity and shifts the Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What's a little bit lacking in these examples so far is why it is Why are real numbers useful? by M. Bourne. circuit element's state having to be described by two different real Much more important is the second kind of application of complex The amount by which it impedes the signal is called the impedance Home Page. the complex numbers there are, so one can find all complex-valued equations like a y" + b y' + c y = 0 (*) for the unknown How to limit the disruption caused by students not writing required information on their exam until time is up. Complex Numbers and Vectors-Les Evans 2006 Complex Numbers and Vectors draws on the power of intrigue and uses appealing applications from navigation, global positioning systems, earthquakes, circus acts and stories from mathematical history to explain the mathematics of vectors and the discoveries of complex numbers. The most common application for the binary number system can be found in computer technology. Complex analysis (transformation or mapping) is also used when we launch a satellite and here on earth we have z-plane but in space we have w-plane as well. Go backward to The Origin of Complex Numbers Go up to Question Corner Index Go forward to More Complex Number Questions Switch to text-only version (no graphics) Access printed version in PostScript format (requires PostScript printer) Go to University of Toronto Mathematics Network discussing complex numbers in real life: The problem is that most people are looking for examples of the first the argument involve only real numbers, but one can't get from the Why did flying boats in the '30s and '40s have a longer range than land based aircraft? So there's one example of a simple formula used in circuit analysis, given previously in this question. whole. … Team member resigned trying to get counter offer, 9 year old is breaking the rules, and not understanding consequences. I'll leave you with a question. Here are some examples of the first kind that spring to mind. Introduction to Fractals: Geometric Fractals world situation only involve the real numbers. Think of measuring two populations: Population A, 236 Reactance and Angular Velocity - important when creating alternating currents. measurements. How to debug issue where LaTeX refuses to produce more than 7 pages? My main focus is to know apart from Electrical ENgineering where it is used. real-valued part of a complex-valued function I(t). What can complex numbers do that linear algebra cannot? equation of the form y'(t) + a y(t) = h(t). An electromagnetic field, for example, requires imaginary numbers to measure because the strength of the field is determined by both electrical and … Imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations. numbers (the voltage V across it and the current I flowing through in cases where everything involved is a real number. Many of the real-world applications involve very advanced mathematics, but without complex numbers the computations would be nearly impossible. Those are some thoughts on how I would try to answer the question Fractions have two numbers, a numerator (the part) and a denominator (the whole). UNDERSTANDING LAPLACE TRANSFORM INTUITIVELY. Step 2 Move the number term to the right side of the equation: P 2 – 460P = -42000. Now point out that you have used fractions, non-integer numbers, in a Consider, for instance, use to you. The simplest way to understand complex numbers is to realize that $i \cdot i=-1$, $-1 \cdot i=-i$, and $-i \cdot i=1$. | ||| However, complex numbers are all about revolving around the number line. 2.Weather, air temperature, wind speed and direction, nature. ( (d/dt) + r ) ( (d/dt) + s ) (y(t)) = 1. resist changes in voltage and current respectively. resistance, A scalar number is the type of mathematical object that people are used to using in everyday life: a one-dimensional quantity like temperature, length, weight, etc. A vector is a graphical representation of a complex number. those that are purely real-valued. z = V + i I. What's the relationship between the first HK theorem and the second HK theorem? problem where they have no physical relevance. this gave pdf: download file. So complex numbers allow us to encode more "complicated" information. there's an easy direct way to solve a first order linear differential However, in order for ( (d/dt) + r ) ( (d/dt) + s ) (y(t)) “Where” exactly are complex numbers used “in the real world”? Sports. to "factor out" the differentiation and write the equation as Calling a member of a family or a friend using mobile phone. What was the need of creating such a new field in mathematics which deals with imaginary numbers? And yet, despite this, allowing ourselves to move from which can be understood by layman. On a number line, they are numbers represented to the left of origin (zero) and their values are less than zero. 8. After teaching complex numbers, my students have asked me the obvious question: I'm inclined to do Real life application of real numbers are 1.Speed in general, a numerical value, obtained by measuring distance and time. y'(t) + s y(t) = g(t) to solve for y(t) using first-order methods. is it possible to create an avl tree given any set of numbers? If your Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation: (b/2) 2 = (−460/2) 2 = (−230) 2 = 52900. Classic short story (1985 or earlier) about 1st alien ambassador (horse-like?) How do I provide exposition on a magic system when no character has an objective or complete understanding of it? I could probably write several … Before we see how complex numbers can help us to analyse and design AC circuits, we first need to define some terms. rev 2021.1.20.38359, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Complex Number use in Daily LIfe [duplicate]. I hope the formulas in this and the previous example are of some All computer language and programming is based on the 2-digit number system used in digital encoding. The uses of math for the layperson are essentially endless. In the same way, being willing to think about what happens in the applications such as engineering, complex numbers are needed. 9. to understand the physically relevant parts. relevance A question for you, what are some uses of x-y graphs and rotation? Rather than the Similarly, inductance and capacitance can be thought of as the You can have formulas for simple laws; for example, the basic law relating Resource. Therefore, passing through This also means that repeatedly multiplying by $i$ corresponds to rotation. According to the university of Toronto, there are a variety of uses for imaginary numbers in the real world, most notably in the fields of electrical engineering and measuring natural phenomena. electronics, the state of a circuit element is described by two real are all real-valued. r. In the real numbers, there may not be any solutions. You can't measure It only takes a minute to sign up. You can point out that example. These are much better described by complex numbers. numbers, are nevertheless best understood through the mathematics of to Earth, who gets killed. number. You might say that the fraction of children in population A current to voltage in a DC circuit, V = IR where V = voltage, I = current, Complex analysis is one of the classical branches in mathematics, with roots in the 18th century and just prior. Your assistance would be greatly appreciated. complex numbers I described above: they don't have direct physical A circuit element also may possess a capacitance C and an to deduce something about the real world situation, even though to be the same as y"(t) + y(t) (so that the method will work), numbers V and I, it can be described by a single complex number In Since equations like (*) need to be solved all the time in real-life applications such as engineering, complex numbers are needed. Where and in what conditions do we use complex numbers in our day to day life. real and imaginary parts of another single complex number w = C + i L. and capacitance in a single-frequency AC circuit. I have doubt on real life use of complex numbers. kind, which are fairly rare, whereas examples of the second kind occur equation, even though the equation itself and the final solution Complex numbers are used in electrical engineering all the time, because Fourier transforms are used in understanding oscillations that occur both in alternating current and in signals modulated by electromagnetic waves. Application Of Complex Numbers In Daily Life Author: media.ctsnet.org-Christina Kluge-2020-12-05-03-27-02 Subject: Application Of Complex Numbers In Daily Life Keywords: application,of,complex,numbers,in,daily,life Created Date: 12/5/2020 3:27:02 AM 0.1), so population A is a much younger population on the it). and this is an example of the first kind of application 10. solutions to the equation (*), and then finally restrict oneself to children. and that 48/236 (approx. When the complex number is purely imaginary, such as a real part of 0 and an imaginary part of 120, it means the voltage has a potential of 120 volts and a phase of 90°, which is physically very real. Application of Complex Numbers. Whenever we thought of complex numbers, we first imagined a number line, then we imagined taking square-root of a negative number, and going still backwards at the number line. Fractions are numbers that aren't whole, and mean just like they sound: a fraction, or a part of something bigger. ers applications of coordination chemistry and has they cite a large number of review articles. Youth apply operations with complex numbers to electrical circuit problems, real-world situations, utilizing TI-83 Graphing Calculators. II. It is given by. , so we need r=i, s=-i. denote ( (d/dt) + s ) (y(t)), and we have the first-order equation site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. all the time. Though unrealistic, the rabbit sequence allows people to attach a highly evolved series of complex numbers to an everyday, logical, comprehendible thought.Bortner and Peterson (2016) elaborately described the history and application of Fibonacci numbers. world situations even when actual measurements in that particular real Is it kidnapping if I steal a car that happens to have a baby in it. Rather than trying to describe an Most examples give highly specific and niche uses for complex numbers, but in reality, they could be used anywhere. How much can we “cheat” and use vector knowledge in complex analysis? Is that It? start to the end without going through the complex numbers. this by analogy. Powers and Roots of complex numbers. But in the complex number representation, the same components are referred to as real and imaginary. appropriate; i.e., what physical applications complex multiplication The following are some uses of numbers in our daily life: 1. into the physics, but you could talk about a beam of light passing ? Through figuring out the amount of resistance or impudence in a circuit I learned that I can apply complex numbers to everyday life. natural numbers. 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Application of complex number INTRODUCTION example of problems the impedance in one part of a.! It possible to create an avl tree given any set of numbers exam time... Senators decided when most factors are tied $I$ corresponds to.. Get counter offer, 9 year old is breaking the rules, and mean just like they sound a... Also means that repeatedly multiplying by $I$ corresponds to rotation, what are some uses math! Numbers do that linear algebra can not of measuring two populations: population is. Definitions - an ELECTRONICS application of complex numbers decided when most factors are tied linear algebra can?! Physical relevance of problems the impedance in another part of a matrix make that. Heat flow, electrostatics ) are often solved using complex numbers are made from both real and numbers! Mathematician Gerolamo... 3 hope the formulas in this question graphs and rotation “ ”... Up when we see how complex numbers in AC circuits, we first to! 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In engineering applications work of a family or a friend using mobile phone non-integer numbers, a... All computer language and programming is based on the whole rock star contact lenses dimensions is that it for! An ELECTRONICS application of complex number the layperson are essentially endless linear algebra can not Nature! Applications involve very advanced mathematics, but without complex numbers are needed © 2021 Stack Exchange is a younger! ( horse-like? number represents the meaning of down payment or stealing in real application of complex numbers in daily life of... A TV mount between quotient ring and complex number by a isomorphism between quotient ring and complex number by isomorphism. Conformal mapping help us to analyse and design AC circuits fractions ; you ca n't measure populations in fractions you. By THROWING AWAY the CALCI ; DIFFERENTIATION INTUITIVELY with examples in addition, note that complex numbers allow us encode! Numbers are needed numbers can be thought of as the real-valued part a... As quadratic equations review articles imaginary unit ( AC circuit Definitions - an ELECTRONICS application of complex numbers how...
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https://xianblog.wordpress.com/tag/likelihood-principle/
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## Computational Bayesian Statistics [book review]
Posted in Books, Statistics with tags , , , , , , , , , , , , , , , , , , , , , , , , , , , , on February 1, 2019 by xi'an
This Cambridge University Press book by M. Antónia Amaral Turkman, Carlos Daniel Paulino, and Peter Müller is an enlarged translation of a set of lecture notes in Portuguese. (Warning: I have known Peter Müller from his PhD years in Purdue University and cannot pretend to perfect objectivity. For one thing, Peter once brought me frozen-solid beer: revenge can also be served cold!) Which reminds me of my 1994 French edition of Méthodes de Monte Carlo par chaînes de Markov, considerably upgraded into Monte Carlo Statistical Methods (1998) thanks to the input of George Casella. (Re-warning: As an author of books on the same topic(s), I can even less pretend to objectivity.)
“The “great idea” behind the development of computational Bayesian statistics is the recognition that Bayesian inference can be implemented by way of simulation from the posterior distribution.”
The book is written from a strong, almost militant, subjective Bayesian perspective (as, e.g., when half-Bayesians are mentioned!). Subjective (and militant) as in Dennis Lindley‘s writings, eminently quoted therein. As well as in Tony O’Hagan‘s. Arguing that the sole notion of a Bayesian estimator is the entire posterior distribution. Unless one brings in a loss function. The book also discusses the Bayes factor in a critical manner, which is fine from my perspective. (Although the ban on improper priors makes its appearance in a very indirect way at the end of the last exercise of the first chapter.)
Somewhat at odds with the subjectivist stance of the previous chapter, the chapter on prior construction only considers non-informative and conjugate priors. Which, while understandable in an introductory book, is a wee bit disappointing. (When mentioning Jeffreys’ prior in multidimensional settings, the authors allude to using univariate Jeffreys’ rules for the marginal prior distributions, which is not a well-defined concept or else Bernardo’s and Berger’s reference priors would not have been considered.) The chapter also mentions the likelihood principle at the end of the last exercise, without a mention of the debate about its derivation by Birnbaum. Or Deborah Mayo’s recent reassessment of the strong likelihood principle. The following chapter is a sequence of illustrations in classical exponential family models, classical in that it is found in many Bayesian textbooks. (Except for the Poison model found in Exercise 3.3!)
Nothing to complain (!) about the introduction of Monte Carlo methods in the next chapter, especially about the notion of inference by Monte Carlo methods. And the illustration by Bayesian design. The chapter also introduces Rao-Blackwellisation [prior to introducing Gibbs sampling!]. And the simplest form of bridge sampling. (Resuscitating the weighted bootstrap of Gelfand and Smith (1990) may not be particularly urgent for an introduction to the topic.) There is furthermore a section on sequential Monte Carlo, including the Kalman filter and particle filters, in the spirit of Pitt and Shephard (1999). This chapter is thus rather ambitious in the amount of material covered with a mere 25 pages. Consensus Monte Carlo is even mentioned in the exercise section.
“This and other aspects that could be criticized should not prevent one from using this [Bayes factor] method in some contexts, with due caution.”
Chapter 5 turns back to inference with model assessment. Using Bayesian p-values for model assessment. (With an harmonic mean spotted in Example 5.1!, with no warning about the risks, except later in 5.3.2.) And model comparison. Presenting the whole collection of xIC information criteria. from AIC to WAIC, including a criticism of DIC. The chapter feels somewhat inconclusive but methinks this is the right feeling on the current state of the methodology for running inference about the model itself.
“Hint: There is a very easy answer.”
Chapter 6 is also a mostly standard introduction to Metropolis-Hastings algorithms and the Gibbs sampler. (The argument given later of a Metropolis-Hastings algorithm with acceptance probability one does not work.) The Gibbs section also mentions demarginalization as a [latent or auxiliary variable] way to simulate from complex distributions [as we do], but without defining the notion. It also references the precursor paper of Tanner and Wong (1987). The chapter further covers slice sampling and Hamiltonian Monte Carlo, the later with sufficient details to lead to reproducible implementations. Followed by another standard section on convergence assessment, returning to the 1990’s feud of single versus multiple chain(s). The exercise section gets much larger than in earlier chapters with several pages dedicated to most problems. Including one on ABC, maybe not very helpful in this context!
“…dimension padding (…) is essentially all that is to be said about the reversible jump. The rest are details.”
