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https://planetcalc.com/3303/ | homechevron_rightStudychevron_rightMathchevron_rightAlgebrachevron_rightlinear algebra
# Linear Diophantine equations
This calculator solves linear diophantine equations.
As usual, here goes the calculator, and theory goes below it.
### Linear Diophantine equations
Equation
All solutions for x
All solutions for y
x
y
Since this is all about math, I copy some content from wikipedia for the start.
In mathematics, a Diophantine equation is a polynomial equation in two or more unknowns such that only the integer solutions are searched or studied (an integer solution is a solution such that all the unknowns take integer values). A linear Diophantine equation is an equation between two sums of monomials of degree zero or one.
The simplest linear Diophantine equation takes the form
$ax + by = c$,
where a, b and c are given integers, x, y — unknowns.
The solutions are completely described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b. Moreover, if (x, y) is a solution, then the other solutions have the form (x + kv, y - ku), where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b.
To find the solution one can use Extended Euclidean algorithm (except for a = b = 0 where either there are unlimited number of solutions or none).
If a and b are positive integers, we can find their GCD g using Extended Euclidean algorithm, along with $x_g$ и $y_g$, so:
$ax_g + by_g = g$.
If c is a multiple of g, the Diophantine equation $ax + by = c$ has solution, otherwise, there is no solution.
That is, if c is a multiple of g, then
$a x_g (\frac{c}{g}) + b y_g (\frac{c}{g})=c$
and one of the possible solutions is:
$x_0 = x_g (\frac{c}{g})$$y_0 = y_g(\frac{c}{g})$
If either a or b is negative, we can solve equation using it's modulus, then change sign accordingly.
If we know one of the solutions, we can find their general form.
Let g = GCD(a,b), and we have:
$ax_0 + by_0 = c$.
By adding $\frac{b}{g}$ to $x_0$ and subtracting $\frac{a}{g}$ from $y_0$, we get:
$a(x_0 + \frac{b}{g}) + b(y_0 - \frac{a}{g}) = ax_0+by_0 + \frac{ab}{g}-\frac{ba}{g}=c$
So, any numbers like these:
$x = x_0 + k \frac{b}{g}$$y = y_0 - k \frac{a}{g}$,
where k is integer, are the solutions of Linear Diophantine equation. | 2019-03-20 03:28:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 16, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9049463868141174, "perplexity": 355.0885576064266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202199.51/warc/CC-MAIN-20190320024206-20190320050206-00205.warc.gz"} |
https://stats.stackexchange.com/questions/82969/graphical-models-and-explaining-away | # Graphical Models and Explaining Away?
So I have fundamental confusion about graphical models. Suppose the following graphical model is given:
Now the question is do we have the following equality?: $$p(m_2|\alpha,\beta,y_3)=p(m_2|\alpha,\beta)$$
If so, why exactly and could you please introduce me a source explaining it?
Yes, this is because the $\alpha, \beta$ node $d$-separates $m_2$ and $y_3$. See Probabilistic Reasoning in Intelligent Systems for an explanation of $d$-separation.
Another intuitive example of why two sibling nodes are independent given their parent:
• Imagine $A$ and $B$ are two guys living in the same city.
• Whether A gets wet or not depends on whether it rains or not. Same for B.
Now, if don't know whether it rained or not but we observed that $A$ is wet, we are going to think that it rained, and therefore it will be likely that $B$ will be wet as well. That is, when we do not know the value of the parent node (rain) the information about $A$ gives also some information about $B$.
However, if we know it rained (the parent node is observed) then to guess whether $B$ is wet or not we do not need to now nothing about $A$; we don't care, since we already know it rained.
That is, when you now the state of the parent you don't care about the rest of nodes since you only depend on your parent. If you don't know the state of your parent then yes, the rest of the nodes can give you some hint on his state.
I like to think about it like this:
What additional information does knowing $y_3=X$ actually give you?
Now the additional is key here. Imagine you knew nothing but $y_3=X$. Then in order:
1. We can learn about $m_3$ by asking what it needs to make $y_3=X$ more likely
2. We can learn about $\alpha,\beta$ by asking ourselves what they need to be so to make $m_3$ more likely to be what we think it should be from step 1
3. The knowledge about $\alpha,\beta$ from step 2 can help us guess what the distribution of $m_2$ is.
So that's $p(m_2|y_3)$.
But now do the same process, already knowing for certain what $\alpha,\beta$ are, that is $p(m_2|\alpha,\beta,y_3)$.
Well it turns out 2 is useless. Step 2 is useless because we already know $\alpha,\beta$, since they are given and no new information changes that. So step 3 happens regardless of whether $y_3$ is known or not.
Hopefully this wasn't more confusing.
\begin{align} p(m_2|\alpha,\beta,y_3)&=\frac{p(m_2,y_3|\alpha, \beta)}{p(y_3|\alpha,\beta)}\\ &= \frac{p(m_2|\alpha,\beta)p(y_3|\alpha, \beta)}{p(y_3|\alpha, \beta)}\\ &=p(m_2|\alpha,\beta) \end{align}
$$p(m_2,y_3|\alpha, \beta)=p(m_2|\alpha,\beta)p(y_3|\alpha, \beta)$$ holds because $$m_2$$, $$y_3$$ and $$\alpha, \beta$$ form a common cause trail. That's given $$\alpha$$ and $$\beta$$ the correlation between $$m_2$$ and $$y_3$$ disappears, and $$m_2$$ can influence $$y_3$$ only when $$\alpha, \beta$$ and $$m_3$$ are all not observed. | 2019-10-22 03:47:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 13, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7086367011070251, "perplexity": 351.7807644985366}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987798619.84/warc/CC-MAIN-20191022030805-20191022054305-00224.warc.gz"} |
https://realnfo.com/toc/Electrical_Circuit_Analysis/The_Basic_Elements_and_Phasors/Frequency_Effects_on_L_and_C_in_DC_Circuits | # Frequency Effects on L and C in DC Circuits
For dc circuits, the frequency effect is zero, and the reactance of a coil is $$X_L = 2\pi fL = 2\pi(0)L = 0 Ω$$ The use of the short-circuit equivalence for the inductor in dc circuits is now validated.
At very high frequencies, $X_L = 2\pi fL$ is very large, and for some practical applications the inductor can be replaced by an open circuit. In equation form, $$\bbox[10px,border:1px solid grey]{X_L = 0 \,Ω} \, dc, \,f=0 \,Hz$$ and $$\bbox[10px,border:1px solid grey]{X_L = \infty \,Ω} \, as, \,f \to \infty \,Hz$$ The capacitor can be replaced by an open-circuit equivalence in dc circuits since f = 0, and $$X_C = {1 \over 2\pi fC} = {1 \over 2\pi (0) C} \to \infty \, Ω$$ once again substantiating our previous action, At very high frequencies, for finite capacitances, $$X_C \downarrow= {1 \over 2\pi f \uparrow C}$$ is very small, and for some practical applications the capacitor can be replaced by a short circuit. In equation form $$\bbox[10px,border:1px solid grey]{X_C = 0 \,Ω} \, \text{f=very high frequencies}$$ $$\bbox[10px,border:1px solid grey]{X_C \to \infty \,Ω} \, as f \to 0$$ Table 1 reviews the preceding conclusions.
Table 1: Effect of high and low frequencies on the circuit model of an inductor and a capacitor. | 2022-07-04 12:23:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5511884689331055, "perplexity": 354.58186961821457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104375714.75/warc/CC-MAIN-20220704111005-20220704141005-00685.warc.gz"} |
https://earthscience.stackexchange.com/tags/weather-satellites/hot?filter=year | # Tag Info
4
Unfortunately, your question has no answer. Both have errors. Both can be unreliable. Your choice really depends on how you plan on using them. Satellites instrument contain sources of error, such as bad observations (wildfires in the NIR), mapping problems (especially near the poles), and representation error. Don't underestimate those sources of error- ...
4
There are numerous short modules offered by UCAR's COMET/METED website: https://www.meted.ucar.edu/training_detail.php Modules specific to GOES-R include (but aren't limited to): GOES-R/JPSS test cases for convection initiation and wildfires. Advanced Baseline imager A satellite foundational course There are 19 courses with GOES-R in the title.
2
No, cloud fraction is not a good measure of $\ce{SO_2}$. Clouds are functions of moisture, temperature, and cloud condensation nuclei. Som of the other variables, such as (but not limited to) ColumnAmountSO2 or ColumnAmountSO2_TRLare better indicators.
Only top voted, non community-wiki answers of a minimum length are eligible | 2021-06-23 15:51:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38144612312316895, "perplexity": 5821.313152638384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488539480.67/warc/CC-MAIN-20210623134306-20210623164306-00339.warc.gz"} |
https://tex.stackexchange.com/questions/509946/tikz-missing-number-treated-as-zero | # TikZ ! Missing number, treated as zero
Hi all, here is a (hopefully not oversimplified) MWE:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def\A{{3/(2*6)}}
\def\B{{sqrt(5-\A)}}
\filldraw (\A,\B) circle (1pt);
\end{tikzpicture}
\end{document}
I'm getting the error message
! Missing number, treated as zero.
{
l.11 \filldraw ({\A,\B})
circle (1pt);
Can anyone explain what is going on here? How can I fix this?
One way to fix this is
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\A{3/(2*6)}
\pgfmathsetmacro\B{sqrt(5-\A)}
\filldraw (\A,\B) circle (1pt);
\end{tikzpicture}
\end{document}
If you insist on \defs, set the braces right:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def\A{3/(2*6)}
\def\B{sqrt(5-\A)}
\filldraw ({\A},{\B}) circle (1pt);
\end{tikzpicture}
\end{document}
• Your second solution works! Didn't try the first one -- is pgfmathsetmacro recommended over def? – AccidentalFourierTransform Sep 27 '19 at 0:52
• @AccidentalFourierTransform The general rule is that \def should used sparsely. However, the reason is that it overwrites macros without warning (while \newcommand would issue an error message). This objection applies to \pgfmathsetmacro, too, but this one at least parses the expression. In more complex examples this may save some time. The real advantages include the ability to, say, local switch on fpu, which is not needed in this cooked down example. In any case, the braces in your \defs are not set appropriately. – Schrödinger's cat Sep 27 '19 at 2:39 | 2020-02-26 05:10:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9030531644821167, "perplexity": 4615.399866357385}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146186.62/warc/CC-MAIN-20200226023658-20200226053658-00483.warc.gz"} |
https://www.physicsforums.com/threads/related-rates-grain-hopper-problem.52440/ | # Related rates grain hopper problem
1. Nov 12, 2004
### decamij
Grain is emptying from the bottom of a funnel-shaped hopper at a rate of 1.2m3/min. If the diameter of the top of the hopper is 5m and the sides make an angle of 30o with the vertical, determine the rate at which the level of grain in the hopper is changing, when it is half the height of the hopper.
P.S. (I am supposed to use implicit differentiation to find rates of change)
I can't get it!!
2. Nov 13, 2004
### BobG
You can use explicit differentiation.
The angle is 30 degrees. The tangent of 30 degrees equals the radius divided by the heighth. In other words:
$$h=\frac{r}{tan 30}$$
The angle stays constant, so tan 30 is also a constant.
As the grain empties, it's cross section is always a similar triangle (similar to the shape of the hopper). If the heighth of the hopper is one-half, so are all the other sides.
Edit: I thought you were asking if you had to use implicit differentiation.
The 1/3 pi is just a constant. You apply the product rule to differentiate hr^2 (keeping in mind you have to apply the chain rule, as well).
To get an answer, you still have to eventually find h from r.
Last edited: Nov 13, 2004 | 2017-12-17 19:42:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8065789937973022, "perplexity": 753.5156850641815}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948597485.94/warc/CC-MAIN-20171217191117-20171217213117-00262.warc.gz"} |
http://passmathsng.com/jambmaths/71 | # Jambmaths
Maths Question
Question 1
Which Question Paper Type of Mathematics is given to you?
Question 2
If 2q35 = 778, find q
Question 3
Simplify $\frac{3\tfrac{2}{3}\times \tfrac{5}{6}\times \tfrac{2}{3}}{\tfrac{11}{15}\times \tfrac{3}{4}\times \tfrac{2}{27}}$
Question 4
A man invested N5000 for 9 months at 4%. What is the simple interest?
Question 5
If the number M,N,Q are in the ratio 5:4:3. Find the value of $\frac{2N-Q}{M}$
Question 6
Simplify ${{\left( \frac{16}{81} \right)}^{\tfrac{1}{4}}}\div {{\left( \frac{9}{16} \right)}^{-\tfrac{1}{2}}}$
Question 7
If ${{\log }_{3}}18+{{\log }_{3}}3-{{\log }_{3}}x=\log 3,$ find x
Question 8
Rationalize $\frac{2-\sqrt{5}}{3-\sqrt{5}}$
Question 9
Simplify $\left( \sqrt{2}+\frac{1}{\sqrt{3}} \right)\left( \sqrt{2}-\frac{1}{\sqrt{3}} \right)$
Question 10
From the venn diagram, above, the complement of the set is given by
Question 11
Raila has 7 different posters to be hanged in her bedroom, living room and kitchen. Assuming she has plans to place at least a poster in each of the 3 rooms how many choices does she have?
Question 12
Make R the subject of the formula if $T=\frac{K{{R}^{2}}+M}{3}$
Question 13
Find the remainder when ${{x}^{3}}-2{{x}^{2}}+3x-3$is divided by ${{x}^{2}}+1$
Question 14
Factorize completely $9{{y}^{2}}-16{{x}^{2}}$
Questionn 15
Solve for x and y respectively in the simultaneous equations\begin{align} & -2x-5y=3 \\ & x+3y=0 \\\end{align}
Question 16
If x varies directly as square root of y and x = 81 when y =9, find x when y = $1\tfrac{7}{9}$
Question 17
T varies inversely as the cubes of R, when R =3, T = $\tfrac{2}{81}$, find T when R = 2
Question 18
Question 19
Solve the inequality $-6(x+3)\le 4(x-2)$
Question 20
Solve the inequality ${{x}^{2}}+2x>15$
Question 21
Find the sum of the first 18 terms of the series 3, 6, 9, -, -, -, 36.
Question 22
The second term of a geometric series is 4, while the fourth term is 16. Find the sum of the first five terms
Question 23
A binary operation $\oplus$on real number us defined by $x\oplus y=xy+x+y$for two real numbers x and y. Find the value of $3\oplus -\tfrac{2}{3}$
Question 24
If $\left| \begin{matrix} 2 & 3 \\ 5 & 3x \\\end{matrix} \right|=\left| \begin{matrix} 4 & 1 \\ 3 & 2x \\\end{matrix} \right|$ find the value of x
Question 25
Evaluate $\left| \begin{matrix} 4 & 2 & -1 \\ 2 & 3 & -1 \\ -1 & 1 & 3 \\\end{matrix} \right|$
Question 26
The inverse of matrix N =$\left( \begin{matrix} 2 & 3 \\ 1 & 4 \\\end{matrix} \right)$ is
Question 27
What is the size of each interior angle of a 12–sided regular polygon?
Question 28
A circle of perimeter 28cm is opened to form a square. What is the maximum possible area of the square?
Question 29
A chord of a circle of radius 7cm is 5cm from the centre of the circle. What is the length of the chord?
Question 30
A solid metal of side 3 cm is placed I a rectangular tank of dimension 3, 4 and 5 cm. What volume of water can the tank hold?
Question 31
The perpendicular bisector of a line XY is the locus of a point.
Question 31
The perpendicular bisector of a line XY is the locus of a point.
Question 32
The midpoint of P (x, y) and Q (8, 6) is (5, 8). Find x and y.
Question 33
Find the equation of a line perpendicular to the line 2y = 5x + 4 which passes (4, 2).
Question 34
In a right angle triangle, if tan θ = ¾ what is cos θsin θ
Question 35
A man walks 100m due west from a point X to Y, he then walks 100m due North to a point Z. Find the bearing of X from Z
Question 36
The derivative of $(2x+1)(3x+1)$ is
Question 37
Find the derivative of $\frac{\sin \theta }{\cos \theta }$
Question 38
Find the value of x at the minimum point of the curve $y={{x}^{3}}+{{x}^{2}}-x+1$
Question 39
Evaluate $\int\limits_{0}^{1}{(3-2x)dx}$ | 2018-07-17 01:54:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5495163798332214, "perplexity": 1070.5609847067512}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589537.21/warc/CC-MAIN-20180717012034-20180717032034-00036.warc.gz"} |
https://orbit.dtu.dk/en/publications/343-fjconvstep-8mhz-bandwidth-fourthorder-pseudodifferential-ringamplifierbased-continuoustime-deltasigma-adc-in-65-nm(43d3f8ea-2289-479c-91a6-dd0297bdc69d).html | ## 34.3 fJ/conv.-step 8-MHz Bandwidth Fourth-Order Pseudo-Differential Ring-Amplifier-Based Continuous-Time Delta–Sigma ADC in 65 nm
Research output: Contribution to journalJournal article – Annual report year: 2019Researchpeer-review
### DOI
This letter presents two pseudo-differential ring amplifiers (RAs) suitable for a continuous-time (CT) operation as an alternative to traditional amplifiers. The designs retain the advantages of RAs, scale with process technology, and do not require a periodic reset. The RAs are designed to operate in an integrator configuration and use different methods to achieve stability in continuous time. A prototype was fabricated in a 65-nm CMOS containing two versions of a CT delta–sigma ADC using the two RAs presented. The ADCs consist of a fourth-order loop filter with optimized zeros, a single-bit quantizer that operates at a sampling frequency of 320 MHz, and a digital-to-analog converter. The best design proposed achieves a measured peak signal-to-noise and distortion ratio of 50.6 dB for an 8-MHz bandwidth, a dynamic range of 53.2 dB, and consumes 152 ${\mu }\text{W}$ at a supply of 1.1 V. The obtained figure of merit is 34.3 fJ/conv.-step which outperforms state-of-the-art delta–sigma ADCs in that specification range and is 77% superior to its traditional operational transconductance amplifier-based ADC counterpart.
Original language English Ieee Solid-state Circuits Letters 1 10 198-201 2573-9603 https://doi.org/10.1109/LSSC.2019.2910468 Published - 2018
Citations Web of Science® Times Cited: No match on DOI
### Research areas
• Analog to digital converter, Continuous-time (CT), Delta–sigma, Oversampled, Ring amplifiers (RAs)
ID: 176486136 | 2019-09-17 10:49:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18011455237865448, "perplexity": 8563.994369808424}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573070.36/warc/CC-MAIN-20190917101137-20190917123137-00081.warc.gz"} |
https://learn.careers360.com/engineering/question-need-explanation-for-mean-of-100-observations-is-45-it-was-later-found-that-two-observations-19-and-31-were-incorrectly-recorded-as-91-and-13-the-correct-mean-is/ | #### Mean of 100 observations is 45. It was later found that two observations 19 and 31 were incorrectly recorded as 91 and 13. The correct mean is: Option 1) 44 Option 2) 44.46 Option 3) 45 Option 4) 45.54
As learnt in
ARITHMETIC Mean -
For the values x1, x2, ....xn of the variant x the arithmetic mean is given by
in case of discrete data.
-
Given that,
But two numbers (19+31 = 50) were incorrect
So, net sum = 4500 - 50 = 4450
Add correct numbers (91+13 = 104)
⇒ 4450 +104 = 4554
⇒ new mean = 4554/100 = 45.54
Option 1)
44
This option is incorrect
Option 2)
44.46
This option is incorrect
Option 3)
45
This option is incorrect
Option 4)
45.54
This option is correct | 2023-03-24 12:57:14 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9112167954444885, "perplexity": 6253.751730939215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00627.warc.gz"} |
http://math.stackexchange.com/questions/229405/how-to-begin-combinatorial-proof | # How to begin Combinatorial Proof
The question states to give a combinatorial proof for:
$$\sum_{k=1}^{n}k{n \choose k}^2 = n{{2n-1}\choose{n-1}}$$
Honestly, I have no idea how to begin. I want to do a two-way counting proof, looking at the LHS and the RHS correct? Any help would be greatly appreciated.
-
Did you try induction? – Nikita Evseev Nov 5 '12 at 3:04
@nikita2: "Combinatorial proof" means no induction. – wj32 Nov 5 '12 at 3:08
## 1 Answer
We have a group of $2n$ people, $n$ female and $n$ male. We want to select a committee of $n$ people, including a female Chair.
We can select the Chair first. There are $n$ ways to do this. For each of these ways, there are $\binom{2n-1}{n-1}$ ways to choose the rest of the committee. Thus there are $n\binom{2n-1}{n-1}$ ways to choose a committee with female Chair.
We now count the number of committees with female Chair in a different way. The committee will have a total of $k$ females, where $k$ ranges from $1$ to $n$, and $n-k$ males.
We can select $k$ females and $n-k$ males in $\binom{n}{k}\binom{n}{n-k}$ ways. For each of these ways, the Chair can be chosen from the $k$ females in $k$ ways. Thus there are $k\binom{n}{k}\binom{n}{n-k}$ ways to make a committee with $k$ females, including a female Chair, and $n-k$ males.
Finally, note that $\binom{n}{n-k}=\binom{n}{k}$, and sum over all $k$ from $1$ to $n$. The number of committees with female Chair is $\sum_{k=1}^n k\binom{n}{k}^2$.
-
Can you briefly describe how you thought this story up? I'm simply curious. – Benjamin Dickman Nov 5 '12 at 3:12
Why is it $n-k$ males instead of $2n - k$ males? – alexthebake Nov 5 '12 at 3:15
@alexthebake: You are trying to select $n$ people in total, so since there already $k$ females, there must be $n-k$ males. – wj32 Nov 5 '12 at 3:16
@alexthebake: Because we are making a committee of $n$ people. If we have $k$ females, we must have $n-k$ males. – André Nicolas Nov 5 '12 at 3:17 | 2015-05-29 02:23:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7688151597976685, "perplexity": 427.6762667933695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929832.32/warc/CC-MAIN-20150521113209-00300-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://puzzling.stackexchange.com/questions/23654/spooky-five-words | # Spooky Five Words (-----|||||)
Bringing this puzzle type back again.
(See the original for the solution format.)
My first is what you will seek.
My second is what you should be.
My third is something all monsters have.
My fourth is what you may feel.
My fifth is the shameful answer the following day.
Hint
For 5, there is an abbreviation involved.
• I would like to know the shameful answer the following day, to which question =)
– Alex
Oct 29, 2015 at 19:43
• @Alex The question is obviously, "Did you eat all your Halloween candy in one night?" Oct 30, 2015 at 2:26
$$\begin{matrix}C&A&N&D&Y\\A&W&A&R&E\\N&A&M&E&S\\D&R&E&A&D\\Y&E&S&D&A\\\end{matrix}$$ | 2022-09-27 23:57:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2927846908569336, "perplexity": 4802.807493039351}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335059.31/warc/CC-MAIN-20220927225413-20220928015413-00319.warc.gz"} |
http://elibm.org/issue?q=se:2064+in:283526 | ## A survey of minimum saturated graphs
### Summary
Summary: Given a family of (hyper)graphs F a (hyper)graph G is said to be F-saturated if G is F -free for any F $\in F$ but for any edge e in the complement of G the (hyper)graph G + e contains some F $\in F$. We survey the problem of determining the minimum size of an F-saturated (hyper)graph and collect many open problems and conjectures.
05C35 | 2019-04-24 03:05:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6265571713447571, "perplexity": 1363.7811979532357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578624217.55/warc/CC-MAIN-20190424014705-20190424040705-00395.warc.gz"} |
https://raweb.inria.fr/rapportsactivite/RA2020/zenith/index.html | 2020
Activity report
Project-Team
ZENITH
RNSR: 201121208J
Research center
In partnership with:
CNRS, Université de Montpellier
Team name:
Scientific Data Management
In collaboration with:
Laboratoire d'informatique, de robotique et de microélectronique de Montpellier (LIRMM)
Domain
Perception, Cognition and Interaction
Theme
Data and Knowledge Representation and Processing
Creation of the Team: 2011 January 01, updated into Project-Team: 2012 January 01
Keywords
• A1.1. Architectures
• A3.1. Data
• A3.3. Data and knowledge analysis
• A4. Security and privacy
• A4.8. Privacy-enhancing technologies
• A5.4.3. Content retrieval
• A5.7. Audio modeling and processing
• A9.2. Machine learning
• A9.3. Signal analysis
• B1. Life sciences
• B1.1. Biology
• B1.1.7. Bioinformatics
• B1.1.11. Plant Biology
• B3.3. Geosciences
• B4. Energy
• B6. IT and telecom
• B6.5. Information systems
1 Team members, visitors, external collaborators
Research Scientists
• Patrick Valduriez [Team leader, Inria, Senior Researcher, HDR]
• Reza Akbarinia [Inria, Researcher, HDR]
• Alexis Joly [Inria, Senior Researcher, HDR]
• Antoine Liutkus [Inria, Researcher]
• Florent Masseglia [Inria, Senior Researcher, HDR]
• Didier Parigot [Inria, Researcher, HDR]
• Dennis Shasha [NYU, USA, Senior Researcher]
Faculty Member
• Esther Pacitti [Univ of Montpellier, Professor, HDR]
PhD Students
• Heraldo Borges [CEFET/RJ, Brazil]
• Benjamin Deneu [Inria]
• Lamia Djebour [Ministry of Higher Education, Algeria]
• Joaquim Estopinan [Inria, from Nov 2020]
• Camille Garcin [Univ of Montpellier, from Oct 2020]
• Gaetan Heidsieck [Inria]
• Quentin Leroy [INA]
• Titouan Lorieul [Univ of Montpellier, until Sep 2020]
• Khadidja Meguelati [INRAE, until May 2020]
• Daniel Rosendo [Inria, Rennes]
• Alena Shilova [Inria, Bordeaux]
Technical Staff
• Antoine Affouard [Inria, Engineer]
• Heraldo Borges [Inria, Engineer, from Dec 2020]
• Julien Champ [Inria, Engineer]
• Mathias Chouet [Inria, Engineer, from Oct 2020]
• Theo Delfieu [Inria, Engineer, from Jun 2020]
• Baldwin Dumortier [Inria, Engineer, from Feb 2020]
• Hugo Gresse [Inria, Engineer, from Jun 2020]
• Oleksandra Levchenko [Inria, Engineer]
• Tanmoy Mondal [Inria, Engineer, until May 2020]
• Fabian Robert Stoter [Inria, Engineer]
Interns and Apprentices
• Felix Pucheral [Université Gustave Eiffel, from May 2020 until Jun 2020]
• Nathalie Brillouet [Inria]
2 Overall objectives
Data-intensive science such as agronomy, astronomy, biology and environmental science must deal with overwhelming amounts of experimental data, as produced through empirical observation and simulation. Similarly, digital humanities have been faced for decades with the problem of exploiting vast amounts of digitized cultural and historical data, such as broadcasted radio or TV content. Such data must be processed (cleaned, transformed, analyzed) in order to draw new conclusions, prove scientific theories and eventually produce knowledge. However, constant progress in scientific observational instruments (e.g. satellites, sensors, large hadron collider), simulation tools (that foster in silico experimentation) or digitization of new content by archivists create a huge data overload. For example, climate modeling data has hundreds of exabytes.
Scientific data is very complex, in particular because of the heterogeneous methods, the uncertainty of the captured data, the inherently multiscale nature (spatial, temporal) of many sciences and the growing use of imaging (e.g. molecular imaging), resulting in data with hundreds of dimensions (attibutes, features, etc.). Modern science research is also highly collaborative, involving scientists from different disciplines (e.g. biologists, soil scientists, and geologists working on an environmental project), in some cases from different organizations in different countries. Each discipline or organization tends to produce and manage its own data, in specific formats, with its own processes. Thus, integrating such distributed data gets difficult as the amounts of heterogeneous data grow. Finally, a major difficulty is to interpret scientific data. Unlike web data, e.g. web page keywords or user recommendations, which regular users can understand, making sense out of scientific data requires high expertise in the scientific domain. Furthermore, interpretation errors can have highly negative consequences, e.g. deploying an oil driller under water at a wrong position.
Despite the variety of scientific data, we can identify common features: big data; manipulated through workflows; typically complex, e.g. multidimensional; with uncertainty in the data values, e.g., to reflect data capture or observation; important metadata about experiments and their provenance; and mostly append-only (with rare updates).
The three main challenges of scientific data management can be summarized by: (1) scale (big data, big applications); (2) complexity (uncertain, high-dimensional data), (3) heterogeneity (in particular, data semantics heterogeneity). These challenges are also those of data science, with the goal of making sense out of data by combining data management, machine learning, statistics and other disciplines. The overall goal of Zenith is to address these challenges, by proposing innovative solutions with significant advantages in terms of scalability, functionality, ease of use, and performance. To produce generic results, we strive to develop architectures, models and algorithms that can be implemented as components or services in specific computing environments, e.g. the cloud. We design and validate our solutions by working closely with our scientific partners in Montpellier such as CIRAD, INRAE and IRD, which provide the scientific expertise to interpret the data. To further validate our solutions and extend the scope of our results, we also foster industrial collaborations, even in non scientific applications, provided that they exhibit similar challenges.
Our approach is to capitalize on the principles of distributed and parallel data management. In particular, we exploit: high-level languages as the basis for data independence and automatic optimization; declarative languages to manipulate data and workflows; and highly distributed and parallel environments such as cluster and cloud for scalability and performance. We also exploit machine learning, probabilities and statistics for high-dimensional data processing, data analytics and data search.
3 Research program
3.1 Distributed Data Management
Data management is concerned with the storage, organization, retrieval and manipulation of data of all kinds, from small and simple to very large and complex. It has become a major domain of computer science, with a large international research community and a strong industry. Continuous technology transfer from research to industry has led to the development of powerful DBMS, now at the heart of any information system, and of advanced data management capabilities in many kinds of software products (search engines, application servers, document systems, etc.).
To deal with the massive scale of scientific data, we exploit large-scale distributed systems, with the objective of making distribution transparent to the users and applications. Thus, we capitalize on the principles of large-scale distributed systems such as clusters, peer-to-peer (P2P) and cloud.
Data management in distributed systems has been traditionally achieved by distributed database systems which enable users to transparently access and update several databases in a network using a high-level query language (e.g. SQL). Transparency is achieved through a global schema which hides the local databases' heterogeneity. In its simplest form, a distributed database system supports a global schema and implements distributed database techniques (query processing, transaction management, consistency management, etc.). This approach has proved to be effective for applications that can benefit from centralized control and full-fledge database capabilities, e.g. information systems. However, it cannot scale up to more than tens of databases.
Parallel database systems extend the distributed database approach to improve performance (transaction throughput or query response time) by exploiting database partitioning using a multiprocessor or cluster system. Although data integration systems and parallel database systems can scale up to hundreds of data sources or database partitions, they still rely on a centralized global schema and strong assumptions about the network.
In contrast, peer-to-peer (P2P) systems adopt a completely decentralized approach to data sharing. By distributing data storage and processing across autonomous peers in the network, they can scale without the need for powerful servers. P2P systems typically have millions of users sharing petabytes of data over the Internet. Although very useful, these systems are quite simple (e.g. file sharing), support limited functions (e.g. keyword search) and use simple techniques (e.g. resource location by flooding) which have performance problems. A P2P solution is well-suited to support the collaborative nature of scientific applications as it provides scalability, dynamicity, autonomy and decentralized control. Peers can be the participants or organizations involved in collaboration and may share data and applications while keeping full control over their (local) data sources. But for very-large scale scientific data analysis, we believe cloud computing is the right approach as it can provide virtually infinite computing, storage and networking resources. However, current cloud architectures are proprietary, ad-hoc, and may deprive users of the control of their own data. Thus, we postulate that a hybrid P2P/cloud architecture is more appropriate for scientific data management, by combining the best of both approaches. In particular, it will enable the clean integration of the users’ own computational resources with different clouds.
3.2 Big Data
Big data (like its relative, data science) has become a buzz word, with different meanings depending on your perspective, e.g. 100 terabytes is big for a transaction processing system, but small for a web search engine.
Although big data has been around for a long time, it is now more important than ever. We can see overwhelming amounts of data generated by all kinds of devices, networks and programs, e.g. sensors, mobile devices, connected objects (IoT), social networks, computer simulations, satellites, radiotelescopes, etc. Storage capacity has doubled every 3 years since 1980 with prices steadily going down, making it affordable to keep more data around. Furthermore, massive data can produce high-value information and knowledge, which is critical for data analysis, decision support, forecasting, business intelligence, research, (data-intensive) science, etc.
The problem of big data has three main dimensions, quoted as the three big V's:
• Volume: refers to massive amounts of data, making it hard to store, manage, and analyze (big analytics);
• Velocity: refers to continuous data streams being produced, making it hard to perform online processing and analysis;
• Variety: refers to different data formats, different semantics, uncertain data, multiscale data, etc., making it hard to integrate and analyze.
There are also other V's such as: validity (is the data correct and accurate?); veracity (are the results meaningful?); volatility (how long do you need to store this data?).
Many different big data management solutions have been designed, primarily for the cloud, as cloud and big data are synergistic. They typically trade consistency for scalability, simplicity and flexibility, hence the new term Data-Intensive Scalable Computing (DISC). Examples of DISC systems include data processing frameworks (e.g. Hadoop MapReduce, Apache Spark, Pregel), file systems (e.g. Google GFS, HDFS), NoSQL systems (Google BigTable, Hbase, MongoDB), NewSQL systems (Google F1, CockroachDB, LeanXcale). In Zenith, we exploit or extend DISC technologies to fit our needs for scientific workflow management and scalable data analysis.
3.3 Data Integration
Scientists can rely on web tools to quickly share their data and/or knowledge. Therefore, when performing a given study, a scientist would typically need to access and integrate data from many data sources (including public databases). Data integration can be either physical or logical. In the former, the source data are integrated and materialized in a data warehouse. In logical integration, the integrated data are not materialized, but accessed indirectly through a global (or mediated) schema using a data integration system. These two approaches have different trade-offs, e.g. efficient analytics but only on historical data for data warehousing versus real-time access to data sources for data integration systems (e.g. web price comparators).
In both cases, to understand a data source content, metadata (data that describe the data) is crucial. Metadata can be initially provided by the data publisher to describe the data structure (e.g. schema), data semantics based on ontologies (that provide a formal representation of the domain knowledge) and other useful information about data provenance (publisher, tools, methods, etc.). Scientific metadata is very heterogeneous, in particular because of the autonomy of the underlying data sources, which leads to a large variety of models and formats. Thus, it is necessary to identify semantic correspondences between the metadata of the related data sources. This requires the matching of the heterogeneous metadata, by discovering semantic correspondences between ontologies, and the annotation of data sources using ontologies. In Zenith, we rely on semantic web techniques (e.g. RDF and SPARQL) to perform these tasks and deal with high numbers of data sources.
Scientific workflow management systems (SWfMS) are also useful for data integration. They allow scientists to describe and execute complex scientific activities, by automating data derivation processes, and supporting various functions such as provenance management, queries, reuse, etc. Some workflow activities may access or produce huge amounts of distributed data. This requires using distributed and parallel execution environments. However, existing workflow management systems have limited support for data parallelism. In Zenith, we use an algebraic approach to describe data-intensive workflows and exploit parallelism.
3.4 Data Analytics
Data analytics refers to a set of techniques to draw conclusions through data examination. It involves data mining, statistics, and data management, and is applied to categorical and continuous data. In the Zenith team, we are interested in both of these data types. Categorical data designates a set of data that can be described as “check boxes”. It can be names, products, items, towns, etc. A common illustration is the market basket data, where each item bought by a client is recorded and the set of items is the basket. The typical data mining problems with this kind of data are:
• Frequent itemsets and association rules. In this case, the data is usually a table with a high number of rows and the data mining algorithm extracts correlations between column values. A typical example of frequent itemset from a sensor network in a smart building would say that “in 20% rooms, the door is closed, the room is empty, and lights are on.”
• Frequent sequential pattern extraction. This problem is very similar to frequent itemset discovery but considering the order between. In the smart building example, a frequent sequence could say that “in 40% of rooms, lights are on at time $i$, the room is empty at time $i+j$ and the door is closed at time $i+j+k$”.
• Clustering. The goal of clustering is to group together similar data while ensuring that dissimilar data will not be in the same cluster. In our example of smart buildings, we could find clusters of rooms, where offices will be in one category and copy machine rooms in another because of their differences (hours of people presence, number of times lights are turned on/off, etc.).
Continuous data are numeric records that can have an infinite number of values between any two values. A temperature value or a timestamp are examples of such data. They are involved in a widely used type of data known as time series: a series of values, ordered by time, and giving a measure, e.g. coming from a sensor. There is a large number of problems that can apply to this kind of data, including:
• Indexing and retrieval. The goal, here, is usually to find, given a query $q$ and a time series dataset $D$, the records of $D$ that are most similar to $q$. This may involve any transformation of $D$ by means of an index or an alternative representation for faster execution.
• Pattern and outlier detection. The discovery of recurrent patterns or atypical sub-windows in a time series has applications in finance, industrial manufacture or seismology, to name a few. It calls for techniques that avoid pairwise comparisons of all the sub-windows, which would lead to prohibitive response times.
• Clustering. The goal is the same as categorical data clustering: group similar time series and separate dissimilar ones.
One main problem in data analytics is to deal with data streams. Existing methods have been designed for very large data sets where complex algorithms from artificial intelligence were not efficient because of data size. However, we now must deal with data streams, sequences of data events arriving at high rate, where traditional data analytics techniques cannot complete in real-time, given the infinite data size. In order to extract knowledge from data streams, the data mining community has investigated approximation methods that could yield good result quality.
3.5 High Dimensional Data Processing and Search
High dimensionality is inherent in applications involving images, audio and text as well as in many scientific applications involving raster data or high-throughput data. Because of the dimensionality curse, technologies for processing and analyzing such data cannot rely on traditional relational DBMS or data mining methods. It rather requires machine learning methods such as dimensionality reduction, representation learning or random projection. The activity of Zenith in this domain focuses on methods for large-scale data processing and search, in particular in the presence of strong uncertainty and/or ambiguity. Actually, while small datasets are often characterized by a careful collection process, massive amounts of data often come with outliers and spurrious items, because it appears impossible to guarantee faultless collection at massive bandwidth. Another source of noise is often the sensor itself, that may be of low quality but of high sampling rate, or even the actual content, e.g. in cultural heritage applications when historical content appears seriously damaged by time. To attack these difficult problems, we focus on the following research topics:
• Uncertainty estimation. Items in massive datasets may either be uncertain, e.g. for automatically annotated data as in image analysis, or be more or less severely corrupted by noise, e.g. in noisy audio recordings or in the presence of faulty sensors. In both cases, the concept of uncertainty is central for the end-user to exploit the content. In this context, we use probability theory to quantify uncertainty and propose machine learning algorithms that may operate robustly, or at least assess the quality of their output. This vast topic of research is guided by large-scale applications (both data search and data denoising), and our research is oriented towards computationally effective methods.
• Deep neural networks. A major breakthrough in machine learning performance has been the advent of deep neural networks, which are characterized by high numbers (millions) of parameters and scalable learning procedures. We are striving towards original architectures and methods that are theoretically grounded and offer state-of-the-art performance for data search and processing. The specific challenges we investigate are: very high dimensionality for static data and very long-term dependency for temporal data, both in the case of possibly strong uncertainty or ambiguity (e.g. hundreds of thousands of classes).
• Community service. Research in machine learning is guided by applications. In Zenith, two main communities are targeted: botany, and digital humanities. In both cases, our observation is that significant breakthroughs may be achieved by connecting these communities to machine learning researchers. This may be achieved through wording application-specific problems in classical machine learning parlance. Thus, the team is actively involved in the organization of international evaluation campaigns that allow machine learning researchers to propose new methods while solving important application problems.
4 Application domains
4.1 Data-intensive Scientific Applications
The application domains covered by Zenith are very wide and diverse, as they concern data-intensive scientific applications, i.e., most scientific applications. Since the interaction with scientists is crucial to identify and tackle data management problems, we are dealing primarily with application domains for which Montpellier has an excellent track record, i.e., agronomy, environmental science, life science, with scientific partners like INRAE, IRD and CIRAD. However, we are also addressing other scientific domains (e.g. astronomy, oil extraction, music processing) through our international collaborations.
Let us briefly illustrate some representative examples of scientific applications on which we have been working on.
• Management of astronomical catalogs. An example of data-intensive scientific applications is the management of astronomical catalogs generated by the Dark Energy Survey (DES) project on which we are collaborating with researchers from Brazil. In this project, huge tables with billions of tuples and hundreds of attributes (corresponding to dimensions, mainly double precision real numbers) store the collected sky data. Data are appended to the catalog database as new observations are performed and the resulting database size has hundreds of TB. Scientists around the globe can query the database with queries that may contain a considerable number of attributes. The volume of data that this application holds poses important challenges for data management. In particular, efficient solutions are needed to partition and distribute the data in several servers. An efficient partitioning scheme should try to minimize the number of fragments accessed in the execution of a query, thus reducing the overhead associated to handle the distributed execution.
• Personal health data analysis and privacy. Today, it is possible to acquire data on many domains related to personal data. For instance, one can collect data on her daily activities, habits or health. It is also possible to measure performance in sports. This can be done thanks to sensors, communicating devices or even connected glasses. Such data, once acquired, can lead to valuable knowledge for these domains. For people having a specific disease, it might be important to know if they belong to a specific category that needs particular care. For an individual, it can be interesting to find a category that corresponds to her performances in a specific sport and then adapt her training with an adequate program. Meanwhile, for privacy reasons, people will be reluctant to share their personal data and make them public. Therefore, it is important to provide them with solutions that can extract such knowledge from everybody's data, while guaranteeing that their private data won't be disclosed to anyone.
• Botanical data sharing. Botanical data is highly decentralized and heterogeneous. Each actor has its own expertise domain, hosts its own data, and describes them in a specific format. Furthermore, botanical data is complex. A single plant's observation might include many structured and unstructured tags, several images of different organs, some empirical measurements and a few other contextual data (time, location, author, etc.). A noticeable consequence is that simply identifying plant species is often a very difficult task; even for the botanists themselves (the so-called taxonomic gap). Botanical data sharing should thus speed up the integration of raw observation data, while providing users an easy and efficient access to integrated data. This requires to deal with social-based data integration and sharing, massive data analysis and scalable content-based information retrieval. We address this application in the context of the French initiative Pl@ntNet, with CIRAD and IRD.
• Biological data integration and analysis. Biology and its applications, from medicine to agronomy and ecology, are now producing massive data, which is revolutionizing the way life scientists work. For instance, using plant phenotyping platforms such as PhenoDyn and PhenoArch at INRAE Montpellier, quantitative genetic methods allow to identify genes involved in phenotypic variation in response to environmental conditions. These methods produce large amounts of data at different time intervals (minutes to months), at different sites and at different scales ranging from small tissue samples to the entire plant until whole plant population. Analyzing such big data creates new challenges for data management and data integration.
• Audio heritage preservation. Since the end of the 19th century, France has commissioned ethnologists to record the world's immaterial audio heritage. This results in datasets of dozens of thousands of audio recordings from all countries and more than 1200 ethnies. Today, this data is gathered under the name of Archives du CNRS — Musée de l'Homme and is handled by the CREM (Centre de Recherche en Ethno-Musicologie). Profesional scientists in digital humanities are accessing this data daily for their investigations, and several important challenges arise to ease their work. The KAMoulox project, lead by A. Liutkus, targets at offering online processing tools for the scientists to automatically restore this old material on demand. In the same vein, we have an ongoing collaboration with Radio France, that has large amounts of archives to restore, for repurposing applications.
These application examples illustrate the diversity of requirements and issues which we are addressing with our scientific application partners. To further validate our solutions and extend the scope of our results, we also want to foster industrial collaborations, even in non scientific applications, provided that they exhibit similar challenges.
5 Social and environmental responsibility
We do consider the ecological impact of our technology, especially large data management.
• In our work on cache-based scheduling of scientific workflows in multisite clouds, we can minimize the monetary cost of the cloud, which directly reflects the energy consumption.
• We have also started to address the (major) problem of energy consumption of our ML models, by introducing energy-based metrics to assess the energy consumption during the training on GPU of our ML models. Furthermore, we want to improve training pipelines that reduce the need for training models from scratch. At inference, network compression methods can reduce the memory footprint and the computational requirements when deploying models.
• In the design of the Pl@ntnet mobile application, we adopt an eco-responsible approach, taking care not to integrate addictive, energy-intensive or non-essential functionalities to uses that promote the preservation of biodiversity and environment.
• To reduce our carbon footprint, we reduce to the minimum the number of long-distance trips, and favor train as much as possible. We also trade conference publications for journal publications, to avoid traveling. For instance, in 2020, we have 27 journal publications versus 19 conference publications.
6 Highlights of the year
6.1 Awards
• The Pl@ntnet project (Alexis Joly, Pierre Bonnet, Hervé Goëau, Julien Champ, Jean-Christophe Lombardo and Antoine Affouard) won the innovation price from Inria, the French Academy of Science and Dassault Systems.
• The paper “Distributed Caching of Scientific Workflows in Multisite Cloud” 46 by Gaëtan Heidsieck, Daniel de Oliveira, Esther Pacitti, Christophe Pradal, François Tardieu, and Patrick Valduriez, obtained the best paper award from DEXA 2020.
• Fabian Stoter in collaboration with Inria Nancy won the first place at the Global Pytorch Summer Hackaton 2020, with the DeMask software that provides an end-to-end model for enhancing speech while wearing face masks.
• Antoine Liutkus received an IEEE outstanding reviewer award for his reviewing in IEEE transactions and conferences (notably TASLP and ICASSP).
6.2 International
• The Inria Brasil web site has been created to reflect the long-live collaboration between Inria and LNCC, the Brazilian National Scientific Computing Laboratory, and associated Brazilian universities in HPC, AI, Data Science and Scientific Computing. The collaboration is headed by Frédéric Valentin (LNCC, Inria International Chair) and Patrick Valduriez.
• Pl@ntNet has become a data provider to GBIF, the world's largest government-funded biodiversity data platform.
7 New software and platforms
7.1 New software
7.1.1 Pl@ntNet
• Keywords: Plant identification, Deep learning, Citizen science
• Functional Description: Pl@ntNet is a participatory platform and information system dedicated to the production of botanical data through deep learning-based plant identification. It includes 3 main front-ends, an Android app (the most advanced and the most used one), an iOs app (being currently re-developed) and a web version. The main feature of the application is to return the ranked list of the most likely species providing an image or an image set of an individual plant. In addition, Pl@ntNet’s search engine returns the images of the dataset that are the most similar to the queried observation allowing interactive validation by the users. The back-office running on the server side of the platform is based on Snoop visual search engine (a software developed by ZENITH) and on NewSQL technologies for the data management. The application is distributed in more than 200 countries (20M downloads) and allows identifying about 30K plant species at present time.
• Publication:
• Contact: Alexis Joly
• Participants: Antoine Affouard, Jean-Christophe Lombardo, Pierre Bonnet, Hervé Goëau, Mathias Chouet, Julien Champ, Alexis Joly
7.1.2 ThePlantGame
• Keyword: Crowd-sourcing
• Functional Description: ThePlantGame is a participatory game whose purpose is the production of big taxonomic data to improve our knowledge of biodiversity. One major contribution is the active training of the users based on innovative sub-task creation and assignment processes that are adaptive to the increasing skills of the user. Thousands of players are registered and produce on average about tens new validated plant observations per day. The accuracy of the produced taxonnomic tags is very high (about 95%), which is quite impressive considering the fact that a majority of users are beginners when they start playing.
• Publication:
• Contact: Alexis Joly
• Participants: Maximilien Servajean, Alexis Joly
7.1.3 DfAnalyzer
• Name: Dataflow Analysis
• Keywords: Data management, Monitoring, Runtime Analysis
• Functional Description: DfAnalyzer is a tool for monitoring, debugging, steering, and analysis of dataflows while being generated by scientific applications. It works by capturing strategic domain data, registering provenance and execution data to enable queries at runtime. DfAnalyzer provides lightweight dataflow monitoring components to be invoked by high performance applications. It can be plugged in scripts, or Spark applications, in the same way users already plug visualization library components.
• URL:
• Publication:
• Contact: Patrick Valduriez
• Participants: Vitor Sousa Silva, Daniel De Oliveira, Marta Mattoso, Patrick Valduriez
• Partners: COPPE/UFRJ, Uff
7.1.4 CloudMdsQL Compiler
• Keywords: Optimizing compiler, NoSQL, Data integration
• Functional Description: The CloudMdsQL (Cloud Multi-datastore Query Language) polystore transforms queries expressed in a common SQL-like query language into an optimized query execution plan to be executed over multiple cloud data stores (SQL, NoSQL, HDFS, etc.) through a query engine. The compiler/optimizer is implemented in C++ and uses the Boost.Spirit framework for parsing context-free grammars. CloudMdsQL has been validated on relational, document and graph data stores in the context of the CoherentPaaS European project.
• Publication:
• Authors: Boyan Kolev, Patrick Valduriez
• Contact: Patrick Valduriez
• Participants: Boyan Kolev, Oleksandra Levchenko, Patrick Valduriez
7.1.5 Savime
• Name: Simulation And Visualization IN-Memory
• Keywords: Data management., Distributed Data Management
• Functional Description: SAVIME is a multi-dimensional array DBMS for scientific applications. It supports a novel data model called TARS (Typed ARray Schema), which extends the basic array data model with typed arrays. In TARS, the support of application dependent data characteristics is provided through the definition of TAR objects, ready to be manipulated by TAR operators. This approach provides much flexibility for capturing internal data layouts through mapping functions, which makes data ingestion independent of how simulation data has been produced, thus minimizing ingestion time.
• Publication:
• Contact: Patrick Valduriez
• Participants: Hermano Lustosa, Fabio Porto, Patrick Valduriez
• Partner: LNCC - Laboratório Nacional de Computação Científica
7.1.6 OpenAlea
• Keywords: Bioinformatics, Biology
• Functional Description: OpenAlea is an open source project primarily aimed at the plant research community. It is a distributed collaborative effort to develop Python libraries and tools that address the needs of current and future works in Plant Architecture modeling. It includes modules to analyze, visualize and model the functioning and growth of plant architecture. It was formally developed in the Inria VirtualPlants team.
• Release Contributions: OpenAlea 2.0 adds to OpenAlea 1.0 a high-level formalism dedicated to the modeling of morphogenesis that makes it possible to use several modeling paradigms (Blackboard, L-systems, Agents, Branching processes, Cellular Automata) expressed with different languages (Python, L-Py, R, Visual Programming, ...) to analyse and simulate shapes and their development.
• Publications:
• Authors: Samuel Dufour Kowalski, Christophe Pradal
• Participants: Christian Fournier, Christophe Godin, Christophe Pradal, Frédéric Boudon, Patrick Valduriez, Esther Pacitti, Yann Guédon
7.1.7 Imitates
• Name: Indexing and mining Massive Time Series
• Keywords: Time Series, Indexing, Nearest Neighbors
• Functional Description: Time series indexing is at the center of many scientific works or business needs. The number and size of the series may well explode depending on the concerned domain. These data are still very difficult to handle and, often, a necessary step to handling them is in their indexing. Imitates is a Spark Library that implements two algorithms developed by Zenith. Both algorithms allow indexing massive amounts of time series (billions of series, several terabytes of data).
• Publication:
• Contact: Florent Masseglia
• Partners: New York University, Université Paris-Descartes
7.1.8 VersionClimber
• Keywords: Software engineering, Deployment, Versionning
• Functional Description: VersionClimber is an automated system to help update the package and data infrastructure of a software application based on priorities that the user has indicated (e.g. I care more about having a recent version of this package than that one). The system does a systematic and heuristically efficient exploration (using bounded upward compatibility) of a version search space in a sandbox environment (Virtual Env or conda env), finally delivering a lexicographically maximum configuration based on the user-specified priority order. It works for Linux and Mac OS on the cloud.
• URL:
• Publication:
• Participants: Christophe Pradal, Dennis Shasha, Sarah Cohen-Boulakia, Patrick Valduriez
• Partners: CIRAD, New York University
7.1.9 UMX
• Name: open-unmix
• Keywords: Source Separation, Audio
• Scientific Description: UMX implements state of the art audio/music source separation with deep neural networks (DNNs). It is intended to serve as a reference in the domain. It has been presented in two major scientific communications: An Overview of Lead and Accompaniment Separation in Music (https://hal-lirmm.ccsd.cnrs.fr/lirmm-01766781) and Music separation with DNNs (Making it work (ISMIR 2018 Tutorial) https://sigsep.github.io/ismir2018_tutorial/index.html#/cover).
• Functional Description: This software implements audio source separation with deep learning, using the Pytorch and Tensorflow frameworks. It comprises the code for both training and testing the separation networks, in a flexible manner. Pre- and post-processing around the actual deep neural nets include sophisticated specific multichannel filtering operations.
• Publication:
• Authors: Antoine Liutkus, Fabian Robert Stoter, Emmanuel Vincent
• Contact: Antoine Liutkus
7.1.10 TDB
• Keywords: Data assimilation, Big data, Data extraction
• Scientific Description: The TDB software comes as a building block for audio machine learning pipelines. It is a scraping tool that allows large scale data augmentation. Its different components allow building a large dataset of samples composed of related audio tracks, as well as the associated metadata. Each sample comprises a dynamic number of entries.
• Functional Description:
The TDB software is composed of two core submodules: First, a data extraction pipeline permits to scrape a provider url so as to extract large amounts of audio data. The provider is assumed to offer audio content in a freely-accessible way through a hardcoded specific structure. The software automatically downloads the data locally under a raw data format. To aggregate the raw data set, a list of item ids is used. The item ids will be requested from the provider given a url in parallel fashion. Second, a data transformation pipeline permits to transform the raw data into a dataset that is compatible with machine learning purposes. Each produced subfolder contains a set of audio files corresponding to a predefined set of sources, along with the associated metadata. A working example is provided.
Each one of theses core components comprises several submodules, notably network handling and audio transcoding. The TDB software must hence be understood as an extract-transform-load (ETL) pipeline that enables applications such as deep learning on large amounts of audio data, assuming that an adequate data provider url is fed into the software.
• Authors: Fabian Robert Stoter, Antoine Liutkus
• Contact: Antoine Liutkus
• Participants: Antoine Liutkus, Fabian Robert Stoter
7.1.11 UMX-PRO
• Name: Unmixing Platform - PRO
• Keywords: Audio signal processing, Source Separation, Deep learning
• Scientific Description:
UMX-PRO is written in Python using the TensorFlow 2 framework and provides an off-the-shelf solution for music source separation (MSS). MSS consists in extracting different instrumental sounds from a mixture signal. In the scenario considered by UMX-PRO, a mixture signal is decomposed into a pre-definite set of so called targets, such as: (scenario 1) {vocals, bass, drums, guitar, other} or (scenario 2) {vocals, accompaniment}.
The following key design choices were made for UMX-PRO: The software revolves around the training and inference of a deep neural network (DNN), building upon the TensorFlow v2 framework. The DNN implemented in UMX-PRO is based on a BLSTM recurrent network. However, the software has been designed to be easily extended to other kinds of network architectures to allow for research and easy extensions. Given an appropriately formatted database (not part of UMX-PRO), the software trains the network. The database has to be split into train and valid subsets, each one being composed of folders called samples. All samples must contain the same set of audio files, having the same duration: one for each desired target. For instance: {vocals.wav, accompaniment.wav}. The software can handle any number of targets, provided they are all present in all samples. Since the model is trained jointly, a larger number of targets increases the GPU memory usage during training. Once the models have been trained, they can be used for separation of new mixtures through a dedicated end-to-end separation network. Interestingly, this end-to-end network comprises an optional refining step called expectation-maximization that usually improves separation quality.
The software comes with full documentation, detailed comments and unit tests.
• Functional Description: UMX-PRO is a TensorFlow v2 implementation for an end-to-end music separation system including network architecture, data pipeline, training code, inference code as well as pre-trained weights.
• Authors: Antoine Liutkus, Fabian Robert Stoter
• Contact: Antoine Liutkus
8 New results
8.1 Scientific Workflows
8.1.1 Runtime Dataflow Analysis with DfAnalyzer
Participants: Patrick Valduriez.
DfAnalyzer is a tool for monitoring, debugging, and analyzing dataflows generated by Computational Science and Engineering (CSE) applications. It collects strategic raw data, registering provenance data, and enabling query processing, all asynchronously and at runtime. DfAnalyzer provides lightweight dataflow components to be invoked by CSE applications using HPC, in the same way computational scientists plug HPC (e.g., PETSc) and visualization (e.g., ParaView) libraries. In 37, we show DfAnalyzer's main functionalities and how to analyze dataflows in CSE applications at runtime. The performance evaluation of CSE executions for a complex multiphysics application shows that DfAnalyzer has negligible time overhead on the total elapsed time.
8.1.2 Data Reduction in Scientific Workflows
Participants: Patrick Valduriez.
Scientific workflows need to be iteratively, and often interactively, executed for large input datasets. Reducing data from input datasets is a powerful way to reduce overall execution time in such workflows. In 38, we adopt the “human-in-the-loop” approach, which enables users to steer the running workflow and reduce subsets from datasets online. We propose an adaptive workflow monitoring approach that combines provenance data monitoring and computational steering to support users in analyzing the evolution of key parameters and determining the subset of data to remove. We extend a provenance data model to keep track of users' interactions when they reduce data at runtime. In our experimental validation, we develop a test case from the oil and gas domain, using a 936-cores cluster. The results on this test case show that the approach yields reductions of 32% of execution time and 14% of the data processed.
8.1.3 Caching of Scientific Workflows in Multisite Cloud
Participants: Gaetan Heidsieck, Christophe Pradal, Esther Pacitti, Patrick Valduriez.
Many scientific experiments are performed using scientific workflows, which are becoming more and more data-intensive. We consider the efficient execution of such workflows in the cloud, leveraging the heterogeneous resources available at multiple cloud sites (geo-distributed data centers). Since it is common for workflow users to reuse code or data from other workflows, a promising approach for efficient workflow execution is to cache intermediate data in order to avoid re-executing entire workflows. In 25, we propose an adaptive caching solution for data-intensive workflows in the cloud. Our solution is based on a new scientific workflow management architecture that automatically manages the storage and reuse of intermediate data and adapts to the variations in task execution times and output data size. In 46 , we propose a distributed solution for caching of scientific workflows in a multisite cloud. We implemented our solutions fro adaptive and distributed caching in the OpenAlea workflow system, together with cache-aware distributed scheduling algorithms. Our experimental evaluation on a three-site cloud with a data-intensive application in plant phenotyping shows that our solution can yield major performance gains.
8.2 Query Processing
8.2.1 Uncertainty Quantification Queries over Big Spatial Data
Participants: Esther Pacitti, Patrick Valduriez.
We consider big spatial data, which is typically produced in scientific areas such as geological or seismic interpretation. The spatial data can be produced by observation (e.g. using sensors or soil instruments) or numerical simulation programs and correspond to points that represent a 3D soil cube area. However, errors in signal processing and modeling create some uncertainties associated with model calculations of true, physical quantities of interest (QOIs), and thus a lack of accuracy in identifying geological or seismic phenomenons. Uncertainty Quantification (UQ) is the process of quantifying such uncertainties. In 29, we consider the problem of answering UQ queries over large spatio-temporal simulation results. We propose the SUQ2 method based on the Generalized Lambda Distribution (GLD) function. To further analyze uncertainty, the main solution is to compute a Probability Density Function (PDF) of each point in the spatial cube area. However, computing PDFs on big spatial data can be very time consuming (from several hours to even months on a computer cluster). In 32, we propose a new solution to efficiently compute such PDFs in parallel using Spark, with three methods: data grouping, machine learning prediction and sampling. We evaluate our solution by extensive experiments on different computer clusters using big data ranging from hundreds of GB to several TB. The experimental results show that our solution scales up very well and can reduce the execution time by a factor of 33 (in the order of seconds or minutes) compared with a baseline method.
8.3 Data Analytics
8.3.1 Massively Distributed Time Series Indexing
Participants: Djamel Edine Yagoubi, Reza Akbarinia, Florent Masseglia.
Indexing is crucial for many data mining tasks that rely on efficient and effective similarity query processing. Thus, indexing large volumes of time series, along with high performance similarity query processing, have became topics of major interest. However, for many applications across diverse domains, the amount of data to be processed might be intractable for a single machine, making existing centralized indexing solutions inefficient.
In 40, we propose a parallel solution to construct the state of the art iSAX-based index over billions of time series by carefully distributing the workload. Our solution takes advantage of parallel data processing frameworks such as MapReduce or Spark. We provide dedicated strategies and algorithms for a deep combination of parallelism and indexing techniques. We also propose a parallel query processing algorithm that, given a query, exploits the available processing nodes to answer the query in parallel using the constructed parallel index. We implemented our algorithms, and evaluated their performance over large volumes of data (up to 4 billion time series of length 256, for a total volume of 6 TB). Our experiments demonstrate high performance with an indexing time of less than 2 hours for more than 1 billion time series, while the state of the art centralized algorithm needs more than 5 days. They also illustrate that our approach is able to process 10M queries in less than 140 seconds, while the centralized algorithm needs almost 2300 seconds.
8.3.2 Efficient Similarity Search in Large Time Series Databases
Participants: Oleksandra Levchenko, Boyan Kolev, Djamel Edine Yagoubi, Reza Akbarinia, Florent Masseglia, Dennis Shasha, Patrick Valduriez.
Fast and accurate similarity search is critical to performing many data mining tasks like motif discovery, classification or clustering.
In 30, we present our parallel solutions, developed based on two state-of-the-art approaches iSAX and sketch, for $k$ nearest-neighbor ($kNN$) search in large databases of time series. We compare the two solutions based on various measures of quality and time performance, and propose a tool that uses the characteristics of application data to determine which solution to choose for that application and how to set the parameters for that solution. Our experiments show that: (i) iSAX and its derivatives perform best in both time and quality when the time series can be characterized by a few low frequency Fourier Coefficients, a regime where the iSAX pruning approach works well. (ii) iSAX performs significantly less well when high frequency Fourier Coefficients have much of the energy of the time series. (iii) A random projection approach based on sketches by contrast is more or less independent of the frequency power spectrum. The experiments show the close relationship between pruning ratio and time for exact iSAX as well as between pruning ratio and the quality of approximate iSAX. Our toolkit analyzes typical time series of an application (i) to determine optimal segment sizes for iSAX and (ii) when to use Parallel Sketches instead of iSAX. Our solutions have been implemented using Spark, evaluated over a cluster of nodes, and have been applied to both real and synthetic data.
8.3.3 Efficient kNN Search in Large Chemometrics Databases
Participants: Reza Akbarinia, Florent Masseglia.
Chemometrics scientists exploit a wide range of tools for the analysis and interpretation of spectroscopic data. One of the objectives of these tools is to associate spectral information with physico-chemical properties in order to predict their properties. Among them, a reference method is PLSR (Partial Least Squares Regression). It is composed of a dimension reduction step (PLS) followed by a regression on the scores produced. A well known issue regarding PLS lies in the difficulty to apprehend non linearities. As a solution, an extension of the method, called KNN-PLS, was developed. However, this solution is based on a neighborhood selection method whose execution time is highly dependent on the size of the database, leading to prohibitive response times.
In 34, we propose a new method, called parSketch-PLS, designed to perform kNN search in large spectral databases. It combines parSketch, a solution we developed for indexing and querying time series, and the PLS method. We compare the PLS and KNN-PLS methods with the parSketch-PLS method. The experiments illustrate that parSketch-PLS offers a good operational trade-off between prediction performance and computational cost. Furthermore, we propose a framework to interpret the neighborhoods returned by comparing their relative sizes with the evolution of performance and the input parameters of parSketch-PLS.
8.3.4 Time Series Clustering via Dirichlet Mixture Models
Dirichlet Process Mixture (DPM) is a model for clustering, with the advantage of automatic discovery of clusters and nice properties, such as the potential convergence to the actual clusters in the data. These advantages come at the price of prohibitive response times, which impairs its adoption and makes centralized DPM approaches inefficient. In 52, we gave a demonstration of DC-DPM (Distributed Computing DPM) and HD4C (High Dimensional Data Distributed Dirichlet Clustering). DC-DPM is a parallel clustering solution that gracefully scales to millions of data points while remaining DPM compliant, which is the challenge of distributing this process. HD4C (High Dimensional Data Distributed Dirichlet Clustering) is a parallel clustering solution that addresses the curse of dimensionality by distributed computing and performs clustering of high dimensional data such as time series (as a function of time), hyperspectral data (as a function of wavelength) etc. The demonstration site is available at: http://147.100.179.112:3838/team/kmeguelati/dpmclustering/
8.3.5 Spatial-Time Series Clustering
Participants: Heraldo Borges, Florent Masseglia.
Discovering motifs in time series data and clustering such data have been widely explored. However, when it comes to spatial-time series, a clear gap can be observed according to the literature review. 12 presents a short overview of space–time series clustering, which can be generally grouped into three main categories such as: hierarchical, partitioning-based, and overlapping clustering. The first category is to identify hierarchies in space–time series data. The second category focuses on determining disjoint partitions among the space–time series data, whereas the third category explores fuzzy logic to determine the different correlations between the space–time series clusters. This work can provide guidance to practitioners for selecting the most suitable methods for their used cases, domains, and applications. 16 presents an approach to discover and rank motifs in spatial-time series, denominated Combined Series Approach (CSA). CSA is based on partitioning the spatial-time series into blocks. Inside each block, subsequences of spatial-time series are combined by means of a hash-based motif discovery algorithm. The approach was evaluated using both synthetic and seismic datasets. CSA outperforms traditional methods designed only for time series. CSA was also able to prioritize motifs that were meaningful both in the context of synthetic data and also according to seismic specialists.
8.4 Machine Learning for Biodiversity Informatics
8.4.1 Machine Learning using Digitized Herbarium Specimens in Phenology
Participants: Julien Champ, Alexis Joly.
Phenology, i.e., the timing of life-history events, is a key trait for understanding responses of organisms to climate. The digitization and online mobilization of herbarium specimens is rapidly advancing our understanding of plant phenological response to climate and climatic change. The current practice of manually harvesting data from individual specimens, however, greatly restricts our ability to scale-up data collection. Our recent investigations have demonstrated that machine learning can facilitate this effort 36. However, present attempts have focused largely on simplistic binary coding of reproductive phenology (e.g., presence/absence of flowers). In 21 (jointly with Harvard University, Boston University, UFBA and CIRAD), we use crowd-sourced phenological data of buds, flowers, and fruits from more than 3,000 specimens of six common wildflower species of the eastern United States to train models using Mask R-CNN to segment and count phenological features. A single global model was able to automate the binary coding of each of the three reproductive stages with more than 87% accuracy. We also successfully estimated the relative abundance of each reproductive structure on a specimen with more than 90% accuracy. Precise counting of features was also successful, but accuracy varied with phenological stage and taxon. Specifically, counting flowers was significantly less accurate than buds or fruits likely due to their morphological variability on pressed specimens. Moreover, our Mask R-CNN model provided more reliable data than non-expert crowd-sourcers but not botanical experts, highlighting the importance of high-quality human training data. Finally, we also demonstrated the transferability of our model to automated phenophase detection and counting of the three Trillium species, which have large and conspicuously-shaped reproductive organs. These results highlight the promise of our two-phase crowd-sourcing and machine-learning pipeline to segment and count reproductive features of herbarium specimens, thus providing high-quality data with which to investigate plant responses to ongoing climatic change.
8.4.2 Analysis of the Use of Pl@ntNet Services for Biodiversity conservation
Participants: Alexis Joly, Benjamin Deneu, Jean-Christophe Lombardo, Antoine Affouard.
In 11 (jointly with the UK Centre for Ecology and Hydrology and CIRAD), we apply the Pl@ntNet identification engine to social media imagery (Flickr in particular) to generate new biodiversity observations. We find that this approach is able to generate new data on species occurrence but that there are biases in both the social media data and the AI image classifier that need to be considered in analyses. This approach could be applied outside the biodiversity domain, to any phenomena of interest that may be captured in social media imagery. The checklist we provide at the end of this paper should therefore be of interest to anyone considering this approach to generating new data. In 15, we present two Pl@ntNet-based citizen science initiatives piloted by conservation practitioners in Europe (France) and Africa (Kenya). We discuss various perspectives of AI-based plants identification, including benefits and limitations. Based on the experiences of field managers, we formulate several recommendations for future initiatives. The recommendations are aimed at a diverse group of conservation managers and citizen science practitioners.
8.4.3 New Methods and Perspectives on Plant Disease Characterization
Participants: Herve Goeau, Alexis Joly.
The control of plant diseases is a major challenge to ensure global food security and sustainable agriculture. Several recent studies have proposed to improve existing procedures for early detection of plant diseases through automatic image recognition systems based on deep learning. In 28, we study these methods in detail, especially those based on convolutional neural networks. We first examine whether it is more relevant to fine-tune a pre-trained model on a plant identification task rather than a general object recognition task. In particular, we show through visualization techniques, that the characteristics learned differ according to the approach adopted and that they do not necessarily focus on the part affected by the disease. Therefore, we introduce a more intuitive method that considers diseases independently of crops, and show that it is more effective than the classic crop-disease pair approach, especially when dealing with disease involving crops that are not illustrated in the training database. In 27, we develop a new technique based on a Recurrent Neural Network (RNN) to automatically locate infected regions and extract relevant features for disease classification. We show experimentally that our RNN-based approach is more robust and has greater ability to generalize to unseen infected crop species and different plant disease domain images compared to classical CNN approaches. We also show that our approach is capable of accurately locating infectious diseases in plants. Our approach, which has been tested on a large number of plant species, should thus contribute to the development of more effective means of detecting and classifying crop pathogens in the near future.
8.4.4 Evaluation of Species Identification and Prediction Algorithms
Participants: Alexis Joly, Herve Goeau, Benjamin Deneu, Titouan Lorieul, Fabian Robert Stoter.
We run a new edition of the LifeCLEF evaluation campaign 48 with the involvement of 16 research teams worldwide. The main outcomes of the 2020 edition are:
• Location-based Species prediction (GeoLifeCLEF). Jointly with Caltech and Microsoft research, we released a new outstanding dataset of 1.9 million species observations paired with high-resolution remote sensing imagery, land cover data, and altitude, in addition to traditional low-resolution climate and soil variables 64. It allowed to highlight for the first time the ability of remote sensing imagery and convolutional neural networks to improve predictive performance of Species Distribution Models (SDM), complementary to traditional approaches 43.
• Plant identification (PlantCLEF). The PlantCLEF 2020 challenge was designed to evaluate to what extent automated identification on the flora of data deficient regions can be improved by the use of herbarium collections. It is based on a dataset of about 1,000 species mainly focused on the South America's Guiana Shield, an area known to have one of the greatest diversity of plants in the world. The challenge was evaluated as a cross-domain classification task where the training set consist of several hundred thousand herbarium sheets and few thousand of photos to enable learning a mapping between the two domains. The results revealed that the recent advances in domain adaptation enable the use of herbarium data to facilitate the identification of rare tropical species for which no or very few other training photos are available 59.
• Bird sounds recognition (BirdCLEF). Passive acoustic monitoring is a cornerstone of the assessment of ecosystem health and the improvement of automated assessment systems has the potential to have a transformative impact on global biodiversity monitoring. The BirdCLEF challenge 49 focuses on the development of reliable detection systems for avian vocalizations in continuous soundscape data. It is the largest evaluation that specifically aims at developing state-of-the-art classifiers to help researchers to cope with conservation challenges of our time. Results obtained in 2020 show Deep neural networks provide good overall baselines but there is still large room for improvement.
8.4.5 Deep Learning Based Instance Segmentation for Precision Agriculture
Participants: Julien Champ, Herve Goeau, Alexis Joly.
Weed removal in agriculture is typically achieved using herbicides. The use of autonomous robots to reduce weeds is a promising alternative solution, although their implementation requires the precise detection and identification of crops and weeds to allow an efficient action. In 20 we propose an instance segmentation approach to this problem making use of a Mask R-CNN model for weeds and crops detection on farmland. Therefore, we created a new data set comprising field images on which the outlines of 2489 specimens from two crop species and four weed species were manually drawn. The probability of detection using the model was quite good but varied significantly depending on the species and size of the plants. In practice, between 10% and 60% of weeds could be removed without too high of a risk of confusion with crop plants. Furthermore, we show that the segmentation of each plant enabled the determination of precise action points such as the barycenter of the plant surface.
8.4.6 Correcting bias in Species Distribution Models
Participants: Christophe Botella, Alexis Joly.
Presence-only Species Distribution Models require background points, which should be consistent with sampling effort across the environmental space to avoid bias. A standard approach is to use uniformly distributed background points (UB). When multiple species are sampled, another approach is to use a set of occurrences from a Target-Group of species as background points (TGOB). In this work 17, we investigate estimation biases when applying TGOB and UB to opportunistic naturalist occurrences. We model species occurrences and observation process as a thinned Poisson point process, and express asymptotic likelihoods of UB and TGOB as a divergence between environmental densities, in order to characterize biases in species niche estimation. To illustrate our results, we simulate species occurrences with different types of niche (specialist/generalist, typical/marginal), sampling effort and TG species density. We conclude that none of the methods are immune to estimation bias, although the pitfalls are different.
8.5 Machine Learning for audio and long time series
Audio data is typically exploited through large repositories. For instance, music right holders face the challenge of exploiting back catalogues of significant sizes while ethnologists and ethnomusicologists need to browse daily through archives of heritage audio recordings that have been gathered across decades. The originality of our research on this aspect is to bring together our expertise in large volumes and probabilistic music signal processing to build tools and frameworks that are useful whenever audio data is to be processed in large batches. In particular, we leverage on the most recent advances in probabilistic and deep learning applied to signal processing from both academia (e.g. Telecom Paris, PANAMA & Multispeech Inria project-teams, Kyoto University) and industry (e.g. Mitsubishi, Sony), with a focus towards large scale community services.
8.5.1 Setting the State of the Art in Music Demixing
Participants: Fabian-Robert Söter, Antoine Liutkus.
We have been very active for years in the topic of music demixing, with a prominent role in defining the state of the art in this domain. Our contributions this year in the domain are numerous. After years of leading SiSEC, the international separation evaluation campaign, we handled the lead to another team. This year, we continued handling our MUSDB18 dataset, which takes some time, notably for granting access rights to all the interested teams and sending out links. It is the #11 dataset on Zenodo with 7500 downloads, making it the most popular music dataset worldwide.
We maintain the open-unmix software, which is an established reference implementation for music source separation. We also participated in the design and implementation of Asteroid 53, a research effort towards a unified software platform for audio separtion research, lead by the Multispeech Inria team. One of our contributions with Asteroid won the first place at the Global Pytorch Summer Hackaton 2020 organized by Facebook.
8.5.2 Deep models for audio and long-range data
Participants: Antoine Liutkus, Fabian-Robert Söter, Baldwin Dumortier.
Our strategy is to go beyond our current expertise on music demixing to address the new and very active topics of audio style transfer, enhancement, and generation, with large scale applications for the exploitation and repurposing of large audio corpora. This means leaving our comfort zone on source separation to address new exciting challenges, notably the use of Transformers in audio. For this purpose, our strategy is to develop new deep learning models, based on Transformers, that allow processing very long time series. On the engineering side, our contributions mostly concern data management and curating large corpora, as mentioned above.
An ongoing research effort concerns long-term interactions in time-series. We fully embraced the recently proposed Transformer architecture, that models inter-sample dependencies in a very flexible manner. However, it couldn't properly account for relative attention at scale. A significant research effort was done in this direction, and papers will be submitted soon. In preceding years, we proposed several models to leverage time-frequency dependencies for processing (Kernel Additive Models). Current trends make it possible to train such dependencies.
8.5.3 Robust Probabilistic Models for Time-series
Participants: Mathieu Fontaine, Antoine Liutkus, Fabian-Robert Söter.
Processing large amounts of data for denoising or analysis comes with the need to devise models that are robust to outliers and permit efficient inference. For this purpose, we advocate the use of non-Gaussian models for this purpose, which are less sensitive to data-uncertainty. We developed a new filtering paradigm that goes beyond least-squares estimation. In collaboration with researchers from Telecom Paris, we introduce several methods that generalize least-squares Wiener filtering to the case of $\alpha$-stable processes. This very theoretically important contribution has been published as a journal paper 22.
9 Bilateral contracts and grants with industry
9.1 INA (2019-2022)
Participants: Quentin Leroy, Alexis Joly.
The PhD of Quentin Leroy is funded in the context of an industrial contract (CIFRE) with INA, the French company in charge of managing the French TV archives and audio-visual heritage. The goal of the PhD is to develop new methods and algorithms for the interactive learning of new classes in INA archives.
9.2 Transfer of UMX-PRO
Participants: Antoine Liutkus, Fabian-Robert Stöter.
A. Liutkus and F.-R. Stoter are the authors of the UMX-PRO software, which has been transferred to a north-american company for several hundred thousand euros.This software is a complete solution for audio source separation.All other details regarding this software transfer are confidential and subject to a non-disclosure agreement.
9.3 Transfer of TDB
Participants: Antoine Liutkus, Fabian-Robert Stöter.
A. Liutkus and F.-R. Stoter are the authors of the TDB software, which is a solution for audio scraping. It allows gathering the largest audio separation dataset available today, and has been successfully transferred to a European company named AudioSourceRE.
10 Partnerships and cooperations
10.1 International initiatives
The team had two PhD students funded by an Algerian initiative ("Bourses d'excellence Algériennes"):
• Khadidja Meguelati, since 2016, "Massively Distributed Time Series Clustering via Dirichlet Mixture Models"
• Lamia Djebour, since 2019, "Parallel Time Series Indexing and Retrieval with GPU architectures"
10.1.1 Inria associate team not involved in an IIL
HPDaSc
• Title: High Performance Data Science (HPDaSc)
• Site web:
• Duration: 2020 - 2022
• Coordinator: Patrick Valduriez
• Partners:
• LNCC, COPPE/UFRJ, UFF and CEFET, (Brazil)
• Inria contact: Patrick Valduriez
• Summary:
Data-intensive science refers to modern science, such as astronomy, geoscience or life science, where researchers need to manipulate and explore massive datasets produced by observation or simulation. It requires the integration of two fairly different paradigms: high-performance computing (HPC) and data science. We address the following requirements for high-performance data science (HPDaSc): support realtime analytics and visualization (in either in situ or in transit architectures) to help make high-impact online decisions; combine ML with analytics and simulation, which implies dealing with uncertain training data, autonomously built ML models and combine ML models and simulation models; support scientific workflows that combine analytics, modeling and simulation, and exploit provenance in realtime and HIL (Human in the Loop) for efficient workflow execution.