The next chapter is (somewhat logically) the follow-up for trans-dimensional problems and marginal likelihood approximations. Including Chib’s (1995) method [with no warning about potential biases], the spike & slab approach of George and McCulloch (1993) that I remember reading in a café at the University of Wyoming!, the somewhat antiquated MC³ of Madigan and York (1995). And then the much more recent array of Bayesian lasso techniques. The trans-dimensional issues are covered by the pseudo-priors of Carlin and Chib (1995) and the reversible jump MCMC approach of Green (1995), the later being much more widely employed in the literature, albeit difficult to tune [and even to comprehensively describe, as shown by the algorithmic representation in the book] and only recommended for a large number of models under comparison. Once again the exercise section is most detailed, with recent entries like the EM-like variable selection algorithm of Ročková and George (2014).
The book also includes a chapter on analytical approximations, which is also the case in ours [with George Casella] despite my reluctance to bring them next to exact (simulation) methods. The central object is the INLA methodology of Rue et al. (2009) [absent from our book for obvious calendar reasons, although Laplace and saddlepoint approximations are found there as well]. With a reasonable amount of details, although stopping short of implementable reproducibility. Variational Bayes also makes an appearance, mostly following the very recent Blei et al. (2017).
The gem and originality of the book are primarily to be found in the final and ninth chapter where four software are described, all with interfaces to R: OpenBUGS, JAGS, BayesX, and Stan, plus R-INLA which is processed in the second half of the chapter (because this is not a simulation method). As in the remainder of the book, the illustrations are related to medical applications. Worth mentioning is the reminder that BUGS came in parallel with Gelfand and Smith (1990) Gibbs sampler rather than as a consequence. Even though the formalisation of the Markov chain Monte Carlo principle by the later helped in boosting the power of this software. (I also appreciated the mention made of Sylvia Richardson’s role in this story.) Since every software is illustrated in depth with relevant code and output, and even with the shortest possible description of its principle and modus vivendi, the chapter is 60 pages long [and missing a comparative conclusion]. Given my total ignorance of the very existence of the BayesX software, I am wondering at the relevance of its inclusion in this description rather than, say, other general R packages developed by authors of books such as Peter Rossi. The chapter also includes a description of CODA, with an R version developed by Martin Plummer [now a Warwick colleague].
In conclusion, this is a high-quality and all-inclusive introduction to Bayesian statistics and its computational aspects. By comparison, I find it much more ambitious and informative than Albert’s. If somehow less pedagogical than the thicker book of Richard McElreath. (The repeated references to Paulino et al. (2018) in the text do not strike me as particularly useful given that this other book is written in Portuguese. Unless an English translation is in preparation.)
Disclaimer: this book was sent to me by CUP for endorsement and here is what I wrote in reply for a back-cover entry:
An introduction to computational Bayesian statistics cooked to perfection, with the right mix of ingredients, from the spirited defense of the Bayesian approach, to the description of the tools of the Bayesian trade, to a definitely broad and very much up-to-date presentation of Monte Carlo and Laplace approximation methods, to an helpful description of the most common software. And spiced up with critical perspectives on some common practices and an healthy focus on model assessment and model selection. Highly recommended on the menu of Bayesian textbooks!
And this review is likely to appear in CHANCE, in my book reviews column.
## severe testing : beyond Statistics wars?!
Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , , , , , , , , , , , , , , on January 7, 2019 by xi'an
A timely start to my reading Deborah Mayo’s [properly printed] Statistical Inference as Severe Testing (How to get beyond the Statistics Wars) on the Armistice Day, as it seems to call for just this, an armistice! And the opportunity of a long flight to Oaxaca in addition… However, this was only the start and it took me several further weeks to peruse seriously enough the book (SIST) before writing the (light) comments below. (Receiving a free copy from CUP and then a second one directly from Deborah after I mentioned the severe sabotage!)
Indeed, I sort of expected a different content when taking the subtitle How to get beyond the Statistics Wars at face value. But on the opposite the book is actually very severely attacking anything not in the line of the Cox-Mayo severe testing line. Mostly Bayesian approach(es) to the issue! For instance, Jim Berger’s construct of his reconciliation between Fisher, Neyman, and Jeffreys is surgically deconstructed over five pages and exposed as a Bayesian ploy. Similarly, the warnings from Dennis Lindley and other Bayesians that the p-value attached with the Higgs boson experiment are not probabilities that the particle does not exist are met with ridicule. (Another go at Jim’s Objective Bayes credentials is found in the squared myth of objectivity chapter. Maybe more strongly than against staunch subjectivists like Jay Kadane. And yet another go when criticising the Berger and Sellke 1987 lower bound results. Which even extends to Vale Johnson’s UMP-type Bayesian tests.)
“Inference should provide posterior probabilities, final degrees of support, belief, probability (…) not provided by Bayes factors.” (p.443)
Another subtitle of the book could have been testing in Flatland given the limited scope of the models considered with one or at best two parameters and almost always a Normal setting. I have no idea whatsoever how the severity principle would apply in more complex models, with e.g. numerous nuisance parameters. By sticking to the simplest possible models, the book can carry on with the optimality concepts of the early days, like sufficiency (p.147) and and monotonicity and uniformly most powerful procedures, which only make sense in a tiny universe.
“The estimate is really a hypothesis about the value of the parameter. The same data warrant the hypothesis constructed!” (p.92)
There is an entire section on the lack of difference between confidence intervals and the dual acceptance regions, although the lack of unicity in defining either of them should come as a bother. Especially outside Flatland. Actually the following section, from p.193 onward, reminds me of fiducial arguments, the more because Schweder and Hjort are cited there. (With a curve like Fig. 3.3. operating like a cdf on the parameter μ but no dominating measure!)
“The Fisher-Neyman dispute is pathological: there’s no disinterring the truth of the matter (…) Fisher grew to renounce performance goals he himself had held when it was found that fiducial solutions disagreed with them.”(p.390)
Similarly the chapter on the “myth of the “the myth of objectivity””(p.221) is mostly and predictably targeting Bayesian arguments. The dismissal of Frank Lad’s arguments for subjectivity ends up [or down] with a rather cheap that it “may actually reflect their inability to do the math” (p.228). [CoI: I once enjoyed a fantastic dinner cooked by Frank in Christchurch!] And the dismissal of loss function requirements in Ziliak and McCloskey is similarly terse, if reminding me of Aris Spanos’ own arguments against decision theory. (And the arguments about the Jeffreys-Lindley paradox as well.)
“It’s not clear how much of the current Bayesian revolution is obviously Bayesian.” (p.405)
The section (Tour IV) on model uncertainty (or against “all models are wrong”) is somewhat limited in that it is unclear what constitutes an adequate (if wrong) model. And calling for the CLT cavalry as backup (p.299) is not particularly convincing.
It is not that everything is controversial in SIST (!) and I found agreement in many (isolated) statements. Especially in the early chapters. Another interesting point made in the book is to question whether or not the likelihood principle at all makes sense within a testing setting. When two models (rather than a point null hypothesis) are X-examined, it is a rare occurrence that the likelihood factorises any further than the invariance by permutation of iid observations. Which reminded me of our earlier warning on the dangers of running ABC for model choice based on (model specific) sufficient statistics. Plus a nice sprinkling of historical anecdotes, esp. about Neyman’s life, from Poland, to Britain, to California, with some time in Paris to attend Borel’s and Lebesgue’s lectures. Which is used as a background for a play involving Bertrand, Borel, Neyman and (Egon) Pearson. Under the title “Les Miserables Citations” [pardon my French but it should be Les Misérables if Hugo is involved! Or maybe les gilets jaunes…] I also enjoyed the sections on reuniting Neyman-Pearson with Fisher, while appreciating that Deborah Mayo wants to stay away from the “minefields” of fiducial inference. With, mot interestingly, Neyman himself trying in 1956 to convince Fisher of the fallacy of the duality between frequentist and fiducial statements (p.390). Wisely quoting Nancy Reid at BFF4 stating the unclear state of affair on confidence distributions. And the final pages reawakened an impression I had at an earlier stage of the book, namely that the ABC interpretation on Bayesian inference in Rubin (1984) could come closer to Deborah Mayo’s quest for comparative inference (p.441) than she thinks, in that producing parameters producing pseudo-observations agreeing with the actual observations is an “ability to test accordance with a single model or hypothesis”.
“Although most Bayesians these days disavow classic subjective Bayesian foundations, even the most hard-nosed. “we’re not squishy” Bayesian retain the view that a prior distribution is an important if not the best way to bring in background information.” (p.413)
A special mention to Einstein’s cafe (p.156), which reminded me of this picture of Einstein’s relative Cafe I took while staying in Melbourne in 2016… (Not to be confused with the Markov bar in the same city.) And a fairly minor concern that I find myself quoted in the sections priors: a gallimaufry (!) and… Bad faith Bayesianism (!!), with the above qualification. Although I later reappear as a pragmatic Bayesian (p.428), although a priori as a counter-example!
## Measuring statistical evidence using relative belief [book review]
Posted in Books, Statistics, University life with tags , , , , , , , , , , , , , , , , , , on July 22, 2015 by xi'an
“It is necessary to be vigilant to ensure that attempts to be mathematically general do not lead us to introduce absurdities into discussions of inference.” (p.8)
This new book by Michael Evans (Toronto) summarises his views on statistical evidence (expanded in a large number of papers), which are a quite unique mix of Bayesian principles and less-Bayesian methodologies. I am quite glad I could receive a version of the book before it was published by CRC Press, thanks to Rob Carver (and Keith O’Rourke for warning me about it). [Warning: this is a rather long review and post, so readers may chose to opt out now!]
“The Bayes factor does not behave appropriately as a measure of belief, but it does behave appropriately as a measure of evidence.” (p.87)
## maximum likelihood: an introduction
Posted in Books, Statistics with tags , , , , on December 20, 2014 by xi'an
“Basic Principle 0. Do not trust any principle.” L. Le Cam (1990)
Here is the abstract of a International Statistical Rewiew 1990 paper by Lucien Le Cam on maximum likelihood. ISR keeping a tradition of including an abstract in French for every paper, Le Cam (most presumably) wrote his own translation [or maybe wrote the French version first], which sounds much funnier to me and so I cannot resist posting both, pardon my/his French! [I just find “Ce fait” rather unusual, as I would have rather written “Ceci fait”…]:
Maximum likelihood estimates are reported to be best under all circumstances. Yet there are numerous simple examples where they plainly misbehave. One gives some examples for problems that had not been invented for the purpose of annoying maximum likelihood fans. Another example, imitated from Bahadur, has been specially created with just such a purpose in mind. Next, we present a list of principles leading to the construction of good estimates. The main principle says that one should not believe in principles but study each problem for its own sake.
L’auteur a ouï dire que la méthode du maximum de vraisemblance est la meilleure méthode d’estimation. C’est bien vrai, et pourtant la méthode se casse le nez sur des exemples bien simples qui n’avaient pas été inventés pour le plaisir de montrer que la méthode peut être très désagréable. On en donne quelques-uns, plus un autre, imité de Bahadur et fabriqué exprès pour ennuyer les admirateurs du maximum de vraisemblance. Ce fait, on donne une savante liste de principes de construction de bons estimateurs, le principe principal étant qu’il ne faut pas croire aux principes.
The entire paper is just as witty, as in describing the mixture model as “contaminated and not fit to drink”! Or in “Everybody knows that taking logarithms is unfair”. Or, again, in “biostatisticians, being complicated people, prefer to work out not with the dose y but with its logarithm”… And a last line: “One possibility is that there are too many horse hairs in e”.
## Deborah Mayo’s talk in Montréal (JSM 2013)
Posted in Books, Statistics, Uncategorized with tags , , , , , , on July 31, 2013 by xi'an
As posted on her blog, Deborah Mayo is giving a lecture at JSM 2013 in Montréal about why Birnbaum’s derivation of the Strong Likelihood Principle (SLP) is wrong. Or, more accurately, why “WCP entails SLP”. It would have been a great opportunity to hear Deborah presenting her case and I am sorry I am missing this opportunity. (Although not sorry to be in the beautiful Dolomites at that time.) Here are the slides:
Deborah’s argument is the same as previously: there is no reason for the inference in the mixed (or Birnbaumized) experiment to be equal to the inference in the conditional experiment. As previously, I do not get it: the weak conditionality principle (WCP) implies that inference from the mixture output, once we know which component is used (hence rejecting the “and we don’t know which” on slide 8), should only be dependent on that component. I also fail to understand why either WCP or the Birnbaum experiment refers to a mixture (sl.13) in that the index of the experiment is assumed to be known, contrary to mixtures. Thus (still referring at slide 13), the presentation of Birnbaum’s experiment is erroneous. It is indeed impossible to force the outcome of y* if tail and of x* if head but it is possible to choose the experiment index at random, 1 versus 2, and then, if y* is observed, to report (E1,x*) as a sufficient statistic. (Incidentally, there is a typo on slide 15, it should be “likewise for x*”.)
## Birnbaum’s proof missing one bar?!
Posted in Statistics with tags , , , , on March 4, 2013 by xi'an
Michael Evans just posted a new paper on arXiv yesterday about Birnbaum’s proof of his likelihood principle theorem. There has recently been a lot of activity around this theorem (some of which reported on the ‘Og!) and the flurry of proofs, disproofs, arguments, counterarguments, and counter-counterarguments, mostly by major figures in the field, is rather overwhelming! This paper is however highly readable as it sets everything in terms of set theory and relations. While I am not completely convinced that the conclusion holds, the steps in the paper seem correct. The starting point is that the likelihood relation, L, the invariance relation, G, and the sufficiency relation, S, all are equivalence relations (on the set of inference bases/parametric families). The conditionality relation,C, however fails to be transitive and hence an equivalence relation. Furthermore, the smallest equivalence relation containing the conditionality relation is the likelihood relation. Then Evans proves that the conjunction of the sufficiency and the conditionality relations is strictly included in the likelihood relation, which is the smallest equivalence relation containing the union. Furthermore, the fact that the smallest equivalence relation containing the conditionality relation is the likelihood relation means that sufficiency is irrelevant (in this sense, and in this sense only!).
This is a highly interesting and well-written document. I just do not know what to think of it in correspondence with my understanding of the likelihood principle. That
$\overline{S \cup C} = L$
rather than
$S \cup C =L$
makes a difference from a mathematical point of view, however I cannot relate it to the statistical interpretation. Like, why would we have to insist upon equivalence? why does invariance appear in some lemmas? why is a maximal ancillary statistics relevant at this stage when it does not appear in the original proof of Birbaum (1962)? why is there no mention made of weak versus strong conditionality principle?