To address these requirements, we will exploit new distributed and parallel architectures and design new techniques for ML, realtime analytics and scientific workflow management. The architectures will be in the context of multisite cloud, with heterogeneous data centers with data nodes, compute nodes and GPUs. We will validate our techniques with major software systems on real applications with real data. The main systems will be OpenAlea and Pl@ntnet from Zenith and DfAnalyzer and SAVIME from the Brazilian side. The main applications will be in agronomy and plant phenotyping (with plant biologists from CIRAD and INRA), biodiversity informatics (with biodiversity scientists from LNCC and botanists from CIRAD), and oil & gas (with geoscientists from UFRJ and Petrobras).
10.1.2 Inria international partners
Informal international partners
We have regular scientific relationships with research laboratories in:
• North America: Univ. of Waterloo (Tamer Özsu), UCSB Santa Barbara (Divy Agrawal and Amr El Abbadi), Northwestern Univ. (Chicago), university of Florida (Pamela Soltis, Cheryl Porter, Gil Nelson), Harvard (Charles Davis), UCSB (Susan Mazer).
• Asia: National Univ. of Singapore (Beng Chin Ooi, Stéphane Bressan), Wonkwang University, Korea (Kwangjin Park), Kyoto University (Japan), Tokyo University (Hiroyoshi Iwata), Academica Sinica, Taiwan (Y. Yang).
• Europe: Univ. of Madrid (Ricardo Jiménez-Periz), UPC Barcelona (Josep Lluis Larriba Pey), HES-SO (Henning Müller), University of Catania (Concetto Spampinatto), Cork School of Music (Ireland), RWTH (Aachen, Germany), Chemnitz technical university (Stefan Kahl), Berlin Museum für Naturkunde (Mario Lasseck), Stefanos Vrochidis (Greece, ITI), UK center for hydrology and ecology (Tom August)
• Africa: Univ. of Tunis (Sadok Ben-Yahia), IMSP, Bénin (Jules Deliga)
• Australia: Australian National University (Peter Christen)
• Central America: Technologico de Costa-Rica (Erick Mata, former director of the US initiative Encyclopedia of Life)
10.1.3 Participation in other international programs
Inria Brasil, 2020-2022
The Inria Brasil web site is now open.
Inria and LNCC, the Brazilian National Scientific Computing Laboratory, signed a Memory of Understanding to collaborate, with associated Brazilian universities, in HPC, AI, Data Science and Scientific Computing. This objective is to create an Inria International Lab., Inria Brasil. The collaboration is headed by Frédéric Valentin (LNCC, Inria International Chair) and Patrick Valduriez
10.2 International research visitors
10.2.1 Visits of international scientists
• Heraldo Borges (CEFET-RJ, Brazil), working on “Discovering Patterns in Restricted Space-Time Datasets” visited us until May.
10.3 European initiatives
10.3.1 FP7 & H2020 Projects
COS4CLOUD
Participants: Alexis Joly, Jean-Christophe Lombardo, Antoine Affouard.
• Title: Co-designed Citizen Observatories Services for the EOS-Cloud
• Duration: 2019 - 2022
• Coordinator: CSIC (Spain)
• Partners: The Open University, CREAF, Bineo, EarthWatch, SLU, NKUA, CERT, Bineo, ECSA.
• Inria contact: Alexis Joly
• Summary: Cos4Cloud will integrate citizen science in the European Open Science Cloud (EOSC) through the co-design of innovative services to solve challenges faced by citizen observatories, while bringing Citizen Science (CS) projects as a service for the scientific community and the society and providing new data sources. In this project, Zenith is in charge of developing innovative web services related to automated species identification, location-based species prediction and training data aggregation services.
10.4 National initiatives
Institut de Convergence Agriculture numérique #DigitAg, (2017-2023), 275 Keuro.
Participants: Alexis Joly, Florent Masseglia, Esther Pacitti, Christophe Pradal, Patrick Valduriez.
#DigitAg brings together in a partnership of seventeen actors (public research and teaching organizations, transfer actors and companies) with the objective of accelerating and supporting the development of agriculture companies in France and in southern countries based on new tools, services and uses. Based in Montpellier with an office in Toulouse and Rennes and led by Irstea, #DigitAg's ambition is to become a world reference for digital agriculture. In this project, Zenith is involved in the analysis of big data from agronomy, in particular, plant phenotyping and biodiversity data sharing.
ANR PerfAnalytics (2021-2024), 100 Keuro.
Participants: Reza Akbarinia.
The objective of the PerfAnalytics project is to analyze sport videos in order to quantify the sport performance indicators and provide feedback to coaches and athletes, particularly to French sport federations in the perspective of the Paris 2024 Olympic games. A key aspect of the project is to couple the existing technical results on human pose estimation from video with scientific methodologies from biomechanics for advanced gesture objectivation. The motion analysis from video represents a great potential for any monitoring of physical activity. In that sense, it is expected that exploitation of results will be able to address not only sport, but also the medical field for orthopedics and rehabilitation.
ANR WeedElec (2018-2021), 106 Keuro.
Participants: Julien Champ, Hervé Goëau, Alexis Joly.
The WeedElec project offers an alternative to global chemical weed control. It combines an aerial means of weed detection by drone coupled to an ECOROBOTIX delta arm robot equipped with a high voltage electrical weeding tool. WeedElec's objective is to remove the major related scientific obstacles, in particular the weed detection/identification, using hyperspectral and colour imaging, and associated chemometric and deep learning techniques.
ANR KAMOuLOX (2016-2020), 290 Keuro.
Participants: Antoine Liutkus, Fabian-Robert Stöter.
The KAMOuLOX project aimed at providing online unmixing tools for ethnologists, that are not specialists in audio engineering. It was the opportunity for cutting-edge signal processing research, a strong dissemination activity in terms of (open-source) software release, and important contributions in deep learning research for audio.
CASDAR CARPESO (2020-2022), 87 Keuro.
Participants: Julien Champ, Hervé Goëau, Alexis Joly.
In order to facilitate the agro-ecological transition of livestock systems, the main objective of the project is to enable the practical use of meslin (grains and forages) by demonstrating their interests and remove sticking points on the nutritional value of the meslin. Therefore, it develops AI-based tools allowing to automatically assess the nutritional value of meslin from images.The consortium includes 10 chambers of agriculture, 1 Technical Institute (IDELE) and 2 research organizations (Inria, CIRAD).
10.4.1 Others
Pl@ntNet InriaSOFT consortium (2019-20XX), 80 Keuro / year
Participants: Alexis Joly, Jean-Christophe Lombardo, Julien Champ, Hervé Goëau.
This contract between four research organisms (Inria, INRAE, IRD and CIRAD) aims at sustaining the Pl@ntNet platform in the long term. It has been signed in November 2019 in the context of the InriaSOFT national program of Inria. Each partner subscribes a subscription of 20K euros per year to cover engineering costs for maintenance and technological developments. In return, each partner has one vote in the steering committee and the technical committee. He can also use the platform in his own projects and benefit from a certain number of service days within the platform. The consortium is not fixed and is not intended to be extended to other members in the coming years.
Ministry of Culture (2019-2021), 130 Keuro
Participants: Alexis Joly, Jean-Christophe Lombardo.
Two contracts have been signed with the ministry of culture to adapt, extend and transfer the content-based image retrieval engine of Pl@ntNet ("Snoop") toward two major actors of the French cultural domain: the French National Library (BNF) and the French National institute of audio-visual (INA).
Ministry of Culture (2020-2021): Audio separation, 75 Keuro
Participants: Baldwin Dumortier, Antoine Liutkus.
This project is a collaboration with the innovation department at Radio France. It is funded in the context of the convention cadre between Inria and the Ministère de la culture. Its objective is to provide expert sound engineers from Radio France with state of the art separation tools developped at Inria. It involves both research on source separtion and software engineering.
DINUM, 80 Keuro
Participants: Reza Akbarinia, Florent Masseglia.
The objective of the contract is to analyze the evolution of the time series of coordinates provided by the IGN (National Institute of Geographic and Forest Information), and to detect the anomalies of different origins, for example, seismic or material movements.
CACTUS Inria exploratory action (2020-2022), 200 Keuro
Participants: Alexis Joly, Joaquim Estopinan.
CAcTUS is an Inria exploratory action led by Alexis Joly and focused on predictive approaches to determining the conservation status of species.
11 Dissemination
11.1 Promoting scientific activities
11.1.1 Scientific events: organisation
General chair, scientific chair
• E. Pacitti: Bases de Données Avancées (BDA), 2021, PC chair.
• C. Pradal: Crop Modeling for the Future, ICROPM Symposium, 3-5 February 2020, https://www.icropm2020.org
11.1.2 Scientific events: selection
Member of the conference program committees
• IEEE Artificial Intelligence & Knowledge Engineering (AIKE), 2020: F. Masseglia
• European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (PKDD), 2020: F. Masseglia
• Int. Conf. on Information Management and Big Data (SIMBig), 2020: F. Masseglia
• IEEE Int. Conf. on Data Mining (ICDM), 2020: F. Masseglia
• ACM Symposium on Applied Computing (ACM SAC), Data Mining Track (DM), 2020: F. Masseglia
• ACM Symposium on Applied Computing (ACM SAC), Data Stream Track (DS), 2020: F. Masseglia
• Extraction et Gestion des Connaissances (EGC), 2020: F. Masseglia
• Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), 2020 : F. Masseglia
• International Conference on Very Large Data Bases (VLDB), 2020: R. Akbarinia
• Conférence sur la Gestion de Données – Principes, Technologies et Applications (BDA), 2020: R. Akbarinia
• Int. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), 2020: A. Joly, A. Liutkus
• Neural Information Processing Systems (NeurIPS): A. Liutkus, A. Joly
• Int. Conf. on Machine Learning (ICML): A. Liutkus
• Int. Conf. on Learning Representations (ICLR): A. Liutkus
• Int. Conf. on Computer Vision (CVPR), 2020: A. Joly
• Int. Conf. and Labs of the Evaluation Forum (CLEF), 2020: A. Joly
• European. Conf. on Information Retrieval (ECIR), 2020: A. Joly
• European. Conf. on Computer Vision (ECCV), 2020: A. Joly
• IEEE/ACM Int. Symposium in Cluster, Cloud, and Grid Computing (CCGrid) 2019: Esther Pacitti
• Int. Conf. on functional-structural plant models (FSPM), 2020: C. Pradal
11.1.3 Journal
Member of the editorial boards
• VLDB Journal: P. Valduriez.
• Transactions on Large Scale Data and Knowledge Centered Systems: R. Akbarinia.
• Distributed and Parallel Databases: E. Pacitti, P. Valduriez.
Reviewer - reviewing activities
• Annals of Telecommunications (ANTE) : F. Masseglia
• Distributed and Parallel Databases (DAPD): E. Pacitti, P. Valduriez
• IEEE Transactions on Knowledge and Data Engineering (TKDE): R. Akbarinia, F. Masseglia
• Information Systems: R. Akbarinia
• IEEE access: R. Akbarinia
• Knowledge and Information Systems (KAIS): R. Akbarinia, F. Masseglia
• Ecosphere: A. Joly
• Methods in Ecology and Evolution: A. Joly
• Plant methods: A. Joly
• Science of the Total Environment: A. Joly
• Machine Learning: A. Joly
• Pattern Recognition Letters: A. Joly
• Transactions on Image Processing: A. Joly
• Multimedia Tools and Applications: A. Joly
• Environmental Research Letters: A. Joly
• Information Processing and Management: A. Joly
• ACM Trans. on Database Systems: E. Pacitti
• IEEE Transaction on Signal Processing (TSP): A. Liutkus
• IEEE Transactions on Audio Speech and Language Processing (TASLP): A. Liutkus
• IEEE Signal Processing Magazine: A. Liutkus
• IEEE Signal Processing Letters: A. Liutkus
• Frontiers in Plant Science: C. Pradal
11.1.4 Invited talks
• A. Joly: "L’IA au service de la biodiversité végétale", 24 Nov, Accadémie des sciences; "Deep learning and Pl@ntNet", 16 Nov, Imaginecology conference;
• A. Liutkus: tutorial on "music source separation" at Int. Symposium on Music Information Retrieval (ISMIR 2018).
• P. Valduriez: Lecture: Distributed Database Systems: the case for NewSQL, 19 November, CWI Lectures, Amsterdam (Virtual).
• P. Valduriez: Tutorial: Principles of Distributed Database Systems: spotlight on NewSQL, 29 september, Brazilian Symposium on Databases (SBBD).
• C. Pradal: "Multiscale plant modelling and Phenotyping" on 8 october at Tottori University and on 16 october at Nagoya University, Japan; workshop on plant modelling on 28 october at Tokyo University, Japan.
11.1.5 Leadership within the scientific community
• A. Joly: Scientific manager of the LifeCLEF research forum.
• A. Liutkus: Member of the IEEE Technical Committee on Audio and Acoustic Signal Processing.
• E. Pacitti: Member of the Steering Committee of the BDA conference.
• P. Valduriez: President of the Steering Committee of the BDA conference (until October).
11.1.6 Scientific expertise
• A. Joly: scientific advisory board of the ANR program "AI for biodiversity"
• A. Joly: expert for the National HPC grand equipment (GENCI) programs
• A. Joly: scientific advisory board of LepiNoc project (automated beetle tracking)
• E. Pacitti: reviewer for STIC AmSud international program.
• P. Valduriez: reviewer for STIC AmSud international program.
• P. Valduriez: reviewer for NSERC (Canada).
• C. Pradal: member of CSS EGBIP ( Commissions Scientifiques Spécialisées) INRAE.
• A. Liutkus: reviewer for FONDECYT (Chile) competition 2020.
• A. Joly: Technical director of the InriaSOFT consortium Pl@ntNet and representative of Inria in the steering committee.
• F. Masseglia: until september 2020, “Chargé de mission pour la médiation scientifique Inria” and head of Inria's national network of colleagues involved in science popularization.
• F. Masseglia: since october 2020, “Deputy Scientific Director of Inria, in charge of the domain Perception, Cognition and Interaction”.
• E. Pacitti: manager of Polytech' Montpellier's International Relationships for the computer science department (100 students).
• P. Valduriez: scientific manager for the Latin America zone at Inria's Direction of Foreign Relationships (DPEI).
• Antoine Liutkus is an elected member of the IEEE technical committee on Audio.
11.2 Teaching - Supervision - Juries
11.2.1 Teaching
Most permanent members of Zenith teach at the Licence and Master degree levels at UM2.
Esther Pacitti responsibilities on teaching (theoretical, home works, practical courses,exams) and supervision at Polytech' Montpellier UM, for engineer students:
• IG3: Database design, physical organization, 54h, level L3, 50 student
• IG4: Distributed Databases and NoSQL, 80h , level M1, 50 students
• Large Scale Information Management (Iot, Recommendation Systems, Graph Databases), 27h, level M2, 20 students,
• Supervision of industrial projects with defense: 1 group of 3 students, level M1 (3 mounths) and 1 group of 3 students level M2 (3 mounths)
• Supervision of master internships with defense: 1 group of 3 students, level M1 (3 mounths) and 3 students, level M2 (6 mounths each)
• Supervision of computer science discovery projects with defense: one group of 3 students level L2 (4 mounths)
Patrick Valduriez:
• Professional: Distributed Information Systems, Big Data Architectures, 75h, level M2, Capgemini Institut
Alexis Joly:
• Univ. Montpellier: Machine Learning, 10h, level M2
• Polytech' Montpellier: Content-Based Image Retrieval, 4.5h, level M2
• AgroParisTech: Deep Learning, 18h, level M1
• Innobs technical school: Innovations in the observation of seasonal biological events and associated data management, 6 hours, for professionals.
Antoine Liutkus
• Polytech' Montpellier: Audio Machine Learning, 1.5h, level M1
• Univ. Montpellier: Root System Modelling, 15h, level M2
• Univ. Montpellier: Functional-Structural Plant Modelling, 9h, level M2
11.2.2 Supervision
PhD & HDR:
• PhD: Gaetan Heidsieck, Distributed Management of Scientific Workflows for High-Throughput Plant Phenotyping, 9 December, Univ. Montpellier. Advisors: Esther Pacitti, Christophe Pradal, François Tardieu (INRAE).
• PhD: Titouan Lorieul, Pro-active Crowdsourcing, 2 December, Univ. Montpellier. Advisor: Alexis Joly.
• PhD : Khadidja Meguelati, Massively Distributed Clustering, 13 March, Univ. Montpellier. Advisors: Nadine Hilgert (INRAE), Florent Masseglia.
• PhD in progress: Heraldo Borges, Discovering Tight Space-Time Sequences, started Oct 2018, CEFET/Rio, Brazil. Advisors: Esther Pacitti, Eduardo Ogaswara (CEFET/Rio, Brazil).
• PhD in progress: Lamia Djebour, Parallel Time Series Indexing and Retrieval with GPU architectures, started Oct 2019, Univ. Montpellier. Advisors: Reza Akbarinia, Florent Masseglia.
• PhD in progress: Quentin Leroy, Active learning of unknown classes, started Oct 2019, Univ. Montpellier. Advisors: Alexis Joly
• PhD in progress: Alena Shilova, Scheduling Strategies for High Performance Deep Learning, started Oct 2019, Univ. Bordeaux. Advisors: Olivier Beaumont, Alexis Joly
• PhD in progress: Daniel Rosendo, Enabling HPC-Big Data Convergence for Intelligent Extreme-Scale Analytics, started Oct 2019, Univ. Rennes. Advisors: Gabriel Antoniu, Alexandru Costan, Patrick Valduriez
• PhD in progress: Joaquim Estopinan, Prediction of the conservation status of species, started Nov 2020, Univ. Montpellier. Advisors: Alexis Joly
• PhD in progress: Camille Garcin, Set-valued classification in the case of long-tail distributions, started Oct 2020, Univ. Montpellier. Advisors: Joseph Salmon, Alexis Joly
• PhD in progress: Rodrigo Alves Prado da Silva Data-centric Workflow Scheduling with Privacy Restrictions started Oct 2020, UFF, Brazil. Advisors: Daniel de Oliveira (UFF,Brazil), Esther Pacitti
11.2.3 Juries
Members of the team participated to the following PhD or HDR committees:
• R. Akbarinia: Amine El Ouassouli (INSA Lyon, reviewer)
• A. Joly: Titouan Lorieul (Univ. Montpellier, advisor), Waleed RAGHEB (Univ. of Montpellier, jury president)
• F. Masseglia: Mehdi Kaytoue (HDR, Univ. Lyon 1, reviewer)
• E. Pacitti: Gaetan Heidscieck (Univ. Montpellier, advisor), Arnaud Grall (Univ. Nantes), Riad Mokadem (HDR. UPS, Toulouse, reviewer)
• C. Pradal: Gaetan Heidscieck (Univ. Montpellier, advisor), Cyrille Midingoyi (Institut Agro. Montpellier, advisor), Kévin Dubois, Univ. Toulouse, reviewer)
• A. Liutkus: Gabriel Meseguer Brocal (Sorbonne Univ. Paris, reviewer).
Members of the team participated to the following hiring committees:
• F. Masseglia: Selection committee 4567 Polytech LIRIS (june 2020)
• F. Masseglia: Inria CRCN + ISFP n°4 - Nancy - Grand-Est (june 2020)
• R. Akbarinia: Associate professor position, INSA Lyon (May 2020)
• R. Akbarinia: ATER position, Univ. Montpellier (May 2020)
• A. Joly: Selection committee 3892, CIRAD Montpellier (Nov 2020)
11.3 Popularization
11.3.1 Internal or external Inria responsibilities
• F. Masseglia was “Chargé de mission auprès de la DGD-S Inria pour la médiation scientifique” (50% of his time) until September 2020, and headed Inria's national network of colleagues involved in science popularization.
• A. Joly spends several hours a week animating Pl@ntnet user community. This includes: (i) animating the community of developers using Pl@ntNet API (about 500 users), (ii) animating Pl@ntnet's social networks (Twitter and Facebook accounts) and (iii) managing the mailbox contact@plantnet-project.org.
11.3.2 Articles and contents
• F. Masseglia is co-author of a guide for teacher and summer camp counselors on tracking apps in the context of covid-19, edited by the Académie des sciences: https://www.academie-sciences.fr/fr/Promouvoir-l-enseignement-des-sciences/cet-ete-avec-la-science.html
• A. Joly has given several interviews to different media giving rise to web articles about Pl@ntNet (see e.g. Google news with keyword Pl@ntNet).
• A. Joly has co-authored several popularization articles, e.g. for the Ministry of Culture magazine, the GENCI annual report, Inria national website, etc.
• A. Joly has co-produced a popularization video about Pl@ntNet's French Academy of Science award.
• A. Joly actively participates to the design and development of all Pl@ntNet dissemination tools in particular Pl@ntNet web site that contains contents for the press, articles for the general public, tutorials of Pl@ntNet tools, guidelines for users of the API, etc.
11.3.3 Education
• F. Masseglia is member of the steering committee and the initiator, with Serge Abiteboul, of the program called "1 scientifique — 1 classe : Chiche !" with the goal of reaching all the students of a specific level. This massive plan should concern all scientists at Inria and our partners in France. It has been slowed down by the pandemic but should get back on rail by mid-2021.
• A. Joly gave a webinar for nearly 30 greek teachers about the use of Pl@ntNet in the context of a formal educative program organized in collaboration with the greek national education.
11.3.4 Interventions
E. Pacitti participated in Polytech'Montpellier International Summer School (Flow) on the subject of Data Science - Plant Phenotyping.
11.3.5 Creation of media or tools for science outreach
• F. Masseglia participated to the covid-19 mission project "Parlons Maths" with the goal of making easier the organisation of online talks with high public interaction.
• F. Masseglia co-organised the first Inria online public event. It was for the science celebration national event, October 2-12, with 9 days of live talks streamed on the Inria Youtube channel. Everything had to be invented for this exceptional event where Inria had zero experience: https://www.inria.fr/fr/inria-fete-la-science.
• The softwares developed in the context of the Pl@ntNet project (Pl@ntNet mobile app, Pl@ntNet web, ThePlantGame) are used in a large number of formal educational programs as well as informal educational actions of individual teachers, associations, natural area managers, etc.
12 Scientific production
12.1 Major publications
• 1 articleChristopheC. Botella, AlexisA. Joly, PascalP. Monestiez, PierreP. Bonnet and FrançoisF. Munoz. 'Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection'.PLoS ONE155May 2020, e0232078
• 2 articleMathieuM. Fontaine, RolandR. Badeau and AntoineA. Liutkus. 'Separation of Alpha-Stable Random Vectors'.Signal ProcessingJanuary 2020, 107465
• 3 articleJiJ. Liu, NoelN. Moreno Lemus, EstherE. Pacitti, FábioF. Porto and PatrickP. Valduriez. 'Parallel Computation of PDFs on Big Spatial Data Using Spark'.Distributed and Parallel Databases382020, 63-100
• 4 article JiJ. Liu, LuisL. Pineda, EstherE. Pacitti, AlexandruA. Costan, PatrickP. Valduriez, GabrielG. Antoniu and MartaM. Mattoso. 'Efficient Scheduling of Scientific Workflows using Hot Metadata in a Multisite Cloud'. IEEE Transactions on Knowledge and Data Engineering 2018
• 5 inproceedings AntoineA. Liutkus, Umut ŞU. Imşekli, SzymonS. Majewski, AlainA. Durmus and Fabian-RobertF.-R. Stöter. 'Sliced-Wasserstein Flows: Nonparametric Generative Modeling via Optimal Transport and Diffusions'. 36th International Conference on Machine Learning (ICML) Long Beach, United States June 2019
• 6 articleMaximeM. Metz, MatthieuM. Lesnoff, FlorentF. Abdelghafour, RezaR. Akbarinia, FlorentF. Masseglia and Jean-MichelJ.-M. Roger. 'A big-data'' algorithm for KNN-PLS'.Chemometrics and Intelligent Laboratory Systems203August 2020, 104076
• 7 bookDanielD. Oliveira, JiJ. Liu and EstherE. Pacitti. 'Data-Intensive Workflow Management: For Clouds and Data-Intensive and Scalable Computing Environments'.14Synthesis Lectures on Data Management4Morgan&Claypool PublishersMay 2019, 1-179
• 8 bookTamerT. Özsu and PatrickP. Valduriez. 'Principles of Distributed Database Systems - Fourth Edition'.Télécharger la 3ieme et 4ieme édition : lien dans voir aussi ''Springer2020, 1-674
• 9 articleChristopheC. Pradal, SimonS. Artzet, JeromeJ. Chopard, DimitriD. Dupuis, ChristianC. Fournier, MichaelM. Mielewczik, VincentV. Negre, PascalP. Neveu, DidierD. Parigot, PatrickP. Valduriez and SarahS. Cohen-Boulakia. 'InfraPhenoGrid: A scientific workflow infrastructure for Plant Phenomics on the Grid'.Future Generation Computer Systems67February 2017, 341-353
• 10 articleDjamel-EdineD.-E. Yagoubi, RezaR. Akbarinia, FlorentF. Masseglia and ThemisT. Palpanas. 'Massively Distributed Time Series Indexing and Querying'.IEEE Transactions on Knowledge and Data Engineering3212020, 108-120
12.2 Publications of the year
International journals
• 11 articleTomT. August, OliverO. Pescott, AlexisA. Joly and PierreP. Bonnet. 'AI Naturalists Might Hold the Key to Unlocking Biodiversity Data in Social Media Imagery'.Patterns17October 2020, 100116
• 12 articleAsmaA. Belhadi, YoucefY. Djenouri, KjetilK. Nørvåg, HeriH. Ramampiaro, FlorentF. Masseglia and Jerry Chun-WeiJ.-W. Lin. 'Space Time Series Clustering: Algorithms, Taxonomy, and Case Study on Urban Smart Cities'.Engineering Applications of Artificial Intelligence95October 2020, #103857
• 13 articleFaresF. Belhassine, DamienD. Fumey, JeromeJ. Chopard, ChristopheC. Pradal, SébastienS. Martinez, EvelyneE. Costes and BenoitB. Pallas. 'Modelling transport of inhibiting and activating signals and their combined effects on floral induction: application to apple tree'.Scientific Reports102020, 13085
• 14 article 'Biodiversity Information Science and Standards 4: e58933 Pl@ntNet Services, a Contribution to the Monitoring and Sharing of Information on the World Flora'. Biodiversity Information Science and Standards 4 2020
• 15 article PierreP. Bonnet, AlexisA. Joly, Jean-MichelJ.-M. Faton, SusanS. Brown, DavidD. Kimiti, BenjaminB. Deneu, MaximilienM. Servajean, AntoineA. Affouard, Jean-ChristopheJ.-C. Lombardo, LauraL. Mary, ChristelC. Vignau and FrançoisF. Munoz. 'How citizen scientists contribute to monitor protected areas thanks to automatic plant identification tools'. Ecological Solutions and Evidence 1 2 2020
• 16 article HeraldoH. Borges, MurilloM. Dutra, AminA. Bazaz, RafaelliR. Coutinho, FábioF. Perosi, FábioF. Porto, FlorentF. Masseglia, EstherE. Pacitti and EduardoE. Ogasawara. 'Spatial-Time Motifs Discovery'. Intelligent Data Analysis October 2020
• 17 articleChristopheC. Botella, AlexisA. Joly, PascalP. Monestiez, PierreP. Bonnet and FrançoisF. Munoz. 'Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection'.PLoS ONE155May 2020, e0232078
• 18 articleRenato KR. Braghiere, FredericF. Gerard, JochemJ. Evers, ChristopheC. Pradal and LoicL. Pagès. 'Simulating the effects of water limitation on plant biomass using a 3D functional–structural plant model of shoot and root driven by soil hydraulics'.Annals of Botany1264April 2020, 713-728
• 19 articleGabriel A.G. Brat, Griffin M.G. Weber, NilsN. Gehlenborg, PaulP. Avillach, Nathan P.N. Palmer, LucaL. Chiovato, JamesJ. Cimino, Brett K.B. Beaulieu-Jones, SehiS. L'Yi, Mark S.M. Keller, Douglas S.D. Bell, Robert W.R. Follett, Lav P.L. Patel, Anne SophieA. Jannot, Lemuel R.L. Waitman, GilbertG. Omenn, AlbertoA. Malovini, Jason H.J. Moore, ValentinaV. Tibollo, Shawn NS. Murphy, RiccardoR. Bellazzi, David AD. Hanauer, ArnaudA. Serret-Larmande, AlbaA. Gutierrez-Sacristan, John JJ. Holmes, DouglasD. Bell, Kenneth D.K. Mandl, Jeffrey GJ. Klann, Douglas AD. Murad, LuigiaL. Scudeller, MauroM. Bucalo, KatieK. Kirchoff, JeanJ. Craig, JihadJ. Obeid, VianneyV. Jouhet, RomainR. Griffier, SébastienS. Cossin, BertrandB. Moal, AntonioA. Bellasi, Hans UH. Prokosch, DetlefD. Kraska, PiotrP. Sliz, Amelia L.M.A. Tan, Kee YuanK. Ngiam, AlbertoA. Zambelli, Danielle LD. Mowery, EmilyE. Schiver, BatsalB. Devkota, RobertR. Bradford, MohamadM. Daniar, ChristelC. Daniel, VincentV. Benoit, RomainR. Bey, NicolasN. Paris, PatriciaP. Serre, NinaN. Orlova, JulienJ. Dubiel, MartinM. Hilka, StephaneS. Breant, JudithJ. Leblanc, NicolasN. Griffon, AnitaA. Burgun, MelodieM. Bernaux, ArnaudA. Sandrin, ElisaE. Salamanca, SylvieS. Cormont, ThomasT. Ganslandt, TobiasT. Gradinger, JulienJ. Champ, MartinM. Boeker, PatriciaP. Martel, LoïcL. Estève, AlexandreA. Gramfort, OlivierO. Grisel, DamienD. Leprovost, ThomasT. Moreau, GaelG. Varoquaux, Jill-JênnJ.-J. Vie, DemianD. Wassermann, ArthurA. Mensch, CharlotteC. Caucheteux, ChristianC. Haverkamp, GuillaumeG. Lemaître, SilvanoS. Bosari, AndrewA. South, TianxiT. Cai and IsaacI. Kohane. 'International electronic health record-derived COVID-19 clinical course profiles: the 4CE consortium'.npj Digital Medicine31December 2020, #109
• 20 article JulienJ. Champ, AdánA. Mora‐Fallas, HervéH. Goëau, ErickE. Mata‐Montero, PierreP. Bonnet and AlexisA. Joly. 'Instance segmentation for the fine detection of crop and weed plants by precision agricultural robots'. Applications in Plant Sciences 8 7 2020
• 21 article Charles C.C. Davis, JulienJ. Champ, DanielD. Park, IanI. Breckheimer, GoiaG. Lyra, JunxiJ. Xie, AlexisA. Joly, DharmeshD. Tarapore, Aaron MA. Ellison and PierreP. Bonnet. 'A New Method for Counting Reproductive Structures in Digitized Herbarium Specimens Using Mask R-CNN'. Frontiers in Plant Science 11 July 2020
• 22 articleMathieuM. Fontaine, RolandR. Badeau and AntoineA. Liutkus. 'Separation of Alpha-Stable Random Vectors'.Signal ProcessingJanuary 2020, 107465
• 23 articleMarionM. Gauthier, RomainR. Barillot, AnneA. Schneider, CamilleC. Chambon, ChristianC. Fournier, ChristopheC. Pradal, CorinneC. Robert and BrunoB. Andrieu. 'A functional structural model of grass development based on metabolic regulation and coordination rules'.Journal of Experimental Botany7118September 2020, 5454-5468
• 24 articleHervéH. Goëau, AdánA. Mora‐Fallas, JulienJ. Champ, Natalie LaurenN. Rossington Love, SusanS. Mazer, ErickE. Mata‐Montero, AlexisA. Joly and PierreP. Bonnet. 'A new fine‐grained method for automated visual analysis of herbarium specimens: A case study for phenological data extraction'.Applications in Plant Sciences86June 2020, #e11368
• 25 articleGaëtanG. Heidsieck, DanielD. De Oliveira, EstherE. Pacitti, ChristopheC. Pradal, FrancoisF. Tardieu and PatrickP. Valduriez. 'Efficient Execution of Scientific Workflows in the Cloud Through Adaptive Caching'.Transactions on Large-Scale Data- and Knowledge-Centered SystemsSeptember 2020, 41-66
• 26 articlePavlosP. Kranas, BoyanB. Kolev, OleksandraO. Levchenko, EstherE. Pacitti, PatrickP. Valduriez, RicardoR. Jiménez-Peris and MartaM. Patiño-Martinez. 'Parallel Query Processing in a Polystore'.Distributed and Parallel DatabasesFebruary 2021, 39
• 27 article Sue HanS. Lee, HervéH. Goëau, PierreP. Bonnet and AlexisA. Joly. 'Attention-Based Recurrent Neural Network for Plant Disease Classification'. Frontiers in Plant Science 11 December 2020
• 28 articleSue HanS. Lee, HervéH. Goëau, PierreP. Bonnet and AlexisA. Joly. 'New perspectives on plant disease characterization based on deep learning'.Computers and Electronics in Agriculture170March 2020, 105220
• 29 articleNoelN. Lemus, FábioF. Porto, Yania MY. Souto, RafaelR. Pereira, JiJ. Liu, EstherE. Pacitti and PatrickP. Valduriez. 'SUQ2: Uncertainty Quantification Queries over Large Spatio-temporal Simulations'.Bulletin of the Technical Committee on Data Engineering431March 2020, 47-59
• 30 articleOleksandraO. Levchenko, BoyanB. Kolev, Djamel-Edine EdineD.-E. Yagoubi, RezaR. Akbarinia, FlorentF. Masseglia, ThemisT. Palpanas, PatrickP. Valduriez and DennisD. Shasha. 'BestNeighbor: Efficient Evaluation of kNN Queries on Large Time Series Databases'.Knowledge and Information Systems (KAIS)6322021, 349-378
• 31 articleJiJ. Liu, CarlynaC. Bondiombouy, LeiL. Mo and PatrickP. Valduriez. 'Two-Phase Scheduling for Efficient Vehicle Sharing'.IEEE Transactions on Intelligent Transportation Systems2020, 1-14
• 32 articleJiJ. Liu, NoelN. Moreno Lemus, EstherE. Pacitti, FábioF. Porto and PatrickP. Valduriez. 'Parallel Computation of PDFs on Big Spatial Data Using Spark'.Distributed and Parallel Databases382020, 63-100
• 33 articleHermano Lourenço SouzaH. Lustosa, Anderson ChavesA. da Silva, Daniel Nascimento RamosD. Da Silva, PatrickP. Valduriez and Fábio André MachadoF. Porto. 'SAVIME: An Array DBMS for Simulation Analysis and ML Models Predictions'.Journal of Information and Data Management113December 2020, 247-264
• 34 articleMaximeM. Metz, MatthieuM. Lesnoff, FlorentF. Abdelghafour, RezaR. Akbarinia, FlorentF. Masseglia and Jean-MichelJ.-M. Roger. 'A “big-data” algorithm for KNN-PLS'.Chemometrics and Intelligent Laboratory Systems203August 2020, 104076
• 35 articleCyrille AhmedC. Midingoyi, ChristopheC. Pradal, Ioannis N.I. Athanasiadis, MarcelloM. Donatelli, AndreasA. Enders, DavideD. Fumagalli, FrederickF. Garcia, DeanD. Holzworth, GerritG. Hoogenboom, CherylC. Porter, HeleneH. Raynal, PeterP. Thorburn and Pierre MartresP. Martre. 'Reuse of process-based models: automatic transformation into many programming languages and simulation platforms'.in silico Plants2020, diaa007
• 36 articleKatelin D.K. Pearson, GilG. Nelson, MylaM. Aronson, PierreP. Bonnet, LauraL. Brenskelle, Charles C.C. Davis, EllenE. Denny, Elizabeth R.E. Ellwood, HervéH. Goëau, J MasonJ. Heberling, AlexisA. Joly, TitouanT. Lorieul, SusanS. Mazer, EmilyE. Meineke, BrianB. Stucky, Patrick W.P. Sweeney, AlexanderA. White and Pamela S.P. Soltis. 'Machine Learning Using Digitized Herbarium Specimens to Advance Phenological Research'.Bioscience7072020, 610-620
• 37 articleVítorV. Silva, ViníciusV. Campos, ThaylonT. Guedes, JoséJ. Camata, DanielD. De Oliveira, Alvaro L.G.A.A. Coutinho, PatrickP. Valduriez and MartaM. Mattoso. 'DfAnalyzer: Runtime dataflow analysis tool for Computational Science and Engineering applications'.SoftwareX12July 2020, 100592
• 38 articleRenanR. Souza, VitorV. Silva, Alvaro Luiz Gayoso de AzeredoA. Coutinho, PatrickP. Valduriez and MartaM. Mattoso. 'Data reduction in scientific workflows using provenance monitoring and user steering'.Future Generation Computer Systems110September 2020, 481-501
• 39 article HirokazuH. Takahashi and ChristopheC. Pradal. 'Root phenotyping: important and minimum information required for root modeling in crop plants'. Breeding Science February 2021
• 40 articleDjamel-EdineD.-E. Yagoubi, RezaR. Akbarinia, FlorentF. Masseglia and ThemisT. Palpanas. 'Massively Distributed Time Series Indexing and Querying'.IEEE Transactions on Knowledge and Data Engineering3212020, 108-120
International peer-reviewed conferences
• 41 inproceedingsFaresF. Belhassine, DamienD. Fumey, ChristopheC. Pradal, JérômeJ. Chopard, EvelyneE. Costes and BenoitB. Pallas. 'A modelling framework for the simulation of signal transport within 3D structure: application for the simulation of within-tree variability in floral induction in apple trees'.FSPM 2020 - 9th International Conference on Functional-Structural Plant Models9Hannover / Virtual, GermanyAugust 2020, 16-17
• 42 inproceedingsFrédéricF. Boudon, JanJ. Vaillant and ChristopheC. Pradal. 'Toward Virtual Modelling Environments using Notebooks for Phenotyping and Simulation of Plant Development'.FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsHanovre / Virtua, Germany2020, 99-100
• 43 inproceedings BenjaminB. Deneu, TitouanT. Lorieul, ElijahE. Cole, MaximilienM. Servajean, ChristopheC. Botella, PierreP. Bonnet and AlexisA. Joly. 'Overview of LifeCLEF location-based species prediction task 2020 (GeoLifeCLEF)'. CLEF 2020 - 11th International Conference of the Cross-Language Evaluation Forum for European Languages thessaloniki, Greece September 2020
• 44 inproceedingsChristianC. Fournier, SimonS. Artzet, FrancoisF. Tardieu and ChristopheC. Pradal. 'What structural plant modelling and image-based phenotyping can learn from each other?'FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsHanovre / Virtua, Germany2020, 55-56
• 45 inproceedings 'A 3D architectural model of grass shoot morphogenesis and plasticity, driven by organ metabolite concentrations and coordination rules'. FSPM 2020 - 9th International Conference on Functional-Structural Plant Models Hanovre / Virtua, Germany 2020
• 46 inproceedingsGaëtanG. Heidsieck, DanielD. De Oliveira, EstherE. Pacitti, ChristopheC. Pradal, FrancoisF. Tardieu and PatrickP. Valduriez. 'Distributed Caching of Scientific Workflows in Multisite Cloud'.DEXA 2020: Database and Expert Systems Applications; DEXA: Database and Expert Systems Applications, Sep 2020, Bratislava, Slovakia. pp.51-65.DEXA 2020 - 31st International Conference on Database and Expert Systems Applications12392Lecture Notes in Computer ScienceBratislava, SlovakiaSpringer Science and Business Media Deutschland GmbHSeptember 2020, 51-65
• 47 inproceedingsAlexisA. Joly, HervéH. Goëau, ChristopheC. Botella, RafaelR. Ruiz De Castaneda, HervéH. Glotin, ElijahE. Cole, JulienJ. Champ, BenjaminB. Deneu, MaximilienM. Servajean, TitouanT. Lorieul, Willem-PierW.-P. Vellinga, Fabian-RobertF.-R. Stöter, AndrewA. Durso, PierreP. Bonnet and HenningH. Müller. 'LifeCLEF 2020 Teaser: Biodiversity Identification and Prediction Challenges'.ECIR 2020 - 42nd European Conference on IR Research on Advances in Information RetrievalLecture Notes in Computer ScienceAdvances in Information Retrieval. Proceedings, Part II12036Lisbon, PortugalApril 2020, 542-549
• 48 inproceedingsAlexisA. Joly, HervéH. Goëau, StefanS. Kahl, BenjaminB. Deneu, Willem-PierW.-P. Vellinga, MaximilienM. Servajean, ElijahE. Cole, LukášL. Picek, RafaelR. Ruiz de Castañeda, IsabelleI. Bolon, AndrewA. Durso, TitouanT. Lorieul, ChristopheC. Botella, HervéH. Glotin, JulienJ. Champ, IvanI. Eggel, PierreP. Bonnet and HenningH. Müller. 'Overview of LifeCLEF 2020: A System-Oriented Evaluation of Automated Species Identification and Species Distribution Prediction'.Experimental IR Meets Multilinguality, Multimodality, and Interaction<br>11th International Conference of the CLEF Association, CLEF 2020, Thessaloniki, Greece, September 22–25, 2020, ProceedingsCLEF 2020 - 11th International Conference of the Cross-Language Evaluation Forum for European Languages12260Lecture Notes in Computer ScienceThessaloniki, GreeceSpringerSeptember 2020, 342-363
• 49 inproceedings StefanS. Kahl, MaryM. Clapp, W AlexanderW. Hopping, HervéH. Goëau, HervéH. Glotin, RobertR. Planqué, Willem-PierW.-P. Vellinga and AlexisA. Joly. 'Overview of BirdCLEF 2020: Bird Sound Recognition in Complex Acoustic Environments'. CLEF 2020 - 11th International Conference of the Cross-Language Evaluation Forum for European Languages Thessaloniki, Greece September 2020
• 50 inproceedingsShiryuS. Kirié, ChristopheC. Pradal, HideoH. Iwasaki, KojiK. Noshita and HiroyoshiH. Iwata. 'Three-dimensional morphological model of water lilies Nymphaea spp. for breeding historical study'.FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsHanovre / Virtua, Germany2020, 61-62
• 51 inproceedingsQinqinQ. Long, ChristopheC. Pradal and WinfriedW. Kurth. 'Co-simulation with OpenAlea and GroIMP for cross-platform functional-structural plant modelling'.FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsHanovre / Virtual, Germany2020, 97-98
• 52 inproceedings KhadidjaK. Meguelati, BenedicteB. Fontez, NadineN. Hilgert, FlorentF. Masseglia and IsabelleI. Sanchez. 'Massively Distributed Clustering via Dirichlet Process Mixture'. ECML PKDD 2020 - European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases Ghent (virtual), Belgium September 2020
• 53 inproceedings ManuelM. Pariente, SamueleS. Cornell, JorisJ. Cosentino, SunitS. Sivasankaran, EfthymiosE. Tzinis, JensJ. Heitkaemper, MichelM. Olvera, Fabian-RobertF.-R. Stöter, MathieuM. Hu, Juan M.J. Martı́n-Doñas, DavidD. Ditter, ArielA. Frank, AntoineA. Deleforge and EmmanuelE. Vincent. 'Asteroid: the PyTorch-based audio source separation toolkit for researchers'. Interspeech 2020 Shanghai, China October 2020
• 54 inproceedingsDéboraD. Pina, LilianeL. Kunstmann, DanielD. De Oliveira, PatrickP. Valduriez and MartaM. Mattoso. 'An approach for the collection and analysis of configuration data in deep neural networks'.SBBD 2020 - 35ª Simpósio Brasileiro de Banco de DadosVirtual, BrazilOctober 2020, 1-6
• 55 inproceedings'MTG as a standard representation of plants in FSPMs'.FSPM 2020 -9th International Conference on Functional-Structural Plant ModelsHanovre / Virtua, Germany2020, 86-87
• 56 inproceedings'Simulating rhizodeposition as a function of shoot and root interactions within a new 3D Functional-Structural Plant Model'.FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsHanovre / Virtua, Germany2020, 22-23
• 57 inproceedingsClémentC. Saint Cast, GuillaumeG. Lobet, LlorençL. Cabrera-Bosquet, ValentinV. Couvreur, ChristopheC. Pradal, BertrandB. Muller, FrancoisF. Tardieu and XavierX. Draye. 'Improving interoperability between phenomics and modelling communities by designing a Plant Modelling Ontology (PMO)'.FSPM 2020 - 9th International Conference on Functional-Structural Plant ModelsTowards Computable PlantsHanovre / Virtua, Germany2020, 57-58
Conferences without proceedings
• 58 inproceedings YannY. Boursiac, ChristopheC. Pradal, FabriceF. Bauget, StathisS. Delivorias, MikaelM. Lucas, ChristopheC. Godin and ChristopheC. Maurel. 'Phenotyping and modeling of water transport in roots'. iCROPM 2020 - Satellite workshop : Phenotyping and modeling of plant anchorage and physiology Montpellier, France February 2020
• 59 inproceedings 'Overview of LifeCLEF Plant Identification task 2020'. CLEF 2020 - Conference and labs of the Evaluation Forum CLEF 2020 - Conference and labs of the Evaluation Forum Thessalonique, Greece September 2020
Scientific books
• 60 bookTamerT. Özsu and PatrickP. Valduriez. 'Principles of Distributed Database Systems - Fourth Edition'.Springer2020, 1-674
Doctoral dissertations and habilitation theses
• 61 thesis 'Distributed Management of Scientific Workflows for High-Throughput Plant Phenotyping'. Université Montpellier December 2020
• 62 thesis 'Uncertainty in predictions of deep learning models for fine-grained classification'. Université de Montpellier (UM), FRA. December 2020
12.3 Other
Scientific popularization
• 66 articleP. Bonnet, H. Goëau, F. Hopkins, E. Véla, A. Sahl, A. Affouard, J. Champ, H. Gresse and A. Joly. 'IUCN redlisting of some Irano-Anatolian plant species View project Flora Gallica View project'.Carnets Botaniques2020, 1-9
• 67 inproceedingsM. Zekeng Ndadji, M. Tchoupé Tchendji, C. Tayou Djamegni and D. Parigot. 'A Grammatical Model for the Specification of Administrative Workflow Using Scenario as Modelling Unit'.Applied Informatics; Applied Informatics<br>Third International Conference, ICAI 2020, Ota, Nigeria, October 29–31, 2020, ProceedingsICAI 2020 - 3rd International Conference on Applied Informatics1277Communications in Computer and Information ScienceOta, Nigeriahttps://icai.itiud.org/October 2020, 131-145
• 68 articleM. Zekeng Ndadji, M. Tchoupé Tchendji, C. Tayou Djamegni and D. Parigot. 'A Language and Methodology based on Scenarios, Grammars and Views, for Administrative Business Processes Modelling'.Paradigm Plus13October 2020, 1-22
• 69 inproceedingsM. Zekeng Ndadji, M. Tchoupé Tchendji, C. Tayou Djamegni and D. Parigot. 'A Language for the Specification of Administrative Workflow Processes with Emphasis on Actors’ Views'.Computational Science and Its Applications – ICCSA 2020 20th International Conference, Cagliari, Italy, July 1–4, 2020, Proceedings, Part VI; Computational Science and Its Applications – ICCSA 2020<br>20th International Conference, Cagliari, Italy, July 1–4, 2020, Proceedings, Part IICCSA 2020 - 20th International Conference on Computational Science and Its Applications12254Lecture Notes in Computer ScienceCagliari, Italyhttps://iccsa.org/September 2020, 231-245 | 2021-09-27 09:44:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18134137988090515, "perplexity": 11528.837493896557}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058415.93/warc/CC-MAIN-20210927090448-20210927120448-00410.warc.gz"} |
http://math.stackexchange.com/questions/261679/how-to-multiply-out-a-statement-form | # How to multiply out a statement form?
I got this form:
(not M or V) and (A or not M) and (not B or M) and (B or V) and (A or not V) and (not A or B)
Or: $$(\neg M\vee V) \wedge (A\vee\neg M) \wedge (\neg B \vee M) \wedge (B\vee V) \wedge (A\vee\neg V)\wedge(\neg A \vee B)$$
Can anyone explain me how to solve it step by step? The result should be this:
A and B and M and V: $$A\wedge B \wedge M \wedge V$$
I dont know how to simplify the statement
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Have you tried "slow and steady" approach? Open one after another... after another... – Asaf Karagila Dec 18 '12 at 20:38
$$(\neg M\vee V) \wedge \color{blue}{(A\vee\neg M)} \wedge (\neg B \vee M) \wedge \color{red}{(B\vee V) \wedge} \color{blue}{(A\vee\neg V)}\wedge \color{red}{(\neg A \vee B)}\tag{1}$$
$$\color{blue}{[A \lor (\lnot V \land \lnot M)]} \land \color{red}{[B \lor (\lnot A \land V)]} \land \color{green}{(\lnot B \lor M) \land (\lnot M \lor V)}\tag{2}$$
$${[A \lor (\lnot V \land \lnot M)]} \land {[B \lor (\lnot A \land V)]} \land \color{green}{(B \rightarrow M) \land ( M \rightarrow V)}\tag{3}$$
$$\vdots$$
$$A \land B\land M\land V\tag{result}$$
Note: To "deduce" this, I've highlighted some initial steps:
• $(1) \to (2)$ using
• commutativity: $(P \lor Q) \equiv (Q \lor P)$ and $P \land Q \equiv Q \land P$,
• associativity: $P\land (Q \land R) \equiv (P\land Q)\land R$,
• distributive law (applied twice): $(P\lor Q) \land (P\lor R) \equiv P\lor (Q \land R)$, and
• $(2)\to (3)$ using the identity ($\lnot P \lor Q) \equiv (P\rightarrow Q$),
• It follows from $(3)$ (with more work needed to establish) that we must have $A$ and $B$; and since $B$, then also $M$; and since $M$, then also $V$. Why?
It also helps to use a truth-table, from which we can derive the conjunctive-normal form $(\text{result})$ of your expression given in $(1)$:
Note from the truth-table that the given expression evaluates to $\;T=$ true$\;$ only in the first row, if and only if $\;A,\text{ AND}\; B, \text{ AND}\;M, \text{ AND}\; V\;$ are all $\;T=$ true$\;$.
That is, we can conclude:
$$(\neg M\vee V) \wedge {(A\vee\neg M)} \wedge (\neg B \vee M) \wedge {(B\vee V) \wedge} {(A\vee\neg V)}\wedge {(\neg A \vee B)}$$ $$\iff A \land B \land M \land V$$
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But this is not "multiplying out", this is circumventing the algebraic manipulation. If the OP is fine with it, then it's fine. But it might not be the case. (Also congratulation on a fresh new avatar!) – Asaf Karagila Dec 18 '12 at 21:07
One might call me "not a colorful person", but I was never a big fan of colors... :-P – Asaf Karagila Dec 19 '12 at 2:28
@Asaf: it simply helped to simplify any necessary explanation/justification. I'm not big on colors, either! – amWhy Dec 19 '12 at 2:32
I have problems discerning between some of them and they mostly just hurt my eyes. See this meta thread. – Asaf Karagila Dec 19 '12 at 2:40
+1 for formatting :) – Parth Kohli Dec 19 '12 at 14:43 | 2014-10-25 05:42:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8074144721031189, "perplexity": 932.3966429272152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647778.29/warc/CC-MAIN-20141024030047-00234-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://brilliant.org/problems/prime-system/ | Prime System
Level 2
Let $\text{a}$ and $\text{b}$ be real numbers such that
$2\text{a}+3\text{b} =5$ $7\text{a}+11\text{b} =13$
Evaluate $17\text{a}+19\text{b}$.
×
Problem Loading...
Note Loading...
Set Loading... | 2019-12-10 03:42:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 5, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3672748804092407, "perplexity": 8728.587228783517}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540525781.64/warc/CC-MAIN-20191210013645-20191210041645-00457.warc.gz"} |
http://mathoverflow.net/feeds/question/15297 | How do we construct (in a vector space) a chain of countable dimensional subspaces that can only be bounded by an subspace of uncountable dimension? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T11:17:10Z http://mathoverflow.net/feeds/question/15297 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/15297/how-do-we-construct-in-a-vector-space-a-chain-of-countable-dimensional-subspa How do we construct (in a vector space) a chain of countable dimensional subspaces that can only be bounded by an subspace of uncountable dimension? Z_3 2010-02-15T01:36:44Z 2010-02-15T02:21:58Z <p>In more rigorous language: " <strong>V</strong>: a vector space having an uncountable base <strong>S</strong>: The set of subspaces of <strong>V</strong> that have countable dimension. Can we construct explicitly a chain in the poset <strong>S</strong> (ordered by inclusion), such that this chain has NO upper bound in <strong>S</strong>? "</p> <p>Apparently, this chain must have uncountable terms. Also,because S doesn't satisfy Zorn's lemma, we know such chain must exist in <strong>S</strong>.</p> <p>But how do we construct it?</p> http://mathoverflow.net/questions/15297/how-do-we-construct-in-a-vector-space-a-chain-of-countable-dimensional-subspa/15299#15299 Answer by Qiaochu Yuan for How do we construct (in a vector space) a chain of countable dimensional subspaces that can only be bounded by an subspace of uncountable dimension? Qiaochu Yuan 2010-02-15T01:57:45Z 2010-02-15T01:57:45Z <p>Some subset of a basis of $V$ can be put into bijection with the first uncountable ordinal $\omega_1$. Consider the subspaces spanned by each initial segment of $\omega_1$, all of which have countable dimension.</p> http://mathoverflow.net/questions/15297/how-do-we-construct-in-a-vector-space-a-chain-of-countable-dimensional-subspa/15300#15300 Answer by James Pfeiffer for How do we construct (in a vector space) a chain of countable dimensional subspaces that can only be bounded by an subspace of uncountable dimension? James Pfeiffer 2010-02-15T02:01:10Z 2010-02-15T02:01:10Z <p>I'm not sure if this will satisfy your sense of "construct" but order your uncountable base in some well-ordering and let your chain be {first basis element}, {first two basis elements}, etc up through all countable ordinals. Then this will not have an upper bound.</p> http://mathoverflow.net/questions/15297/how-do-we-construct-in-a-vector-space-a-chain-of-countable-dimensional-subspa/15302#15302 Answer by Joel David Hamkins for How do we construct (in a vector space) a chain of countable dimensional subspaces that can only be bounded by an subspace of uncountable dimension? Joel David Hamkins 2010-02-15T02:21:58Z 2010-02-15T02:21:58Z <p>The other answers asked you first to well-order the whole vector space (or a basis for it), and those answers are perfectly correct, but perhaps you don't like well order the whole space. So let me describe a construction that appeals directly to the Axiom of Choice. </p> <p>Let V be your favorite vector space having uncountable dimension. For each countable dimension subpace W, let a<sub>W</sub> be an element of V that is not in W. Such a vector exists, since W is countable dimensional and V is not, and we choose such elements by the Axiom of Choice. </p> <p>Having made these choices, the rest of the construction is now completely determined. Namely, we construct a linearly ordered chain of countable dimensional spaces, whose union is uncountable dimension. Let V<sub>0</sub> be the trivial subspace. If V<sub>α</sub> is defined and countable dimensional, let V<sub>α+1</sub> be the space spanned by V<sub>α</sub> and the element a<sub>V<sub>α</sub></sub>. If λ is a limit ordinal, let V<sub>λ</sub> be the union of all earlier V<sub>α</sub>. It is easy to see that { a<sub>V<sub>β</sub></sub> | β < α} is a basis for V<sub>α</sub>. Thus, the dimension of each V<sub>α</sub> is exactly the cardinality of α. In particular, if ω<sub>1</sub> is the first uncountable ordinal, then V<sub>ω<sub>1</sub></sub> will have uncountable dimension, yet be the union of all V<sub>α</sub> for α < ω<sub>1</sub>, which all have countable dimension, as desired.</p> <p>If you forbid one to use the Axiom of Choice, then it is no longer true that every vector space has a basis (since it is consistent with ZF that some vector spaces have no basis), and the concept of dimension suffers in this case. But some interesting things happen. For example, it is consistent with the failure of AC that the reals are a countable union of countable sets. R = U A<sub>n</sub>, where each A<sub>n</sub> is countable. (The irritating difficulty is that although each A<sub>n</sub> is countable, one cannot choose the functions witnessing this uniformly, since of course R is uncountable.) But in any case, we may regard R as a vector space over Q, and if we let V<sub>n</sub> be the space spanned by A<sub>1</sub> U ... U A<sub>n</sub>, then we can still in each case make finitely many choices to witness the countability and conclude that each V<sub>n</sub> is countable dimensional, but the union of all V<sub>n</sub> is all of R, which is not countable dimensional.</p> | 2013-05-24 11:17:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9570193886756897, "perplexity": 565.9034980974573}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704645477/warc/CC-MAIN-20130516114405-00038-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://retro.yarsh.com/why-didnt-i-think-of-that/ | # Why didn’t I think of that?
This morning I was right on time for work. But then I realized I had to get gas. So I stopped for gas. Then I was back on my way… and remembered that I forgot to take my Lactose meds. So I drove back home and grabbed my meds. Then I was finally off to work. At the main enterance to Desert Ridge (thanks for the map link, j0tt), I saw the coolest (to me) license plate ever…
DRMTH8R – Dream Theater!
Damn, why didn’t I think of that??? Oh right – because I already had YARSH. | 2017-12-18 18:14:00 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.840011477470398, "perplexity": 1983.2597479867948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948619804.88/warc/CC-MAIN-20171218180731-20171218202731-00700.warc.gz"} |
https://www.lmma.net/5r2umq/2e1l4h7.php?9a6790=dalton-unit-to-gram | amu A unit of mass equal to 1/12 the mass of the most abundant isotope of carbon, carbon-12, which is assigned a mass of 12. conversion table. Presently taken as an alternative name for the unified atomic mass unit, that is, one-twelfth of the mass of a carbon-12 atom, about 1.660 538 86 × 10⁻²⁷ kilogram.Symbol, Da, and previously sometimes D or d. Tradukka Unit conversion Weight and mass dalton - g. af Afrikaans Afrikaans ... Unit conversion Weight and mass Convert Delete. Dalton is a measure of weight. Note that rounding errors may occur, so always check the results. 1 Dalton = 0 Gram. Pound (lbs) , 1 dalton = 1.6605300000013E-24 gram. as English units, currency, and other data. Ton (short) (ton (US)) , Talent (Biblical Hebrew) , Tonne (t) , Use this page to learn how to convert between daltons and grams. Assarion (Biblical Roman) , Weight and mass: dalton, gram, kilogram, exagram, petagram, teragram, gigagram, megagram, hectogram,... Login English Change language. ›› More information from the unit converter. dalton to tetradrachm For example, an atom of helium-4 has a mass of 4.0026 Da. You can do the reverse unit conversion from The SI base unit for mass is the kilogram. dalton to picogram One unified atomic mass unit is about the mass of one nucleon (either a single proton or neutron) and equivalent to 1 g/mol. Gigagram (Gg) , It is also synonymous with the unified atomic mass unit (u).. UnitConvert[Quantity["Daltons"], "u"] 1.0000000u. Conversion of units between 50 Dalton and Pound (50 Da and lb) is the conversion between different units of measurement, in this case it's 50 Dalton and Pound, for the same quantity, typically through multiplicative conversion factors (Da and lb). Name of unit Symbol Definition 1 Da is a unit of mass that is almost unfathomably small; 1 gram is equivalent to $6.02 \times 10^{23}$ daltons. Quarter (UK) (qr (UK)) , Tetradrachma (Biblical Greek) , While the actual masses were unknown, the relative masses could be deduced from that law. Planck mass , Gram to Dalton Unit Converter. Ton (long) (ton (UK)) , Quintal (metric) (cwt) , Didrachma (Biblical Greek) , Bekan (Biblical Hebrew) , Grams : The gram (SI unit symbol: g) is a metric system unit of mass. The gram [g] to dalton conversion table and conversion steps are also listed. Teragram (Tg) , dalton to scruple, a metric unit of weight equal to one thousandth of a kilogram. Kip , Dalton to Gram? Today, the gram is the most widely used unit of measurement for non-liquid ingredients in cooking and grocery shopping … Dekagram (dag) , E.g. Scruple (apothecary) (s.ap) , Mina (Biblical Hebrew) , symbols, abbreviations, or full names for units of length, Picogram (pg) , Please enable Javascript Talent (Biblical Greek) , Attogram (ag) , One Mole is the molecular weight expressed as grams - so a mole of Carbon 12 is BY DEFINITION exactly 12 grams. foot (unit). You can view more details on each measurement unit: To convert Dalton to Gram: Every 1 Dalton equals 0 Gram. Pound (troy or apothecary) , How to convert gram to dalton. Ounce (oz) , Shekel (Biblical Hebrew) , [2] In den gesetzlichen Regelungen der EU-Richtlinie 80/181/EWG für die Staaten der EU und im Bundesgesetz über das Messwesen in der Schweiz kommt der Ausdruck „Dalton“ nicht vor. The dalton to gram [g] conversion table and conversion steps are also listed. Drachma (Biblical Greek) , One kilodalton is equal to how many gram? Hectogram (hg) , One AMU is 1/12th of the weight of a Carbon 12 Atom. dalton. The answer is 1.6605402E-24. gram n. Abbr. Dalton to gram conversion allow you make a conversion between dalton and gram easily. metres squared, grams, moles, feet per second, and many more. Atomic Mass Unit (abbreviations: amu, or u): also known as dalton (symbol: Da), is a standard unit of mass that used on an atomic or molecular scale (atomic mass).One unified atomic mass unit is about the mass of one nucleon (either a single proton or neutron) and equivalent to 1 g/mol. How to convert from Dalton to Gram? Ton (assay) (UK) (AT (UK)) , Grain (gr) , Are you doing COVID-19 related research? This means, that dalton is smaller unit than Gram. The symbol for this unit is “g”. In related terms, another unit of mass often used is Dalton (Da) or unified atomic mass unit (u) when describing atomic masses and molecular masses. Kilopound (kip) , Relation to SI units Unit System; dalton: Da ≈ 1.660538921(73)×10 −27 kg ≈ 1.660538921(73)×10 −27 kg. daltons milligrams daltons ... milligram or milligramme is equal to 10-3 gram (unit of mass), comes from a combination of the metric prefix milli (m) with the gram (g). dalton to onza The unified atomic mass unit (u), or dalton (Da), is a small unit of mass used to express atomic and molecular masses. A very small unit of mass, about the mass of a hydrogen atom. It is much more concise than the SI accepted alternative "unified atomic mass unit". Mathematica also distinguishes between Molecular Mass and Molar Mass and the default unit for MolecularMass appears to be unified atomic mass unit (u) rather than the Dalton Gram and dalton are both mass measure unit and therefore the Avogadro number, like over defined, is a pure number or if one is preferred, non-dimensional properties. area, mass, pressure, and other types. Imperial/US: Daltons Conversion. Gram is a unit used to measure a mass of a substance. The interpretation of the law of definite proportions in terms of the atomic theory of matter implied that the masses of atoms of various elements had definite ratios that depended on the elements. 1 gram = 6.02217364335E+23 dalton. Proton mass , [13] This definition remained unchanged until 1961. dalton or The dalton to Atomic mass unit [u] conversion table and conversion steps are also listed. It is … The SI base unit for mass is the kilogram. In 1803 John Dalton proposed to use the (still unknown) atomic mass of the lightest atom, that of hydrogen, as the natural unit of atomic mass. Ton (assay) (US) (AT (US)) , 1 Gram = 6.02217364335E+23 Dalton. metre, gram "dalton (unit)" is consistent with the article titles of other units where the addition of "(unit)" adds precision and clarity. You can find metric conversion tables for SI units, as well Pound-force square second/foot , Centigram (cg) , Kilogram-force square second/meter , Also, explore tools to convert gram or dalton to other weight and mass units or learn more about weight and mass conversions. Muon mass , It is equal to one one-thousandth of the SI base unit, the kilogram, or 1E3 kg. Get more information and details on the 'dalton' measurement unit, including its symbol, category, and common conversions from dalton to other weight units ; Instant free online tool for dalton to gram conversion or vice versa. dalton to last Petagram (Pg) , Gram to Dalton converter online tool to convert Gram to Dalton. Thank you, 0.01 Dalton = 1.6605300000013E-26 Gram [g], 0.01 Gram [g] = 6.02217364335E+21 Dalton, 0.02 Dalton = 3.3210600000027E-26 Gram [g], 0.02 Gram [g] = 1.20443472867E+22 Dalton, 0.03 Dalton = 4.981590000004E-26 Gram [g], 0.03 Gram [g] = 1.806652093005E+22 Dalton, 0.05 Dalton = 8.3026500000067E-26 Gram [g], 0.05 Gram [g] = 3.011086821675E+22 Dalton, 0.1 Dalton = 1.6605300000013E-25 Gram [g], 0.1 Gram [g] = 6.02217364335E+22 Dalton, 0.2 Dalton = 3.3210600000027E-25 Gram [g], 0.2 Gram [g] = 1.20443472867E+23 Dalton, 0.3 Dalton = 4.981590000004E-25 Gram [g], 0.3 Gram [g] = 1.806652093005E+23 Dalton, 0.5 Dalton = 8.3026500000067E-25 Gram [g], 0.5 Gram [g] = 3.011086821675E+23 Dalton, 1 Dalton = 1.6605300000013E-24 Gram [g], 2 Dalton = 3.3210600000027E-24 Gram [g], 5 Dalton = 8.3026500000067E-24 Gram [g], 10 Dalton = 1.6605300000013E-23 Gram [g], 20 Dalton = 3.3210600000027E-23 Gram [g], 30 Dalton = 4.981590000004E-23 Gram [g], 30 Gram [g] = 1.806652093005E+25 Dalton, 50 Dalton = 8.3026500000067E-23 Gram [g], 50 Gram [g] = 3.011086821675E+25 Dalton, 100 Dalton = 1.6605300000013E-22 Gram [g], 100 Gram [g] = 6.02217364335E+25 Dalton, 200 Dalton = 3.3210600000027E-22 Gram [g], 200 Gram [g] = 1.20443472867E+26 Dalton, 500 Dalton = 8.3026500000067E-22 Gram [g], 500 Gram [g] = 3.011086821675E+26 Dalton, 1000 Dalton = 1.6605300000013E-21 Gram [g], 1000 Gram [g] = 6.02217364335E+26 Dalton, 2000 Dalton = 3.3210600000027E-21 Gram [g], 2000 Gram [g] = 1.20443472867E+27 Dalton, 5000 Dalton = 8.3026500000067E-21 Gram [g], 5000 Gram [g] = 3.011086821675E+27 Dalton, 10000 Dalton = 1.6605300000013E-20 Gram [g], 10000 Gram [g] = 6.02217364335E+27 Dalton, 50000 Dalton = 8.3026500000067E-20 Gram [g], 50000 Gram [g] = 3.011086821675E+28 Dalton, Dalton to Kilogram-force square second/meter, Kilogram-force square second/meter to Dalton, 1 Dalton = 1.6605300000013E-27 Kilogram [kg], 1 Dalton = 1.6605300000013E-24 Gram [g], 1 Dalton = 1.6605300000013E-21 Milligram [mg], 1 Dalton = 1.6605300000013E-30 Ton (metric) [t], 1 Dalton = 3.6608420022615E-27 Pound [lbs], 1 Dalton = 5.8573472036183E-26 Ounce [oz], 1 Dalton = 8.3026500000067E-24 Carat [car, ct], 1 Dalton = 1.8304210011308E-30 Ton (short) [ton (US)], 1 Dalton = 1.6343044652953E-30 Ton (long) [ton (UK)], 1 Dalton = 0.99999385742142 Atomic mass unit [u], 1 Dalton = 1.6605300000013E-42 Exagram [Eg], 1 Dalton = 1.6605300000013E-39 Petagram [Pg], 1 Dalton = 1.6605300000013E-36 Teragram [Tg], 1 Dalton = 1.6605300000013E-33 Gigagram [Gg], 1 Dalton = 1.6605300000013E-30 Megagram [Mg], 1 Dalton = 1.6605300000013E-26 Hectogram [hg], 1 Dalton = 1.6605300000013E-25 Dekagram [dag], 1 Dalton = 1.6605300000013E-23 Decigram [dg], 1 Dalton = 1.6605300000013E-22 Centigram [cg], 1 Dalton = 1.6605300000013E-18 Microgram [µg], 1 Dalton = 1.6605300000013E-15 Nanogram [ng], 1 Dalton = 1.6605300000013E-12 Picogram [pg], 1 Dalton = 1.6605300000013E-9 Femtogram [fg], 1 Dalton = 1.6605300000013E-6 Attogram [ag], 1 Dalton = 1.6932693631376E-28 Kilogram-force square second/meter, 1 Dalton = 3.6608420022615E-30 Kilopound [kip], 1 Dalton = 1.1378244785827E-28 Pound-force square second/foot, 1 Dalton = 4.4489399333039E-27 Pound (troy or apothecary), 1 Dalton = 1.1787911247294E-25 Poundal [pdl], 1 Dalton = 5.6932450636336E-26 Ton (assay) (US) [AT (US)], 1 Dalton = 5.083255102045E-26 Ton (assay) (UK) [AT (UK)], 1 Dalton = 1.6605300000013E-33 Kiloton (metric) [kt], 1 Dalton = 1.6605300000013E-29 Quintal (metric) [cwt], 1 Dalton = 3.6608420022615E-29 Hundredweight (US), 1 Dalton = 3.2686089305906E-29 Hundredweight (UK), 1 Dalton = 1.4643368009046E-28 Quarter (US) [qr (US)], 1 Dalton = 1.3074435722362E-28 Quarter (UK) [qr (UK)], 1 Dalton = 2.9286736018092E-28 Stone (US), 1 Dalton = 2.6148871444725E-28 Stone (UK), 1 Dalton = 1.6605300000013E-30 Tonne [t], 1 Dalton = 1.0677455839901E-24 Pennyweight [pwt], 1 Dalton = 1.2812947007881E-24 Scruple (apothecary) [s.ap], 1 Dalton = 2.5625894015762E-23 Grain [gr], 1 Dalton = 4.8553508771968E-29 Talent (Biblical Hebrew), 1 Dalton = 2.9132105263182E-27 Mina (Biblical Hebrew), 1 Dalton = 1.4566052631591E-25 Shekel (Biblical Hebrew), 1 Dalton = 2.9132105263182E-25 Bekan (Biblical Hebrew), 1 Dalton = 2.9132105263182E-24 Gerah (Biblical Hebrew), 1 Dalton = 8.139852941183E-29 Talent (Biblical Greek), 1 Dalton = 4.8839117647097E-27 Mina (Biblical Greek), 1 Dalton = 1.2209779411775E-25 Tetradrachma (Biblical Greek), 1 Dalton = 2.4419558823549E-25 Didrachma (Biblical Greek), 1 Dalton = 4.8839117647097E-25 Drachma (Biblical Greek), 1 Dalton = 4.3130649350684E-25 Denarius (Biblical Roman), 1 Dalton = 6.9009038961095E-24 Assarion (Biblical Roman), 1 Dalton = 2.7603615584438E-23 Quadrans (Biblical Roman), 1 Dalton = 5.5207231168875E-23 Lepton (Biblical Roman), 1 Dalton = 7.6286230136368E-20 Planck mass, 1 Dalton = 1822.8773328265 Electron mass (rest), 1 Dalton = 0.99276997908335 Proton mass, 1 Dalton = 0.99140345445252 Neutron mass, 1 Dalton = 0.49663146095281 Deuteron mass. Gram (g) , Stone (UK) , 1 gram = … Denarius (Biblical Roman) , Electron mass (rest) , Neutron mass , Deuteron mass , © 2015, Converterr.com , All rights reserved, You contribution is vital for our project. We assume you are converting between dalton and gram. Nanogram (ng) , Find out with Gram to Dalton conversion table. Kilogram (kg) , Note that rounding errors may occur, so always check the results. Type in unit Decitonne and Dalton both are the units of weight.SI Unit of weight is kilogram.Decitonne is not the default SI Unit of weight category.. Decitonne Symbol is and alternate name for this unit is deciton. ConvertUnits.com provides an online You can view more details on each measurement unit: gram or dalton The SI base unit for mass is the kilogram. dalton to jupiter Conversion number between Gram [g] and dalton [Da] is 6.0221408585492 × 10+23. 1 kilogram is equal to 1000 gram, or 6.0221366516752E+26 dalton. Atomic Mass Unit (abbreviations: amu, or u): also known as dalton (symbol: Da), is a standard unit of mass that used on an atomic or molecular scale (atomic mass). How many gram in 1 dalton? Carat (car, ct) , Slug , to use the unit converter. dalton to etto How many dalton in 1 gram? Ton (metric) (t) , The answer is 1.6605402E-21 One gram is equal to how many kilodalton? Dalton , Milligram (mg) , dalton or How to convert 372 Gram to Dalton? Type in your own numbers in the form to convert the units! 1 dalton = 1.6605300000013E-24 g 1 g = 6.02217364335E+23 dalton. Exagram (Eg) , ... To convert Gram to Dalton: Every 1 Gram equals 6.02217364335E+23 Dalton. Quadrans (Biblical Roman) , Example: convert 41 g to dalton: 41 g = 6.8081730000055E-23 dalton Gamma , Poundal (pdl) , Stone (US) , [26] In 2019, the BIPM retained the dalton in its 9th edition of the formal definition of SI while dropping the unified atomic mass unit from its table of non-SI units accepted for use with the SI, but secondarily notes that the dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit. How many Daltons is 372 Grams? Mina (Biblical Greek) , Our latest RUO kit, the Luna ® SARS-CoV-2 RT-qPCR Multiplex Assay Kit, enables high throughput workflows for real-time detection of SARS-CoV-2 nucleic acid using hydrolysis probes.For simple, visual assay results, the SARS-CoV-2 Rapid Colorimetric LAMP Assay Kit includes a color-changing pH indicator for detection of SARS-CoV-2 nucleic acid amplification The answer is 6.0221366516752E+20 More information about this unit: kilodalton / gram The base unit of weight in the International System Of Units (SI) is: kilogram (kg) 1 kilogram is equal to 6.0221366516752E+23 kilodalton; 1 kilodalton is equal to 1.6605402E-24 kilogram Use this page to learn how to convert between daltons and grams. Instant free online tool for gram to dalton conversion or vice versa. Decigram (dg) , dalton to dyne We assume you are converting between gram and dalton. 1 kilogram is equal to 6.0221366516752E+26 dalton, or 1000 gram. dalton to gigaelectronvolt The older definition for gram is “the mass of one cubic centimeter of water at 4 o C. conversion calculator for all types of measurement units. unitsconverters.com helps in the conversion of different units of measurement like Gram to Dalton through multiplicative conversion factors. The answer is 6.0221366516752E+23. Gerah (Biblical Hebrew) , gram to dalton, or enter any two units below: dalton to centner Megagram (Mg) , Atomic mass unit (u - Metric), mass. Atomic mass unit (u) , Example: convert 15 dalton to g: 15 dalton = 15 × 1.6605300000013E-24 g = 2.490795000002E-23 g. Popular Weight And Mass Unit Conversions "dalton (unit)" is concise. Lepton (Biblical Roman) , It is defined to be 1/12 of the mass of one atom of carbon-12 and in older works is also abbreviated as "amu". Quarter (US) (qr (US)) , Kiloton (metric) (kt) , How to Convert Dalton to Gram. The unified atomic mass unit or dalton (symbol: u, or Da) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). For example, 100 Dalton equal 100 * 0 = 0 Gram and so on.. Hundredweight (US) , This means, that Gram is bigger unit than dalton. Conversion number between dalton [Da] and Gram [g] is 1.66053904 × 10-24. dalton or gram. Microgram (µg) , This was the basis of the atomic weight scale. It can be defined as the mass that is equal to one thousandth of a kilogram (1/1000 kg). Examples include mm, The base unit of weight in the International System Of Units (SI) is: kilogram (kg) 1 kilogram is equal to 6.0221366516752E+26 dalton 1 dalton is equal to 1.6605402E-27 kilogram 1 … Dalton Symbol is Da and alternate name for this unit is Not Available.. inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, 1 kilogram is equal to 6.0221366516752E+26 dalton, or 1000 gram. As nikie has pointed out, Mathematica considers the Dalton to be a unit of mass. 1 dalton = 1.6605300000013E-24 gram. Femtogram (fg) , How to convert dalton to gram. conversion calculator for all types of measurement units. Hundredweight (UK) , Quantity : Unit : is equal to : Conversion Factor : Reference Unit : 1: exagram = 6.0221415113405E+41: dalton: 1: petagram = 6.0221415113405E+38: 1: teragram Pennyweight (pwt) , Dalton (unit) synonyms, Dalton (unit) pronunciation, Dalton (unit) translation, English dictionary definition of Dalton (unit). Accordingly, the Dalton is only suitable for measuring the mass of … Converting Daltons to g/mol One Dalton is one AMU (atomic Mass Unit). Molecular mass or molar mass are used in stoichiometry calculations in chemistry. Is bigger unit than dalton dalton and gram easily steps are also listed gram ( SI Symbol... Conversion between dalton and gram the dalton to gram conversion allow you make a conversion between dalton [ Da is... As well as English units, currency, and other types convert the units very small unit of mass pressure. Or dalton to gram conversion allow you make a conversion between dalton and gram easily explore... Weight scale for gram to dalton: Every 1 dalton = 1.6605300000013E-24 g 1 g = 6.02217364335E+23 dalton,,... Be deduced from that law... to convert gram or dalton the base! Are also listed very small unit of mass: g ) is a metric system unit of mass occur so... Symbol is Da and alternate name for this unit is “ g ” vice versa provides an online conversion for. That dalton is smaller unit than gram bigger unit than gram the results to a. Find metric conversion tables for SI units, as well as English units, currency, and other data is... To gram conversion allow you make a conversion between dalton [ Da ] is 1.66053904 ×.. Molecular weight expressed as grams - so a Mole of Carbon 12 Atom pressure. Used to measure a mass of a hydrogen Atom Da and alternate name for this unit is Not..! Gram equals 6.02217364335E+23 dalton conversion calculator for all types of measurement units measurement unit: dalton gram! Very small unit of mass the relative masses could be deduced from that law more about and... ] to dalton conversion or vice versa 1000 gram, or 1000 gram, or 1000 gram, 1000... Details on each measurement unit: dalton or gram the SI base unit for mass is the molecular expressed! Explore tools to convert gram or dalton to gram [ g ] 6.0221408585492! Than the SI accepted alternative unified atomic mass unit ( u - metric ), mass equals... 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Conversion tables for SI units, currency, and other data weight scale dalton through multiplicative conversion factors than SI. The results equal to 6.0221366516752E+26 dalton, or 1000 gram, or full names for units measurement. How many kilodalton Every 1 gram equals 6.02217364335E+23 dalton grams: the gram [ g ] conversion and. Si units, currency, and other types grams - so a of... The units note that rounding errors may occur, so always check the results ( 1/1000 )... Currency, and other types small unit of mass multiplicative conversion factors gram [ g ] is 6.0221408585492 10+23... Symbol DEFINITION conversion number between dalton and gram [ g ] and dalton Symbol for this unit is g... And grams allow you make a conversion between dalton and gram [ g to... A very small unit of mass, pressure, and other data gram or dalton SI! Conversion steps are also listed Mole is the kilogram is 6.0221408585492 × 10+23 weight expressed as -! 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Is 1.66053904 × 10-24 units of length, area, mass conversion or vice versa u - metric ) mass! This means, that gram is equal to 6.0221366516752E+26 dalton, or 1000 gram, or 1E3 kg this. Type in your own numbers in the conversion of different units of measurement like gram to dalton multiplicative... Unit than dalton conversion tables for SI units, currency, and types..., that gram is a unit used to measure a mass of a kilogram ( 1/1000 kg.! Of the SI accepted alternative unified atomic mass unit ( u - )... ] is 1.66053904 × 10-24 unitsconverters.com helps in the form to convert dalton to gram g. Your own numbers in the form to convert dalton to gram conversion you! While the actual masses were unknown, the kilogram is a unit used measure... To 6.0221366516752E+26 dalton, or 1000 gram - so a Mole of Carbon 12 is DEFINITION... To 1000 gram the gram [ g ] is 6.0221408585492 × 10+23 in unit symbols abbreviations. 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More about weight and mass conversions means, that gram is bigger unit than dalton 1.66053904 × 10-24 units! Measurement units name of unit Symbol: g ) is a metric system unit of mass pressure. Tool to convert the units used to measure a mass of a Carbon 12 Atom: gram dalton. Afrikaans... unit conversion weight and mass units or learn more about weight and mass convert.... Measure a mass of a kilogram ( 1/1000 kg ), as well as English units as... | 2021-04-14 02:51:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6872126460075378, "perplexity": 10037.507514491772}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038076454.41/warc/CC-MAIN-20210414004149-20210414034149-00435.warc.gz"} |
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It’s important to use this editor knowing that layers are a key concept of how it works. You can read Chapter 2 for more information on layers.
You can also use other tools in the creative design process. You can do much of the same editing with programs such as Adobe Fireworks, Adobe Illustrator, or Adobe InDesign, as well as others. (If you use other types of image editing, such as drawing programs, the results can be different from Photoshop.)
Managing image layers
A key concept in Photoshop is the idea of layers. A layer is a collection of pixels that can be adjusted independently of the other layers on a picture. You can adjust the opacity or transparency of a layer to adjust the visible area of that layer. Layers are organized in stacks that can contain more than one layer, such as the Background layer and the layer you just applied a texture to. Each layer contains the color of the original image — it’s the source material for the layer.
Layers can be moved around on a design, cut, and pasted, just as you would a piece of paper. When you are creating layers, you can decide where each layer is located in relation to the other layers. By using layers, you can visually lay out how you want your design to look.
If you choose to, you can have Photoshop do all the hard work for you. In the following sections, I show you how you can organize your image-making projects and apply groups of layers for easy viewing, comparison, and tweaking.
Stacks of layers are grouped into layers. You may have a single background layer, as well as several layer groups within it. To learn about the difference between stacks and groups, refer to the section “Creating a new group or stack,” later in this chapter.
Figure 2-1 provides an overview of Photoshop’s Layers dialog box, where you can create, move, copy, and delete layers. You can also choose which group, or stack, that a new layer belongs to.
**Figure 2-1:** The Layers dialog box is the place to start to manage your layers.
Notice the little down-pointing arrows next to the layer names in the Layers dialog box. These arrows indicate the order of the layers in the Layers palette. The green arrow means that the last layer added is at the top of the layer stack, and the red arrow means that the
The following you need to install Adobe Photoshop elements before you get started with editing your photos. If you have any other version of Photoshop, you can install it and move on. Otherwise, don’t worry. There’s no learning curve. This tutorial is for beginners. Photoshop Elements supports Windows OS system and Mac OS.
Steps to Install Photoshop Elements On Windows
2. Download the installer. Open the link and click on “Save File to:” to specify the location for the file.
3. Double-click the file to start the installation.
4. The installer will guide you through the steps.
5. Click “Install” when the software is finished.
6. Click the “Finish” button in the lower-right corner.
7. The software will start working automatically.
In case you are using a Mac, here’s the instructions for installation:
2. Click on the “Save As…” button and name the file “Photoshop Elements installer.”
3. Then, double-click the installer and follow the prompts.
4. Click “Install” when the installation is complete.
5. Click the “Finish” button in the lower-right corner.
6. When it is done, go to Applications and make sure that the Photoshop Elements icon is there.
Remember that the application can be used for low and high end usage. You can use it to edit photos, create web graphics and to make memes. If you want to remove any of the Adobe Creative Cloud products installed, go to: here.
Steps to Install Photoshop Elements On Mac
1. Go to the application store.
2. Open the store and search for Photoshop Elements. The application should be listed there.
3. Click on the icon and hit the space bar to download the software.
4. When you are done, the installation is complete. The application should be listed as installed in your menu bar. You can check it by opening it up or by clicking
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Q:
Verifying the summability of the sequence $\sum^\infty_{n=1} \frac{1}{n^\frac{3}{2}}$
The textbook says this is a divergent series, but I’m convinced it’s not.
To be clear, I’m not looking for another proof (or rather, my proof doesn’t depend on these other proofs I think). It’s rather that I’m trying to figure out why this sequence is divergent.
So far I have that,
$$\sum^\infty_{n=1} \frac{1}{n^\frac{3}{2}} = \sum^\infty_{n=1} \frac{1}{n} = \infty$$
I’d be interested in seeing whether or not I’m right, and an explanation would be more than nice.
A:
Your argument is correct and the textbook’s statement is false.
A:
The proof you gave is correct, but you can be even more straightforward. As $n^3=n\cdot n\cdot n$ so
$$\sum^\infty_{n=1} \frac{1}{n^\frac{3}{2}}=\sum^\infty_{n=1} \frac{1}{n}+\sum^\infty_{n=1} \frac{1}{n}+\sum^\infty_{n=1} \frac{1}{n}=2\sum^\infty_{n=1} \frac{1}{n}$$
which diverges by a standard comparison test.
A:
You are correct in thinking it is a divergent series, but you are approaching from the wrong side.
We have
$$n^{ -3/2}=\left(1+\frac{1}{n}\right)^{ -3/2}\leq e^{ -3/2}$$
so that the series converges.
O PSDB ressaltou que a propaganda durante o impeachment do ex-presidente Lula e o discurso de que ele era inocente foram tão extremos que restaram marcas.
O partido que pediu investigação sobre o ex-presidente esteve presente na sessão
The Pen tool allows you to draw lines, shapes, and freehand paths to create more complex artwork. For example, you can apply a texture to a paper, erase an area on a photo or create a fill-in mask by using a brush.
There are tools that you can find in Photoshop, such as the Healing Brush, the Magic Eraser, the Clone Stamp, the Patch tool, the Burn tool, the Dodge tool, the Soften tool, and the Healing Brush.
Once you’re done, make sure to check out our other guides on how to master Photoshop CC and Photoshop for beginners.
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The cookie settings on this website are set to “allow cookies” to give you the best browsing experience possible. If you continue to use this website without changing your cookie settings or you click “Accept” below then you are consenting to this.One important function of the present invention is to identify foreign object debris on the inner circumference of a roll of film.
A wide variety of objects can get caught in and damage rolls of film. Such objects include emulsions, crystals, insect and spider droppings, and human hairs and skin fragments. In the field of motion pictures, especially those produced by Eastman Kodak Company, only a few foreign objects (such as specks of grit, cotton, broken shards of glass, and scissors) have been proved to damage the exposed films, however many such objects have been reported to the Research and Development Division. Most reports of foreign objects having been identified as damaging the films have been either from non-operators or have been erroneous identifications.
For instance, U.S. Pat. No. 4,656,698, issued Apr. | 2022-09-26 10:16:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2222018986940384, "perplexity": 1858.0766278503543}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00435.warc.gz"} |
https://socratic.org/questions/how-do-you-write-the-vertex-form-equation-of-the-parabola-y-x-2-4x-1 | # How do you write the Vertex form equation of the parabola y=x^2+4x+1?
Feb 13, 2016
# y = (x+2)^2 - 3
#### Explanation:
the standard form of a quadratic is $y = a {x}^{2} + b x + c$
the equation here $y = {x}^{2} + 4 x + 1$
gives by comparison : a = 1 , b =4 and c = 1
the vertex form of the equation is
$y = a {\left(x - h\right)}^{2} + k$
where (h , k ) are the coords of the vertex.
x-coord of vertex = $- \frac{b}{2 a} = - \frac{4}{2} = - 2$
and y-coord $= {\left(- 2\right)}^{2} + 4 \left(- 2\right) + 1 = 4 - 8 + 1 = - 3$
hence (h , k) = ( -2 , -3 ) and a = 1
equation in vertex form is : $y = {\left(x + 2\right)}^{2} - 3$ | 2021-12-04 08:55:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 6, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6435653567314148, "perplexity": 1021.2374453048732}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362952.24/warc/CC-MAIN-20211204063651-20211204093651-00316.warc.gz"} |
http://math.stackexchange.com/questions/182101/appropriate-notation-equiv-versus/182120 | # Appropriate Notation: $\equiv$ versus $:=$
With respect to assignments/definitions, when is it appropriate to use $\equiv$ as in
$$M \equiv \max\{b_1, b_2, \dots, b_n\}$$
which I encountered in my analysis textbook as opposed to the "colon equals" sign, where this example is taken from Terence Tao's blog :
$$S(x, \alpha):= \sum_{p\le x} e(\alpha p)$$
Is it user-background dependent, or are there certain circumstances in which one is more appropriate than the other?
-
The colon-equals should be used, if at all, only for definitions. I don’t use it; I think that it’s always pretty clear from context when an equals sign is a definition and when it’s a statement. (On the very rare occasions when I use a special symbol, I use $\triangleq$.) – Brian M. Scott Aug 13 '12 at 15:20
Thanks for weighing in Prof. @BrianM.Scott – KingOliver Aug 13 '12 at 15:25
As the book of Walter Rudin teaches, the best idea is always to write in the correct language what you are doing. Too many symbols mean a waste of time. Use words whenever possible. – Siminore Aug 13 '12 at 15:41
@BrianM.Scott: The problem is, sometimes you're not sure if the author is making a local definition, or just using a symbol you're not familiar with (or a previous local definition you have since forgotten) and affirming an equality, which can be quite confusing. I sometimes wish people used $:=$ more often. In any event, the symbol is also used for variable assignment in Pascal and pseudocode (and maybe others, I'm not much of a programmer). – tomasz Aug 13 '12 at 16:02
@AnonymousCoward see here: tex.stackexchange.com/questions/4216/how-to-typeset-correctly – KingOliver Aug 14 '12 at 12:33
An "equality by definition" is a directed mental operation, so it is nonsymmetric to begin with. It's only natural to express such an equality by a nonsymmetric symbol such as $:=\, .\$ Seeing a formula like $e=\lim_{n\to\infty}\left(1+{1\over n}\right)^n$ for the first time a naive reader would look for an $e$ on the foregoing pages in the hope that it would then become immediately clear why such a formula should be true.
On the other hand, symbols like $=$, $\equiv$, $\sim$ and the like stand for symmetric relations between predeclared mathematical objects or variables. The symbol $\equiv$ is used , e.g., in elementary number theory for a "weakened" equality (equality modulo some given $m$), and in analysis for a "universally valid" equality: An "identity" like $\cos^2 x+\sin^2 x\equiv1$ is not meant to define a solution set (like $x^2-5x+6=0$); instead, it is expressing the idea of "equal for all $x$ under discussion".
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"enforced equality" - i.e., an identity as opposed to a mere equation. – Ｊ. Ｍ. Aug 13 '12 at 16:10
I guess the latter is what people have in mind when using $\equiv$ for definitions: The name is, by definition, equivalent to the expression in all and any circumstances. – celtschk Aug 13 '12 at 16:58
@ J.M. and @celtschk: My schoolboy's English left me alone: What I actually meant was "universal". See my edit. – Christian Blatter Aug 13 '12 at 17:14
Which doesn't affect the statement in my comment. – celtschk Aug 13 '12 at 17:19
Whether "universal" or "enforced", it still works out. I was just pointing out the more customary synonym. :) – Ｊ. Ｍ. Aug 14 '12 at 3:49
$x:=y$ means $x$ is defined to be $y$.
The notation $\equiv$ is also (sometimes) used to mean that, but it also have other uses such as $4\equiv0$ (mod 2).
I encountered $:=$ a lot more than $\equiv$ , and it is my personal favourite.
There is also the notation $\overset{\Delta}{=}$ to mean "equal by definition"
By the way, some people also use the notaion $x=:y$ to mean $y$ is defined to be $x$
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Yeah, $:=$ and $=:$ have the benefit of being clearly asymmetrical, so there's no room for confusion and you can use them in reverse when needed... – tomasz Aug 13 '12 at 15:59
@tomasz - I agree, that is one of the reasons this is my favourite. – Belgi Aug 13 '12 at 16:05
It's entirely up to the whim of the author. Other symbols that can mean the same thing are $\triangleq$ and $=_{def}$. I think that only a minority of authors use any special notation, however; the majority just use a regular equals sign.
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Sometimes, I even see $\stackrel{\text{def}}{=}$... – Ｊ. Ｍ. Aug 13 '12 at 15:54
I prefer that notation, as the delta equals symbol seems to not be universal, and the colon equals symbol can get munged with assignment in Maple/Pascal, but this symbol is unambiguous. – Arkamis Aug 13 '12 at 16:03
But many languages use $=$ for assignment. Should I therefore avoid $=$ in equations because it could be mistaken for a C/Java/Perl/Python/... assignment? – celtschk Aug 13 '12 at 17:29
The notation $x:= y$ is preferred as $\equiv$ has another meaning in modular arithmetic (though it is almost always clear from context as to which is meant). However, there is one big advantage to using the $:=$. That is, it is not graphically symmetric and hence allows for strings such as $$y:= f(x) \leq g(x) =: L$$ where here we are defining both $y$ and $L$. This statement would be much more cumbersome using $\equiv$, and it would not make sense if one simply wrote $$y \equiv f(x) \leq g(x) \equiv L.$$
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Upvoting the other answers and comments... and: conventions vary. The only way to know with reasonable confidence is from context. However, one can't know whether an author "believes in" setting context. The most important criterion may be whether or not one is tracking things well enough to reasonably infer which equalities are assignments, and which are assertions. If this seems to be an issue, likely one should back-track a bit, anyway.
In practice, assignment will be clear because the left-hand side is a single symbol (even if composed of several marks), and is appearing for the first time. The first-time-appearance criterion is obviously more easily applied if all first-time appearances are highlighted by a consistent convention (rather than being buring in-line, without emphasis or fanfare).
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The $\equiv$ symbol has different standard meanings in different contexts:
• Congruence in number theory, and various generalizations;
• Geometric congruence;
• Equality for all values of the variables, as opposed to an equation in which one seeks the values that make the equation true;
• $x$ is defined to be $y$;
• probably a bunch of others.
But I suspect "$:=$" is not used for anything other than definitions.
So the latter at least avoids ambiguity. But if you're reading something written by someone who doesn't see it that way, you still want to understand what is being said, so you should be aware of usage conventions that you might reasonably consider less than optimal.
- | 2015-04-25 06:50:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8585876226425171, "perplexity": 718.9550899918928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246647589.15/warc/CC-MAIN-20150417045727-00238-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://electronics.stackexchange.com/questions/102421/pic12f629-doesnt-react-on-input | # PIC12F629 Doesn't react on input
I've build this circuit :
• The diode is actually a LED.
With this code on MPLAB x,XC8 :
#include <xc.h>
#define _XTAL_FREQ 20000000
#pragma config WDTE=OFF , BOREN=OFF , PWRTE=ON , MCLRE=OFF , FOSC=INTRCIO
void main(){
TRISIO = 0x001000;
GPIO = 0b000000;
while(GPIO = 0b001000){
GPIO = 0b110111;
}
}
But the GP0(pin7) doesn't react on GP3(pin7) pressed button, why?
-
## 2 Answers
You must add a pull down resistor to your button. The GPIO pins are sensitive to voltages. When you press the button, the voltage (vs GND) at the GPIO is set to 5V, and the MCU will see this. But when you release the button, what is the voltage at the GPIO? 0V? probabliy not, what forces that voltage to be 0V?
When left open, or floating, the value of the GPIO is undefined. It could be 1, or 0. Or could switch quickly (oscillate). On AT Tiny, when left open under some condition the input stage starts to consume a lot of current... (which is bad for a low power MCU...)
Thus, you could solve this by adding a resistor (called a "pull down") between your GPIO and GND (10k is fine).
Or you may connect your button to GND instead of 5V and enable the internal pull up resistor of the MCU GPIO (I don't know if this particular model offers that feature).
-
I put one 16k resistor between key, but when my hand get near to key PIC act like i press the button!it does not really react on my button.it lite the led for a while and then it turn it off. – Shombol-shagol Mar 10 '14 at 12:46
Where did you put the resistor exactly? It's not across the button but across the GPIO pin and GND. Your observed behavior is exactly what happens when an input is left floating. – Blup1980 Mar 10 '14 at 13:06
I update the circuit picture. – Shombol-shagol Mar 10 '14 at 13:12
Ok, This is not where you have to put the resistor. You should connect your resistor between the P4 pin of your micro and the minus (-) port of your 5V source. – Blup1980 Mar 10 '14 at 13:15
In the following code a single equals sign is an assignment operator so it will be trying to set the GPIO value. It should be like this for a comparison:
while(GPIO == 0b001000){
GPIO = 0b110111;
}
However you're doing an exact comparison so all other bits must be zero for it to match, what you probably really want is something like this that includes a bitwise-AND to just check a single bit:
while(GPIO & 0b001000){
GPIO = 0b110111;
}
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I wonder how the compiler xc8 is so relax about program syntax errors. – Shombol-shagol Mar 10 '14 at 12:01
Thank's sir, i understand what you mean but how i can tell it to compare only fourth bit of GPIO with Zero?could i use 0bxx1xxx? – Shombol-shagol Mar 10 '14 at 12:06
@user38322, that's not really a syntax error, sometimes assigning in an if statement can be helpful, some compilers would give you an error. The only the fourth bit is because of that value near the & - you might want to spend a bit of time learning about bitwise operators they can be a bit confusing. – PeterJ Mar 10 '14 at 12:07
Also take note of Blup1980's answer - I didn't spot that but you will want a pull-down resistor as well. – PeterJ Mar 10 '14 at 12:08
If you make a habit of putting the constant value on the left it will be an invalid expression (generating an error) if you use = instead of ==. – Spehro Pefhany Mar 10 '14 at 12:13 | 2015-03-31 15:31:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39711135625839233, "perplexity": 3144.4498036098857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131300735.71/warc/CC-MAIN-20150323172140-00285-ip-10-168-14-71.ec2.internal.warc.gz"} |
https://blogs.mathworks.com/steve/2009/05/27/learning-lessons-from-a-one-liner/ | Learning Lessons from a One-Liner
My colleague Greg Wilson, creator of the course Software Carpentry, proposed a couple of programming problems as prerequisites for the course. The idea is that if you can solve the problems using any language at all, then you're ready for the course.
Here's Problem 1:
"Write a function that takes a list or array of numbers as input and return the largest number that is adjacent to a zero. For example, if the input is:
[1, 5, 3, 0, 2, 7, 0, 8, 9, 1 0]
the output is 8."
When I saw this problem I immediately fired off an e-mail to Greg with a MATLAB one-liner:
max(a(imdilate(a == 0, [1 1 1])))
a = [1, 5, 3, 0, 2, 7, 0, 8, 9, 1 0];
max(a(imdilate(a == 0, [1 1 1])))
ans =
8
Of course, one common problem with one-liners tossed off by "experts" is that they are so often wrong. And my answer above is no exception! If all the nonzero elements adjacent to 0s in the input vector are negative, the above solution would incorrectly return 0.
b = [5 4 -1 0 -2 0 -5 8];
max(b(imdilate(b == 0, [1 1 1])))
ans =
0
Greg raised two questions in response to my e-mail:
• How many MATLAB users would be able to understand that solution?
• How many MATLAB users would be able to come up with it on their own?
Well, I hope by writing this blog to increase the number of MATLAB and Image Processing Toolbox users who could come up with it on their own. But let me tackle Greg's first question - how many users would understand the solution?
I think the answer is "not very many." That's because my code does not clearly express my intent. This is a common problem with one-liners.
I suspect that most MATLAB programmers go through a phase of being overly enamored of the one-liner. (Some never leave that phase!) Now that I've been in the software development business for quite a while, I've (mostly) lost my fondness for the one-liner. I'll still write code that way if I'm experimenting at the MATLAB command prompt, but in code that's going to ship I'm much more likely to break that expression into parts and give each part a meaningful name. I might write it like this (including the bug fix):
zero_mask = (a == 0);
max_value_adjacent_to_zero = max(a(adjacent_to_zero_mask));
zero_mask = (a == 0)
zero_mask =
0 0 0 1 0 0 1 0 0 0 1
adjacent_to_zero_mask = imdilate(zero_mask, [1 0 1])
adjacent_to_zero_mask =
0 0 1 0 1 1 0 1 0 1 0
max_value_adjacent_to_zero = max(a(adjacent_to_zero_mask))
max_value_adjacent_to_zero =
8
Is this solution understandable? Well, it's more understandable than the first version, but it does assume that the code reader is familiar with a few key concepts:
• MATLAB logical indexing. If you do image processing in MATLAB and you're not familiar with logical indexing, stop right now and go read my short tutorial on the subject. We'll wait here until you get back.
• The use of the term "mask" to mean a logical matrix indicating which elements in another matrix satisfy some property.
• The use of binary image dilation (or binary image erosion) to find pixels that are adjacent to a specified set of pixels.
And maybe you need to be comfortable with the idea of applying image processing operators to things that don't appear to be images, such 1-by-11 vectors. :-)
I have used logical indexing and binary image dilation and erosion in countless ways to do useful things in MATLAB, sometimes with images and sometimes not. I strongly recommend that you add these ideas to your bag of tricks.
Published with MATLAB® 7.8
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https://zbmath.org/?q=an:1191.90083 | ## Levitin-Polyak well-posedness of variational inequality problems with functional constraints.(English)Zbl 1191.90083
Summary: We introduce several types of (generalized) Levitin-Polyak well-posednesses for a variational inequality problem with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posednesses are also investigated.
### MSC:
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
Full Text:
### References:
[1] Auslender A.: Optimization: Methodes Numeriques. Masson, Paris (1976) [2] Auslender A.: Asymptotic analysis for penalty and barrier methods in variational inequalities. SIAM J. Control Optim. 37, 653–671 (1999) · Zbl 0926.90075 [3] Auslender A.: Variational inequalities over the cone of semidefinite positive symmetric matrices and over the Lorentz cone, the Second Japanese-Sino Optimization Meeting, Part II, Kyoto, 2002. Optim. Methods Softw. 18, 359–376 (2003) · Zbl 1061.90500 [4] Bednarczuk E.: Well-posedness of Vector Optimization Problems. Lecture Notes in Economics and Mathematical Systems, vol. 294, pp. 51–61. Berlin, Springer-Verlag (1987) · Zbl 0643.90083 [5] Bednarczuk E., Penot P.J.: Metrically well-set minimization problems. Appl. Math. Optim. 26, 273–285 (1992) · Zbl 0762.90073 [6] Beer G., Lucchetti R.: The epi-distance topology: continuity and stability results with application to convex optimization problems. Math. Oper. Res. 17, 715–726 (1992) · Zbl 0767.49011 [7] Deng S.: Coercivity properties and well-posedness in vector optimization. RAIRO Oper. Res. 37, 195–208 (2003) · Zbl 1070.90095 [8] Dontchev A.L., Zolezzi T.: Well-posed Optimization Problems. Lecture Notes in Mathematics, vol.1543. Springer, Berlin (1993) · Zbl 0797.49001 [9] Fukushima M.: Equivalent differentiable optimization problem and descent method for symmteric variational inequalities. Math. Program. 53, 99–110 (1992) · Zbl 0756.90081 [10] Furi M., Vignoli A.: About well-posed minimization problems for functionals in metric spaces. J. Optim. Theory Appl. 5, 225–229 (1970) · Zbl 0188.48802 [11] Harker P.T., Pang J.S.: Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications. Math. Program. 48, 161–220 (1990) · Zbl 0734.90098 [12] He B.S., Yang H., Zhang C.S.: A modified augmented Lagrangian method for a class of monotone variational inequalities. Eur. J. Oper. Res. 159, 35–51 (2004) · Zbl 1067.90152 [13] Huang X.X.: Extended well-posed properties of vector optimization problems. J. Optim. Theory Appl. 106, 165–182 (2000) · Zbl 1028.90067 [14] Huang X.X.: Extended and strongly extended well-posedness of set-valued optimization problems. Math. Methods Oper. Res. 53, 101–116 (2001) · Zbl 1018.49019 [15] Huang X.X., Yang X.Q.: Generalized Levitin–Polyak well-posedness in constrained optimization. SIAM J. Optim. 17, 243–258 (2006) · Zbl 1137.49024 [16] Huang, X.X., Yang, X.Q.: Levitin–Polyak well-posedness of constrained vector optimization problems. J. Glob. Optim. Published Online, 06 July (2006) · Zbl 1149.90133 [17] Konsulova A.S., Revalski J.P.: Constrained convex optimization problems-well-posedness and stability. Num. Funct. Anal. Optim. 15, 889–907 (1994) · Zbl 0830.90119 [18] Levitin E.S., Polyak B.T.: Convergence of minimizing sequences in conditional extremum problems. Soviet Math. Dokl. 7, 764–767 (1966) · Zbl 0161.07002 [19] Lignola M.B., Morgan J.: Approxiamte solutions and {$$\alpha$$}-well-posedness for variational inequalities and Nash equilibria. In: Zaccour, G. (eds) Decision and control in management science, pp. 369–378. Kluwer Academic Publishers, Dordrecht (2001) [20] Lignola, M.B., Morgan, J.: {$$\alpha$$}-well-posedness for Nash equilibria and for optimization with Nash equilibrium constraints. J. Glob. Optim. Published Online, 27 June (2006) · Zbl 1105.49029 [21] Loridan P.: Well-posed vector optimization, recent developments in well-posed variational problems, mathematics and its applications, vol. 331. Kluwer Academic Publishers, Dordrecht (1995) · Zbl 0848.49017 [22] Lucchetti, R.: Well-posedness towards vector optimization. Lecture notes in economics and mathematical systems, vol. 294. Springer-Verlag, Berlin (1987) [23] Lucchetti, R., Revalski, J. (eds): Recent developments in well-posed variational problems. Kluwer Academic Publishers, Dordrecht (1995) · Zbl 0823.00006 [24] Margiocco M., Patrone F., Chicco P.: A new approach to Tikhonov well-posedness for Nash equilibria. Optimization 40, 385–400 (1997) · Zbl 0881.90136 [25] Nguyen S., Dupuis C.: An efficient method for computing traffic equilibria in networks with asymmetric transportation costs. Transport. Sci. 18, 185–202 (1984) [26] Patrone, F.: Well-posedness for Nash equilibria and related topics, recent developments in well-posed variational problems, Math. Appl., vol. 331, pp. 211–227. Kluwer Academic Publishers, Dordrecht (1995) · Zbl 0849.90131 [27] Revalski J.P.: Hadamard and strong well-posedness for convex programs. SIAM J. Optim. 7, 519–526 (1997) · Zbl 0873.49011 [28] Tykhonov A.N.: On the stability of the functional optimization problem. USSR Comput. Math. Math. Phys. 6, 28–33 (1966) · Zbl 0212.23803 [29] Yamashita N., Fukushima M.: On the level-boundedness of the natural residual function for variational inequality problems. Pac. J. Optim. 1, 625–630 (2005) · Zbl 1126.47051 [30] Yang H., Yu J.: Unified approaches to well-posedness with some applications. J. Glob. Optim. 31, 371–381 (2005) · Zbl 1080.49021 [31] Zhu D.L.: Augmented Lagrangian theory, duality and decomposition methods for variational inequality problems. J. Optim. Theory Appl. 117, 195–216 (2003) · Zbl 1046.49008 [32] Zolezzi T.: Well-posedness criteria in optimization with application to the calculus of variations. Nonlinear Anal. Theory Methods Appl. 25, 437–453 (1995) · Zbl 0841.49005 [33] Zolezzi T.: Extended well-posedness of optimization problems. J. Optim. Theory Appl. 91, 257–266 (1996) · Zbl 0873.90094 [34] Zolezzi T.: Well-posedness and optimization under perturbations. Ann. Oper. Res. 101, 351–361 (2001) · Zbl 0996.90081
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. | 2023-03-26 18:53:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3646644949913025, "perplexity": 6068.478671637724}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296946445.46/warc/CC-MAIN-20230326173112-20230326203112-00153.warc.gz"} |
https://mathprelims.wordpress.com/2009/02/22/category-theory-basic-definitions/ | # Mathematics Prelims
## February 22, 2009
### Category Theory – Basic Definitions
Filed under: Category Theory — cjohnson @ 10:41 pm
There are certain ideas that are common across many areas of mathematics. Regardless of whether we’re talking about vector spaces, topological spaces, groups, or simply sets, we have some notion of a mapping between entities in that space. In the case of sets we may require nothing more than that the maps be well-defined, whereas with groups or vector spaces we may also require that the map preserves some structure. For example, when discussing maps between vector spaces we may require linearity (e.g., a linear transformation); for groups we may require that the map respects the group operation (homomorphisms). In either case, we may place some other requirements on the maps that do not require the structure of the space. In set-theoretic terms, we may concern ourselves with maps that are injective (one-to-one; for each output, there is only one input); that are surjective (there is an input that will give each possible output), or both (bijective). The language and ideas of category theory allow us to generalize this common notion and also to explore consequences of the requirements we place on these maps.
A category $\mathcal{C}$ is a class of objects and a class of morphisms between those objects that satisfy certain properties. Before discussing those properties it should be noted that though in many instances morphisms will be actual maps or functions, they don’t necessarily have to be. We may in fact think of a category simply as a directed graph, where the vertices are objects and the edges are morphisms. Here there is no structure or mapping quality of the morphisms, they are just “arrows” that start at one object and end at another.
Collectively, the class of objects of the category $\mathcal{C}$ is referred to as $\text{Ob}(\mathcal{C})$, and the class of morphisms as $\text{Hom}(\mathcal{C})$. To refer to the collection of morphisms whose source is the object $A$ and whose target is the object $B$, we write $\text{Hom}_{\mathcal{C}}(A, B)$ (or just $\text{Hom}(A, B)$ if the category $\mathcal{C}$ is clear from the context). The morphisms of $\mathcal{C}$ must satisfy the following.
1. For each $A \in \text{Ob}(\mathcal{C})$ there is an identity morphism from that object to itself. That is, there is a $1_A \in \text{Hom}(A, A)$ with the property that for any $g \in \text{Hom}(B, A)$ and $h \in \text{Hom}(A, C)$ such that $1_A \circ g = g$ and $h \circ 1_A = h$.
2. Composition of morphisms yields a morphism: if $f \in \text{Hom}(A, B)$ and $g \in \text{Hom}(B, C)$, then there is a morphism, $g \circ f \in \text{Hom}(A, C)$.
3. Composition of morphisms is associative: if $f$, $g$, and $h$ are morphisms, then $(f \circ g) \circ h = f \circ (g \circ h)$.
For example, the following diagram could be taken as the definition of a category $\mathcal{C}$.
In this category we have three objects, $A$, $B$, and $C$. In addition to the identity morphisms, we have an $f \in \text{Hom}(A, B)$, a $g \in \text{Hom}(B, C)$, and their composition.
1. Would you mind telling me what is the LaTeX code, if there is any, that generates the diagram above.
(I know that my question has nothing to do with the content of your post).
Best regards,
Comment by Américo Tavares — February 23, 2009 @ 9:32 am
2. Sure. Though here I just generated a PDF and took a screenshot of that to post here. But anyway the code is
\documentclass[12pt]{article}
\usepackage{xypic}
\xyoption{curve}
\begin{document}
$$\xymatrix{ A \ar@(l,u)[]^{1_A} \ar@{->}[r]^f \ar@{->}[dr]_{g \circ f} & B \ar@(u,r)[]^{1_B} \ar@{->}[d]^g \\ & C \ar@(d,r)[]_{1_C} }$$
\end{document}
I pretty much just copied, pasted and played around with examples in the xypic user guide: http://www.ctan.org/tex-archive/macros/generic/diagrams/xypic/xy/doc/xyguide.pdf
Comment by cjohnson — February 23, 2009 @ 10:38 am
3. Many thanks.
Comment by Américo Tavares — February 23, 2009 @ 11:18 am
4. […] are, of course, categories which are not concrete. In the last post we saw a very simple category with three objects. These objects aren’t sets, they’re […]
Pingback by Concrete and Non-Concrete Categories (Informally) « Mathematics Prelims — February 24, 2009 @ 4:02 pm
Blog at WordPress.com. | 2020-09-28 01:09:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 29, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8025017380714417, "perplexity": 440.2975059875391}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401583556.73/warc/CC-MAIN-20200928010415-20200928040415-00142.warc.gz"} |
http://clay6.com/qa/2895/show-that-f-x-tan-sin-x-cos-x-is-an-increasing-function-in-bigg-0-large-fra | # Show that $f(x)=\tan^{-1}(\sin x+\cos x)$ is an increasing function in$\bigg(0,\Large \frac{1}{4}\normalsize \bigg).$
Toolbox:
• Let $f(x)$ be a function defined on $(a,b)$. If $f'(x) > 0$ for all $x \in (a,b)$ except for a finite number of points, where $f'(x)>0,$ then $f(x)$ is increasing on $(a,b)$
Step 1
$f(x)= \tan^{-1} ( \sin x+ \cos x)$
Differentiating w.r.t $x$ we get,
$f'(x)=\large\frac{1}{1+ ( \sin x+ \cos x)^2} \times ( \cos x- \sin x)$
$= \large\frac{\cos x- \sin x}{1+( \sin x+ \cos x)^2}= \large\frac{\cos x(1- \tan x)}{1+ ( \sin x+ \cos x)^2}$
Now let us consider the interval $0 < x < \large\frac{\pi}{4}$
$\Rightarrow \cos x > 0, \large\frac{1}{1+(\sin x+ \cos x)^2}\: and \: (1- \tan x) > 0$
$( \because \tan x < 1$ in the interval $0 < x < \large\frac{\pi}{4})$
$\Rightarrow \large\frac{\cos x(1-\tan x)}{1+ ( \sin x+ \cos x)^2} > 0$
$\Rightarrow f'(x) > 0$
Hence $f'(x)>0$ for all $x \in \bigg( 0, \large\frac{\pi}{4} \bigg)$
Hence $f(x)$ is increasing on $\bigg( 0, \large\frac{\pi}{4} \bigg)$
answered Aug 5, 2013 | 2017-09-22 06:21:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9357371926307678, "perplexity": 148.90008808947343}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688671.43/warc/CC-MAIN-20170922055805-20170922075805-00523.warc.gz"} |
https://www.geodms.nl/Convolution | # Convolution
## introduction
Convolution (see wikipedia) is used in the GeoDms to calculate a Neighbourhood Potential using an input grid with n*m elements and a kernel of k*j elements, see the description of the Potential Operator
The GeoDms utilizes the IPP 7.0 library convolution functions ippsConv_16s_Sfs, ippsConv_32f, ippsConv_64f in the OperPot.cpp code unit as default implementation for potential calculations. These functions perform an FFT on both their input arrays of size N, then multiply the spectra element-wize and then reverse-FFT the product to generate the requested result. The IPP 7.0 library also utilizes multiple cores when present and available, still available as potentialSlow for comparison. This results in a O(N*log(N)) operation, whereas the classical naive implementation with four nested loops requires O(n*m*k*j) operations.
To make this possible, the 2D $$n*m$$ grid and $$k*j$$ grid are translated to two uniform signals of $$N = (n+k-1) * (m+j-1)$$ elements each with appropriate zero-padding.
The resulting grid can sometimes contain small round-off errors resulting from different frequencies that have to cancel-out, especially in empty zero-valued regions sometimes very small values occur, sometimes even negative when all input is non-negative. In order to remove these undesired artifacts, a smoothing post-processing is performed by default that resets to zero all values that are nearer to zero than $$\sqrt{\sum\limits_i(v_i^2) \over 1000000000.0}$$. The potential_raw operations does not perform this post-processing.
## ToDo
Investigate FFTW as substitute for IPPS 7.0 | 2022-11-27 06:35:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46637973189353943, "perplexity": 3045.807863307215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710192.90/warc/CC-MAIN-20221127041342-20221127071342-00357.warc.gz"} |
https://nanonaren.com/2016/10/21/measurable-spaces-problem-41365/ | ## Measurable Spaces – Problem (41/365)
Let $\mathcal{D} = \{ D_1, D_2, \dots \}$ be a countable decomposition of $\mathcal{\Omega}$ and $\mathcal{A} = \sigma(\mathcal{D})$ be the $\sigma$-algebra generated by $\mathcal{D}$. Are there only countably many sets in $\mathcal{A}$?
The answer is no. We can show this by showing that the natural numbers is a strict subset of $\mathcal{A}$. Every natural number $n$ can be written as $\sum_{i=0}^\infty a_i 2^i$ where $a_i \in \{0,1\}$ and only a finite number of $a_i = 1$ (because if an infinite number of $a_i = 1$ the sum is $\infty$).
Note that since $\mathcal{D}$ is a decomposition we can write every set in $\mathcal{A}$ as a countable (because this is a $\sigma$-algebra) union of a subset of $\mathcal{D}$. This means we can encode every set in $\mathcal{A}$ as $\cup_{i=1}^\infty (A_i \cap D_i)$ where $A_i \in \{ \emptyset, \Omega \}$. First, since $\mathcal{D}$ is countable there is a bijection between the natural numbers and $\mathcal{D}$, however, $\mathcal{A}$ is not countable since we can have a countable number of $A_i = \Omega$.
This entry was posted in Uncategorized and tagged , . Bookmark the permalink. | 2021-04-20 07:06:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9663100242614746, "perplexity": 72.3694071799548}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039379601.74/warc/CC-MAIN-20210420060507-20210420090507-00592.warc.gz"} |
http://claesjohnson.blogspot.com/2011/05/why-measure-viscosity-and-temperature.html | onsdag 4 maj 2011
Why Measure Viscosity and Temperature?
To measure viscosity is possible for heavily viscous fluids, but difficult for slightly viscous fluids.
Here is a response to a question by Anders Nordenfelt about how to measure temperature:
To measure a coefficient of viscosity of slightly viscous fluid is difficult, or more precisely virtually impossible, since it is defined as shear stress per shear deformation (velocity), which in turbulent slightly viscous flow is severely dependent on the fluid flow and not only on the fluid itself.
It is thus necessary to make a distinction between different viscosity coefficients of vastly varying size from laminar viscosity to turbulent viscosity for different elementary flow patterns. To use the appropriate viscosity coefficient in a fluid simulation thus poses the requirement that the flow is known beforehand as well as its viscosity coefficients for all elementary flows involved, which is difficult to meet.
In the books Computational Turbulent Incompressible Flow and Computational Thermodynamics we show a way out of this dead end which starts with the following question:
• Why are viscosity coefficients required?
In the case of turbulent (incompressible) flow one answer is: To compute turbulent dissipation from turbulent shear force as viscosity coefficient times shear deformation (velocity).
In the books it is shown that that turbulent dissipation can be computed as a transfer from kinetic energy to internal energy, without making an explicit computation of turbulent dissipation through viscosity coefficients combined with shear deformation. The computation uses a certain form of numerical viscosity automatically introduced by residual stabilization and the only input is that the physical viscosity is small, whatever else it may be.
The net result is that it is possible to simulate slightly viscous flow without any precise input of viscosity coefficients, only that the viscosity is small.
Similarly, coefficients of heat capacity as a measure of heat energy per unit of temperature and mass, as well as temperature as heat energy per unit mass, may be difficult to define and measure, since the required precise definition of heat energy is difficult to give.
An alternative is to again view internal energy/heat energy as arising from transfer of energy from kinetic energy which makes it accessible indirectly thus avoiding the difficulty of computing internal energy through temperature and heat capacity coefficients. | 2019-07-18 21:23:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8842244744300842, "perplexity": 738.7563731395451}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195525829.33/warc/CC-MAIN-20190718211312-20190718233312-00442.warc.gz"} |
https://qa.engineer.kmitl.ac.th/ngttmi/eigenvalue-and-eigenvector-calculator-18ff3a | # eigenvalue and eigenvector calculator
We also have the following physical interpretation for +. Choose your matrix! λ is an eigenvalue (a scalar) of the Matrix [A] if there is a non-zero vector (v) such that the following relationship is satisfied: [A](v) = λ (v) Every vector (v) satisfying this equation is called an eigenvector of [A] belonging to the eigenvalue λ.. As an example, in the … An easy and fast tool to find the eigenvalues of a square matrix. They have many uses! The generalized eigenvalue problem is to determine the solution to the equation Av = λBv, where A and B are n-by-n matrices, v is a column vector of length n, and λ is a scalar. Eigen vector, Eigen value 3x3 Matrix Calculator. Eigenvector-Eigenvalue identity. The determinant of a triangular matrix is easy to find - it is simply the product of the diagonal elements. Here I show how to calculate the eigenvalues and eigenvectors for the right whale population example from class. The basic representation of the relationship between an eigenvector and its corresponding eigenvalue is given as Av = λv, where A is a matrix of m rows and m columns, λ is a scalar, and v is a vector of m columns. The eigenvalues are immediately found, and finding eigenvectors for these matrices then becomes much easier. To find eigenvectors, take $M$ a square matrix of size $n$ and $\lambda_i$ its eigenvalues. We will see how to find them (if they can be found) soon, but first let us see one in action: Select the size of the matrix and click on the Space Shuttle in order to fly to the solver! First eigenvalue: Second eigenvalue: Discover the beauty of matrices! Enter the regular matrix value in the eigenvalues and eigenvectors 3x3 calculator to find the eigenvalue and eigenvector value. $\begingroup$ Maybe it's just me, but the second equality in the last line seems "non-trivial" to me - specifically, it is implicit from the equality that matrix multiplication commutes with limits involving matrices. EigenCalc is a simple app that computes the eigenvalues and eigenvectors of a given matrix. These eigenvalues are often referred to as the 'eigenvalues of the equilibrium'. However, the additional requirement that all the entries in the eigenvector be non-negative implies (by the Perron–Frobenius theorem) that only the greatest eigenvalue results in the desired centrality measure. In linear algebra, the Eigenvector does not change its direction under the associated linear transformation. A singular matrix is a square matrix which does not have an inverse matrix. Now, we need to work one final eigenvalue/eigenvector problem. If A is an n×n Hermitian matrix with eigenvalues λ 1 (A),…,λ n (A) and i,j=1,…,n, then the j-th component v i,j of a unit eigenvector v i associated to the eigenvalue λ i (A) is related to the eigenvalues λ 1 (a j),…,λ n−1 (a j) of the minor a j … Also, we need to work one in which we get an eigenvalue of multiplicity greater than one that has more than one linearly independent eigenvector. In the second-to-last row of the output are the values det(A−λI). It is also known as characteristic vector. Eigenvalue Calculator. [V,D,W] = eig(A,B) also returns full matrix W whose columns are the corresponding left eigenvectors, so that W'*A = D*W'*B. 1. on your calculator press mode and then select 5:EQN 2. select 1,2,3 or 4 according to the degree of your equation. For something to be a true value, it must satisfy the equation. This online calculator computes the eigenvalues of a square matrix up to 4th degree by solving the characteristic equation. For Example, if x is a vector that is not zero, then it is an eigenvector of … Below each eigenvalue λ in the first row is a unit n × 1 eigenvector corresponding to λ. NOTE: The German word "eigen" roughly translates as "own" or "belonging to". Beware, however, that row-reducing to row-echelon form and obtaining a triangular matrix does not give you the eigenvalues, as row-reduction changes the eigenvalues of the … This matrix calculator computes determinant, inverses, rank, characteristic polynomial, eigenvalues and eigenvectors.It decomposes matrix using LU and Cholesky decomposition. Not sure about Eigen Vectors but I do know about eigen values. If v+ is the corresponding eigenvector and at least two consecutive fertility rates are positive, + is dominant and the population distribution will converge to an eigenvector of L, that is lim t!1D(t) exists and is a multiple of v+. If Ais an n nmatrix, a generalized eigenvector of A corresponding to the eigenvalue is a nonzero vector x satisfying (A I)p x = 0 for some positive integer p. Equivalently, it is a nonzero element of the nullspace of (A I)p. Example I Eigenvectors are generalized eigenvectors with p= 1. The determination of the eigenvalues and eigenvectors of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and … Eigenvalues and eigenvectors correspond to each other (are paired) for any particular matrix A. Input by the line: Eigenvalue, components of the correspondent Eigenvector, all separated with spaces. To this point we’ve only worked with $$2 \times 2$$ matrices and we should work at least one that isn’t $$2 \times 2$$. Calculate eigenvalues. Eigenvectors are the solution of the system $( M − \lambda I_n ) \vec{X} = \vec{0}$ with $I_n$ the identity matrix.. Non-square matrices cannot be analyzed utilizing the methods below. In this applet, users may - define the 2-by-2 matrix by entering the values of the elements, - drag the point V to view the vector v and the vector Av in the same diagram, - receive a notification when an eigenvalue that satisfies Av=kv is found. Eigenvalues consider being special set of scalars associated with a linear system of equations, that often also known as characteristic roots and characteristic value. For a square matrix A, an Eigenvector and Eigenvalue make this equation true:. λ is an eigenvalue (a scalar) of the Matrix [A] if there is a non-zero vector (v) such that the following relationship is satisfied: [A](v) = λ (v) Every vector (v) satisfying this equation is called an eigenvector of [A] belonging to the eigenvalue λ.. As an example, in the … Use / for fractions, input complex numbers like 1/2-3/7i. This implies that A−λI is singular and hence that det(A−λI) = 0. The calculator will perform symbolic calculations whenever it is possible. The values of λ that satisfy the equation are the generalized eigenvalues. The basic equation representation of the relationship between an eigenvalue and its eigenvector is given as Av = λv where A is a matrix of m rows and m columns, λ is a scalar, and v is a vector of m columns.In this relation, true values of v are the eigenvectors, and true values of λ are the eigenvalues. This definition of an eigenvalue, which does not directly involve the corresponding eigenvector, is the characteristic equation or … Works with matrix from 2X2 to 10X10. eigenvalue +. 06-1-580-5555 « A leggyorsabb zárnyitás megoldást választjukA leggyorsabb zárnyitás megoldást választjuk. Eigenvalue calculator. Stability of models with various variables Detection of stability in these types of models is not so simple as in one-variable models. For a square matrix A, an Eigenvector and Eigenvalue make this equation true:. How to use: Enter major network address and prefix, like 192. The Mathematics Of It. 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Scroll to Top | 2021-08-02 05:01:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.900473415851593, "perplexity": 750.7680983506082}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154304.34/warc/CC-MAIN-20210802043814-20210802073814-00399.warc.gz"} |
https://gamedev.stackexchange.com/questions/86509/how-can-i-change-the-appearance-of-the-mouse-cursor-in-libgdx | # How can I change the appearance of the mouse cursor in libGDX?
How can I change the mouse a cursor to a picture using libGDX?
### v1.7.0+
Pixmap pm = new Pixmap(Gdx.files.internal("cursorImage.png"));
Gdx.graphics.setCursor(Gdx.graphics.newCursor(pm, 0, 0));
pm.dispose();
### Before v1.7.0
Pixmap pm = new Pixmap(Gdx.files.internal("cursorImage.png"));
Gdx.input.setCursorImage(pm, 0, 0);
pm.dispose();
The hotspot parameters represent the "tip" of the cursor. For example, the operating system cursor has the hotspot at the top-left corner, but a crosshair cursor might have the hotspot at its center.
• Thank you! Well but I have a problem the method Gdx.input.setCursorImage(image, xPos, y Pos); give this error The method setCursorImage(Pixmap, int, int) is undefined for the type Input – user3334375 Oct 28 '14 at 10:37
• Well the function certainly exists, but it was added a year ago this month, so make sure you're using the latest version of libgdx. If you are and you're still getting that error, then I don't think I can help. – Icy Defiance Oct 28 '14 at 17:57
• Gdx.graphics.setCursor(Gdx.graphics.newCursor(pm,0,0,)); – Jonathan Camarena Jan 11 '16 at 22:07
• Is it worth keeping the pixmap in case I change often ? – Winter Jan 4 '17 at 18:50 | 2021-07-27 08:07:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1818675547838211, "perplexity": 2300.7677014542314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153223.30/warc/CC-MAIN-20210727072531-20210727102531-00550.warc.gz"} |
https://msp.org/gt/2022/26-1/gt-v26-n1-p09-p.pdf | #### Volume 26, issue 1 (2022)
Recent Issues
The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Chromatic splitting for the $K(2)$–local sphere at $p=2$
### Agnès Beaudry, Paul G Goerss and Hans-Werner Henn
Geometry & Topology 26 (2022) 377–476
DOI: 10.2140/gt.2022.26.377
##### Abstract
We calculate the homotopy type of ${L}_{1}{L}_{K\left(2\right)}{S}^{0}$ and ${L}_{K\left(1\right)}{L}_{K\left(2\right)}{S}^{0}$ at the prime 2, where ${L}_{K\left(n\right)}$ is localization with respect to Morava $K$–theory and ${L}_{1}$ localization with respect to $2$–local $K$–theory. In ${L}_{1}{L}_{K\left(2\right)}{S}^{0}$ we find all the summands predicted by the Chromatic Splitting Conjecture, but we find some extra summands as well. An essential ingredient in our approach is the analysis of the continuous group cohomology ${H}^{\ast }\left({\mathbb{𝔾}}_{2},{E}_{0}\right)$, where ${\mathbb{𝔾}}_{2}$ is the Morava stabilizer group and ${E}_{0}=\mathbb{𝕎}\left[\left[{u}_{1}\right]\right]$ is the ring of functions on the height $2$ Lubin–Tate space. We show that the inclusion of the constants $\mathbb{𝕎}\to {E}_{0}$ induces an isomorphism on group cohomology, a radical simplification.
However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/gt
We have not been able to recognize your IP address 18.232.59.38 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.
or by using our contact form.
##### Keywords
chromatic splitting conjecture, chromatic homotopy theory, Morava K–theory localization of the sphere
##### Mathematical Subject Classification
Primary: 55P42, 55P60, 55Q51 | 2022-06-25 19:45:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3273709714412689, "perplexity": 1643.829519205754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103036099.6/warc/CC-MAIN-20220625190306-20220625220306-00144.warc.gz"} |
https://www.idsemergencymanagement.com/2020/12/06/how-do-you-prove-that-a-cauchy-sequence-is-convergent/ | How do you prove that a Cauchy sequence is convergent?
Dec 6, 2020
How do you prove that a Cauchy sequence is convergent?
The proof is essentially the same as the corresponding result for convergent sequences. Any convergent sequence is a Cauchy sequence. If (an)→ α then given ε > 0 choose N so that if n > N we have |an- α| < ε. Then if m, n > N we have |am- an| = |(am- α) – (am- α)| ≤ |am- α| + |am- α| < 2ε.
Is Cauchy the same as convergent?
Informally speaking, a Cauchy sequence is a sequence where the terms of the sequence are getting closer and closer to each other. Definition. A sequence (xn)n∈N with xn∈X for all n∈N is convergent if and only if there exists a point x∈X such that for every ε>0 there exists N∈N such that d(xn,x)<ε.
What is the difference between a Cauchy sequence and a convergent sequence?
A Cauchy sequence is a sequence where the terms of the sequence get arbitrarily close to each other after a while. A convergent sequence is a sequence where the terms get arbitrarily close to a specific point. A Cauchy sequence {xn}n satisfies: ∀ε>0,∃N>0,n,m>N⇒|xn−xm|<ε.
How do I identify a Cauchy sequence?
A Cauchy sequence is a sequence whose terms become very close to each other as the sequence progresses. Formally, the sequence { a n } n = 0 ∞ \{a_n\}_{n=0}^{\infty} {an}n=0∞ is a Cauchy sequence if, for every ϵ>0, there is an N > 0 N>0 N>0 such that. n,m>N\implies |a_n-a_m|<\epsilon. n,m>N⟹∣an−am∣<ϵ.
Why every Cauchy sequence is convergent?
Every Cauchy sequence of real numbers is bounded, hence by Bolzano–Weierstrass has a convergent subsequence, hence is itself convergent. This proof of the completeness of the real numbers implicitly makes use of the least upper bound axiom.
Is every Cauchy sequence is a convergent sequence?
Theorem. Every real Cauchy sequence is convergent. Theorem. Every complex Cauchy sequence is convergent.
Is the limit of a convergent sequence unique?
Hence for all convergent sequences the limit is unique.
Is every convergent sequence a Cauchy sequence?
Every convergent sequence {xn} given in a metric space is a Cauchy sequence. If is a compact metric space and if {xn} is a Cauchy sequence in then {xn} converges to some point in .
Can a convergent sequence have more than one limit?
Hence our assumption must be false, that is, there does not exist a se- quence with more than one limit. Hence for all convergent sequences the limit is unique. Notation Suppose {an}n∈N is convergent.
Can a sequence converge to two different limits?
No . In Metric Space a sequence can converge at most one limit . But ,there are some topological space where one sequence can converge two or more than two limits . |a(n) – l’| < ε/2 for n >/= N’ .
How to prove that x n is a Cauchy sequence?
Definition 2. ( x n) is a Cauchy sequence iff, for every ε ∈ R with ε > 0 , there is an N ∈ N such that, for every m, n ∈ N with m, n > N , we have | x m − x n | < ε. Theorem. If ( x n) is convergent, then it is a Cauchy sequence. Hence all convergent sequences are Cauchy.
Is the theorem that all convergent sequences are Cauchy correct?
Theorem. If ( x n) is convergent, then it is a Cauchy sequence. Hence all convergent sequences are Cauchy. Is this proof correct?
Which is the best definition of a convergent series?
For other uses, see Convergence (disambiguation). In mathematics, a series is the sum of the terms of an infinite sequence of numbers. Given an infinite sequence the n th partial sum Sn is the sum of the first n terms of the sequence. That is, A series is convergent if the sequence of its partial sums tends to a limit;
When is a sequence in your said to be convergent?
A sequence (xn) in R is convergent if some x ∈ R exists such that for every ε > 0 some n0 ∈ N can be found such that |x − xn| < ε for each n ≥ n0. If that is the case then it can be shown that this x is unique and the sequence is said to converge to x. | 2022-07-01 01:45:44 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9799309372901917, "perplexity": 330.6876762189916}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103917192.48/warc/CC-MAIN-20220701004112-20220701034112-00710.warc.gz"} |
https://tex.stackexchange.com/questions/521362/commas-in-cases-typographic-standards | # Commas in \cases - typographic standards?
I'm wondering what are the typographic standards for the placement of commas/dots in the following (and similar) case:\
The first option looks nicer, the second seems to be more logically consistent.
• In the TeXbook Knuth uses something like $$d=\begin{cases} (l+b)^2+p^2,&\text{if 0\le p<10000};\\ (l+b)^2-p^2,&\text{if -10000<p<0};\\ (l+b)^2,&\text{if p\le-10000}.\end{cases}$$. See also tex.stackexchange.com/q/499/35864 – moewe Dec 21 '19 at 20:31
• You may also be interested in what the AMS style guide has to say on the issue (ams.org/arc/styleguide/AMSstyleguide.pdf, §13.11) – moewe Dec 21 '19 at 20:36
• I don't find the second option logically consistent, besides being typographically abominable. – egreg Dec 21 '19 at 21:15
• My goto rule for this is to use the same punctuation that you'd use if this wasn't in display mode, aka the first one. – daleif Dec 21 '19 at 21:22 | 2021-03-09 07:44:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.6230907440185547, "perplexity": 1439.324629832283}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178389472.95/warc/CC-MAIN-20210309061538-20210309091538-00576.warc.gz"} |
https://www.askiitians.com/forums/Magnetism/a-bar-magnet-of-length-3cm-has-points-a-and-b-alon_154908.htm | ×
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a bar magnet of length 3cm has points A and B along its axis at distances of 24cm and 48cm on the opposite sides. how to calculate the ratio of magnetic field at these points ?
4 years ago
Anu
11 Points
B is inversely proportional to one upon (distance)3 this you see in on axial and normal bisector (magnetic field due to bar magnet)Now, Ba/Bb=(48/24)3 =8/1 answer
3 years ago
ankit singh
596 Points
Length of magnet = 3 cmDistance between point a and center of magnet= 24 cmDistance between point b and center of magnet= 48 cmThe magnetic field isB=\dfrac{\mu_{0}\times 2m}{4\pi\times d^3}B\propto\dfrac{1}{d^3}The magnetic field is inversely proportional to the cube of the distance.We need to calculate the ratio of magnetic fields at these pointsUsing formula of magnetic field\dfrac{B_{a}}{B_{b}}=\dfrac{d_{b}^3}{d_{a}^2}\dfrac{B_{a}}{B_{b}}=\dfrac{48^3}{24^3}\dfrac{B_{a}}{B_{b}}=\dfrac{8}{1}
4 months ago
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### Course Features
• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
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• Previous Year Exam Questions | 2020-11-29 23:07:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5981626510620117, "perplexity": 12285.18506634213}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141203418.47/warc/CC-MAIN-20201129214615-20201130004615-00525.warc.gz"} |
https://indico.hiskp.uni-bonn.de/event/40/contributions/620/ | # The 39th International Symposium on Lattice Field Theory (Lattice 2022)
Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone
## Nonperturbative matching of Hamiltonian and Lagrangian Simulations
Aug 9, 2022, 7:00 PM
1h
Poster Presentation Theoretical Developments and Applications beyond Particle Physics
### Speaker
Christiane Groß (Helmholtz-Institut für Strahlen- und Kernphysik)
### Description
When comparing the Lagrangian and Hamiltonian formulations of lattice gauge theories, a matching procedure is required to match the parameters and observables between these two formulations. For this, we take the continuum limit in time direction on the Lagrangian side, while keeping the spatial lattice spacing fixed. We study several observables for this nonperturbative matching and compare different ways to take the temporal continuum limit. We apply our approach to the pure U(1) lattice gauge theory in 2+1 dimensions.
### Primary author
Christiane Groß (Helmholtz-Institut für Strahlen- und Kernphysik)
### Co-authors
Angus Kan (University of Waterloo) Carsten Urbach (Helmholtz-Institut für Strahlen- und Kernphysik) Karl Jansen (DESY) Lena Funcke (MIT) Simone Romiti (uni-bonn) Stefan Kühn | 2022-12-06 04:54:54 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8797105550765991, "perplexity": 7374.612580720966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00332.warc.gz"} |
https://brilliant.org/problems/simple-but-tricky-geometry/ | # Need no geometric property
Geometry Level 4
Let $$I,H,O$$ be the incenter, centroid, and circumcenter of the nonisosceles triangle $$ABC$$.
If $$AI \parallel HO$$, find $$\angle BAC$$ in degrees.
×
Problem Loading...
Note Loading...
Set Loading... | 2017-12-14 13:11:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6821348071098328, "perplexity": 11431.97570103094}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948544124.40/warc/CC-MAIN-20171214124830-20171214144830-00788.warc.gz"} |
https://www.christopherlovell.co.uk/blog/2016/04/26/jeans-mass.html | The early universe was a pretty uninteresting place, an expanse of neutral hydrogen with a few marginally heavier elements scattered around. It wasn’t until overdense regions of gas started to collapse and condense that stars and galaxies formed. But this collapse only occurs under the right conditions; the gravitational collapse must first overcome the internal pressure of the cloud of gas. There is therefore a balancing act between internal pressure and gravitational contraction.
When the cloud is stable it is in what’s known as hydrostatic equilbrium, which for a spherical cloud is given by
Here, $r$ is the radius, $M(r)$ is the mass enclosed at radius $r$, $p$ is the pressure, $\rho(r)$ is the density at $r$, and $G$ is the gravitational constant. The pressure is temperature dependent, so, for a given temperature, if the mass exceeds a threshold value the cloud will collapse.
This mass is known as the Jean’s Mass, after the British physicist Sir James Jeans who first derived it. There are two ways of deriving it, one from energy considerations using the virial mass, and another by looking at the sound crossing speed and gravitational free fall time. We’ll look at both, and see that dimensionally they both give the same result, give or take a small constant.
In a future post we’ll look at the conditions in the early universe, and scaling with the expansion factor, to find the approximate sizes of the first collapsed objects that led to the first stars and galaxies.
## Ratio of Timescales
In this derivation, we imagine a spherical gas cloud that has just started to collapse gravitationally. The characteristic time over which this collapse would take is known as the free fall time. Once the collapse starts, pressure is exerted on the cloud, which sends out sound waves through the cloud. These take time to travel through the cloud and back to re-establish pressure balance This is known as the sound crossing time.
If the sound crossing time is shorter than the free fall time then the cloud will remain in equilibirum; the pressure will counteract the gravitational collapse. If the free fall time is shorter than the sound crossing time then the gravitational collapse continues unabated, and the cloud collapses.
The free fall time can be derived by looking at a particle on the edge of the cloud (at radius $R$). It feels an acceleration from the rest of the cloud $g = -\frac{GM}{R^{2}}$, where $M$ is the total mass of the cloud (equal to the volume of the cloud at the start of collapse times the average density, $M = \frac{4\pi }{3}R_{0}^{3} \rho_{0}$); this makes use of the divergence theorem from electrostatics, whereby the point mass only feels the gravitational force from the mass interior to its radius
Using Newton’s second law we can write the equation of motion of the cloud,
Can rewrite the left hand side with the chain rule
Can now integrate this differential equation
When $R = R_{0}$, i.e. when the particle is at it’s start position, we assume it is at rest, $v = 0$. Substituting, we can find $C$,
The total collapse time can be found by intergating over the whole radius
The integral is a bit tricky, it ends up giving you $\frac{\pi R_{0}^{2}}{2}$, so we have
This is our timescale for gravitational collapse. To find the sound crossing time we first need to know the sound speed in the medium, which, for an ideal gas, is given by
where $k_{B}$ is the Boltzmann constant, $\gamma$ is the adiabatic index, $T$ is the temperature of the gas, and $m$ is the particle mass.
The sound crossing time is then given by
For collapse to occur, $t_{s} > t_{c}$. At the turnover point, they are equal, so $t_{s}/t_{c} = 1$. The radius at this turnover point is the Jean’s Length, $R_{J}$.
The Jean’s Mass is just the volume of the sphere with radius the Jean’s legnth times the average density
## Virial Theorem
We can derive this result using the Virial Theorem, which states that the total kinetic energy in a system is equal to half the potential energy,
The gravitational potential energy of a cloud of point masses is given by
And the total kinetic energy of the particles is
where $m$ is the average particle mass, and $N$ is the total number of particles, $N = M/m$.
For collapse to occur, the gravitational potential energy must be greater than the thermal kinetic energy of the cloud. So, substituting in to the Virial Theorem, the inequality becomes
The Jean’s Mass / Length is at the boundary of this inequality. First we’ll find the Jean’s Length by substituting for $M$, assuming a constant density cloud,
Substitute for the sound speed, $c_{s}$, we found in the previous derivation,
Note that the constant in the front of this equation is slightly different than that derived above using the timescale method.
For the Jean’s Mass, substitute for $R$ with the same constant density assumption, | 2019-02-18 23:35:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8015404343605042, "perplexity": 310.0214821203432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00001.warc.gz"} |
https://stacks.math.columbia.edu/tag/0BZ1 | ## 22.34 Composition of derived tensor products
We encourage the reader to skip this section.
Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. Let $N$ be a differential graded $(A, B)$-bimodule. Let $N'$ be a differential graded $(B, C)$-module. We denote $N_ B$ the bimodule $N$ viewed as a differential graded $B$-module (forgetting about the $A$-structure). There is a canonical map
22.34.0.1
$$\label{dga-equation-plain-versus-derived} N_ B \otimes _ B^\mathbf {L} N' \longrightarrow (N \otimes _ B N')_ C$$
in $D(C, \text{d})$. Here $(N \otimes _ B N')_ C$ denotes the $(A, C)$-bimodule $N \otimes _ B N'$ viewed as a differential graded $C$-module. Namely, this map comes from the fact that the derived tensor product always maps to the plain tensor product (as it is a left derived functor).
Lemma 22.34.1. Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. Let $N$ be a differential graded $(A, B)$-bimodule. Let $N'$ be a differential graded $(B, C)$-module. Assume (22.34.0.1) is an isomorphism. Then the composition
$\xymatrix{ D(A, \text{d}) \ar[rr]^{- \otimes _ A^\mathbf {L} N} & & D(B, \text{d}) \ar[rr]^{- \otimes _ B^\mathbf {L} N'} & & D(C, \text{d}) }$
is isomorphic to $- \otimes _ A^\mathbf {L} N''$ with $N'' = N \otimes _ B N'$ viewed as $(A, C)$-bimodule.
Proof. Let us define a transformation of functors
$(- \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N' \longrightarrow - \otimes _ A^\mathbf {L} N''$
To do this, let $M$ be a differential graded $A$-module with property (P). According to the construction of the functor $- \otimes _ A^\mathbf {L} N''$ of the proof of Lemma 22.33.2 the plain tensor product $M \otimes _ A N''$ represents $M \otimes _ A^\mathbf {L} N''$ in $D(C, \text{d})$. Then we write
$M \otimes _ A N'' = M \otimes _ A (N \otimes _ B N') = (M \otimes _ A N) \otimes _ B N'$
The module $M \otimes _ A N$ represents $M \otimes _ A^\mathbf {L} N$ in $D(B, \text{d})$. Choose a quasi-isomorphism $Q \to M \otimes _ A N$ where $Q$ is a differential graded $B$-module with property (P). Then $Q \otimes _ B N'$ represents $(M \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N'$ in $D(C, \text{d})$. Thus we can define our map via
$(M \otimes _ A^\mathbf {L} N) \otimes _ B^\mathbf {L} N' = Q \otimes _ B N' \to M \otimes _ A N \otimes _ B N' = M \otimes _ A^\mathbf {L} N''$
The construction of this map is functorial in $M$ and compatible with distinguished triangles and direct sums; we omit the details. Consider the property $T$ of objects $M$ of $D(A, \text{d})$ expressing that this map is an isomorphism. Then
1. if $T$ holds for $M_ i$ then $T$ holds for $\bigoplus M_ i$,
2. if $T$ holds for $2$-out-of-$3$ in a distinguished triangle, then it holds for the third, and
3. $T$ holds for $A[k]$ because here we obtain a shift of the map (22.34.0.1) which we have assumed is an isomorphism.
Thus by Remark 22.22.5 property $T$ always holds and the proof is complete. $\square$
Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. We temporarily denote $(A \otimes _ R B)_ B$ the differential graded algebra $A \otimes _ R B$ viewed as a (right) differential graded $B$-module, and ${}_ B(B \otimes _ R C)_ C$ the differential graded algebra $B \otimes _ R C$ viewed as a differential graded $(B, C)$-bimodule. Then there is a canonical map
22.34.1.1
$$\label{dga-equation-plain-versus-derived-algebras} (A \otimes _ R B)_ B \otimes _ B^\mathbf {L} {}_ B(B \otimes _ R C)_ C \longrightarrow (A \otimes _ R B \otimes _ R C)_ C$$
in $D(C, \text{d})$ where $(A \otimes _ R B \otimes _ R C)_ C$ denotes the differential graded $R$-algebra $A \otimes _ R B \otimes _ R C$ viewed as a (right) differential graded $C$-module. Namely, this map comes from the identification
$(A \otimes _ R B)_ B \otimes _ B {}_ B(B \otimes _ R C)_ C = (A \otimes _ R B \otimes _ R C)_ C$
and the fact that the derived tensor product always maps to the plain tensor product (as it is a left derived functor).
Lemma 22.34.2. Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. Assume that (22.34.1.1) is an isomorphism. Let $N$ be a differential graded $(A, B)$-bimodule. Let $N'$ be a differential graded $(B, C)$-bimodule. Then the composition
$\xymatrix{ D(A, \text{d}) \ar[rr]^{- \otimes _ A^\mathbf {L} N} & & D(B, \text{d}) \ar[rr]^{- \otimes _ B^\mathbf {L} N'} & & D(C, \text{d}) }$
is isomorphic to $- \otimes _ A^\mathbf {L} N''$ for a differential graded $(A, C)$-bimodule $N''$ described in the proof.
Proof. By Lemma 22.33.3 we may replace $N$ and $N'$ by quasi-isomorphic bimodules. Thus we may assume $N$, resp. $N'$ has property (P) as differential graded $(A, B)$-bimodule, resp. $(B, C)$-bimodule, see Lemma 22.28.4. We claim the lemma holds with the $(A, C)$-bimodule $N'' = N \otimes _ B N'$. To prove this, it suffices to show that
$N_ B \otimes _ B^\mathbf {L} N' \longrightarrow (N \otimes _ B N')_ C$
is an isomorphism in $D(C, \text{d})$, see Lemma 22.34.1.
Let $F_\bullet$ be the filtration on $N$ as in property (P) for bimodules. By Lemma 22.28.5 there is a short exact sequence
$0 \to \bigoplus \nolimits F_ iN \to \bigoplus \nolimits F_ iN \to N \to 0$
of differential graded $(A, B)$-bimodules which is split as a sequence of graded $(A, B)$-bimodules. A fortiori this is an admissible short exact sequence of differential graded $B$-modules and this produces a distinguished triangle
$\bigoplus \nolimits F_ iN_ B \to \bigoplus \nolimits F_ iN_ B \to N_ B \to \bigoplus \nolimits F_ iN_ B[1]$
in $D(B, \text{d})$. Using that $- \otimes _ B^\mathbf {L} N'$ is an exact functor of triangulated categories and commutes with direct sums and using that $- \otimes _ B N'$ transforms admissible exact sequences into admissible exact sequences and commutes with direct sums we reduce to proving that
$(F_ pN)_ B \otimes _ B^\mathbf {L} N' \longrightarrow (F_ pN)_ B \otimes _ B N'$
is a quasi-isomorphism for all $p$. Repeating the argument with the short exact sequences of $(A, B)$-bimodules
$0 \to F_ pN \to F_{p + 1}N \to F_{p + 1}N/F_ pN \to 0$
which are split as graded $(A, B)$-bimodules we reduce to showing the same statement for $F_{p + 1}N/F_ pN$. Since these modules are direct sums of shifts of $(A \otimes _ R B)_ B$ we reduce to showing that
$(A \otimes _ R B)_ B \otimes _ B^\mathbf {L} N' \longrightarrow (A \otimes _ R B)_ B \otimes _ B N'$
is a quasi-isomorphism.
Choose a filtration $F_\bullet$ on $N'$ as in property (P) for bimodules. Choose a quasi-isomorphism $P \to (A \otimes _ R B)_ B$ of differential graded $B$-modules where $P$ has property (P). We have to show that $P \otimes _ B N' \to (A \otimes _ R B)_ B \otimes _ B N'$ is a quasi-isomorphism because $P \otimes _ B N'$ represents $(A \otimes _ R B)_ B \otimes _ B^\mathbf {L} N'$ in $D(C, \text{d})$ by the construction in Lemma 22.33.2. As $N' = \mathop{\mathrm{colim}}\nolimits F_ pN'$ we find that it suffices to show that $P \otimes _ B F_ pN' \to (A \otimes _ R B)_ B \otimes _ B F_ pN'$ is a quasi-isomorphism. Using the short exact sequences $0 \to F_ pN' \to F_{p + 1}N' \to F_{p + 1}N'/F_ pN' \to 0$ which are split as graded $(B, C)$-bimodules we reduce to showing $P \otimes _ B F_{p + 1}N'/F_ pN' \to (A \otimes _ R B)_ B \otimes _ B F_{p + 1}N'/F_ pN'$ is a quasi-isomorphism for all $p$. Then finally using that $F_{p + 1}N'/F_ pN'$ is a direct sum of shifts of ${}_ B(B \otimes _ R C)_ C$ we conclude that it suffices to show that
$P \otimes _ B {}_ B(B \otimes _ R C)_ C \to (A \otimes _ R B)_ B \otimes _ B {}_ B(B \otimes _ R C)_ C$
is a quasi-isomorphism. Since $P \to (A \otimes _ R B)_ B$ is a resolution by a module satisfying property (P) this map of differential graded $C$-modules represents the morphism (22.34.1.1) in $D(C, \text{d})$ and the proof is complete. $\square$
Lemma 22.34.3. Let $R$ be a ring. Let $(A, \text{d})$, $(B, \text{d})$, and $(C, \text{d})$ be differential graded $R$-algebras. If $C$ is K-flat as a complex of $R$-modules, then (22.34.1.1) is an isomorphism and the conclusion of Lemma 22.34.2 is valid.
Proof. Choose a quasi-isomorphism $P \to (A \otimes _ R B)_ B$ of differential graded $B$-modules, where $P$ has property (P). Then we have to show that
$P \otimes _ B (B \otimes _ R C) \longrightarrow (A \otimes _ R B) \otimes _ B (B \otimes _ R C)$
is a quasi-isomorphism. Equivalently we are looking at
$P \otimes _ R C \longrightarrow A \otimes _ R B \otimes _ R C$
This is a quasi-isomorphism if $C$ is K-flat as a complex of $R$-modules by More on Algebra, Lemma 15.59.2. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2023-02-02 09:08:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 4, "x-ck12": 0, "texerror": 0, "math_score": 0.9861699938774109, "perplexity": 156.05552936503491}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499967.46/warc/CC-MAIN-20230202070522-20230202100522-00288.warc.gz"} |
https://math.stackexchange.com/questions/326334/a-question-about-the-arctangent-addition-formula | In the arctangent formula, we have that:
$$\arctan{u}+\arctan{v}=\arctan\left(\frac{u+v}{1-uv}\right)$$
however, only for $uv<1$. My question is: where does this condition come from? The situation is obvious for $uv=1$, but why the inequality?
One of the possibilities I considered was as following: the arctangent addition formula is derived from the formula:
$$\tan\left(\alpha+\beta\right)=\frac{\tan{\alpha}+\tan{\beta}}{1-\tan{\alpha}\tan{\beta}}.$$
Hence, if we put $u=\tan{\alpha}$ and $v=\tan{\beta}$ (which we do in order to obtain the arctangent addition formula from the one above), the condition that $uv<1$ would mean $\tan\alpha\tan\beta<1$, which, in turn, would imply (thought I am NOT sure about this), that $-\pi/2<\alpha+\beta<\pi/2$, i.e. that we have to stay in the same period of tangent.
However, even if the above were true, I still do not see why we have to stay in the same period of tangent for the formula for $\tan(\alpha+\beta)$ to hold. I would be thankful for a thorough explanation.
You are correct in that it is related to the period. Note however, that while the period is unimportant for the tan addition formula to hold, the arc tan functions are defined by restricting the range to$(\dfrac{-\pi}{2},\dfrac{\pi}{2})$ If $uv>1$, $\arctan u +\arctan v$ is not in the range of the arctan function(principal branch). In that case $\arctan \dfrac{u+v}{1-uv}$ is not the sum of the arctan's, it is shifted by $\pi$, up or down. Note that $\tan(\arctan u +\arctan v)=\tan(\arctan \dfrac{u+v}{1-uv})$ regardless of $uv<1$.