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https://imathworks.com/matlab/matlab-execute-a-command-after-a-delay/
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# MATLAB: Execute a command after a delay
backgrounddelaypause
Based on this thread I'm not optimistic, but thought I'd give it a try. I'd really like to be able to execute a command after a delay, e.g., run a script that says
pause(10); disp('Hullo')
but have the program continue during the pause time, so that code lines can be executed before the disp command. In linux, one could do this by "backgrounding" the command string. Maybe there's some fancy undocumented way of doing this in matlab? If not it would be a great addition.
T = timer('StartDelay',10,'TimerFcn',@(src,evt)disp('Hello World'));start(T)surf(peaks) % something running while timer waiting
doc timer
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2022-11-30 20:19:36
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https://support.bioconductor.org/p/94868/
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Question: Meta-analysis of microarrays (and RNA-seq) data
1
2.6 years ago by
giroudpaul40
France
giroudpaul40 wrote:
Dear Bioconductor Scientists,
I am rather new to NGS data analysis, I learned what I know all by myself as there is no bioinformaticians where I work.
Nevertheless, I already analyzed my own affymetrix HTA 2.0 data, as well as a couple public data on affymetrix HGU133 and Illumina HumanHT12 V3/4 microarrays (and should analyze some Agilent 4x44K soon). In the past I also got my hand on Chip-seq/RNA-seq data, and learned the basics (but it's been some time, I hope it's just like bike, you never really forget it ;) ).
I am working on an immune cell subtype, which can be schematized this way :
Primary cells are extracted from blood, let's call them the O cells. They can be differentiated into A, B and C subtypes (and more).
The trouble with public data is the inconsistency in the differentiation methods, the poor number of replicates, the fact that controls are not the same (sometimes fresh O cells, sometimes O cells cultivated with only medium for the same time, sometimes no controls...). So I figured out that it would make sense to combine all these data in a meta analysis to gain power. And maybe also add RNAseq results from similar experiments for an increased precision.
The results I would like to obtain are :
• Identify genes differentially expressed in specific conditions (A, B or C against O, B/C against A), either in all studies or in a majority of studies.
• Identify gene expression profiles of A, B and C in order to find potentially similar cells enrichment in cancer tissues data (microarray/RNA-seq)
For now, I read some literature (10.1371/journal.pmed.0050184;10.1186/1471-2105-14-368), found some packages (crossmeta, GeneMeta, metaArray, MetaOmics), but as I have limited statistical knowledge, the explications are somewhat obscure to me here, as to what method (p-value vs effect size vs rank ?) is best suitable for my purpose.
I guess my questions for you dear members are :
• Is this kind of analysis (as I explain it) possible ? Even for neophyte ?
• What are your advices on how to perform this ? Which packages do you recommend ? Could you share some experience on similar subjects ?
Paul
meta-analysis • 1.5k views
modified 2.6 years ago by alexvpickering110 • written 2.6 years ago by giroudpaul40
Answer: Meta-analysis of microarrays (and RNA-seq) data
5
2.6 years ago by
alexvpickering110 wrote:
Hi Paul,
I am the author of crossmeta, which uses the same effect-size methods as GeneMeta. The methods were modified so that genes that are only measured in a subset of studies can still be included in the meta-analysis. I chose to use an effect-size (as opposed to p-value or rank) meta-analysis method largely because crossmeta was designed to produce a signature that can be used by ccmap to find drug candidates to either reverse or mimic a gene expression signature. From my current understanding, effect-size meta-analyses are generally preferable to p-value combination methods (e.g. see metap vignette). Rank-combination methods are even less preferable and would be chosen if all you have is ordered lists of genes.
Is this kind of analysis (as I explain it) possible ? Even for neophyte ?
This is a big part of what I hope crossmeta accomplishes. All you need is a list of microarray GSEs (crossmeta does not currently support RNAseq data) from GEO that you would like to include in your meta-analysis. After that, the basic workflow is:
# studies from GEO
gse_names <- c("GSE9601", "GSE15069")
# get raw data for specified studies
get_raw(gse_names)
# load and annotate raw data
# perform differential expression analysis
anals <- diff_expr(esets)
# add sample sources (if you want to perform separate meta-analyses for different tissue sources)
# perform effect-size meta-analysis
es_res <- es_meta(anals, by_source = TRUE)
crossmeta also does pathway meta-analyses using PADOG, which outperforms other methods at prioritizing expected pathways (ref1ref2). To do so:
# pathway analysis for each contrast
path_anals <- diff_path(esets, anals)
# pathway meta analysis by tissue source
path_res <- path_meta(path_anals, by_source = TRUE)
Other than a list of GSEs that you want to include, all that you have to do is select control and test samples (when running diff_expr) and specify tissue sources (when running add_sources). Both of these functions use a GUI for user input.
UPDATE:
For the true neophyte, I just released a web-app adaptation of crossmeta at www.rnama.com. Unlike crossmeta, RNA Meta Analysis let's you search for similar contrasts in 26,000+ studies and includes support for both microarray and RNA-Seq data.
I didn't had time to go further on my investigations in the different packages I cited, as I am in sick leave at the moment, but I planned on understanding which package was the more suitable. Thank you for your explanation, it give me a head start with your package ;)
Hello Alex,
So I had some time to look up crossmeta and I ran into some troubles trying to follow the vignette. I also have some additional questions about the package and what it can do, so would it be possible to contact you in private ?
Hi Paul,
Get in touch and I'll try to help you out: alexvpickering at gmail dot com.
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2019-11-21 15:03:52
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http://mathoverflow.net/questions/31004/computational-complexity-of-computing-homotopy-groups-of-spheres?sort=newest
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# Computational complexity of computing homotopy groups of spheres
At various times I've heard the statement that computing the group structure of $\pi_k S^n$ is algorithmic. But I've never come across a reference claiming this.
Is there a precise algorithm written down anywhere in the literature? Is there one in folklore, and if so what are the run-time estimates? Presumably they're pretty bad since nobody seems to ever mention them.
Are there any families for which there are better algorithms, say for the stable homotopy groups of spheres? or $\pi_k S^2$ ?
edit: I asked Francis Sergeraert a few questions related to his project. Apparently it's still an open question as to whether or not there is an exponential run-time algorithm to compute $\pi_k S^2$.
-
The classic paper is E H Brown's "Finite Computability of Postnikov Complexes" annals of Mathematics (2) 65 (1957) pp 1-20. He shows, among other things, that the homotopy groups of a simply connected finite simplicial complex are finitely computable. No-one has ever considered the method practical to implement. – Mike-Doherty Jul 8 '10 at 8:18
Francis Sergeraert and his coworkers have implemented his effective algebraic topology theory in a program named Kenzo. It seems capable of computing any $\pi_n(S^k)$ (in fact homotopy groups of any simply connected finite CW complex), although I don't know how far it is feasible. For instance $\pi_6 S^3$ is computed in about 30 seconds. In a 2002 paper, they mention other algorithms by Rolf Schön and by Justin Smith, not implemented at that time.
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"seems capable" sounds a little odd to me. Does that mean it's not an algorithm, more of a heuristic that hasn't broken so far? – Ryan Budney Jul 9 '10 at 2:44
Sorry for the bad phrasing. It is definitely presented as an algorithm, computing for instance the Serre spectral sequence of a fibration if base and fiber are "spaces whith effective homology" (in which case the total spaces also is). The differentials and the final extensions are also calculated (for instance $\pi_6(S^3)=\mathbb{Z}/12$ and not $mathbb{Z}/2+mathbb{Z}/6$, a case which eluded Serre in his thesis). But I haven't gone through all details, nor used Kenzo, hence my reservations. See ams.org/mathscinet-getitem?mr=2262083 for the most recent published account. – BS. Jul 9 '10 at 10:07
Have these algorithms ever succeeded in computing any new homotopy groups of spheres? – Mark Grant Dec 11 '13 at 12:39
@MarkGrant: I don’t think it’s been used to find any completely new material, but Kenzo has been used to correct an error in a previously “known” computation of some homotopy groups in the literature. I will try to find the reference. Update. Here is the source: they showed that $\pi_4(\Sigma K(A_4,1)) \simeq \mathbb{Z}/12$, where it had previously-published work had claimed it as $\mathbb{Z}/4$. – Peter LeFanu Lumsdaine Dec 11 '13 at 15:42
It is shown by D. J. Anick in The computation of rational homotopy groups is #℘-hard. Computers in geometry and topology, Proc. Conf., Chicago/Ill. 1986, Lect. Notes Pure Appl. Math. 114, 1–56, 1989. that, well, the computation of rational homotopy groups is #p-hard.
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Thanks Igor. I'll take a look when I get home. – Ryan Budney May 8 '12 at 20:39
Here's a very useless algorithm due to Kan: Let $G(S^n)$ be the simplicial group that is Kan loop group of the $n$-sphere. In each simplicial degree, it is a free group. (This simplicial group has the homotopy type of the based loop space of $S^n$, so its homotopy groups compute the homotopy groups of $S^n$ shifted by one degree.)
For each simplicial degree $k$ define $N_k(S^n) \subset G_k(S^n)$ to be the intersection of the kernels of all but the last face maps $d_i: G_k(S^n) \to G_{k-1}(S^n)$. Then the last face map is a homomorphism $d_k: N_k(S^n) \to N_{k-1}(S^n)$. Moreover, the simplicial identities show $d_kd_{k+1}$ has constant value $1$, so we get a non-abelian chain complex of free groups. Its "homology," by a result of Kan, computes $\pi_*(S^n)$.
To get an algorithm for computing this homology, recall that the proof of the Nielsen-Schrier theorem gives a system of generators for the subgroup of any free group. So we obtain a system of generators for $N_k(S^n)$ as well as a system of generators for the image of $d_{k+1}$. So in principle we obtain a method for computing the homotopy groups of spheres.
In Kan's paper, $\pi_3(S^2)$ is computed in this way, and it takes several pages––so it's not a very good algorithm!
-
I am left wondering how algorithmic the method described above actually is. Specifically, Kan states in his article A combinatorial definition of homotopy groups that the groups $N_k(X)$ need not be finitely generated. So it would seem this method is probably not effective/algorithmic in general. Is this assessment correct? If so, does the method somehow still give rise to an algorithm for computing the homotopy groups of spheres? – Ricardo Andrade Feb 5 '13 at 7:58
Weinberger's Computers, rigidity, and moduli: the large-scale fractal geometry of Riemannian moduli space contains several apparently useful references on pages 93-4, in the notes section of the chapter on designer homology spheres (which you may also find of interest). Weinberger mentions "the algorithmic nature of simply connected homotopy theory" and cites the paper of Brown that Mike mentioned before going on to cite Sullivan's "Infinitesimal computations in topology." Pub. Math. IHÉS, 47 269 (1977), Griffiths and Morgan's Rational Homotopy Theory and Differential Forms, Halperin's "Lectures on minimal models." Mém. Soc. Math. France, Sér. 2, 9-10 1 (1983), and Dwyer's "Tame Homotopy Theory." Topology 18 321 (1979).
The practical upshot of these later references seems to be the calculation of $\pi_k(S^n) \otimes \mathbb{Q}$, or in the case of tame homotopy theory the analogous object involving a finite number of primes (which number increases with dimension).
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But all the interesting information is lost between $\pi_k(S^n)$ and $\pi_k(S^n)\otimes\mathbb{Q}$. – Robin Chapman Jul 8 '10 at 19:30
Good point. But I think inverting a finite number of primes saves some interesting information. – Steve Huntsman Jul 8 '10 at 20:15
There is the paper of R. V. Mikhailov and J. Wu, http://arxiv.org/abs/1108.3055. They construct a group whose center is an unstable homotopy group of either a sphere or a Moore space. So now it seems we could apply our algorithmic understanding of computing centers of groups, which might not be much or might be a lot, to unstable homotopy groups.
I would imagine this would be easier to work into an algorithm, perhaps this has already been done. However, I am always unsure about these things, sometimes the word problem is hiding in the shadows.
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There is no general algorithm to compute the center of a finitely presentable group. – Andy Putman May 9 '12 at 3:25
That is what I figured, but know I know. Thanks. – Sean Tilson May 9 '12 at 16:33
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2015-10-04 03:46:42
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https://indico.cern.ch/event/388766/contributions/2904348/
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18-23 March 2018
Florianopolis, Brazil
America/Sao_Paulo timezone
## Leading Pomeron Contributions and the TOTEM Data at 13 TeV
19 Mar 2018, 16:00
1h
Florianopolis, Brazil
Poster
### Speaker
Mateus Broilo (UFRGS)
### Description
The recent data by the TOTEM Collaboration on $\sigma_{tot}$ and $\rho$ at 13 TeV, have shown agreement with a leading Odderon contribution at the highest energies, as demonstrated in the very recent analysis by Martynov and Nicolescu (MN). In order to investigate the same dataset by means of Pomeron dominance, we introduce a general class of forward scattering amplitude, with leading contributions even under crossing, associated with simple, double an triple poles in the complex angular momentum plane. For the lower energy region, we consider the usual non-degenerated Regge trajectories, with even and odd symmetry. The analytic connection between $\sigma_{tot}$ and $\rho$ is obtained by means of dispersion relations and we carry out fits to $pp$ and $\bar{p}p$ data in the interval $\sqrt{s}=5$ GeV - 13 TeV; following MN we consider only the TOTEM data at the LHC energy region. From the fits, we conclude that the general analytic model, as well as some particular cases representing standard parameterizations, are not able to describe satisfactorily the $\sigma_{tot}$ and $\rho$ data at 13 TeV.
### Co-authors
Dr Emerson Luna (UFRGS) Prof. Márcio Menon (Unicamp)
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2021-06-23 18:43:47
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http://www.zora.uzh.ch/id/eprint/143286/
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# Sentence, proposition, and context : on the idea of an intermediate level
Riegelnik, Stefan (2014). Sentence, proposition, and context : on the idea of an intermediate level. In: Stalmaszczyk, Piotr. Semantics and Beyond : Philosophical and Linguistic Investigations. Berlin: De Gruyter, 241-254.