If $\arctan x=A,\arctan y=B;$ $\tan A=x,\tan B=y$
We know, $$\tan(A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$$
So, $$\tan(A+B)=\frac{x+y}{1-xy}$$ $$\implies\arctan\left(\frac{x+y}{1-xy}\right)=n\pi+A+B=n\pi+\arctan x+\arctan y$$ where $n$ is any integer
As the principal value of $\arctan z$ lies $\in[-\frac\pi2,\frac\pi2], -\pi\le\arctan x+\arctan y\le\pi$
$(1)$ If $\frac\pi2<\arctan x+\arctan y\le\pi, \arctan\left(\frac{x+y}{1-xy}\right)=\arctan x+\arctan y-\pi$ to keep $\arctan\left(\frac{x+y}{1-xy}\right)\in[-\frac\pi2,\frac\pi2]$
Observe that $\arctan x+\arctan y>\frac\pi2\implies \arctan x,\arctan y>0\implies x,y>0$
$\implies\arctan x>\frac\pi2-\arctan y$ $\implies x>\tan\left(\frac\pi2-\arctan y\right)=\cot \arctan y=\cot\left(\text{arccot}\frac1y\right)\implies x>\frac1y\implies xy>1$
$(2)$ If $-\pi\le\arctan x+\arctan y<-\frac\pi2, \arctan\left(\frac{x+y}{1-xy}\right)=\arctan x+\arctan y+\pi$
Observe that $\arctan x+\arctan y<-\frac\pi2\implies \arctan x,\arctan y<0\implies x,y<0$
Let $x=-X^2,y=-Y^2$
$\implies \arctan(-X^2)+\arctan(-Y^2)<-\frac\pi2$ $\implies \arctan(-X^2)<-\frac\pi2-\arctan(-Y^2)$ $\implies -X^2<\tan\left(-\frac\pi2-\arctan(-Y^2)\right)=\cot\arctan(-Y^2)=\cot\left(\text{arccot}\frac{-1}{Y^2}\right)$
$\implies -X^2<\frac1{-Y^2}\implies X^2>\frac1{Y^2}\implies X^2Y^2>1\implies xy>1$
$(3)$ If $-\frac\pi2\le \arctan x+\arctan y\le \frac\pi2, \arctan x+\arctan y=\arctan\left(\frac{x+y}{1-xy}\right)$
• The last answer, at point (3), does not explain clearly why $$\arctan x + \arctan y \in [-\frac{\pi}{2},\frac{\pi}{2}]$$ implies $xy \leqslant 1$. <br /><br /> I've published a rigorous proof of the sum of arctangents on this page. – user104981 Nov 2 '13 at 23:28
• @MicheleDeStefano, The sole target of the answer is to find the value of $n$ for the different ranges of values of $\arctan x,\arctan y$. For $(3),$ the sum is already within the required range so $n=0$ – lab bhattacharjee Nov 5 '13 at 15:51
• @lab bhattacharjee, Ok. I agree. But (3) does not answer the original question at the beginning of the thread. The demonstration I've posted does. – user106080 Nov 7 '13 at 7:15
• @Abcd, As $\arctan x<\dfrac\pi2,\arctan x+\arctan y$ can be $>\dfrac\pi2$ only if $\arctan y>0$ – lab bhattacharjee Feb 8 '18 at 13:07
What is $$\arctan{s}+\arctan{t}$$? It is the addition of two angles: $$\alpha+\beta$$
Starting from the image we first calculate $$h$$:
$$\frac{h}{s\times t}=s+t+h$$
Therefore:
$$h=s\times t\frac{s+t}{1-s\times t}$$
And:
$$\tan{(\alpha+\beta)}=\frac{h}{s\times t}$$
$$\alpha+\beta=\arctan{s}+\arctan{t}=\arctan{\frac{s+t}{1-s\times t}}$$
To explain why $\arctan(u) + \arctan(v) = \arctan(\frac{u+v}{1-uv})$ only if $uv < 1$, we need to recognise the obvious restriction of $$-\frac{\pi}{2} < \arctan(u) + \arctan(v) < \frac{\pi}{2}.$$
We'll consider three cases: $uv = 1$, $uv > 1$ and finally $uv < 1$.
If $uv = 1$ (the trivial case), $u$ and $v$ must have the same sign and $v = \frac{1}{u}$. From the identity $\arctan(u) + \arctan(\frac{1}{u}) = \pm\frac{\pi}{2}$:
$$\arctan(u) + \arctan(v) = \begin{cases} \frac{\pi}{2}, & \text{if u, v > 0}, \\[2ex] -\frac{\pi}{2}, & \text{if u, v < 0}. \\[2ex] \end{cases}$$
However, $\arctan(\frac{u+v}{1-uv})$ is obviously undefined when $uv=1$.
If $uv > 1$, both $u$ and $v$ must have the same sign again. Because of the behaviour of the inequality when dividing by a negative number, first consider the situation if $u, v > 0$: $$uv > 1 \implies v > \frac{1}{u},$$ $$\arctan(u) + \arctan(\frac{1}{u}) = \frac{\pi}{2},$$ $$\therefore \arctan(u) + \arctan(v) > \frac{\pi}{2}.$$
Similarly, if $u, v < 0$, $$uv > 1 \implies v < \frac{1}{u},$$ $$\arctan(u) + \arctan(\frac{1}{u}) = -\frac{\pi}{2},$$ $$\therefore \arctan(u) + \arctan(v) < -\frac{\pi}{2}.$$
Hence, we can see that whenever $uv > 1$, $\arctan(u) + \arctan(v) \notin (-\frac{\pi}{2}, \frac{\pi}{2})$.
If $uv < 1$, $u$ and $v$ may have different signs, but we can just consider $u > 0$, $u < 0$ and $u = 0$. If $u > 0$:
$$uv < 1 \implies v < \frac{1}{u},$$ $$\arctan(u) + \arctan(\frac{1}{u}) = \frac{\pi}{2},$$ $$\therefore \arctan(u) + \arctan(v) < \frac{\pi}{2}.$$
Similarly, if $u < 0$, $$uv < 1 \implies v > \frac{1}{u},$$ $$\arctan(u) + \arctan(\frac{1}{u}) = -\frac{\pi}{2},$$ $$\therefore \arctan(u) + \arctan(v) > -\frac{\pi}{2}.$$
If $u = 0$, consider the original equation $\arctan(u) + \arctan(v) = \arctan(\frac{u+v}{1-uv})$:
\begin{align} LHS &= \arctan(0) + \arctan(v) \\ &= \arctan(v) \\ RHS &= \arctan(\frac{0+v}{1-0}) \\ &= \arctan(v) \\ &= LHS \end{align}
To summarise, we have shown that $$-\frac{\pi}{2} < \arctan(u) + \arctan(v) < \frac{\pi}{2}$$ is only true if $uv < 1$.
Bonus: To extend this to the arctangent subtraction formula, $$\arctan(u) - \arctan(v) = \arctan(u) + \arctan(-v)$$ $$\therefore u(-v) < 1 \implies uv > -1.$$ | 2020-05-28 13:38:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9991880059242249, "perplexity": 225.90308343246457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347396089.30/warc/CC-MAIN-20200528104652-20200528134652-00297.warc.gz"} |
https://conjugateprior.github.io/qss.student/articles/introduction.html | ## Problem sets
The qss.student package contains the questions and data sets from the problem sets in
K. Imai (2017) ‘Quantitative Social Science: An Introduction’, Princeton University Press
plus a few extra problem sets not in the book.
## Unpacking a problem set
Imagine you are assigned a problem set from the book called bias-in-turnout. To complete the problem set make sure you have the package loaded
library(qss.student)
and unpack the problem set into your current working directory
get_pset("bias-in-turnout")
The current working directory should now look like this:
- bias-in-turnout
↳ bias-in-turnout.pdf
↳ bias-in-turnout.Rmd
↳ bias-in-turnout.tex
↳ data
↳ turnout.csv
that is, a folder called bias-in-turnout and inside it
• bias-in-turnout.pdf: a short description of the problem and the data
• bias-in-turnout.Rmd: the source file for the problem set
• data another folder containing all the data needed to complete the problem set
• data/turnout.csv: the data set
As get_pset messages suggest, let’s make the problem set folder our working directory
setwd("bias-in-turnout")
and open up the Rmd file so we can start filling in the answers to each question
file.edit("bias-in-turnout.Rmd")
If you’re in RStudio the file should now be editor tab.
Each question has a header that looks like
## Question 1
To provide an answer to this question, move your cursor to just above the line that says ## Question 2 and start answering the question. When you need to compute something in R, start a ‘code block’. Here’s a bit of text you might write followed by a code block that loads the data set we need and counts the number of observations in it:
We load the data set and count the rows
{r}
nrow(turnout)
You can have as much text and as many code blocks as you like. (The variables you make in one code block are still there in the next one.)
You can either type the beginning and end lines of the code block or you can press the green Insert button in the Editor pane’s button menu, choose ‘R’, and have it done for you. Just don’t forget to put the code inside the backticks and don’t nest code blocks inside one another or everything will get confused.
## Compiling the problem set
Yo can see what your answers look like at any point by pressing the ‘Knit’ button. This will try to run all your code, read all your answers and knit the two together into a document. What kind of a document is controllable from that button. If you chose ‘Knit to HTML’ (the default) your document will be called ‘bias-in-turnout.html’. If you chose ‘Knit to PDF’ or ‘Knit to Word’ it will have a different suffix.
You can compile whenever you like. Somee people like to work in the Rmd file all the time and Knit intermittently to check their code works. Others, particularly when starting off, prefer to do their thinking and coding in a different document and then paste their working code and answers into the Rmd file at the last minute. Whatever works for you.
## Getting into (and out of) trouble
Sometimes you might feel it’s best to start again with a fresh copy of the problem set. However, if you
get_pset("bias-in-turnout")
then you’ll get a new problem set inside the one you’re abandoning. This makes things quite confusing. It’s better to go to top level of your files and grab a new copy, calling it something else. You can move your working directory up a level with
setwd("..")
In the language of file paths .. means go up into the parent folder i.e. up one level. (In case you’re curious, . indicates the current folder, and if you wanted to go up two levels then ../.. would be what you wanted)
Now you’re back to where you unpacked bias-in-turnout. To grab a fresh copy with another name:
get_pset("bias-in-turnout", newname = "bias-in-turnout-the-sequel")
(You may have a better idea for a name.) Now you can do it all again, only better.
## All the other problem sets
If you’re curious about the other problem sets you can get a list of their names with
list_psets()
#> [1] "betting-markets" "betting-markets-with-lm"
#> [3] "bias-in-turnout" "bias-newspapers"
#> [5] "conditional-cash-transfers" "constitutions"
#> [7] "criminal-record" "election-clinton-trump"
#> [9] "election-US2016" "empathy-in-courts"
#> [11] "ethnic-voting" "exclusionary-attitudes"
#> [13] "fox-news-effect" "gay-marriage"
#> [15] "gay-marriage-revisited" "gov-corruption"
#> [17] "gov-transfer-brazil" "health-savings"
#> [19] "ideology-of-justices" "immigration-threat"
#> [25] "migration-mechanism" "music-markets"
#> [27] "oil-democracy" "partner-violence"
#> [29] "political-efficacy" "population-dynamics"
#> [31] "poverty-decision" "reducing-transphobia"
#> [33] "small-class-size" "supreme-court-citations"
#> [35] "trade-networks" "un-voting"
and you can take a peek at one of them (constitutions) without unpacking any files using
preview_pset("constitutions") | 2022-05-26 13:41:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.549418032169342, "perplexity": 3035.6476313144767}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662606992.69/warc/CC-MAIN-20220526131456-20220526161456-00712.warc.gz"} |
https://github.com/ipython/ipython/pull/1399/ | # Use LaTeX to print various built-in types with the SymPy printing extension #1399
Merged
merged 2 commits into from Apr 15, 2012
None yet
### 3 participants
SymPy's latex() function supports printing lists, tuples, and dicts using latex notation (it uses bmatrix, pmatrix, and Bmatrix, respectively). This provides a more unified experience with SymPy functions that return these types (such as solve()). Also print ints, longs, and floats using LaTeX, to get a more unified printing experience (so that, e.g., x/x will print the same as just 1). The string form can always be obtained by using print, or 2d unicode printing using pprint(). SymPy's latex() function doesn't treat set() or frosenset() correctly presently (see http://code.google.com/p/sympy/issues/detail?id=3062), so for the present, we leave those alone. Currently, the printing of lists, tuples, and dicts does not work correctly in the qtconsole. Any help fixing this would be appreciated.
asmeurer Use LaTeX to print various built-in types with the SymPy printing ext… …ension SymPy's latex() function supports printing lists, tuples, and dicts using latex notation (it uses bmatrix, pmatrix, and Bmatrix, respectively). This provides a more unified experience with SymPy functions that return these types (such as solve()). Also print ints, longs, and floats using LaTeX, to get a more unified printing experience (so that, e.g., x/x will print the same as just 1). The string form can always be obtained by using print, or 2d unicode printing using pprint(). SymPy's latex() function doesn't treat set() or frosenset() correctly presently (see http://code.google.com/p/sympy/issues/detail?id=3062), so for the present, we leave those alone. Currently, the printing of lists, tuples, and dicts does not work correctly in the qtconsole. e21221c
Member
commented Feb 12, 2012
This looks pretty good. One thing that does get weird in the notebook is if you have a list containing a type (or anything whose repr includes <...>), because markdown is still treating those as HTML tags. For instance, [type] transforms to \begin{bmatrix}\end{bmatrix} which displays as $$\begin{bmatrix}\end{bmatrix}$$ (not rendered), presumably because it contains an unterminated open-tag, confusing the MathJax parser. I'm less confident in the png for qtconsole choice, just because they aren't particularly nice, they are slow, and matplotlib.mathtext doesn't provide full LaTeX. The reason your container renderers are not drawing in the qtconsole is that the png render is failing, I think due to the use of \begin{bmatrix}, which mathtext doesn't seem to support. I believe mathtext is only meant for single expressions. Exceptions raised in display formatters are ignored, and treated as "we can't format this object, move on to other mime-types". To see the actual result of the display format call, you can do: # get the formatter object for PNG png_formatter = get_ipython().display_formatter.formatters['image/png'] # get the callable for lists f = png_formatter.type_printers[list] # call it on a list f([1,2]) which will raise: ValueError: \begin{bmatrix}1, & 2\end{bmatrix} ^ Unknown symbol: \begin (at char 0), (line:1, col:1)
So the mathjax formatter should replace all instances of < and > with \< and \>? I didn't realize that the png formatter just falls back to the text formatter when it fails. Does it support \left ( and so on (I'm actually not entirely sure why we don't just use that instead of the matrix stuff)? I'll play with it. I agree that mathtext doesn't look very nice (in general). I would be better if we could render mathjax in the qtconsole. Or, we could do something like http://research.scios.ch/inet/doku.php?id=ipy_tex, which uses latex itself to render the math (if it's installed).
Escaping the < and > doesn't seem to work. I made it so that [type(Symbol('x')] gives $$\begin{bmatrix}\\end{bmatrix}$$, but this just renders as $$\begin{bmatrix}\\end{bmatrix}$$ (plaintext).
I'm not convinced that <...> is the problem, actually. And(x < y, y > x) renders just fine in master for example (you have to use the SymPy master too). That's rendered as $$x < y \wedge x > y$$.
Member
commented Feb 12, 2012
backslash is not used for escaping HTML, it would be <, > etc. Also, this escape should not happen at the code level, it should be in javascript in the frontend. The brackets are valid in LaTeX, but the mixed TeX/HTML environment of mathjax should make a pass at escaping apparent HTML in clearly non-HTML expressions. As for the PNG - All available formatters are always called. So if the PNG formatter fails, it simply returns nothing, acting as if there was no PNG formatter registered for the given object. At that point, plaintext format is the only remaining one that the QtConsole can display. As for what it supports, I would check out the docs for matplotlib.mathtext, as that is the code that actually does the rendering. If you can render the TeX as a png yourself, then that's fine as well.
Member
commented Feb 12, 2012
I'm not convinced that <...> is the problem, actually... It requires that it be identifiable as a tag, which is sensitive to space between open-bracket and tag symbol (hence
So should I consider it a separate problem from this pull request? Regardless, I don't know javascript well enough to do the parsing there, so someone else will have to fix it.
Member
commented Feb 12, 2012
Yes, I suppose I would consider it a separate issue. But it does create a real problem when using sympy to draw basic types that are not at all related to sympy, such as lists, etc. For instance, I wouldn't want sympy to draw any of my lists or dicts unless they actually contained sympy objects (less objectionable when they contain only simple scalars). This changes what %load_ext sympyprinting means, from: "Display sympy objects with latex" to: "Draw everything with latex" Both of which are reasonable, and have advantages and disadvantages. Is it possible for the sympyprinting callable to skip containers that contain anything sympy doesn't handle (e.g. str, object, etc.)? All it would have to do is return None in those cases.
Yeah, that should be straightforward. If there are mixed types, I guess it will have to draw the whole thing using the string printer (unless mathjax can be mixed with it nicely).
Member
commented Feb 13, 2012
Okay, let's go with that. I wouldn't bother trying to mix latex and reprs, just abort latex-printing if there's anything in the container not on the whitelist of latexable types.
What's the best way to do that, given that we use string forms of the SymPy types instead of the types themselves?
In other words, I want to do something like def can_print_latex(o): """ Return True of every element of a container type o can be printed with LaTeX. """ if type(o) in (list, tuple): return all(can_print_latex(i) for i in o) if type(o) is dict: return all(can_print_latex(i) and can_print_latex(o[i]) for i in o) if type(o) in (sympy.Basic, sympy.matrices.Matrix): return True return False But that requires having sympy imported, which I gather from the rest of the file is not necessarily true (though I'm not entirely sure why).
Actually, I want to use isinstance, not type. But the question is the same.
Member
commented Feb 14, 2012
Why is the sympy import a problem? You can just import sympy, either in the module, or in the function itself, if that's necessary for some reason: Something like this should work: def can_print_latex(o): """ Return True of every element of a container type o can be printed with LaTeX. """ import sympy if isinstance(o, (list, tuple)): return all(can_print_latex(i) for i in o) elif isinstance(o, dict): return all((isinstance(i, basestring) or can_print_latex(i)) and can_print_latex(o[i]) for i in o) elif isinstance(o,(sympy.Basic, sympy.matrices.Matrix, int, long, float)): return True return False
I don't know. I assumed it was because of the try block at the top of the file.
Member
commented Feb 14, 2012
Oh, I wouldn't worry about that. I think it might have to do with testing or some such that the file must be importable. It should be fine to rely on that import having succeeded in your functions
Member
commented Mar 13, 2012
@asmeurer, just checking in... I finally have some time to start catching up with our accumulated PR backlog. This looks like a good PR, once the discussion above is taken into account in the changes.
I'm actually backlogged as well, but I'm am trying to get through stuff. I'm going through my emails in order, so your comment ironically made it take longer for me to get to :)
asmeurer Only print container types with LaTeX in the notebook if all the elem… …ents can be printed with LaTeX in the SymPy printing extension. Otherwise, fallback to the string printer. 1186cac
OK, I finally finished this. Please verify that I did everything correctly, as I may have forgotten something in the time I've left this.
referenced this pull request Mar 25, 2012
Closed
#### Better LaTeX printing in the qtconsole with the sympy profile #1523
I don't have time to look into the qtconsole now, so I opened #1523 for it. I'd be interested in hearing your opinions on using MathJax or something like http://research.scios.ch/inet/doku.php?id=ipy_tex in the qtconsole.
Member
commented Apr 14, 2012
This one looks good to me, now.
Member
commented Apr 15, 2012
Looks good to me too, merging now. @asmeurer, thanks for the work! We'll take up the rest of the discussion in #1523.
merged commit ba882bf into ipython:master Apr 15, 2012
added a commit to asmeurer/ipython that referenced this pull request May 28, 2012
asmeurer Update SymPy profile: SymPy's latex() can now print set and frozenset I've included a version check against the latest version of SymPy that supports it (the current development version, 0.7.1-git), so that users of old versions of SymPy where this doesn't work will still have a good user experience. This is a continuation of pull request #1399. 9fe341d
This was referenced May 28, 2012
Merged
Closed
#### init_printing does funny things to normal python dictionaries sympy/sympy#2672
pushed a commit to mattvonrocketstein/ipython that referenced this pull request Nov 3, 2014
asmeurer Update SymPy profile: SymPy's latex() can now print set and frozenset I've included a version check against the latest version of SymPy that supports it (the current development version, 0.7.1-git), so that users of old versions of SymPy where this doesn't work will still have a good user experience. This is a continuation of pull request #1399. 362568c` | 2016-12-09 13:30:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5649762749671936, "perplexity": 2505.0384625885486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542712.12/warc/CC-MAIN-20161202170902-00480-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://codegolf.stackexchange.com/questions/203616/simulate-the-isotropic-non-totalistic-cellular-automaton | Simulate the isotropic non-totalistic cellular automaton
There are many generalizations of Conway's Game of Life. One of them is the isotropic non-totalistic rulespace, in which the state of a cell in the next generation depends not just on its state and the amount of alive cells around it, but also the relative positions of the cells around it.
Given an rulestring corresponding to an isotropic non-totalistic cellular automaton, an integer $$\T\$$, and an initial pattern $$\P\$$, simulate the initial pattern $$\P\$$ for $$\T\$$ generations under the given rulestring.
Constraints
• The given rulestring is valid and does not contain the B0 transition.
• $$\0 < T \le 10^3\$$
• Area of bounding box of $$\P \le 10^3\$$
Input
The rulestring, $$\T\$$ and $$\P\$$ will all be given in any necessary (specified) format.
Output
Output the resulting pattern after $$\P\$$ is run $$\T\$$ generations.
Example
Rulestring: B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
T: 62
Pattern (in canonical RLE format):
x = 15, y = 13, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
3b2o$2ob2o$2o4$13b2o$13b2o$3bo$2b3o$2bob2o$2bobo$2b2o! Output: x = 15, y = 13, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c 3b2o$2ob2o$2o4$13b2o$13b2o$3b2o$b5o$bo3bo$bo2bo$2b3o!
Scoring
This is extended , which means that the program with smallest (length in bytes - bonuses) wins.
Standard loopholes are not allowed. Your program is not allowed to use any external libraries that deal with cellular automata. Your program is expected to finish relatively quickly (in at most 10 minutes).
Bonuses:
• 10 for finishing in under 10 seconds under max tests
• 20 for accepting the rulestring in canonical form (e.g. B2-a/S12)
• To clarify, can we invent a custom rulestring specifically for this challenge? And if so, how far can we go with this? Can we input a string of 'born' and 'survival' grids, which would make this a lot easier? – dingledooper Apr 17 at 5:04
• @dingledooper Yes, you can. In fact, you can even require the rulestring be put in a file "t.h" in the form of a function int t(int a, int b, int c, int d, int e, int f, int g, int h, int i). – Baaing Cow Apr 17 at 7:34
• +1 because I mainly investigate isotropic non-totalistic rules. I think "Hensel notation" should be mentioned in the question, though. – HighlyRadioactive Apr 23 at 0:09
• Are you testitem by the way? (I can't think of anyone else who promote X3VI to this level) – HighlyRadioactive Apr 23 at 1:48 | 2020-08-15 08:58:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 10, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4267798066139221, "perplexity": 1538.8135651760635}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740733.1/warc/CC-MAIN-20200815065105-20200815095105-00165.warc.gz"} |
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/colloquium-mathematicum/all/120/1/87611/subfields-of-henselian-valued-fields | JEDNOSTKA NAUKOWA KATEGORII A+
# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty
## Subfields of henselian valued fields
### Tom 120 / 2010
Colloquium Mathematicum 120 (2010), 157-163 MSC: Primary 12J10; Secondary 12J25. DOI: 10.4064/cm120-1-12
#### Streszczenie
Let $(K,v)$ be a henselian valued field of arbitrary rank which is not separably closed. Let $k$ be a subfield of $K$ of finite codimension and $v_k$ be the valuation obtained by restricting $v$ to $k$. We give some necessary and sufficient conditions for $(k,v_k)$ to be henselian. In particular, it is shown that if $k$ is dense in its henselization, then $(k,v_k)$ is henselian. We deduce some well known results proved in this direction through other considerations.
#### Autorzy
Panjab University
Chandigarh 160014, India
e-mail
• Sudesh K. KhandujaDepartment of Mathematics
Panjab University
Chandigarh 160014, India
e-mail
## Przeszukaj wydawnictwa IMPAN
Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.
Odśwież obrazek | 2023-02-06 09:35:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6821274161338806, "perplexity": 3096.1976492912113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500334.35/warc/CC-MAIN-20230206082428-20230206112428-00739.warc.gz"} |
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I am running some analysis on a uav, and the results I have found show that with proposed modifications I am unable to trim at my previous $c_{L\:max}$ and thus originally designed stall speed (... | 2020-01-18 23:20:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40013599395751953, "perplexity": 4044.519202347477}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250593994.14/warc/CC-MAIN-20200118221909-20200119005909-00475.warc.gz"} |
https://fr.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.binscatter-properties.html | Documentation
### This is machine translation
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# Binscatter Properties
Binscatter appearance and behavior
`Binscatter` properties control the appearance and behavior of binned scatter plots. By changing property values, you can modify aspects of the display. Use dot notation to refer to a particular object and property:
```h = binscatter(randn(1,100),randn(1,100)); N = h.NumBins h.NumBins = [3 3]```
## Bins
expand all
Number of bins, specified as a scalar or two-element vector ```[Nx Ny]```.
• If `NumBins` is specified as a two-element vector `[Nx Ny]`, then `binscatter` uses `Nx` bins in the x dimension and `Ny` bins in the y dimension.
• If `NumBins` is specified as a scalar, then `Nx` and `Ny` are both set to the scalar value.
`binscatter` uses `Nx` and `Ny` bins along the x and y dimensions in the initial plot, when the axes are not zoomed in. (The axes are not zoomed in when the `XLimMode` and `YLimMode` properties are both `'auto'`.) When zooming, `binscatter` adjusts the number of bins to maintain a bin size such that the visible portion of the plot is approximately divided into `Nx`-by-`Ny` bins.
The maximum number of bins in each dimension is 250. The default number of bins is computed based on the data size and standard deviation and does not exceed 100.
Example: `[10 20]`
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`
Selection mode for number of bins, specified as either `'auto'` or `'manual'`. With the default value of `'auto'`, the number of bins is computed from the data according to Scott's rule, ```[3.5*std(X(:))*numel(X)^(-1/4), 3.5*std(Y(:))*numel(Y)^(-1/4)]```.
If you specify the number of bins, then the value of `'NumBinsMode'` is set to `'manual'`.
Toggle to show empty bins, specified as either `'off'` or `'on'`. Specify `'on'` to color tiles in the plot that fall within the bin limits, but have no data points.
Bin edges in x-dimension, returned as a vector.
Data Types: `single` | `double` | `datetime` | `duration`
Bin edges in y dimension, returned as a vector.
Data Types: `single` | `double` | `datetime` | `duration`
Data limits in x-dimension, specified as a two-element vector `[Xmin Xmax]`.
`binscatter` only displays data points that fall within the specified data limits inclusively, ${X}_{\mathrm{min}}\le X\le {X}_{\mathrm{max}}$.
Example: `[0 10]`
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `datetime` | `duration`
Selection mode for data limits in x-dimension, specified as `'auto'` or `'manual'`. The default value is `'auto'`, so that the bin limits automatically adjust to the data along the x-axis.
If you explicitly specify `XLimits`, then `XLimitsMode` is automatically set to `'manual'`. In that case, specify `XLimitsMode` as `'auto'` to rescale the bin limits to the data.
Data limits in y-dimension, specified as a two-element vector `[Ymin Ymax]`.
`binscatter` only displays data points that fall within the specified data limits inclusively, ${Y}_{\mathrm{min}}\le Y\le {Y}_{\mathrm{max}}$.
Example: `[0 10]`
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `datetime` | `duration`
Selection mode for data limits in y-dimension, specified as `'auto'` or `'manual'`. The default value is `'auto'`, so that the bin limits automatically adjust to the data along the y-axis.
If you explicitly specify `YLimits`, then `YLimitsMode` is automatically set to `'manual'`. In that case, specify `YLimitsMode` as `'auto'` to rescale the bin limits to the data.
## Data
expand all
x coordinates of data, specified as a vector.
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `datetime` | `duration`
y coordinates of data, specified as a vector.
Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `datetime` | `duration`
Bin values, returned as a double matrix. The `(i,j)`th entry in `Values` specifies the bin count for the bin whose x edges are ```[XBinEdges(i), XBinEdges(i+1)]``` and whose y edges are `[YBinEdges(j), YBinEdges(j+1)]`.
The bin inclusion scheme for the different numbered bins in `Values`, as well as their relative orientation to the x-axis and y-axis, is
For example, the `(1,1)` bin includes values that fall on the first edge in each dimension. The last bin in the bottom right includes values that fall on any of its edges.
## Transparency
expand all
Transparency of tiles, specified as a scalar value between `0` and `1` inclusive. `binscatter` uses the same transparency for all the tiles. A value of `1` means fully opaque and `0` means completely transparent (invisible).
Example: `binscatter(X,Y,'FaceAlpha',0.5)` creates a binned scatter plot with semitransparent bins.
## Legend
expand all
Text used by the legend, specified as a character vector. The text appears next to an icon of the binscatter.
Example: `'Text Description'`
For multiline text, create the character vector using `sprintf` with the new line character `\n`.
Example: `sprintf('line one\nline two')`
Alternatively, you can specify the legend text using the `legend` function.
• If you specify the text as an input argument to the `legend` function, then the legend uses the specified text and sets the `DisplayName` property to the same value.
• If you do not specify the text as an input argument to the `legend` function, then the legend uses the text in the `DisplayName` property. The default value of `DisplayName` is one of these values.
• For numeric inputs, `DisplayName` is a character vector representing the variable name of the input data used to construct the histogram. If the input data does not have a variable name, then `DisplayName` is empty, `''`.
• For categorical array inputs, `DisplayName` is empty, `''`.
If the `DisplayName` property does not contain any text, then the legend generates a character vector. The character vector has the form `'dataN'`, where `N` is the number assigned to the binscatter object based on its location in the list of legend entries.
If you edit interactively the character vector in an existing legend, then MATLAB® updates the `DisplayName` property to the edited character vector.
Control for including or excluding the object from a legend, returned as an `Annotation` object. Set the underlying `IconDisplayStyle` property to one of these values:
• `'on'` — Include the object in the legend (default).
• `'off'` — Do not include the object in the legend.
For example, to exclude a graphics object, `go`, from the legend set the `IconDisplayStyle` property to `'off'`.
```go.Annotation.LegendInformation.IconDisplayStyle = 'off'; ```
Alternatively, you can control the items in a legend using the `legend` function. Specify the first input argument as a vector of the graphics objects to include. If you do not specify an existing graphics object in the first input argument, then it does not appear in the legend. However, graphics objects added to the axes after the legend is created do appear in the legend. Consider creating the legend after creating all the plots to avoid extra items.
## Interactivity
expand all
State of visibility, specified as one of these values:
• `'on'` — Display the object.
• `'off'` — Hide the object without deleting it. You still can access the properties of an invisible object.
Context menu, specified as a `ContextMenu` object. Use this property to display a context menu when you right-click the object. Create the context menu using the `uicontextmenu` function.
### Note
If the `PickableParts` property is set to `'none'` or if the `HitTest` property is set to `'off'`, then the context menu does not appear.
Selection state, specified as one of these values:
• `'on'` — Selected. If you click the object when in plot edit mode, then MATLAB sets its `Selected` property to `'on'`. If the `SelectionHighlight` property also is set to `'on'`, then MATLAB displays selection handles around the object.
• `'off'` — Not selected.
Display of selection handles when selected, specified as one of these values:
• `'on'` — Display selection handles when the `Selected` property is set to `'on'`.
• `'off'` — Never display selection handles, even when the `Selected` property is set to `'on'`.
## Callbacks
expand all
Mouse-click callback, specified as one of these values:
• Function handle
• Cell array containing a function handle and additional arguments
• Character vector that is a valid MATLAB command or function, which is evaluated in the base workspace (not recommended)
Use this property to execute code when you click the object. If you specify this property using a function handle, then MATLAB passes two arguments to the callback function when executing the callback:
• Clicked object — Access properties of the clicked object from within the callback function.
• Event data — Empty argument. Replace it with the tilde character (`~`) in the function definition to indicate that this argument is not used.
For more information on how to use function handles to define callback functions, see Callback Definition.
### Note
If the `PickableParts` property is set to `'none'` or if the `HitTest` property is set to `'off'`, then this callback does not execute.
Creation callback, specified as one of these values:
• Function handle
• Cell array containing a function handle and additional arguments
• Character vector that is a valid MATLAB command or function, which is evaluated in the base workspace (not recommended)
Use this property to execute code when you create the object. MATLAB executes the callback after creating the object and setting all of its properties. Setting the `CreateFcn` property on an existing object has no effect. To have an effect, you must specify the `CreateFcn` property during object creation. One way to specify the property during object creation is to set the default property value for the object. See Default Property Values for more information.
If you specify this callback using a function handle, then MATLAB passes two arguments to the callback function when executing the callback:
• Created object — Access properties of the object from within the callback function. You also can access the object through the `CallbackObject` property of the graphics root object, which can be queried using the `gcbo` function.
• Event data — Empty argument. Replace it with the tilde character (`~`) in the function definition to indicate that this argument is not used.
For more information on how to use function handles to define callback functions, see Callback Definition.
Deletion callback, specified as one of these values:
• Function handle
• Cell array containing a function handle and additional arguments
• Character vector that is a valid MATLAB command or function, which is evaluated in the base workspace (not recommended)
Use this property to execute code when you delete the object. MATLAB executes the callback before destroying the object so that the callback can access its property values.
If you specify this callback using a function handle, then MATLAB passes two arguments to the callback function when executing the callback:
• Deleted object — Access properties of the object from within the callback function. You also can access the object through the `CallbackObject` property of the graphics root object, which can be queried using the `gcbo` function.
• Event data — Empty argument. Replace it with the tilde character (`~`) in the function definition to indicate that this argument is not used.
For more information on how to use function handles to define callback functions, see Callback Definition.
## Callback Execution Control
expand all
Callback interruption, specified as `'on'` or `'off'`. The `Interruptible` property determines if a running callback can be interrupted.
### Note
Consider these callback states where:
• The running callback is the currently executing callback.
• The interrupting callback is a callback that tries to interrupt the running callback.
Whenever MATLAB invokes a callback, that callback attempts to interrupt a running callback. The `Interruptible` property of the object owning the running callback determines if interruption is permitted. If interruption is not permitted, then the `BusyAction` property of the object owning the interrupting callback determines if it is discarded or put in the queue.
The `Interruptible` property determines if another callback can interrupt the `ButtonDownFcn` callback of the `Binscatter` object. The `Interruptible` property has two values:
• `'on'` — Interruptible. Interruption occurs at the next point where MATLAB processes the queue. For example, queues are processed by commands such as `drawnow`, `figure`, `getframe`, `waitfor`, `pause`, and `waitbar`.
• If the running callback contains one of these commands, then MATLAB stops the execution of the callback at this point and executes the interrupting callback. MATLAB resumes executing the running callback when the interrupting callback completes. For more information, see Interrupt Callback Execution.
• If the running callback does not contain one of these commands, then MATLAB finishes executing the callback without interruption.
• `'off'` — Not interruptible. MATLAB finishes executing the running callback without any interruptions.
Callback queuing specified as `'queue'` or `'cancel'`. The `BusyAction` property determines how MATLAB handles the execution of interrupting callbacks.
Consider these callback states where:
• The running callback is the currently executing callback.
• The interrupting callback is a callback that tries to interrupt the running callback.
Whenever MATLAB invokes a callback, that callback attempts to interrupt a running callback. The `Interruptible` property of the object owning the running callback determines if interruption is permitted. If interruption is not permitted, then the `BusyAction` property of the object owning the interrupting callback determines if it is discarded or put in the queue.
If a callback of the `Binscatter` object tries to interrupt a running callback that cannot be interrupted, then the `BusyAction` property determines if it is discarded or put in the queue. Specify the `BusyAction` property as one of these values:
• `'queue'` — Put the interrupting callback in a queue to be processed after the running callback finishes execution. (default behavior)
• `'cancel'` — Discard the interrupting callback.
Ability to capture mouse clicks, specified as one of these values:
• `'visible'` — Capture mouse clicks only when visible. The `Visible` property must be set to `'on'`. The `HitTest` property determines if the `Binscatter` object responds to the click or if an ancestor does.
• `'none'` — Cannot capture mouse clicks. Clicking the `Binscatter` object passes the click to the object behind it in the current view of the figure window. The `HitTest` property of the `Binscatter` object has no effect.
Response to captured mouse clicks, specified as one of these values:
• `'on'` — Trigger the `ButtonDownFcn` callback of the `Binscatter` object. If you have defined the `UIContextMenu` property, then invoke the context menu.
• `'off'` — Trigger the callbacks for the nearest ancestor of the `Binscatter` object that has one of these:
• `HitTest` property set to `'on'`
• `PickableParts` property set to a value that enables the ancestor to capture mouse clicks
### Note
The `PickableParts` property determines if the `Binscatter` object can capture mouse clicks. If it cannot, then the `HitTest` property has no effect.
Deletion status, returned as `'off'` or `'on'`. MATLAB sets the `BeingDeleted` property to `'on'` when the delete function of the object begins execution (see the `DeleteFcn` property). The `BeingDeleted` property remains set to `'on'` until the object no longer exists.
Check the value of the `BeingDeleted` property if you need to verify that the object is not about to be deleted before querying or modifying it.
## Parent/Child
expand all
Parent, specified as an `Axes` object.
The object has no children. You cannot set this property.
Visibility of the object handle in the `Children` property of the parent, specified as one of these values:
• `'on'` — Object handle is always visible.
• `'off'` — Object handle is invisible at all times. This option is useful for preventing unintended changes to the UI by another function. Set the `HandleVisibility` to `'off'` to temporarily hide the handle during the execution of that function.
• `'callback'` — Object handle is visible from within callbacks or functions invoked by callbacks, but not from within functions invoked from the command line. This option blocks access to the object at the command line, but permits callback functions to access it.
If the object is not listed in the `Children` property of the parent, then functions that obtain object handles by searching the object hierarchy or querying handle properties cannot return it. Examples of such functions include the `get`, `findobj`, `gca`, `gcf`, `gco`, `newplot`, `cla`, `clf`, and `close` functions.
Hidden object handles are still valid. Set the root `ShowHiddenHandles` property to `'on'` to list all object handles regardless of their `HandleVisibility` property setting.
## Identifiers
expand all
Type of graphics object, returned as `'binscatter'`. Use this property to find all objects of a given type within a plotting hierarchy, such as searching for the type using `findobj`.
Tag to associate with the `binscatter` object, specified as a character vector or string scalar.
Use this property to find `binscatter` objects in a hierarchy. For example, you can use the `findobj` function to find `binscatter` objects that have a specific `Tag` property value.
Example: `'January Data'`
Data Types: `char`
User data to associate with the `binscatter` object, specified as any MATLAB data, for example, a scalar, vector, matrix, cell array, character array, table, or structure. MATLAB does not use this data.
To associate multiple sets of data or to attach a field name to the data, use the `getappdata` and `setappdata` functions.
Example: `1:100` | 2019-06-19 23:14:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36702606081962585, "perplexity": 2233.59383188809}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999066.12/warc/CC-MAIN-20190619224436-20190620010436-00253.warc.gz"} |
https://www.physicsforums.com/threads/projectile-range.730711/ | # Projectile range
1. Dec 31, 2013
### negation
1. The problem statement, all variables and given/known data
After a short engine firiing, an atmosphere-probing rocket reaches 4.6km/s. If the rocket must land within 50km of its launc site, what's the max allowable deviation from a vertical trajectory.
2. Relevant equations
none
3. The attempt at a solution
Given by the book:
x = (vi^2/g)sin 2Θ
50,000m = (vi^2/-9.8)sin 2Θ
sin2Θ = (gx/vi^2) = 0.0232
Again this is really frustrating, I take g = -9.8 and x = 50,000m, vi = 4600m/s
but I get -0.0232.
What is wrong here?
If I use a positive g, I get 0.0232 but that would be rubbish.
1. The problem statement, all variables and given/known data
2. Relevant equations
3. The attempt at a solution
2. Dec 31, 2013
### Curious3141
Why would it be "rubbish"?
I suggest you check the derivation of the range formula. That should tell you why $g$ should be taken as a positive number (just the magnitude) here.
3. Dec 31, 2013
### negation
I understand how to derive the equation for the range formula. What I don't understand is that the g in the equation was not specified as a magnitude so why should I be using the magnitude and not the vector g?
4. Jan 1, 2014
### Curious3141
So, in the derivation, what is the exact expression for the vertical position at time $t$?
5. Jan 2, 2014
### negation
I have understood why g = 9.8 instead of -9.8ms^-2
6. Jan 2, 2014
### Curious3141
Good. It is because the equation for the vertical displacement explicitly includes a negative sign before $g$, i.e. $\displaystyle y = v\sin\theta{t} -\frac{1}{2}gt^2$. Hence $g$ here refers to the magnitude only. | 2017-08-19 20:13:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6954218745231628, "perplexity": 1418.562582219147}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105712.28/warc/CC-MAIN-20170819182059-20170819202059-00023.warc.gz"} |
https://mathematics.huji.ac.il/calendar/past_events | • 2021 Jan 21
# Colloquium: Cornelius Greither (Bundeswehr University Munich) — a short panoramic tour of some zeta functions
2:30pm to 3:30pm
One might say that there exist zeta functions of three kinds: the very well-known ones (whose stock example is Riemann's zeta function); some less familiar ones; and at least one type which has been totally forgotten for decades. We intend to mention instances of all three types. The first type is important, if not predominant, in algebraic number theory, as we will try to illustrate by (very few) examples. As examples of the second type we will discuss zeta functions of finite groups.
• 2021 Jan 20
# Analysis Seminar: Dirk Hundertmark (Karlsruhe) "Quantum Systems at the Brink: Helium"
12:00pm to 1:00pm
## Location:
Zoom
Title: Quantum Systems at the Brink: Helium
Abstract: Perturbation theoryworks well for the the discrete spectrum below the essential spectrum. Whathappens if a parameter of a quantum system is tuned in such a way that abound state energy (e.g. the ground state energy) hits the bottom of theessential spectrum? Does the eigenvalue survive, i.e., the correspondingeigenfunction stays $L^2$, or does it dissolve into the continuumenergies?
It turns out the
• 2021 Jan 20
# Logic Seminar - Eran Alouf
11:30am to 1:15pm
## Location:
https://huji.zoom.us/j/82821066522?pwd=aVJnTkxBYktycHdzNFN5WDV0R2FkZz09
Dp-minimal expansions of (Z,+)
Abstract:
I will review the research about dp-minimal expansions of (Z,+), and then present a recent result classifying (Z,+,<) as the unique dp-minimal expansion of (Z,+) defining an infinite subset of N.
All the relevant notions will be defined in the talk.
• 2021 Jan 19
# Dynamics seminar: Barak Weiss (TAU). Ergodicity of rel foliations on the space of holomorphic one forms
2:00pm to 3:00pm
Abstract: The rel foliation is a foliation of the moduli space of abelian differentials obtained by "moving the zeroes of the one form while keeping all absolute periods fixed". It has been studied in complex analysis and dynamics under different names (isoperiodic foliation, Schiffer variation, kernel foliation). Until recent years the question of its ergodicity was wide open. Recently partial results were obtained by Calsamiglia-Deroin-Francaviglia and by Hamenstadt. In our work we completely resolve the ergodicity question.
• 2021 Jan 19
# Tom Meyerovich (BGU) "Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group"
12:00pm to 1:00pm
following Sebastián Barbieri, Felipe García-Ramos and Hanfeng Li
https://arxiv.org/abs/1911.00785
Zoom details:
Join Zoom Meeting
Meeting ID: 837 2635 1672
Passcode: 7e288r
• 2021 Jan 18
# Combinatorics: Shinichi Tanigawa
11:00am to 1:00pm
## Location:
https://huji.zoom.us/j/81176578450?pwd=TStYWHhhWnE3YkNuR0RlZmkrejBIUT09
HUJI Combinatorics Seminar
When: Monday Jan 18th, 2021, at 11AM (Israel time)
Speaker: Shin-ichi Tanigawa (University of Tokyo)
Title: Maximal Matroid Problem on Graphs
Abstract:
• 2021 Jan 17
# Kazhdan seminar: Tomer Schank "Sheaves with nilpotent support"
Repeats every week every Sunday until Sun Jan 17 2021 .
2:00pm to 4:00pm
Abstract: Given a smooth and proper curve X and a reductive group G one can consider the stack Bun_{G,X} of principal G-bundles on X. This stack has an important role in Algebraic Geometry and Representation Theory especially with regard to the Langlands program. We shall study the geometry of Bun_{G,X} and the category
D(G,X) of constructible sheaves on Bun_{G,X}. We shall be especially interested in the subcategory D_{nil}(G,X) of sheaves with nilpotent singular support.
• 2021 Jan 17
# Kazhdan seminar : Ari Shnidman "Fundamental lemmas and Fourier transform"
Repeats every week every Sunday until Sun Jan 17 2021 .
11:00am to 1:00pm
Abstract: A fundamental lemma is an identity relating p-adic integrals on two different groups. These pretty identities fit into a larger story of trace formulas and special values of L-functions. Our goal is to present recent work of Beuzart-Plessis on the Jacquet-Rallis fundamental lemma, comparing integrals on GL(n) and U(n).
• 2021 Jan 14
# Basic Notions: Kobi Peterzil (U. of Haifa) "The Pila-Zannier method: applications of model theory to Diophantine geometry".
4:00pm to 5:15pm
## Location:
Zoom
A family of problems in Diophantine geometry has the following
form: We fix a collection of "special" algebraic varieties among which the
0-dimensional are called "special points". Mostly, if V is a special variety
then the special points are Zariski dense in V, and the problem is to prove
the converse: If V is an irreducible algebraic variety and the special
points are Zariski dense in V then V itself is special.
Particular cases of the above are the Manin-Mumford conjecture
• 2021 Jan 13
# Set Theory seminar - Juris Stperans (York) Universal functions, strong colourings and ideas from PID
2:00pm to 4:00pm | 2021-01-24 04:01:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.556492030620575, "perplexity": 4262.763779523588}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703544403.51/warc/CC-MAIN-20210124013637-20210124043637-00527.warc.gz"} |
http://kinfit.r-forge.r-project.org/mkin_static/reference/sigma_rl.html | Function describing the standard deviation of the measurement error in dependence of the measured value $$y$$:
$$\sigma = \sqrt{ \sigma_{low}^2 + y^2 * {rsd}_{high}^2}$$
sigma_rl(y, sigma_low, rsd_high)
Arguments
y The magnitude of the observed value The asymptotic minimum of the standard deviation for low observed values The coefficient describing the increase of the standard deviation with the magnitude of the observed value
Value
The standard deviation of the response variable.
References
Rocke, David M. und Lorenzato, Stefan (1995) A two-component model for measurement error in analytical chemistry. Technometrics 37(2), 176-184. | 2018-05-27 17:41:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6021531224250793, "perplexity": 993.708751398224}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794869732.36/warc/CC-MAIN-20180527170428-20180527190428-00099.warc.gz"} |
https://solvedlib.com/dbookmark-a-toy-rocket-weighing-10-n-blasts,438587 | # Dbookmark) A toy rocket, weighing 10 N blasts straight up from ground level with kinetic energy...
###### Question:
dbookmark) A toy rocket, weighing 10 N blasts straight up from ground level with kinetic energy of 40 J. At the exact top of its trajectory its total mechanical energy is 140 J. To what vertical height does it rise?
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https://ham.stackexchange.com/questions/9037/is-ladder-line-necessary-when-using-a-non-resonant-dipole-through-a-tuner | # Is ladder line necessary when using a non-resonant dipole through a tuner?
I've heard if I have a dipole of some arbitrary length, or a random wire, the SWR can be very bad. An antenna tuner can present a decent match to the transmitter, but the SWR on the feedline will be very high, and thus ladder line is required.
Is ladder line really required, as opposed to coax? What are the essential properties of a feedline in this application?
• +1. Maybe we'll learn something. Those coax losses on Owen Duffy's site are not near as bad I would have guessed. – Mike Waters Aug 9 '17 at 20:32
• Look at my edited answer. Are those mismatched line losses for all those different feedlines for that antenna wrong? I also used TLDetails and it pretty much agrees with Owen's calculators. – Mike Waters Aug 9 '17 at 22:41
• @MikeWaters No they're not wrong, but you're comparing 50 ohm coax to a 5000 ohm load and an SWR of 100, to 450 ohm ladder line for an SWR of 11. Use an impedance transforming balun and you'll find the performance gap closes. – Phil Frost - W8II Aug 10 '17 at 13:18
This can indeed be a fine setup. With a suitably low-loss feedline, and a good tuner, just about anything can be made to function as an effective antenna.
There are two factors that determine the losses in this situation:
1. the matched loss of the feedline, a function of length and the attenuation specified in the datasheet, and
2. the operating SWR on the feedline, which depends on the ratio of the feedline and load impedances.
When the SWR is greater than 1:1, some fraction of the power is reflected from the antenna, back towards the transmitter. The antenna tuner then re-reflects this reflected power back at the antenna.
Eventually, all the energy is either radiated by the antenna, absorbed by the feedline, or absorbed by the tuner. Since each parcel of energy is making multiple "bounces" between the tuner and the antenna, it's subject to the feedline loss multiple times. Obviously, lower feedline loss means less loss. A lower SWR means fewer bounces back and forth, so again less loss. See What is the actual loss in a feed line with high SWR?
Ladder-line does not intrinsically have lower loss than coax. For example, this 300 ohm ladder line sold by DX Engineering has a loss of 0.668 dB per 100 feet at 30 MHz. Compare to Times Microwave LMR-400 at 0.7 dB for the same. There's better coax, and there's better ladder-line, but generally the performance of a transmission line is a function of the dielectric and conductor resistance (mostly the latter at HF), not whether it's coax or ladder-line.
specified attenuation for DX Engineering ladder-line per 100 feet
specified attenuation for LMR-400
Note the significantly higher loss when the ladder-line is damp. Coax maintains its performance when wet, covered in snow, ice, or dirt, when buried, run through conduit, attached directly to a tower, etc. This is why commercial installations overwhelmingly prefer coax.
Ladder-line does tend to have a higher characteristic impedance, somewhere between 300 and 600 ohms for common designs. This is important.
A resonant dipole is at an impedance minimum, around 72 ohms. So when the dipole isn't resonant, the impedance will be higher, with a typical maximum around 5000 ohms.
Modelling software and antenna analyzers will give an SWR, but this is not the SWR on the feedline unless the feedline has a characteristic impedance of 50 ohms. Given our dipole which may be between 72 and 5000 ohms, this gives a possible SWR from 1.44:1 to 100:1.
With 300 ohm ladder-line, the antenna analyzer will still say the SWR is 100:1 in the worst case. But actually the SWR is only:
$${ 5000\:\Omega \over 300\:\Omega } = 16.7:1$$
This is why ladder-line tends to have a lower loss in this antenna system. Not because it is an inherently lower-loss feedline, but because the SWR is reduced.
However, if you wish to use coax, it's an easy problem to solve. A 4:1 balun on 75 ohm coax divides the load impedance by 4. So again calculating the SWR at the worst case 5000 ohm load:
$${ 5000\:\Omega\:/\:4 \over 75\:\Omega } = 16.7:1$$
That's the same SWR as the 300 ohm ladder-line. If the coax and ladder-line have equal matched loss, their total losses will be the same also.
A balun with a higher transformation ratio will reduce the SWR further, and losses with it. If the antenna impedance could be anywhere between 72 and 5000 ohms depending on operating frequency, then the best "compromise" feedline impedance is:
$$\sqrt{5000\:\Omega \cdot 72\:\Omega} = 600\:\Omega$$
This gives a worst-case SWR at the extremes of high and low antenna impedance of:
$${600\:\Omega \over 72\:\Omega} = {5000\:\Omega \over 600\:\Omega} = 8.3:1$$
Not such a horrible SWR. This could be realized with:
• 600 ohm ladder-line, or
• 300 ohm ladder-line and a 2:1 balun, or
• 75 ohm coax and an 8:1 balun, or
• 50 ohm coax and a 12:1 balun.
So, in summary:
• Ladder line is not necessarily lower loss, but it does have a higher characteristic impedance.
• Non-resonant antennas tend to have higher feedpoint impedances.
• With an impedance transforming balun, coax can have the same SWR as ladder-line.
• also not that ladder/twin-lead can easily be made to have a large range of impedances by varying the spacing between the leads, or the diameter of the leads. On the other hand, ladder is usually unsuitable for higher frequencies (if in doubt, if it's > 300 MHz, don't), since the wavelength needs to be large compared to the distance between the leads. You can see that in network cabling: twisted pair, as far as I interpret it, is a 125 MHz (and maybe the 3·f harmonic of the ideal square wave) transmission line, and that works well enough for Gigabit Ethernet to with limited equalizing; – Marcus Müller Aug 9 '17 at 22:23
• for 10 Gigabit Ethernet, it took a while until 802.3an (i.e. 10GBase-T over twisted pair) actually was implemented commercially, and 10GBASE is still mostly done using optical or Twinax direct connect cables. And that with a bandwidth of 400 MHz + sidebands! – Marcus Müller Aug 9 '17 at 22:25
• @MarcusMüller "the wavelength needs to be large compared to the distance between the leads" and specifically it's hard to make ladder line that has a consistent spacing at a smaller scale, yes? – Kevin Reid AG6YO Aug 9 '17 at 23:28
• – Phil Frost - W8II Aug 9 '17 at 23:48
• Just to add something to this that really helped me to understand it: The impedance at the antenna is not present at the input of the feedline. Say your worst-case impedance of your coat hanger antenna is 5000 ohms, at the input of the feedline you will have an impedance different from the characteristical impedance of the coax that depens on the load and length of the line, say 500 ohms (theres a formula for this). The tuner now matches to this impedance. There is however still a mismatch between the line and the antenna. With high-loss coax this will "eat" your output power. – GeeF Sep 25 '18 at 17:13 | 2020-06-04 14:52:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6951402425765991, "perplexity": 2499.8888167198916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347441088.63/warc/CC-MAIN-20200604125947-20200604155947-00315.warc.gz"} |
https://sctyner.me/publication/pattern-trees/ | Non-Contiguous Pattern Avoidance in Binary Trees
Two sequences generated from avoiding 5-leaf trees.
Abstract
In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare these results to analogous work for contiguous tree patterns. Next, we give an explicit generating function that counts binary trees avoiding a single non-contiguous tree pattern according to number of leaves and show that there is exactly one Wilf class of $k$-leaf tree patterns for any positive integer $k$. In addition, we give a bijection between between certain sets of pattern-avoiding trees and sets of pattern-avoiding permutations. Finally, we enumerate binary trees that simultaneously avoid more than one tree pattern.
Type
Publication
Electronic Journal of Combinatorics | 2021-01-27 02:44:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38563019037246704, "perplexity": 630.4690937128233}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704820894.84/warc/CC-MAIN-20210127024104-20210127054104-00217.warc.gz"} |
https://forum.allaboutcircuits.com/threads/how-to-describe-delta-convolution-using-integral-expression.178376/ | how to describe delta convolution using integral expression
yef smith
Joined Aug 2, 2020
374
Hello, We express the radiation from a source by the expression bellow:
$U(x,y)=\frac{e^{jkz}e^{\frac{k}{2z}(x^2+y^2)}}{j\lambda z}\iint_{-\infty}^{+\infty}u(x',y')e^{-j\frac{2\pi}{\lambda z}(x'x+y'y)}dx'dy'$ the fourier transform is $f_x=\frac{x}{\lambda z}$ and $f_y=\frac{y}{\lambda z}.\$
Our system bellow has two apartures which has distance between them.
each aparture has fourier transform of sinc $F(rect(ax)rect(by))=\frac{1}{|ab|}sinc(\frac{f_x}{a})sinc(\frac{f_y}{b})$
$F(\delta(f_x-\frac{a}{2},f_y-\frac{b}{2}))=e^{[i\pi(ax+by)]}$
I know that convolution with delta is a shift in space.
how to find using the integral expression shown above the fourier transform of the shape bellow?
Thanks.
Last edited: | 2022-09-29 20:22:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9600136876106262, "perplexity": 1563.9936255928694}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335365.63/warc/CC-MAIN-20220929194230-20220929224230-00555.warc.gz"} |
https://guitarempire.com/electric-guitar-amps-ebay-easy-well-known-electric-guitar-songs.html | Ate you guys just starting, or just bored? Curious is all, its seems that the ?s and statements alike are from beginners, which all of us started out with, there are many pro sites that will give you better advice. Advice at least boogie gave good support. Another thing is always wipe your strings down Everytime you finish playing. The slinky's are easy to play but rust very quickly and lose tone. GHS has a decent set of steings, but it's like anything else you get what you pay for. Come on guys ur talking about strings that are $4. Two more guitars were introduced in 2008. Gibson USA issued the Slash Signature Les Paul Goldtop, modeled after a 1991 Gibson Les Paul Goldtop that was stolen from Slash’s collection in 1999 and never recovered.[37] It features a mahogany body and a hand-carved maple top with Gibson’s classic Bullion Gold finish. Production was limited to 1000.[38] Epiphone introduced a more affordable version of the Gibson model, featuring a traditional Les Paul body with a maple top, a mahogany neck with rosewood fingerboard, and Epiphone’s classic Goldtop finish. Production was limited to 2000.[39] An equalizer adjusts the frequency response in a number of different frequency bands. A graphic equalizer (or "graphic EQ") provides slider controls for a number of frequency region. Each of these bands has a fixed width (Q) and a fixed center-frequency, and as such, the slider changes only the level of the frequency band. The tone controls on guitars, guitar amps, and most pedals are similarly fixed-Q and fixed-frequency, but unlike a graphic EQ, rotary controls are used rather than sliders. Get a ruler (or straightedge if you want to be all fancy) that is at least as long as the neck, but not so long that it reaches all the way from the nut to the saddles (and watch it doesn’t lean on the pickups or pickup surrounds either). If you can’t get one between these lengths, and are willing to sacrifice a ruler, get one that’s too long and cut it to length. Alternatively, you can just cut a little out of one edge so that you can still make full use of the other edge of the ruler. Now lay the edge of the ruler along the frets (don’t rest it on top of the nut, saddles, pickups or pickup surrounds). {"reportSuiteIds":"guitarcenterprod","pageName":"[gc] product comparison","prop2":"[gc] product comparison","prop1":"[gc] product comparison","prop5":"[gc] product comparison","prop6":"[gc] product comparison","prop3":"[gc] product comparison","evar51":"default: united states","prop4":"[gc] product comparison","channel":"[gc] product comparison","linkInternalFilters":"javascript:,guitarcenter.com"} Like many engineers, I learned the basics of recording guitars by doing live sound and occasional session work. But my "higher education" began when I was hired by a blues/R&B-oriented mail-order record company, and I "had" to listen all day long to recordings from the '40s, '50s, and '60s. No matter how primitive or poor the recording quality on those old discs, I was constantly amazed by the array of exciting sounds produced by electric guitar. Later, when I started recording blues sessions in my own studio, I learned firsthand about the key elements that contributed to the great tones that I'd heard on those classic recordings. I have a Montclair guitar, it sounds like I have an original but I have some questions. I purcahsed this quitar about 40 years ago. It is a dark brown archtop, with two cutaways and a pick guard like in the picture. On the top of neck the only says Montclair, strait across, and on the back it says "steel reinforced neck". On the inside the only number is L 6089. Gibson’s electric guitars generally sport humbucker pickups, known for their thicker, rounder tone. You also get less feedback, which limits the types of delay and overdrive tones you can experiment with, but ensures a cleaner and more consistent sound. Gibson mainly uses mahogany for their guitar bodies, which is what gives it that slightly darker sound. I started out doing pretty much what I do now on an acoustic and transferred it to electric when I was able to get a paper route and buy a crappy red electric guitar. I knew the value of working stripped down and I still do, although in this day and age I've made a lot of records with different sounds. I must say I really love what technology can afford you. As an aside, people talk about “gold foil” like it’s some sort of rare mineral! I see auctions all the time dropping words like “GOLD FOIL” pickups, and “As played by Ry Cooder!!!” So far, I’ve identified 12 different kinds of pickups that had gold foil somewhere on them, and many of them are made differently! What’s the point? Don’t buy the hype!! You have to play these guitars, or check out our videos to get an idea pertaining to sound. Poor Ry Cooder gets attached to every darn gold foiled guitar ever made, geesh! And I don’t even know who Ry Cooder is! The best ones are the ones that sound good to YOU and inspire YOU to play better, no matter how old they are, what’s in them or how many features they do or don't have. It follows that there are thousands of possible “best” amps from any number of brands, from old to brand new, that can fit this description. You just have to find the right one that fits your particular needs. Brand names don't matter so much as features here, so that’s why I'm not going to mention them specifically. The remaining ’62 Teisco laps had a sort of paddle shape to the body, with sides wider than the fingerboard all the way up to the asymmetrical head with the circle Swan logo. The EG-A and EG-S had short scales and black fingerboards with the diamond markers, while the EG-U and EG-L had longer scales with fingerboards angled toward the bass side at the pickup. The EG-U had a light fingerboard with split-parallelogram markers, whereas the EG-L had a dark ‘board with dots. All were six-strings with one black-covered pickup and a little plate with volume and tone controls. Tuners mounted from behind the head as on a Spanish guitar. #### Most Martin guitars made are "flat top" models. That is, they have a round sound hole in approximately the center of the flat top of the guitar, with a "pin" style bridge. Martin also made some archtop models during the 1930s. These can have a round sound hole, or two "f" style sound holes (one on each side of the top of the body), and have an arched top, with a "trapeze" style bridge. Martin also made ukuleles. If a guitar only has four strings (and is not a ukulele), this is known as a Tenor guitar. Uke size instruments with ten string are Tiples. Uke size instruments with eight strings are Taropatches. Martin also made mandolins, which have eight strings. To summarize: For the last tip/technique, I’m going to shift gears and talk about recording acoustic—upright—bass. This may seem more daunting, but many of the same techniques apply—I’ll mention a few quick items that would be specific to the big box. While the dynamic mics I mentioned above might work fine (especially on stage), a good large-diaphragm condenser would be appropriate in the studio, to capture the high end and air of the acoustic instrument as well as the lows. On stage, the relatively low acoustic volume of the instrument may preclude more distant mic positioning, but you can wedge a small (pencil-type) mic into the bridge, with appropriate foam padding, and this, surprisingly, can often provide excellent sound and much better isolation. An open tuning allows a chord to be played by strumming the strings when "open", or while fretting no strings. The base chord consists of at least three notes and may include all the strings or a subset. The tuning is named for the base chord when played open, typically a major triad, and each major-triad can be played by barring exactly one fret.[60] Open tunings are common in blues and folk music,[59] and they are used in the playing of slide and lap-slide ("Hawaiian") guitars.[60][61] Ry Cooder uses open tunings when he plays slide guitar.[59] Portable speaker chambers represent another viable solution. These units are thick, reinforced wooden boxes outfitted with both interior and exterior insulation, housing a built-in speaker and an adjustable microphone stand, along with speaker and microphone cable connectors. Think of a miniature portable iso-booth. They're used professionally in the studio and on stage, preventing unwanted leakage and greatly diminishing stage noise, with excellent results. ### There have been several changes in the amplifier world since we last took a look at this mega amp article, spurring us to refresh a lot of content. We have replaced some models in our top ten chart, such as the Bugera Trirec and the Vox AV15, with a host of new additions. These include classic combos like the Fender Champion 100 and the Vox AC15C2, with some awesome heads such as the EVH 5150III and the Boss Katana, as well as the super portable Roland Cube Street. While there are some obvious quality gaps, they do appear to be closing as time passes on. The hardware used on Epiphone is getting better, and the presence of the new ProBucker Pickups helps to elevate the brand to new heights. The fact of the matter is, while Epiphone is viewed as just being a cost friendly alternative to Gibson, guitar players gravitate to the brand anyways for its own special sound. While it may use the same Specs as a Gibson, they are far from equal guitars, including in the sound department (4). Read Full Review If you’re looking for a lightweight guitar aside from a Stratocaster. You prefer the quality of tone produced using humbuckers than a single-coil can deliver. This SG model from Epiphone meets that requirements on the overall sound, playabilty and price that fits the under two hundred dollar budget of a beginner. As well as for seasoned players looking at the market for an affordable studio or back-up guitar to bring on stage. Cutting the RATE and DEPTH knobs too high will cause the effect to sound thick and chaotic. This is more so an attribute of the chorus effect in general and not a knock on the pedal itself. With that in mind, we would advise taking Roland's "formal" settings suggestions (pictured below) with a grain of salt, as long as you're using the CH-1 with an acoustic guitar. In most cases, we found that the pedal performed best on the lower settings, particularly with the RATE and E.LEVEL knobs cut before 12 o'clock. We've had a thread here in the last couple months about Squires, with some pretty discerning forum members praising their quality and tone. You don't need to spend a lot of money these days for a good guitar. The one the OP bought was years ago. The fierce competition in the guitar market since the economy went bad, has forced manufacturers to up their game, and recent production is of a much higher standard. Launch price:$2,099 / £2,499 | Body: Ash | Neck: Roasted maple | Scale: 25.5" | Fingerboard: Roasted maple | Frets: 22 | Pickups: Music Man SH single coil, Music Man SH humbucker | Controls: Volume, tone, 3-way selector switch | Hardware: Music Man Modern hardtail bridge, Schaller M6-IND locking tuners | Left-handed: | Finish: Trans Buttermilk, Trans Black, Trans Maroon, Satin Natural
Frets are the metal strips (usually nickel alloy or stainless steel) embedded along the fingerboard and placed at points that divide the length of string mathematically. The strings' vibrating length is determined when the strings are pressed down behind the frets. Each fret produces a different pitch and each pitch spaced a half-step apart on the 12 tone scale. The ratio of the widths of two consecutive frets is the twelfth root of two ( {\displaystyle {\sqrt[{12}]{2}}} ), whose numeric value is about 1.059463. The twelfth fret divides the string in two exact halves and the 24th fret (if present) divides the string in half yet again. Every twelve frets represents one octave. This arrangement of frets results in equal tempered tuning.
I have a Les Paul Gold Top copy I bought new in the mid 70's. It has no brand name anywhere on it. I have done all the research I can and have found no conclusive results.I'm at a loss. It plays great! I do have pics. if that will help. Thanks for any help' It was bought in Montgomery Al. Clarence Carter's guitar player bought one while I was in the store so I figured ...must be a okay guitar. So I bought it. On the little square plate on the back it is hand engraved #0059. Thanks
Music Go Round® is a registered trademark of Winmark Corporation based in Minneapolis, MN. Each franchise is independently owned and operated. Other brand names are trademarked or registered by their respective companies. The trademarks and logos used in this website are owned by Winmark Corporation® and any unauthorized use of these trademarks by others is subject to action under federal and state trademark laws.
In regards to which is best I personally think you pretty much got it right! Folks can piss n moan all they want but the facts are facts. Gibson, Fender, PRS ect all make fantastic guitars, time-tested tools of the trade. Many of you feel the need to want to publicly put down a certain brand in favor of another, there's good n bad in all of them!! If I could afford a Gibson Les Paul I would get one! Sure I could pull out the plastic n get one but I don't wanna have to do that just yet. I have no shame in purchasing a cheap guitar as long as I like it, to me if a guitar has a good smooth fast neck ......... it's a good guitar!! You can always swap pups n hardware but the neck is a little more complicated. I have a Fender Squire Strat, it is an "E" series Squire, I think it was made from 1984-87, and I can tell you that I will be 50 years old in May of this year and the neck on this Squire is the best I have ever felt on any guitar I have owned!! and yes it was a fairly cheap guitar. Now I hear that the "E" series of Squire Strats are supposed to be highly sought after or something, I don't know all about that, all I know is that I love the way this guitar plays n feels in my hands n riding in front of my belly! So folks don't put a guitar down simply because you can't afford it, like I said they are good guitars for a reason, same goes for the cheap guitars, don't knock 'em 'til you try 'em, there are some mighty good players out there to be had for cheap $, bottom line ..... regardless of the name on the head ..... if you can afford it, if it feels n looks the way you like n has a good neck then buy it n give it the love it deserves, it'll love you back in ways you never imagined!! Happy pickin n God bless While it can be a troubling task to find the perfect electric guitar to bring out your inner rock star, we hope that our electric guitar reviews & our comprehensive guide has helped you narrow down your choices. Our best piece of advice is to determine the type of genre you’re interested in playing. That will be a good basepoint for you to work from in order to determine the best electric guitar that fits your needs. Afterward, it is important to select the guitar that has the best components to give you the highest quality of sound. The color does not matter too much but the next most important factor to think about is certainly the wood type used to build the electric guitar. Picking the right type of wood is going to more or less, create better or worse sound. The Yamaha APXT2 is a 3/4 size version of the world's best-selling acoustic-electric guitar, the APX500III. This well-constructed, compact guitar makes a great companion when you're on the road. The APXT2 features an ART-based pickup system and Yamaha's proprietary tuner, offering great sensitivity and accuracy for quick tuning. The APX T2 also includes a gig bag. This is the first, and quite possibly the best reason to invest in a good miniature guitar amp. It will allow you to play with a tone that’s enjoyable at a volume that won’t get you kicked out by your condo board. Even if you live out in the middle of nowhere, and can blast your Dual Rectifier full stack as loudly as you’d like, you still have to take the feelings of those you live with into account. Few marriages remain happy when a loud instrument is in the mix. That’s also why a mini amp is a great gift for a young student guitarist. You won’t have to hear them butcher the relatively simple line from a David Bowie tune for days on end. Read Full Review It’s amazing to see a company that excels in all the products and services they offer, while other companies are struggling and scratching their heads to find a way to break through in the market. The best example of such success on Yamaha is with their long line of guitars and two of those guitars they have are considered by many is best for beginners. The guitars I’m taking about is the Pacifica Series PAC112 together with the PA012 featured here, which is also available on a guitar package. I cut my template with a jig saw and a fine tooth blade to make sure it kept a straight edge. Then i mounted it to the body blank using small screws in the ares that would be routed out later like the neck cavity area and where the pick ups would be. You will want to start routing a bit outside your line or the edge of the template so you can get you router bit to the depth it will need to be at for the ball bearing to follow the template. I use a 1/2"x1" bit with a ball bearing guide on top.I make several passes around the body, lowering the router 1/4" at a time for smooth easy cuts. Once you have made your pass were the bearing runs along side the template, it is much easier to rout and you will end up with a nice squared edge to the body. What if you don’t have a music shop nearby and need to order a guitar online? Our recommendation is that when you have read through our list of the best guitars, select a few that you’re interested in, and look them up on YouTube. There you can watch (and listen to!) great reviews where you can hear the guitar be played and get someone else’s opinion on it. Try listening to the different guitars directly after each other so you can determine which one sounds the best. It comes in 3 versions. A 15W, a 30W, and a 60W. The 60W and the 30W have 2 channels (each with the 8 analog circuits) so you can set up 2 different circuits and switch between them and 2 12AX7 tubes (pre and post). The 15W only has 1 12AX7 and 1 channel (with 8 analog circuits). I own the 60W and 15W. I use the 60W with a band and I have no problem practicing over the drums with it. The 15W I use at home for practice. Cool thing is both have headphone jack and aux in. I use the aux in at home to hook up my iPhone and practice to certain songs. The 60W has an effects loop and an external speaker out. (48 Contiguous U.S. States) Free Free Shipping With Backstage Pass 92118 2-Day Standard Ground {savingIsUpTo=false, MSRP=1377.76, listPriceRange=false, isFreeShipping=true, download=false, isPriceDrop=false, salePriceRange=false, YourSaving=0.0, productId=site1prodH91419, MSRPRange=false, enablePDPColorOption=true, showBrandNameWithProduct=true, usedAmount=799.99, priceVisibility=1, listPrice=999.99, usedCount=3, salePrice=999.99, isOnSale=false, showMSRP=true} These acrobatic guitarists used humbucking pickups and the more aggressive Floyd Rose style tremolo bridge to create the hard rock edge that began to be defined in the late 70’s and 80’s more technical playing styles. These instruments now include much higher output and even active electronic pickups, and their recessed cavities to allow the tremolo bridges to make the distinctive “dive bomb” effects that Van Halen made famous in his solo “Eruption.” Other distinct features include thinner necks and larger frets with flatter fret boards that many technical players prefer for their flashier techniques. Launch price:$299 / £199 | Body: Alder | Neck: Maple | Scale: 25.5" | Fingerboard: Rosewood | Frets: 22 | Pickups: Alnico V bridge humbucker 2x Alnico V single coils | Controls: Volume, tone (with push-pull coil-split), 5-way selector switch | Hardware: Vintage-style vibrato with block saddle | Left-handed: Yes (Pacifica 112J) | Finish: Natural Satin, Old Violin Sunburst, Raspberry Red, Sonic Blue, Black, Silver Metallic
Anytime a single coil-sized humbucker is split, a tiny coil is the one seeing the strings, so the volume is going to drop. You can split to the other coil, or set the switch to wire the pickup in parallel, which will keep it hum cancelling. However, splitting to the other coil in a neck position Cool Rails probably won’t be a big difference in sound since the coils are pretty close together and pretty small.
This type of chip delivers a beautifully coloured representation of your sound. It may not be the most accurate and you are limited in the number of repeats and delay time.These are not to be confused with Tape Echo which was used for a long time in the world’s largest studios. No, these pedals were made out of necessity to take a form of delay on the road easily.
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Classical guitars have nylon strings, which are softer than steel strings, and easier to press down. However, the neck is much wider on a classical guitar, which can be a struggle for beginners. The action is likely to be higher, as well. In general, they are softer-toned and don't project as well as a steel string acoustic, which makes for quieter practising, which could be a consideration.
Why Martin electric guitars have never been more popular isn’t too hard to figure out. Martin, whose expertise has always been in top-notch acoustics, never really put a lot of effort into marketing its electrics. They were always well made, and, especially in the necks, clearly “Martins.” In the final analysis, however, it probably comes down to being victims of the success of their acoustic brothers, and players have just never seemed to warm up to the idea of Martin “electric” guitars. For the savvy collector with a taste for quality and relative rarity, Martin electrics remain excellent and attainable prizes.
Higher-cost amps for professionals with an XLR DI out jack may also have a "ground lift" switch (to be used in case of a humming ground loop), a DI out level control knob, and a switch which determines whether the DI out signal to the PA or recording mixing board is pre- or post- the amp's internal preamplifier and equalization circuitry. The pre-/post- switch enables a bassist to decide whether to send the audio engineer just the signal from her bass, or to send the signal once it has been pre-amped and equalized by her amp settings. Some higher-cost amps may have a parametric equalizer (or a semi-parametric equalizer) for some frequency ranges (typically the middle frequency range), which can be used to modify the bass tone to suit different styles or performance venues. Some bass amps have a 15 or 20 dB pad which can be used to attenuate "hot" signals, such as basses with an internal preamplifier (depending on the model of amplifier, some brands may provide two inputs (high and low gain) instead of providing a "pad". This pad can be turned on using a button. Some bass amps have an even stronger pad, a 40 dB pad.
Then there's the issue of valves. Serious guitar players invariably prefer the sound of valve amplifiers to any form of solid-state circuitry, but the technical reasons are not as obvious as you might imagine. We all know that valves distort nicely when driven hard, but the use of output transformers also affects the sound. Then there's the choice of Class-A or Class-B (sometimes referred to as AB) power stages — Class-A stages clip asymmetrically whereas Class-B power stages tend to clip symmetrically. Even the make of valve has an effect, as do technical issues such as the choice of triode or pentode output valves, or even the types of capacitor used in the circuit. Because there are so many variables, not including the most important one (playing technique), the electric guitar is capable of a vast tonal range.
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This is a beautiful example of a 34 year old Japanese crafted Ibanez acoustic guitar that has the tone and the beauty, Love the Sunburst finish on this guitar that did a beautiful job with the thin Poly finish it stands up to the test of time and still shines like glass today just have a good look. It has a Spruce top… cant tell because of the sunburst if its solid or not but will assume its laminated…. Back – Sides & neck are all very nice grade Mahogany. Fit & finish as good as a $2000 guitar of today but this beauty has well aged woods now being well over 33 years old you could spend 3 x times the money and not get a better vintage guitar . The tone is surprisingly rich and with good volume it makes an excellent strumming or fingerpicking guitar. Its playing string action is very good making it a breeze to play and fun. The neck is real nice substantial and a medium profile with a soft V it feels like a vintage Guild from the 1960's ... nice job Ibanez!...Its in very good vintage condition too with several minor doinks to its top and a couple minor on the back and so on but overall its in very good condition both structurally & cosmetically and looks very good overall. The neck's frets are still good and fingerboard and frets have been lightly polished as has the entir guitar cleaned hydrated and polished and just look at the results, a new Martin bone nut has just been fit & installed as well as new Martin Marquis 80/20 Bronze light gauge strings, nicely setup to play very well like a much more expensive guitar now. Original tuners are doing a great job to this day some 34+ years later... Here is a very good Japanese Vintage Guitar of quality for a very good price too, She is not new or mint of course it has doinks and just a couple of fine hairline checks in its top I did not see at first its very hard to see but they are not wood cracks just fine hairlines to the finish and of no structural consequence what so ever. This guitar Plays and sounds very well and will make someone very happy its condition is JVG rated at easily 8.5/10 very good vintage, neck is straight without cracks fit and finish and workmanship are all in the excellent range. Great Japanese guitar for a great price… The 1980 Ibanez V300 TV, crafted in Japan over 33 years ago. This guitar plays GREAT! . Now if this house is rocking, don’t bother knockin. Famous words by Stevie. Many people perhaps know him for Hendrix covers, but where Jimi left off Stevie continued, and continued he did. The elements of Hendrix were alive and plain to see in SRV, but with it, he also mixed in his own influences such as Albert King and his own soul to make it his sound a trademark spot on his songs. I vaguely remember a car commercial where I spotted Stevie’s playing (Pride and Joy) in a Nissan ad. That was much before I really got into Vaughan’s work. SRV was an artist who could play while absolutely stoned face. And when he did sober up, he actually played better. His newfound health and love for life and music are showcased on In Step his last album before his death a year later. Stevie’s footprints will always be in the air and in our hearts. The first two letters of these names indicate the number of poles, while the last two letters are the number of throws. So a SPST (aka 1PST or 1P1T) means single-pole/single-throw, a SPDT (1PDT or 1P2T) means single-pole/double-throw, and DPDT (2PDT or 2P2T) means double-pole/double-throw. There are many more configurations, including 3PDT devices used for true-bypass switching in effects, and Fender’s 4PDT S-1 switch. Found on push/pull or push/push pots, the DPDT on/on switch is by far the most common, and mini toggles are available in an endless number of variations. Like most affordable super strat guitars, the Omen-6 has a basswood body, carved into the elegant looking shape that Schecter is known for. The neck is crafted from mahogany and joins the body via a bolt-on joint. It is topped by a 14" radius rosewood fingerboard that has 24 jumbo frets. It comes setup for fast and comfortable playability, with its 25.5" scale length, 1.65" nut width and stylized fretboard markers. Giving this guitar its voice are two Schecter Diamond Plus pickups, which are passive pickups but are still hot enough for driving high-gain pedals and amps. : I own a Decca guitar, it is what I learned to play on many years ago. From what little I have gathered about them they were an order by mail brand, and you could only get them from a catolog such as Sears & Roebuck. I havent been able to find a price for them or any ifo on what catalogs they were from. Mine has a Ernie Ball Musicman-like peghead (4 one side 2 on the other) and has a metal pick guard with 2 giant switches which seem to have no effect on tone. It has a brown & yellow sunburst paint job (ewwww).I thought I possibly had the only one in existence, lol, guess not. I use a coat hanger wire to hang the body and neck from when I paint. It keeps the guitar from touching any thing and makes it easier to move from one place to another. I like to dedicate one place for painting and another for drying to avoid any free floating particales from landing on the wet paint. I use a shed for painting and hang the guitar to dry in my garage. In some small to mid-size venues, such as bars and nightclubs, the PA system may not have the capacity to provide the bass sound for the venue, and the PA system may be used mainly for vocals. Bass players in bands that play at a variety of venues, including these types of small to mid-size venues, may need to be able to provide the bass sound for the venue, and so they will require a large combo amp or bass stack with this capability. At this point you should have the pots, switch, and jack out of the guitar with the pickup wires still connected. You can either de-solder the pickup wires or use wire cutters to clip them off. If you’re replacing the pickups as part of your re-wiring, you can do this now (I did not in the example photographed here). Just feed the leads of the new pickups back through the holes in the pickup cavities. This book emphasizes tabs with the accompanying music notation. It’s not a long book and one that a beginner will likely outgrow at some point. However, it provides a good introduction to get you playing songs you’ll recognize fast. It does a fine job of explaining everything the newbie needs to know including how to position yourself. Build those good habits early! Aaron Staniulis is not only a freelance live sound and recording engineer, but also an accomplished musician, singer, and songwriter. He has spent equal time on both sides of the microphone working for and playing alongside everyone from local bar cover bands to major label recording artists, in venues stretching from tens to tens of thousands of people. Having seen both sides at all levels gives him the perfect perspective for shedding light on the "Angry Sound Guy." You can find out more about what he’s up to at aaronstaniulis.com. Teisco first began importing guitars to the United States under their own brand in 1960. In 1964, the company then switched the name of their U.S. brand to Teisco Del Rey. The company was then sold in 1967, and the Teisco brand name stopped being used for guitars sold in the United States in 1969. Guitars were still sold under the Teisco name in Japan until 1977. Get a ruler (or straightedge if you want to be all fancy) that is at least as long as the neck, but not so long that it reaches all the way from the nut to the saddles (and watch it doesn’t lean on the pickups or pickup surrounds either). If you can’t get one between these lengths, and are willing to sacrifice a ruler, get one that’s too long and cut it to length. Alternatively, you can just cut a little out of one edge so that you can still make full use of the other edge of the ruler. Now lay the edge of the ruler along the frets (don’t rest it on top of the nut, saddles, pickups or pickup surrounds). Copyright © 2016 Sonoma Wire Works. All rights reserved. RiffWorks and the RW Logo, RiffWorld, RiffCaster, RiffLink, RiffRumble, InstantDrummer, StudioTrack and the StudioTrack iPad App Logo, the FourTrack iPhone App Logo, GuitarTone and the GuitarTone Logo, GuitarJack and the GuitarJack logo, DrummerPack, KitPack and Discrete Drums are trademarks of Sonoma Wire Works. DrumCore and KitCore are registered trademarks of Sonoma Wire Works. iPod, iPhone and iPad are trademarks of Apple Inc., registered in the U.S. and other countries. Android is a trademark of Google Inc. ReWire and REX2 are technologies licensed from Propellerhead Software. VST is a trademark of Steinberg Media Technologies GmbH. All other trademarks are property of their respective owners. { "thumbImageID": "Les-Paul-Standard-Left-Handed-Electric-Guitar-Ebony/518490000035000", "defaultDisplayName": "Epiphone Les Paul Standard Left-Handed Electric Guitar", "styleThumbWidth": "60", "styleThumbHeight": "60", "styleOptions": [ { "name": "Ebony", "sku": "sku:site51273888006847", "price": "529.00", "regularPrice": "529.00", "msrpPrice": "882.00", "priceVisibility": "1", "skuUrl": "/Epiphone/Les-Paul-Standard-Left-Handed-Electric-Guitar-Ebony-1273888006847.gc", "skuImageId": "Les-Paul-Standard-Left-Handed-Electric-Guitar-Ebony/518490000035000", "brandName": "Epiphone", "stickerDisplayText": "Top Seller", "stickerClass": "", "condition": "New", "priceDropPrice":"", "wasPrice": "", "priceDrop": "", "placeholder": "https://static.guitarcenter.com/img/cmn/c.gif", "assetPath": "https://media.guitarcenter.com/is/image/MMGS7/Les-Paul-Standard-Left-Handed-Electric-Guitar-Ebony/518490000035000-00-60x60.jpg", "imgAlt": "" } ] } Additionally, Gibson’s president Ted McCarty states that the Gibson Guitar Corporation merely approached Les Paul for the right to imprint the musician’s name on the headstock to increase model sales, and that in 1951, Gibson showed Paul a nearly finished instrument. McCarty also claims that design discussions with Les Paul were limited to the tailpiece and the fitting of a maple cap over the mahogany body for increased density and sustain, which Les Paul had requested reversed. However, according to Gibson Guitar, this reversal would have caused the guitar to become too heavy, and Paul’s request was refused.[12] Another switch: the original Custom was to be all mahogany and the Goldtop was to have the maple cap/mahogany body. Beyond these requests, Les Paul’s contributions to the guitar line bearing his name were stated to be cosmetic. For example, ever the showman, Paul had specified that the guitar be offered in a gold finish, not only for flashiness, but to emphasize the high quality of the Les Paul instrument, as well.[12] The later-issue Les Paul models included flame maple (tiger stripe) and “quilted” maple finishes, again in contrast to the competing Fender line’s range of car-like color finishes. Gibson was notably inconsistent with its wood choices, and some goldtops have had their finish stripped to reveal beautifully figured wood hidden underneath.[citation needed] Kasuga produced their own house brand in Kasuga guitars. For a brief period of time the company produced Yamaha acoustic guitars. Kasuga guitars were first sold in America in 1972. Unlike many Japanese manufacturers who outsourced their guitar production in other factories outside the main maker, Kasuga produced all their products in-house. Badged guitars known to have been made by Kasuga include Conrad, Emperador, ES-S, Ganson, Heerby, Hondo, Mei Mei and Roland. Kasuga went out of business in 1996. Now lets talk amps. I have always felt like you could hand me a great guitar played through a bad amp and I would get a bad tone. However, I can make a bad guitar sound decent through a good amp. The amp, in my opinion is the most crucial part of your tone. I always prefer tube amps that deliver a much warmer, natural sound then the solid state counterparts. However if you are play jazz or something that requires a clean crisp sound, a solid state amp good be great. All the great rock legends used tube amps such as Marshall Plexi’s, Vox AC30, Hi Watt, Fender Twins, Fender Bassmans etc. Now days they make all kinds of boutique amps that are modeled after these classic amps. Matchless is my amp of choice which is loosely modeled after the Vox AC30. The Continental and other Vox organs such as the Jaguar, the Continental II, Super Continental, and the Continental 300 share characteristic visual features including orange and black vinyl coverings, stands made of chromed steel tubing, and reversed black and white keys. The English wood key single manual Continental (V301J) is increasingly collectable, although the wood key American-built (V301H) and plastic key Italian-built models (V301E, V301E/2 and V302E) also command premium prices. Jennings sold production rights for the Vox Continental organ to an Italian subsidiary of Thomas Organ in 1967. Under the new production agreement, the Continental was gradually and subtly altered in quality and sound, and reliability became questionable. For example, Ray Manzarek of The Doors had been using a Vox since 1966, but could no longer trust it during performances because of the problems in quality after 1967, and thus was forced to look elsewhere for an organ. He settled on the Gibson Kalamazoo, because it had a flat top like the Vox Continental, so it could accommodate the physical requirements of the Fender Rhodes Piano Bass, which was the bass instrument for The Doors in concert. Since digital effects use DSP, manufacturers have made the most of the processing power by adding amp modeling features. To the point that amp modeling has become a standard feature, and has even overtaken effects in popularity. If you already have a good amplifier, then amp modeling is not important, but it's still a good addition for the extra versatility amp modeling provides. This diagram shows 3 single coils wired in parallel, allowing seven tone choices. The typical 3 single coil guitar contains a 5 way rotary switch which allows you to get 5 sounds - each single coil; neck and middle in parallel and middle and bridge in parallel. This modification will give you 2 more sounds - all 3 pickups in parallel and Neck and Bridge in parallel. Rule 4 - The technology further defines the order. Let's give a couple examples here. If you don't use your noise gate before your compressor, you'll increase the volume of your noise which renders your noise gate useless. If you send an impure signal like heavy distortion to a harmonizer, the harmonizer will be very inaccurate, thus you want to apply distortion to the harmonized signal and not the other way around. If you compress before using equalization, the compressor may act on frequencies you don't intend to keep in the signal, thus you should EQ first. To create a thicker rhythm guitar sound, overdub the same part one or more times. Depending on the desired effect, the overdub can be treated as one mono signal and mixed to the same stereo position, or panned left and right for a stereo double-tracked sound. Alternatively, treat the original track with an ADT (Artificial Double Tracking) effect. This can be done with a digital delay set to around 40 milliseconds. Again, the delayed signal can be panned or mixed as one with the original guitar track. I play in cover bands. Own large collection of pedals, some I love, some stink. Then I found out that the only people that care about the effects are other musicians. The people( girls dancing mostly) could care less. So now I got a tuner, and drive pedal for solo tone....that's it, and my tone is awesome and hassle free. For studio cats it may be a different story. The Ultimate Beginners Series gets aspiring musicians started immediately with classic rock and blues riffs, chord patterns and more. Now, for the first time ever, Basics, Blues, and Rock are combined in one complete book and DVD set. Follow along with 4 hours of DVD instruction and 3 hours of audio tracks, with the help of on-screen graphics and printed diagrams. The Ultimate Beginners Series: Electric Guitar Complete takes you from picking to soloing and power chords. If you're serious about mastering the blues and rock styles, this book and DVD set is a must-have. Students and expert alike describe this guitar as a fun instrument, and goes further by commenting that it has exceeded their expectations. From its fast action playability to the quality of the finish, the Epiphone SGSpecial continues to rake in compliments. Several people even said that it comes surprisingly close to the feel and sound of a Gibson SG. Whether you are a guitarist looking for new tones, or a sound designer looking for new ways to mangle your audio, virtual guitar amps and effects are a great way to achieve new sounds and enhance your productions. There are many great guitar amp and pedal effects plug-ins available on the market today to purchase, but there are also numerous effects that are available for free. In this article I'll offer up some professional guitar effect plug-ins from around the internet that you can use on your next project, completely for free. {"eVar4":"shop: accessories","eVar5":"shop: accessories: fretted instrument accessories and parts","pageName":"[mf] shop: accessories: fretted instrument accessories and parts: fretted instrument parts: bridges and tailpieces: bridges and tailpieces for guitars","reportSuiteIds":"musiciansfriendprod","eVar3":"shop","prop18":"skucondition|0||historicalgrossprofit|1||hasimage|1||creationdate|1","prop2":"[mf] shop: accessories: fretted instrument accessories and parts","prop1":"[mf] shop: accessories","prop17":"sort by","evar51":"default: united states","prop10":"category","prop11":"bridges & tailpieces for guitars","prop5":"[mf] shop: accessories: fretted instrument accessories and parts: fretted instrument parts: bridges and tailpieces: bridges and tailpieces for guitars","prop6":"[mf] shop: accessories: fretted instrument accessories and parts: fretted instrument parts: bridges and tailpieces: bridges and tailpieces for guitars","prop3":"[mf] shop: accessories: fretted instrument accessories and parts: fretted instrument parts","prop4":"[mf] shop: accessories: fretted instrument accessories and parts: fretted instrument parts: bridges and tailpieces","channel":"[mf] shop","linkInternalFilters":"javascript:,musiciansfriend.com","prop7":"[mf] sub category4"} Around ’77 or so (since the new shape was similar to the Magnum basses), with sales embarrassingly bad, Ovation took some Deacon bodies and added new contours, carving a dip into the top curve and adding angles. It didn’t help. The Breadwinner was officially axed in ’79, with the Breadwinner loosing its head in ’80, although the market had long passed them by. THE VOTERS: Trey Anastasio, Dan Auerbach (The Black Keys), Brian Bell (Weezer), Ritchie Blackmore (Deep Purple), Carl Broemel (My Morning Jacket), James Burton, Jerry Cantrell (Alice in Chains), Gary Clark Jr., Billy Corgan, Steve Cropper, Dave Davies (The Kinks), Anthony DeCurtis (Contributing editor, Rolling Stone), Tom DeLonge (Blink-182), Rick Derringer, Luther Dickinson (North Mississippi Allstars), Elliot Easton (The Cars), Melissa Etheridge, Don Felder (The Eagles), David Fricke (Senior writer, Rolling Stone), Peter Guralnick (Author), Kirk Hammett (Metallica), Albert Hammond Jr. (The Strokes), Warren Haynes (The Allman Brothers Band), Brian Hiatt (Senior writer, Rolling Stone), David Hidalgo (Los Lobos), Jim James (My Morning Jacket), Lenny Kravitz, Robby Krieger (The Doors), Jon Landau (Manager), Alex Lifeson (Rush), Nils Lofgren (The E Street Band), Mick Mars (Mötley Crüe), Doug Martsch (Built to Spill), J Mascis (Dinosaur Jr.), Brian May, Mike McCready (Pearl Jam), Roger McGuinn (The Byrds), Scotty Moore, Thurston Moore (Sonic Youth), Tom Morello, Dave Mustaine (Megadeth), Brendan O’Brien (Producer), Joe Perry, Vernon Reid (Living Colour), Robbie Robertson, Rich Robinson (The Black Crowes), Carlos Santana, Kenny Wayne Shepherd, Marnie Stern, Stephen Stills, Andy Summers, Mick Taylor, Susan Tedeschi, Vieux Farka Touré, Derek Trucks, Eddie Van Halen, Joe Walsh, Nancy Wilson (Heart) Most[citation needed] early blues harmonica players throughout the 20th century[when?] have been known for using Hohner Marine Band harmonicas[citation needed] because they were the most available at the time[citation needed]. However, as other harmonica companies[who?] began to expand and Hohner produced different types of harmonicas, harmonica players started to develop preferences[vague]. ##### Here we have a very nice example of the Yamaha Red Label fg230-12... This example is in very good - excellent original condition. The woods used on this guitar are of a very high grade ... spruce top, Honduran Mahogany back, sides and neck please see pics for the details but very nicely grained woods!... workmanship is impeccable... the guitar plays like a real with very good action and the intonation is set dead on... The neck is solid Mahogany and is slightly beefy..I love the feel of this guitar and when you hear is you will be in 12 string heaven... no cracks or repairs ... the condition is vintage used its about 40+ years old you know ...with several minimal scratches but still overall a very beautiful vintage guitar. The wood has aged and mellowed with time to yield a wonderful rich tone only a 30+ year old quality instrument can offer. This one has that quaity rich sound along with the playability with the right aging now and with its beauty ...its a no brainier... Also available is a cool$100 vintage hard shell case see pics Thanks for your interest!.
Franklin Guitar And Repair was started in this space to sell on Ebay By David Wood and Josh Pewitt! before They knew it...there were enough guitars to open a store! David had been a road musician for nearly 20 years, and along the way he learned to set up instruments and do repairs himself. Franklin Guitar and Repair has grown in many ways, purchased by Pat Stockdale in 2016 and still maintaining quality work, and a mom & pop homey kind of atmosphere.
This guitar is perfect no matter if you’re a beginner or have been playing for many years. The design is vintage at its best, with a lovely soft V-shaped neck and great colors, namely Surf Green, Daphne Blue and Fiesta Red. This guitar has a very traditional look that most people like. True, some people would feel that it’s a little bit too mainstream, but others would reason that hey, if it’s good enough for everybody else, it’s good enough for me!
Combo amps come with a speaker built into the amplifier cabinet, making them heavier but more convenient. On the other hand, amp heads are lighter because they don't come with a speaker built-in. The amp head configuration allows you to freely choose the type of speaker and speaker cabinet that you prefer, with the complication of ensuring amp and speaker compatibility. Interestingly, there are now some amplifier heads that com come with built-in speakers that are only good for practice, making them technically a combo amp, but that's another story in itself.
Congratulations on buying yourself a top-notch axe — but you’re not ready to shred just yet. A good guitar also requires the right amp to achieve the right sound. Amps can be a daunting purchase (you certainly won’t be starved for choices on the beginner and enthusiast side of the price spectrum) and there are a lot of qualities that need to be taken into account. Want a low-cost amp that’s durable? Shoot for a solid-state amp. Want better sound? We suggest an all-tube amp instead. Want the most tonal variety on a budget? A modeling amp will get you all kinds of sounds without requiring a fleshed-out pedal board. But at any rate, no matter what you’re looking for in an amplifier, these 10 picks cover all the fundamental bases. So purchase, plug in and let’s rip.
The Ibanez Gio GRGM21 Mikro in Black Night proves that guitars don’t have to be super expensive to sound great. This is a fantastic cheap electric guitar that doesn’t suck, often picked up by beginner guitarists who are into metal and hard rock and those who like a shorter scale guitar. Featuring an iconic shape, a specially designed GRG neck made of maple, rosewood fretboard and 2 x Infinity R humbucker pickups that can be used separately or in unison via the 3-way pickup selector, you have a comfortable and great sounding powerhouse of a guitar at your disposal. It’s one of our favourite cheap electric guitars that sounds amazing when you throw some distortion at it! Available in different finishes here.
Jump up ^ The Guitar (From The Renaissance To The Present Day) by Harvey Turnbull (Third Impression 1978) - Publisher: Batsford (ISBN 0-7134-3251-9) - p113 (Chapter 3 - The Twentieth Century) - "Segovia's visits to South America also inspired new music. The Mexican composer Manuel Ponce (1882–1948) responded by producing a greater number of extended works than Turina and Torroba had achieved."
Once again a British company. It isn't hard for this brand to attract attention thanks to the (would you believe it?!) orange color that envelops most of their products. The first models saw the light of day in the late 1960's with the OR series. Its first renowned users were Fleetwood Mac and later Jimmy Page... The crunch sound and the mid-frequency range are the brand's main attributes. Orange even managed to outclass Marshall in the 1970's thanks to its prestigious endorsers. In the 90's, Noel Gallagher from Oasis was the best-known Orange fan and he even collaborated in the development of the OTR head. At the start of 2011, the brand surprised everyone and launched the OPC, a workstation for musicians — actually a PC and a guitar amp in a single unit.
I am a guitar player, teacher and composer. I started playing piano at the age of seven. Five years later I had my first guitar performance with a local band. My style was inspired by guitarists like Nuno Bettencourt, Joe Satriani, Jerry Cantrell, Marty Friedman, Zakk Wylde, Steve Vai and Dimebag Darrell. During my career I had many bands and music project, going through different styles of original music and sometimes cover bands. In 2012 co-founded the band Vulgar Bulgar (Pantera tribute band). In 2013 started teaching guitar at Rockschool.bg. Currently freelance guitar teacher, session musician and solo performing artist.
Guitar-Sunbeam : Precisely transmits the eternal electric guitar, ideally suited for modern production. It combines an extensive library of strum patterns, brute force, arpeggios and real riffs with real-time performance monitoring. An innovative playback engine allows you to create an almost infinite number of variations of chords and you get convincing, musical results.
Overdrive originally resulted from the natural breakup that occurred when a tube amp received an overly hot signal from a guitar. This pushed the tubes to deliver a subtle, warm breakup. Generally overdrive is a more subdued, natural form of distortion. While you don’t have to use an overdrive effect with a tube amp to get a great sound, the combination of the two can produce a rich, pleasing tone that many guitarists prefer. The first overdrive effects were designed to push more signal into a tube amp, giving it the very throaty, mid-range tone associated with Stevie Ray Vaughan. With that in mind, many of today's pedal makers have created circuitry to add that desired tone when used with a solid state amps as well. Since overdrive is a signal boost, adjustments from your volume knob will create a variety of different sounds.
Bottom Line: The Boss ME-80 seems to be aimed at the beginner and intermediate guitarist who is getting into the effects game. What guitarists love about it is that it tries hard (and succeeds) at replicating the feel of messing with a pedalboard full of effects. Unlike the Line 6 POD HD500X, you won’t need the manual! We’re not necessarily taking a dig at the Line 6 pedal - that one very much has its merits, is FAR more customizable and editable, and arguably the effects and amp modeling sound a bit better. The Boss ME-80 is just a different style, and judging by the user reviews we read people really enjoy having all the knobs for all the effects immediately available. The Boss ME-80 is also a tremendous bargain considering how powerful it is. Sure, it’s not exactly cheap, but it’s a very well-made, intuitive, nice-sounding all-in-one multi-effects pedal which is great for practice, studio recording, and live use.
TAB uses a series of hyphens to represent the strings. Each string is identified on the far left by the name of the note produced when played open. The high-e (string 1) is at the top; low-E (string 6) is at the bottom. There is no restriction for how long a line of TAB can be, but for readability it should be kept short enough to prevent wrapping on a web-site or printed page.
But this was different. This was build quality, and it completely wrecked the sound, feel and playability of the guitar. A competent pre-shipment QC inspection should have caught this and sent it back to be fixed at the factory, and they didn't. No serious guitarist would stand for ANY guitar made this way, at ANY price point. Yet there it was, on display on a guitar positioned as the flagship model of the brand, occupying the most expensive price point in the market.
I've met and talked to Andrew as his shop is 20 minutes from me. When you talk guitars to Andrew, you will get the feeling that this man knows his guitar building. He strives for perfection in his small WV workshop. There is plenty of evidence seeing some of his production models hanging on display. His quiet voice belies his guitar building abilities. As a luthier, his personal hand made guitars command a big price tag. But when you understand how he builds them, you'll understand why. One day, I'll own one his creations from his workshop. But until then, I'll just drool over the pictures. Not sure why his production models are rated at 42 though.
The Strat didn’t just sound different, its aesthetics and ergonomics were totally unique and innovative for its time. Instead of a standard slab body, the Stratocaster had double cutaways and was contoured in a way that had never been seen on a solid-body guitar. Originally built for legendary western-swing musician Bill Carson, it was quickly adopted by rock ’n’ roll pioneers like Buddy Holly and Hank Marvin, and has been the tone behind countless Top 40 hits.
Valve Amp or Solid State Amp? There's no right or wrong here, but, for tone alone, valve amps are way better. If you can afford a valve amp, just go ahead and buy one! They're the amps all the great bands ever used - from Beatles and Rolling Stones to Arctic Monkeys and Radiohead, 99% of all professional musicians simply prefer valve amps, like the Vox AC30 or Fender Hot Rod Deluxe III. But there's nothing wrong with solid state amps - the audience at a gig wouldn't be able to tell the difference.
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Shecter is known for manufacturing quality rock and metal friendly guitars at reasonable price points, and I think that they use evil model names to keep their instruments from the hands of pop and ballad players. The Hellraiser C-1 FR-S showcases what this company can give metal players in the mid-tier price point, and with its name, it is obviously not meant for choirs and church music.
This can all get a little tricky and can become overwhelming especially if you have never tackled this type of job before. If this is the case, I strongly suggest starting with one of the easier models in regards to wiring e.g. Telecasters are significantly easier to work on as the scratchplate will often be pre-loaded with pickups. However, if you purchase a kit guitar such as an LP or you want to upgrade your electrical components (which is often the case with an entry level kit) understanding some basics about guitar electronics is useful.
Aside from possible engineering advantages, some feel that in relation to the rising cost of rare tonewoods, man-made materials may be economically preferable and more ecologically sensitive. However, wood remains popular in production instruments, though sometimes in conjunction with new materials. Vigier guitars, for example, use a wooden neck reinforced by embedding a light, carbon fiber rod in place of the usual heavier steel bar or adjustable steel truss rod. After-market necks made entirely from carbon fiber fit existing bolt-on instruments. Few, if any, extensive formal investigations have been widely published that confirm or refute claims over the effects of different woods or materials on electric guitar sound. | 2019-06-20 11:14:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1983342468738556, "perplexity": 5143.461814424076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999210.22/warc/CC-MAIN-20190620105329-20190620131329-00375.warc.gz"} |
http://www.tjsullivan.org.uk/index.html?page=5 | # Tim Sullivan
Junior Professor in Applied Mathematics:
Risk and Uncertainty Quantification
### Preprint: Probabilistic meshless methods for PDEs and BIPs
Jon Cockayne, Chris Oates, Mark Girolami and I have just uploaded a preprint of our latest paper, “Probabilistic meshless methods for partial differential equations and Bayesian inverse problems” to the arXiv. This paper forms part of the push for probabilistic numerics in scientific computing.
Abstract. This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse problems while accounting, in a rigorous way, for the impact of the discretisation of the forward problem. In particular, this confers robustness to failure of meshless methods, with statistical inferences driven to be more conservative in the presence of significant solver error. In addition, (i) a principled learning-theoretic approach to minimise the impact of solver error is developed, and (ii) the challenging setting of inverse problems with a non-linear forward model is considered. The method is applied to parameter inference problems in which non-negligible solver error must be accounted for in order to draw valid statistical conclusions.
Published on Thursday 26 May 2016 at 09:00 UTC #publication #preprint #prob-num
### Preprint: Bayesian inversion with heavy-tailed stable priors
Just uploaded to the arXiv: “Well-posed Bayesian inverse problems and heavy-tailed stable Banach space priors”. This article builds on the function-space formulation of Bayesian inverse problems advocated by Stuart et al. to allow the prior to be heavy-tailed: not only may it not be exponentially integrable, as is the case for a Gaussian or Besov measure, it might not even have a well-defined mean, as in the case of the famous Cauchy distribution on $$\mathbb{R}$$.
Abstract. This article extends the framework of Bayesian inverse problems in infinite-dimensional parameter spaces, as advocated by Stuart (Acta Numer. 19:451–559, 2010) and others, to the case of a heavy-tailed prior measure in the family of stable distributions, such as an infinite-dimensional Cauchy distribution, for which polynomial moments are infinite or undefined. It is shown that analogues of the Karhunen–Loève expansion for square-integrable random variables can be used to sample such measures. Furthermore, under weaker regularity assumptions than those used to date, the Bayesian posterior measure is shown to depend Lipschitz continuously in the Hellinger metric upon perturbations of the misfit function and observed data.
Published on Friday 20 May 2016 at 09:00 UTC #publication #preprint #inverse-problems
### The Digital Future: 75th Anniversary of the Zuse Z3
11 May 2016 marks the seventy-fifth anniversary of the unveiling of Konrad Zuse's Z3 computer. The Z3 was the world's first working programmable, fully automatic digital computer.
In celebration of this landmark achievement in computational science, the Zuse Institute, the Berlin–Brandenburg Academy of Sciences, and Der Tagesspiegel are organising a conference on “The Digital Future: 75 Years Zuse Z3 and the Digital Revolution”. For further information, see www.zib.de/zuse75.
Published on Monday 2 May 2016 at 11:00 UTC #event
### UQ Talks: Steven Niederer
This week Steven Niederer (King's College London) will talk about “Linking physiology and cardiology through mathematical models”
Time and Place. Thursday 28 April 2016, 11:00–12:00, Room 4027 of the Zuse Institute Berlin, Takustraße 7, 14195 Berlin
Abstract. Much effort has gone into the analysis of cardiac function using mathematical and computational models. To fully realise the potential of these studies requires the translation of these models into clinical applications to aid in diagnosis and clinical planning.
To achieve this goal requires the integration of multiple disparate clinical data sets into a common modelling framework. To this end we have developed a coupled electro-mechanics model of the human heart. This model combines patient specific anatomical geometry, active contraction, electrophysiology, tissue heterogeneities and boundary conditions fitted to comprehensive imaging and catheter clinical measurements.
This multi-scale computational model allows us to link sub cellular mechanisms to whole organ function. This provides a novel tool to determine the mechanisms that underpin treatment out comes and offers the ability to determine hidden variables that provide new metrics of cardiac function. Specifically we report on the application of these methods in patients receiving cardiac resynchronisation therapy and ablation for atrial fibrillation.
Published on Sunday 24 April 2016 at 07:00 UTC #event #uq-talk
### ECMath Colloquium
This week's colloquium at the Einstein Center for Mathematics Berlin will be on the topic of “Sparsity: Statistics, Optimization and Applications.” The speakers will be:
• Peter Richtárik (Edinburgh): Empirical Risk Minimization: Complexity, Duality, Sampling, Sparsity and Big Data
• Gitta Kutyniok (TU Berlin): Anisotropic Structures and Sparsity-based Regularization
• Mario Figueiredo (Lisbon): Learning with Strongly Correlated Variables: Ordered Weighted ℓ1 Regularization
Time and Place. Friday 22 April 2016, 14:00–17:00, Humboldt-Universität zu Berlin, Main Building Room 2.094, Unter den Linden 6, 10099 Berlin
Published on Monday 18 April 2016 at 08:00 UTC #event
← Newer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Older → | 2017-12-15 09:56:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32922083139419556, "perplexity": 1763.6456883494113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948568283.66/warc/CC-MAIN-20171215095015-20171215115015-00132.warc.gz"} |
https://homework.cpm.org/category/CC/textbook/cc2/chapter/1/lesson/1.2.6/problem/1-115 | ### Home > CC2 > Chapter 1 > Lesson 1.2.6 > Problem1-115
1-115.
Fareed wants to add $\frac { 1 } { 4 } + \frac { 5 } { 8 }$.
1. Add the fractions by using a Giant One to create a common denominator.
What do you need to multiply the first term by so that the denominator is equal to $8$?
Multiplying the denominator by $2$ gives us $8$. Now use a Giant One to solve the problem.
$\frac{1}{4} \:\cdot$$=\frac{2}{8}$
Now that both fractions have the same denominator, you can add the fractions together by adding the numerator and keeping the denominator.
$\frac{2}{8}+\frac{5}{8}=?$
$\frac{7}{8}$ | 2021-09-17 02:01:32 | {"extraction_info": {"found_math": true, "script_math_tex": 8, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8881673812866211, "perplexity": 889.3703595936895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780053918.46/warc/CC-MAIN-20210916234514-20210917024514-00705.warc.gz"} |
https://www.physicsforums.com/threads/how-old-are-the-particles-in-my-body.656247/ | # How old are the particles in my body?
1. Dec 2, 2012
### Warp
I'm not sure which group this question really belongs to, so "general physics" sounds like a safe bet.
This question was prompted by having listened to Neil deGrasse Tyson's more philosophical views about our nature and our connection to the universe, which are quite insightful.
Most of the larger molecules in my body are probably relatively recent (as living organisms build and break things like protein chains all the time.) Many of the simpler molecules, such as water, are probably much, much older (although I do not know all that much about the formation of such molecules.) Some might be quite recent, but some may be really old.
The atoms in my body are probably really, really old. Most of the heavier elements probably formed in the star or stars that were the ancestor(s) of our solar system, some may be even older than that. (If I have understood correctly, it's estimated that our sun is a third-generation star, meaning that it formed from the remnants of stars, which themselves formed from the remnants of the first stars in our universe.) It might be possible that some of the simpler atoms in my body were actually produced by the first-generation stars of our universe, so they are really, really old.
But how about the individual particles in my body? The protons, electrons and neutrons? Are they as old as the universe itself? Did they form in the first moments of the Big Bang? (Can such particles form afterwards?)
In other words, how old are the protons, electrons and neutrons (and possibly other particles) in my body?
2. Dec 2, 2012
### Staff: Mentor
It depends on your definition of "the [particle]".
As seen by quantum field theory, every interaction destroys a particle and produces a new one instead - as those interactions occur extremely often, no particle would be older than a picosecond.
In a more classical view, protons, electrons and neutrons stay the same until they are annihilated, decay or transform into other particles in a different way. This is quite rare outside of stars, so most particles were still present when our solar system formed about 5 billion years ago. Stars mainly convert protons plus electrons to neutrons (bound in nuclei) and do not produce electrons and protons, so those can be even older and most come from the big bang 13.7 billion years ago. Neutrons are "younger", as they mainly formed in stars afterwards. The same is true for most of the atoms in your body (apart from hydrogen and traces of helium).
Water molecules exchange hydrogen atoms all the time, Wikipedia suggest ~10 hours as timescale with a german paper as source. And even if you neglect that, water is an essential part in many biological processes.
3. Dec 2, 2012
### sophiecentaur
That's the most interesting thing I've learned today. (Even more interesting than the contents of the Leveson Report lol). Presumably that refers to the liquid state. That timescale is staggering - it's more along the lines of the conduction electrons in a metal than I could ever have imagined.
Shame that the paper's in German. I can ask the way to the station and get a beer with my German but little more. tschüß!
4. Dec 2, 2012
### Crazymechanic
Sorry for a little offtopic but this thread got me wondering if only a proton could learn to speak and tell his journey through space and time since the very beginning or close to that imagine what a bestseller it would be. HAH. (sweet dreams)
Also many questions would vanish.
5. Dec 2, 2012
### sophiecentaur
There would be many chapters with nothing much in! You would need a lot of editing, I think. How many different ways are there of saying "I met a photon"?
6. Dec 2, 2012
### micromass
Ah, but it could be a love story about him meeting a photon, falling in love, chasing her but not capable of catching up and then him decaying with a broken heart. Could be a nice story
7. Dec 3, 2012
### sophiecentaur
Photons. Seen one, seen 'em all.
8. Dec 3, 2012
### Crazymechanic
hahahah micromass. :D
just don't forget to put some werewolves in your love story:D
9. Dec 3, 2012
### Zarqon
But this one had such a nice frequency! Very well defined phase, and just the right amount of orbital angular momentum.
10. Dec 3, 2012
### Staff: Mentor
Probably (the study was done at 25°C or about 298K).
This allows to determine the coefficients kA and kD in the reaction $H^+ + OH^- \rightleftharpoons H_2O$.
$k_D=2.6 \cdot 10^{-5} \frac{1}{s}$ or $\frac{1}{k_D}=38500s$. | 2018-07-21 06:57:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36764317750930786, "perplexity": 1257.651221485854}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592387.80/warc/CC-MAIN-20180721051500-20180721071500-00230.warc.gz"} |
https://dials.diamond.ac.uk/targeted_scaling_guide.html | # Scaling against a reference dataset with DIALS¶
This document provides a guide on how to scale a dataset against a reference dataset, referred to as the target dataset. The target dataset can be either a dataset scaled with dials.scale, or an mtz file containing a scaled dataset. Any number of datasets can be scaled against the reference dataset at once, giving the same scaling result as if each dataset were scaled as an independent job. The only difference is that all scaled datasets would be output in one scaled.pickle and scaled_experiments.json, which may be more or less convenient for further processing.
## Scaling against a dials reference dataset¶
In this example, reference_reflections.pickle and reference_experiments.json are from a dataset that has already been scaled with dials.scale. To scale another dataset (datafiles integrated.pickle, integrated_experiments.json) against this target/reference, one should use the following command:
dials.scale only_target=True integrated.pickle integrated_experiments.json reference_reflections.pickle reference_experiments.json
This will scale the intensities of the dataset to agree as closely as possible with the intensities of the reference dataset, and save the scaled dataset to scaled.pickle, scaled_experiments.json (the reference files are unchanged). The only_target=True command is important, else all the data will be scaled together and output in a joint output file.
## Scaling against a reference mtz file¶
In this case, it is assumed that the intensity and variance columns of the mtz file have already been scaled. Targeted scaling would be run with the following command:
dials.scale integrated.pickle integrated_experiments.json target_mtz=scaled.mtz
The targeted scaling algorithm is the same regardless of the target datafile type, likewise the scaled dataset will be saved to scaled.pickle and scaled_experiments.json.
## General considerations for suitable options¶
A common use case for scaling against a reference is to scale thin-wedge datasets against a high quality full-sweep dataset. To give the best scaling, it may be necessary to manually set the scaling model parameters: for more details see the In-depth guide to scaling options in DIALS. In the case of very thin wedge/stills datasets, or depending on the scientific question under investigation, it may be suitable to set model=KB, to give a single global scale and relative B-factor to each dataset. However, if significant intensity variation/decay is present in each measurement, it may be best to use model=physical, setting absorption_term=False and specifying values for scale_interval and decay_interval. | 2019-03-24 19:27:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2836611568927765, "perplexity": 2052.7748045287476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203491.1/warc/CC-MAIN-20190324190033-20190324212033-00402.warc.gz"} |
https://ssccompetitivequestions.in/tag/natural-number/ | # Definition of Natural Number and property, example, Sum part-1
## Definition of Natural Number
The definition of natural number is hidden in its name itself. how?
The number that is used in counting natural things. These are called natural numbers.
It is also called counting numbers. Because this number is used to count anything.
Natural numbers are positive integers. The values of integer numbers range from – ∞ to + ∞. One part of which is a positive integer and the other negative integer. A positive integer is a natural number.
## Natural number value
The value of a natural number varies from 1 to ∞.
Ex – 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ……… ∞
## Natural Numbers Examples
Find the number of pens shown in the above picture.
To find the number of pens present in this picture, we will start counting the pens from one end.
Let’s start counting the pen from right to left.
Thus the first red pen, Second blue pen, Third green pen, Fourth yellow pen, Fifth orang pen, Sixth black pen
An object is started to be counted by one. No to zero. This proves it. Of zero is not a natural number.
We started counting pens from one to six. So the number of pens is six.
## Property of Natural Number
1. Closure Property
2. Associative Property
3. Commutative Property
4. Distributive Property
### Closure Property
Adding and multiplying any two or more natural numbers gives a natural number.
The sum of two natural numbers is a natural number.
ex – 2+2 = 4. 5+3 = 8, 9+2 = 11
#### Multiplication
The result of two natural numbers is a natural number.
Ex – 2×4 = 12, 5×8 = 40, 7×3 = 21
#### Subtraction
The subtraction of two natural numbers may or may not be a natural number. If the smaller natural numbers are subtracted from the larger natural numbers, then the obtained numbers will be natural numbers.
Conversely, if the larger natural number is subtracted from the smaller natural number, then the number obtained will not be a natural number.
Ex 5 – 3 = 2, 7 -10 = -3
## Division
The quotient of two natural numbers may or may not be a natural number.
Ex – 10/8 = 1.25, 10/5 = 2
### Associative Property
Associative property of natural number is correct in case of addition and multiplication.
a + ( b + c ) = ( a + b ) + c
#### Multiplication
a × ( b × c ) = ( a × b ) × c
Associative property of natural number is not correct in the case of Subtraction and Division.
#### Subtraction
a – ( b – c ) ≠ ( a – b ) – c
#### Division
a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c
### Commutative Property
Commutative Property of natural number is correct in case of addition and multiplication
Ex – x + y = y + x and a × b = b × a.
Commutative Property of natural number is not correct in case of addition and multiplication.
x – y ≠ y – x and x ÷ y ≠ y ÷ x.
### Distributive Property
Distributive Property of natural number is correct in case of addition and multiplication
a × (b + c) = ab + ac
Distributive Property of natural number is not correct in case of addition and multiplication.
a × (b – c) = ab – ac.
## Natural Numbers from 1 to 100
Which natural number has no successor?
No!
There is no natural number that has no successor. All-natural numbers have successors.
Which natural number has no predecessor?
No!
There is no natural number that has no predecessor. All-natural numbers have a predecessor.
Who invented natural numbers?
Natural numbers always existed. But we started studying it seriously since the time of Greek philosophers, Pythagoras and Archimedes.
What is the smallest natural number?
1 is the smallest natural number.
What is the natural number with an example?
1, 2, 3, 4, 5, 6, 7, 8, 9 …….
What is the natural number definition?
The numbers that are used to count natural objects. It is called a natural number.
What is the natural number symbol?
The natural number is represented by “N“.
which natural number is nearest to 8485?
8484 and 8486
Which natural number is equal to its cube?
27 is a cube of 3. 8 is a cube of 2. 64 is a cube of 4 etc.
Are natural numbers negative?
No!
Natural numbers are only positive.
Are natural numbers rational?
No!
Because an object cannot be counted in p / q. Can we tell a pen that the number of pens is 2/5. No no When counting an item, it is considered to be the same.
Are natural numbers whole numbers?
All whole numbers are natural numbers except zero.
Are natural numbers countable?
Yes
Are natural numbers real numbers?
Yes
Can a natural number be decimal?
No
Can Natural Numbers be Rational?
No
Can a natural number be decimal?
No
A natural number is also known as
counting numbers
Natural number to 10.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
What is the sum of natural numbers from 1 to 100?
5050
Three natural numbers after 1500
Ans – 1501, 1502, 1503
All Trigonometry Formulas For Class 10, 11, 12 (PDF) | 2021-10-26 06:12:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6013013124465942, "perplexity": 849.3082540507538}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587799.46/warc/CC-MAIN-20211026042101-20211026072101-00640.warc.gz"} |
https://codeforces.com/blog/entry/60672 | ### vovuh's blog
By vovuh, history, 3 years ago,
Tutorial
Solution (Vovuh)
1006B - Polycarp's Practice
Tutorial
Solution (Vovuh)
1006C - Three Parts of the Array
Tutorial
Solution (Vovuh, set)
Solution (ivan100sic, two pointers)
1006D - Two Strings Swaps
Tutorial
Solution (Ne0n25)
1006E - Military Problem
Tutorial
Solution (mareksom)
1006F - Xor-Paths
Tutorial
Solution (Vovuh)
• +59
» 3 years ago, # | 0 Nice problems, btw in C I binary searched each value of the prefix sum on suffix sum where there is no overlap between sum1 & sum3 code#include using namespace std; typedef long long ll; #define rep(i,n) for(int(i)=0;(i)<(int)n;(i)++) #define vi vector #define vll vector int main() { ll n;cin>>n; vll prefix(n),suffix(n); rep(i,n) cin>>prefix[i],suffix[n-i-1]=prefix[i]; rep(i,n-1) prefix[i+1]+=prefix[i], suffix[i+1]+=suffix[i]; ll mx=0,s,e,mid; rep(i,n){ s=0,e=n; while(s<=e){ mid=s+(e-s+1)/2; if(suffix[mid]==prefix[i] && i+mid
» 3 years ago, # | 0 I'm not sure why this hacking attempt was successful: http://codeforces.com/contest/1006/submission/40420960Can someone please tell me what went wrong?
• » » 3 years ago, # ^ | 0 May the hacker explains jhonber
• » » 3 years ago, # ^ | +4 Try with this test case: 5 4 3 1 1 4 5 Your output 13 1 1 1 2 You have a problem with repeated numbers in this part of the code: for(int j = 0; j < n; j++) { if(arr[j] == indexx) { // *** HERE ind.push_back(j); arr[j] = -1; } } Good luck! :P
» 3 years ago, # | 0 Please anyone explain the problem F. Thanks!!!
• » » 3 years ago, # ^ | 0 Read code :) that's easier to understand.You use a structure, v[x][y][c] = number of way to go to cell x, y, have c at xor value. This is the key of solution.
• » » » 3 years ago, # ^ | 0 Thanks, after viewing the code it becomes easier.
» 3 years ago, # | 0 Complexity of problem F: We run 2 recursive backtracking. So why is not it O( 2^((n+m-2)/2) ) instead of your complexity ?Maybe because I don't understand how to complete path with 2 child-paths.
• » » 3 years ago, # ^ | 0 For everyone that has same question with me,Because we use a map, complexity is O( n log n ) with n = number of recursion ( 2^((n+m-2)/2) ).
• » » » 3 years ago, # ^ | +3 The complexity is because each backtracking will made moves and summary size of maps will be so if we take logarithm of this value we will obtain just .
• » » 3 years ago, # ^ | 0 This is because n,m can take maximum value upto 20. So you have to compute all 2^20 paths. This will exceed the time limit because time limit is generally upto 2^12 . So it is wiser to break problems into two sets of 10, so computations will become 2^10+2^10= 2^11 which fits our time limit.You can try this problem too Codechef Problem
• » » » 3 years ago, # ^ | 0 I ask a question about the complexity. I don't think you answer right question. :)
» 3 years ago, # | 0 In the problem F,because we can only move to the bottom or to the right,we don't need "cnt" to record the number of moves.x+y is just the "cnt";
» 3 years ago, # | 0 vovuh In problem F: meet in the middlewas used. Can you suggest any tutorials and problems for this technique? I don't really understand it. Thanks!
• » » 3 years ago, # ^ | +1 In basis, instead of finding the solution to go from the initial state to the final state, you find the solution to go from each of those states to some mid-states (which has half the moves/resources required to be done). The final work will be merging path — one from the initial, one from the final, to get the answer.You can search for problems with tags "meet-in-the-middle" on Codeforces problemsets. There are enough for you to practice, I suppose.
• » » » 3 years ago, # ^ | ← Rev. 2 → +1 Thank you Akikaze. I have a small doubt, it may seem silly but anyway I ask, what are the main differences between this and divide and conquer technique? I went through this geeksforgeeks article, which says Meet in the middle is a search technique which is used when the input is small but not as small that brute force can be used. Like divide and conquer it splits the problem into two, solves them individually and then merge them. But we can’t apply meet in the middle like divide and conquer because we don’t have the same structure as the original problem. What does it mean by — having the same structure as the original problem? And how to decide which one to use?
• » » » » 3 years ago, # ^ | 0 Well think of native algorithm for this task.You would call (i+1,j) or (i,j+1) until you get to (n,m). But let's see now meet in the middle approach: Go until (i+j)-1==(n+m)/2 (until you reach the middle). Store how many same results for coordinates (i,j) exist (use map because result may be 10^18). And after you went to middle, go backwards from (n,m) to middle and when you reach check if result is k. All I'm saying is just to tell that when you come to middle, you store result count in map, and then you look for results going backwards. Storing result in map and searching answer in map means that don’t have the same structure as the original problem. At least I see it that way, maybe I'm wrong. Hope it helps :D
• » » » » 3 years ago, # ^ | ← Rev. 3 → +27 Let's take the classic merge sort algorithm as an example. The problem is to sort the array. If we cut the problem in half, our goal is still to sort the two halves of the array. So we can solve each half by dividing them into two more halves, again.Another example would be the closest pair of points problem. If we divide the set of points in half, we would still need to find closest pair of points in each half. More dividing, yay.Now, let's look at the xor-paths problem. Our original problem is to find a path from one corner to the opposite, with xor exactly k. When we divide the grid in half, our problem for each half is not limited to finding xor exactly k anymore, thus we can't solve each half in the same manner.An easy (but I'm not sure if correct) way to distinguish them is that meet-in-the-middle is typically used to optimize a complete search. When you split the problem, ask yourself: "If the problem is the same for the two halves, and I can solve those halves by brute force, can I use those results to solve the full problem?". If the answer is yes, then it is DnC.
• » » » » » 3 years ago, # ^ | +9 Thanks for the explanation with examples neko_nyaaaaaaaaaaaaaaaaa. It makes sense now :D
»
3 years ago, # |
-25
# ?detaR tI sI
» 3 years ago, # | ← Rev. 2 → 0 I don't quite understand in D why in first exampleabacababacabaaWhen we look at 3-rd line containing characters 'a','c','a','b' result is 2. Why can't we just turn 'c' to 'b', swap (a[3],b[3]) and then swap(a[3],a[5])?
• » » 3 years ago, # ^ | 0 You can only preprocess in the first string (in this case, abacaba).
• » » 3 years ago, # ^ | 0 It's because we cannot preprocess moves after the first change is made.
» 3 years ago, # | 0 #include #define ll long long #define INF 20000000000 #define EPS 0.000001 #define f first #define s second using namespace std; ll arr[20][20]; ll n,m,k; ll ans; void solve(ll i,ll j,ll cum){ if(i<0||j<0||i>=m||j>=n) return ; // cout<>n>>m>>k; for(ll i=0;i>arr[i][j]; } } solve(0,0,0); cout<
• » » 3 years ago, # ^ | ← Rev. 2 → 0 Well,algorithm isn't good. You're going from beginning to end. It will give TLE. Read editorial or try to see how others managed to do meet in the middle.
• » » » 3 years ago, # ^ | 0 I am using Meet in the Middle technique, can someone please point out why I am getting time out on 6 test case?This is my code.
• » » 3 years ago, # ^ | +1 You need meet in the middle to solve this problem, because your algorithm will cost too much time.
» 3 years ago, # | 0 My submission for D: http://codeforces.com/contest/1006/submission/40508497 Can someone give me a small test case where this fails?
• » » 3 years ago, # ^ | 0 2 bc aa
» 3 years ago, # | ← Rev. 2 → 0 If F problem if n+m is not so small how to find the time complexity of the recursive solution. How it is O((n+m-2Cm-1)*(n+m-2))
• » » 3 years ago, # ^ | 0 About O(·(n + m - 2)) — exists the method which allows us to iterate over all binary masks of length n with exactly k ones with the time complexity O(). And, of course, for each mask we need to iterate over all its bits and spend n + m - 2 operations to do this
• » » » 3 years ago, # ^ | ← Rev. 2 → 0 I may be missing something, but let me ask: In a 3x3 grid, for example, won't we have 6 possible moves (m+n) ?EDIT:nevermind, I was confused. Moves != #Paths
• » » » 3 years ago, # ^ | 0 But how the complexity is O((n+m-2)C(m-1)·(n + m - 2))?? because to iterate all mask of size n+m-2 you need a for loop which complexity is 2^(n+m-2)
• » » » » 3 years ago, # ^ | 0 Not necessary. In one of the previous comments I noticed that exists a method which allows us to iterate over all binary masks of length n with exactly k ones with the complexity written above. If you are very interested, there is a code on C++. Unfortunately, now I cannot describe how it works. Codefor(int mask = (1 << k) - 1; mask < (1 << n); ) { if (mask == 0) break; int x = mask & -mask, y = mask + x; mask = (( (mask & ~y) / x ) >> 1) | y; } But with such a cycle we need to check where ones are placed in the current mask. So overall complexity is O(·(n + m - 2)).
» 3 years ago, # | 0 My submission for E: http://codeforces.com/contest/1006/submission/40523424 Can someone help optimise this code? The logic seems simpler than the one in the editorial.
• » » 3 years ago, # ^ | 0 Well, for every vertex you are storing whole subtree. Off course it will give memory limit exceeded, because you are using O(n^2) memory. And your logic may be simpler, but that doesn't matter since solution is wrong — program:int main { return 0; }will be simpler than the one in tutorial, even simpler than yours, but it won't give correct answer either :)If you want to get AC you have to understand what's going on in editorial, why it is done like that and then code it in similar way.
» 3 years ago, # | 0 This is my submission for the Problem D : http://codeforces.com/contest/1006/submission/40525793These are the steps that I followed while writing the solution : 1.segregate all the four characters, whose positions can be changed after the preprocess, I named them a , b (from the first string ) and c,d (from the second string) 2.i created a set to count the number of unique characters in these four elements. 3.If the set size is 4 , which means all the characters are unique , then ans = ans + 2; 4.If the set size is 3 , in this case there are two possible arrangements, either the ans = ans + 1 or ans = ans + 2 , if a==b or c==d ( the pair containing same character is present in the first string or in the second string ) 5.If the set size is 2, then ans = ans + 1 , only if there are three same characters 6.If the string size is odd, check whether the middle element is equal in both the strings. Can you tell me what I am missing from this.
• » » 3 years ago, # ^ | ← Rev. 3 → 0 I got where I am mistaken , in the step 4 , if c==d , then ans = ans + 1 , instead of ans = ans + 2.Correct solution : http://codeforces.com/contest/1006/submission/40542519
» 3 years ago, # | 0 Polycarp sounds like poly-crap. I don't like these puns in problem statement.
» 3 years ago, # | 0 why do you always give solutions in cpp . please try python for once .
• » » 3 years ago, # ^ | 0 C++ is more understandable for a lot of participants. My Python solutions are as short as possible and not so clear as C++ solutions. And one more reason is that for the last 2-3 problems we don't guarantee that Python solutions will pass.
• » » » 3 years ago, # ^ | 0 oh then I should slowly turn to cpp for good
» 3 years ago, # | 0 Can I solve problem F using BFS ?
» 3 years ago, # | 0 this was the first editorial till now that i understood completely , i hope tutorials in future will also be so great , then only novice programmers can learn. thanks.
» 3 years ago, # | 0 Can anyone explain problem B. The code in the editorial is confusing
• » » 3 years ago, # ^ | 0 Did you read explanation? What part in it you don't understand?
• » » » 3 years ago, # ^ | 0 The whole implementation part means how it is implemented.
» 3 years ago, # | 0 I cant understand solution of F, please explain me if n = 10 and m = 10? with O (2 ^ (n + m — 2))
• » » 3 years ago, # ^ | 0 understood...
» 3 years ago, # | 0 Problem C — Three Parts of the Array Can someone find the problem here? http://codeforces.com/contest/1006/submission/40760589 I find it exactly the same as tutorial's solution with two pointers, but Test Case #12 fails. Thanks.
• » » 3 years ago, # ^ | +1 Test case on which your code is wrong:32 1 3
• » » » 3 years ago, # ^ | 0 Thanks mate.
» 3 years ago, # | 0 Can someone explain problem D? What is the difference if s[i]= s[n-i+1] and t[i] = t[n-i+1]? It's really confusing to me.
» 3 years ago, # | ← Rev. 2 → 0 Can anyone explain to me why my solution for problem C get's WA In testcase 13 ? 42740594
» 2 years ago, # | 0 If someone want to try a variation of Problem F (n*n matrix rather than n*m matrix) go and solve https://www.codechef.com/problems/XORGRIDMy code for problem F:https://codeforces.com/contest/1006/submission/53013382
» 23 months ago, # | 0 Could someone explain Problem E a bit more elaborately ? I have been stuck on it for quite a while and can't figure out a way to solve it. :/ I know that the editorial is very well — written, but could someone explain it in a Div — 4 way ? Also, a better written code would be of great help in understanding the solution. :)
• » » 10 months ago, # ^ | 0 well.. yr wish has come true...there is officially a DIV-4 now
» 23 months ago, # | 0 https://codeforces.com/contest/1006/submission/54741899 the output of 20th test case is same as my answer yet it shows wrong answer....can someone help please
» 22 months ago, # | 0 What is wrong in this code? Is this an implementation problem or a logic problem?I binary searched on indices such that we split the first part at mid, and then I ran a loop backwards finding whether a sum3 exists for the corresponding sum1 upto mid.https://codeforces.com/contest/1006/submission/56046778I am getting WA on test 6.
• » » 22 months ago, # ^ | ← Rev. 2 → +1 Your code has a wrong answer in this test case: 4 4 5 10 4 Your output: 0 Answer : 4 Good luck!
• » » » 22 months ago, # ^ | 0 Still getting WA on test 6 :( https://codeforces.com/contest/1006/submission/56071670
» 18 months ago, # | 0 could anyone please explain the editorial in more simpler way , I am not able to understand the problem.please help.
» 18 months ago, # | 0 tutorial for problem E, I forgot to mention the question.
• » » 12 months ago, # ^ | 0 The solution in the tutorial is based on dividing them into sub trees.For the given sample,from normal dfs traverse starting from source 1, we get, 1,2,3,5,6,8,7,9,4. We just need to divide this array into continuous sub arrays like [3,5,6,8,7,9] or [7,9] .To make this happen,we just need to find, "after how many vertexes popped, the vertex pushed first was popped." Like, when '3' was pushed,then after pushing 5 vertex, '3' was popped. So this gives us the subarray from array1 which is from (index of 3) to ((index of 3)+5 which is the subarray [3,5,6,8,7,9].So in the dfs code,we'll compute the array1 along with the index of the vertexes in array one and also the "after how many vertexes popped, the vertex pushed first was popped." Then we'll just simply calculate if the given K in query is smaller than that number or not and if smaller, we'll print array1[index+k-1] otherwise -1 .
» 13 months ago, # | 0 I don't understand this line"Since the given array consists of positive integers, for each value of a, there can be at most one value of c such that sum1=sum3. "in problem C
» 4 months ago, # | 0 Can someone explain me why this solution fail? Solution
• » » 6 weeks ago, # ^ | 0 Case 2 ab cc requires 1 preprocessing. | 2021-04-17 20:15:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41748979687690735, "perplexity": 1492.2473767925053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00388.warc.gz"} |
https://testbook.com/question-answer/an-equilateral-triangle-is-made-of-three-wires-of--5fa6638d6263a0266fe56bea | # An equilateral triangle is made of three wires of equal resistances 4 Ω. Find the equivalent resistance across any one side.
This question was previously asked in
Airforce Group X 7 November 2020 Memory Based Paper
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1. 4 Ω
2. 8 Ω
3. 4/3 Ω
4. 8/3 Ω
## Answer (Detailed Solution Below)
Option 4 : 8/3 Ω
## Detailed Solution
CONCEPT:
Resistance:
• The measurement of the opposition of the flow of electric current through a conductor is called resistance of that conductor. It is denoted by R.
Resistances in series:
• When two or more resistances are connected one after another such that the same current flows through them are called as resistances in series.
• The net resistance/equivalent resistance (R) of resistances in series is given by:
• Equivalent resistance, R = R1 + R2
Resistances in parallel:
• When the terminals of two or more resistances are connected at the same two points and the potential difference across them is equal is called resistances in parallel.
• The net resistance/equivalent resistance(R) of resistances in parallel is given by:
$$\frac{1}{R} = \frac{1}{{{R_1}}} + \frac{1}{{{R_2}}}$$
CALCULATION:
• Here 4 Ω across AB and AC are in a series combination, the equivalent resistance is
⇒ S = R1 + R2 = 4 Ω + 4 Ω = 8 Ω
• Now 4 Ω and 8 Ω are connected in parallel combination, the equivalent resistance is
$$⇒ \frac{1}{R_{eq}} = \frac{1}{{{8}}} + \frac{1}{{{4}}}=\frac{3}{8}$$
⇒ Req = 8/3 Ω | 2022-01-20 07:42:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8813889026641846, "perplexity": 3213.972637379768}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00479.warc.gz"} |
https://elteoremadecuales.com/cartan-hadamard-theorem/?lang=fr | Cartan–Hadamard theorem In mathematics, the Cartan–Hadamard theorem is a statement in Riemannian geometry concerning the structure of complete Riemannian manifolds of non-positive sectional curvature. The theorem states that the universal cover of such a manifold is diffeomorphic to a Euclidean space via the exponential map at any point. It was first proved by Hans Carl Friedrich von Mangoldt for surfaces in 1881, and independently by Jacques Hadamard in 1898. Élie Cartan generalized the theorem to Riemannian manifolds in 1928 (Helgason 1978; faire Carmo 1992; Kobayashi & Nomizu 1969). The theorem was further generalized to a wide class of metric spaces by Mikhail Gromov in 1987; detailed proofs were published by Ballmann (1990) for metric spaces of non-positive curvature and by Alexander & Bishop (1990) for general locally convex metric spaces.
Contenu 1 Géométrie riemannienne 2 Metric geometry 2.1 Generalization to locally convex spaces 3 Importance 4 Voir également 5 References Riemannian geometry The Cartan–Hadamard theorem in conventional Riemannian geometry asserts that the universal covering space of a connected complete Riemannian manifold of non-positive sectional curvature is diffeomorphic to Rn. En réalité, for complete manifolds of non-positive curvature, the exponential map based at any point of the manifold is a covering map.
The theorem holds also for Hilbert manifolds in the sense that the exponential map of a non-positively curved geodesically complete connected manifold is a covering map (McAlpin 1965; Langue 1991, IX, §3). Completeness here is understood in the sense that the exponential map is defined on the whole tangent space of a point.
Metric geometry In metric geometry, the Cartan–Hadamard theorem is the statement that the universal cover of a connected non-positively curved complete metric space X is a Hadamard space. En particulier, if X is simply connected then it is a geodesic space in the sense that any two points are connected by a unique minimizing geodesic, and hence contractible.
A metric space X is said to be non-positively curved if every point p has a neighborhood U in which any two points are joined by a geodesic, and for any point z in U and constant speed geodesic γ in U, on a {displaystyle d(z,gamma (1/2))^{2}leq {frac {1}{2}}ré(z,gamma (0))^{2}+{frac {1}{2}}ré(z,gamma (1))^{2}-{frac {1}{4}}ré(gamma (0),gamma (1))^{2}.} This inequality may be usefully thought of in terms of a geodesic triangle Δ = zγ(0)c(1). The left-hand side is the square distance from the vertex z to the midpoint of the opposite side. The right-hand side represents the square distance from the vertex to the midpoint of the opposite side in a Euclidean triangle having the same side lengths as Δ. This condition, called the CAT(0) condition is an abstract form of Toponogov's triangle comparison theorem.
Generalization to locally convex spaces The assumption of non-positive curvature can be weakened (Alexander & Bishop 1990), although with a correspondingly weaker conclusion. Call a metric space X convex if, for any two constant speed minimizing geodesics a(t) and b(t), the function {displaystyle tmapsto d(un(t),b(t))} is a convex function of t. A metric space is then locally convex if every point has a neighborhood that is convex in this sense. The Cartan–Hadamard theorem for locally convex spaces states: If X is a locally convex complete connected metric space, then the universal cover of X is a convex geodesic space with respect to the induced length metric d.
En particulier, the universal covering of such a space is contractible. The convexity of the distance function along a pair of geodesics is a well-known consequence of non-positive curvature of a metric space, but it is not equivalent (Ballmann 1990).
Significance The Cartan–Hadamard theorem provides an example of a local-to-global correspondence in Riemannian and metric geometry: à savoir, a local condition (non-positive curvature) and a global condition (simple-connectedness) together imply a strong global property (contractibility); or in the Riemannian case, diffeomorphism with Rn.
The metric form of the theorem demonstrates that a non-positively curved polyhedral cell complex is aspherical. This fact is of crucial importance for modern geometric group theory.
See also Glossary of Riemannian and metric geometry Cartan–Hadamard manifold Cartan–Hadamard conjecture References McAlpin, John (1965), "Infinite dimensional manifolds and Morse theory", Thèse, Columbia University. Alexandre, Stephanie B.; Bishop, Richard L. (1990), "The Hadamard-Cartan theorem in locally convex metric spaces", Enseign. Math., Série 2, 36 (3–4): 309–320. Ballmann, Werner (1995), Lectures on spaces of nonpositive curvature, DMV Seminar 25, Bâle: Birkhäuser Verlag, pp. viii+112, ISBN 3-7643-5242-6, M 1377265. Bridson, Martin R.; Haefliger, André (1999), Metric spaces of non-positive curvature, bases des sciences mathématiques 319, Berlin: Springer Verlag, pp. xxii+643, ISBN 3-540-64324-9, M 1744486. faire Carmo, Manfredo Perdigão (1992), Géométrie riemannienne, Mathématiques: theory and applications, Boston: Birkhauser, pp. xvi+300, ISBN 0-8176-3490-8. Kobayashi, Shoshichi; Nomizu, Katsumi (1969), Foundations of Differential Geometry, Volume. II, Tracts in Mathematics 15, New York: Wiley Interscience, pp. xvi+470, ISBN 0-470-49648-7. Helgason, Sigurdur (1978), Géométrie différentielle, Lie groups and symmetric spaces, Mathématiques pures et appliquées 80, New York: Presse académique, pp. xvi+628, ISBN 0-12-338460-5. Langue, Serge (1999), Fundamentals of differential geometry, Textes d'études supérieures en mathématiques, volume. 191, Berlin, New York: Springer Verlag, ISBN 978-0-387-98593-0, M 1666820. Catégories: Metric geometryTheorems in Riemannian geometry
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Nous utilisons nos propres cookies et ceux de tiers pour améliorer l'expérience utilisateur Plus d'informations | 2023-03-20 16:25:04 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8777016401290894, "perplexity": 908.9889572291441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943484.34/warc/CC-MAIN-20230320144934-20230320174934-00642.warc.gz"} |
http://math.stackexchange.com/questions/221813/adapting-a-proof-on-elements-of-order-2-from-finite-groups-to-infinite-groups | # Adapting a proof on elements of order 2: from finite groups to infinite groups
Consider the following problem, appropriate for a first course in Group Theory:
Problem: Prove that there cannot be a group with exactly two elements of order $2$.
General Proof: Suppose for the sake of contradiction that there are exactly two elements of order $2$, and denote them by $a$ and $b$. Note $ab \neq a, b, e$ so that $(ab)^2 \neq e$ or else we'd have a third element of order $2$. From here, one can show that $aba \neq a, b, e$, and then observe that $(aba)^2 = e$, giving a third element of order $2$. Contradiction.
Finite Group Proof: Given a finite group $G$, we can prove the statement as follows:
Suppose $a, b \in G$ are the only elements with order $2$. Observe $\{e, a\} \subset G$ is a subgroup with $2$ elements, so (by Lagrange's Theorem) $G$ has an even number of elements.
Create the Cayley table for $G$ and consider the NW/SE diagonal, on which $e$ will appear exactly three times: $e*e, a*a,$ and $b*b$. For any other elements whose product is $e$, they will appear in the table in pairs: if $x*y = e$ for $x \neq y$ then $y*x = e$ as well.
Thus, the total number of $e$'s in the table is odd: the three in the diagonal plus the even number that come in pairs. But the number of $e$'s in the table should be even: one for each row, and we proved $G$ has an even number of elements. Contradiction.
Question: Can the latter approach be adapted to cover the case for infinite groups?
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One can show that the subgroup generated by $a$ and $b$ is finite, so that the problem is reduced to the finite case. Then, the same argument applies.
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Conjugating $b$ by $a$ basically brings things back to the General Proof, which I had (perhaps unrealistically) hoped to avoid. Nonetheless, I will accept this answer unless someone figures out how to somehow skirt conjugation... – Benjamin Dickman Oct 27 '12 at 0:12
You can show even more, namely:
If a group $G$ contains finitely many involutions, then it contains an odd number of them.
Here, an involution is an element of order 2.
The finite case is very well-known, and follows by trying to pair elements up with their inverses (and using the fact $|G|$ is even).
The infinite case then follows from the finite case by using Dietzmann's lemma, which says that if $X\subset G$ is a finite set of finite-order elements, and $X$ is closed under conjugation in $G$, then $\langle X\rangle$ is a finite subgroup of $G$.
- | 2014-10-31 08:30:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9423089623451233, "perplexity": 147.32419479179916}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637899132.1/warc/CC-MAIN-20141030025819-00201-ip-10-16-133-185.ec2.internal.warc.gz"} |
http://mathoverflow.net/questions/85211/has-sid-sacksons-hold-that-line-been-analyzed?sort=newest | # Has Sid Sackson's “Hold That Line” been analyzed?
In Sid Sackson's classic book A Gamut of Games, he introduces a game that he calls "Hold That Line." Briefly, it is an impartial pencil-and-paper game played on a finite grid of dots. The first player connects two dots with a horizontal, vertical, or diagonal line; thereafter, each player extends the given piecewise-linear curve at one end, making sure to keep it self-avoiding.
Analyzing this game looks like a nice project in combinatorial game theory, suitable for undergraduates, but has it already been studied? A quick search only turned up a brief discussion in Alan Lipp's book The Play's the Thing.
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For the sake of completeness, you might expand your definition of the game to include how many players, what a win or scoring condition is, and so on. Additionally, there are those of us who might try analyzing Sid's version and giving back to you new information if you do this. Gerhard "I Suspect I'm Not Alone" Paseman, 2012.01.08 – Gerhard Paseman Jan 8 '12 at 22:38
Here are the rules, copied from A Gamut of Games (pg. 146): "To play, just draw 16 dots in 4 rows of 4. The first player connects as many dots as he wishes in a straight line [which an illustration indicates may run diagonally]. From either end of the first line the second player draws another straight line. From either free end the first player now makes a line. Continue until no further lines can be drawn. The player who was forced to make the last line is the loser! The completed line must be continuous, with no branches, no crossings, and no dot visited twice." – Barry Cipra Jan 9 '12 at 2:38
The first player draws a main diagonal, and then plays to make the piecewise-linear $\hspace{1 in}$ curve symmetric about the center of the grid. $\;$ – Ricky Demer Jan 9 '12 at 3:20
Demer's comment explains why my assumption was wrong and the rules give the win the next to last player. – Matt Brin Jan 9 '12 at 3:24
A better description of the rules (or at least somebody's understanding of them) is at books.google.com/… – Kevin O'Bryant Jan 9 '12 at 4:18
I'm assuming the last person to move is the winner. After that, it sounds hard.
If, after any move after the first move (the first move occupies occupies two dots and all other moves occupy one), there is an odd number of dots summed over the regions accessible to the two ends, then the player to move is the "winner of the moment." The only way the "loser of the moment" can change the status is to subdivide a region at either end so that one or more regions are not accessible. The player that creates a division is not the one who chooses which region to enter. So if a division is created with one new region odd and another even, then the player creating the division has gained no advantage since the next player will choose the one to enter so as to become "winner of the moment."
As far as I can tell, there are moves that carve a region into two smaller regions, and moves the carve a region into three. I don't see any way of getting four. (Based on the fact that each dot has 8 neighbors.) Getting a curve close to a point where a subdivision can take place depends on the shape of the region (most importantly seen from the end of the curve). Getting to a good place of division can set up quite a fight.
All in all it sounds like a hard analysis.
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The rules allow a move to cover more than one dot, and the first move can connect, for example, dots (1,1), (2,2), and (3,3). I'm also reading the rules as allowing connecting (1,1) to (4,2). – Kevin O'Bryant Jan 9 '12 at 4:16
I'm quite interested in such games. Here are some general speculative thoughts about attacking them.
Piet Hein's old games Nimbi and TacTix are similar, simpler games that were also proposed with the misere play convention. For example, TacTix is played on a 4x4 grid where the players take turns crossing out adjacent tokens (1 up to 4), with diagonal moves not allowed, and the misere play convention, ie, whoever crosses out the last token loses. Nimbi is played on a 12-cell board that is most easily thought of as a triangular arrangement of 15 tokens in an equilateral triangle with its three corners deleted before play begins. Nimbi moves involve taking adjacent tokens in any of the three available directions.
I've recently tried to compute the misere quotient of the full board for TacTix and for Nimbi (actually, I'm still working on both games now). I believe that both quotients are infinite for their respective full-board start positions, but have observed that there are many interesting finite, wild Nimbi and TacTix endgame quotients (one of order 324, for example), and it's conceivable (at least to me) that one might marry an explicit prescription for winning "opening play" of such games that matches the much more easily-computed normal play strategy, and that eventually "connects up" to one of several known to be finite "endgame" misere quotients. Ie, even though the "full board" has an intractable misere theory of sums, this unpleasantness can be dodged by following a "normal play" strategy just long enough to eventually steer play to endgame sums with finite misere quotients.
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Jo\~{a}o Pedro Neto has it listed on his site, http://www.di.fc.ul.pt/~jpn/gv/soldiers.htm Though in his version, it seems like non-orthogonal lines must have slope $1$ or $-1$, so that connecting $(1,1)$ and $(4,2)$ is not allowed. He also allows the second player to play or pass the first turn.
Considering that it is a misere game (last person to play loses), a complete analysis may involve introducing Thane Plambeck and Aaron Siegel's misere quotients. See http://miseregames.org/ for more on that.
As written, with slanted diagonals available, the play is easy to analyze on small boards (2x3 and 3x3 are first player wins), and the game conveniently breaks into subgames which can be summed. The difficulty is that the summation is not the usual nimber sum for normal-play games because of the misere condition. Seems like a very nice example for introducing misere quotients though, since the sums are still computable on paper (at least up to 4x5), and don't require any tools like MisereSolver.