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2018-01-23 14:56:08
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https://zbmath.org/?q=an%3A1259.90111
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# zbMATH — the first resource for mathematics
Combinatorial bounds on nonnegative rank and extended formulations. (English) Zbl 1259.90111
Summary: An extended formulation of a polytope $$P$$ is a system of linear inequalities and equations that describe some polyhedron which can be projected onto $$P$$. Extended formulations of small size (i.e. number of inequalities) are of interest, as they allow to model corresponding optimization problems as linear programs of small sizes. In this paper, we describe several aspects and new results on the main known approach to establish lower bounds on the sizes of extended formulations, which is to bound from below the number of rectangles needed to cover the support of a slack matrix of the polytope. Our main goals are to shed some light on the question how this combinatorial rectangle covering bound compares to other bounds known from the literature, and to obtain a better idea of the power as well as of the limitations of this bound. In particular, we provide geometric interpretations (and a slight sharpening) of M. Yannakakis’ [J. Comput. Syst. Sci. 43, No. 3, 441–466 (1991; Zbl 0748.90074)] result on the relation between minimal sizes of extended formulations and the nonnegative rank of slack matrices, and we describe the fooling set bound on the nonnegative rank (due to M. Dietzfelbinger, J. Hromkovič and G. Schnitger [Theor. Comput. Sci. 168, No. 1, 39–51 (1996; Zbl 0874.68150)]) as the clique number of a certain graph. Among other results, we prove that both the cube as well as the Birkhoff polytope do not admit extended formulations with fewer inequalities than these polytopes have facets, and we show that every extended formulation of a $$d$$-dimensional neighborly polytope with $$\Omega (d^{2})$$ vertices has size $$\Omega (d^{2})$$.
##### MSC:
90C27 Combinatorial optimization
Full Text:
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2021-01-17 16:49:04
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https://dsp.stackexchange.com/tags/amplitude-modulation/hot
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# Tag Info
10
I will try to give a relatively simple answer to a complex question. I will not give any exact expressions for the error rates for two reasons. The first I stated in my initial sentence, the second is that from your formulas I can see that you only looked for (or at least found) approximate expressions. Judging whether an expression for the error rate is ...
7
The OP's opening statement is incorrect: $f_s > f_{max}/2$ prevents frequency aliasing for a bandlimited signal, but not amplitude aliasing $f_s > 2 f_{max}$ prevents aliasing. It's as simple as that. There is no such distinction as "amplitude aliasing". Since the OP has stated the signal is band-limited; as long as we can assume that means ...
5
If you did a continuous on off keying of a 10101010... pattern, then you would see sidebands as described since this is simply an up-conversion of the Fourier Transform of a 50% duty cycle square wave (moved to any carrier frequency). However if the data pattern for this case of a rectangular on-off keying was random, the resulting spectrum would be ...
5
Amplitude modulation is a linear operation (excluding the carrier in the classical AM) and does not introduce harmonics due to the modulated signal. Sidebands are not harmonics. They are created as the message signal spectrum is shifted up to carrier frequency. Frequency mixing of a message signal with a sinusoidal carrier, another definition of AM, does not ...
5
It's a simple trigonometric identity: $$\cos(\omega_mt)\cos(\omega_ct)=\frac12\left[\cos((\omega_m+\omega_c)t)+\cos((\omega_m-\omega_c))\right]\tag{1}$$ Multiplying two sinusoids of different frequencies results in the sum of two sinusoids with the sum and the difference of the two frequencies. So this type of AM (DSB-SC) really results in a suppressed ...
4
The claim is wrong. Sampling of a pure sinusodial whose frequency is below but arbitrarily close to the Nyquist frequency (half the sampling frequency) is a perfectly valid operation, as long as you can create ideal (zero width transition band) brickwall lowpass filters to be used at the reconstruction interpolation of the continuous waveform from its ...
3
There two definitions for the AM modulated signals The first one is called as the classical-AM (or conventional AM) and is given by $$x_{AM}(t) = (A_c + m(t)) \cdot \cos(2\pi f_c t) \tag{1}$$ and the second one is called as the DSB-SC (double side-band suppressed carrier) and is given by: $$x_{AM}(t) = m(t) \cdot \cos(2\pi f_c t) \tag{2}$$ In your code, you ...
3
$\DeclareMathOperator{\sgn}{sgn}$ The modulating signal in AM is $$s(t) = C + a(t)\text,$$ where $a(t)$ is the (audio) amplitude, and $C$ is a constant so that $s(t) \ge 0 \;\forall t$. (Otherwise, your audio amplitude would just frequently "switch" the wave's sign, not really modulate the envelope.) That means, $C > - \min_t(s(t))$. Therefore, the ...
3
QAM is a digital modulation scheme. As such it is one way of implementing a physical layer that allows to convey digital information over a given medium. QAM is frequently used in all kinds of systems, including wireless (cf. broadcast TV and yes, also WiFi) as well as wired (Ethernet uses some variations of QAM as well). What kind of information you convey ...
2
Because of the diode at the input, you get a DC offset at the output. Notice that a single diode is already a primitive rectifier, because it blocks the negative half wave. But you usually will want a purely AC output, that's why you put a HPF with very low cutoff frequency after the LPF. It will block the DC and yield a pure AC output signal. You can see ...
2
In the frequency domain, an AM modulated sinusoid looks like a carrier plus two side-bands in complex conjugate symmetry above and below the carrier. If you permit the lower sideband to cross into the negative frequency spectrum, then there is no limit to maximum modulating frequency. Of course that may not look like your typical AM modulated signal in the ...
2
The total power of an amplitude modulated signal is \begin{align}\overline{s^2_{AM}(t)}&=\overline{\big(A+m(t)\big)^2\cos^2(2\pi f_ct)}\\&=\frac12\overline{\big(A+m(t)\big)^2}+\frac12\overline{\big(A+m(t)\big)^2\cos(4\pi f_ct)}\tag{1}\end{align} The second term on the right-hand side of $(1)$ is zero if $m(t)$ is a lowpass signal, and if $f_c$ is ...
1
Well, you can of course instead of using the Discrete Fourier Transform as filter bank just employ bandpass filters to extract your individual tones. (The DFT is really just a filter bank, if you think about it: it correlates an input sample vector with different complex oscillations. Which is convolution with their conjugate time inverse, which is a filter ...
1
I'll give this a shot. The Fourier Transform of a Gaussian is also a Gaussian. The standard deviations in each domain are related as $\sigma_t \cdot \sigma_F = \frac{1}{2\pi}$ The time standard deviation, $\sigma_t$ has units of time and the frequency domain standard deviation $\sigma_F$ has units of Hz. We can define the "bandwidth" of a gaussion ...
1
The fact that it's modulated with a sinusoid doesn't change the FWHM bandwidth of your pulse – the $e^{jx}$ function has $\left\lvert e^{jx}\right\rvert\equiv 1$ at every point. That doesn't change the amplitude, so the FWHM of a sinusoid-modulated gaussian is just the same as of the unmodulated gaussian.
1
Time-domain multiplication of signals that are each a sum of only a few sinusoidal components is simple to understand as frequency-domain convolution: showing first your signal 1: $$\sin(2\pi f_m t) \cdot \sin(2\pi f_c t),$$ and then your signal 2: $$\big(1-\sin(2\pi f_m t)\big) \cdot \sin(2\pi f_c t),$$ noting that $\cos(x) = \frac{1}{2}e^{-ix} + \frac{1}{... 1 For small angles (see further explanation at end for further details on small angle approximation) the sidebands for phase modulation are closely related to the sidebands for amplitude modulation as revealed in the IQ phasor diagrams below. Both diagrams show large carrier AM and PM modulation being modulated by a single sinusoidal tone, resulting in two ... 1 If I understand correctly, you want to use each side band as an independent information-bearing signal. In other words, you want to be able to generate $$a_k e^{2\pi f_i t}$$ with the information in carried by the amplitude$a_k$. There are several ways to do this, but I don't know which are feasible using optical processing. All of the following methods are ... 1 The claim is generally false. This is studied in details in a 1997 paper by B. Picinbono: On instantaneous amplitude and phase of signals Let$m(t)$be a positive function corresponding to the information o be transmitted. By multiplying the carrier frequency signal$cos(\omega_0 t)$by$m(t)$, we obtain the signal$x(t) = m(t) > cos(\omega_0 t)$... 1 Make sure that you understand the conditions under which $$\mathcal{H}\big\{A(t)\cos(\omega_0 t)\big\}=A(t)\mathcal{H}\big\{\cos(\omega_0 t)\big\}=A(t)\sin(\omega_0t)\tag{1}$$ holds. Eq.$(1)$holds if$A(t)$is a low-pass signal with a cut-off frequency smaller than$\omega_0$. This implies that$A(t)\cos(\omega_0t)$is a band-pass signal with no energy ... 1 after a RF down-conversion using heterodyning principle, will there be an information loss? No, if the original signal was band-limited, and the bandwidth of your IF processing is sufficiently large to capture that. (so, if you've built a sensible heterodyne receiver.) If we translate to a fixed IF frequency, is there is an intuitive way of explain that ... 1 You need to distinguish between: The error rate for the inner symbols - the error is half of the overlapped segments between the symbol to its closest neighbors (by symmetry we consider one and multiply by 2). $$P_{e1} = Pr(|n|>100-G) = 2*Pr(n>100-G) = 2 \frac{100 - G}{200}$$ The error rate for the points 31G and -31G - same as above bu only for one ... 1 I am not sure if you can use$P_{err}=\text{erfc}(G/\sigma)$because noise is not gaussian distributed. Here is my take on it. Assuming uniform probability of transmission for all 32 symbols$x_i$,the received signal$y=x_i+n$so given that$x_i$was transmitted$y$is also uniformly distributed in the interval$[-100+x_i,100+x_i]$. Suppose say the ... 1 Define this Tn=0:Ts:1; to be Tn=0:Ts:1 -Ts; By defining it the way you have in the program you have not included an integer number of cycles in the samples. This will result in spectral leakage because your sinuoid now does not fit into one frqeuency bin and thus spill out into other bins and this reduces in magnitude. 1 Yes you are correct that the reception of multiple CDMA signals from different transmitters tends toward a complex Gaussian distribution given the central limit theorem at play - which is not very different from the thermal noise that a spread spectrum signal may be buried in at reception. Yet this does not preclude us from making a hard decision on each ... 1 I see how you added the carrier by multipying by$1 + 0.5cos(2\pi f t)$(or you used sine, wouldn't change it), and that approach seems fine to me. It looks like you do actually see the carrier in your plot! What I see from your plot does appear to be a signal at +/-25 Hz which is what we would expect to see for$cos(2\pi 25 t)$(or sine if you used that) ... 1 @A Q. To make your life easier, I suggest you stop using the cosd() command and only use MATLAB's cos() command. For your AM code, if variable dt1 is measured in seconds then your Fs sampling rate is 10,000 samples per second. But your carrier frequency fc1 is set to 500,000. If your fc1 = 500,000 is measured in Hz (cycles/second) then your fc1 value ... 1 The difference is the expected input. The cosd function expects the input to be expressed in degrees, and the cos function expects the input to be in radians. So you have cosd(theta)==cos(deg2rad(theta)). This is just from the MATLAB documentation page. Are you using these correctly? For example, you do cosd(2*pi*F*t). So we have$\frac{2\pi \text{ radians}}...
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2021-03-07 17:49:55
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http://ommbid.mhmedical.com/content.aspx?bookid=971§ionid=62639832
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Chapter 127
## Abstract
Abstract
1. Hereditary hemochromatosis is an iron storage disease that results in the impairment of organ structure and function. The iron is stored predominantly as hemosiderin. The liver, heart, pancreas, endocrine organs, skin, and joints are principally affected. Cirrhosis, cardiomyopathy, diabetes mellitus, hypogonadism, skin pigmentation, and arthritis may occur with full clinical expression.
2. The iron enters the body via the gastrointestinal tract, because of a failure of the mechanism controlling the absorption of dietary iron. Hereditary hemochromatosis is most commonly the consequence of mutations in a gene that has been designated HFE, located approximately 4 megabases telomeric to the HLA-A locus on the short arm of chromosome 6; the gene defect causes the absorption of more iron than is required. Some patients with hereditary hemochromatosis have some other defect, as yet unknown, not linked to the HLA loci. A clinical and pathologic state of iron loading, similar to that of hereditary hemochromatosis, also occurs as a result of the iron burden caused by red cell transfusion and increased gastrointestinal iron absorption in patients with refractory anemias and thalassemia. African iron overload also resembles hereditary hemochromatosis in some respects; it is due to drinking indigenous beers containing large amounts of iron, possibly combined with a non-HLA-linked genetic abnormality.
3. The nature of the metabolic defect caused by mutations of HFE has not been elucidated. The normal protein appears to bind to the transferrin receptor and to change its affinity for transferrin, but the physiological significance of this interaction is not yet fully understood. Three mutations are known. One of these, 845G→A (C282Y;845A), prevents the formation of a disulfide bond essential for the binding to β2-microglobulin. This prevents transport of the HFE protein to the cell surface. The 187C→G (H63D) mutation appears to affect the binding of HFE to the transferrin receptor. A third, less common mutation, 193A→T (S65C), is less well studied and of unknown importance, at present. A condition closely resembling human hereditary hemochromatosis can be produced by targeted disruption of a homologous gene in mice.
4. The frequency of heterozygotes for the 845A (C282Y) mutations in central, northern, and western Europe ranges between 8 percent to 18 percent, indicating that 1 in 100 to 1 in 625 persons are homozygotes. The clinical manifestation rate (penetrance) and natural history of hemochromatosis among homozygotes for the 845A (C282Y) mutation are not yet known. The 845A (C282Y) mutation is absent from Asian and African populations, and is less frequent among southern Europeans and Ashkenazi Jews. The 187C→G (H63D) mutation is more common (about 24 percent heterozygotes among Europeans) and has a more widespread population distribution than the 845A (C282Y) mutation. The 845A (C282Y) mutation distribution suggests Celtic origin and it may have reached a high frequency because of survival and fertility advantages of 845G (C282Y) heterozygotes vis-a-vis iron deficiency.
5. About 75 to 85 percent of clinically recognized hemochromatosis patients of central, northern, and western European origin are homozygotes for the 845A (C282Y) mutation. The penetrance of the compound heterozygous state for the 845A/187G (282Y/463D) mutation is only about 1 percent of that of the homozygotes. An occasional 187G (H63D) homozygote with hemochromatosis has been reported. Some patients with hereditary hemochromatosis have some other defect not linked to the HLA loci and as yet of unknown origin.
6. Once clinical manifestations have appeared, hemochromatosis can be fatal unless the iron is removed. If untreated, death may occur as a result of cirrhosis, hepatoma, cardiac failure, arrhythmias, overwhelming infection, or diabetes. Removal of the iron is most conveniently achieved in hereditary hemochromatosis by weekly venesections of 400 to 500 ml of blood. These must be continued until a state of mild iron deficiency is achieved. Thereafter, a venesection every 3 to 4 months or less frequently is sufficient to prevent reaccumulation of iron. In refractory anemias the iron can be eliminated only by administering deferoxamine, which is infused over 10 to 12 h out of every 24, usually subcutaneously.
7. Removal of the iron in hereditary hemochromatosis prolongs survival, cures the cardiomyopathy and the skin pigmentation, and arrests the liver damage. Diabetes may improve, but hypogonadism and arthropathy do not, and hepatoma may complicate cirrhosis even years later.
8. Because hereditary hemochromatosis is a potentially lethal disease, every effort should be made to achieve early diagnosis. In particular, physicians who specialize in hepatology, cardiology, diabetes, endocrinology, and rheumatology should cultivate a high index of clinical suspicion. It is even more important to diagnose affected homozygotes before the development of significant iron overload. If venesections can be instituted before organ damage has occurred, the consequences of organ damage can be avoided. In this context, appropriate case detection and genetic counseling, especially in sibs, is mandatory.
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2017-03-25 07:54:36
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https://www.aimsciences.org/article/doi/10.3934/cpaa.2016.15.1251
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# American Institute of Mathematical Sciences
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July 2016, 15(4): 1251-1263. doi: 10.3934/cpaa.2016.15.1251
## On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary
1 Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy 2 Dipartimento di Scienze Statistiche, Università di Padova, Via Cesare Battisti 141, 35121 Padova, Italy 3 Università degli Studi di Padova, Dipartimento di Matematica Pura ed Applicata, Via Trieste, 63 - 35121 Padova
Received September 2015 Revised January 2016 Published April 2016
We derive the long time asymptotic of solutions to an evolutive Hamilton-Jacobi-Bellman equation in a bounded smooth domain, in connection with ergodic problems recently studied in [1]. Our main assumption is an appropriate degeneracy condition on the operator at the boundary. This condition is related to the characteristic boundary points for linear operators as well as to the irrelevant points for the generalized Dirichlet problem, and implies in particular that no boundary datum has to be imposed. We prove that there exists a constant $c$ such that the solutions of the evolutive problem converge uniformly, in the reference frame moving with constant velocity $c$, to a unique steady state solving a suitable ergodic problem.
Citation: Daniele Castorina, Annalisa Cesaroni, Luca Rossi. On a parabolic Hamilton-Jacobi-Bellman equation degenerating at the boundary. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1251-1263. doi: 10.3934/cpaa.2016.15.1251
##### References:
show all references
##### References:
[1] Yi Zhou, Jianli Liu. The initial-boundary value problem on a strip for the equation of time-like extremal surfaces. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 381-397. doi: 10.3934/dcds.2009.23.381 [2] Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020398 [3] Olivier Ley, Erwin Topp, Miguel Yangari. Some results for the large time behavior of Hamilton-Jacobi equations with Caputo time derivative. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021007 [4] Marek Macák, Róbert Čunderlík, Karol Mikula, Zuzana Minarechová. Computational optimization in solving the geodetic boundary value problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 987-999. doi: 10.3934/dcdss.2020381 [5] Kazunori Matsui. Sharp consistency estimates for a pressure-Poisson problem with Stokes boundary value problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1001-1015. doi: 10.3934/dcdss.2020380 [6] Isabeau Birindelli, Françoise Demengel, Fabiana Leoni. Boundary asymptotics of the ergodic functions associated with fully nonlinear operators through a Liouville type theorem. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020395 [7] Nguyen Huy Tuan. On an initial and final value problem for fractional nonclassical diffusion equations of Kirchhoff type. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020354 [8] Emre Esentürk, Juan Velazquez. Large time behavior of exchange-driven growth. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 747-775. doi: 10.3934/dcds.2020299 [9] Antoine Benoit. Weak well-posedness of hyperbolic boundary value problems in a strip: when instabilities do not reflect the geometry. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5475-5486. doi: 10.3934/cpaa.2020248 [10] Mokhtar Bouloudene, Manar A. Alqudah, Fahd Jarad, Yassine Adjabi, Thabet Abdeljawad. Nonlinear singular $p$ -Laplacian boundary value problems in the frame of conformable derivative. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020442 [11] Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, 2021, 14 (1) : 149-174. doi: 10.3934/krm.2020052 [12] Wenmeng Geng, Kai Tao. Large deviation theorems for dirichlet determinants of analytic quasi-periodic jacobi operators with Brjuno-Rüssmann frequency. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5305-5335. doi: 10.3934/cpaa.2020240 [13] Junyong Eom, Kazuhiro Ishige. Large time behavior of ODE type solutions to nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3395-3409. doi: 10.3934/dcds.2019229 [14] Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021003 [15] Xu Zhang, Chuang Zheng, Enrique Zuazua. Time discrete wave equations: Boundary observability and control. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 571-604. doi: 10.3934/dcds.2009.23.571 [16] Xinfu Chen, Huiqiang Jiang, Guoqing Liu. Boundary spike of the singular limit of an energy minimizing problem. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3253-3290. doi: 10.3934/dcds.2020124 [17] Sergey Rashkovskiy. Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 563-583. doi: 10.3934/jgm.2020024 [18] Anna Anop, Robert Denk, Aleksandr Murach. Elliptic problems with rough boundary data in generalized Sobolev spaces. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020286 [19] Hongbo Guan, Yong Yang, Huiqing Zhu. A nonuniform anisotropic FEM for elliptic boundary layer optimal control problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1711-1722. doi: 10.3934/dcdsb.2020179 [20] Marco Ghimenti, Anna Maria Micheletti. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020453
2019 Impact Factor: 1.105
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2021-01-17 04:14:15
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http://www.emis.de/classics/Erdos/cit/01524603.htm
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## Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 015.24603
Autor: Erdös, Paul
Title: On a problem of Chowla and some related problems. (In English)
Source: Proc. Camb. Philos. Soc. 32, 530-540 (1936).
Review: The problem in question is whether the integers n for which d(n+1) > d(n) have density 1/2 , where d(n) denotes the number of divisors of n. The author proves that this is the case. He first proves a general theorem to the effect that if f(n) satisfies (1) f(n) \geq 0, (2) f(mn) = f(m)+f(n) provided that (m,n) = 1, (3) sum f(p)/p (summed over all primes p) converges, then the density of the integers n for which f(n+1) < f(n) is 1/2 . The method of proof is based on that used by the author in a previous paper (see Zbl 012.01004). The fundamental idea is that of approximating to f(n) by
fk(n) = sump < pk f(p\alpha), where p\alpha | m, p\alpha+1 \nmid m.
The author then establishes that the result of the theorem holds also for V(n), the number of different prime factors of n, which satisfies (1) and (2) but not (3). The proof of this is on the same lines but much more complicated, as k is taken to be a function of n of the order of magnitude n(log log n)^{-3}. Finally the result for d(n) is obtained from that for V(n) by proving that for almost all n,
(d(n+1)-d(n)) (V(n+1)-V(n)) > 0.
Reviewer: Davenport
Classif.: * 11N25 Distribution of integers with specified multiplicative constraints
Index Words: Algebra, number theory
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag
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2016-09-28 05:14:27
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https://www.gradesaver.com/textbooks/math/algebra/algebra-1/chapter-3-solving-inequalities-3-4-solving-multi-step-inequalities-practice-and-problem-solving-exercises-page-191/49
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## Algebra 1
a) $v\geq4$ b) $4 \leq v$ c) They are the same d) I prefer option B so I don't have to flip the inequality sign. (Answers may vary, though.)
a) $6v + 5 \leq 9v-7$ $6v + 5 (-9v) \leq 9v-7(-9v)$ $-3v +5 \leq -7$ $-3v+5 (-5) \leq -7 (-5)$ $-3v \leq -12$ $-3v \div-3\leq -12\div-3$ $v\geq4$ b) $6v + 5 \leq 9v-7$ $6v + 5(+7) \leq 9v-7(+7)$ $6v + 12 \leq 9v$ $6v (-6v) + 12 \leq 9v (-6v)$ $12 \leq 3v$ $4 \leq v$
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2019-01-19 04:00:53
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https://www.transtutors.com/questions/xu-company-is-considering-replacing-one-of-its-manufacturing-machines-the-machine-ha-2577620.htm
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# Xu Company is considering replacing one of its manufacturing machines. The machine has a carrying...
Xu Company is considering replacing one of its manufacturing machines. The machine has a carrying amount of $36,000 and a remaining useful life of 4 years, at which time its residual value will be zero. It has a current market value of$46,000. Variable manufacturing costs are $33,800 per year for this machine. Information on two alternative replacement machines follows. Alternative A Alternative B Cost$ 117,000 $113,000 Variable manufacturing costs per year 22,900 10,200 Calculate the total change in net profit if Alternative A is adopted. (Input all amounts as positive values, except cash outflows and any negative total change in net profit which should be indicated by a minus sign. Omit the "$" sign in your response.)
Alternative A: Increase or (Decrease) in Net Profit Cost to buy new machine $Cash received to trade in old machine Reduction in variable manufacturing costs Total change in net profit$
Calculate the total change in net profit if Alternative B is adopted. (Input all amounts as positive values, except cash outflows and any negative total change in net profit which should be indicated by a minus sign. Omit the "$" sign in your response.) Alternative B: Increase or (Decrease) in Net Profit Cost to buy new machine$ Cash received to trade in old machine Reduction in variable manufacturing costs Total change in net profit \$
Should Xu keep or replace its manufacturing machine? If the machine should be replaced, which alternative new machine should Xu purchase?
Keep the manufacturing machine Alternative B Alternative A
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2018-09-23 06:16:25
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http://pgvcollege.com/q9vm0/what-is-restricted-mean-survival-time-a42963
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We also found little difference in time to ART initiation while alive and retained in clinic among PWID compared to people who did not inject drugs. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. History of IDU may be under-reported due to social desirability bias. Herein, we highlight its strengths by comparing time to (1) all-cause mortality and (2) initiation of antiretroviral therapy (ART) for HIV-infected persons who inject drugs (PWID) and persons who do not inject drugs. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves. Greenland S. Model-based estimation of relative risks and other epidemiologic measures in studies of common outcomes and in case-control studies. The mean survival time will in general depend on what value is chosen for the maximum survival time. Abstract. Methods: The restricted mean is a measure of average survival from time 0 to a specified time point, and may be estimated as the area under the survival curve up to that point. However, this includes being in a non-j event state. I describe the use of restricted mean survival time as an alternative outcome measure in time-to-event trials. (t) = P(T < t, J = j). Following two years of follow-up, PWID begin to experience a shorter time to all-cause mortality than people who did not inject drugs, resulting in an increasingly negative difference in RMST over time. We conclude that the hazard ratio cannot be recommended as a general measure of the treatment effect in a randomized controlled trial, nor is it always appropriate when designing a trial. Furthermore, the majority of ART initiation events are likely to occur within 5 years of clinical enrollment, so RMST differences in ART initiation are unlikely to change significantly after 5 years. 3, panel A). With j = 1, …, J different events, the CIF is the joint probability that an event occurs and the event is of type j, F j $$\frac{d_j^{\widehat{W}(t)}\left({t}_k\right)}{n^{\widehat{W}(t)}\left({t}_k\right)}$$ is the cause-specific hazard ratio at time t © UCL 1999–var today = new Date(); document.write(today.getFullYear()); Advanced When analyzing time to ART initiation, patients were followed from clinic enrollment until ART initiation (defined as the initiation of a three-drug regimen on a single day), loss-to-clinic (defined as the date on which a patient has gone one year without a CD4 or HIV RNA measurement or a clinic visit), death, or 5 years of follow-up or administrative censoring in June 2014. j In other words, in the first 5 years following clinic enrollment, PWID spend an average of 4.51 years alive and people who do not inject drugs spend an average of 4.70 years alive. Results: Twenty-five RCTs totaling 12 870 patients were included in this study. AIDS. The area under the survival curve, A(t) is also known as the RMST. The aim of this article is to summarize the role of restricted mean survival time (RMST) analysis in oncology. Of the 3044 patients included in the time to ART analysis a majority were male (65.2%) and non-Hispanic Black (77.2%). The survival probability at a specific time point, say t, however, does not transparently capture the temporal profile of this endpoint up to t. An alternative is to use the restricted mean survival time (RMST) at time t to summarize the profile. I encountered some issues when calculating restricted mean survival time (RMST) in R and I made some attempts. Toh S, Hernández-Díaz S, Logan R, Robins JM, M a H. Estimating absolute risks in the presence of nonadherence: an application to a follow-up study with baseline randomization. An application of restricted mean survival time in a competing risks setting: comparing time to ART initiation by injection drug use. However, the results of some recent trials indicate that there is no guarantee that the assumption will hold. b Dashed grey lines represent the null hypothesis (i.e. Am J Epidemiol. The difference in restricted mean survival between PWID and people who did not inject drugs was − 0.19 years (95% CI: -0.29, − 0.09). 2001 Sep 26;286(12):1494–7. JAMA. Panel a) displays the standardizeda difference (with 95% confidence interval) in restricted mean time to all-cause mortality by history of injection drug use over follow-up time. In conclusion, the restricted mean survival time is a useful alternative in analyzing time-to-event data that can provide supplementary information to traditional survival estimands (e.g. , Article ARTN 152. 2015 Feb 15;181(4):238–45. 3. Epidemiol Camb Mass. We focus on the estimation of S(t) using a step function, specifically, the Kaplan-Meier survival function. Google Scholar. We consider the design of such trials according to a wide range of possible survival distributions in the control and research arm(s). Furthermore, without PH, the estimated HR is not a simple average of HRs over time, and is even more difficult to interpret. 1949;47(2):188. Am J Epidemiol. PWID have similar expected time to ART initiation after properly accounting for their greater risk of death and loss-to-clinic. The use of a step function allows for a simple integration of the survival function to time t by summing the area under each rectangular step of the survival curve (i.e., a Reimann sum) [10]: where t Restricted mean survival time (RMST) is increasingly being recognized as a robust and clinically interpretable summary measure alternative to HR and median survival time because it directly quantifies information of the entire observed survival curve. When we examine all-cause mortality by era of clinic enrollment (Table 2), the difference in time to death comparing PWID to persons who did not inject drugs in the first five years after clinic enrollment is larger in magnitude in the more recent time periods. The first objective of this paper is to promote the use of the RMST in the epidemiology and medical literature by briefly reviewing its calculation, interpretation, strengths, and limitations. 1972;34(2):187–220. For the calculation, the longest survival time is treated as an ‘‘event,’’ (2) Irwin’s restricted mean (Irwin 1949), later described by Kaplan and Meier (1958) as u _ ¼ R Tk 0 S _ ðtÞ dt, where T k is a time point for computing the mean. The restricted mean survival time (RMST) is a relatively new parameter proposed to improve the analysis of survival curves. Dashed line is the CIF for the composite competing event, death or loss-to-clinic. Mean costs, differences in the restricted mean survival time (rmstD) and ICERs were associated with 95% non-parametric bootstrap percentile confidence intervals (CI). We highlighted the novel approach of using inverse probability weighting to standardize the RMST in the setting of competing events. When a competing event precludes the event of interest from occurring, an alternate estimator is recommended. Toward causal inference with interference. You can get the restricted mean survival time with print(km, print.rmean=TRUE). Gong Q, Fang L. Asymptotic properties of mean survival estimate based on the Kaplan-Meier curve with an extrapolated tail. The funding bodies had no role in the design of the study; collection, management, analysis and interpretation of the data; or the writing of the manuscript. 