- | 2016-05-28 16:22:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5029604434967041, "perplexity": 1193.724392423354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049278042.30/warc/CC-MAIN-20160524002118-00159-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://www.freelancer.com.ru/projects/net/nid-specialist-net-14482011/?ngsw-bypass=&w=f | # i nid specialist .net -- 3
so in notepad you just put this C:\projects\in2l\in2lbrowser in a file and call it in2lbrowser@[url removed, login to view] and save it as a file with no extension and put that where the old extension folder was
oh also, mike had set up a special community that only syncs a little bit of data i think that i use on my vm. just so i dont need all of the subscription stuff but i can still get the link content
my full setup is a VM + Visual Studio Code + Whatever version of FF you are testing + The Git folders set up in place of where the normal extensions would usually be on a production unit
and then i just open up to the root of those two extension folders and modify them. and then when you launch teh firefox in the background with those pointer files you are working on live code essentially
you can just use text editor though
Навыки: .NET
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( 146 отзыв(-а, -ов) ) ploiesti, Romania
ID проекта: #14482011
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$25 USD за 1 день (0 отзывов(-а)) 0.0 sandhuharit Harit Sandhu BDM Company: GHS INFOTECH PVT LTD. As you requires a software build to support your digital growth strategy. This software will allow you expose your brand to organic audiences via search engines, Больше$25 USD за 1 день | 2021-01-16 13:12:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38128918409347534, "perplexity": 6105.589325445925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703506640.22/warc/CC-MAIN-20210116104719-20210116134719-00336.warc.gz"} |
https://www.flybacktolove.com/site/archive.php?tag=list-of-lifetime-drama-films-6853b2 | You can also download it, Armed with both sets of points, we calculate the Affine Transform by using OpenCV function, We then apply the Affine Transform just found to the src image, The center with respect to which the image will rotate, The angle to be rotated. src: input image. We just got our first transformed image! You may note that the size and orientation of the triangle defined by the 3 points change. We use the function, Applies a Rotation to the image after being transformed. We know $$M$$ and $$X$$. This video is part of the Udacity course "Computational Photography". Parameters: In this tutorial we will see how to warp a single triangle in an image to another triangle in a different image. OpenCV provides two transformation functions, cv2.warpAffine and cv2.warpPerspective, with which you can have all kinds of transformations. Then cv2.getAffineTransform will create a 2×3 matrix which is to be passed to cv2.warpAffine. 450. views 1. answer no. Attention geek! In other words, after an affine transform parallel lines continue to be parallel. Formal Technical Review (FTR) in Software Engineering, Write Interview In the following paragraphs, we will see how different affine matrices can scale, resize, flip or rotate images. Once we have the affine transformation matrix, we use the warpAffine function to apply this matrix to the input image. OpenCV provides two transformation functions, cv.warpAffine and cv.warpPerspective, with which you can perform all kinds of transformations. In computer graphics people deal with warping triangles all the time because any 3D surface can approximated by triangles. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. From the above, We can use an Affine Transformation to express: Rotations (linear transformation) Translations (vector addition) Scale operations (linear transformation) you can see that, in essence, an Affine Transformation represents a relation between two images. Smoothing data by using high degree B-spline Smoothing. close, link Scaling. Fig: Projective and Affine Transformation. From the above, we can use an Affine Transformation to express: you can see that, in essence, an Affine Transformation represents a relation between two images. Strengthen your foundations with the Python Programming Foundation Course and learn the basics. Transformations are used to change the geometry of the contents within the image. Syntax: cv2.getPerspectiveTransform(src, dst). Doing affine transformation in OpenCV is very simple. OpenCV is the huge open-source library for computer vision, machine learning, and image processing and now it plays a major role in real-time operation which is very important in today’s systems. We now apply the found rotation to the output of our previous Transformation: Finally, we display our results in two windows plus the original image for good measure: We just have to wait until the user exits the program. The usual way to represent an Affine Transformation is by using a $$2 \times 3$$ matrix. Preferable interpolation methods are cv2.INTER_AREA for shrinking and cv2.INTER_CUBIC (slow) & cv2.INTER_LINEAR for zooming. I have an image on which I apply affine transforms (several of them in a row). By default, interpolation method used is cv2.INTER_LINEARfor all resizing purposes. Look at the figure below: the points 1, 2 and 3 (forming a triangle in image 1) are mapped into image 2, still forming a triangle, but now they have changed notoriously. Scaling is ⦠alignment. The actual implementations of the geometrical transformations, from the most generic Remap and to the simplest and the fastest Resize, need to solve the 2 main problems with the above formula: affine. Scaling is just resizing of the image. Our information for $$M$$ may be explicit (i.e. Translation and Euclidean transforms are special cases of the Affine transform. An integer value representing the size of the output image. However, in OpenCV there is [â¦] To get the transformation matrix, we have a function called getAffineTransform in OpenCV. You can perform affine translation on an image using the warpAffine() method of the imgproc class. affine. Mat warpDst = Mat.zeros( src.rows(), src.cols(), src.type() ); Imgproc.warpAffine( src, warpDst, warpMat, warpDst.size() ); Mat rotMat = Imgproc.getRotationMatrix2D( center, angle, scale ); Imgproc.warpAffine( warpDst, warpRotateDst, rotMat, warpDst.size() ); System.loadLibrary(Core.NATIVE_LIBRARY_NAME); parser = argparse.ArgumentParser(description=, srcTri = np.array( [[0, 0], [src.shape[1] - 1, 0], [0, src.shape[0] - 1]] ).astype(np.float32), dstTri = np.array( [[0, src.shape[1]*0.33], [src.shape[1]*0.85, src.shape[0]*0.25], [src.shape[1]*0.15, src.shape[0]*0.7]] ).astype(np.float32), center = (warp_dst.shape[1]//2, warp_dst.shape[0]//2). The problem is that after executing them, sometimes happens that parts of the transformed image go outside of the view window and are not visible (as a result of the transformation). ; Use the OpenCV function cv::getRotationMatrix2D to obtain a $$2 \times 3$$ rotation matrix; Theory What is an Affine Transformation? For instance, for a picture like: after applying the first Affine Transform we obtain: and finally, after applying a negative rotation (remember negative means clockwise) and a scale factor, we get: String filename = args.length > 0 ? 2. Rotations (linear transformation) 2.2. brightness_4 Let's explain this in a better way (b). Mathematically, it is the process of transforming a pixel in a specific coordinate (x,y) in the input image to a new coordinate (xâ,yâ) in the output image. By using our site, you Note: For more information, refer to OpenCV Python Tutorial. dst: Coordinates of the corresponding quadrangle vertices in the destination image. Python: Running estimateRigidTransform in opencv/python; 8uC1 or 8uC3 error Affine transformation of a portion of an image-C++ [closed] estimateRigidTransform returns scale 0. cv2.warpAffine() results in an image shifted by 0.5 pixel. Different interpolation methods are used. flags: combination of interpolation methods (see resize() ) and the optional flag A square when transformed using a Homography can change to any quadrilateral. dsize: size of the output image. dst: output image that has the size dsize and the same type as src. So, we use affine transformations when we need to transform our image. ... How would I do Face Alignment on JPEG face images in OpenCv while using Java? votes 2014-10-27 04:41:45 -0500 R.Saracchini. midpoint of a line remains the midpoint after transformation). We use cookies to ensure you have the best browsing experience on our website. Parameters: Goal . To obtain $$T$$ we only need to apply $$T = M \cdot X$$. Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. There are a few ways to do it. In openCV, to obtain a transformation Read more⦠An affine transformation is composed of rotations, translations, scaling and shearing. c++. face. Mat warp_dst = Mat::zeros( src.rows, src.cols, src.type() ); 'Code for Affine Transformations tutorial. M: transformation matrix. ', A transformation that can be expressed in the form of a, We mentioned that an Affine Transformation is basically a, We know both $$X$$ and T and we also know that they are related. However, the affine transform is not flexible enough to transform a square to an arbitrary quadrilateral. Transformations . In this tutorial you will learn how to: Use the OpenCV function cv::warpAffine to implement simple remapping routines. In OpenCV an affine transform is a 2×3 matrix. We will display it in one bit. The size of the image can be specified manually, or you can specify the scaling factor. This rotation is with respect to the image center, The tutorial's code is shown below. Armed with both sets of points, we calculate the Affine Transform by using OpenCV function getAffineTransform: warp_mat = getAffineTransform (srcTri, dstTri); We get as an output a . Affine transformation is a function which transform an image while preserving the points, straight lines and planes i.e., the set of parallel lines remain parallel after performing affine transformation. src: Coordinates of quadrangle vertices in the source image. How to set input type date in dd-mm-yyyy format using HTML ? Experience. This transform has 8 parameters. In the case when the user specifies the forward mapping: , the OpenCV functions first compute the corresponding inverse mapping: and then use the above formula. So, a pixel value at fractional coordinates needs to be retrieved. Translations (vector addition) 2.3. Writing code in comment? To find the transformation matrix, we need three points from input image and their corresponding locations in the output image. $A = \begin{bmatrix} a_{00} & a_{01} \\ a_{10} & a_{11} \end{bmatrix}_{2 \times 2} B = \begin{bmatrix} b_{00} \\ b_{10} \end{bmatrix}_{2 \times 1}$, $M = \begin{bmatrix} A & B \end{bmatrix} = \begin{bmatrix} a_{00} & a_{01} & b_{00} \\ a_{10} & a_{11} & b_{10} \end{bmatrix}_{2 \times 3}$. Considering that we want to transform a 2D vector $$X = \begin{bmatrix}x \\ y\end{bmatrix}$$ by using $$A$$ and $$B$$, we can do the same with: $$T = A \cdot \begin{bmatrix}x \\ y\end{bmatrix} + B$$ or $$T = M \cdot [x, y, 1]^{T}$$, $T = \begin{bmatrix} a_{00}x + a_{01}y + b_{00} \\ a_{10}x + a_{11}y + b_{10} \end{bmatrix}$. Please use ide.geeksforgeeks.org, generate link and share the link here. Following is the input image: Images can be broken down into triangles and warped. Read the image; Define the 3 pairs of corresponding points (See image above) Calculate the transformation matrix using cv2.getAffineTransform() Apply the affine transformation using cv2.warpAffine() Make sure you read up on the components of this matrix. code. OpenCV is the huge open-source library for computer vision, machine learning, and image processing and now it plays a major role in real-time operation which is very important in todayâs systems. The 2-by-3 matrix ) or it can come as a geometric relation between points. How would I do n't think rotation+shift transform exists between your sets of ⦠affine invariant image., M, dsize, dst, flags, borderMode, borderValue ) find the transformation matrix, can! Used to perform the transformation matrix which is to find \ ( M\ and!:Warpaffine to implement simple remapping routines to find \ ( M\ ) the scaling factor the function, a! T = M \cdot X\ ) images like translation, rotation, affine transformation transformation we need apply., faces, or you can perform all kinds of transformations images translation..., flags, borderMode, borderValue ) then our task is to be retrieved which is find! Face Alignment on JPEG Face images in OpenCV while using Java the Python Programming Foundation course learn... Geometric operations performed on an image, changes the spatial relationships of the defined! More⦠Fig: Projective and affine transformation is composed of rotations, translations, scaling and shearing preparations Enhance Data. We use the function, Applies a rotation to the image of ⦠invariant...: Coordinates of quadrangle vertices in the source image to find_obj.py, but uses the affine is... This in a 2 x 3 sized matrix of rotations, translations, scaling shearing... Affine matrices can scale, resize, flip or rotate images ones on the other affine transformation opencv account... Quadrangle vertices in the example figure ( in the output image that has the size dsize the... Part of the triangle defined by the 3 points change resizing of affine transformation opencv corresponding quadrangle in... Diagonal and zeros elsewhere as Numpuy, Python is capable of processing affine transformation opencv! Your interview preparations Enhance your Data Structures concepts with the OpenCV function cv::warpAffine to implement remapping! To any quadrilateral task is to be retrieved on JPEG Face images in OpenCV while using Java as the of... Would I do Face Alignment on JPEG Face images in OpenCV an affine transformation we need transform! Cv2.Getaffinetransform will create a 2×3 matrix on our website information, refer to OpenCV Python.. Warpmat = Imgproc.getAffineTransform ( called ASIFT [ 1 ] OpenCV an affine transformation opencv transform not. Matrix to the image pixels method used is cv2.INTER_LINEARfor all resizing purposes OpenCV tutorial... 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The Theory section ) so, we can analyze the simplest case in which it relates three points it. By clicking on the other hand can account for some 3D effects ( but not all..
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http://cachestocaches.com/2 | # Welcome toCaches to Caches
This blog is devoted to the broad interests of Gregory J Stein, which includes topics such as Numerical Modeling, Web Design, Robotics, and a number of my individual hobby projects. If there's any article you would like to see, or something you've been wondering about, be sure to let me know on Twitter.
## My Workflow with Org-Agenda
I'm sure we've all had the same experience with "fully-featured" todo-list and project management programs: each had their own niceties, but none quite delivered on their promise. I've been using the built-in org-mode within Emacs for quite some time now, so I figured it was high time that I really made it my own.
For the last year, many of my customization options were taken directly from the unbelievably detailed Guide by Bernt Hansen and remained unchanged for some time. However, the guide contained an overwhelming amount of information, which made it difficult to determine precisely what features I would find most useful.
Even if you don't use this post for your own configurations, I highly recommend looking at Bernt's exhaustive guide.
I'm writing this short guide in an effort to introduce the features in org-mode which I've found I can't live without. I'll go over how I use org-mode, and it's powerful built-in summary/calendar view known as org-agenda, in both my work and in my hobby projects. I also include some details about how everything was implemented, or at the very least provide the reader with references to understand my code. This guide is only an introduction to my workflow and is by no means self-contained (unlike Bernt's)! Feel free to comment below or get in touch with me if you have any questions.
Org also has some nice export tools built in, so that I can easily share my notes with colleagues.
## Have You Tried Using a 'Nearest Neighbor Search'?
Thu 31 Mar 2016
Roughly a year and a half ago, I had the privelage of taking a graduate "Introduction to Machine Learning" course under the tutelage of the fantastic Professor Leslie Kaelbling. While I learned a great deal over the course of the semester, there was one minor point that she made to the class which stuck with me more than I expected it to at the time: before using a really fancy or sophisticated or "in-vogue" machine learning algorithm to solve your problem, try a simple Nearest Neighbor Search first.
Let's say I gave you a bunch of data points, each with a location in space and a value, and then asked you to predict the value of a new point in space. What would you do? Perhaps the values of you data are binary (just +s and -s) and you've heard of Support Vector Machines. Should you give that a shot? Maybe the values are continuously valued (anything on the real number line) and you feel like giving Linear Regression a whirl. Or you've heard of the ongoing Deep Learning Revolution and feel sufficiently bold as to tackle this problem with a Neural Net.
...or you could simply find the closest point in your dataset to the one you're interested in and offer up the value of this "nearest neighbor". A Nearest Neighbor Search is perhaps the simplest procedure you might conceive of if presented with a machine-learning-type problem while under the influence of some sort of generalized "veil of ignorance". Though there exist slightly more complicated variations in the algorithm, the basic principle of all of them is effectively the same.
## The Physics of Maxwell's Equations
Wed 16 Mar 2016
The original motivation for this post was the first homework prompt I encountered in graduate school at MIT, while I was taking a course on linear optics:
The course was taught by Prof. Jim Fujimoto, who pioneered optical coherence tomography.
Describe the Physics behind Maxwell's Equations.
Deceptively simple, the prompt was designed to encourage me and my peers to think more about the physical implications of the well-known Maxwell's Equations, which detail the behavior of electromagnetism, one of the fundamental forces of nature. Our responses were not supposed to be steeped in derivations or overly sophisticated equations, but were instead supposed to build intuition. I was quite proud of my response (and it earned the highest grade in the class), so I have included it here in an effort to convey my passion for these elegant, and profound, equations.
Here, I aim to delve into the fundamentals of electromagnetism, with the goal of making this post accessable to those who may not have a particularly strong mathematical background while including enough analysis so that it may be useful and interesting to those who do. More than anything, the purpose is to imbue the reader with some of the physical intuition behind electromagnetism.
## How We Teach Programming, and Where We're Going Wrong
Fri 5 Feb 2016
On the heels of President Obama's recent pledge to increase funding for computer science education in U.S. schools, I worry about the future of education in the discipline. Without a doubt, teaching students how to program is a must for ensuring that the United States can modernize its workforce and compete on a global scale. However, the ways in which programming is taught in schools often lacks real grounding, and effort needs to be made in order distance general education in computer science from the training given to computer scientists.
The purpose of learning how to code is not to become an expert programmer (just as learning mathematics is not for the express purpose of creating mathematicians), but is to allow people to recognize when a little bit of simple programming can save a huge amount of time and effort. Many introductory and online courses in programming focus too much on abstract skills and not enough on how these skills can be practically applied.
Abstract skills, like algorithms, are assuredly important, but when was the last time any of you coded your own merge-sort.
## Disabling Ubuntu's Broken Wi-Fi Driver
Sun 17 Jan 2016
Tags Ubuntu
Since I started using Ubuntu on more of my machines, I've encountered myriad issues relating to the wireless internet. Every few minutes, my wireless internet would simply dropout without warning and often without even realizing that the connection had vanished. Reconnecting was a nightmare, and was frequently most easily accomplished by simply rebooting my machine. Even when the wireless was 'working', pinging google.com (with ping google.com) would be slow and unreliable. Worst of all, this issue would often even limit my ability to get any work done for stretches of time, not to mention that it would invariably put me in a foul mood.
Admittedly, this post is mostly for my own reference, since it's decently well documented online if you know what you're looking for. However, if it can be helpful to any of you, that's motivation enough for putting this here.
## Getting Started with Use-Package
Mon 24 Aug 2015
Tags Emacs
Of all the packages I use to enhance my productivity in emacs, use-package is perhaps the most useful. With it, I can automatically download and install other packages from the emacs package databases when it detects they're missing. Since I'm constantly switching computers, virtual machines, and operating systems, having this functionality is essential for making sure I don't miss a beat when I'm starting from scratch; I simply clone the emacs config files from my GitHub repository and open emacs and I'm almost immediately ready to go.
This short guide shows how to ensure that use-package also automatically installs, and how to get the most out of the use-package features.
## Technologies Behind Caches To Caches
Mon 10 Aug 2015
There are a number of different technologies which have gone into creating this blog. Now that it's mostly complete (though I'm constantly tweaking its look), I figure I should give a list of these different tools so that someone can use it as a starting point for their own site. Though I've created a blog, many of the steps I've gone through are useful for anyone creating a small, content-driven website of their own.
In short, this site (and my personal website) are hosted on a single Amazon T2.micro instance using Django and Apache and formatted using Bootstrap (and modified using Less). However, there's much more to it than that. I also made my mark in social media, being sure to get the pages associated with my site. See more details after the jump. | 2018-04-21 09:23:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34453317523002625, "perplexity": 987.1933974948215}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945111.79/warc/CC-MAIN-20180421090739-20180421110739-00132.warc.gz"} |
https://codereview.stackexchange.com/questions/18223/expressing-multiple-and-conditions-in-ruby | # Expressing multiple AND conditions in ruby
In ruby, is there a more concise way of expressing multiple AND conditions in an if statement?
For example this is the code I have:
if first_name.blank? and last_name.blank? and email.blank? and phone.blank?
#do something
end
Is there a better way to express this in Ruby? 1.9.2 or 1.9.3
if [first_name, last_name, email, phone].all?(&:blank?)
#do something
end
Caveat: While and/&& short-circuit the expression (that's it, only the needed operands are evaluated), an array evaluates all its items in advance. In your case it does not seem something to worry about (they seem cheap attributes to get), but if you ever need lazy evaluation and still want to use this approach, it's possible using procs, just slightly more verbose:
p = proc
if [p{first_name}, p{last_name}, p{email}, p{phone}].all? { |p| p.call.blank? }
#do something
end
• I received an undefined method 'all' on the code example above. See repl.it/D7X – koa Nov 5 '12 at 7:50
• @koa: all?. The enumerable methods are a must read (really, read and understand them one by one). ruby-doc.org/core-1.9.3/Enumerable.html – tokland Nov 5 '12 at 8:02
• Sometimes the logic setting up a condition is the worst part of programming, and, after getting done, still won't look right. It's like staring at a word and it just doesn't look like it's spelled right, though you know it is. I generally try to go with whatever combination results in the most concise, yet readable, code for the long-term. After I get done writing it, it could be passed to several other programmers so I don't want them coming back later asking what-the-heck that code does. I've used all? against an array, and chains of && and ||, depending on what felt right. – the Tin Man Nov 9 '12 at 5:08
• @the Tin Man. Thanks for commenting. I think we had our differences in the past about how to write logic, didn't we? :-) I agree that it's hard to get it right, logic is so important (is there anything more important in an app?) that it deserves to invest time on it. For me the best logic is that which resembles mathematical logic, that uses no early "return"s, in-line conditionals, nor any other imperative stuff. Just the good old logic expressions. – tokland Nov 9 '12 at 11:32
• When I was writing assembly language, Perl and C, I wrote my conditionals a lot more tersely and concisely. Languages like Ruby encourage a more expressive coding style, that tries to sit between a conversation with the computer, and cold-logic. I prefer conciseness over verbosity personally, but not everyone can deal with Perl-like code, so I try to adjust. In your answer above, your point about short-circuiting is important, especially as the list of conditions grows. Blindly looping over every element can become costly so && and || become important. – the Tin Man Nov 9 '12 at 14:03 | 2019-12-12 07:01:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2665804326534271, "perplexity": 2421.730382398808}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00100.warc.gz"} |
http://sixty-north.com/blog/the-super-mystery-resolved | # Good with Computers
The Sixty North Blog
# The super() Mystery Resolved
In the previous articles in this series1 we uncovered a small mystery regarding how Python’s super() works, and we looked at some of the underlying mechanics of how super() really works. In this article we’ll see how those details work together to resolve the mystery.
# The mystery revisited
As you’ll recall, the mystery we uncovered has to do with how a single use of super() seemed to invoke two separate implementations of a method in our SortedIntList example. As a reminder, our class diagram looks like this:
Inheritance graph
SimpleList defines a simplified list API, and IntList and SortedList each enforce specific constraints on the contents of the list. The class SortedIntList inherits from both IntList and SortedList and enforces the constraints of both base classes. Interestingly, though, SortedIntList has a trivial implementation:
class SortedIntList(IntList, SortedList):
pass
How does SortedIntList do what it does? From the code it seems that SortedIntList does no coordination between its base classes, and certainly the base classes don’t know anything about each other. Yet somehow SortedIntList manages to invoke both implementations of add(), thereby enforcing all of the necessary constraints.
# super() with no arguments
We’ve already looked at method resolution order, C3 linearization, and the general behavior of super instances. The final bit of information we need in order to resolve the mystery is how super() behaves when called with no arguments.2 Both IntList and SortedList use super() this way, in both their initializers and in add().
For instance methods such as these, calling super() with no arguments is the same as calling super() with the method’s class as the first argument and self as the second. In other words, it constructs a super proxy that uses the MRO from self starting at the class implementing the method. Knowing this, it’s easy to see how, in simple cases, using super() is equivalent to “calling the base class implementation”. In these cases, type(self) is the same as the class implementing the method, so the method is resolved using everything in that class’s MRO except the class itself. The next entry in the MRO will, of course, be the class’s first base class, so simple uses of super() are equivalent to invoking a method on the first base class.
A key point to notice here is that type(self) will not always be the same as the class implementing a specific method. If you invoke super() in a method on a class with a subclass, then type(self) may well be that subclass. You can see this in a trivial example:
>>> class Base:
... def f(self):
... print('Type of self in Base.f() =', type(self))
...
>>> class Sub(Base):
... pass
...
>>> Sub().f()
Type of self in Base.f() = <class '__main__.Sub'>
Understanding this point is the final key to seeing how SortedIntList works. If type(self) in a base class is not necessarily the type of the class implementing the method, then the MRO that gets used by super() is not necessarily the MRO of the class implementing the method…it may be that of the subclass. Since the entries in type(self).mro() may include entries that are not in the MRO for the implementing class, calls to super() in a base class may resolve to implementations that are not in the base class’s own MRO. In other words, Python’s method resolution is – as you might have guessed – extremely dynamic and depends not just on a class’s base classes but its subclasses as well.
# Method resolution order to the rescue
With that in mind, let’s finally see how all of the elements – MRO, no-argument super(), and multiple inheritance – coordinate to make SortedIntList work. As we’ve just seen, when super() is used with no arguments in an instance method, the proxy uses the MRO of self which, of course, will be that of SortedIntList in our example. So the first thing to look at is the MRO of SortedIntList itself:
>>> SortedIntList.mro()
[<class 'SortedIntList'>,
<class 'IntList'>,
<class 'SortedList'>,
<class 'SimpleList'>,
<class 'object'>]
A critical point here is that the MRO contains IntList and SortedList, meaning that both of them can contribute implementations when super() is used.
Next, let’s examine the behavior of SortedIntList when we call its add() method.3 Because IntList is the first class in the MRO which implements add(), a call to add() on a SortedIntList resolves to IntList.add():
class IntList(SimpleList):
# ...
self._validate(item)
And this is where things get interesting!
In IntList.add() there is a call to super().add(item), and because of how no-argument super() calls work, this is equivalent to super(IntList, self).add(item). Since type(self) == SortedIntList, this call to super() uses the MRO for SortedIntList and not just IntList. As a result, even though IntList doesn’t really “know” anything about SortedList, it can access SortedList methods via a subclass’s MRO.
In the end, the call to super().add(item) in IntList.add() takes the MRO of SortedIntList, find’s IntList in that MRO, and uses everything after IntList in the MRO to resolve the method invocation. Since that MRO-tail looks like this:
[<class 'SortedList'>, <class 'SimpleList'>, <class 'object'>]
and since method resolution uses the first class in an MRO that implements a method, the call resolves to SortedList.add() which, of course, enforces the sorting constraint.
So by including both of its base classes in its MRO4 – and because IntList and SortedList use super() in a cooperative way – SortedIntList ensures that both the sorting and type constraint are enforced.
# No more mystery
We’ve seen that a subclass can leverage MRO and super() to do some pretty interesting things. It can create entirely new method resolutions for its base classes, resolutions that aren’t apparent in the base class definitions and are entirely dependent on runtime context.
Used properly, this can lead to some really powerful designs. Our SortedIntList example is just one instance of what can be done. At the same time, if used naively, super() can have some surprising and unexpected effects, so it pays to think deeply about the consequences of super() when you use it. For example, if you really do want to just call a specific base class implementation, you might be better off calling it directly rather than leaving the resolution open to the whims of subclass developers. It may be cliche, but it’s true: with great power comes great responsibility.
For more information on this topic, you can always see the Inheritance and Subtype Polymorphism module of our Python: Beyond the Basics course on PluralSight.5
1. Note that calling super() with no arguments is only supported in Python 3. Python 2 users will need to use the longer explicit form.
2. The same logic applies to it’s __init__() which also involves calls to super()
3. Thanks, of course, to how C3 works
### Stay in Touch
Our business hours are 08:00 to 16:00 CET/CEST. | 2017-03-27 22:25:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3371044397354126, "perplexity": 2846.7802067934977}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189534.68/warc/CC-MAIN-20170322212949-00182-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://zbmath.org/?q=an:0912.32026 | # zbMATH — the first resource for mathematics
Metric rigidity theorems on Hermitian locally symmetric manifolds. (English) Zbl 0912.32026
Series in Pure Mathematics. 6. Singapore: World Scientific. xiv, 278 p. (1989).
Hermitian symmetric spaces have long played a central role in classical complex differential geometry and they have been studied with various points of view in mind. The purpose of this monograph is to study the problem of characterizing canonical metrics on Hermitian locally symmetric spaces in terms of curvature conditions. As well, these metric rigidity theorems and their proofs are applied to the study of holomorphic maps between Hermitian locally symmetric spaces of the same type in order to get various rigidity theorems on holomorphic maps.
The presentation is divided into two parts. The first part contains a wealth of background material about complex differential geometry on Hermitian locally symmetric spaces, e.g. Hermitian connections, their curvatures, notions of positivity and negativity of curvature, explicit calculations of the curvature tensor of the Kähler form of the Bergman metric on classical bounded symmetric domains, etc. Also included is some of the author’s work on Hermitian metric rigidity in the case of compact quotients of bounded symmetric domains [N. Mok, Ann. Math., II. Ser. 125, No. 1, 105-152 (1987; Zbl 0616.53040)]. Suppose $$X$$ is a compact quotient of an irreducible bounded symmetric domain of rank $$\geq 2$$ and $$h$$ is a Hermitian metric of (Griffiths) seminegative curvature. Then $$h$$ is a constant multiple of the Kähler-Einstein metric $$g$$. The monograph presents an expanded version of these results, e.g. description of and an integral formula on the characteristic bundle $$\mathcal S$$, along with those in another paper by the author [Math. Ann. 276, No. 2, 177-204 (1987; Zbl 0612.53029].
The second part contains more recent developments. First, an extension of metric rigidity theorems to the case of finite volume due to W-K. To [Invent. Math. 95, No. 3, 559-578 (1989; Zbl 0668.53034)] is given. Next the immersion problem between complex hyperbolic space forms according to the author [“Local biholomorphisms between Hermitian locally symmetric spaces of noncompact type”, Preprint; per bibl.], and H. D. Cao and the author [Invent. Math. 100, No. 1, 49-61 (1990; Zbl 0698.53035)] is treated. Then follows a Hermitian metric rigidity theorem on locally homogeneous vector bundles.
The last chapter has a result of I.-H. Tsai [J. Differ. Geom. 33, No. 3, 717-729 (1991; Zbl 0718.53042)] on a rigidity theorem for holomorphic maps between irreducible Hermitian symmetric spaces of compact type. At the end there are four appendices dealing with some background material, e.g. on semisimple Lie algebras and their representations and on a dual generalized Frankel conjecture.
##### MSC:
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 32Q15 Kähler manifolds 32Q45 Hyperbolic and Kobayashi hyperbolic manifolds 32Q20 Kähler-Einstein manifolds 53C35 Differential geometry of symmetric spaces | 2021-10-22 19:37:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6633048057556152, "perplexity": 356.8417323099844}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585518.54/warc/CC-MAIN-20211022181017-20211022211017-00012.warc.gz"} |
https://www.languageaudiobooks.com/wi02ywx7/9cdab8-scrolls-pathfinder-2e | When taking the Craft Scroll feat, it says that you can now craft scrolls. Also, I am pretty familiar with PF2 and I know a lot about TES, so feel free to inbox me if you want help. If you're a human you can easily gain access to two spell lists without having to take the 2 other feats before taking a 2nd dedication (level 9 human ancestry feat). A scroll contains a single spell that you can cast without having to expend a spell slot. To learn more, see our tips on writing great answers. Looking good! It updates your remaining spell slots as you prepare and cast spells. Glad to see my fave race (Bosmer) in there. Eyes of Night: If you don't already get Darkvision between your Ancestry and the Changeling Heritage traits, this is an absolute must.The ability to see in darkness is simply too good to pass up. Pathfinder 2e scrolls have precious little information, as far as I can tell. Makes those first caster dedication feats a lot better than I thought. A scroll has AC 9, 1 hit point, hardness 0, and a break DC of 8. Character optimization guide for the Pathfinder 2e Dhampir. Pathfinder Adventure: The Fall of Plaguestone (P2) by Jason Bulmahn | Aug 1, 2019. In addition to your daily scrolls from the Basic and Expert Scroll Caches, add a single scroll with a 6th-level spell. Thank you so much for the feedback! For a 4-week old project, it's definitely uplifting hearing a few people being excited about this, so thank you! Asked to referee a paper on a topic that I think another group is working on, The English translation for the Chinese word "剩女". Thanks for contributing an answer to Role-playing Games Stack Exchange! The Advanced Player's Guide for Pathfinder 2e is here! The only truly accurate way might be to all caster classes but Sorcerer Uncommon, make Sorcerers Int-based, reflavour bloodlines as something learned rather than innate, and then come up with a few bloodlines to fit the various ways people learn magic. It only takes a minute to sign up. As much as I love creating stuff, I know I have to have at least a few people on watch so I don’t get carried away haha. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Pathfinder training simplified to a choice of 5 options (swords, scrolls, spells, generalist, field commission.) How can a supermassive black hole be 13 billion years old? Pathfinder Training. It takes way too long to open and slows my computer down when I do because it has to load so many overlapping images, and this is a gaming laptop. What I'm confused about is "plus the traits of the spell stored on it." I also noticed you don't give any Ancestry a top-level special ability like Darkvision. Get it as soon as Mon, Jan 18. ISBN 978-1-60125-268-5 99 $22.99$22.99. We've ranked the 10 best for those seeking a strong and powerful character. A scroll tube , or scroll case , is often used to protect scrolls from, for instance, damage by … The traits for a scroll vary based on the spell it contains. A scroll can be Crafted to contain nearly any spell, so the types of scrolls available are limited only by the number of spells in the game. What's the legal term for a law or a set of laws which are realistically impossible to follow in practice? Alternatively, just bookmark the Pathfinder 2nd Edition News tag, if Pathfinder 2E news is all you want to see. Prerequisite(s) Expert Scroll Cache. When I flipped to Chapter 3 of the Pathfinder 2E Advanced Player’s Guide, I was expecting to see a healthy handful of archetype options. I do want to keep with this, but if it doesn’t seem to be working out for the other ancestries I’ll have to rework it. It calculates your spells per day per level. For sure something I want to implement and work with at a later date though. Scrolls that hold three or more spells are usually fitted with reinforcing rods at each end rather than simple strips of leather. Level 1. Consumables changed. The exceptions are cantrips, focus spells, and rituals, none of which can be put on scrolls. Me: yeaahh why would I take the feat if it's not going to benefit me somehow. New comments cannot be posted and votes cannot be cast, More posts from the Pathfinder2e community. UK - Can I buy things for myself through my company? It’s comments like these that make me excited and happy to be working on this. 0. Shop Pathfinder 2E RPG: Pawns Base Assortment at Miniature Market. A scroll has AC 9, 1 hit point, hardness 0, and a break DC of 8. Shop Adventure Gear Deck - Pathfinder 2E RPG at Fantasy Games, South Bend, Indiana. Certainly! It’s great for covering things that are universal to all the elves/human races, while still allowing those unique touches like, for example, the Colovian/Nibenese distinction for Imperials. Seeing what works and what doesn’t is critical, so getting thorough responses is a blessing. rev 2021.1.21.38376, The best answers are voted up and rise to the top, Role-playing Games 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. I want to make something that’s respectable to the universe it’s based in and the system I chose to make it on. However there are some things that all Characters have in common. Just want to thank you again for this response. Pathfinder 2e scrolls have precious little information, as far as I can tell. roseville helicopter activity today Likes. 1: Races of Nature Unleashed (PF2) December 2, 2020; Aegis of Empires 5: Race for Shataakh-Uulm (Pathfinder Second Edition) November 21, 2020 You might also want to look into PF2 homebrew formatting options, rather than 5e ones. Press question mark to learn the rest of the keyboard shortcuts. Reinstall the Pathfinder 2e system using foundry and the problem should be resolved. Pathfinder 2nd edition seems to shake things up and change the game up, pretty much everything is different except for the skill points, which have been changed a … The images are high-res, and the water coloring really does a number on the space the PDF takes up. Moving to today, I offer you all a small compilation of what I've done. Can a faerie dragon (improved familiar) use all scrolls and wands with spells from the sorcerer/wizard list? That's just a whole lot of work and cuts out a whole lot of Pathfinder.The other, possibly bigger thing is how you're going to capture the general 'be who you want' feeling in the pf2's structure. Here is my categorised feedback: General acknowledgements: So a big thing is how you're gonna do magic in this, because TES doesn't really distinguish Arcane from Divine, let alone Occult and Primal (in fact, it's mostly all Primal outside of Mysticism and some other specific spells). I’d have to agree with the other commenter that the high quality images chug the pdf’s loading time unfortunately. I look forward to seeing what you do with it. If you do decide to do something text based and want a Pathfinder aesthetic, have a look at scribe.pf2.tools! Because you’re the one Casting the Spell, use your spell attack roll and spell DC. Can an open canal loop transmit net positive power over a distance effectively? Scroll Trickster: Paizo: Pathfinder Advanced Player’s Guide: Scrounger: Paizo: ... Pathfinder Lost Omens World Guide (Second Edition) Swashbuckler: Paizo: Pathfinder Advanced Player’s Guide: ... Latest Pathfinder 2e! Do i need a chain breaker tool to install new chain on bicycle? Having the birthsigns is a pretty big part, but at the moment it’s not my primary focus. More religious folk tend to use more restoration, but restoration is still a school used by the mages guild. I'm coming to Pathfinder 2e from D&D 5th edition where only Wizards could learn new spells from scrolls or spellbooks. Would having only 3 fingers/toes on their hands/feet effect a humanoid species negatively? I stated this in another reply I made, but I’ll state it again here. Use MathJax to format equations. The best place on Earth for nerds. That is, I have a selection of heritages and feats that any elf ancestry can take, and the same for humans. I want people to be excited by this, but I also want them to be able to view it without burning out their CPUs lol. You've got some really fun ideas, though I do have some concerns about the balance of some - namely the Altmer armour ones. Why do small merchants charge an extra 30 cents for small amounts paid by credit card? You can create magic scrolls. What rarities should be assigned to each of the DMG's Magic Item Tables A through I? Pathfinder RPG Bestiary 2 (First Edition), p. 15. RS-25E cost estimate but sentence confusing (approximately: help; maybe)? Your scroll collection is incredible, brimming with eldritch power, and you can prepare far more of them than an ordinary scroll trickster. Actual cost of magic items where the spell has costly material component? At 20th level, add a scroll with a 7th-level spell. So the scroll itself does not have a Tradition, but gains it when used. Thanks x. Get it as soon as Thu, Dec 10. Races that do have definite internal variants (namely the beast races) could easily be handled by having various top-level special abilities. A scroll contains a single spell you can cast without a spell slot. More Buying Choices $11.99 (45 … Community Contributed Macros In this section you'll find a number of community contributed "Macros" which help speed up your games by reducing the amount of steps it takes to adjust something, grant something or adjudicate something. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. How does Eldritch Conduit for Rogues Work? Make it easy to track your spellcasting in the Pathfinder RPG. From classic creatures like serpentfolk and jabberwock, returning favorit Scribing a scroll takes 2 hours if its base price is 250 gp or less, otherwise scribing a scroll takes 1 day for each 1,000 gp in its base price. I don't quite know how to reconcile this without sacrificing trueness to one side or the other. Press J to jump to the feed. This scaling keeps cantrips a reliable source of damage output at any level, though you'll still want to rely on leveled spells when they suit the situation rather than counting on cantrips as your only source of damage output. The other classes that learned spells, like Sorcerors and Warlocks, could only do so by levelling up. Latest Pathfinder 2e! Pathfinder 2e scrolls have precious little information, as far as I can tell. An unofficial subreddit for anything related to the Pathfinder Second Edition tabletop role-playing game. How should I set up and execute air battles in my session to avoid easy encounters? Asking for help, clarification, or responding to other answers. For Argonians, I'd just use the same abilities that pf2 Lizardfolk get, and I'd give Bosmer a +1 to saves against disease, but idk about Altmer; maybe a cantrip? 4.5 out of 5 stars 159. Since blending character builds is pretty normal with TES, I'd consider making the Free Archetype variant rule a recommended standard. Treasury of Winter (Pathfinder Second Edition) December 11, 2020; Ugchi Ancestry December 5, 2020; Ancestral Anthologies Vol. Is it kidnapping if I steal a car that happens to have a baby in it? This volunteer-built game system for Foundry Virtual Tabletop provides comprehensive support for the Pathfinder Second Edition Tabletop Role Playing Game created by Paizo. Top Level: I'd suggest prioritising Free ability boosts rather than two specific ones - it means players are less likely to be restricted from certain builds. MathJax reference. A few days ago, I uploaded an alternate ancestry I had crafted; the Altmer, or High Elf. Nerds on Earth. The Good of Pathfinder 2e. Because your number of cantrips are limited, try to split your options … Each gives bonus lore at 1st level, bonus skill feat at 5th level. New classes, items, spells, archetypes and more await you in this must-have supplemental book. Paperback$17.99 $17. Spell Tracker keeps track of everything related to spellcasting and magic in one place. Share. First Century [] 2E 1 — Beginning of the Second Era.. By decree of Potentate Versidue-Shaie, year one of the Second Era begins on the first of Morning Star.The marking of the new era commemorates the demise of the Reman Dynasty and Versidue-Shaie's official assumption of stewardship of the Second Empire. Paizo #2104 Pathfinder 2E Bestiary 2 Hardcover BookRelease Date: May 2020 Pathfinder 2E Bestiary 2 With more than 350 classic and brand new monsters, this 320-page hardcover rulebook greatly expands on the foes found in the Pathfinder Bestiary. Role-playing Games Stack Exchange is a question and answer site for gamemasters and players of tabletop, paper-and-pencil role-playing games. Though this has been something I've purely done in my free time on my own (when I am both not working, and not in class), the initial response I got from the various subreddits has been really positive and brings with it, a great sense of hope. To Cast a Spell from a scroll, the spell must appear on your spell list. Having a feel for the power level of the other races is crucial to finding that balance. It remembers which spells you know. All in all, I'm glad you're doing this. Having that professional look is an “end-game” and purely serves right now as the ideal. You could do Argonian heritages as different levels of hist sap consumption. All my past releases (both general and ancestry specific) are listed in the discord's change-log chat. Paizo Publishing, LLC. FIVE MAJOR POINTS The traits for a scroll vary based on the spell it contains. Though this has been something I've purely done in my free time on my own (when I am both not working, and not in class), the initial response I got from the various subreddits has been really positive and brings with it, a great sense of hope. A scroll has AC 9, 1 hit point, hardness 0, and a break DC of 8. One of the first decisions you have to make when creating a role-playing character is determining what class you want to play as. I've been working on a personal project to create an overhaul for Pathfinder 2e in the Elder Scrolls setting. By Danyell Marshall Aug 09, 2019. It’s definitely in a proof of concept stage at the moment, and I’ll likely be switching to a text-based format for community use/viewing. It always makes me laugh "your taking that feat so your npc can make weapons, scrolls etc" . UESPC: The Unofficial Elder Scrolls Pathfinder Conversion [2e] Homebrew. And by the Nine Divines, stay on the space the PDF takes up 2e news is gathered from source! To expend a spell scroll without holding it scrolls Pathfinder Conversion [ 2e ] homebrew stated in CRB... Saxophone mouthpieces stated this in another reply I made, but I would to! Jan 18 saved this, so which are the deadliest Caches, add scroll. Like crazy can not be cast, more posts from the Basic and Expert scroll,! Other classes that learned spells, generalist, field commission. & D 5th Edition where only Wizards learn! Guide for Pathfinder 2e wizard schools races ) could easily be handled by having various top-level special abilities can buy... Role-Playing game more Buying Choices$ 11.99 ( 45 … Pathfinder 2e scrolls have precious little information, far. Set of laws which are the deadliest power, and by the Divines... To give specific feedback 'll keep an eye out for new ones explicitly... Races that do have one question about crafting scrolls, because I n't! Use all scrolls and wands with spells from the Basic and Expert scroll Caches, add a scroll is,! General and ancestry specific ) are listed in the discord 's change-log chat be limited to what ’ “... One of the spell also gains the appropriate trait for your Tradition ( arcane, divine if. On the spell stored on it. at Miniature Market gamemasters and of... Your answer ”, you 've done cool I 've spent a rigorous reading! D 5th Edition where only Wizards could learn new spells from scrolls or books news is all want... Make me excited and happy to be the best it can be search, tools and! At 5th level you in this must-have supplemental book to finding that balance variant... Actual cost of magic items where the spell stored scrolls pathfinder 2e it. out there, and that is by!: you can now Craft scrolls 5 options ( swords, scrolls, because I do n't know. Rolled up from both ends to form a double cylinder designing Imperials wasn ’ t too,! Dungeons and Dragons this venture of mine taking too much PF out Nedes, etc limited to ’. Player 's Guide for Pathfinder 2e in the Post to a permanent one, my.... With the other Base Assortment at Miniature Market discord 's change-log scrolls pathfinder 2e press question to. N'T think it 's explicitly stated in the Pathfinder Second Edition tabletop role-playing game ©. Order to cast a spell slot my past releases ( both general and ancestry )... ( if at all like how magic works in TES more restoration, but at the moment ’. And cast spells wizard schools unofficial Elder scrolls setting of laws which are realistically impossible to follow in practice on! Going to want to do something text based and want a Pathfinder aesthetic, have a look at scribe.pf2.tools pretty! Want this thing to be the best version of itself it can be put on.. Support for the new Pathfinder 2e system using foundry and the same for humans assigned to each of these be! 2E mega tome plus the traits for a scroll is divine, if Pathfinder 2e scrolls have little! See my fave race ( Bosmer ) in there doesn ’ t is critical, but I D... Three or more spells are usually fitted scrolls pathfinder 2e reinforcing rods at each end rather than simple strips of.. Wands with spells from scrolls or books confusing ( approximately: help ; maybe ) question about crafting,. Fave race ( Bosmer ) in there or books to Pathfinder 2e scrolls have little. Cast the spell ( or use Trick magic Item ) exceptions are cantrips, focus spells, like and! Policy and cookie policy and Expert scroll Caches, add a single spell you can create scroll. Prima Wiki Italiana Dedicata a Pathfinder GDR remaining spell slots as you prepare and cast spells own options... To want to do something about how graphically intensive the file is in later versions but at the moment ’. I need a chain breaker tool to install new chain on bicycle definitely going to want see... Actual mechanics, you agree to our terms of service, privacy policy and cookie policy more folk... Revisit when I have a selection of heritages and put birthsigns there as a kind of universal heritage user. To agree with the other races is crucial to finding that balance sure something I want to revisit when have! Spell effects available under the community religious folk tend to use more,! User contributions licensed under cc by-sa big part, but idk what yet one question crafting... Later date though for humans classes can learn new spells from scrolls or?. That Tradition in order to cast a spell from a scroll with a 6th-level spell idea is genius will! Give specific feedback December 5, 2020 ; Ancestral Anthologies Vol bought 5e... Would I take the feat if it 's definitely uplifting hearing a few days ago, 'd. Ugchi ancestry December 5, 2020 ; Ugchi ancestry December 5, 2020 ; ancestry... Far more of them than an ordinary scroll trickster CRB anywhere, rolling characters and pondering monster creation the... Double cylinder a better idea to scrap heritages and feats that any Elf ancestry can take, and the coloring! Each specific race is still its own ancestry with its own ancestry with its own ancestry with its ancestry... Better idea to scrap heritages and put birthsigns there as a kind of heritage! Want a Pathfinder aesthetic, have a Tradition, but at the it! Internal variants ( namely the beast races ) could easily be handled by having top-level. Text based and want a Pathfinder aesthetic, have a couple out by the Nine Divines, stay on spell!, p. 15 because you ’ re the one Casting the spell must appear on your spell attack roll spell. But sentence confusing ( approximately: help ; maybe ) I cast a spell slot do Argonian heritages as levels. Could only do so by levelling up with at a later date though t too,! As soon as Mon, Jan 18 of magical options the one Casting spell... | Aug 1, 2019 see this become the best version of itself it can,., none of which can be should be assigned to each of these may be limited to what ’ loading! A hindrance while the options for each of these may be limited to what s... Namely the beast races ) could easily be handled by having various top-level special ability like Darkvision take, a! Always has the consumable, magical, and rituals, none of can... Being excited about this, and that is determined by the end of this week! At scribe.pf2.tools 5e to Pathfinder 2e in the Elder scrolls setting I stated this in another reply I made but... Sure something I want to play as being interested in this must-have supplemental book spent a rigorous reading! Session to avoid easy encounters orders over \$ 25 shipped by Amazon each! In my session to avoid easy encounters the news is all you want to thank you so! Fave race ( Bosmer ) in there the roads too many to give specific feedback blending! Ancestral Anthologies Vol paper-and-pencil role-playing Games Stack Exchange Inc ; user contributions under. Is adjusted ( if at all ) for modern instruments this must-have supplemental book ancestry December 5, 2020 Ugchi. Faerie dragon ( improved familiar ) use all scrolls and wands with spells from scrolls or books shortcuts. Familiar ) use all scrolls and wands with spells from the community rituals, of... That all characters have in common Pawns Base Assortment at Miniature Market and happy to the... Best tenor saxophone mouthpieces laws which are realistically impossible to follow in practice of! Powerful character of Winter ( Pathfinder Second Edition rules, database search, tools and... With a decentralized organ system under cc by-sa Italiana Dedicata a Pathfinder GDR Shipping on over... Updates your remaining spell slots as you prepare and cast spells things that characters... 9, 1 hit point, hardness 0, and scroll traits, plus the traits of the DMG magic... But at the moment it ’ s gon na be a better idea to scrap heritages feats... The discord 's change-log chat only Wizards could learn new spells from the community! N'T give any ancestry a top-level special abilities remaining duration of active spell effects be limited to what s! Is all you want to thank you again for this response eldritch power, and you can create a has... Myself through my company and too rules intensive my search, tools and... Imperials wasn ’ t is critical, so thank you all so much for interested... Put on scrolls the ideal both ends to form a double cylinder this game... Spells, generalist, field commission. ranked the 10 best for those seeking a strong powerful. Venture of mine that has been a bit of a hindrance far more of than! Hit point, hardness 0, and a break DC of 8 about how graphically intensive the is. By having various top-level special abilities one side or the other forward to seeing works. Is not at all ) for modern instruments, etc without taking too much out... Points it always makes me laugh your taking that feat so your npc can make weapons scrolls! Ability like Darkvision definitely be testing this ) only do so by levelling up takes... Clarification, or primal ) to cast the spell stored on it. it can be, by! Supplemental book see my fave race ( Bosmer ) in there would to! | 2021-04-12 22:27:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24323947727680206, "perplexity": 4655.16761815167}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038069267.22/warc/CC-MAIN-20210412210312-20210413000312-00467.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-4a-5-2a-3 | # How do you solve 4a - 5 = 2a - 3?
Oct 20, 2016
$a = 1$
#### Explanation:
collect terms in a on the left side of the equation and numeric values on the right side.
subtract 2a from both sides.
$4 a - 2 a - 5 = \cancel{2 a} \cancel{- 2 a} - 3$
$\Rightarrow 2 a - 5 = - 3$
$2 a \cancel{- 5} \cancel{+ 5} = - 3 + 5$
$\Rightarrow 2 a = 2$
$\frac{\cancel{2} a}{\cancel{2}} = \frac{2}{2}$
$\Rightarrow a = 1 \text{ is the solution}$ | 2020-02-20 11:48:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5717037916183472, "perplexity": 1138.6296722029103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144722.77/warc/CC-MAIN-20200220100914-20200220130914-00527.warc.gz"} |
http://rinterested.github.io/statistics/df_betas.html | ### OLS DIAGNOSTICS:
First off, setting up a toy example, from the first rows of the dataset mtcars:
d = mtcars[1:6,] # The dataset
fit = lm(mpg ~ wt + disp, d) # The OLS model
X = model.matrix(fit) # The model matrix X
H = X %*% (solve(t(X) %*% X) %*% t(X)) # The hat matrix
diagonal = hat(model.matrix(fit)) # The diagonal of the hat matrix
#### Dfbeta:
DFBETA measures the difference in each parameter estimate with and without a presumably influential point. There is a DFBETA for each point and each observation (if there are $$N$$ points and $$k$$ variables there are $$N\times k$$ DFBETAs).
# Let's look at the leverage of the fist entry in the database:
d[1,]
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21 6 160 110 3.9 2.62 16.46 0 1 4 4
# First calculate the coefficients fitting the model without this entry:
dno = d[-1,]
fitno = lm(mpg ~ wt + disp, dno)
coefficients(fit) - coefficients(fitno)
## (Intercept) wt disp
## -1.5146662238 0.5115198590 -0.0008971436
# More expediently,
dfbeta(fit)[1,]
## (Intercept) wt disp
## -1.5146662238 0.5115198590 -0.0008971436
#### Leverage or influence or hat value:
In statistics, the projection matrix , sometimes also called the influence matrix or hat matrix , maps the vector of response values (dependent variable values) to the vector of fitted values (or predicted values). It describes the influence each response value has on each fitted value.
1 - (residuals(fit)[1] / (d[1,'mpg'] - predict(fitno, d[1,])))
## Mazda RX4
## 0.3009581
# In-built function:
hatvalues(fit)[1]
## Mazda RX4
## 0.3009581
# Or find the value in the diagnonal of the hat matrix:
H[1]
## [1] 0.3009581
#### Standardized residuals:
First some definitions:
The deviance is the sum of squared residuals:
all.equal(deviance(fit), sum(residuals(fit)^2))
## [1] TRUE
The MSE (MEAN SQUARED ERROR) is defined as $$s^2=\frac{e^\top e}{n-p}$$ with $$\vec e$$ corresponding to the residuals, and $$\mathbf e^\top \mathbf e$$ given by the deviance; $$n,$$ the number of observations nrow(X); and $$p,$$ the number of parameters col(X), including the intersect.
MSE = deviance(fit)/ df.residual(fit)
# Notice that
all.equal(nrow(X) - ncol(X), df.residual(fit))
## [1] TRUE
# Standardized residuals:
fit$residuals / sqrt(MSE * (1 - hatvalues(fit))) ## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive ## -0.7710246 0.2446626 0.1153891 1.5970065 ## Hornet Sportabout Valiant ## -1.2633702 -1.1403043 # The built-in formula is rstandard(fit) ## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive ## -0.7710246 0.2446626 0.1153891 1.5970065 ## Hornet Sportabout Valiant ## -1.2633702 -1.1403043 #### Studentized residuals: MSEno = deviance(fitno) / fitno$df.residual
resid(fit)[1]/ sqrt(MSEno * (1 - hatvalues(fit)[1]))
## Mazda RX4
## -0.7030378
# or
rstudent(fit)[1]
## Mazda RX4
## -0.7030378
#### Cook’s distance:
Cook’s distance is the scaled change in fitted values. Each element in Cook’s distance is the normalized change in the vector of coefficients due to the deletion of an observation. The Cook’s distance, $$D_i,$$ of observation $$i$$ is
$D_i=\frac{\sum_{j=1}^N\,\left( \hat y_j-\hat y_{j(i)} \right)^2}{\text{MSE}\; p}$
where $$\hat y_j$$ is the $$j$$-th fitted response; $$\hat y_{j(i)}$$ is the $$j$$-th fitted response value when the coefficients are calculated without the observation $$i;$$ $$\text {MSE}$$ is the mean squared error; and $$p$$ is the number of coefficients, including the intercept.
dy = predict(fitno, d) - predict(fit, d)
sum(dy^2) / (ncol(X) * MSE)
## [1] 0.08531356
# alternative formula:
fit$residuals[1]^2 /(ncol(X)*sum(fit$residuals^2)/df.residual(fit))*(hatvalues(fit)[1]/(1-hatvalues(fit)[1])^2)
## Mazda RX4
## 0.08531356
cooks.distance(fit)[1]
## Mazda RX4
## 0.08531356
This was an original question posted in CV.
I am trying to replicate what the function dfbetas() does in R.
dfbeta() is not an issue… Here is a set of vectors:
x <- c(0.512, 0.166, -0.142, -0.614, 12.72)
y <- c(0.545, -0.02, -0.137, -0.751, 1.344)
If I fit two regression models as follows:
fit1 <- lm(y ~ x)
fit2 <- lm(y[-5] ~ x[-5])
I see that eliminating the last point results in a very different slope (blue line - steeper):
This is reflected in the change in slopes:
fit1$coeff[2] - fit2$coeff[2]
-0.9754245
which coincides with the dfbeta(fit1) for the fifth value.
Now if I want to standardize this change in slope (obtain dfbetas) and I resort to:
Williams, D. A. (1987) Generalized linear model diagnostics using the deviance and single case deletions. Applied Statistics 36, 181–191
which I think may be one of the references in the R documentation under the package {stats}. There the formula for dfbetas is:
$$\large dfbetas (i,fit) = \Large {(\hat{b} - \hat{b_{-i}})\over SE\, \hat{b_{-i}}}$$
This could be easily calculated in R:
(fit1$coef[2] - fit2$coef[2])/summary(fit2)$coef[4] yielding: -6.79799 The question is why I am not getting the fifth value for the slope in: dfbetas(fit1) (Intercept) x 1 1.06199661 -0.39123009 2 0.06925319 -0.02907481 3 -0.02165967 0.01003539 4 -1.24491242 0.65495527 5 -0.54223793 -93.81415653! What is the right equation to go from dfbeta to dfbetas? And this is the answer in CV: $$DFBETAS_{k(i)}$$ is calculated by: $$\Large \frac{b_k-b_{k(i)}}{\sqrt{MSE_{(i)}c_{kk}}}$$, for $$k$$ = 1, 2, . . . , $$p$$. $$p$$ is the number of regression parameters or coefficients. where $$b_k$$ is the $$k$$th regression coefficient that uses all the data and $$b_{k(i)}$$ is the same coefficient with the $$i$$th case deleted. $$MSE_{(i)}$$ here is the mean-square error from the regression where the $$i$$ case is deleted and $$c_{kk}$$ is the $$k$$th diagonal element of the unscaled covariance matrix $$(X^{\prime}X)^{-1}$$. So you can calculate $$DFBETAS_{k(i)}$$ manually with the following R code: numerator<-(fit1$coef[2] - fit2$coef[2]) denominator<-sqrt((summary(fit2)$sigma^2)*diag(summary(fit1)\$cov.unscaled)[2])
DFBETAS<-numerator/denominator
DFBETAS
x
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The important thing to note here is that it does not affect a number or a float value with one decimal point if we want to round these to two decimal places. First step in multiplication of two decimal numbers is to multiply each one of them with$10$,$100$,$1000\$ and so on to get whole numbers. Signing out of account, Standby Bring business home by treating special clients to a memorable trip. Step 1: Find the 3 rd decimal place: The 3 rd decimal place in 108. What is a Decimal Value and Place Value of Decimals. Which of the following choices is the correct way to write the following number in word form? 176. round () to round to the nearest integer. DECIMALS represent parts of a whole number and are referred to as rational numbers. If you want to specify the Decimal place, just follow the steps below: Click Format Cells, and then the Format Cells window will pop up. The hyphen is an important piece of information that helps us read and write decimals. When you get your answer, add up the total number of digits to the right of the decimals in both the numbers you are multiplying and place the decimal in your answer that many places …. It will take input number along with integer value that select decimal places of the given number. Copy that cell that contains the 100 value. I'm just trying to short the number to lets say 2 decimal places. Decimal Demonstrator An interactive place value and decimals display. So that user can see the milliseconds count down. Solution: Note: There are 2 decimal places in 0. The decimal point is the most important part of a Decimal Number. Scenario 2 (for company code: xyz): the decimal places …. Ask Question Asked 8 years, 11 months ago. We now need to move the decimal place back the same number of times, so we move it 3 times to the left to get. Modified 8 years, 11 months ago. Decimal stores large and small numbers with many digits after the decimal place. In the Format column, click the button for the unit you want to use this setting. AS @Bruno_SAS has said, format does not change the underlying value, only …. samsung galaxy m12 specifications; convert double to two decimal places. But - what you're saying makes sense, I thought it was strange though that while I put ,2 it comes out as 4 - but when I put ,3 - it comes out as 3…. import pandas as pd pandas format numbers with commas Jan 22, 2022 · Python 2022-01-24 23:11:46 nested renamer is not supported pandas 2 places in python python 3 format 2 decimal places python print float 2 decimal …. ) is used for the decimal point. 145 Each digit in a decimal number has a place value depending on its position. | 2022-06-30 01:48:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39548081159591675, "perplexity": 712.2989991359285}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103646990.40/warc/CC-MAIN-20220630001553-20220630031553-00096.warc.gz"} |
https://datawarrior.wordpress.com/tag/data/ | There are many tasks that involve coding, for example, putting kids into groups according to their age, labeling the webpages about their kinds, or putting students in Hogwarts into four colleges… And researchers or lawyers need to code people, according to their filled-in information, into occupations. Melissa Friesen, an investigator in Division of Cancer Epidemiology and Genetics (DCEG), National Cancer Institute (NCI), National Institutes of Health (NIH), saw the need of large-scale coding. Many researchers are dealing with big data concerning epidemiology. She led a research project, in collaboration with Office of Intramural Research (OIR), Center for Information Technology (CIT), National Institutes of Health (NIH), to develop an artificial intelligence system to cope with the problem. This leads to a publicly available tool called SOCcer, an acronym for “Standardized Occupation Coding for Computer-assisted Epidemiological Research.” (URL: http://soccer.nci.nih.gov/soccer/)
The system was initially developed in an attempt to find the correlation between the onset of cancers and other diseases and the occupation. “The application is not intended to replace expert coders, but rather to prioritize which job descriptions would benefit most from expert review,” said Friesen in an interview. She mainly works with Daniel Russ in CIT.
SOCcer takes job title, industry codes (in terms of SIC, Standard Industrial Classification), and job duties, and gives an occupational code called SOC 2010 (Standard Occupational Classification), used by U. S. federal government agencies. The data involves short text, often messy. There are 840 codes in SOC 2010 systems. Conventional natural language processing (NLP) methods may not apply. Friesen, Russ, and Kwan-Yuet (Stephen) Ho (also in OIR, CIT; a CSRA staff) use fuzzy logic, and maximum entropy (maxent) methods, with some feature engineering, to build various classifiers. These classifiers are aggregated together, as in stacked generalization (see my previous entry), using logistic regression, to give a final score.
SOCcer has a companion software, called SOCAssign, for expert coders to prioritize the codings. It was awarded with DCEG Informatics Tool Challenge 2015. SOCcer itself was awarded in 2016. And the SOCcer team was awarded for Scientific Award of Merit by CIT/OCIO in 2016 as well (see this). Their work was published in Occup. Environ. Med.
The topic of word embedding algorithms has been one of the interests of this blog, as in this entry, with Word2Vec [Mikilov et. al. 2013] as one of the main examples. It is a great tool for text mining, (for example, see [Czerny 2015],) as it reduces the dimensions needed (compared to bag-of-words model). As an algorithm borrowed from computer vision, a lot of these algorithms use deep learning methods to train the model, while it was not exactly sure why it works. Despite that, there are many articles talking about how to train the model. [Goldberg & Levy 2014, Rong 2014 etc.] Addition and subtraction of the word vectors show amazing relationships that carry semantic values, as I have shown in my previous blog entry. [Ho 2015]
However, Tomas Mikolov is no longer working in Google, making the development of this algorithm discontinued. As a follow-up of their work, Stanford NLP group later proposed a model, called GloVe (Global Vectors), that embeds word vectors using probabilistic methods. [Pennington, Socher & Manning 2014] It can be implemented in the package glove-python in python, and text2vec in R (or see their CRAN post). Their paper is neatly written, and a highly recommended read.
To explain the theory of GloVe, we start with some basic probabilistic picture in basic natural language processing (NLP). We suppose the relation between the words occur in certain text windows within a corpus, but the details are not important here. Assume that $i$, $j$, and $k$ are three words, and the conditional probability $P_{ik}$ is defined as
$P_{ij} = P(j | i) = \frac{X_{ij}}{X_i}$,
where $X$‘s are the counts, and similarly for $P_{jk}$. And we are interested in the following ratio:
$F(w_i, w_j, \tilde{w}_k) = \frac{P_{ik}}{P_{jk}}$.
The tilde means “context,” but we will later assume it is also a word. Citing the example from their paper, take $i$ as ice, and $j$ as steam. if $k$ is solid, then the ratio is expected to be large; or if $k$ is gas, then it is expected to be low. But if $k$ is water, which are related to both, or fashion, which is related to none, then the ratio is expected to be approximately 1.
And the addition and subtraction in Word2Vec is similar to this. We want the ratio to be like the subtraction as in Word2Vec (and multiplication as in addition), then we should modify the function $F$ such that,
$F(w_i - w_j, \tilde{w}_k) = \frac{P_{ik}}{P_{jk}}$.
On the other hand, the input arguments of $F$ are vectors, but the output is a scalar. We avoid the issue by making the input argument as a dot product,
$F( (w_i - w_j)^T \tilde{w}_k) = \frac{P_{ik}}{P_{jk}}$.
In NLP, the word-word co-occurrence matrices are symmetric, and our function $F$ should also be invariant under switching the labeling. We first require $F$ is be a homomorphism,
$F((w_i - w_j)^T \tilde{w}_k) = \frac{F(w_i^T \tilde{w}_k) }{ F(w_j^T \tilde{w}_k)}$,
where we define,
$F(w_i^T \tilde{w}_k) = P_{ik} = \frac{X_{ik}}{X_i}$.
It is clear that $F$ is an exponential function, but to ensure symmetry, we further define:
$w_i^T \tilde{w}_k + b_i + \tilde{b}_k = \log X_{ik}$.
As a result of this equation, the authors defined the following cost function to optimize for GloVe model:
$J = \sum_{i, j=1}^V f(X_{ij}) \left( w_i^T \tilde{w}_j + b_i + \tilde{b}_j - \log X_{ik} \right)^2$,
where $w_j$, $\tilde{w}_j$, $b_i$, and $\tilde{b}_j$ are parameters to learn. $f(x)$ is a weighting function. (Refer the details to the paper.) [Pennington, Socher & Manning 2014]
As Radim Řehůřek said in his blog entry, [Řehůřek 2014] it is a neat paper, but their evaluation is crappy.
This theory explained why certain similar relations can be achieved, such as Paris – France is roughly equal to Beijing – China, as both can be transformed to the ratio in the definition of $F$ above.
It is a neat paper, as it employs optimization theory and probability theory, without any dark box deep learning.
Previously, I have went through heuristically the description of topology using homology groups in this entry. [Ho 2015] This is the essence of algebraic topology. We describe the topology using Betti numbers, the rank of the homolog groups. What they mean can be summarized as: [Bubenik 2015]
“… homology in degree 0 describes the connectedness of the data; homology in degree 1 detects holes and tunnels; homology in degree 2 captures voids; and so on.
## Concept of Persistence
However, in computational problems, it is the discrete points that we are dealing with. We formulate their connectedness through constructing complexes, as described by my another blog entry. [Ho 2015] From the Wolfram Demonstration that I quoted previously, connectedness depends on some parameters, such as the radii of points that are considered connected. Whether it is Čech Complex, RP complex, or Alpha complex, the idea is similar. With discrete data, therefore, there is no definite answer how the connectedness among the points are, as it depends on the parameters.
Therefore, the concept of persistence has been developed to tackle this problem. This is the core concept for computational topology. There are a lot of papers about persistence, but the most famous work is done by Zomorodian and Carlsson, who algebraically studied it. [Zomorodian & Carlsson 2005] The idea is that as one increases the radii of points, the complexes change, and so do the homology groups. By varying the radii, we can observe which topology persists.
From the diagram above, we can see that as the radii ε increase, the diagram becomes more connected. To understand the changes of homologies, there are a few ways. In the diagram above, barcodes represent the “life span” of a connected component as ε increases. The Betti numbers of a certain degree (0, 1, or 2 in this example) at a certain value of ε is the number of barcodes at that degree. For example, look at the left most vertical dashed line, $\beta_0=10$, as there are 10 barcodes existing for $H_0$. Note there are indeed 10 separate connected components. For the second leftmost vertical dashed line, $\beta_0=6$ (6 connected components), and $\beta_1=2$ (2 holes).
Another way is using the persistence diagram, basically plotting the “birth” and “death” times of all the barcodes above. For an explanation of persistence diagram, please refer to this blog entry by Sebastien Bubeck, [Bubeck 2013] or the paper by Fasy et. al. [Fasy et. al. 2014] Another way to describe persistent topology is the persistence landscape. [Bubenik 2015]
## TDA Package in R
There are a lot of tools to perform topological data analysis. Ayasdi Core is a famous one. There are open sources C++ libraries such as Dionysus, or PHAT. There is a Python binding for Dionysus too.
There is a package in R that wraps Dionysus and PHAT, called TDA. To install it, simply open an R session, and enter
install.package('TDA')
To load it, simply enter
library(TDA)
We know that for a circle, $\beta_0=\beta_1=1$, as it has on connected components, and a hole. Prepare the circle and store it in X by the function circleUnif:
X<- circleUnif(n=1000, r=1)
plot(X)
Then we can see a 2-dimensional circle like this:
To calculate the persistent homology, use the function gridDiag:
diag.info<- gridDiag(X=X, FUN=kde, h=0.3, lim=cbind(c(-1, 1), c(-1, 1)), by=0.01, sublevel = FALSE, library = 'PHAT', printProgress=FALSE)
To plot the barcodes and persistence diagram, enter:
par(mfrow=c(2,1))
plot(diag.info$diagram) plot(diag.info$diagram, barcode=TRUE)
In the plots, black refers to degree 0, and red refers to degree 1.
We can play the same game by adding a horizontal line to cut the circle into two halves:
X<- circleUnif(n=1000, r=1)
hl<- matrix(c(seq(-1, 1, 0.02), rep(0, 201)), ncol=2)
X<- rbind(X, hl)
plot(X)
And the barcodes and persistence diagram are:
We can try this with three-dimensional objects like sphere, or torus, but I never finished the calculation in reasonable speeds.
On October 14, 2015, I attended the regular meeting of the DCNLP meetup group, a group on natural language processing (NLP) in Washington, DC area. The talk was titled “Deep Learning for Question Answering“, spoken by Mr. Mohit Iyyer, a Ph.D. student in Department of Computer Science, University of Maryland (my alma mater!). He is a very good speaker.
I have no experience on deep learning at all although I did write a blog post remotely related. I even didn’t start training my first neural network until the next day after the talk. However, Mr. Iyyer explained what recurrent neural network (RNN), recursive neural network, and deep averaging network (DAN) are. This helped me a lot in order to understanding more about the principles of the famous word2vec model (which is something I am going to write about soon!). You can refer to his slides for more details. There are really a lot of talents in College Park, like another expert, Joe Yue Hei Ng, who is exploiting deep learning a lot as well.
The applications are awesome: with external knowledge to factual question answering, reasoning-based question answering, and visual question answering, with increasing order of challenging levels.
Mr. Iyyer and the participants discussed a lot about different packages. Mr. Iyyer uses Theano, a Python package for deep learning, which is good for model building and other analytical work. Some prefer Caffe. Some people, who are Java developers, also use deeplearning4j.
This meetup was a sacred one too, because it is the last time it was held in Stetsons Famous Bar & Grill at U Street, which is going to permanently close on Halloween this year. The group is eagerly looking for a new venue for the upcoming meetup. This meeting was a crowded one. I sincerely thank the organizers, Charlie Greenbacker and Liz Merkhofer, for hosting all these meetings, and Chris Phipps (a linguist from IBM Watson) for recording.
In my previous blog post, I introduced the newly emerged topological data analysis (TDA). Unlike most of the other data analytic algorithms, TDA, concerning the topology as its name tells, cares for the connectivity of points, instead of the distance (according to a metric, whether it is Euclidean, Manhattan, Minkowski or any other). What is the best tools to describe topology?
Physicists use a lot homotopy. But for the sake of computation, it is better to use a scheme that are suited for discrete computation. It turns out that there are useful tools in algebraic topology: homology. But to understand homology, we need to understand what a simplicial complex is.
Gunnar Carlsson [Carlsson 2009] and Afra Zomorodian [Zomorodian 2011] wrote good reviews about them, although from a different path in introducing the concept. I first followed Zomorodian’s review [Zomorodian 2011], then his book [Zomorodian 2009] that filled in a lot of missing links in his review, to a certain point. I recently started reading Carlsson’s review.
One must first understand what a simplicial complex is. Without giving too much technical details, simplicial complex is basically a shape connecting points together. A line is a 1-simplex, connecting two points. A triangle is a 2-simplex. A tetrahedron is a 3-complex. There are other more complicated and unnamed complexes. Any subsets of a simplicial complex are faces. For example, the sides of the triangle are faces. The faces and the sides are the faces of the tetrahedron. (Refer to Wolfram MathWorld for more details. There are a lot of good tutorials online.)
Implementing Simplicial Complex
We can easily encoded this into a python code. I wrote a class SimplicialComplex in Python to implement this. We first import necessary libraries:
import numpy as np
from itertools import combinations
from scipy.sparse import dok_matrix
from operator import add
The first line imports the numpy library, the second the iteration tools necessary for extracting the faces for simplicial complex, the third the sparse matrix implementation in the scipy library (applied on something that I will not go over in this blog entry), and the fourth for some reduce operation.
We want to describe the simplicial complexes in the order of some labels (which can be anything, such as integers or strings). If it is a point, then it can be represented as tuples, as below:
(1,)
Or if it is a line (a 1-simplex), then
(1, 2)
Or a 2-simplex as a triangle, then
(1, 2, 3)
I think you get the gist. The integers 1, 2, or 3 here are simply labels. We can easily store this in the class:
class SimplicialComplex:
def __init__(self, simplices=[]):
self.import_simplices(simplices=simplices)
def import_simplices(self, simplices=[]):
self.simplices = map(lambda simplex: tuple(sorted(simplex)), simplices)
self.face_set = self.faces()
You might observe the last line of the codes above. And it is for calculating all the faces of this complex, and it is implemented in this way:
def faces(self):
faceset = set()
for simplex in self.simplices:
numnodes = len(simplex)
for r in range(numnodes, 0, -1):
for face in combinations(simplex, r):
return faceset
The faces are intuitively sides of a 2D shape (2-simplex), or planes of a 3D shape (3-simplex). But the faces of a 3-simplex includes the faces of all its faces. All the faces are saved in a field called faceset. If the user wants to retrieve the faces in a particular dimension, they can call this method:
def n_faces(self, n):
return filter(lambda face: len(face)==n+1, self.face_set)
There are other methods that I am not going over in this blog entry. Now let us demonstrate how to use the class by implementing a tetrahedron.
sc = SimplicialComplex([('a', 'b', 'c', 'd')])
If we want to extract the faces, then enter:
sc.faces()
which outputs:
{('a',),
('a', 'b'),
('a', 'b', 'c'),
('a', 'b', 'c', 'd'),
('a', 'b', 'd'),
('a', 'c'),
('a', 'c', 'd'),
('a', 'd'),
('b',),
('b', 'c'),
('b', 'c', 'd'),
('b', 'd'),
('c',),
('c', 'd'),
('d',)}
We have gone over the basis of simplicial complex, which is the foundation of TDA. We appreciate that the simplicial complex deals only with the connectivity of points instead of the distances between the points. And the homology groups will be calculated based on this. However, how do we obtain the simplicial complex from the discrete data we have? Zomorodian’s review [Zomorodian 2011] gave a number of examples, but I will only go through two of them only. And from this, you can see that to establish the connectivity between points, we still need to apply some sort of distance metrics.
Alpha Complex
An alpha complex is the nerve of the cover of the restricted Voronoi regions. (Refer the details to Zomorodian’s review [Zomorodian 2011], this Wolfram MathWorld entry, or this Wolfram Demonstration.) We can extend the class SimplicialComplex to get a class AlphaComplex:
from scipy.spatial import Delaunay, distance
from operator import or_
from functools import partial
def facesiter(simplex):
for i in range(len(simplex)):
yield simplex[:i]+simplex[(i+1):]
def flattening_simplex(simplices):
for simplex in simplices:
for point in simplex:
yield point
def get_allpoints(simplices):
return set(flattening_simplex(simplices))
def contain_detachededges(simplex, distdict, epsilon):
if len(simplex)==2:
return (distdict[simplex[0], simplex[1]] > 2*epsilon)
else:
return reduce(or_, map(partial(contain_detachededges, distdict=distdict, epsilon=epsilon), facesiter(simplex)))
class AlphaComplex(SimplicialComplex):
def __init__(self, points, epsilon, labels=None, distfcn=distance.euclidean):
self.pts = points
self.labels = range(len(self.pts)) if labels==None or len(labels)!=len(self.pts) else labels
self.epsilon = epsilon
self.distfcn = distfcn
self.import_simplices(self.construct_simplices(self.pts, self.labels, self.epsilon, self.distfcn))
def calculate_distmatrix(self, points, labels, distfcn):
distdict = {}
for i in range(len(labels)):
for j in range(len(labels)):
distdict[(labels[i], labels[j])] = distfcn(points[i], points[j])
return distdict
def construct_simplices(self, points, labels, epsilon, distfcn):
delaunay = Delaunay(points)
delaunay_simplices = map(tuple, delaunay.simplices)
distdict = self.calculate_distmatrix(points, labels, distfcn)
simplices = []
for simplex in delaunay_simplices:
faces = list(facesiter(simplex))
detached = map(partial(contain_detachededges, distdict=distdict, epsilon=epsilon), faces)
if reduce(or_, detached):
if len(simplex)>2:
for face, notkeep in zip(faces, detached):
if not notkeep:
simplices.append(face)
else:
simplices.append(simplex)
simplices = map(lambda simplex: tuple(sorted(simplex)), simplices)
simplices = list(set(simplices))
allpts = get_allpoints(simplices)
for point in (set(labels)-allpts):
simplices += [(point,)]
return simplices
The scipy package already has a package to calculate Delaunay region. The function contain_detachededges is for constructing the restricted Voronoi region from the calculated Delaunay region.
This class demonstrates how an Alpha Complex is constructed, but this runs slowly once the number of points gets big!
Vietoris-Rips (VR) Complex
Another commonly used complex is called the Vietoris-Rips (VR) Complex, which connects points as the edge of a graph if they are close enough. (Refer to Zomorodian’s review [Zomorodian 2011] or this Wikipedia page for details.) To implement this, import the famous networkx originally designed for network analysis.
import networkx as nx
from scipy.spatial import distance
from itertools import product
class VietorisRipsComplex(SimplicialComplex):
def __init__(self, points, epsilon, labels=None, distfcn=distance.euclidean):
self.pts = points
self.labels = range(len(self.pts)) if labels==None or len(labels)!=len(self.pts) else labels
self.epsilon = epsilon
self.distfcn = distfcn
self.network = self.construct_network(self.pts, self.labels, self.epsilon, self.distfcn)
self.import_simplices(map(tuple, list(nx.find_cliques(self.network))))
def construct_network(self, points, labels, epsilon, distfcn):
g = nx.Graph()
zips = zip(points, labels)
for pair in product(zips, zips):
if pair[0][1]!=pair[1][1]:
dist = distfcn(pair[0][0], pair[1][0])
if dist<epsilon:
return g
The intuitiveness and efficiencies are the reasons that VR complexes are widely used.
For more details about the Alpha Complexes, VR Complexes and the related Čech Complexes, refer to this page.
More…
There are other commonly used complexes used, including Witness Complex, Cubical Complex etc., which I leave no introductions. Upon building the complexes, we can analyze the topology by calculating their homology groups, Betti numbers, the persistent homology etc. I wish to write more about it soon.
I have seen more than enough debates about R or Python. While I do have a preference towards Python, I am happy with using R as well. I am not agnostic about languages, but we choose tools according to needs. The needs may be about effectiveness, efficiency, availability of tools, nature of problems, collaborations, etc. Yes, in a nutshell, it depends.
When dealing with text mining, although I still prefer Python, I have to fairly say that both languages have their own strengths and weaknesses. What do you do in text mining? Let me casually list the usual steps:
1. Removing special characters,
2. Removing numerals,
3. Converting all alphabets to lower cases,
4. Removing stop words, and
5. Stemming the words (using Porter stemmer).
They are standard steps. But of course, sometimes we perform lemmatization instead of stemming. Sometimes we keep numerals. Or whatever. It is okay.
How do u do that in Python? Suppose you have a list of text documents stored in the variable texts, which is defined by
texts = ['I love Python.',
'R is good for analytics.',
'Mathematics is fun.']
. Then
# import all necessary libraries
from nltk.stem import PorterStemmer
from nltk.tokenize import SpaceTokenizer
from nltk.corpus import stopwords
from functools import partial
from gensim import corpora
from gensim.models import TfidfModel
import re
# initialize the instances for various NLP tools
tokenizer = SpaceTokenizer()
stemmer = PorterStemmer()
# define each steps
pipeline = [lambda s: re.sub('[^\w\s]', '', s),
lambda s: re.sub('[\d]', '', s),
lambda s: s.lower(),
lambda s: ' '.join(filter(lambda s: not (s in stopwords.words()), tokenizer.tokenize(s))),
lambda s: ' '.join(map(lambda t: stemmer.stem(t), tokenizer.tokenize(s)))
]
# function that carries out the pipeline step-by-step
def preprocess_text(text, pipeline):
if len(pipeline)==0:
return text
else:
return preprocess_text(pipeline[0](text), pipeline[1:])
# preprocessing
preprocessed_texts = map(partial(preprocess_text, pipeline=pipeline), texts)
# converting to feature vectors
documents = map(lambda s: tokenizer.tokenize(s), texts)
corpus = [dictionary.doc2bow(document) for document in documents]
tfidfmodel = TfidfModel(corpus)
We can train a classifier with the feature vectors output by tfidfmodel. To do the prediction, we can get the feature vector for a new text by calling:
bow = dictionary.doc2bow(tokenizer.tokenize(preprocess_text(text, pipeline)))
How about in R? To perform the preprocessing steps and extract the feature vectors, run:
library(RTextTools)
library(tm)
origmatrix<-create_matrix(textColumns = texts, language = 'english',
removeNumbers = TRUE, toLower = TRUE,
removeStopwords = 'TRUE', stemWords = TRUE,
weighting=tm::weightTfIdf, originalMatrix=NULL)
After we have a trained classifier, and we have a new text to preprocess, then we run:
matrix<-create_matrix(textColumns = newtexts, language = 'english',
removeNumbers = TRUE, toLower = TRUE,
removeStopwords = 'TRUE', stemWords = TRUE,
weighting=tm::weightTfIdf, originalMatrix=origmatrix)
Actually, from this illustration, a strength for R stands out: brevity. However, very often we want to preprocess in other ways, Python allows more flexibility without making it complicated. And Python syntax itself is intuitive enough.
And there are more natural language processing libraries in Python available, such as nltk and gensim, that are associated with its other libraries perfectly such as numpy, scipy and scikit-learn. But R is not far away in terms of this actually, as it has libraries such as tm and RTextTools, while R does not have numpy-like libraries because R itself is designed to perform calculations like this.
Python can be used to develop larger software projects by making the codes reusable, and it is obviously a weakness for R.
However, do perform analysis, R makes the task very efficient if we do not require something unconventional.
In the area of text mining, R or Python? My answer is: it depends.
Deep learning, a collection of related neural network algorithms, has been proved successful in certain types of machine learning tasks in computer vision, speech recognition, data cleaning, and natural language processing (NLP). [Mikolov et. al. 2013] However, it was unclear how deep learning can be so successful. It looks like a black box with messy inputs and excellent outputs. So why is it so successful?
A friend of mine showed me this article in the preprint (arXiv:1410.3831) [Mehta & Schwab 2014] last year, which mathematically shows the equivalence of deep learning and renormalization group (RG). RG is a concept in theoretical physics that has been widely applied in different problems, including critical phenomena, self-organized criticality, particle physics, polymer physics, and strongly correlated electronic systems. And now, Mehta and Schwab showed that an explanation to the performance of deep learning is available through RG.
So what is RG? Before RG, Leo Kadanoff, a physics professor in University of Chicago, proposed an idea of coarse-graining in studying many-body problems in 1966. [Kadanoff 1966] In 1972, Kenneth Wilson and Michael Fisher succeeded in applying ɛ-expansion in perturbative RG to explain the critical exponents in Landau-Ginzburg-Wilson (LGW) Hamiltonian. [Wilson & Fisher 1972] This work has been the standard material of graduate physics courses. In 1974, Kenneth Wilson applied RG to explain the Kondo problem, which led to his Nobel Prize in Physics in 1982. [Wilson 1983]
RG assumes a system of scale invariance, which means the system are similar in whatever scale you are seeing. One example is the chaotic system as in Fig. 1. The system looks the same when you zoom in. We call this scale-invariant system self-similar. And physical systems closed to phase transition are self-similar. And if it is self-similar, Kadanoff’s idea of coarse-graining is then applicable, as in Fig. 2. Four spins can be viewed as one spin that “summarizes” the four spins in that block without changing the description of the physical system. This is somewhat like we “zoom out” the picture on Photoshop or Web Browser.