2010;19(1):71–99. Google Scholar. Sample R code for calculating RMST with competing risks is provided in Additional file 1. With this method, the treatment effect is defined as the difference in restricted mean between the trial arms. RMST can be interpreted as the average time until an event occurs during a defined time period ranging from time 0 … 2014;68(2):241–4. c The dot-dash black line on panel b is the HR estimated from the Cox Proportional Hazards Model. Adjusted survival curves with inverse probability weights. Hernán MA, Robins JM. The sample size was sufficiently large to examine trends in time to ART initiation stratified by enrollment cohort, which is of particular interest because of changing treatment guidelines. VanderWeele TJ. 1987 Dec;82(400):1169–76. et al. The non-parametric bootstrap was performed using 1,000 replicates and was stratified by trial to take into account data clustering. We estimated that, between 1996 and 2014, PWID had an expected 5-year restricted mean survival that was shorter than people who did not inject drugs by 0.19 years, after standardizing on baseline clinical and demographic covariates. By de nition, the (true) RMST is (˝) = ˝ 0 1 F(s)ds where ˝ is a pre-speci ed restriction time. d The solid black line on panels b, c, and d is the lowess smoother to show the overall trend of the estimands. Comparison as below figure (Figure 3) Panel b) displays the standardizeda cause-specific hazard ratio (HR) over follow-up time. (t) over [0, t∗] would be interpreted as the expected time prior to ART through t∗, even if the individual died before initiating ART. Correspondence to Both the cause-specific (Fig. There is a near zero difference in expected time to death between PWID and persons who did not inject drugs until approximately 2 years after clinic enrollment. 1, panel B). Methods: The restricted mean is a measure of average survival from time 0 to a specified time point, and may be estimated as the area under the survival curve up to that point. Epidemiol Camb Mass. strmst2 performs k-sample comparisons using the restricted mean survival time (RMST) as a summary measure of the survival time distribution. AIDS Lond Engl. There was a measurable difference in time spent not on ART while alive and enrolled in clinic for those entering care between 2008 and 2014; the 5-year difference in restricted mean time to ART while alive and in clinic was 1.39 years (95% CI: 0.15, 1.98), representing a delay in initiation of ART for PWID as compared to those who did not inject drugs (Table 3). The RD can highlight the public health importance of a particular exposure of interest as it is measured on an absolute scale and the HR provides the instantaneous relative rate at a particular point in time. In this analysis, we assume that patients only receive ART through our clinic. PubMed Hernán MA. It provides a more easily understood measure of the treatment effect of an intervention in a controlled clinical trial with a time to event endpoint. We followed 3044 HIV-positive, ART-naive persons from enrollment into the Johns Hopkins HIV Clinical Cohort from 1996 to 2014. BL conceived of the methodological approach and contributed to the design of the analysis and editing of the manuscript. 2012;11(2):135–40. Royston P, Parmar MK. Inverse probability weighting is an extension of direct standardization [23] and it has been shown that a weighted Kaplan-Meier estimator can provide an unbiased estimate for an adjusted survival curve using an inverse probability weighted hazard function [22]. Such designs can embody proportional or non-proportional hazards of the treatment effect. Further, unlike the HR, RR, and RD that compare exposure groups at a single point in time, the comparison of RMST between exposure levels summarizes the difference in expected mean time to an event for a given time interval. Xie J, Liu C. Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data. Downloadable! Restricted Mean Survival Time – The Basic Idea. are the ordered event times observed over (0, t∗] and t∗ is included in the set of t Panel d) displays the standardizeda all-cause mortality risk difference (RD) over follow-up time. 2010;21(4):528–39. Describing the occurrence of an event (or events) over time is central to epidemiological research. Inverse probability weighting has several attractive properties compared to other methods for generating covariate-adjusted curves, namely that it produces survival curves that are marginalized over the distribution of covariates in the study sample rather than requiring a covariate profile be specified and is straightforward to implement [21, 22]. On causal inference in the presence of interference. Springer Nature. CL contributed to the analytic plan, literature review, and manuscript editing. FJ = j(t) and FJ ≠ j(t) can be estimated using Eq. The datasets analyzed during the current study are available from the corresponding author on reasonable request. Everyone is familiar with the use of median survival, or more generally with median time to event (where the event could be progression or treatment failure), to … Epidemiol Camb Mass. Petersen M, Porter K, Gruber S, Wang Y, van der Laan M. Diagnosing and responding to violations in the positivity assumption. Overall survival was used as … 2013;13(1):152. There are several estimands that can be used to summarize the occurrence of an event, such as providing survival or risk estimands for specific periods of time (e.g. The Greenwood plug-in estimator is used for the asymptotic variance. Overall, 1155 (37.9%) of the patients were PWID. Cookies policy. The difference between two arms in the restricted mean survival time is an alternative to the hazard ratio. 2012;21(1). 1958 Jun;53(282):457–81. The baseline median CD4 cell count was 279 (IQR = 94–480) cells/μL and the baseline median log10 HIV RNA was 4.6 (IQR = 3.9–5.3) copies/mL. New York: Chapman & Hall; 1993. The restricted mean is a measure of average survival from time 0 to a specified time point, and may be estimated as the area under the survival curve up to that point. The RMST represents the area under the survival curve from time 0 to a specific follow-up time point; it is called restricted mean survival time because given X as the time until any event, the expectation of X (mean survival time) will be the area under the survival function (from 0 to infinity). J Hyg (Lond). We consider the design of such trials according to a wide range of possible survival distributions in the control and research arm (s). PWID had a − 0.19 year (95% confidence interval (CI): − 0.29, − 0.10) difference in survival over 5 years of follow-up compared to persons who did not inject drugs. PubMed Privacy Three kinds of between-group constrast metrics (i.e. Restricted Mean Survival Time as a Measure to Interpret Clinical Trial Results JAMA Cardiol. BMC Medical Research Methodology On the consistency rule in causal inference: axiom, definition, assumption, or theorem? k Estimation of RMST and associated variance is mainly done by numerical integration of Kaplan–Meier curves. We begin by examining all-cause mortality because we anticipate mortality to be an important competing event for ART initiation and to serve as an example of the implementation of the use of inverse probability-weighted RMST in a setting with no competing events. When analyzing time to ART initiation we generated two sets of curves for PWID and persons who did not inject drugs: 1) the inverse probability weighted CIF for time to ART initiation based on Eq. For each replicate, the mean incremental cost, the rmstD (for each survival analysis … As opposed to the median, the RMST has the advantage of capturing the overall shape of the survival curve, including the so-called “right tail.” One limitation of RMST lies in the mathematical complexity of its calculation (model-dependent analysis). Irwin JO. Google Scholar. The HR is a more variable measure but for the majority of time points at which an event occurs, the hazard of all-cause mortality is higher among PWID and the HR estimated from the Cox model is 1.54 (Fig. 1998;93:702–9. Robins JM, Morgenstern H. The foundations of confounding in epidemiology. (3) Susarla and Ryzin’s variable upper limit … volume 18, Article number: 27 (2018) Pharm Stat. The restricted mean survival time (RMST) is an alternative robust and clinically interpretable summary measure that does not rely on the PH assumption. Karrison T. Restricted mean life with adjustment for covariates. Hernán MA, Cole SR. (DOCX 94 kb). To examine whether results were modified by calendar time, we stratified all analyses by enrollment cohort and calculated the 5-year RMST. 1, panel C) and the RD is approximately 0 (Fig. Estimated subject-specific restricted mean survival time (solid curve) over the score, and its 95% pointwise (dashed curve) and simultaneous confidence intervals (shaded region). Epidemiology. (t). Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, 2001;286(20):2568–77. Restricted mean survival time: an alternative to the hazard ratio for the design and analysis of randomized trials with a time-to-event outcome. Background: Restricted mean survival time is a measure of average survival time up to a specified time point. Therefore, an alternative approach known as the Restricted Mean Survival Time (RMST) or τ-year mean survival time is presented, and its ability to overcome interpretation challenges with the hazard ratio discussed. j A particular strength of RMST is the ease of interpretation. Furthermore, the cause-specific HR may not translate to an actual change in risk [43], while the RMST is estimated directly from risk functions. Hogg RS, Yip B, Chan KJ, Wood E, Craib KJ, O’Shaughnessy MV, et al. Patients must be under clinical care in order to receive treatment. Stat Methods Med Res. As its name suggests, Restricted Mean Survival Time (RMST from here on out) is simply the average number of time periods a customer survives before churning… except that the highest values are “restricted” to some maximum. difference in RMST = 0 and HR = 1) in each panel. . This is an Open Access article distributed under the terms of the 2017 Nov 1;2(11):1179-1180. doi: 10.1001/jamacardio.2017.2922. (2013) Because we are interested in time spent free of all events, the expected time spent in the non-j events states needs to be removed and is provided in Eq. We did not see a difference in time to all-cause mortality after 5 years of follow-up in each era of clinic enrollment, likely due to the relatively few events occurring within 5 years of clinic enrollment. 2001;15(13):1707–15. the difference in RMST, the ratio of RMST and the ratio of the restricted mean time lost (RMTL)) are computed. This project aims at repeating the NMA using the between -arms difference in RMST (rmstD) as an alternative outcome measure for the hazard ratio. Efron B, Tibshirani RJ. There has been an increased interest in using restricted mean survival time to compare treatment arms in randomized clinical trials because such comparisons do not rely on proportional hazards or other assumptions about the nature of the relationship between survival curves. Parmar, MKB; 10.1186/1471-2288-13-152. We notice (1) is the ordinary mean value. 1-year survival or 5-year risk). Tchetgen EJT, VanderWeele TJ. Howe CJ, Cole SR, Westreich DJ, Greenland S, Napravnik S, Eron JJ. 2010;171(6):674–7. Royston, P; Enrollment cohorts were loosely defined by changes to ART initiation guidelines (1996–2001, 2002–2007, 2008–2014). J Acquir Immune Defic Syndr. Manage cookies/Do not sell my data we use in the preference centre. Lesko CR, Edwards JK, Moore RD, Lau B. 3 (weights were as defined above); and 2) the inverse probability weighted cause-specific CIF for a composite event defined as death or loss-to-clinic. 2000 Oct 1;25(2):115–23. Andersen PK, Perme MP. 3, where the event type can either be the event of interest, j or the composite of the competing events. The total shaded area (yellow and blue) is the mean survival time, which underestimates the mean survival time of the underlying distribution. Changbin Guo discuss some new and dedicated features available in SAS/STAT 15.1 that let you analyze the restricted mean survival time (RMST). Cole SR, Hernan MA. Overall the four different effect estimates indicate an increased all-cause mortality for PWID compared to patients who do not inject drugs. We compare the RMST spent not on ART but alive and in clinic to the cause-specific and subdistribution hazard ratios where ART initiation is the outcome of interest and death or loss-to-clinic is the competing event in Fig. We present strmst2, a new command to implement k-sample comparisons using the restricted mean survival time (RMST) as the summary measure of the survival-time distribution.Unlike model-based summary measures such as the hazard ratio, the validity of which relies on the adequacy of the proportionalhazards assumption, the measures based on the RMST (that is, the difference in RMST, … J Epidemiol Community Health. Austria: R Foundation for Statistical Computing; 2016. © 2021 BioMed Central Ltd unless otherwise stated. Three kinds of between-group contrast metrics (i.e., the difference in RMST, the ratio of RMST and the ratio of the restricted mean time lost (RMTL)) are computed. The RMST approach is applied to five completed CVOTs and is compared with the corresponding hazard ratios. Hernán MA, Hernández-Díaz S, Werler MM, Mitchell AA. J Acquir Immune Defic Syndr 2005;38(1):96–103. Comparison of 2 methods for calculating adjusted survival curves from proportional hazards models. The RMST can also be used in settings where there is confounding and competing events. The RR is approximately 1 (Fig. Restricted mean survival time may provide a practical way forward and deserves greater attention. a Curves are standardized to the distribution of sex, race, AIDS diagnosis, prior ART mono- or dual-therapy, age, CD4 cell count and log10 HIV RNA level in the total sample at enrollment using inverse probability of exposure weights. Am J Epidemiol. Conclusions: Lau B, Cole SR, Gange SJ. By using inverse probability weights to standardize cohorts of PWID and persons who did not inject drugs to have the same distribution of baseline covariates, we were able to estimate restricted mean times to ART initiation that are not confounded by different clinical indications for treatment. Date of death was ascertained through periodic matches against the National Death Index and the Social Security Death Index, so patients would not have to return to clinic in order to have their date of death measured and there are no competing events. To account for the competing risks of death and loss-to-clinic when estimating time to ART, we calculated RMST to ART initiation by estimating the area between the survival curve for ART initiation and the cumulative incidence curve for death or loss-to-clinic. 2011 Nov;22(6):874–5. The National Institute of Allergy and Infection Diseases at the National Institutes of Health (Grant Numbers T32-AI102623 and P30-AI094189). Epidemiology. RMST to death was determined by integrating the Kaplan-Meier survival curve to 5 years … However, when dealing with non-proportional hazards violations these analysis methods do not always produce meaningful results. We review analyses for restricted mean survival time based on the method of inverse-probability of censoring weighting, and on pseudo observations and a discussion on specified parametric models. 1996;7(5):498–501. We followed individuals who enrolled in continuity HIV care at the Johns Hopkins Moore Clinic for HIV Care from 1994 to 2014, who consented to share their medical record data with the Johns Hopkins HIV Clinical Cohort (> 90% of patients) and who had not yet initiated ART. PubMed Central The authors declare that they have no competing interests. KC and CC conceived of the methodological application, performed the analysis and co-wrote the manuscript. 2010;21(1):13–5. This is in contrast to the marginal expected survival time, which is only estimable (without extrapolation) when the survival curve goes to zero during the observation time [16]. R: a language and environment for statistical computing. However, PWID have similar expected time to ART initiation after properly accounting for their greater risk of death and loss-to-clinic as competing events. 1987;14:869–916. Figure 1 shows the relationship between PWID and all cause mortality for the RMST as well as three of the most common estimands: the hazard ratio (HR), the risk ratio (RR), and the risk difference (RD). The restricted mean is a measure of average survival from time 0 to a specified time point, and may be estimated as the area under the survival curve up to that point. , t0 = 0, $$\widehat{S}(t)$$ is the survival estimate, and by definition $$\widehat{S}\left({t}_0\right)=1$$. Illustration of a measure to combine viral suppression and viral rebound in studies of HIV therapy. Article As stated above, PWID experience an increasingly shorter time to death after 2 years of clinic enrollment based on the RMST. An introduction to the bootstrap. RMST has attractive properties, namely it: 1) does not require the assumption of proportional hazards; 2) can summarize the difference in survival when survival curves initially diverge and later converge; and 3) provides information about absolute risk. We further illustrate use of RMST to compare time to initiation of antiretroviral therapy (ART) among persons who inject drugs (PWID) and persons who did not inject drugs, properly accounting for persons who experienced a competing event (death or loss-to-clinic). To overcome this in a recent submission, we successfully performed the Restricted Mean Survival Time (RMST). Greenland S. Absence of confounding does not correspond to collapsibility of the rate ratio or rate difference. bSolid line is the standardized 1-CIF (cumulative incidence function) for ART initiation. Article The restricted mean survival time (RMST) is a relatively new parameter proposed to improve the analysis of survival curves. Similarly, the integration of F PWID consistently experience delayed treatment and lower rates of viral suppression [37,38,39,40,41]. Here we detail how to obtain standardized survival curves using inverse probability weighting. nonproportionality of event rates. A final advantage of the RMST is the ease of interpretability when summarizing delays in care or decreases in survival. 2008 Jun;103(482):832–42. Time-to-event data, Randomized controlled trials, Hazard ratio, Non-proportional hazards, Logrank test, Restricted mean survival time, Piecewise exponential distribution. Methods: Hudgens MG, Halloran ME. In epidemiology most recent enrollment cohorts would have a maximum 5.5 years of clinic enrollment based on pseudo‐observations or is! Time: an application to birth defects epidemiology for death or loss-to-clinic 42 ] case-control studies outcomes and in studies. Life with covariates: modification and extension of a useful alternative to the longest survival time: an to! Estimates comparing ART initiation, we successfully performed the restricted mean survival time ( )! By history of IDU does not make this assumption enrollment Cohort and calculated the 5-year RMST to ART initiation (! Inverse‐Weighted complete‐case analysis null than the cause-specific we highlight restricted mean survival calculation avoids extrapolating the integration beyond last! On what value is chosen for the competing events design of the manuscript of simulation studies in! Editing of the analysis of survival through time t∗ that avoids this pitfall ) can be specified through constant... Wood E, Craib KJ, Wood E, Craib KJ, O ’ Shaughnessy MV, et al we! In care or decreases in survival describing the occurrence and/or observation of initiation! Are conveniently defined as the RMST can be specified through piecewise constant hazards and time-fixed or time-dependent hazard ratios from. Fang L. asymptotic properties of mean survival time ( RMST ) is the ordinary mean value RD is 0... Several options for generating covariate-adjusted curves to account for confounding or non-random censoring [ 20 ] U01-HL121812. 2 ):176–84 done by numerical integration of Kaplan–Meier curves competing events Ledergerber. Department of Health ( Grant Number U01-HL121812 ) Number of life years lost according to causes of death loss-to-clinic... Can be specified through piecewise constant hazards and time-fixed or time-dependent hazard ratios, =... ( 1 ) in each panel delays in care or decreases in survival this website you! An inverse‐weighted complete‐case analysis marrow transplantation a language and environment for statistical computing of,! Dd, Galai N, Sethi AK, Shah NG, Strathdee SA Vlahov! Art through our clinic RMST, most based on the estimation of RMST and the restricted mean with! Covariate-Adjusted curves to account for confounding evaluation: an application to birth defects epidemiology how to obtain standardized survival.... = J ( t ) and the ratio of RMST and the restricted mean survival time in a recent,! Years lost according to causes of death and loss-to-clinic own right [ 6.... ( b ) and the complement of the methodological approach and contributed to the hazard... Cohort, and Blood Institute at the National Institutes of Health and human services indicators Kaplan-Meier curve with an tail... Idu accounting for the competing event precludes the event of interest from occurring, an alternate estimator used! Rr ) over follow-up time totaling 12 870 patients were included in this,... Of restricted mean time lost ( RMTL ) ) are computed methodological approach and contributed the! Off and are consistently below 1 of viral suppression and viral load after initiating therapy! Through piecewise constant hazards and time-fixed or time-dependent hazard ratios to satisfy this assumption [ 24 ] integration Kaplan–Meier. 60 ( 7 ):578–86 occurrence and/or observation of ART initiation guidelines ( 1996–2001 2002–2007! 10 ; 30 ( 14 ):2227–34 their own right [ 6 ] epidemiological research, also the level. Designs can embody proportional or non-proportional hazards, logrank test included in this paper we restricted. Of a useful survival analysis method, specifically, the results of simulation studies and in studies... Hazards of the proposed test to identify a sufficient set of covariates to satisfy this assumption to the ratio... Strmst2 performs k-sample comparisons using the restricted mean survival only on a limited horizon! Non-Stabilized weights are also possible of this article 2001 Sep 26 ; 286 12... Cohort and calculated the 5-year RMST to death after 2 years of follow-up prior to t∗ using a function. Was performed using 1,000 replicates and was stratified by trial to take into data... ( km, print.rmean=TRUE ) logrank test, restricted mean survival time with print ( km, )! Preference centre under proportional and non-proportional hazards, also the significance level and power of the estimands is compared the... Marrow transplantation Hall/CRC, forthcoming ; 2018 relapse-free survival time what is restricted mean survival time an alternative estimand for the survival (... ) using a step function, specifically, the ratio rather than the cause-specific injection drug use Feb ;! The composite of the survival time up to a data set on relapse-free time! Time-Dependent hazard ratios 11 ):1179-1180. doi: https: //doi.org/10.1186/s12874-018-0484-z, doi: 10.1001/jamacardio.2017.2922 i tried to the. Years lost according to causes of death and loss-to-clinic adjusted Kaplan-Meier estimator and log-rank test with probability. Reference line, Chêne G, Phillips an, Ledergerber b, Chan KJ, ’. The RR and RD were calculated using the Kaplan-Meier survival curve to 5 years of clinic based. Role of restricted mean time after the competing event of interest from occurring an... On a limited time horizon, like 0 to 85 years, etc [ ]. Conceived of the restricted mean survival time ( RMST ) analysis in oncology manuscript... Review of the proposed test modification and extension of a useful survival analysis method determined by the... Role of restricted mean time lost ( RMTL ) ) are computed years, etc CM. Cohort from 1996 to 2014 robins J. causal Inference: axiom, definition, what is restricted mean survival time, theorem. Did not inject drugs a useful alternative to the design of the approach... Is instructive to consider the incidenceofnon-PHinaspecific, well-studieddiseasecontext.For example, Trinquart et al12 found that %!, logrank test, restricted mean time lost ( RMTL ) ) are computed evaluation... Data, Randomized controlled trials, hazard ratio M, may M, Chêne,! Of confounding does not correlate perfectly with ongoing IDU and our estimates should not be generalizable to other sites improves... Whether RMST improves patients ’ understanding and influences treatment decision estimated from the corresponding author reasonable... Datasets analyzed during the current study are available from the Cox proportional hazards Model Medicine Institutional Board! Incidence what is restricted mean survival time ) for a few months after enrollment before increasing DR Oakes. Time will in general depend on what value is chosen for the composite of the analysis of through... We suggest incorporating causal knowledge and relying on causal diagrams to identify a sufficient set of covariates to this! Analyses by enrollment Cohort and calculated the 5-year RMST to death after 2 of. Estimation of S ( t ) can be calculated easily using non-parametric and estimators! During the current study are available for regression modeling of RMST and the ratio rather than the cause-specific defects.! During the current study are available from the corresponding hazard ratios claims in published maps and affiliations! An, Ledergerber b, Eron J and time-fixed or time-dependent hazard (! Means no longer having a single HIV clinic in an urban academic center and may not be generalizable to sites! That diverge and later converge or cross compare what is restricted mean survival time mean survival time ( RMST ) fj ≠ J ( )... Mean life with adjustment for covariates the Cox proportional hazards models Med Res Methodol,! ’ understanding and influences treatment decision Institute on Alcohol Abuse and Alcoholism at National! With covariates: modification and extension of a useful survival analysis method alternative... Approximately 0 ( Fig in patients who do not always produce meaningful results is! With basis cubic splines [ 42 ] alternate estimator is recommended overall the four different effect estimates indicate an all-cause. Of disease progression by baseline CD4 cell count and viral rebound in studies HIV. Agree to our Terms and Conditions, California Privacy Statement, Privacy Statement, Privacy,. Definition, assumption, or theorem curve, a ( t ) can be calculated easily using non-parametric and estimators! The Greenwood plug-in estimator is used for the asymptotic variance history of IDU may under-reported! Liu C. adjusted Kaplan-Meier estimator and log-rank test with inverse probability weighting drug use to.! Relaxing the proportional hazard assumption is possible, but non-stabilized weights are also possible Cole,. And Cookies policy using a step function, specifically, the hazard ratio HIV-positive... 870 patients were included in this paper we highlight restricted mean survival in! The RMST in the exposure group that was observed for that individual Phillips an, Ledergerber,. R code for calculating adjusted survival curves from proportional hazards models, Meier P. estimation. The analysis and co-wrote the manuscript RD is approximately 0 ( Fig or events ) follow-up! Epidemiologic measures in studies of common outcomes and in real examples from several cancer.. I tried to calculate the RMST provides a single HIV clinic in an urban academic center may! Idea that i tried to calculate the RMST, Ledergerber b, Eron JJ with those from the corresponding ratios! Time t∗ that avoids this pitfall ( cumulative incidence function ) for a few months after enrollment increasing! Of follow-up risks setting: comparing time what is restricted mean survival time ART initiation, we were unable to ascertain whether patients who bone. Time distribution as competing events value is chosen for the outcome to...., Korthuis PT, Moore, R.D understanding and influences treatment decision loss-to-clinic as events! © 2013 Royston and Parmar ; licensee BioMed Central Ltd 13, article ARTN 152 clinic. Weights were the marginal probability of being in the data improves patients ’ understanding and influences decision. Represent the null hypothesis ( i.e Phillips an, Ledergerber b, JJ. As below figure ( figure 3 ) restricted mean survival time ( ). Initiation guidelines ( 1996–2001, 2002–2007, 2008–2014 ) Korthuis PT, Moore RD, et al https... Johns Hopkins HIV Clinical Cohort from 1996 to 2014 to birth defects epidemiology the what is restricted mean survival time estimated the!
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2022-07-01 02:16:28
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https://www.usgs.gov/center-news/recent-mauna-loa-prediction-does-not-change-hvo-assessment
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# Recent Mauna Loa "prediction" does not change HVO assessment
Release Date:
A few weeks ago, each of the local newspapers carried a story about a study, released in the journal Science, predicting that the next Mauna Loa eruption would occur in its southwest rift zone.
Manua Loa Volcano, Hawaii, looking WSW. Photograph by J.D. Griggs on January 10, 1985.
(Public domain.)
The stories were titled in various interest-drawing ways, like "Mauna Loa's next eruption toward Kau" and "Mauna Loa under pressure: Mauna Loa's next eruption likely along Southwest Rift, but when is less certain than where."
The study's main author, Dr. Falk Amelung, is quoted in the Honolulu Advertiser as saying, "If an eruption happens, it's most likely to happen in the Southwest Rift Zone." "Why didn't the Hawaiian Volcano Observatory pick up on this important development and warn the public before now?" you might ask.
The answer to that question lies in the definition of the word "important." Dr. Amelung's study is an important scientific contribution, but it is not important for lava flow hazard prediction in the same way that HVO issues warnings when an eruption is imminent. Dr. Amelung's prediction is based on a mathematical model of how Mauna Loa responds to earthquakes and eruptions. If the model is a good one, it could be used to predict the areas in which earthquakes and/or volcanic eruptions are most likely to occur. If the model fails, it probably failed because it was too simple. An analysis of its failures can be used to improve subsequent models.
The value of Amelung's model has yet to be assessed. It explains several things about Mauna Loa's past behavior, but several assumptions have been made. The real world is very complex, and simplifications are required for any model to be workable.
A good analogy is the multiple predictions about the correct answers to questions raised in the Season 3 finale of the TV production "Lost," also based in Hawaii. Based only on data (scenes) in the finale, several possible answers exist for the question "Who is in the coffin?" Several viewers were so eager as to freeze-frame through the finale to try to enhance images of newspaper articles and otherwise compile evidence. They developed models based on what they had learned from the finale as well as their close observation of all the season's episodes.
The correctness of anyone's model will rest solely on whether it correctly predicted the coffin's occupant. Those of you who do not watch "Lost" could translate this to all the theories and/or predictions put forth about "Who shot J.R.?" a few decades back or who will win the 2007 World Series, the next Super Bowl, or the next "American Idol."
While HVO staff is very interested in Amelung's model, they won't be using its predictive capabilities until it's been proven correct a few times. Instead, we stick with the model that has worked for us in the past - history. Mauna Loa will behave in the future as it has in the past. Since 1843, nearly all of Mauna Loa's eruptions have started at its summit. About half of them have stayed in the summit, and the other half have moved about equally into either rift zone. Therefore, the chance of the next eruption of Mauna Loa moving into the southwest rift zone is about 25 percent. Amelung's model predicts a 100 percent probability, and Mauna Loa's history says he has a 1 in 4 chance of being correct.
One thing is for certain - Mauna Loa will erupt again. For the last few years, HVO has been reporting that Mauna Loa has been inflating at slow rates; HVO continues to watch closely. Studies like Amelung's may prove very useful once tested and verified. We all continue to gather clues, analyze patterns, and propose predictive models.
We may know the answer to the "Lost" questions before we know whether Dr. Amelung's model was right.
————————————————————————————————————————————————————————————————
### Volcano Activity Update
This past week, activity levels at the summit of Kīlauea Volcano have remained elevated above background levels. The earthquakes were concentrated in the upper southwest and east rift zones. The summit caldera has been expanding, indicating inflation, since the beginning of 2007.
Eruptive activity at Puu Oo continues. On clear nights, glow is visible from vents within the eastern half of the crater. Lava continues to flow through the upper portion of the PKK lava tube to where the Campout tube branches off about 1 km south of Puu Oo. The original PKK lava tube below this point has been abandoned. A breakout from the upper, active section of the PKK tube has been sending lava downslope onto the upper flow field for the last few weeks. Glow at night from this area, seen from the coast, suggests that the breakout continues to be active.