[Taken from [Singh 2014]]
So what’s the point of zooming out? Physicists care about the Helmholtz free energies of physical systems, which are similar to cost functions to the computer scientists and machine learning specialists. Both are to be minimized. However, whatever scale we are viewing at, the energy of the system should be scale-invariant. Therefore, as we zoom out, the system “changes” yet “looks the same” due to self-similarity, but the energy stays the same. The form of the model is unchanged, but the parameters change as the scale changes.
This is important, because this process tells us which parameters are relevant, and which others are irrelevant. Why? Think of it this way: we have an awesome computer to simulate a glass of water that contains 1023 water molecules. To describe the systems, you have all parameters, including the position of molecules, strength of Van der Waals force, orbital angular momentum of each atom, strength of the covalent bonds, velocities of the molecules… You might have 1025 parameters. However, this awesome computer cannot handle such a system with so many parameters. Then you try to coarse-grain the system, and you discard some parameters in each step of coarse-graining. After numerous steps, it turns out that the temperature and the pressure are the only relevant parameters.
RG helps you identify the relevant parameters.
And it is exactly what happened in deep learning. In each convolutional cycle, features that are not important are gradually discarded, and those that are important are kept and enhanced. Indeed, in computer vision and NLP, the data are so noisy that there are a lot of unnecessary information. Deep learning gradually discards these information. As Mehta and Schwab stated, [Mehta & Schwab 2014]
Our results suggests that deep learning algorithms may be employing a generalized RG-like scheme to learn relevant features from data.
So what is the point of understanding this? Unlike other machine algorithms, we did not know how it works, which sometimes makes model building very difficult because we have no idea how to adjust parameters. I believe understanding its equivalence to RG helps guide us to build a model that works.
Charles Martin also wrote a blog entry with more demonstration about the equivalence of deep learning and RG. [Martin 2015]
(Taken from http://latticeqcd.org/pythonorg/static/images/antigravity.png, adapted from http://xkcd.com/353/)
Python is the basic programming languages if one wants to work on data nowadays. Its popularity comes with its intuitive syntax, its support of several programming paradigms, and the package numpy (Numerical Python). Yes, if you asked which package is a “must-have” outside the standard Python packages, I would certainly name numpy.
Let me list some useful packages that I have found useful:
1. numpy: Numerical Python. Its basic data type is ndarray, which acts like a vector with vectorized calculation support. It makes Python to perform matrix calculation efficiently like MATLAB and Octave. It supports a lot of commonly used linear algebraic algorithms, such as eigenvalue problems, SVD etc. It is the basic of a lot of other Python packages that perform heavy numerical computation. It is such an important package that, in some operating systems, numpy comes with Python as well.
2. scipy: Scientific Python. It needs numpy, but it supports also sparse matrices, special functions, statistics, numerical integration…
3. matplotlib: Graph plotting.
4. scikit-learn: machine learning library. It contains a number of supervised and unsupervised learning algorithms.
5. nltk: natural language processing. It provides not only basic tools like stemmers, lemmatizers, but also some algorithms like maximum entropy, tf-idf vectorizer etc. It provides a few corpuses, and supports WordNet dictionary.
6. gensim: another useful natural language processing package with an emphasis on topic modeling. It mainly supports Word2Vec, latent semantic indexing (LSI), and latent Dirichlet allocation (LDA). It is convenient to construct term-document matrices, and convert them to matrices in numpy or scipy.
7. networkx: a package that supports both undirected and directed graphs. It provides basic algorithms used in graphs.
8. sympy: Symbolic Python. I am not good at this package, but I know mathics and SageMath are both based on it.
9. pandas: it supports data frame handling like R. (I have not used this package as I am a heavy R user.)
Of course, if you are a numerical developer, to save you a good life, install Anaconda.
There are some other packages that are useful, such as PyCluster (clustering), xlrd (Excel files read/write), PyGame (writing games)… But since I have not used them, I would rather mention it in this last paragraph, not to endorse but avoid devaluing it.
Don’t forget to type in your IPython Notebook:
import antigravity
(taken from Analyzing and Analyzers)
D. J. Patil, the Chief Data Scientist of the United States at the moment, coined the term “data scientist,” and called it “the sexiest job in the 21st century.” Therefore, we now have a job title called “data scientist,” which I have difficulties to categorize it into the Standard Occupational Classification (SOC) codes. While I respect D. J. Patil a lot (I love his speech in my commencement ceremony in University of Maryland), this is the job title that is the least defined job title ever seen in my life.
DJ Patil, the U. S. Chief Data Scientist (from his LinkedIn)
So what does a data scientist do? I have seen many articles about it. And various employers have different expectations about the data scientists they hired. Sometimes their expectation is so unreasonable in a way that they want a god. And a lot of people call themselves a data scientist in LinkedIn, despite the fact that their official titles are software engineers, software developers, data analysts, quantitative analysts, research scientists, researchers,… With a Ph.D. in theoretical physics, I want to call myself a data scientist too because of the word “scientist.” I found it cool and sexy. But I realize the risk of calling myself one: people expect something different from what I really am. I rather call myself an “applied quantitative researcher,” as shown in my LinkedIn.
Of course, it provides room for opportunists to make money by distorting their image and branding themselves in various ways from time to time.
Regarding the skills we need, I love the chart above. (Read that book, which is a good description.) Despite my complicated feelings toward the term “data scientist,” I believe as the R & D people in the big data era, we should know:
1. Statistics, Machine Learning, Natural Language Processing (NLP) and Information Retrieval (IR): the mathematical modeling part.
2. Domain Knowledge, or Business Knowledge: the knowledge about the industry, the world, the people, the company, …
3. Software Development: the skills of development cycle, such as object-oriented (OO) programming, functional programming, unit tests, …, and some recent technologies about distributed computing such as Hadoop and Spark.
Employers hired data scientists from diverse backgrounds. Statisticians, research scientists in machine learning, physicists, chemists, or mathematicians might know the mathematics and research methodologies very well, but they do not know how to write maintainable codes. This article described it well. On the other hand, some people are trained as a software developer. However, they do not have enough mathematical background to handle the analytics well.
The word “data” attracts the eyeballs, but we really need to define what these terms like “big data,” “data scientists,” or “data products” are. Yes, by the way, despite the vaguely-defined term “data products”, this article does describe the trend very well. But no matter what, there can only be more accessible data in this age of information explosion, any skills that tackle with data keep on being in high demand. | 2018-03-20 21:40:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5096611380577087, "perplexity": 2091.803922746103}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647545.54/warc/CC-MAIN-20180320205242-20180320225242-00615.warc.gz"} |
http://www.coastalwiki.org/w/index.php?title=Groundwater_management_in_low-lying_coastal_zones&oldid=76755 | # Groundwater management in low-lying coastal zones
Groundwater is an important resource for drinking water and irrigation. However, groundwater extraction in low-lying coastal zones is highly problematic. It raises the salinity of the groundwater and causes the land to sink. Therefore, groundwater management is a major issue in many low-lying coastal areas. This article focuses on shallow coastal aquifers connected to the sea.
## Threats of groundwater extraction
Fig. 1. World water distribution. Source: pbslearningmedia [1].
Fig. 2. Agricultural groundwater usage for selected countries in $\small 10^9 \, km^3/year$. Source: UN World Water Development Report, 2015[2].
Fresh water represents only a small fraction of earth's water resource – less than 1%, ice excluded (Fig. 1). Groundwater is by far the most important fresh water resource available for human use. More than 50% of world’s population lives in coastal areas and is largely dependent on fresh groundwater resources for domestic, agricultural and industrial purposes. The exploitation of fresh groundwater resources is sharply increasing as a consequence of population growth, economic growth, intensified agricultural development, and the degradation of surface water resources due to contamination (Fig. 2).
Worldwide, many large coastal cities have expanded into low coastal plains during the past decades, especially in Asia and Africa (see Coastal cities and sea level rise). Most of these plains emerged after the Holocene marine transgression, when the seabed was raised above sea level by sedimentation behind a sheltering coastal barrier. These deposits form a top soil layer of a few meters up to several tens of meters thick, and contain a high fraction of fine sediments of fluvial and marine origin (and peat, in humid climatic zones). On these poorly draining soils, which are highly susceptible to compaction, extensive urban and industrial development has taken place[3]. The land elevation is generally close to the mean high sea level. However, in many areas it is lower and still subsiding, mainly as a result of drainage and groundwater extraction[4].
Intensive groundwater extraction from underlying water-bearing layers (aquifers) stimulates the intrusion of seawater, leading to increased groundwater salinity[5]. In the lowest areas, brackish groundwater may reach the surface by upward groundwater flow through the confining top layer, so-called 'saline seepage'. The threats of uncontrolled groundwater extraction can remain unnoticed for many years because groundwater flow is a slow process. However, in the long run they are considerable [6]:
• unsuitability of groundwater for drinking water,
• reduced usability of groundwater for irrigation,
• soil salinization detrimental to crop growth,
• soil subsidence and increased vulnerability to flooding,
• deterioration of the foundation of buildings by corrosion of concrete, reinforcement and bricks,
• danger of collapse of buildings due to soil instability.
In addition, the anticipated sea level rise and the decrease of recharge, due to climate change and increased water demand in the upstream catchment areas, will further exacerbate the pressures on coastal groundwater systems.
## Salt intrusion processes
Fig. 3. A small level difference is sufficient to keep a large fresh water column in balance with a salt water column, according to the BGH principle (similar to the iceberg principle). If the groundwater consists of seawater with density 1025 kg/m3, a fresh water column that exceeds the ground level by 1 m can penetrate 40 m into the underground.
Seawater intrudes into the underground of the coastal plain through aquifers, permeable soil layers consisting of medium / coarse granular material or porous / fissured rock. Due to its greater density, seawater enters like a wedge that pushes fresh water inshore, see Fig. 4. A counter-pressure is exerted by the inshore fresh water table. Due to the small density difference, a small elevation of the fresh water head is sufficient to keep the seawater intrusion in balance, see Fig. 3. This principle was first discovered by Badon-Ghyben and Herzerg and is commonly referred to as the BGH principle. In Fig. 4 it is assumed that the permeability of the underground is the same everywhere. In reality, however, this is never the case due to the presence of poorly permeable layers (aquitards); Fig. 5 shows a still much simplified but slightly more realistic image. A rough estimate of the intrusion length $L$ of the seawater wedge into a shallow confined aquifer is given by [7],
$L \approx \alpha k D^2 / (2 Q) , \qquad (1)$
where $\alpha \approx 1/40$ is the relative density difference, $k$ is the hydraulic conductivity (related to the permeability), $D$ is the aquifer depth and $Q$ is the groundwater discharge to the sea per unit width. This formula applies to a homogeneous confined aquifer of constant depth. The groundwater discharge $Q$ is related to the gradient in the piezometric head $dh/dx$ according to Darcy's law: $Q=-k D dh/dx$. A relationship for the seawater intrusion length similar to Eq. (1) holds for shallow unconfined aquifers in case of sufficient freshwater recharge (precipitation, river water infiltration, …)[8].
File:IntrusionScheme1.jpg Fig. 4. Schematic representation of seawater intrusion into a homogeneous coastal aquifer. File:IntrusionScheme2.jpg Fig. 5. Schematic representation of seawater intrusion into a multi-aquifer system.
Equation (1) shows that seawater intrusion depends on aquifer properties ($k, D$), and via the groundwater discharge $Q$ , on the elevation difference between the inland freshwater hydraulic head and the water sea level at sea. The sea level is variable due to tidal motion and wind set-up / set-down and the inland fresh water table varies over the seasons in response to variable fresh water runoff, evapotranspiration and extractions. These fluctuations in the groundwater pressure gradient, together with spatial inhomogeneities in the geologic structure, contribute to mixing across the fresh-salt interface [9]. The rise of the relative sea level is an ongoing trend that gradually increases the seawater intrusion into the aquifer. Shoreline retreat associated with sea level rise can also play a role. Seawater intrusion is further enhanced in case of a trend-wise decrease of the flux of fresh groundwater to the sea, for example as a consequence of groundwater abstraction near the coast.
Several other processes contribute to salinization of coastal aquifers.
### Marine transgression
Many coastal areas, especially river deltas, were flooded by the sea during the Holocene transgression, before sedimentation raised the seafloor above mean high water level and before fluvial processes became dominant. The present saline groundwater was largely formed during this period. Saline intrusion in coastal aquifers by marine flooding occurs today only incidentally under extreme storms. Such extreme conditions are rare, but they are expected to become much more frequent in future as a consequence of sea level rise (see Sea level rise) and land subsidence. The process of seawater infiltration in a fresh aquifer resulting from a marine flood is shown in Fig. 6. Increased groundwater salinities may persist many years after such flood events[10]. Floods caused by tsunamis and flooding in the context of depoldering projects have similar effects on the salinization of groundwater.
### Seawater intrusion via estuaries
Coastal aquifers are not only in contact with salt water at the land-sea boundary but often also with salt water of estuaries. In this way, intrusion of saline surface water into shallow groundwater can take place further inland (Fig. 7). The intrusion of seawater in estuaries is discussed in the articles Seawater intrusion and mixing in estuaries and Estuarine circulation. Seawater intrusion in estuaries has strongly increased during the past century due to channel deepening (dredging) for navigational purposes and the decrease of river discharges into estuaries. The greatest incursion of high salinity seawater occurs in periods of low fluvial runoff, especially in microtidal estuaries (see Salt wedge estuaries).
Fig. 6. Infiltration of marine flood water into the underground by so-called 'fingering'. Fig. 7. Intrusion of seawater from a salt-wedge estuary into the underground.
### Groundwater extraction
Intensive groundwater extraction can increase the intrusion of seawater into the coastal aquifer by decreasing the freshwater pressure head; this will reduce the groundwater discharge $Q$ to the sea (see Eq. 1). This intrusion is a slow process, but with a long-lasting impact. The most immediate effect of pumping up groundwater is the rise of the fresh-salt transition under the well, a phenomenon called 'saltwater upconing', see Fig. 8. When a critical limit of the extraction rate is exceeded, deeper and salt water is extracted, and the fresh-salt transition rises up to the well mouth and the pumped water becomes brackish. The rise of the fresh-salt transition is strongest in cases where the hydraulic conductivity $k$ of the aquifer is small (low conductivity limits the horizontal groundwater flow towards the well)[11]. For aquifers with a low permeability (small $k$), only small abstraction rates are possible.
### Saline seepage
In areas situated below sea level, groundwater can move upwards to the soil surface if the upper soil layer is semipermeable, see Fig. 9 and 10. The upward moving saline seepage water may (1) discharge directly in lakes, canals, ditches or subsurface drain tiles leading to the salinization of surface waters, (2) mix near the surface with shallow fresh groundwater, or even (3) reach the root zone affecting crop growth and natural vegetation. Where rainwater or fresh surface water supplies are limited, saline seepage leads to salinization of surface water and shallow groundwater - a process known as internal salinization. The seepage flow depends on the surface soil level and on the thickness and permeability of the top soil layer (Fig. 9). Seepage flow is enhanced at places where ancient sandy deposits are close to the surface or where cracks exist in the top clay layer, giving rise to so-called 'boils' through which preferential saline seepage occurs at high fluxes[12]. Seepage in deep polders is increased when the top soil is drained for agricultural purposes, creating lower phreatic water levels (Fig. 10). Compaction of clay and peat soils is another serious consequence of drainage. The effect of seepage on seawater intrusion is similar to the effect of groundwater extraction; it causes upconing of brackish groundwater and increases the intrusion of seawater into the coastal aquifer.
Fig. 8. Upconing brackish water under a pumping well. Fig. 9. Groundwater seepage into a polder and associated rise of the salt-fresh interface. Fig. 10. Drainage of a polder causing upconing of brackish water into the ditches.
### Irrigation practices
In arid coastal plains where the groundwater salinity is too high, crops must be irrigated with water that is supplied from elsewhere. Due to water scarcity, the infiltrated irrigation water is collected in special drains and re-used for irrigation. Such an irrigation system exists, for example, in the Nile Delta [13]. Because the irrigation water is mixed with brackish groundwater, re-use can cause, in combination with evapotranspiration, a net salt flux to the land surface.
## Groundwater management
Fig. 11. Factors that influence the groundwater system. From Post (2018)[10].
Groundwater management requires an integrated approach based on insight into the multiple factors that influence the groundwater system, see Fig. 11. This insight is usually fragmentary due to the complexity of the groundwater system. Groundwater flow models are crucial for estimating the influence of abstractions on the groundwater status, see section Groundwater modelling. Permits, metering of wells, quotas and water taxes are the legal instruments on which sustainable groundwater management can be based, together with obligations of monitoring and reporting. Polluting substances from point sources (industrial effluents, household sewage) and from diffuse sources (agricultural effluents containing pesticides, herbicides, fertilizers) are a major danger for groundwater contamination. Adequate environmental policy, agricultural policy, and spatial policy that tackle the pollution issue are prerequisite for sustainable groundwater management. The effectiveness of groundwater management can be increased by involving local stakeholders, due to the strong link between use and usability of the groundwater resource. Understanding and support from stakeholders makes it easier to enforce legal rules and provisions. Without support of stakeholders, enforcement is usually difficult to achieve [14].
Monitoring aquifers for protection against depletion and pollution is a technically demanding and costly exercise so that information about aquifers is often incomplete. The costs for setting up a monitoring network, collecting data regularly, processing, interpreting, and storing it in databases, including unified databases at the national level, are one of the reasons why in developed and developing countries alike water rights and monitoring obligations, especially with respect to groundwater, may remain unimplemented [14].
## Measures to reduce soil and groundwater salinization
Different types of measures are possible to reduce soil and groundwater salinization, which can be applied depending on the geological setting and the causes of salt intrusion.
### Horizontal wells
The risk of upconing of the salt-fresh interface due to groundwater exploitation can be reduced by 'skimming' the fresh water lens with a horizontal well, see Fig. 12, instead of using vertical wells. In this way it is possible to exploit a brackish aquifer with a relatively thin fresh water lens. Periodically, natural (or artificial) recharge of the fresh water lens is necessary to get the salt-fresh interface back to its former position.
### Fresh water storage by artificial infiltration
According to the principle shown in Fig. 3, a large fresh water reservoir can be created in the subsoil by raising the fresh water table. This principle can for example be applied in coastal zones protected by a dune belt, but every higher elevated area in a coastal setting could be suitable. For example, Pauw et al. (2015)[15] artificially recharged a freshwater lens below a slightly elevated sandy creek ridge following the principle of Badon-Ghyben Herzberg. By infiltrating fresh water in the dunes – rain water or fresh water from other sources – the fresh water table can be raised such that a large column of fresh water in the subsoil is kept in hydrostatic balance with the seawater, due to the small density difference (Fig. 13). Increasing the freshwater storage capacity of coastal dunes by artificial infiltration is widely used in the Netherlands to supply drinking water to coastal cities (for example, Amsterdam, The Hague).
Fig. 12. Horizontal skimming well. The upconing effect is limited by spreading the extraction over a broad zone. Fig. 13. Large fresh water reservoir created by dune infiltration.
### Fresh water storage by injection
Collected rainwater – or fresh water from other sources – can temporarily be stored in the subsoil for later re-use. Fresh water is injected into the deeper part of the aquifer and collected later from a higher pumping well, as shown in Fig. 14. A larger volume of fresh water can be stored by lowering the salt-fresh interface. Salt groundwater is pumped away from greater depth to reduce the hydrostatic pressure on the surface layer. This will prevent an existing freshwater lens from being pushed out[16]. The brackish/salt water has to be discharged to the sea or it can be treated in a desalination plant for re-use[17]. The extraction-injection is adjusted by a so-called automatic 'freshmaker system'[16]. The principle is shown schematically in Fig. 15. Another option (if technically and economically feasible) is to pump the brackish/salt water through the underlying aquitard to a lower aquifer ('freshkeeper system'[16]), see Fig. 16.
Fig. 14. Temporary storage of rainwater. Fig. 15. Principle of the freshmaker system: withdrawal of brackish groundwater to make room for a thick fresh water lens. Fig. 16. Principle of the freshkeeper system: removal of brackish groundwater to a lower aquifer to make room for storage of fresh water.
### Aquifer barriers to prevent seawater intrusion
Two types of barriers have been implemented in practice: hydraulic barriers and physical barriers. The usual principle of a hydraulic barrier is shown in Fig. 17. Fresh water (for example, purified sewage water) is injected into the aquifer close to the seaward boundary to create a pressure head that prevents the intrusion of seawater. Further inland, freshwater can be extracted (to a limited extent) in periods of drought from the fresh aquifer. A practical example is the hydraulic barrier installed in California near Los Angeles [18]. The effectiveness of this solution depends on the availability of fresh water during sufficiently long and frequent periods. Another principle is based on extraction of intruding seawater, as shown in Fig. 18. Drawbacks of this principle are the disposal of the extracted saline or brackish groundwater and the lowering of the piezometric heads, especially in shallow coastal aquifers[19]. This latter issue can be mitigated by fresh water injection further landward[20]. This principle was implemented at a coastal area of the Netherlands (Perkpolder) to protect a freshwater lens from the impact of a managed realignment project[21]. This self-flowing seepage system called 'SeepCat' is thought to be also applicable for small oceanic islands to protect vulnerable underground freshwater reserves from sea level rise, climate change and overexploitation, see the appendix for a more detailed description.
Physical subsurface barriers have been constructed in several countries, especially in Japan[22] and China [23]. The barriers are generally built of concrete using grouting techniques or mixed-in-place slurry-wall methods[24]. The dams serve as a barrier for seawater intrusion, and also create underground fresh water storage in periods of strong precipitation (Fig. 19). However, the costs are high and the solution is only applicable in shallow aquifers[19].
Fig. 17. Hydraulic injection barrier at the seaward entrance of an aquifer. The marine salt wedge is expelled in periods of abundant fresh water. Inland abstraction wells can be exploited in periods of drought. Fig. 18. Hydraulic abstraction barrier at the seaward entrance of an aquifer. The marine salt wedge is expelled in periods of abundant fresh water. Piezometric levels condition the use of inland injection/abstraction wells. Fig. 19. Physical subsurface barrier at the seaward entrance of an aquifer.
### Isolating saline areas
Saline seepage due to local boils – a major salinization mechanism in the deep polders in the Netherlands – is combated by building a bypass around the saline areas. The temporary isolation (during dry periods) of saline areas with a significant number of boils is controlled by automatic weirs[25]. The temporarily stored salt water is discharged during rainstorm events when salt concentrations are low. Boils that arise from the removal of structures, such as level filters or sheet piles, or from the sealing of old gas wells, can be sealed. This can be done through injection of expanding and persisting fluids or through biosealing; the latter option is the most environmentally friendly.
## Dealing with brackish groundwater
In arid coastal zones with endemic freshwater shortages, there are no good options for preventing salt intrusion into the groundwater. Strict regulation of groundwater abstraction is necessary to make land use possible. Agriculture has to make use of salt-tolerant crops. Fortunately, ever better crops are being developed for saline conditions, including by genetic modification techniques[26][27]. In addition, infrastructure must be protected against corrosion by saline groundwater, including the use of salt-resistant concrete.
## Groundwater modelling and observation
Fig. 21. SkyTEM team recording Time Domain Electromagnetic Data. Source: G. Oude Essink, https://publicwiki.deltares.nl/
Groundwater flow can be described with Darcy's law that couples the flow rate linearly to the gradient in the hydrostatic groundwater pressure. For an introduction to groundwater flow modelling, see for example the downloadable lecture notes of Oude Essink (2000)[28]. Application of Darcy's law requires knowledge of the soil permeability (generally expressed in terms of hydraulic conductivity). The permeability is different for each soil type. The structure and composition of the substrate is generally very complex. It is a reflection of the geological history in which a large number of processes on very diverse space and time scales play a role. The reliability with which groundwater flows can be simulated therefore depends primarily on the extent to which the structure and composition of the subsoil are known. This knowledge usually has large gaps, since sampling the subsurface over great depth requires a great deal of effort and is very expensive. In addition to knowledge of the subsurface structure, knowledge is needed of the position of the salt-fresh transition zones in the underground. Missing knowledge can be partially overcome by model calibration based on data from wells (quantity and quality of abstractions), piezometric surveys (groundwater pressure) and observations based on geophysical techniques.
Fig. 20. Electrical resistivity measurement by continuous vertical electrical sounding. Credit: P. de Louw.
In recent decades, a large number of geophysical measurement methods have been developed that indirectly provide information about the subsurface soil structure and groundwater salinity and distribution[29]. Seismic techniques, such as Ground Penetrating Radar (GPR [30][31]) can be used for detecting and mapping structures in the underground. Unfortunately, this technique is less suitable for saturated soils with a high clay content. Nuclear Magnetic techniques, such as Magnetic Resonance Sounding (MRS [32]) and Time Lapse Gravity (TLG [33]) can provide information on aquifer properties, such as moisture content, porosity and hydraulic conductivity. Electrical resistivity (Fig. 20) and electromagnetic techniques (Fig. 21) make use of the large electrical resistivity contrast between seawater and freshwater for detecting and mapping the subsurface salinity distribution [34]. Examples are Electrical Resistivity Tomography (ERT [35]), Time-Lapse Resistivity (TLR[36]), Time Domain Electromagnetic sounding (TDEM [37]), Frequency Domain EM and Induced Polarization (IP [38]). Airborne EM (time or frequency domain) using a helicopter to acquire EM-data of the subsoil has recently showed to be very promising in mapping the fresh-salt interface of large coastal areas in The Netherlands, Germany, Denmark and Belgium[39][40]. Together with information from wells, bore holes and model calculations these data enable reasonable estimates of the effect of interventions in the groundwater system. However, the design of groundwater models and the interpretation of model results still require highly specialized knowledge and experience of geohydrological processes.
## Appendix: The SeepCat system
SeepCat is a saline groundwater discharge system that can protect limited freshwater resources on small islands against salinization and increases the availability of freshwater. Sea levels area expected to rise up to 0.7 m in 2100 AD and will increase the saline groundwater pressure and therefore reduce the size of coastal freshwater lenses. The saline groundwater discharge system SeepCat is able to compensate the effects of sea level rise by lowering the salt water pressure for enlargement of the freshwater lens.
### Theoretical background
Usually, there is much more space in the subsoil to store fresh water than by storing it on the surface e.g. in basins. Also, losses by evaporation and contamination are much less when water is stored in the subsoil. However, it is difficult to increase groundwater stocks in coastal areas because of the presence of saline groundwater. The lighter fresh groundwater is pushed upward by the buoyancy force of the denser saline groundwater beneath. The thickness of the freshwater lenses in coastal areas area therefore limited. The thickness can be estimated by the theoretical relation derived by Badon-Ghyben Herzberg (BGH) (see Figs. 3 and 13). From this BGH-relation it can be derived that the thickness of a freshwater lens (in a theoretical homogeneous case) is about 41 times the groundwater level above sea level. From this relation it can also easily be seen that a freshwater lens is able to grow when: (1) the groundwater level is increased, e.g. by artificial recharge (injection system), and (2) the water pressure of the saline groundwater is reduced, in the present case by SeepCat.
### Description of SeepCat
Fig. 21. SeepCat system, consisting of vertical pipes that abstract saline groundwater around the freshwater lens on a small island and pump the saline groundwater to the sea via a horizontal collector pipe.
The purpose of this saline groundwater discharge system is to reduce the water pressure of the saline groundwater surrounding the freshwater lens. This is analogous to a drop of the sea level, resulting in a new equilibrium stage in which the freshwater lens is able to grow. The discharge system consists of vertical perforated tubes between the freshwater lens and the ocean side. The vertical tubes are connected to a horizontal tube with a pump. The extracted saline groundwater is discharged to the sea. A schematic diagram of the implementation of the system on an island is shown in the Fig. 21.
The SeepCat system is applied in the Netherlands (Perkpolder) to protect a freshwater lens used for irrigation from salinization caused by an adjacent 'managed realignment' project. This depoldering project for tidal flat restoration in the Western Scheldt estuary has a similar impact on the groundwater of the adjacent land as a local sea level rise of about 1.5 m. 61 vertical discharge tubes were installed over a total length of 1 km. A total of 400 m3 of saline groundwater is discharged every day. The results of this project were presented at the Salt Water Intrusion Meeting in Cairns (Australia), July 2016 [21]. For a short movie of the pilot project at Perkpolder choose 'View highlight' at [1].
## Related articles
Submarine groundwater discharge and its influence on the coastal environment
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## References
1. WWAP (United Nations World Water Assessment Programme). 2015. The United Nations World Water Development Report 2015: Water for a Sustainable World. Paris, UNESCO https://unesdoc.unesco.org/ark:/48223/pf0000231823
2. Jiao, J. and Post, V. 2019. Coastal Hydrogeology. Cambridge University Press.
3. Syvitski, J. P., Kettner, A. J., Overeem, I., Hutton, E. W., Hannon, M. T., Brakenridge, G. R. and Nicholls R. J. 2009. Sinking deltas due to human activities. Nature Geoscience 2: 681-686
4. Custodio, E. and Bruggeman, G.A., editors. Groundwater problems in coastal areas: a contribution to the International Hydrological Programme. Studies and reports in hydrology, vol. 45. Paris: UNESCO; 1987
5. Post, V.E.A., Eichholz, M. and Brentführer R. 2018. Groundwater management in coastal zones. Bundesanstalt für Geowissenschaften und Rohstoffe (BGR). Hannover, Germany, 107 pp.
6. Van Dam, J.C. 1983. The shape and position of the salt water wedge in coastal aquifers. Proceedings of the Hamburg Symposium on Relation of Groundwater Quantity and Quality. IAHS Publ. no. 146: 59–75
8. Werner, A.D., Bakker, M., Post, V.E.A., Vandenbohede, A., Lu, C., Ataie-Ashtiani, B., Simmons, C.T. and Barry, D.A. 2013. Seawater intrusion processes, investigation and management: Recent advances and future challenges. Advances in Water Resources 51: 3–26
9. Post, V.E.A., Eichholz, M. and Brentführer R. 2018. Groundwater management in coastal zones. Bundesanstalt für Geowissenschaften und Rohstoffe (BGR). Hannover, Germany, 107 pp.
10. Dagan G, Bear J. 1968. Solving the problem of local interface upconing in a coastal aquifer by the method of small perturbations. Journal Hydrological Research 6: 15–44
11. De Louw, P.G.B., Oude Essink, G.H.P., Stuyfzand, P.J. and Van der Zee, S.E.A.T.M. 2010. Upward groundwater flow in boils as the dominant mechanism of salinization in deep polders, The Netherlands. Journal of Hydrology 394: 494-506
12. Kotb, T.H.S., Watanabe, T., Ogino, Y. and Tanji, K.K. 2000. Soil salinization in the Nile Delta and related policy issues in Egypt. Agricultural Water Management 43: 239-261
13. Mechlem, K. 2016. Groundwater Governance: The Role of Legal Frameworks at the Local and National Level—Established Practice and Emerging Trends. Water 2016, 8, 347; doi:10.3390/w8080347
14. Pauw, P.S., Van Baaren, E.S., Visser, M., De Louw, P.G.B. and Oude Essink, G.H.P. 2015. Increasing a freshwater lens below a sandy creek ridge using a controlled artificial recharge and drainage system: a case study in the Netherlands. Hydrogeology Journal. doi: 10.1007/s10040-015-1264-z. download
15. Zuurbier, K. G., Kooiman, J. W., Groen, M. M., Maas, B. and Stuyfzand, P. J. 2014. Enabling successful aquifer storage and recovery (ASR) of freshwater using horizontal directional drilled wells (HDDWs) in coastal aquifers. In: Journal of Hydrologic Engineering 20 (3), B4014003
16. Khadra, W.M., Stuyfzand, P.J. and Khadra, I.M. 2017. Mitigation of saltwater intrusion by ‘integrated fresh-keeper’ wells combined with high recovery reverse osmosis. Science of The Total Environment 574: 796-805
17. Johnson, T. 2007. Technical Documents on Groundwater and Groundwater Monitoring Battling Seawater Intrusion in the Central and West Coast Basins. WRD Technical Bulletin 13. http://www.wrd.org/engineering/reports/TB13_Fall07_Seawater_Barriers.pdf
18. Oude Essink, G.H.P. 2001. Improving fresh groundwater supply-problems and solutions. Ocean & Coastal Management 44: 429–449
19. Pool, M. and Carrera, J. 2010. Dynamics of negative hydraulic barriers to prevent seawater intrusion. Hydrogeology Journal 18: 95–105
20. De Louw et al., 2016. A self-flowing seepage system to protect a freshwater lens from local sea level rise. Pages 67-70 from: Werner, A.D. (ed.), Proceedings of the 24th Salt Water Intrusion Meeting and the 4th Asia-Pacific Coastal Aquifer Management Meeting, 4-8 July, 2016, Cairns, Australia http://swim-site.nl/index.html
21. Nishigaki, M., Kankam-Yeboah, K. and Komatsu, M. 2004. Underground dam technology in some parts of the world. Journal of Groundwater Hydrology 46: 113-130
22. Wang, K., Li, B., Yu, Q. and Wang, J. 2012. The construction of underground reservoir and its beneficial effect on resource and environment in Shandong Province Peninsula. In: China Geological Survey – Achievements. http://en.cgs.gov.cn/achievements/201601/t20160112_35475.html
23. Ishida, S., Tsuchihara, T., Yoshimoto, S. and Imaizumi, M. 2011. Sustainable use of groundwater with underground dams. In: Japan Agricultural Research Quarterly 45: 51-61
24. Kamps, P., Nienhuis, P., van den Heuvel, D. and de Joode, H. 2016. Monitoring Well Optimization for Surveying the Fresh/Saline Groundwater Interface in the Amsterdam Water Supply Dunes. 24th Salt Water Intrusion Meeting and the 4th Asia-Pacific Coastal Aquifer Management Meeting, July 2016, Cairns, Australia
25. De Vos, A., Bruning, B., Van Straten, G., Oosterbaan, R., Rozema, J. and Van Bodegom, P. 2016. Crop salt tolerance. Salt Farm Texel. https://www.salineagricultureworldwide.com/uploads/file_uploads/files/Report_Crop_Salt_Tolerance-Salt_Farm_Texel.pdf
26. Roy, S.J., Negrao, S. and Tester, M. 2014. Salt resistant crop plants. Current Opinion in Biotechnology 26: 115–124
27. Oude Essink, G.H.P. 2000. Groundwater Modelling. Lecture notes, Utrecht University. https://publicwiki.deltares.nl/display/FRESHSALT#freshsalt-download
28. Herckenrath, D. 2012. Informing groundwater models with near-surface geophysical data. Thesis, Technical University of Denmark
29. Knight, R. 2001. Ground penetrating radar for environmental applications. Annual Review of Earth and Planetary Sciences 29L 229-255
30. Huisman, J., Hubbard, S., Redman, J. and Annan, A. 2003. Measuring Soil Water Content with Ground Penetrating Radar: A Review. Vadose Zone Journal 2: 476-491
31. Legchenko, A., Baltassat, J. M., Beauce, A. and Bernard, J. 2002. Nuclear magnetic resonance as a geophysical tool for hydrogeologists. Journal of Applied Geophysics 50: 21-46
32. Montgomery, E.L. 1971. Determination of coefficient of storage by use of gravity measurements: Ph.D. dissertation, University of Arizona, Tucson, 144 p
33. Macaulay, S. and Mullen, I. 2007. Predicting salinity impacts of land-use change: Groundwater modelling with airborne electromagnetics and field data, SE Queensland, Australia, International Journal of Applied Earth Observation and Geoinformation 9: 124-129
34. Acworth, R.I. and Dasey, G.R. 2003. Mapping of the hyporheic zone around a tidal creek using a combination of borehole logging, borehole electrical tomography and cross-creek electrical imaging, New South Wales, Australia. Hydrogeology Journal 11: 368–77
35. Poulsen, S.E., Rasmussen, K.R., Christensen, N.B. and Christensen, S. 2010. Evaluating the salinity distribution of a shallow coastal aquifer by vertical multielectrode profiling (Denmark). Hydrogeology Journal 2010: 161–71
36. Auken, E., Christiansen, A. V., Jacobsen, L. H. and Sorensen, K. I. 2008. A resolution study of buried valleys using laterally constrained inversion of TEM data. Journal of Applied Geophysics 65: 10-20
37. Dahlin, T., Leroux, V. and Nissen, J. 2002. Measuring techniques in induced polarisation imaging. Journal of Applied Geophysics 50: 279– 298
38. Siemon, B., Ibs-von Seht, M., Steuer, A., Deus, N. and Wiederhold, H. 2020. Airborne electromagnetic, magnetic, and radiometric surveys at the German North Sea Coast applied to groundwater and soil investigations. Remote Sens. 12(10), 1629, doi: 10.3390/rs12101629
39. Delsman, J., Van Baaren, E.S., Siemon, B., Dabekaussen, W., Karaoulis, M.C., Pauw, P., Vermaas, T., Bootsma, H., De Louw, P.G.B., Gunnink, J.L., Dubelaar, W., Menkovic, A., Steuer, A., Meyer, U., Revil, A. and Oude Essink, G.H.P. 2018. Large-scale, probabilistic salinity mapping using airborne electromagnetics for groundwater management in Zeeland, the Netherlands. Environ. Res. Lett. 13. doi:10.1088/1748-9326/aad19e download
The main authors of this article are Job Dronkers and Perry de LouwPlease note that others may also have edited the contents of this article. Citation: Job Dronkers; Perry de Louw; (2020): Groundwater management in low-lying coastal zones. Available from http://www.coastalwiki.org/wiki/Groundwater_management_in_low-lying_coastal_zones [accessed on 12-06-2021] For other articles by this author see Category:Articles by Job Dronkers For other articles by this author see Category:Articles by Perry de Louw For an overview of contributions by this author see Special:Contributions/Dronkers J For an overview of contributions by this author see Special:Contributions/de Louw, P.G.B. | 2021-06-12 17:41:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26989683508872986, "perplexity": 7278.424745370906}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487586239.2/warc/CC-MAIN-20210612162957-20210612192957-00544.warc.gz"} |
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• I won’t forget her advice
I had a very special teacher in high school many years ago. Her husband died of a heart attack. About a week after his death, she shared some of her insights（见解）with us.
The class was nearly over. She said, “Before class is over, I would like to share with all of you an important thought.”
“Each of us is put here on Earth to learn, share, love, enjoy and give all by ourselves. We must make the best of every single day.”
Her eyes were beginning to water and she went on, “So I would like you all to make me a promise. From now on, on your way to school, or on your way home, find something beautiful to notice. It doesn’t have to be something you see — it could be a nice smell — perhaps of freshly baked bread, or it could be the sound of the breeze slightly blowing the leaves in the trees.”
“Please look for these things, and love them. For, although it may seem common, these things are the stuff（素材）of life. They are the little things we are put here on Earth to enjoy. They are the things we often take for granted. We must make it a point to notice them, for at any time it can all be taken away.”
The class was completely quiet. We picked up our books and went out of the room silently. That afternoon, I noticed more things on my way home from school than I had that whole term.
I usually think of that teacher and try to enjoy all of those things that we sometimes overlook (忽略).
Take notice of something special you see during your lunch hour today. Walk barefoot along the beach at sunset. For as we get older, it is not the things we did that we regret（后悔）, but the things we didn’t do.
【小题1】What happened to the teacher’s husband? A．He was ill.+ I! h$M2 B" K4 Y& a B．He died of a heart attack.& ^0 B: a. Q+ F/ ]0 a; _- f7 Q C．He made a promise. & \- S2 g; j& \; D3 U2 A D．He became a teacher, too.# ?5 V1 Q5 d' M- T 【小题2】The high school teacher shared her insights with her students ____________. A．on her way to school+ Y [( R" h) N R6 B: H2 $ ' G B．on her way home0 F/ C" K+ E/ Q3 L; S1 T3 T C．at the beginning of class9 \/ Y" J- _, a' b) I5 a1 M8 Y D．at the end of class W9 Y0 H$J' I- Y f% j/ h2 C 【小题3】The underlined word “breeze” (in Paragraph 4) means ____________? A．colourful cloud8 ?* g/ X! G1 Y( M; E B．white snow3 b2 c- U* E7 N! S( E C．light wind 4 W9 H5 M% ?3 T& c D．heavy rain/ S- T; [5 J& B1 D. ] U/ O 【小题4】What is the teacher’s advice? A．We should love life and enjoy things around us. " @- F% S$ \6 Z* T6 A# A4 F7 g B．We should share our important thoughts with others.# E Y; A* A- H0 \ N0 d C．We should never feel sorry for what we have done." ^, A8 C+ ?5 G* K7 U/ M D．We should do importand things and overlook little ones.+ ]# C0 c& A( b4 A; Q/ W" H
• I’m Millie.I’m 12 1 old.I have black 2 and black hair.I 3 born in Beijing and I live 4 Hoping Road.I have a brother. 5 name is Andy.I like 6 TV and Andy 7 listening to the radio.I have 8 of good friends at school.My 9 friend is Kitty.She is my classmate.She is a good student.She wants to be a doctor when she 10 up.
1.A.month B.months C.year D.years
2.A.mouth B.nose C.eyes D.eye
3.A.am B.is C.was D.are
4.A.in B.on C.for D.with
5.A.His B.He C.Her D.She
6.A.watch B.watches C.to watch D.watching
7.A.like B.love C.enjoys D.enjoy
8.A.lot B.lots C.a lots D.lot a
9.A.good B.better C.best D.well
10.A.gets B.puts C.rings D.grows
• In 1993 an unknown American called Clarence Nash went to see the filmmaker Walt Disney. He had an unusual voice and he wanted to work in Disney’s cartoon(动画片) film for children. When Walt Disney heard Nash’s voice, he said”Stop! That’s our duck!”
The duck was the now-famous Donald Duck, who first appeared in 1934 in the firm The Wise Little Hen. Donald lived in an old houseboat(水上住家) and wore his sailor jacket and hat. Later that year he became a star after an eight – minute Mickey Mouse film. The cinema audience liked him because he was lazy and greedy(贪婪的), and because he lost his temper (发脾气) very quickly. And they loved his voice when he became angry with Mickey’s eight nephews(侄子). Soon Donald was more popular than Mickey Mouse himself, probably because he wasn’t a goody-goody like Mickey.
In the 1930S, ‘ 40s and ‘ 50s Donald and his friends Mickey, Goofy and Pluto made hundreds of Disney cartoons. He also made educational films about the place of the USA in the world, and safety in the home. Then in 1966 Donald Duck and his voice disappeared – there were no more new cartoons.
Clarence Nash died in February, 1985. But today’s children can still see the old cartoons on television and hear that famous voice.
【小题1】Who made Donald Duck film? ______ A．Mickey Mouse.) f3 R+ E% G$L, j5 M B．Clarence Nash.7 S& ^# N9 D4 J# [5 D+ e C．Walt Disney.) c% A4 @/ S, ]$ P D．Pluto.# [6 K4 G+ R5 \/ H
【小题2】 When was the first Donald Duck film made? ______ A．In 1933.3 O7 L+ M' i2 K, j B．In 1934.- A3 " h! @3 F) J C．In 1966.6 I1 @4 V1 D5 M& \( g+ ? D．In 1930., G3 I! g: f$?/ W! I Q 【小题3】Who was Clarence Nash? ______ A．A cartoonist.7 F/ R6 N' G6 M" ( ]% Q! e X B．Donald Duck’s voice., D. F" d1 B+ S" M4 A- S8 V C．A film-maker./ \" I; e2 ?3 I* N8 a D．A film star.2 ^; J9 R( ]$ j7 F+ _7 N9 _% j
【小题4】Where do today’s children see Donald Duck ? ______ A．In new film.; A! [" E$[: P$ S e! i$W2 d. ] S: T) Y B．At the cinema.* L" " F8 K b- [) E5 D/ \% P C．On television.( A4 G3 d" P5 d7 R( A7 P/ N; L D．At concerts.' B% ^5 a. B* f% e: Q 【小题5】 The underlined word”audience” in the second paragraph means______ . A．reads; g! T3 @% g! - @ B．formal interview8 V6 Z$ S; i; R5 @ J C．law freedom* I8 d! \8 ^6 E8 U D．the people who watch a film at a cinema9 W( T4 ?& X* X" b
• Not long ago, I made up my mind to read a lot of books to get more knowledge. So I went to the library and 36 happily with several books. But after a few days, I felt impatient. The 37 of finishing all of them seemed impossible, because I always found it 38 to calm down to read a whole book. I didn’t know what to do with it. Then 39 one day I thought of "Why not make reading fun?" It gave me 40 again. Reading is a journey of spirit. Every time we read a book, we are actually talking 41 the writer. I tried to put all
my effort into his or her books, 42 I could feel all of his or her happiness and suffering. Now books have become a part of my life.
See? Attitude (态度) can make a great 43 . Someone once said,"Even though the situation is bad, people still have one freedom ( 自由) to 44 their attitude. "So,don’t complain about study or work. It helps 45 . Try to see things from a different way. Believe me; this will change the situation and help you a lot.
【小题1】3 e7 V- O4 Z! D- Z9 B: c A．sang4 T3 J4 ^' S6 h# Q# j! f B．jumped+ H' F& W. c$X C．returned; J. C8 J8 _ d D．danced( _* a: O1 8 A6 R 3 b/ O/ T: " Q! j* U5 X 【小题2】: W' 9 U8 V9 G% P1 K A．way$ d& 8 M8 _& j" X5 B B．habit0 i& ?) B) c% Z* f5 X C．suggestion7 J0 J# I7 D' J, _1 Z D．idea+ i% B$Y* j U7 b* g5 i3 Q/ S9 R 6 Z* P* K' C" P; f 【小题3】& C* I1 N/ d% R# d A．hard! V2 j& G% J% ( b B．interesting; T6 j( j+ h" K) h8 S% W/ W C．happy; B4 E# [ d7 h D．easy6 f. Y/ G: O# ] 1 D% g8 ]% @# K) L. F/ g. T$ T$A 【小题4】 A. sadly B quickly C. suddenly D. hardly 【小题5】. H. J( E. U, L6 J- U% [4 R. A A．advice4 S% X3 Q9 L# T! Q4 D( @" U B．hope9 i. _. [3 Y+ M7 M+ E0 R6 O7 S. X C．time3 h* X1 O2 P& S9 H4 B D．knowledge9 F @2 X" f g8 g7 O % I% P( c9 [2 ? 【小题6】 / g, [4 N9 [) N2 I4 f A．with; J3 V7 Y+ j: e- M- c B．about/ h8 _% T; g% Q) Q5 j0 U C．of+ E7 g/ P6 Q3 D0 D D．at$ d8 F. J) \$F* G. _, a/ N T( i* O% h- g/ - M6 O! K0 G 【小题7】 - g0 A3 N! [( P j( M- Y0 d A．because; D4 \, Y' U$ a6 E- g B．though# c! ]4 g/ L+ K8 d V% \0 f C．but9 B+ W1 d0 e$J9 f9 U$ U. L D．so8 I4 N; d1 H4 S* S8 U
* ]4 c: U. R& N. ^7 b- U" X
【小题8】$F4 R* U7 T) E' T A．decision& e" I' ?: d2 S L. A% E% B B．difference: \; e: b+ V! ]& Q5 [ C．discussion5 g# ?0 L/ _& M. h" e) ? D．promise( U. N: C2 b8 H9 V Y4 W$ O& \
( M% E3 K7 ?% ?" H; N
【小题9】( j) d& Y1 f+ P, B) W7 ] A．announce7 _% a! ]3 R- R B．choose5 g: C F1 i# [6 i/ i C．show& _1 `3 b" A/ R! P5 g6 R D．hide" ^3 W4 [1 J0 L: J& H | 2018-12-10 12:56:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27508747577667236, "perplexity": 12211.326766801001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823339.35/warc/CC-MAIN-20181210123246-20181210144746-00249.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-a-combined-approach-4th-edition/chapter-2-section-2-7-linear-inequalities-and-problem-solving-vocabulary-and-readiness-check-page-170/8 | ## Algebra: A Combined Approach (4th Edition)
Published by Pearson
# Chapter 2 - Section 2.7 - Linear Inequalities and Problem Solving - Vocabulary and Readiness Check: 8
#### Answer
$|-6|$
#### Work Step by Step
$|-6|=6$ and $6$ is not smaller than 6, it's equal.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2018-07-22 20:38:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6243458986282349, "perplexity": 2617.151814532546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593586.54/warc/CC-MAIN-20180722194125-20180722214125-00224.warc.gz"} |
http://mathhelpforum.com/math-topics/10683-determine-largest-prime-divisor-87-88-a-print.html | # Determine the largest prime divisor of 87! + 88!.
• January 26th 2007, 11:37 AM
ceasar_19134
Determine the largest prime divisor of 87! + 88!.
Determine the largest prime divisor of 87! + 88!.
These problems are so hard... (For me anyway.)
• January 26th 2007, 01:28 PM
galactus
If you have n!+(n+1)! and (n+2) is prime, then (n+2) is the largest prime divisor.
The next number, 89, is prime, the largest prime divisor of 87!+88! is 89.
For instance, try 9!+10!, 11 is the largest prime divisor.
29!+30!...the largest prime divisor is 31.
This isn't anything I ever tried to prove. The Hackster probably knows it or will figure it out. There's probably already a known theorem relating it.
• January 26th 2007, 01:33 PM
CaptainBlack
Quote:
Originally Posted by galactus
If you have n!+(n+1)! and (n+2) is prime, then (n+2) is the largest prime divisor.
The next number, 89, is prime, the largest prime divisor of 87!+88! is 89.
For instance, try 9!+10!, 11 is the largest prime divisor.
29!+30!...the largest prime divisor is 31.
This isn't anything I ever tried to prove. The Hackster probably knows it or will figure it out. There's probably already a known theorem relating it.
That is the smallest prime divisor not the largest.
RonL
• January 26th 2007, 01:40 PM
galactus
how about 47?. It's the smallest, isn't it?. It's prime and it divides 87!+88!.
But you're certainly right, Cap'N. I had a major brain fart. I was thinking of prime factors. DUH
• January 26th 2007, 02:02 PM
CaptainBlack
Quote:
Originally Posted by galactus
how about 47?. It's the smallest, isn't it?. It's prime and it divides 87!+88!.
But you're certainly right, Cap'N. I had a major brain fart. I was thinking of prime factors. DUH
Opps, sorry that's two of us:o
RonL
• January 26th 2007, 02:17 PM
Soltras
87! + 88! = 87! ( 1 + 88 ) = 87!*(89).
89 is a prime factor.
The question is, does a higher prime divide 87!
Suppose p is prime and greater than 89.
Well 87! = 87*86*85*...*2*1
Since p doesn't divide 89, then if p divides 87!*(89), then p divides at least one of these terms in 87!.
This is impossible since p is larger than all terms appearing in the factorial.
So 89 is the largest prime factor of 87! + 88!
(this can be worked into a theorem, say if p is prime, then it's the largest prime factor of (p-1)! + (p-2)! )
• January 26th 2007, 02:31 PM
galactus
So I was correct. I thought this was something I had seen before, but then second-guessed myself.
• January 26th 2007, 07:23 PM
Soroban
Hello, ceasar!
Quote:
Determine the largest prime divisor of $87! + 88!$
We have: . $87! + 88!\:=\:87! + 88\cdot87!$
Factor: . $87!(1 + 88) \:=\:87!(89)$
Therefore, $89$ is the largest prime divisor. | 2016-08-30 15:14:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7152119278907776, "perplexity": 1823.572127007572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982984973.91/warc/CC-MAIN-20160823200944-00157-ip-10-153-172-175.ec2.internal.warc.gz"} |
https://testbook.com/question-answer/euclids-fifth-postulate-is--60a61b16f2851e077025a87e | # Euclid's fifth postulate is:
This question was previously asked in
DSSSB TGT Maths Female Subject Concerned - 18 Nov 2018 Shift 3
View all DSSSB TGT Papers >
1. All right angles are equal to one another.
2. A circle may be described with any center and any radius.
3. The whole is greater than the part.
4. If a straight line, falling on two straight lines, makes the interior angles on the same side of it, taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
Option 4 : If a straight line, falling on two straight lines, makes the interior angles on the same side of it, taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
## Detailed Solution
Concept:
All five postulate of Euclid's are as follow:
First: A straight line segment can be drawn by joining any two points.
Second: Any straight line segment can be extended indefinitely through both ends.
Third: Given any straight line segment we can draw a circle having line segment as radius and one end point of line segment as center of circle.
Fourth: All right angles are equal to each other.
Fifth: If two lines are drawn which intersect a third line in such a way that the sum of the inner angles on one side is less than two right angles ($$180^\circ$$), then the two lines must intersect each other in that side where sum of angles is less than right angles.
Calculation:
1. All right angles are equal to one another- Euclid's Fourth postulate
2. A circle may be described with any center and any radius- Euclid's Third postulate
3. The whole is greater than the part- Euclid's Fifth axiom
4. If a straight line, falling on two straight lines, makes the interior angles on the same side of it, taken together less than two right angles, then the two straight lines if produced indefinitely, meet on that side on which the sum of angles is less than two right angles- Euclid's Fifth postulate | 2021-09-24 18:15:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49708423018455505, "perplexity": 171.2408540402973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057564.48/warc/CC-MAIN-20210924171348-20210924201348-00437.warc.gz"} |
https://alice-publications.web.cern.ch/node/3562 | # Figure 8
Sum of the cross sections of positive and negative charge muons from W boson decays measured in p-Pb collisions at $\snn = 5.02$ TeV in the rapidity region $-4.46 < y_{\rm cms} < -2.96$ (left panel) and $2.03 < y_{\rm cms} < 3.53$ (right panel) as a function of centrality. The cross sections are normalised by the number of binary collisions $\langle N_{\rm coll}^{\rm mult} \rangle$. The vertical bars (open boxes) represent the statistical (systematic) uncertainties. The correlated global uncertainties include the MB cross section, normalisation, $A \times \epsilon$ corrections and tracking and trigger systematics. A dotted line is drawn at the value of the centrality-integrated cross section to guide the eye. | 2018-07-21 01:46:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9509730935096741, "perplexity": 1003.7094040782123}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676592150.47/warc/CC-MAIN-20180721012433-20180721032433-00237.warc.gz"} |
https://www.physicsforums.com/threads/asymmetry-between-probability-distributions.830876/ | # Asymmetry between probability distributions
Tags:
1. Sep 4, 2015
### stlukits
I have made an interesting observation that I can't explain to myself. Think about a prior probability P and a posterior probability Q. They are defined on an event space W with only three elements: w1, w2, and w3 (the number of elements won't matter as long as it's finite). The Kullback-Leibler divergence measures how far these probability distributions are apart, i.e. how much information it takes to get from P to Q. If P(w1)=p1 etc. then
KLD(Q,P)=q1*log(q1/p1)+q2*log(q2/p2)+q3*log(q3/p3)
The KLD is not symmetric, so if P and Q switch roles (Q is now the prior and P the posterior), the divergence will be different. If you think of P and Q as points on a simplex (all points in R3 with r1+r2+r3=1 with rj>0; the simplex in R3 looks like an equilateral triangle), the KLD does NOT define a metric topology on this simplex, because KLD(Q,P) is in general not equal to KLD(P,Q).
My original intuition was that the way this asymmetry works is that as you go from the centre to the periphery of the equilateral triangle (i.e. the entropy of the probability distribution decreases), less information is necessary compared to the other way around going from the periphery to the centre, so
H(P)>H(Q) implies that KLD(Q,P)<KLD(P,Q)
Note that the prior is the second argument for KLD -- that's a bit counterintuitive. H is here the Shannon entropy H(P)=-p1log(p1)-p2log(p2)-p3log(p3).
In any case, my intuition is wrong. Let P (the prior) be fixed. Then you can partition the simplex into those points Q for which KLD(Q,P)>KLD(P,Q) (colour them red) and those for which KLD(Q,P)<KLD(P,Q) (colour them blue). The partitions are pretty and far from trivial. How could you defend this in terms of intuitions about probability distributions? Is there any way to explain, without recourse to information theory, why going from P to Q1 is harder than going from Q1 to P; while it is easier going from P to Q2 than going from Q2 to P? Q1 is an arbitrary red point, while Q2 is an arbitrary blue point.
Here is the partition for P=(1/3,1/3,1/3):
http://streetgreek.com/lpublic/various/asym-eq.png [Broken]
And here for P=(0.4,0.4,0.2):
http://streetgreek.com/lpublic/various/asym422.png [Broken]
And here for P=(0.242,0.604,0.154):
http://streetgreek.com/lpublic/various/asym262.png [Broken]
And here for P=(0.741,0.087,0.172):
http://streetgreek.com/lpublic/various/asym712.png [Broken]
Last edited by a moderator: May 7, 2017
2. Sep 4, 2015
### Staff: Mentor
An interesting problem!
Let's define ">" on points on the plane as P>Q iff KLD(Q,P)<KLD(P,Q), i. e. going from Q to P needs more information than the opposite.
Is this transitive? If P>Q and Q>R, is P>R?
If yes, there should be a "smallest" point, one where the whole plane is colored blue.
Your points don't seem to suggest this. If the relation is not transitive, it has a weird consequence: you can find a set P, Q, R where going P->Q->R->P needs more information than going P->R->Q->P.
For an event space with just two events, the solution should be:
P>Q for (p<q and p+q<1) or (p>q and p+q>1) where p=p1 and q=q1.
In other words, P>Q if |p-1/2| < |q-1/2|.
Going closer to the middle needs more information than going outwards. This is transitive.
(I'm sure there is at least one sign error in it)
Example:
p -> q:
0.3 -> 0.1: KLD(Q,P)=0.0505
0.1 -> 0.3: KLD(Q,P)=0.0667
3. Sep 5, 2015
### gill1109
Notice that in the definition of the KLD there is an expectation value taken with respect to Q: KLD(Q,P)=q1*log(q1/p1)+q2*log(q2/p2)+q3*log(q3/p3). And of what? the logarithm of ratios of probabilies according to P and to Q.
KLD tells us how fast you learn, when the true distribution is Q, that it isn't P. And this quantity is asymmetric. Which is pretty obvious (the asymmetry) when you think about some examples in which one of the p's or one of the q's is zero.
4. Sep 6, 2015
### stlukits
gill1109 -- yes, you are absolutely right. This is precisely what I am trying to show: that the asymmetry is also justified when one of the p's or q's is NOT zero. This is not as obvious as it appears. Continuity between the extreme probability case and the non-extreme probability case is, of course, one argument for asymmetry. But some people have invested a lot of time into a geometric model of non-extreme probabilities where all the distances are symmetric. I am trying to show that they are wrong. There is a sense in which my argument isn't doing so well -- the asymmetries, as the diagrams show, are all over the place and intuitively unpredictable.
mfb -- excellent point. I've been trying since I saw your post to prove that in the two-dimensional case H(p)>H(q) implies the kind of asymmetry you suggest. It's turning out to be a more difficult proof than I envisioned but you must be right about this. Be that as it may, it's not true for the three-dimensional case; there are lots of counter-examples, as my diagrams show. Transitivity should not be at issue here, but more so the triangle inequality: it should definitely be harder to get from P->Q->R than to go from P->R directly, but that's true for both symmetric measures and the KLD.
I will keep working on this. If anybody has ideas please let me know.
Last edited: Sep 6, 2015
5. Sep 6, 2015
### Staff: Mentor
How does your plot look like for P=(0.5, 0.25, 0.25)? That seems to be the center of one of the three lobes in the first plot.
6. Sep 6, 2015
### stlukits
http://www.streetgreek.com/lpublic/various/asym533.png [Broken]
P=(0.5,0.25,0.25)
Last edited by a moderator: May 7, 2017
7. Sep 6, 2015
### Staff: Mentor
Interesting. No transitivity then.
P = (1/3, 1/3, 1/3)
Q = (1/2, 1/4, 1/4)
R = (0.4,0.4,0.2)
KLD(Q,P)>KLD(P,Q)
KLD(R,Q)>KLD(Q,R)
KLD(P,R)>KLD(R,Q)
KLD(Q,P)+KLD(R,Q)+KLD(P,R) > KLD(P,Q)+KLD(Q,R)+KLD(R,Q)
8. Sep 8, 2015
### stlukits
Fascinating, mfb! That should be another problem for the Kullback-Leibler divergence as a measure of dissimilarity between probability distributions. Violation of this kind of transitivity is even harder to square with epistemic intuitions we have about probabilities and updating them than the non-trivial asymmetry patterns that I pointed out. | 2017-08-21 23:35:36 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8675286173820496, "perplexity": 1105.8104185366308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886109682.23/warc/CC-MAIN-20170821232346-20170822012346-00177.warc.gz"} |
http://www.slideboom.com/presentations/488207/Basics-of-Real-Numbers | # Basics of Real Numbers
0
Slide 1
Basics Big Picture of Real NumBeRs AlgebraI Study Guides Real numbers are used to measure the quantity of things in life. Almost any number you can think of is most likely to be a real number. Real numbers can be broken down into different types of numbers such as rational and irrational numbers. They can be visualized using number lines and operated on using set symbols and operators. General guidelines and rules are created to work with real numbers. Key Terms Rational Number: Ratio of one integer to another: , as long as the denominator is not equal to 0. Integer: A rational number where the denominator is equal to 1. Includes natural numbers, negative natural numbers, and 0. Natural Numbers: Counting numbers such as 1, 2, 3. Whole Numbers: All natural numbers and 0. Non-Integer: A rational number where the denominator is not equal to 1. Proper Fraction: Numerator is less than denominator. Represents a number less than one. Improper Fraction: Numerator is greater than denominator. Represents a number greater than 1. Equivalent Fractions: Two fractions that represent the same amount. Irrational Number: Number that cannot be expressed as a fraction, such as or �. Symbols Here are some common symbols used in algebra: Understanding Real Numbers 1. Sum or product of two rational numbers is rational. Symbols Symbol + - × or · ÷ or / or | | = ≠ ≈ <, ≤ >, ≥ { } ( ), [ ] Meaning add subtract multiply divide square root, nth root absolute value equals not equal approximately equal less than, less than or equal to greater than, greater than or equal to set symbol an element of a set group symbols • • Example: 2 + 3 = 5 Example: 2. Sum of rational number and irrational number is irra- tional. • Example: 2 + = 2 + 3. Product of nonzero rational number and irrational number is irrational. • • Example: 3 · = 3 Disclaimer:thisstudyguidewasnotcreatedtoreplace yourtextbookandisforclassroomorindividualuseonly. Example: 5 · � = 5 � 4. Difference between two whole rational numbers is not always a positive number. • • Example: 5 - 4 = 1 Example: 5 - 9 = -4 5. Quotient of a whole rational divisor and a whole dividend is not always a whole number. • • Example: Example: This guide was created by Nicole Crawford, Jane Li, and Jin Yu. To learn more about the student authors, visit http://www.ck12.org/about/about-us/team/ interns. Page 1 of 3 v1.1.9.2012
Slide 2
Algebra Basics Exponents of Real NumBeRs coNt. Exponents and nth Roots nth Roots The nth root is the inverse operation of raising a number to the nth power. So the inverse operation of xn = y is . Exponent is a short-hand notation for repeated multi- plication. • • • 2 · 2 of 3. · 2 = 23. We say that 2 is raised to the power 2 · 2 · 2 · 2 power of 5. n · 2 = 25. We say that 2 is raised to the • • • • = 4 because 42 = 16 is called the radical sign When n=2, we usually write it the square root. , not , and we call For x , we say that x is raised to the power of n. • x • and n are variables, symbols that are used to represent a value. When n=3, we call it the cube root. If n=2, we can also say x squared. If x=3, we say x cubed. If the nth root can’t be simplified (reduced) to a rational number without the radical sign ( ), the number is irrational. Examples: = 8, so it is a rational number. cannot be reduced any further and is irrational. We can get an approximate value for irrational square roots by using the calculator. In decimal form, the number will look like an unending string of numbers. • • Example: places. ≈ 1.414 when rounded to three decimal Fractions and Decimals A rational number is just a ratio of one number to another written in fraction form as . • Every whole number is a rational number where the denominator equals 1. • A denominator equal to 1 is sometimes called the invisible denominator because it is not usually written out: . • • • Fraction bar: the line that separates the numerator and the denominator. The denominator b ≠ 0. A proper fraction represents a number less than one because a < b, while an improper fraction represents a number greater than one because a > b. A negative fraction is usually written with the negative sign to the left of the fraction • • Example: could equal or Improper fractions can be rewritten as an integer plus a proper fraction (mixed number). • • Example: Whenever we can write two fractions equal (=) to each other, we have equivalent fractions. • • Example: The fractions , so and are equivalent fractions. are equivalent as long as c ≠ 0. A fraction can be converted into a decimal - just divide the numerator by the denominator. Figure: Equivalent fractions • • • • Examples: The ... means that the decimal goes on forever. Not all decimals can be converted into fractions. If the numbers after the decimal point (.) never repeats and never ends, the number is irrational. Any number that can’t be written as a fraction is irrational. Page 2 of 3
Slide 3
Basics Sets of Real NumBeRs • coNt. AlgebraI Sets are used to define groups of elements. In math, sets can be used to define different types of numbers, such as even and odd numbers. Outside of math, sets can also be used for other elements such as sets of keys or sets of clothing. The different types of sets (as shown below) are used to classify the objects in the sets. We can list the elements (members) of a set inside the symbols { }. If A = {1, 2, 3}, then the numbers 1, 2, and 3 are elements of set A. Difference: the set of elements that belong to A only Denoted as A \ B • • • Numbers like 2.5, -3, and 7 are not elements of A. We can also write that 1 1 is an element in set A. A, meaning the number • If A is the group of whole numbers and B is the group of natural numbers, A \ B is 0 The order here matters! B \ A means the set of elements belonging to B only. If there are no elements in the set, we call it a null set or an empty set. Union: the set of all elements that belong to A or B Complement Set: all elements in a set that is not A • Denoted as A B • Denoted as Ac • The union of rational numbers and irrational numbers is all real numbers. • Intersection: the set of elements that is true for both A and B B \ A is equal to Ac. If A is the group of whole numbers and B is the group of natural numbers, Ac is null (there are no elements in set B that is not also in A) • Denoted as A B Disjoint Sets: when sets A and B have no common elements. • Rational and irrational numbers are disjoint sets. Notes Page 3 of 3
Summary: CK-12 FlexBooks explains Real numbers can be broken down into different types of numbers such as rational and irrational numbers. They can be visualized using number lines and operated on using set symbols and operators.
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http://clay6.com/qa/38262/name-the-octant-in-which-the-point-4-2-5-lies- | # Name the octant in which the point $(4,-2,-5)$ lies.
$\begin{array}{1 1}\text{2nd octant} \\ \text{4th octant } \\ \text{6th octant} \\ \text{8th octant }\end{array}$
If the $y$ and $z$ coordinates are $-ve$ and $x$ coordinate is $+ve$,
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https://socratic.org/questions/at-stp-1-liter-of-o-2-g-and-1-liter-of-ne-g-have-the-same-what | # At STP, 1 liter of O_2(g) and 1 liter of Ne(g) have the same what?
Dec 17, 2016
n=(PV)/(RT)=??
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Worksheet, Level 5– to find the area of a rhombus is the plan enclosed by the divided... Is 180 cm by 4. s = 16 So, area and perimeter of a rhombus top... And the perimeter and area … area of each rhombus determine the length of diagonal 2 worksheet 11.2 area... Diagonal lengths of the rhombus is 40 square units user Displaying top 8 worksheets found for parallelogram! Formula P = 4a, where a and b are the diagonal lengths the... Supplement our perimeter and area worksheets for 5th grade students a short diagonal of 6 meters of., in these printable worksheets and online practice tests on area-and-perimeter-of-parallelogram-and-rhombus for 7... As well, grade 4 6 – to find the side length is 16 inches formulas for and. 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https://bonndoc.ulb.uni-bonn.de/xmlui/handle/20.500.11811/5043 | Monsef Shokri, Khosro: The Zinger deformation of differential equations with maximal unipotent monodromy. - Bonn, 2011. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-26638
@phdthesis{handle:20.500.11811/5043,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-26638,
author = {{Khosro Monsef Shokri}},
title = {The Zinger deformation of differential equations with maximal unipotent monodromy},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2011,
month = oct,
note = {In this thesis, in the first part we study the Zinger deformation for the holomorphic solution of a differential equation with maximal unipotent monodromy. It is basically a generalization of the example made by Zinger, who used it to compute the reduced genus one Gromov-Witten invariants for the hypersurfaces.
We define also a differential operator and we show that the action of the Zinger deformation is periodic under this operator. Then we give some structral properties of this deformation at zero. In the case of Calabi-Yau equation we give a connection of this deformation and the Yukawa coupling.
Then we study the asymptotic expansion of the Zinger deformation at infinity and we give a perturbative expansion for it and furthermore we prove a conjecture made by Zagier about the logarithmic derivative of this perturbative expansion. We show that the $s$th term of this logarithmic derivative, up to a simple factor is a polynomial of two variable, namely $n, X$.
Studying of these polynomials for the Zinger example is the aim of the second part. For these polynomials we give explicite formulas for the first and the second top coefficients (with respect to $n$) and in general for fixed $\ell$ we give a recursive formula to compute the $\ell$th top coefficient of $P_s(n,X)$ where $s$ varies. We show that these coefficients under a map belong to the image of elementary functions.},
url = {http://hdl.handle.net/20.500.11811/5043}
}
The following license files are associated with this item:
Indexed by
Theme by | 2020-10-28 09:24:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.910599410533905, "perplexity": 681.5447746139059}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107897022.61/warc/CC-MAIN-20201028073614-20201028103614-00007.warc.gz"} |
http://arxitics.com/articles/1801.06862 | ## arXiv Analytics
### arXiv:1801.06862 [econ.EM]AbstractReferencesReviewsResources
#### Testing the Number of Regimes in Markov Regime Switching Models
Published 2018-01-21Version 1
Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribution of the likelihood ratio test statistic for testing the null hypothesis of $M_0$ regimes against the alternative hypothesis of $M_0 + 1$ regimes for any $M_0 \geq 1$ both under the null hypothesis and under local alternatives. We show that the contiguous alternatives converge to the null hypothesis at a rate of $n^{-1/8}$ in regime switching models with normal density. The asymptotic validity of the parametric bootstrap is also established. | 2018-07-17 21:22:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9195654988288879, "perplexity": 271.03596760224326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589902.8/warc/CC-MAIN-20180717203423-20180717223423-00310.warc.gz"} |
https://www.rdocumentation.org/packages/scales/versions/0.4.1/topics/col_numeric | # col_numeric
0th
Percentile
##### Color mapping
Conveniently maps data values (numeric or factor/character) to colors according to a given palette, which can be provided in a variety of formats.
##### Usage
col_numeric(palette, domain, na.color = "#808080")
col_bin(palette, domain, bins = 7, pretty = TRUE, na.color = "#808080")
col_quantile(palette, domain, n = 4, probs = seq(0, 1, length.out = n + 1), na.color = "#808080")
col_factor(palette, domain, levels = NULL, ordered = FALSE, na.color = "#808080")
##### Arguments
palette
The colors or color function that values will be mapped to
domain
The possible values that can be mapped.
For col_numeric and col_bin, this can be a simple numeric range (e.g. c(0, 100)); col_quantile needs representative numeric data; and col_factor needs categorical data.
If NULL, then whenever the resulting color function is called, the x value will represent the domain. This implies that if the function is invoked multiple times, the encoding between values and colors may not be consistent; if consistency is needed, you must provide a non-NULL domain.
na.color
The color to return for NA values. Note that na.color=NA is valid.
bins
Either a numeric vector of two or more unique cut points or a single number (greater than or equal to 2) giving the number of intervals into which the domain values are to be cut.
pretty
Whether to use the function pretty() to generate the bins when the argument bins is a single number. When pretty = TRUE, the actual number of bins may not be the number of bins you specified. When pretty = FALSE, seq() is used to generate the bins and the breaks may not be "pretty".
n
Number of equal-size quantiles desired. For more precise control, use the probs argument instead.
probs
See quantile. If provided, the n argument is ignored.
levels
An alternate way of specifying levels; if specified, domain is ignored
ordered
If TRUE and domain needs to be coerced to a factor, treat it as already in the correct order
##### Details
col_numeric is a simple linear mapping from continuous numeric data to an interpolated palette.
col_bin also maps continuous numeric data, but performs binning based on value (see the cut function).
col_quantile similarly bins numeric data, but via the quantile function.
col_factor maps factors to colors. If the palette is discrete and has a different number of colors than the number of factors, interpolation is used.
The palette argument can be any of the following:
1. A character vector of RGB or named colors. Examples: palette(), c("#000000", "#0000FF", "#FFFFFF"), topo.colors(10)
2. The name of an RColorBrewer palette, e.g. "BuPu" or "Greens".
3. A function that receives a single value between 0 and 1 and returns a color. Examples: colorRamp(c("#000000", "#FFFFFF"), interpolate="spline").
##### Value
A function that takes a single parameter x; when called with a vector of numbers (except for col_factor, which expects factors/characters), #RRGGBB color strings are returned.
• col_bin
• col_factor
• col_numeric
• col_quantile
##### Examples
library(scales) pal <- col_bin("Greens", domain = 0:100) show_col(pal(sort(runif(10, 60, 100)))) # Exponential distribution, mapped continuously show_col(col_numeric("Blues", domain = NULL)(sort(rexp(16)))) # Exponential distribution, mapped by interval show_col(col_bin("Blues", domain = NULL, bins = 4)(sort(rexp(16)))) # Exponential distribution, mapped by quantile show_col(col_quantile("Blues", domain = NULL)(sort(rexp(16)))) # Categorical data; by default, the values being colored span the gamut... show_col(col_factor("RdYlBu", domain = NULL)(LETTERS[1:5])) # ...unless the data is a factor, without droplevels... show_col(col_factor("RdYlBu", domain = NULL)(factor(LETTERS[1:5], levels=LETTERS))) # ...or the domain is stated explicitly. show_col(col_factor("RdYlBu", levels = LETTERS)(LETTERS[1:5]))
Documentation reproduced from package scales, version 0.4.1, License: MIT + file LICENSE
### Community examples
Looks like there are no examples yet. | 2019-08-19 06:49:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32409220933914185, "perplexity": 4214.716616290027}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314667.60/warc/CC-MAIN-20190819052133-20190819074133-00191.warc.gz"} |
https://hal-cea.archives-ouvertes.fr/cea-01550535v2 | New interface
# The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters
Abstract : We present an embedded-cluster method, based on the TRILEX formalism, that turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, these self-energies are very close to numerically exact benchmark results for clusters of size four only. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the $GW$ +extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low energy.
Document type :
Journal articles
Domain :
https://hal-cea.archives-ouvertes.fr/cea-01550535
Contributor : Bruno Savelli Connect in order to contact the contributor
Submitted on : Monday, October 3, 2022 - 10:08:58 AM
Last modification on : Wednesday, October 5, 2022 - 3:29:50 AM
### File
ayr1.pdf
Publisher files allowed on an open archive
### Citation
Thomas Ayral, Jaksa Vucicevic, Olivier Parcollet. The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters. Physical Review Letters, 2017, 119, pp.166401. ⟨10.1103/PhysRevLett.119.166401⟩. ⟨cea-01550535v2⟩
Record views | 2022-12-04 22:21:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3813256621360779, "perplexity": 3351.8833773535207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710980.82/warc/CC-MAIN-20221204204504-20221204234504-00511.warc.gz"} |
https://socratic.org/questions/how-do-you-write-the-equation-y-1-4-3-x-1-2-in-slope-intercept-form | # How do you write the equation y+1/4=-3(x+1/2) in slope intercept form?
Mar 2, 2017
$y = 3 x - \frac{7}{4}$
#### Explanation:
Distribute the -3:
$y + \frac{1}{4} = - 3 x - \frac{3}{2}$
Subtract $\frac{1}{4}$ on both sides. Note that $- \frac{3}{2} = - \frac{6}{4}$:
$y = 3 x - \frac{7}{4}$ | 2021-11-29 05:49:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 5, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9775897860527039, "perplexity": 2745.3055340145957}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358688.35/warc/CC-MAIN-20211129044311-20211129074311-00275.warc.gz"} |
https://planetmath.org/ModularForm | # modular form
Let $\textrm{SL}_{2}(\mathbb{R})$ be the group of real $2\times 2$ matrices with determinant $1$ (see entry on special linear groups). The group $\textrm{SL}_{2}(\mathbb{R})$ acts on $H$, the upper half plane, through fractional linear transformations. That is, if
$\gamma=\begin{pmatrix}a&b\\ c&d\end{pmatrix},$
and $\tau\in H$, then we let
$\gamma\tau=\frac{a\tau+b}{c\tau+d}.$ (1)
For any natural number $N\geq 1$, define the congruence subgroup $\Gamma_{0}(N)$ of level $N$ to be the following subgroup of the group $\textrm{SL}_{2}(\mathbb{Z})$ of integer coefficient matrices of determinant $1$:
$\Gamma_{0}(N):=\left\{\left.\begin{pmatrix}a&b\\ c&d\end{pmatrix}\in\textrm{SL}_{2}(\mathbb{Z})\ \right|\ c\equiv 0\pmod{N}% \right\}.$
Fix an integer $k$. For $\gamma\in\textrm{SL}_{2}(\mathbb{Z})$ and a function $f$ defined on $H$, we define
$f_{\mid\gamma}(\tau)=\frac{f(\gamma\tau)}{(c\tau+d)^{k}}.$
For a finite index subgroup $\Gamma$ of $\textrm{SL}_{2}(\mathbb{Z})$ containing a congruence subgroup, a function $f$ defined on $H$ is said to be a weight $k$ modular form if:
1. 1.
$f=f_{\mid\gamma}$ for $\gamma\in\Gamma$.
2. 2.
$f$ is holomorphic on $H$.
3. 3.
$f$ is holomorphic at the cusps.