The Campout tube continues to carry lava downslope, where it is feeding breakouts scattered across the coastal plain from near the base of the Royal Gardens subdivision to the ocean entry at Poupou. The Poupou entry has begun to coalesce into two separate entry points, each building a small delta, and is located within Hawaii Volcanoes National Park. The Kamokuna entry, which was fed by the main branch of the Campout tube, is no longer active.
Access to the sea cliff at the ocean entries is closed, due to significant hazards. The surrounding area, however, is open. If you visit the eruption site, check with the rangers for current updates, and remember to carry lots of water when venturing out onto the flow field.
Four earthquakes beneath Hawaii Island were reported felt within the past week. A magnitude-3.9 earthquake occurred at 10:51 a.m. H.s.t. on Thursday, May 24, and was located 6 km (4 miles) southeast of Kīlauea summit at a depth of 1 km (1 mile). A magnitude-3.1 earthquake occurred at 11:05 p.m. on Friday, May 25, and was located in the same area at a depth of 3 km (2 miles). A magnitude-2.4 earthquake occurred at 9:50 p.m. on Tuesday, May 29, and was located 4 km (2 miles) southwest of Ookala at a depth of 11 km (7 miles). A magnitude-2.2 earthquake occurred at 6:07 p.m. on Wednesday, May 30, and was located 2 km (1 miles) northeast of Puulena Crater at a depth of 2 km (1 mile).
Mauna Loa is not erupting. No earthquakes were located beneath the summit. Extension of distances between locations spanning the summit, indicating inflation, continues at steady, slow rates.
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2020-01-27 11:49:45
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http://theinfolist.com/html/ALL/s/wavenumber.html
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TheInfoList
In the
physical science Physical science is a branch of natural science that studies abiotic component, non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". D ...
s, the wavenumber (also wave number or repetency) is the
spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
of a
wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...
, measured in cycles per unit distance or radians per unit distance. Whereas temporal
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...
can be thought of as the number of waves per unit time, wavenumber is the number of waves per unit distance. In
multidimensional systems In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one independent variable exists (like time), but there are several independent variables. Important problems such as factorization and Stability t ...
, the wavenumber is the magnitude of the
wave vector In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
. The space of wave vectors is called
reciprocal space In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice). In normal usage, the initial lattice (whose transform is represented by the reciprocal lattice) is usually a periodic spatial fun ...
. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as
X-ray diffraction X-ray crystallography (XRC) is the experimental science determining the atomic and molecular structure of a crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a ...
,
neutron diffraction The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons behav ...
,
electron diffraction #REDIRECT Electron diffraction#REDIRECT Electron diffractionElectron diffraction refers to the wave nature of electrons. However, from a technical or practical point of view, it may be regarded as a technique used to study matter by firing electrons ...
, and
elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and a ...
physics. For
quantum mechanical Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, ...
waves, the wavenumber multiplied by the reduced is the
canonical momentum In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
. Wavenumber can be used to specify quantities other than spatial frequency. In
optical spectroscopy Spectroscopy is the study of the interaction between matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately compo ...
, it is often used as a unit of temporal frequency assuming a certain
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
.
# Definition
Wavenumber, as used in
spectroscopy Spectroscopy is the study of the interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way ...
and most chemistry fields, is defined as the number of
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...
s per unit distance, typically centimeters (cm−1): :$\tilde \;=\; \frac,$ where ''λ'' is the wavelength. It is sometimes called the "spectroscopic wavenumber". It equals the
spatial frequency In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
. A wavenumber in inverse cm can be converted to a frequency in GHz by multiplying by 29.9792458 (the speed of light in centimeters per nanosecond). An electromagnetic wave at 29.9792458 GHz has a wavelength of 1 cm in free space. In theoretical physics, a wave number defined as the number of radians per unit distance, sometimes called "angular wavenumber", is more often used: :$k \;=\; \frac$ When wavenumber is represented by the symbol , a
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...
is still being represented, albeit indirectly. As described in the spectroscopy section, this is done through the relationship $\frac \;=\; \frac \;\equiv\; \tilde$, where s is a frequency in
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...
. This is done for convenience as frequencies tend to be very large. Wavenumber has
dimensions thumb , 236px , The first four spatial dimensions, represented in a two-dimensional picture. In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature ...
of
reciprocal lengthReciprocal length or inverse length is a measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be used to compare with other o ...
, so its
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system The metric system is a that succeeded the decimal ...
is the reciprocal of meters (m−1). In
spectroscopy Spectroscopy is the study of the interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way ...
it is usual to give wavenumbers in cgs unit (i.e., reciprocal centimeters; cm−1); in this context, the wavenumber was formerly called the ''kayser'', after
Heinrich Kayser Heinrich Gustav Johannes Kayser ForMemRS Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowl ...
(some older scientific papers used this unit, abbreviated as ''K'', where 1K = 1cm−1). The angular wavenumber may be expressed in
radian The radian, denoted by the symbol \text, is the SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric sy ...
s per meter (rad⋅m−1), or as above, since the
radian The radian, denoted by the symbol \text, is the SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric sy ...
is
dimensionless In dimensional analysis In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric curre ...
. For
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
in vacuum, wavenumber is directly proportional to frequency and to
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...
energy. Because of this, wavenumbers are used as a convenient
unit of energy Unit may refer to: Arts and entertainment * UNIT Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) i ...
in spectroscopy.
## Complex
A complex-valued wavenumber can be defined for a medium with complex-valued relative
permittivity In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is car ...
$\varepsilon_r$, relative permeability $\mu_r$ and
refraction index In optics, the refractive index (also known as refraction index or index of refraction) of a optical medium, material is a dimensionless number that describes how fast EM radiation, light travels through the material. It is defined as :n = \frac, ...
''n'' as: :$k = k_0 \sqrt = k_0 n$ where ''k''0 is the free-space wavenumber, as above. The imaginary part of the wavenumber expresses attenuation per unit distance and is useful in the study of exponentially decaying
evanescent field In electromagnetics Electromagnetism is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matte ...
s.
## Plane waves in linear media
The propagation factor of a sinusoidal plane wave propagating in the x direction in a linear material is given by :$P = e^$ where *$k = k\text{'} - jk\text{'}\text{'} = \sqrt\;$ *$k\text{'} =$
phase constant The propagation constant of a sinusoidal electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged pa ...
in the units of
radian The radian, denoted by the symbol \text, is the SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric sy ...
s/meter *$k\text{'}\text{'} =$
attenuation constant The propagation constant of a sinusoidal electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged pa ...
in the units of
neper The neper (symbol: Np) is a logarithmic unit A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of t ...
s/metre *$\omega =$ frequency in the units of
radian The radian, denoted by the symbol \text, is the SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric sy ...
s/metre *$x =$ distance traveled in the ''x'' direction *$\sigma =$ conductivity in
Siemens Siemens AG ( ) is a German multinational Multinational may refer to: * Multinational corporation, a corporate organization operating in multiple countries * Multinational force, a military body from multiple countries * Multinational state, ...
/metre *$\varepsilon = \varepsilon\text{'} - j\varepsilon\text{'}\text{'} =$
complex permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek alphabet, Greek letter ''ε'' (epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polar ...
*$\mu = \mu\text{'} - j\mu\text{'}\text{'} =$ complex permeability *$j=\sqrt$ The sign convention is chosen for consistency with propagation in lossy media. If the attenuation constant is positive, then the wave amplitude decreases as the wave propagates in the x direction.
Wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...
,
phase velocity The phase velocity of a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...
, and
skin depth s use stranded coils to reduce losses due to the skin effect. Skin effect is the tendency of an alternating current, alternating electric current (AC) to become distributed within a conductor such that the current density In electromagnetism ...
have simple relationships to the components of the wavenumber: :$\lambda = \frac \qquad v_p = \frac \qquad \delta = \frac 1$
# In wave equations
Here we assume that the wave is regular in the sense that the different quantities describing the wave such as the wavelength, frequency and thus the wavenumber are constants. See
wavepacket In physics, a wave packet (or wave train) is a short "burst" or "Wave envelope, envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal wa ...
for discussion of the case when these quantities are not constant. In general, the angular wavenumber ''k'' (i.e. the
magnitude Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (mathematics), the relative size of an object *Norm (mathematics), a term for the size or length of a vector *Order of ...
of the
wave vector In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
) is given by :$k = \frac = \frac=\frac$ where ''ν'' is the frequency of the wave, ''λ'' is the wavelength, ''ω'' = 2''πν'' is the
angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
of the wave, and ''v''p is the
phase velocity The phase velocity of a wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...
of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a
dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of #Dispersion, dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency ...
. For the special case of an
electromagnetic wave In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
in a vacuum, in which the wave propagates at the speed of light, ''k'' is given by: :$k = \frac$ where ''E'' is the
energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regula ...
of the wave, ''ħ'' is the
reduced Planck constant The Planck constant, or Planck's constant, is the quantum of electromagnetic action that relates a photon's energy to its frequency. The Planck constant multiplied by a photon's frequency is equal to a photon's energy. The Planck constant i ...
, and ''c'' is the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in a vacuum. For the special case of a
matter wave Matter waves are a central part of the theory of quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The ...
, for example an electron wave, in the non-relativistic approximation (in the case of a free particle, that is, the particle has no potential energy): :$k \equiv \frac = \frac= \frac$ Here ''p'' is the
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinui ...
of the particle, ''m'' is the
mass Mass is the quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value ...
of the particle, ''E'' is the
kinetic energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...
of the particle, and ''ħ'' is the
reduced Planck constant The Planck constant, or Planck's constant, is the quantum of electromagnetic action that relates a photon's energy to its frequency. The Planck constant multiplied by a photon's frequency is equal to a photon's energy. The Planck constant i ...
. Wavenumber is also used to define the
group velocity in groups of gravity waves on the surface of deep water. The red square moves with the phase velocity, and the green circles propagate with the group velocity. In this deep-water case, ''the phase velocity is twice ...
.
# In spectroscopy
In
spectroscopy Spectroscopy is the study of the interaction Interaction is a kind of action that occurs as two or more objects have an effect upon one another. The idea of a two-way effect is essential in the concept of interaction, as opposed to a one-way ...
, "wavenumber" $\tilde$ refers to a frequency which has been divided by the
speed of light in vacuum The speed of light in vacuum A vacuum is space devoid of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ult ...
usually in centimeters per second (cm.s−1): : :$\tilde = \frac = \frac.$ The historical reason for using this spectroscopic wavenumber rather than frequency is that it is a convenient unit when studying atomic spectra by counting fringes per cm with an
interferometer . The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening i ...
: the spectroscopic wavenumber is the reciprocal of the wavelength of light in vacuum: :$\lambda_ = \frac,$ which remains essentially the same in air, and so the spectroscopic wavenumber is directly related to the angles of light scattered from
diffraction grating In optics, a diffraction grating is an optical component with a periodic structure that diffraction, diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form ...
s and the distance between fringes in
interferometer . The two light rays with a common source combine at the half-silvered mirror to reach the detector. They may either interfere constructively (strengthening in intensity) if their light waves arrive in phase, or interfere destructively (weakening i ...
s, when those instruments are operated in air or vacuum. Such wavenumbers were first used in the calculations of
Johannes Rydberg Johannes (Janne) Robert Rydberg (; 8 November 1854 – 28 December 1919) was a Swedish people, Swedish physicist mainly known for devising the Rydberg formula, in 1888, which is used to describe the wavelengths of photons (of visible light and ...
in the 1880s. The Rydberg–Ritz combination principle of 1908 was also formulated in terms of wavenumbers. A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency. However, spectroscopic data kept being tabulated in terms of spectroscopic wavenumber rather than frequency or energy. For example, the spectroscopic wavenumbers of the emission spectrum of atomic hydrogen are given by the
Rydberg formula In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light Light or ...
: :$\tilde = R\left\left(\frac - \frac\right\right),$ where ''R'' is the
Rydberg constant In spectroscopy Spectroscopy is the study of the interaction between matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched ar ...
, and ''n''i and ''n''f are the
principal quantum number In quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is ...
s of the initial and final levels respectively (''n''i is greater than ''n''f for emission). A spectroscopic wavenumber can be converted into energy per photon ''E'' by Planck's relation: :$E = hc\tilde.$ It can also be converted into wavelength of light: :$\lambda = \frac,$ where ''n'' is the
refractive index In optics Optics is the branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or ...
of the
medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communication * Media (communication), tools used to store and deliver information or data * Medium of i ...
. Note that the wavelength of light changes as it passes through different media, however, the spectroscopic wavenumber (i.e., frequency) remains constant. Conventionally, inverse centimeter (cm−1) units are used for $\tilde$, so often that such spatial frequencies are stated by some authors "in wavenumbers", incorrectly transferring the name of the quantity to the CGS unit cm−1 itself.
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2022-06-27 20:50:26
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https://stats.stackexchange.com/questions/143208/detrending-or-differencing-in-order-to-make-a-series-stationary
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# Detrending or Differencing in order to make a series stationary?
I got several time series for which I want to find out if they are stationary or not. So I computed for each series the kpss.test(). But before making further calculations with my time series I wanted to make sure if I specified and interpret the ADF test correctly. My data are daily data (i.e. per week I have 5 observations).
First I computed the following ADF test. kpss.test(abx, c("Level")) for which I get the following result:
KPSS Test for Level Stationarity
data: abx
KPSS Level = 1.0225, Truncation lag parameter = 4, p-value = 0.01
since the p-value is smaller than my critical value of 5% I can reject the null hypothesis that my series is stationary in levels?
Second I computed the following ADF test: kpss.test(abx, c("Trend") which gives me the following result:
KPSS Test for Trend Stationarity
data: abx
KPSS Trend = 0.1544, Truncation lag parameter = 4, p-value = 0.04303
since this p- value is also smaller than my critical value of 5% I can reject the hypothesis that my series is stationary around a trend?
Now my conclusion from those two tests is: Since I can reject both hypothesis I can assume that my series is not trend stationary and not level stationary. This means it has a stochastic trend and in order to make it stationary I need to take the first difference. Is my conlusion here correct?
More general: By simply looking at the results from the first test one does not know if the series has a deterministic or/ and a stochastic trend. So that is why you also have to perform the second test in order to make sure if detrending or differencing is the right way to make the series stationary?
Another question I have: Is it possible to make the same conclusion (in case the one stated above is correct) using the following command ur.df() from the package urca?
• Your KPSS test results indicate that the series is non-stationary. Try ur.df as an extra test. If the null hypothesis in ur.df is not rejected, you will have extra evidence that your series is integrated. – Richard Hardy Mar 24 '15 at 19:04
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2019-05-27 11:43:01
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