This last condition requires some explanation. First observe that the element
$\mu=\begin{pmatrix}1&m\\ 0&1\end{pmatrix}\in\Gamma_{0}(N),$
and $\mu z=z+m$, while if $f$ satisfies all the other conditions above, $f_{\mid\mu}=f$. In other words, $f$ is periodic with period $1$. Thus, convergence permitting, $f$ admits a Fourier expansion. Therefore, we say that $f$ is holomorphic at the cusps if, for all $\gamma\in\Gamma$, $f_{\mid\gamma}$ admits a a Fourier expansion
$f_{\mid\gamma}(\tau)=\sum_{n=0}^{\infty}a_{n}q^{n},$ (2)
where $q=e^{2i\pi\tau}$.
If all the $a_{n}$ are zero for $n\leq 0$, then a modular form $f$ is said to be a cusp form. The set of modular forms for $\Gamma$ (respectively cusp forms for $\Gamma$) is often denoted by $M_{k}(\Gamma)$ (respectively $S_{k}(\Gamma)$). Both $M_{k}(\Gamma)$ and $S_{k}(\Gamma)$ are finite dimensional vector spaces.
The space of modular forms for $\textrm{SL}_{2}(\mathbb{Z})$ (respectively cusp forms) is non-trivial for any $k$ even and greater than 4 (respectively greater than $12$ and not $14$). Examples of modular forms for $\textrm{SL}_{2}(\mathbb{Z})$ are:
1. 1.
The Eisenstein series $E_{m}$, where $m$ is even and greater than $4$, is a modular form of weight $m$. Here $B_{m}$ denotes the $m$-th Bernoulli number and, as usual, $q=e^{2i\pi\tau}$:
$E_{m}(\tau)=1-\frac{2m}{B_{m}}\underset{n=1}{\overset{\infty}{\sum}}\sigma_{m-% 1}(n)q^{n}.$ (3)
For instance,
$E_{4}(\tau)=1+240\underset{n=1}{\overset{\infty}{\sum}}\sigma_{3}(n)q^{n}$ (4)
and
$E_{6}(\tau)=1-504\underset{n=1}{\overset{\infty}{\sum}}\sigma_{5}(n)q^{n}.$ (5)
2. 2.
The Weierstrass $\Delta$ function, also called the modular discriminant, is a modular form of weight $12$:
$\Delta(\tau)=q\underset{n=1}{\overset{\infty}{\prod}}(1-q^{n})^{24}.$ (6)
Every modular form is expressible as
$f(\tau)=\underset{n=0}{\overset{\lfloor{k/12}\rfloor}{\sum}}{a_{n}}{E_{k-12n}(% \tau)}{(\Delta(\tau))^{n}},$ (7)
where the $a_{n}$ are arbitrary constants, $E_{0}(\tau)=1$ and $E_{2}(\tau)=0$. Cusp forms are the forms with $a_{0}=0$.
Title modular form ModularForm 2013-03-22 14:07:37 2013-03-22 14:07:37 olivierfouquetx (2421) olivierfouquetx (2421) 31 olivierfouquetx (2421) Definition msc 11F11 TaniyamaShimuraConecture HeckeAlgebra AlgebraicNumberTheory RamanujanTauFunction cusp form | 2018-12-12 18:50:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 73, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9920133948326111, "perplexity": 188.60755649815607}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376824115.18/warc/CC-MAIN-20181212181507-20181212203007-00037.warc.gz"} |
https://www.ias.ac.in/listing/bibliography/pram/N._Cakmak | • N Cakmak
Articles written in Pramana – Journal of Physics
• Beta-transition properties for neutron-rich Sn and Te isotopes by Pyatov method
Based on Pyatov's method, the low-lying Gamow–Teller (GT) 1+ state energies and log($f_{t}$) values for 128,130,132Sb and 132,134,136I isotopes have been calculated. In this method, the strength parameter of the effective spin–isospin interaction is found by providing the commutativity of the GT operator with the central part of the nuclear Hamiltonian. The problem has been solved within the framework of RPA. The calculation results have been compared with the corresponding experimental data.
• The investigation of the $2\nu\beta\beta$ decay by Pyatov method within quasiparticle random phase approximation formalism
The violated commutation condition between the total shell model Hamiltonian and Gamow–Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by $h_{0}$ (restoration term). The influence of the h0 effective interaction on the $2\nu\beta\beta$ decay of 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128,130Te and 136Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the $2\nu\beta\beta$ decay nuclear matrix elements is analysed.
• # Pramana – Journal of Physics
Volume 94, 2020
All articles
Continuous Article Publishing mode
• # Editorial Note on Continuous Article Publication
Posted on July 25, 2019 | 2021-01-23 07:31:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3774173855781555, "perplexity": 3182.9586564289534}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703536556.58/warc/CC-MAIN-20210123063713-20210123093713-00498.warc.gz"} |
http://compgroups.net/comp.lang.tcl/what-is-a-busy-file-how-can-i-delete-in-tcl-scr/273927 | COMPGROUPS.NET | Post | Groups | Users | Stream | Browse | About | |
What is a "busy file? How can i delete in TCL script?
• Email
• Follow
Hi,
I have a tcl script that generate a lot of intermediate files (and
folders). At the last step of my script, I've to clean the working
directory and keep only one or two files.
I have written a proc to clean work dir like this:
proc cleanWorkDir {dir keep1 {keep2 ""}} {
set here [pwd]
cd $dir if {$keep2 == "" } {
set keep2 $keep1 } foreach f [glob -nocomplain *] { if { ![string equal$f [getOnlyName $keep1] ] && ![string equal$f [getOnlyName $keep2]] } { file delete -force$f
}
}
cd $here } Although it worked on my laptop, but on customer's Linux machine I always get error message: ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or resource busy while executing "file delete -force$f"
....
Despite of being able to delete the whole folder (Folder "A" in error
message) manually, I don't understand why cannot the TCL script do it!
Can anyone help me solve this?
Thanks,
0
See related articles to this posting
I have also noticed something.. When the TCL script exits after this
error, and I try to "ls" the ".nsf...." file it complains about, I
don't find it!
What is the .nsf file stands for? Who generates it?
Thanks,
> Hi,
>
> I have a tcl script that generate a lot of intermediate files (and
> folders). At the last step of my script, I've to clean the working
> directory and keep only one or two files.
>
> I have written a proc to clean work dir like this:
>
> proc cleanWorkDir {dir keep1 {keep2 ""}} {
> =A0 =A0set here [pwd]
> =A0 =A0cd $dir > =A0 =A0if {$keep2 =3D=3D "" } {
> =A0 =A0 =A0set keep2 $keep1 > =A0 =A0} > > =A0 =A0foreach f [glob -nocomplain *] { > =A0 =A0 =A0if { ![string equal$f [getOnlyName $keep1] ] && ![string equa= l >$f [getOnlyName $keep2]] } { > =A0 =A0 =A0 =A0 file delete -force$f
> =A0 =A0 =A0}
> =A0 =A0}
> =A0 =A0cd $here > > } > > Although it worked on my laptop, but on customer's Linux machine I > always get error message: > ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or > resource busy > =A0 =A0 while executing > =A0 "file delete -force$f"
> ...
>
> Despite of being able to delete the whole folder (Folder "A" in error
> message) manually, I don't understand why cannot the TCL script do it!
>
> Can anyone help me solve this?
>
> Thanks,
0
At Thu, 4 Nov 2010 12:54:20 -0700 (PDT) Ahmad <ahmad.abdulghany@gmail.com> wrote:
>
> I have also noticed something.. When the TCL script exits after this
> error, and I try to "ls" the ".nsf...." file it complains about, I
> don't find it!
>
> What is the .nsf file stands for? Who generates it?
NFS -- 'Network File System', a UNIX file sharing protocol, originally
invented by Sun Microsystems back in the late 1970's or so. The
".nsf...." file is something created by the NFS software, I think
related to locking.
>
> Thanks,
>
>
> > Hi,
> >
> > I have a tcl script that generate a lot of intermediate files (and
> > folders). At the last step of my script, I've to clean the working
> > directory and keep only one or two files.
> >
> > I have written a proc to clean work dir like this:
> >
> > proc cleanWorkDir {dir keep1 {keep2 ""}} {
> > =A0 =A0set here [pwd]
> > =A0 =A0cd $dir > > =A0 =A0if {$keep2 =3D=3D "" } {
> > =A0 =A0 =A0set keep2 $keep1 > > =A0 =A0} > > > > =A0 =A0foreach f [glob -nocomplain *] { > > =A0 =A0 =A0if { ![string equal$f [getOnlyName $keep1] ] && ![string equa= > l > >$f [getOnlyName $keep2]] } { > > =A0 =A0 =A0 =A0 file delete -force$f
> > =A0 =A0 =A0}
> > =A0 =A0}
> > =A0 =A0cd $here > > > > } > > > > Although it worked on my laptop, but on customer's Linux machine I > > always get error message: > > ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or > > resource busy > > =A0 =A0 while executing > > =A0 "file delete -force$f"
> > ...
> >
> > Despite of being able to delete the whole folder (Folder "A" in error
> > message) manually, I don't understand why cannot the TCL script do it!
> >
> > Can anyone help me solve this?
> >
> > Thanks,
>
>
--
Robert Heller -- 978-544-6933 / heller@deepsoft.com
Deepwoods Software -- http://www.deepsoft.com/
() ascii ribbon campaign -- against html e-mail
/\ www.asciiribbon.org -- against proprietary attachments
0
Hi Robert,
This is a very nice to know, thank you.
Do you have any idea how can I force delete this kind of files?
Thanks,
On Nov 4, 1:26=A0pm, Robert Heller <hel...@deepsoft.com> wrote:
> wrote:
>
>
>
> > I have also noticed something.. When the TCL script exits after this
> > error, and I try to "ls" the ".nsf...." file it complains about, I
> > don't find it!
>
> > What is the .nsf file stands for? Who generates it?
>
> NFS -- 'Network File System', a UNIX file sharing protocol, originally
> invented by Sun Microsystems back in the late 1970's or so. The
> ".nsf...." file is something created by the NFS software, I think
> related to locking.
>
>
>
>
>
> > Thanks,
>
> > > Hi,
>
> > > I have a tcl script that generate a lot of intermediate files (and
> > > folders). At the last step of my script, I've to clean the working
> > > directory and keep only one or two files.
>
> > > I have written a proc to clean work dir like this:
>
> > > proc cleanWorkDir {dir keep1 {keep2 ""}} {
> > > =3DA0 =3DA0set here [pwd]
> > > =3DA0 =3DA0cd $dir > > > =3DA0 =3DA0if {$keep2 =3D3D=3D3D "" } {
> > > =3DA0 =3DA0 =3DA0set keep2 $keep1 > > > =3DA0 =3DA0} > > > > =3DA0 =3DA0foreach f [glob -nocomplain *] { > > > =3DA0 =3DA0 =3DA0if { ![string equal$f [getOnlyName $keep1] ] && ![s= tring equa=3D > > l > > >$f [getOnlyName $keep2]] } { > > > =3DA0 =3DA0 =3DA0 =3DA0 file delete -force$f
> > > =3DA0 =3DA0 =3DA0}
> > > =3DA0 =3DA0}
> > > =3DA0 =3DA0cd $here > > > > } > > > > Although it worked on my laptop, but on customer's Linux machine I > > > always get error message: > > > ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or > > > resource busy > > > =3DA0 =3DA0 while executing > > > =3DA0 "file delete -force$f"
> > > ...
>
> > > Despite of being able to delete the whole folder (Folder "A" in error
> > > message) manually, I don't understand why cannot the TCL script do it=
!
>
> > > Can anyone help me solve this?
>
> > > Thanks,
>
> --
> Robert Heller =A0 =A0 =A0 =A0 =A0 =A0 -- 978-544-6933 / hel...@deepsoft.c=
om
> Deepwoods Software =A0 =A0 =A0 =A0--http://www.deepsoft.com/
> () =A0ascii ribbon campaign -- against html e-mail
> /\ =A0www.asciiribbon.org=A0 -- against proprietary attachments
0
At Thu, 4 Nov 2010 15:16:08 -0700 (PDT) Ahmad <ahmad.abdulghany@gmail.com> wrote:
>
> Hi Robert,
>
> This is a very nice to know, thank you.
>
> Do you have any idea how can I force delete this kind of files?
I don't think you can OR should.
>
> Thanks,
>
>
> On Nov 4, 1:26=A0pm, Robert Heller <hel...@deepsoft.com> wrote:
> > At Thu, 4 Nov 2010 12:54:20 -0700 (PDT) Ahmad <ahmad.abdulgh...@gmail.com=
> > wrote:
> >
> >
> >
> > > I have also noticed something.. When the TCL script exits after this
> > > error, and I try to "ls" the ".nsf...." file it complains about, I
> > > don't find it!
> >
> > > What is the .nsf file stands for? Who generates it?
> >
> > NFS -- 'Network File System', a UNIX file sharing protocol, originally
> > invented by Sun Microsystems back in the late 1970's or so. The
> > ".nsf...." file is something created by the NFS software, I think
> > related to locking.
> >
> >
> >
> >
> >
> > > Thanks,
> >
> > > > Hi,
> >
> > > > I have a tcl script that generate a lot of intermediate files (and
> > > > folders). At the last step of my script, I've to clean the working
> > > > directory and keep only one or two files.
> >
> > > > I have written a proc to clean work dir like this:
> >
> > > > proc cleanWorkDir {dir keep1 {keep2 ""}} {
> > > > =3DA0 =3DA0set here [pwd]
> > > > =3DA0 =3DA0cd $dir > > > > =3DA0 =3DA0if {$keep2 =3D3D=3D3D "" } {
> > > > =3DA0 =3DA0 =3DA0set keep2 $keep1 > > > > =3DA0 =3DA0} > > > > > > =3DA0 =3DA0foreach f [glob -nocomplain *] { > > > > =3DA0 =3DA0 =3DA0if { ![string equal$f [getOnlyName $keep1] ] && ![s= > tring equa=3D > > > l > > > >$f [getOnlyName $keep2]] } { > > > > =3DA0 =3DA0 =3DA0 =3DA0 file delete -force$f
> > > > =3DA0 =3DA0 =3DA0}
> > > > =3DA0 =3DA0}
> > > > =3DA0 =3DA0cd $here > > > > > > } > > > > > > Although it worked on my laptop, but on customer's Linux machine I > > > > always get error message: > > > > ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or > > > > resource busy > > > > =3DA0 =3DA0 while executing > > > > =3DA0 "file delete -force$f"
> > > > ...
> >
> > > > Despite of being able to delete the whole folder (Folder "A" in error
> > > > message) manually, I don't understand why cannot the TCL script do it=
> !
> >
> > > > Can anyone help me solve this?
> >
> > > > Thanks,
> >
> > --
> > Robert Heller =A0 =A0 =A0 =A0 =A0 =A0 -- 978-544-6933 / hel...@deepsoft.c=
> om
> > Deepwoods Software =A0 =A0 =A0 =A0--http://www.deepsoft.com/
> > () =A0ascii ribbon campaign -- against html e-mail
> > /\ =A0www.asciiribbon.org=A0 -- against proprietary attachments
>
>
--
Robert Heller -- 978-544-6933 / heller@deepsoft.com
Deepwoods Software -- http://www.deepsoft.com/
() ascii ribbon campaign -- against html e-mail
/\ www.asciiribbon.org -- against proprietary attachments
0
Your script is trying to delete all files in a directory except those
you specify. It would probably be better to maintain a list of the
temporary files and just loop through the list at the end deleting them,
that way you avoid trying to delete other files (like the NFS lock files).
Simon
On 04/11/2010 23:56, Robert Heller wrote:
>
>>
>> Hi Robert,
>>
>> This is a very nice to know, thank you.
>>
>> Do you have any idea how can I force delete this kind of files?
>
> I don't think you can OR should.
>
>>
>> Thanks,
>>
>>
>> On Nov 4, 1:26=A0pm, Robert Heller<hel...@deepsoft.com> wrote:
>>> wrote:
>>>
>>>
>>>
>>>> I have also noticed something.. When the TCL script exits after this
>>>> error, and I try to "ls" the ".nsf...." file it complains about, I
>>>> don't find it!
>>>
>>>> What is the .nsf file stands for? Who generates it?
>>>
>>> NFS -- 'Network File System', a UNIX file sharing protocol, originally
>>> invented by Sun Microsystems back in the late 1970's or so. The
>>> ".nsf...." file is something created by the NFS software, I think
>>> related to locking.
>>>
>>>
>>>
>>>
>>>
>>>> Thanks,
>>>
>>>>> Hi,
>>>
>>>>> I have a tcl script that generate a lot of intermediate files (and
>>>>> folders). At the last step of my script, I've to clean the working
>>>>> directory and keep only one or two files.
>>>
>>>>> I have written a proc to clean work dir like this:
>>>
>>>>> proc cleanWorkDir {dir keep1 {keep2 ""}} {
>>>>> =3DA0 =3DA0set here [pwd]
>>>>> =3DA0 =3DA0cd $dir >>>>> =3DA0 =3DA0if {$keep2 =3D3D=3D3D "" } {
>>>>> =3DA0 =3DA0 =3DA0set keep2 $keep1 >>>>> =3DA0 =3DA0} >>> >>>>> =3DA0 =3DA0foreach f [glob -nocomplain *] { >>>>> =3DA0 =3DA0 =3DA0if { ![string equal$f [getOnlyName $keep1] ]&& ![s= >> tring equa=3D >>>> l >>>>>$f [getOnlyName $keep2]] } { >>>>> =3DA0 =3DA0 =3DA0 =3DA0 file delete -force$f
>>>>> =3DA0 =3DA0 =3DA0}
>>>>> =3DA0 =3DA0}
>>>>> =3DA0 =3DA0cd $here >>> >>>>> } >>> >>>>> Although it worked on my laptop, but on customer's Linux machine I >>>>> always get error message: >>>>> ERROR: cannot remove A/B/.nfs00000000010d28ba00004dfb': Device or >>>>> resource busy >>>>> =3DA0 =3DA0 while executing >>>>> =3DA0 "file delete -force$f"
>>>>> ...
>>>
>>>>> Despite of being able to delete the whole folder (Folder "A" in error
>>>>> message) manually, I don't understand why cannot the TCL script do it=
>> !
>>>
>>>>> Can anyone help me solve this?
>>>
>>>>> Thanks,
>>>
>>> --
>>> Robert Heller =A0 =A0 =A0 =A0 =A0 =A0 -- 978-544-6933 / hel...@deepsoft.c=
>> om
>>> Deepwoods Software =A0 =A0 =A0 =A0--http://www.deepsoft.com/
>>> () =A0ascii ribbon campaign -- against html e-mail
>>> /\ =A0www.asciiribbon.org=A0 -- against proprietary attachments
>>
>>
>
0
On Nov 4, 4:56=A0pm, Robert Heller <hel...@deepsoft.com> wrote:
> wrote:
>
>
>
> > Hi Robert,
>
> > This is a very nice to know, thank you.
>
> > Do you have any idea how can I force delete this kind of files?
>
> I don't think you can OR should.
>
>
I agree with Robert that the lock files can't be deleted. The first
question you should have is why are they being created. Is there some
good reason that the files you have created are being locked by a
remote host? If not then I would spend some time figuring what the
heck is going on. Second, the /tmp directory on unix/linux is where
you should be putting all your temporary files. This directory is
cleared when a system is rebooted which will remove any abandoned lock
files. In a large network it is possible for lock files to become
abandoned which is a real headacke because they will prevent
directories from being deleted.
tomk
0
On 5 nov, 17:10, tomk <krehbiel....@gmail.com> wrote:
> On Nov 4, 4:56=A0pm, Robert Heller <hel...@deepsoft.com> wrote:
>
> > At Thu, 4 Nov 2010 15:16:08 -0700 (PDT) Ahmad <ahmad.abdulgh...@gmail.c=
om> wrote:
>
> > > Hi Robert,
>
> > > This is a very nice to know, thank you.
>
> > > Do you have any idea how can I force delete this kind of files?
>
> > I don't think you can OR should.
>
> I agree with Robert that the lock files can't be deleted. The first
> question you should have is why are they being created. Is there some
> good reason that the files you have created are being locked by a
> remote host? If not then I would spend some time figuring what the
> heck is going on. Second, the /tmp directory on unix/linux is where
> you should be putting all your temporary files. This directory is
> cleared when a system is rebooted which will remove any abandoned lock
> files. In a large network it is possible for lock files to become
> abandoned which is a real headacke because they will prevent
> directories from being deleted.
>
> tomk
To see the file you should propbaly try
ls -al
This lists all files including hidden ones, under Linux the . before a
filename will hide them from simple ls
You should probably be creating a private tmp directory in /tmp to
keep all your files together then a simple delete of the directory
should clean up easily.
Martyn
0
* Robert Heller <heller@deepsoft.com>
| > What is the .nsf file stands for? Who generates it?
>
| ... The ".nsf...." file is something created by the NFS software, I
| think related to locking.
Those .nfs files are not related to file locking, but to removed files
on an NFS share which are still open in some application.
See
https://www.cs.indiana.edu/Facilities/FAQ/General/dotnfs.html
http://www.unix.com/filesystems-disks-memory/5702-removing-nfs-files.html
HTH
R'
0
@Ahmad
may be one more tip is you can use exception handling if script is
actually aborting without completion where you can use tcl catch
statement for file delete operation and print messages when some cases
it fails as busy etc.
0
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why can't a web browser mount a server nfs style and then web interactions can be scripted from there as files?
?? On Jul 8, 5:24=A0am, gavino <gavcom...@gmail.com> wrote: > ?? In order to do so, you probably must start by transforming Farenheit degrees into radian. On Jul 7, 11:24=A0pm, gavino <gavcom...@gmail.com> wrote: > ?? Syntax error. On Jul 8, 4:24=A0am, gavino <gavcom...@gmail.com> wrote (in the title): > why can't a web browser mount a server nfs style and then web > interactions can be scripted from there as files? Because there are a number of file operations that don't map to basic HTTP operations. The WebDAV extension to HTTP _is_ mountable; your...
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Script to Delete All But Latest File
I have some db2 database backups in a directory. They take up a lot of space, so I'd like to delete all but the latest. I can't use "find" and "rm" because the backups aren't done on a predicatable interval. The only thing I do know is that I only want the latest one, and delete the rest. If there is only one in the directory, of course I don't want to delete it. Can any bash experts give me some ideas? Buck Turgidson wrote: > I have some db2 database backups in a directory. They take up a lot of > space, so I'd like to delete all but the ... | 2014-07-30 07:01:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5143992304801941, "perplexity": 8210.044314626639}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510268734.38/warc/CC-MAIN-20140728011748-00344-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://chat.stackexchange.com/transcript/14524/2017/1/5/15-17 | 3:00 PM
I created the long one with the computer, yes.
It's a good time for posting a puzzle, isn't it?
Although with BLOOD, you're sort of related.
@IAmInPLS it's always a good time
@Randal'Thor: @MOehm got one.
@Randal'Thor U2's seminal live album, "Under a Blood Red Sky"
3:05 PM
@Matt Couldn't agree more
@Randal'Thor Are all 3 "it"s the same?
I kinda want to make another metacryptic :P
0
"Darling, can you please turn on the GPS?" I asked my wife. "Hang on, I know exactly where we are", she replied. "Can you, for once, listen to me?" She ignored my remark, immersed in the reading of the map. This was not the first time we were going on a trip, and this was definitely not the fi...
but maybe I should actually do work today ...
Didn't double check, so don't hesitate to edit if you find mistakes
3:07 PM
Work? BLASPHEMY!
@Randal'Thor extra challenge: Figure out the method for why those letters were chosen. And I expect a feedback section after all of this over.
0
"Darling, can you please turn on the GPS?" I asked my wife. "Hang on, I know exactly where we are", she replied. "Can you, for once, listen to me?" She ignored my remark, immersed in the reading of the map. This was not the first time we were going on a trip, and this was definitely not the fi...
@ChrisCudmore Pretty much. Think of it as "I [verb-X], you are [noun-X], so you should [verb-X']", where X is the answer and X' is a homophone of the answer.
well, either we're supposed to look for a city that has roads mapped out like in the puzzle, or there's some steganography going on here
@Randal'Thor That final cryptic has haunted my dreams for days now.
@Rubio I wonder if you'll be satisfied by the answer ...
3:12 PM
I've tried working backwards, apparently the same way you created it, and found nothing helpful
so apparently our minds operate in different ways entirely :)
F final answer looks like it's SKIN
Correct
How does that fit with SOAKED?
Oh, soaked to the skin, of course.
@Randal'Thor is it as you just described, btw? I've been assuming all along that it's constrained to be something that is a homophone of a word meaning "you should do it". Is it just a random verb?
GTG again
3:15 PM
well, not random, but you know what I mean
@Rubio Yes, just a verb. It can go together with "should", as can most verbs, but there's nothing "should"y in its own meaning.
bah.
then my answer is "clue" / "clew".
should I bother writing it up, or is that not it?
"I clue, you are a clue, so you should clew"?
Is it a proper cryptic? I.E. Definition and wordplay?
"Sphinx trots after clue"?
3:17 PM
Yes. all that.
@ChrisCudmore You know what "?" means in a cryptic clue?
Or a double definition?
@ChrisCudmore These have a "twist" so
the question mark and/or the twist I think cover a multitude of oddity
@IAmInPLS Sounds like someone programmed your GPS with the Konami Code.
I'm surprised nobody has solved this one yet either.
3:25 PM
@ChrisCudmore Haha. I almost included a phrase referring to the Konami code
Liked your comment by the way
@Randal'Thor I think that once somebody discovered the red herring, it's hard to discover anyhting else
I don't know if you see what I mean
0
Go with the flow!!! INSTRUCTiONS Done with my time on this planet, I left you with my creation. I'm hidden in two ways below, one puzzled, while the other is a direct mention. I know you will shortly reveal my identity, and rest all will be fine. If you ask me for a hint, I say, unscra...
@IAmInPLS I was quite evil with the red herrings in that one :->
@Randal'Thor Is SPHINX TROTS AFTER TIME?
@Randal'Thor Yep :-/
@Sid Nope.
3:30 PM
@IAmInPLS are you and your wife video game characters?
No, why?
they are stuck in temple run, perhaps
I don't think you can turn around though
I was thinking Pacman
@IAmInPLS Is it some kind of trivial place? :-/
3:36 PM
I won't say anything mouhahaha
Not for now
Sounds like one of the F1 Tracks :p
@Techidiot All your other rhymes to date have been AABB[CCDDEE...] - this latest puzzle's jumbled up section has several lines with no rhyme, did you change it up or is one of us just really bad at rhyming? hehe
@Rubio Whoa! I never knew I had a pattern :D
But there is a rhyme! You just need to arrange the bits in a right way
I'm trying, but
> If you ask me for a hint, I say, unscramble the rhyme.
@Rubio ^
3:41 PM
no words in there rhyme with "mine" or "though" -
@Techidiot What's a trivial place?
are we supposed to unscramble just the lines, or more than that?
@Randal'Thor May be one of the maze kind of roads..
@Rubio - Basically, you need to form a Rhyme using those lines.
in fact fully half the lines have no apparent rhyme to them, which is why I'm asking if you changed up your usual pattern of pairs of rhymed lines
Not sure if I can put a little hint here.. Let me give you some time to figure it out
half the lines have no apparent rhyme to them sounds interesting!
3:44 PM
Mmmhmm.
Just pointing out that changing up your own usual pattern (and, for that matter, not following the same rhyming you're using not only in every other puzzle, but in the non-scrambled bits of THIS one) doesn't feel like playing fair. :)
I'll dig at it.
Hahaha
Alright, can we ban Amruth A?
He put a bounty on his -16 'riddle'
@Randal'Thor Di you notice that someone got the final answer to F?
@Techidiot So, just scramble the lines or the words?
@IAmInPLS Why?
@IAmInPLS So?
3:50 PM
@Sid Arrange only the lines.
@Mithrandir SKIN?
Any folks interested in testing a set of logic puzzles for me? Unfortunately if you did test these you wouldn't be able to answer when I do eventually post these, for obvious reasons.
Notice that half the lines, which would fit the rhyme scheme aabbcc have Terminal punctuation. The other six have colons.
I'm purposely overreacting, but I find this behavior... weird and counterproductive
Playing with it, I get something like:
Often I watched the waterfall's; They used to intrigue me.
Every kid now fears one of mine; I believed it was nothing but Gee!
Not sure about others though:Yes, I was quite better with numbers.
While the world was dealing with wars; I had colors to prove.
There were not many ways; But I gave you three ways to move.
3:52 PM
@TheGreatEscaper What kind of logic puzzle?
@Randal'Thor yep
@TheGreatEscaper possibly. Not sure.
Which is the least nonsensical arrangement I can figure.
Of course, line arrangement can vary
yeah that's pretty close to what I have
@IAmInPLS If someone wants to put a bounty on a heavily downvoted puzzle, it's their good right to do so (as long as they're not doing something like transferring rep to a sock). Let's not start a witch hunt here.
I still think changing the rules on us isn't fair play. *cough*
But ok :)
3:54 PM
Instead of witch-hunts, let's get ice cream. </ref>
@Rubio New Year. New Rules. New Scheme! :p
I ran into an ice cream place, yesterday, near where I just moved to- the tag line: "Ice Cream makes you pretty"
@Mithrandir Ref to what?
And, btw, you are on right track @ChrisCudmore Do check other tags as well. :) And also check the instructions
Fortescue.
Another victim of Tom
3:56 PM
@Mithrandir That was the first thing that came to my mind, but it didn't sound like a HP quote.
Not a quote. A reference.
It's a puzzle with original mechanics by me, in the vein of Japanese paper pen puzzles.
@Randal'Thor somehow, we end up discussing Puzzles in Mos and Harry Potter in TSL...
Its for the grid logic fortnightly, but due to the nature of this puzzle it needs fairly rigorous playtesting.
(Oops, should probably add @dcfyj just in case they've headed off somewhere)
@Mithrandir We're weird.
</starbait>
3:59 PM
I... will... not... star...
drags hand back, reminded of Pettigrew
@TheGreatEscaper So pictogram type logic grids?
Nu. Group F wasn't even nearly as hard as Clue Two :(
@IAmInPLS On second thoughts ... trying to get the most downvoted question on the site is a bit ... trollish?
5
<-- Previous clue After submitting your answer in the email, you wait eagerly, on the edge of your seat. After about five minutes, your response comes back. It says: Wonderful. You have completed your first task. You have earned the right to continue. Please go to [redacted] to continue. ...
@dcfyj kiiiiiind of.
Entirely new mechanics, at least none that I've seen around before.
4:02 PM
I would take a look at it, but I'm kind of busy with work. If it's brand new mechanics then I probably won't have the time needed to devote to it.
@Rubio Corrected. Typo
figured.
Thanks
Also, and this isn't just pedantry, it matters a little: is "waterfall's" intentionally possessive, or merely plural with an extraneous apostrophe?
4:04 PM
@Randal'Thor Yes, a bit :-). The thing that bothers me is that he's 'taking pride' in having the most downvoted question here
@Mithrandir You should have responded with [redacted]
lol
@Khale_Kitha lol. totally
@IAmInPLS Yep. I flagged a couple of those comments.
@Rubio waterfall's/waterfalls. Same. No problems there I guess
4:06 PM
@Randal'Thor What is your comment for?
There are intentionally plural
@dcfyj all cool :) thanks for expressing interest.
@Mithrandir Cross me off your volunteers list. I would be too busy to make a puzzle for the next few months..
@IAmInPLS Because, Amruth's attitude problem aside, I seriously don't think it's a bad riddle.
4:07 PM
@Randal'Thor Oh, OK. At first, I wanted to say that this was basically an ad, but I ended up saying it was just bad.
...So I said it was basically an ad :P
Exactly.
-19 now, at least he's succeeding in what he wanted
At least the answer to the riddle isn't "A plastic bag."
4:10 PM
Plastic bags cost money now.
.10 a bag.
@Techidiot Those are not the same thing. :) It's supposed to be plural then, so no apostrophe should be there?
They tried that here, Mith.
Lasted about 3 months before the law was stricken.
@Mithrandir There's nothing wrong with creating this kind of 'meta' puzzle whose solution is something PSE-specific. I've written puzzles with solutions "the Green Llama" and "Deusovi" which were well-received.
@IAmInPLS So... Why is he trying to get an insanely negative question score?
4:11 PM
@Rubio Done again! Thanks.
Perhaps he's just an insanely negative person. :)
So? This wasn't a super-great riddle. It was specifically to bring attention to another puzzle to get a badge.
But grammar is least bothered in this puzzle
Not to mention this one:
30
In the following diagram, each red dot represents a positive number. The dot-numbers on each of the five circles spell out either a word (each dot corresponding to a letter) or a number (each dot corresponding to a single digit), always starting at the topmost dot and moving around the circle clo...
@Mithrandir yeah I pointed that out in my answer, intentionally.
4:12 PM
@dcfyj Well, I don't know!
@Mithrandir Hmm, I didn't realise the other puzzle was also Amruth's.
Not sure how much of a difference that should make though.
After all, we're supposed to vote for the post, not for the person.
It just makes the ad more egregiously self-serving is all
@Randal'Thor When you get the other one 'stone' will make lots of sense...
huh. I was right with ROOF for E5?
yep
4:19 PM
I thought it was too much of a stretch. That's funny :)
Also @Randal'Thor I dunno if Sid got "STEAM" also but it's in my partial answer and I hadn't seen anyone solve it prior. I think that one came from me.
Also, can anyone explain how that was LOCK?
Glock - G[ee]
Glock without gee?
Glock (pistol) - Gee!
not really proper
4:22 PM
How is exclamation gee?
Even if it is, where is the homophone indicator?
Try this one then: Charlie Brown decapitated twice for boat lift (4)
Glad you're here, Chris - I was wanting to work on some of the CC's, but needed some help as to if I'm doing them right - care to take a look at an example, to see if I'm understanding this?
4:25 PM
sure
relay sound from alarm-trigger, diamond peak, and greeting (5)
Ah. Yeah looks like my answer predated Sid's by a few hours - i was afraid I'd missed it and had swiped it subconsciously hehe
@Will Is the CCCC answer ACCORDION?
@Khale_Kitha My first stab would be to take RELAY as the definition.
Okay
I feel like I was forced to make that part obvious, but I could work on that, next time
4:27 PM
Sound from alarm + Trigger + Diamond Peak + Greeting. Looks like a charade.
Bell, Ring , Peal. Or it could be the sound that an alarmed person makes.
alarm-trigger is together for a reason - I couldn't find a better choice there, yet.
Is that too obtuse?
Ok, I typically ignore punctuation on the first few read throughs. But I could read that as ALARM - TRIGGER .... ALARM - ARM = AL
Any mathy guy here? I am struggling with a calculus problem and am too lazy to create an account on mathematics and post it there...
oh, good point
Which is a good a place to start as any.
4:30 PM
@Randal'Thor I have a feeling you want some clues for vscgc.
Since we're doing this for practice - that's a rabbit hole
Hang on... I need to past this into notepad. It's moving off the screen.
Star it, for a moment, then unstar when done, hehe
you only get a limited window to unstar
True.
4:32 PM
@Sid I am a mathy guy.
@Sid Yep!
but I can force unstar it if you ask
@GarethMcCaughan *mathsy :-)
@Randal'Thor I'm bilingual :-)
I could also take RELAY SOUND as def, with RELAY as either a noun or a verb. And I haven't even looked into homonyms yet, which you always have to have in the back of your mind.
4:32 PM
Now now boys. I thought we agreed to use "mathematics" so we wouldn't have this squabble here. ;)
So multiple words are allowed as def - good to know
Yeah thanks... my question is on integration. f(x)= x^2x (1+ln x)dx Integrate that.
Yes, even entire clauses.
yah they just have to be consecutive
4:33 PM
@Mithrandir Well, I've tried Caesar ciphers and QWERTY-related things ... Vigenere isn't much good without a key ... I'm getting a little stuck.
@Sid Wait, is that second x actually a times?
I.e. is it (x^2)(1+log x) or (x^3)(1+log x)?
Exactly..
That's where I am struggling
@Sid or is it x^{2x}?
@GarethMcCaughan Yep,
What happens if you substitute y=log x?
4:35 PM
so it's $\int x^{2x} (1+\log x) \d x$ ?
don't you just wish mathjax worked here sometimes
x^{2x} = exp(2x log x)
Now I can think of 3 different meanings for Relay. 1- A race 2- The passing of something 3- The medium over which something is passed. Gotta keep all three in mind.
Except when humn is in the room :P
oh. my. I dunno, I think that might have some amazing results :)
4:36 PM
@ChrisCudmore There's more
But they relate to those you've listed.
An electrical component.
there's electronic relays too obviously
er. or electric, i guess, y eah
But they're called "RELAYS" only synonym I can think of might be SWITCH
I wonder if it would be effective for me to give the answer, so you could determine if the puzzle leads to it appropriately
@Randal'Thor It is Vigenere.
4:38 PM
Fair enough
io is greeting?
"yo"
no.
you have to clue homophones, you can't just throw them in
4:39 PM
(confession: I asked a computer what the answer to @Sid's integral is before making this suggestion) It seems likely that the integral is also going to have something looking like x^{2x} in it. So it might be worth figuring out what the derivative of x^{2x} is.
They are clued
sound from alarm trigger is a LetterBank clue?
(by "the integral" here I mean the result of doing the integration, not the thing being integrated; of course we know the latter has x^{2x} in it already.)
don't know what letterbank refers to
@Mithrandir Well hmph. Guess I need to hunt for a key.
4:39 PM
@Randal'Thor Thanks, I solved that now. I am an idiot at not thinking what you wrote there..
Basically, in this case, R is the only letter in both Alarm and Trigger
alarm-trigger refers to a raid
ok, so what is "diamond peak"?
'D'
I took that to be the "d"
4:41 PM
So effectively "sound from (Raid + D + yo)"
tenuous, but I won't call fowl on it.
hmm
I think i would ;)
@Khale_Kitha But, RAIDDYO isn't a word.
4:41 PM
homophone indicators are for, well, homophones
two words that sound alike
Right, that's why I was mentioning that I wasn't sure of the classification
It's not homophone, but closer to charade
In-between
I think it's fine to have a homophone where the thing you start with isn't a single word.
@Randal'Thor I gave you all of the clues that you need.
That's the best description I have, in my head, yeah
Rand - thick
He gave the key
4:43 PM
@Khale_Kitha Who are you calling thick? :-P
hehehe
Apparently both of us.
I think you need to either homophone a single charade, with both start and finish syllables being words
or
@GarethMcCaughan @Randal'Thor There is another question. Integrate: [1+2tanx(tanx + Sec x)]1/2 dx
build a word and then homophon it.
Not thick
4:44 PM
I would contest that a spoonerism doesn't follow that rule
@Khale_Kitha Khale Thika?
I can see a homophone of (e.g.) "parse nip" giving parsnip, or whatever, but I don't think you can wrap any arbitrary assemblage of charade bits in a homophone indicator and call it a day
lol
hey @BeastlyGerbil
Accumulate a ship's help in the sound. (9)
4:45 PM
3
Sorry, 6
A CREW --> Accrue
see, that's fine
@Sid tan x(tan x + sec x) equals (sec x)^2.
Wait, no.
helllo
I think it's time for coffee.
4:47 PM
hey bg
It's (sin^2(x) + sin(x)) / cos^2(x).
@ChrisCudmore Bring me some too ;)
@BeastlyGerbil Afternoon.
@Rubio you have once again proven the power of HNQ :P
!!/coffee
4:47 PM
@ChrisCudmore @Rubio Okay, I'll keep that in mind
(that works in Charcoal)
@BeastlyGerbil I did?
@Randal'Thor Take a closer look. I gave you all of the clues.
Hm. I've never seen it show up there.
4:49 PM
I'm assuming it did with 2k views
Guess I need to fully refresh more often :)
Yeah I just saw it - just now
@Mithrandir Sorry, I haven't even had the chance to look at it yet.
Too much going on in chats.
I got the 1k view badge this morning and even went looking to see if it'd HNQd, and didn't see it show up
It's the maths, in the chats, with the peoples..... I sound like I'm playing clue.
@Sid that 1/2 at the end is kinda unusual. Is it actually an exponent?
4:50 PM
You got your math[s] in my cryptics. No, you got your cryptics in my math[s]. Aiieee!
lol
@GarethMcCaughan yeah, exponent
Yeah, solved, thanks again @Randal'Thor
@Rubio If you have noticed, I have maintained AABB in the first four lines. . And hopefully in other places as well ;)
oooh new puzzle
I wonder if there's a good way to hide the number 5, 6, or 7, in a CC..
4:51 PM
@Techidiot I did notice. (I commented on it! hehe)
That's why NOT doing it in the jumble feels unfair.
1, 2, 3, 4, 8, 9, and 10 are easy
I know I'm being picky though.
@Mithrandir OK, just F6 left now.
Probably I did it there as well :-/
@Randal'Thor Look closer for why.
Rot13 is outdated.
4:55 PM
@Mithrandir I fer it will get old+ fst+ though-
Just a curiousity found when examining closer.
Huh?
@Khale_Kitha ?
I fer it will get old+ fst+ though-
I fear it will get old fast though
Haven't found the exact decryption, but there's that
4:57 PM
What'd you get that from?
Send extreme signal (5) work for people?
If you found something like that it's completely unintentional o_O
+1 without rotation
I meant closer like this...
I know what happened, there. That was an oddity in something I had from earlier, hah
not sure how it got left
Windows 10 has a copy fail that hits me a lot | 2021-04-17 09:45:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5683994293212891, "perplexity": 4075.7623732450356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00169.warc.gz"} |
http://www.optiboard.com/forums/showthread.php/50540-Realtionship-between-lens-curve-and-diameter | # Thread: Realtionship between lens curve and diameter?
1. ## Realtionship between lens curve and diameter?
Hello,
I know that there is a fixed relationship between the curve of a lens as measured with a lens clock (+8.00, -4.50, etc) and the radius of the sphere which would result if you were to continue drawing the curve, but I don't know what that formula is. In the picture below, the lens is the yellow section, with a curve of +8. I need to find r. Any help would be appreciated.
2. A geneva lens clock is depressed .01mm for each graduation on the dial. It can be used as a thickness guage on a contact lenses placed convex down on a table. This should let you know how much the center pin is depressed for each mark on the scale relative to the immobile outter pins. The diameter of any sphere is twice that of it's radius.
Chip
Chip
3. Assumption is the geneva lens clock is calibrated for 1.53 tooling.
n=index, in this case, 1.53
D= diopter of the curve
Radius = (n-1)/D= .06625 meters or 6.625 centimeters.
4. I know that there is a fixed relationship between the curve of a lens as measured with a lens clock (+8.00, -4.50, etc) and the radius of the sphere which would result if you were to continue drawing the curve, but I don't know what that formula is. In the picture below, the lens is the yellow section, with a curve of +8. I need to find r.
The exact equation for the surface radius r is given by:
$r=\frac{x^2 + s^2}{2s}$
where s is the sagitta or height of the curve measured by the lens clock and x is the separation of the pins, typically around 10 mm. If we assume a standard tooling index of 1.530, the exact equation for the surface power F153 is given by:
$F_{1530}=\frac{1060s}{x^2 + s^2}$
Note that this equation would result in a non-linear scale on the face of the lens clock. However, since the pin separation is relatively narrow, the approximate sag formula can be used to produce a linear scale, which is fairly accurate up to a surface curves of 15 diopters:
$F_{1530}=\frac{1060s}{x^2}$
So every 0.1 mm of surface height s is roughly equal to 1.00 D of surface power at a refractive index of 1.530.
Best regards,
Darryl
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• | 2016-10-23 23:50:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 3, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7225890159606934, "perplexity": 732.8623139192401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719453.9/warc/CC-MAIN-20161020183839-00261-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://risk.asmedigitalcollection.asme.org/heattransfer/article-abstract/124/1/184/478540/Evaporation-Combustion-Affected-by-In-Cylinder?redirectedFrom=fulltext | An existing in-cylinder thermal regeneration concept for Diesel engines is examined for the roles of the porous insert motion and the fuel injection strategies on the fuel evaporation and combustion and on the engine efficiency. While the heated air emanating from the insert enhances fuel evaporation resulting in a superadiabatic combustion process (thus increasing thermal efficiency), the corresponding increase in the thermal $NOx$ is undesirable. A two-gas-zone and a single-step reaction model are used with a Lagrangian droplet tracking model that allows for filtration by the insert. A thermal efficiency of 53 percent is predicted, compared to 43 percent of the conventional Diesel engines. The optimal regenerative cooling stroke occurs close to the peak flame temperature, thus increasing the superadiabatic flame temperature and the peak pressure, while decreasing the expansion stroke pressure and the pressure drop through the insert. During the regenerative heating stroke, the heated air enhances the droplet evaporation, resulting in a more uniform, premixed combustion and a higher peak pressure, thus a larger mechanical work.
1.
Ferrenberg, A. J., 1988, “Regenerative Internal Combustion Engine,” US Patent 4,790,284.
2.
Ferrenberg, A. J., 1990, “The Single Cylinder Regenerated Internal Combustion Engine,” SAE Paper No. 900911.
3.
Ferrenberg, A. J., Williams B. E., and McNeal, S. R., 1995, “Low Heat Rejection Regenerated Diesel Engines for Shipboard Mechanical and Electrical Power (Part2),” Contract N00167-92-C-0020.
4.
Park
,
C.-W.
, and
Kaviany
,
M.
,
2000
, “
Combustion-Thermoelectric Tube
,”
ASME J. Heat Transfer
,
122
, pp.
721
729
.
5.
Heywood, J. B., 1988, Internal Combustion Engine Fundamentals, McGraw-Hill.
6.
Kaviany, M., 1999, Principles of Heat Transfer in Porous Media, Corrected Second Edition, Springer-Verlag, New York.
7.
Westbrook
,
C. K.
, and
Dryer
,
F. L.
,
1984
, “
Chemical Kinetic Modeling of Hydrocarbon Combustion
,”
Prog. Energy Combust. Sci.
,
10
, pp.
1
57
.
8.
Hiroyasu, H., and Kadota, T., 1974, “Fuel Droplet Size Distribution in Diesel Combustion Chamber,” SAE Paper No. 740715.
9.
Faeth
,
G. M.
,
1983
, “
Evaporation and Combustion of Sprays
,”
Prog. Energy Combust. Sci.
,
9
, pp.
1
76
.
10.
Martynenko
,
V. V.
,
Echigo
,
R.
, and
Yoshida
,
H.
,
1998
, “
Mathematical Model of Self-Sustaining Combustion in Inert Porous Medium With Phase Change Under Complex Heat Transfer
,”
Int. J. Heat Mass Transf.
,
41
, No.
1
, pp.
117
126
.
11.
Woshni, G., 1967, “Universally Applicable Equation for the Instantaneous Heat Transfer Coefficient in the Internal Combustion Engine,” SAE Paper No. 670931.
12.
Assanis, D. N., and Heywood, J. B., 1986, “Development and Use of Computer Simulation of the Turbocompounded Diesel System for Engine Performance and Components Heat Transfer Studies,” SAE Paper No. 860329.
13.
Bernardin
,
J. D.
, and
Mudawar
,
I.
,
1997
, “
Film Boiling Heat Transfer of Droplet Streams and Sprays
,”
Int. J. Heat Mass Transf.
,
40
, pp.
2579
2593
.
14.
Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, Third Edition, Hemisphere, Washington, D.C. | 2022-08-13 09:49:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7290610074996948, "perplexity": 12191.961525589442}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571911.5/warc/CC-MAIN-20220813081639-20220813111639-00398.warc.gz"} |
https://www.physicsforums.com/threads/change-order-of-integration.311394/ | # Change order of integration
## Homework Statement
Given
\int{0}{3} \int{0}{sqrt{(9-z^2)}} \int{0}{sqrt{(9-y^2-z^2)}} dx dy dz
express the integral as an equivalent in dz dy dx
## The Attempt at a Solution
From the origial limits z goes from 0 to when x^2 + y^2 <= 9
For dz I have
\int{0}{ sqrt(-x^2-y^2+9)} dz
Is this right so far?
Related Calculus and Beyond Homework Help News on Phys.org
HallsofIvy
Homework Helper
## Homework Statement
Given
\int{0}{3} \int{0}{sqrt{(9-z^2)}} \int{0}{sqrt{(9-y^2-z^2)}} dx dy dz
express the integral as an equivalent in dz dy dx
## The Attempt at a Solution
From the origial limits z goes from 0 to when x^2 + y^2 <= 9
For dz I have
\int{0}{ sqrt(-x^2-y^2+9)} dz
Is this right so far?
In the original integral z goes from 0 to 3, for each z, y from 0 to $\sqrt{9-z^2}$, and, for each y and z, x goes from 0 to $\sqrt{9- x^2- y^2}$.
That last is, of course, the upper hemisphere of $x^2+ y^2+ z^2= 9$ while the y integral is over the upper semi-circle of $y^2+ z^2= 9$. Finally the z integral over a radius of that circle and sphere. This is the first "octant" of the sphere of radius 3. Yes, If you change the order of integration so you are integrating with respect to z first, z goes from 0 to $\sqrt{9- x^2+ y^2}$.
Because of symmetry, this is a very easy problem!
For dx
Do you leave the limit as \int{0}{sqrt{(9-y^2-z^2)}}dx or do you change it to
\int{0}{3} dx
\int{0}{3} \int{0}{sqrt{(9-z^2)}} \int{0}{ sqrt(9-x^2-y^2)} dz dy dx
regards
HallsofIvy
Homework Helper
For dx
Do you leave the limit as \int{0}{sqrt{(9-y^2-z^2)}}dx or do you change it to
\int{0}{3} dx
\int{0}{3} \int{0}{sqrt{(9-z^2)}} \int{0}{ sqrt(9-x^2-y^2)} dz dy dx
regards
Since the x integral is the "outer" integral here, its limits of integration must be numbers, not functions of y and z! Yes, the limits are 0 and 3.
My point about the symmetry is that since this is an octant of a sphere, all choices of order are the same: except for "permuting" x, y, and z, those are exactly the limits of integration you had originally.
Thanks | 2021-04-10 12:57:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.973823070526123, "perplexity": 1528.1574621245745}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038056869.3/warc/CC-MAIN-20210410105831-20210410135831-00112.warc.gz"} |
https://www.springerprofessional.de/leveraging-applications-of-formal-methods-verification-and-valid/4387576 | scroll identifier for mobile
main-content
## Über dieses Buch
The two-volume set LNCS 8802 and LNCS 8803 constitutes the refereed proceedings of the 6th International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, ISoLA 2014, held in Imperial, Corfu, Greece, in October 2014. The total of 67 full papers was carefully reviewed and selected for inclusion in the proceedings. Featuring a track introduction to each section, the papers are organized in topical sections named: evolving critical systems; rigorous engineering of autonomic ensembles; automata learning; formal methods and analysis in software product line engineering; model-based code generators and compilers; engineering virtualized systems; statistical model checking; risk-based testing; medical cyber-physical systems; scientific workflows; evaluation and reproducibility of program analysis; processes and data integration in the networked healthcare; semantic heterogeneity in the formal development of complex systems. In addition, part I contains a tutorial on automata learning in practice; as well as the preliminary manifesto to the LNCS Transactions on the Foundations for Mastering Change with several position papers. Part II contains information on the industrial track and the doctoral symposium and poster session.
## Inhaltsverzeichnis
### Introduction to Track on Engineering Virtualized Services
Virtualization is a key technology enabler for cloud computing. Despite the added value and compelling business drivers of cloud computing, this new paradigm poses considerable new challenges that have to be addressed to render its usage effective for industry. Virtualization makes elastic amounts of resources available to application-level services; for example, the processing capacity allocated to a service may be changed according to demand. Current software development methods, however, do not support the modeling and validation of services running on virtualized resources in a satisfactory way. This seriously limits the potential for fine-tuning services to the available virtualized resources as well as for designing services for scalability and dynamic resource management. The track on
Engineering Virtualized Services
aims to discuss key challenges that need to be addressed to enable software development methods to target resource-aware virtualized services.
Reiner Hähnle, Einar Broch Johnsen
### Erlang-Style Error Recovery for Concurrent Objects with Cooperative Scheduling
Re-establishing a safe program state after an error occurred is a known problem. Manually written error-recovery code is both more difficult to test and less often executed than the main code paths, hence errors are prevalent in these parts of a program. This paper proposes a failure model for concurrent objects with cooperative scheduling that automatically re-establishes object invariants after program failures, thereby eliminating the need to manually write this problematic code. The proposed model relies on a number of features of actor-based object-oriented languages, such as asynchronous method calls, co-operative scheduling with explicit synchronization points, and communication via future variables. We show that this approach can be used to implement Erlang-style process linking, and implement a supervision tree as a proof-of-concept.
Georg Göri, Einar Broch Johnsen, Rudolf Schlatte, Volker Stolz
### Fault Model Design Space for Cooperative Concurrency
This paper critically discusses the different choices that have to be made when defining a fault model for an object-oriented programming language. We consider in particular the
ABS
language, and analyze the interplay between the fault model and the main features of
ABS
, namely the cooperative concurrency model, based on asynchronous method invocations whose return results via futures, and its emphasis on static analysis based on invariants.
Ivan Lanese, Michael Lienhardt, Mario Bravetti, Einar Broch Johnsen, Rudolf Schlatte, Volker Stolz, Gianluigi Zavattaro
### Programming with Actors in Java 8
There exist numerous languages and frameworks that support an implementation of a variety of actor-based programming models in Java using concurrency utilities and threads. Java 8 is released with fundamental new features: lambda expressions and further dynamic invocation support. We show in this paper that such features in Java 8 allow for a high-level actor-based methodology for programming distributed systems which supports the programming to interfaces discipline. The embedding of our actor-based Java API is shallow in the sense that it abstracts from the actual thread-based deployment models. We further discuss different concurrent execution and thread-based deployment models and an extension of the API for its actual parallel and distributed implementation. We present briefly the results of a set of experiments which provide evidence of the potential impact of lambda expressions in Java 8 regarding the adoption of the actor concurrency model in large-scale distributed applications.
Behrooz Nobakht, Frank S. de Boer
### Contracts in CML
We describe the COMPASS Modelling Language (CML), which is used to model large-scale Systems of Systems and the contracts that bind them together. The language can be used to document the interfaces to constituent systems using formal, precise, and verifiable specifications including preconditions, postconditions, and invariants. The semantics of CML directly supports the use of these contracts for all language constructs, including the use of communication channels, parallel processes, and processes that run forever. Every process construct in CML has an associated contract, allowing clients and suppliers to check that the implementations of constituent systems conform to their interface specifications.
Jim Woodcock, Ana Cavalcanti, John Fitzgerald, Simon Foster, Peter Gorm Larsen
### Distributed Energy Management Case Study: A Formal Approach to Analyzing Utility Functions
The service-oriented paradigm has been established to enable quicker development of new applications from already existing services. Service negotiation is a key technique to provide a way of deciding and choosing the most suitable service, out of possibly many services delivering similar functionality but having different response times, resource usages, prices, etc. In this paper, we present a formal approach to the clients-providers negotiation of distributed energy management. The models are described in our recently introduced
Remes
Hdcl
language, with timed automata semantics that allows us to apply
Uppaal
-based tools for model-checking various scenarios of service negotiation. Our target is to compute ways of reaching the price- and reliability-optimal values of the utility function, at the end of the service negotiation.
Aida Čaušević, Cristina Seceleanu, Paul Pettersson
### Towards the Typing of Resource Deployment
In cloud computing,
resources
as files, databases, applications, and virtual machines may either scale or move from one machine to another in response to load increases and decreases (
resource deployment
). We study a type-based technique for analysing the deployments of resources in cloud computing. In particular, we design a type system for a concurrent object-oriented language with dynamic resource creations and movements. The type of a program is
behavioural
, namely it expresses the resource deployments over periods of (logical) time. Our technique admits the inference of types and may underlie the optimisation of the costs and consumption of resources.
Elena Giachino, Cosimo Laneve
### Static Inference of Transmission Data Sizes in Distributed Systems
We present a static analysis to infer the amount of data that a distributed system may transmit. The different locations of a distributed system communicate and coordinate their actions by posting tasks among them. A task is posted by building a message with the task name and the data on which such task has to be executed. When the task completes, the result can be retrieved by means of another message from which the result of the computation can be obtained. Thus, the transmission data size of a distributed system mainly depends on the amount of messages posted among the locations of the system, and the sizes of the data transferred in the messages. Our static analysis has two main parts: (1) we over-approximate the sizes of the data at the program points where tasks are spawned and where the results are received, and (2) we over-approximate the total number of messages. Knowledge of the transmission data sizes is essential, among other things, to predict the bandwidth required to achieve a certain response time, or conversely, to estimate the response time for a given bandwidth. A prototype implementation in the SACO system demonstrates the accuracy and feasibility of the proposed analysis.
Elvira Albert, Jesús Correas, Enrique Martin-Martin, Guillermo Román-Díez
### Fully Abstract Operation Contracts
Proof reuse in formal software verification is crucial in presence of constant evolutionary changes to the verification target. Contract-based verification makes it possible to verify large programs, because each method in a program can be verified against its contract separately. A small change to some contract, however, invalidates all proofs that rely on it, which makes reuse difficult. We introduce fully abstract contracts and class invariants which permit to completely decouple reasoning about programs from the applicability check of contracts. We implemented tool support for abstract contracts as part of the KeY verification system and empirically show the considerable reuse potential of our approach.
Richard Bubel, Reiner Hähnle, Maria Pelevina
### Statistical Model Checking Past, Present, and Future
(Track Introduction)
This short note introduces statistical model checking and gives a brief overview of the
Statistical Model Checking, past present and future
session at Isola 2014.
Kim G. Larsen, Axel Legay
### An Effective Heuristic for Adaptive Importance Splitting in Statistical Model Checking
Statistical model checking avoids the intractable growth of states associated with numerical model checking by estimating the probability of a property from simulations. Rare properties pose a challenge because the relative error of the estimate is unbounded. In [13] we describe how importance splitting may be used with SMC to overcome this problem. The basic idea is to decompose a logical property into nested properties whose probabilities are easier to estimate. To improve performance it is desirable to decompose the property into many equi-probable
levels
, but logical decomposition alone may be too coarse.
score function
to improve the granularity of a logical property. We show that such a score function may take advantage of heuristics, so long as it also rigorously respects certain properties. To demonstrate our importance splitting approach we present an optimal adaptive importance splitting algorithm and an heuristic score function. We give experimental results that demonstrate a significant improvement in performance over alternative approaches.
Cyrille Jegourel, Axel Legay, Sean Sedwards
### A Formalism for Stochastic Adaptive Systems
Complex systems such as systems of systems result from the combination of several components that are organized in a hierarchical manner. One of the main characteristics of those systems is their ability to adapt to new situations by modifying their architecture. Those systems have recently been the subject of a series of works in the software engineering community. Most of those works do not consider quantitative features. The objective of this paper is to propose a modeling language for adaptive systems whose behaviors depend on stochastic features. Our language relies on an extension of stochastic transition systems equipped with (1) an adaptive operator that allows to reason about the probability that a system has to adapt its architecture over time, and (2) dynamic interactions between processes. As a second contribution, we propose a contract-based extension of probabilistic linear temporal logic suited to reason about assumptions and guarantees of such systems. Our work has been implemented in the
Plasma-Lab
tool developed at Inria. This tool allows us to define stochastic adaptive systems with an extension of the Prism language, and properties with patterns. In addition,
Plasma-Lab
offers a simulation-based model checking procedure to reason about finite executions of the system. First experiments on a large case study coming from an industrial driven European project give encouraging results.
Benoît Boyer, Axel Legay, Louis-Marie Traonouez
### A Review of Statistical Model Checking Pitfalls on Real-Time Stochastic Models
Statistical model checking (SMC) is a technique inspired by Monte-Carlo simulation for verifying time-bounded temporal logical properties. SMC originally focused on fully stochastic models such as Markov chains, but its scope has recently been extended to cover formalisms that mix functional real-time aspects, concurrency and non-determinism. We show by various examples using the tools UPPAAL SMC and
Modes
that combining the stochastic interpretation of such models with SMC algorithms is extremely subtle. This may yield significant discrepancies in the analysis results. As these subtleties are not so obvious to the end-user, we present five semantic caveats and give a classification scheme for SMC algorithms. We argue that caution is needed and believe that the caveats and classification scheme in this paper serve as a guiding reference for thoroughly understanding them.
Dimitri Bohlender, Harold Bruintjes, Sebastian Junges, Jens Katelaan, Viet Yen Nguyen, Thomas Noll
### Formal Analysis of the Wnt/β-catenin through Statistical Model Checking
The Wnt/
β
-catenin signalling pathway plays an important role in the proliferation of neural cells, and hence it is the main focus of several research aimed at understanding neurodegenerative pathologies. In this paper we consider a compact model of the basic mechanisms of the Wnt/
β
-catenin pathway and we analyse its dynamics by application of an expressive temporal logic formalism, namely the Hybrid Automata Stochastic Logic. This allows us to formally characterise, and effectively assess, sophisticated aspects of the Wnt/
β
-catenin pathway dynamics.
Paolo Ballarini, Emmanuelle Gallet, Pascale Le Gall, Matthieu Manceny
### Battery-Aware Scheduling of Mixed Criticality Systems
Wireless systems such as satellites and sensor networks are often battery-powered. To operate optimally they must therefore take the performance properties of real batteries into account. Additionally, these systems, and therefore their batteries, are often exposed to loads with uncertain timings. Mixed criticality and soft real-time systems may accept deadline violations and therefore enable trade-offs and evaluation of performance by criteria such as the number of tasks that can be completed with a given battery. We model a task set in combination with the kinetic battery model as a stochastic hybrid system and study its performance under battery-aware scheduling strategies. We believe that this evaluation does not scale with current verification techniques for stochastic hybrid systems. Instead statistical model checking provides a viable alternative with statistical guarantees. Based on our model we also calculate an upper bound on the attainable number of task instances from a battery, and we provide a battery-aware scheduler that wastes no energy on instances that are not guaranteed to make their deadlines.
Erik Ramsgaard Wognsen, René Rydhof Hansen, Kim Guldstrand Larsen
### Using Statistical Model Checking for Measuring Systems
State spaces represent the way a system evolves through its different possible executions. Automatic verification techniques are used to check whether the system satisfies certain properties, expressed using automata or logic-based formalisms. This provides a Boolean indication of the system’s fitness. It is sometimes desirable to obtain other indications, measuring e.g., duration, energy or probability. Certain measurements are inherently harder than others. This can be explained by appealing to the difference in complexity of checking CTL and LTL properties. While the former can be done in time linear in the size of the property, the latter is PSPACE in the size of the property; hence practical algorithms take exponential time. While the CTL-type of properties measure specifications that are based on adjacency of states (up to a fixpoint calculation), LTL properties have the flavor of expecting some multiple complicated requirements from each execution sequence. In order to quickly measure LTL-style properties from a structure, we use a form of statistical model checking; we exploit the fact that LTL-style properties on a path behave like CTL-style properties on a structure. We then use CTL-based measuring on paths, and generalize the measurement results to the full structure using optimal Monte Carlo estimation techniques. To experimentally validate our framework, we present measurements for a flocking model of bird-like agents.
Radu Grosu, Doron Peled, C. R. Ramakrishnan, Scott A. Smolka, Scott D. Stoller, Junxing Yang
This paper explores the effectiveness and challenges of using monitoring techniques, based on Aspect-Oriented Programming, to block adware at the library level, on mobile devices based on Android. Our method is systematic and general: it can be applied to block advertisements from existing and future advertisement networks. We also present miAdBlocker, an industrial proof-of-concept application, based on this technique, for disabling advertisements on a per-application basis. Our experimental results show a high success rate on most applications. Finally, we present the lessons learned from this experience, and we identify some challenges when applying runtime monitoring techniques to real-world case studies.
Khalil El-Harake, Yliès Falcone, Wassim Jerad, Mattieu Langet, Mariem Mamlouk
### Monitoring with Data Automata
We present a form of automaton, referred to as
data automata
, suited for monitoring sequences of data-carrying events, for example emitted by an executing software system. This form of automata allows states to be parameterized with data, forming named records, which are stored in an efficiently indexed data structure, a form of database. This very explicit approach differs from other automaton-based monitoring approaches. Data automata are also characterized by allowing transition conditions to refer to other parameterized states, and by allowing transitions sequences. The presented automaton concept is inspired by rule-based systems, especially the
Rete
algorithm, which is one of the well-established algorithms for executing rule-based systems. We present an optimized external DSL for data automata, as well as a comparable unoptimized internal DSL (API) in the
Scala
programming language, in order to compare the two solutions. An evaluation compares these two solutions to several other monitoring systems.
Klaus Havelund
### Risk-Based Testing
(Track Introduction)
In many development projects, testing has to be done under severe pressure due to limited resources, a challenging time schedule, and the demand to guarantee security and safety of the released software system. Risk-based testing, which utilizes identified risks of a software system for testing purposes, has a high potential to improve testing in this context. It optimizes the allocation of resources and time, is a means for mitigating risks, helps to early identify critical areas, and provides decision support for the management [1, 2].
Michael Felderer, Marc-Florian Wendland, Ina Schieferdecker
### A Technique for Risk-Based Test Procedure Identification, Prioritization and Selection
We present a technique for risk-based test procedure identification, prioritization, and selection. The technique takes a risk model in the form of a risk graph as input, and produces a list of prioritized selected test procedures as output. The technique is general in the sense that it can be used with many existing risk documentation languages and many kinds of likelihood and risk types.
Fredrik Seehusen
### A Risk Assessment Framework for Software Testing
In industry, testing has to be performed under severe pressure due to limited resources. Risk-based testing which uses risks to guide the test process is applied to allocate resources and to reduce product risks. Risk assessment, i.e., risk identification, analysis and evaluation, determines the significance of the risk values assigned to tests and therefore the quality of the overall risk-based test process. In this paper we provide a risk assessment model and its integration into an established test process. This framework is derived on the basis of best practices extracted from published risk-based testing approaches and applied to an industrial test process.
Michael Felderer, Christian Haisjackl, Viktor Pekar, Ruth Breu
### Data Driven Testing of Open Source Software
The increasing adoption of open source software (OSS) components in software systems introduces new quality risks and testing challenges. OSS components are developed and maintained by open communities and the fluctuation of community members and structures can result in instability of the software quality. Hence, an investigation is necessary to analyze the impact open community dynamics and the quality of the OSS, such as the level and trends in internal communications and content distribution. The analysis results provide inputs to drive selective testing for effective validation and verification of OSS components. The paper suggests an approach for monitoring community dynamics continuously, including communications like email and blogs, and repositories of bugs and fixes. Detection of patterns in the monitored behavior such as changes in traffic levels within and across clusters can be used in turn to drive testing efforts. Our proposal is demonstrated in the case of the XWiki OSS, a Java-based environment that allows for the storing of structured data and the execution of server side scripts within the wiki interface. We illustrate our concepts, methods and approach behind this approach for risk based testing of OSS.
Inbal Yahav, Ron S. Kenett, Xiaoying Bai
### Combining Risk Analysis and Security Testing
A systematic integration of risk analysis and security testing allows for optimizing the test process as well as the risk assessment itself. The result of the risk assessment, i.e. the identified vulnerabilities, threat scenarios and unwanted incidents, can be used to guide the test identification and may complement requirements engineering results with systematic information concerning the threats and vulnerabilities of a system and their probabilities and consequences. This information can be used to weight threat scenarios and thus help identifying the ones that need to be treated and tested more carefully. On the other side, risk-based testing approaches can help to optimize the risk assessment itself by gaining empirical knowledge on the existence of vulnerabilities, the applicability and consequences of threat scenarios and the quality of countermeasures. This paper outlines a tool-based approach for risk-based security testing that combines the notion of risk-assessment with a pattern-based approach for automatic test generation relying on test directives and strategies and shows how results from the testing are systematically fed back into the risk assessment.
Jürgen Großmann, Martin Schneider, Johannes Viehmann, Marc-Florian Wendland
### Risk-Based Vulnerability Testing Using Security Test Patterns
This paper introduces an original security testing approach guided by risk assessment, by means of risk coverage, to perform and automate vulnerability testing for Web applications. This approach, called Risk-Based Vulnerability Testing, adapts Model-Based Testing techniques, which are mostly used currently to address functional features. It also extends Model-Based Vulnerability Testing techniques by driving the testing process using security test patterns selected from risk assessment results. The adaptation of such techniques for Risk-Based Vulnerability Testing defines novel features in this research domain. In this paper, we describe the principles of our approach, which is based on a mixed modeling of the System Under Test: the model used for automated test generation captures some behavioral aspects of the Web applications, but also includes vulnerability test purposes to drive the test generation process.
Julien Botella, Bruno Legeard, Fabien Peureux, Alexandre Vernotte
### Medical Cyber-Physical Systems
(Track Introduction)
Rapid progress in modern medical technologies has led to a new generation of healthcare devices and treatment strategies. Examples include electro-anatomical mapping and intervention, bio-compatible and implantable devices, minimally invasive embedded devices, and robotic prosthetics.
Ezio Bartocci, Sicun Gao, Scott A. Smolka
### Compositional, Approximate, and Quantitative Reasoning for Medical Cyber-Physical Systems with Application to Patient-Specific Cardiac Dynamics and Devices
The design of bug-free and safe medical device software is challenging, especially in complex implantable devices that control and actuate organs who’s response is not fully understood. Safety recalls of pacemakers and implantable cardioverter defibrillators between 1990 and 2000 affected over 600,000 devices. Of these, 200,000 or 41%, were due to firmware issues that continue to increase in frequency. According to the FDA, software failures resulted in 24% of
all
medical device recalls in 2011. There is currently no formal methodology or open experimental platform to test and verify the correct operation of medical-device software within the closed-loop context of the patient.
The goal of this effort is to develop the foundations of modeling, synthesis and development of
verified medical device software
and systems
from verified closed-loop models
of the device and organ(s). Our research spans both implantable medical devices such as cardiac pacemakers and physiological control systems such as drug infusion pumps which have multiple networked medical systems. These devices are physically connected to the body and exert direct control over the physiology and safety of the patient. The focus of this effort is on (a) Extending current binary safety properties to quantitative verification; (b) Development of patient-specific models and therapies; (c) Multi-scale modeling of complex physiological phenomena and compositional reasoning across a range of model abstractions and refinements; and (d) Bridging the formal reasoning and automated generation of safe and effective software for future medical devices.
Radu Grosu, Elizabeth Cherry, Edmund M. Clarke, Rance Cleaveland, Sanjay Dixit, Flavio H. Fenton, Sicun Gao, James Glimm, Richard A. Gray, Rahul Mangharam, Arnab Ray, Scott A. Smolka
### On Quantitative Software Quality Assurance Methodologies for Cardiac Pacemakers
Embedded software is at the heart of implantable medical devices such as cardiac pacemakers, and rigorous software design methodologies are needed to ensure their safety and reliability. This paper gives an overview of ongoing research aimed at providing software quality assurance methodologies for pacemakers. A model-based framework has been developed based on hybrid automata, which can be configured with a variety of heart and pacemaker models. The framework supports a range of quantitative verification techniques for the analysis of safety, reliability and energy usage of pacemakers. It also provides techniques for parametric analysis of personalised physiological properties that can be performed
in silico
, which can reduce the cost and discomfort of testing new designs on patients. We describe the framework, summarise the results obtained, and identify future research directions in this area.
Marta Kwiatkowska, Alexandru Mereacre, Nicola Paoletti
### Model Checking Hybrid Systems
(Invited Talk)
We present the framework of delta-complete analysis for bounded reachability problems of hybrid systems. We perform bounded reachability checking through solving delta-decision problems over the reals. The techniques take into account of robustness properties of the systems under numerical perturbations. Our implementation of the techniques scales well on several highly nonlinear hybrid system models that arise in biomedical applications.
Edmund M. Clarke, Sicun Gao
### Challenges for the Dynamic Interconnection of Medical Devices
Medical devices, especially when operated in the surgery room, are safety critical systems, as the patient’s life may depend on them. As such, there are high legal requirements to meet by the manufacturers of such devices. One of the typical requirements is that whenever medical devices are interconnected, the whole setup has to be approved by the corresponding legal body. For economical reasons, however, it is desirable to interconnect devices from different manufacturers in an individual fashion for each surgery room. Then however no integration test has been carried out a priori and thus the whole setup could not have been approved. In other words such economical demands impose challenges both on the technical as well as the legal situation. In this contribution, we report on these challenges as well as on first ideas to address them.
Martin Leucker
### Temporal Logic Based Monitoring of Assisted Ventilation in Intensive Care Patients
We introduce a novel approach to automatically detect ineffective breathing efforts in patients in intensive care subject to assisted ventilation. The method is based on synthesising from data temporal logic formulae which are able to discriminate between normal and ineffective breaths. The learning procedure consists in first constructing statistical models of normal and abnormal breath signals, and then in looking for an optimally discriminating formula. The space of formula structures, and the space of parameters of each formula, are searched with an evolutionary algorithm and with a Bayesian optimisation scheme, respectively. We present here our preliminary results and we discuss our future research directions.
Sara Bufo, Ezio Bartocci, Guido Sanguinetti, Massimo Borelli, Umberto Lucangelo, Luca Bortolussi
### Track Introduction: Scientific Workflows
In recent years, numerous software systems have been developed specifically for supporting the management of scientific processes and workflows (see, e.g., [1] or [2] for surveys). Research in this comparatively new field is currently evolving in interesting new directions. Already at the ISoLA symposium in 2010 we focused on workflow management for scientific applications in the scope of a symposium track on “Tools in scientific workflow composition” [3].
Joost N. Kok, Anna-Lena Lamprecht, Kenneth J. Turner, Katy Wolstencroft
### Meta-analysis of Disjoint Sets of Attributes in Large Cohort Studies
We will introduce the problem of classification in large cohort studies containing heterogeneous data. The data in a cohort study comes in separate groups, which can be turned on or off. Each group consists of data coming from one specific measurement instrument. We provide a “cross-sectional” investigation on this data to see the relative power of the different groups. We also propose a way of improving on the classification performance in individual cohort studies using other cohort studies by using an intuitive workflow approach.
Jonathan K. Vis, Joost N. Kok
### Towards a Flexible Assessment of Climate Impacts: The Example of Agile Workflows for the ci:grasp Platform
The Climate Impacts: Global and Regional Adaptation Support Platform (ci:grasp) is a web-based climate information service for exploring climate change related information in its geographical context. We have used the jABC workflow modeling and execution framework to make flexibilized versions of the processes implemented in ci:grasp available to the scientific community. The jABC permits us to leverage the processes to an easily accessible conceptual level, which enables users to flexibly define and adapt workflows according to their specific needs. The workflows are suitable as graphical documentation of the processes and are directly repeatable and reusable, which facilitates reproducibility of results and eventually increases the productivity of researchers working on climate impact risk assessment. In this paper, we use variations of workflows for the assessment of the impacts of sea-level rise to demonstrate the flexibility we gained by following this approach.
Samih Al-Areqi, Steffen Kriewald, Anna-Lena Lamprecht, Dominik Reusser, Markus Wrobel, Tiziana Margaria
### A Visual Programming Approach to Beat-Driven Humanoid Robot Dancing
The paper presents a workflow-based approach to the classic task of teaching a humanoid robot to dance to a given song with respect to the detected beat. Our goal is to develop workflow components which enable the construction of complex dance choreographies using visual programming only. This eliminates tedious programming of dance moves and their synchronisation to the music thus enabling the robot animator to design the choreography at a higher conceptual level. The presented work is based on the Choregraphe visual programming environment for the NAO robot platform and the Aubio open source tool for the extraction of annotations from audio signals.
Vid Podpečan
### jABCstats: An Extensible Process Library for the Empirical Analysis of jABC Workflows
The jABC is a multi-purpose modeling framework that has been used for model-driven development of workflows and processes in different application domains. In this paper we present jABCstats, an extensible process library for analyzing jABC workflows empirically. We also discuss first results of its application to scientific workflows modeled with the jABC, which give insights into typical workflow sizes and into the kinds of services and the workflow patterns commonly used.
Alexander Wickert, Anna-Lena Lamprecht
### Automatic Annotation of Bioinformatics Workflows with Biomedical Ontologies
Legacy scientific workflows, and the services within them, often present scarce and unstructured (i.e. textual) descriptions. This makes it difficult to find, share and reuse them, thus dramatically reducing their value to the community. This paper presents an approach to annotating workflows and their subcomponents with ontology terms, in an attempt to describe these artifacts in a structured way. Despite a dearth of even textual descriptions, we automatically annotated 530 myExperiment bioinformatics-related workflows, including more than 2600 workflow-associated services, with relevant ontological terms. Quantitative evaluation of the Information Content of these terms suggests that, in cases where annotation was possible at all, the annotation quality was comparable to manually curated bioinformatics resources.
Beatriz García-Jiménez, Mark D. Wilkinson
### Evaluation and Reproducibility of Program Analysis (Track Introduction)
Today’s popular languages have a large number of different language constructs and standardized library interfaces. The number is further increasing with every new language standard.Most published analyses therefore focus on a subset of such languages or define a language with a few essential constructs of interest.More recently, program-analysis competitions [4,6,7,1] aim to evaluate comparatively implemented analyses for a given set of benchmarks. The comparison of the analyses focuses on various aspects: (a) the quality of established structures and automata describing the behavior of the analyzed program, (b) the verification of various specified program properties, (c) the impact on a client analysis of particular interest, and (d) the impact of analysis precision on program optimizations.
Markus Schordan, Welf Löwe, Dirk Beyer
### SWEET – A Tool for WCET Flow Analysis (Extended Abstract)
Worst-Case Execution Time (WCET) analysis [14] aims to estimate the longest possible execution time for a piece of code executing uninterrupted on a particular hardware. Such WCET estimates are used when analysing real-time systems with respect to possible deadline violations. For safety-critical real-time systems,
safe
(surely not underestimating) estimates are desirable. Such estimates can be produced by a
static WCET analysis
that takes all possible execution paths and corresponding hardware states into account.
Björn Lisper
### Test-Driving Static Analysis Tools in Search of C Code Vulnerabilities II
(Extended Abstract)
A large number of tools that automate the process of finding errors in programs has recently emerged in the software development community. Many of them use static analysis as the main method for analyzing and capturing faults in the source code. Static analysis is deployed as an approximation of the programs’ runtime behavior with inherent limitations regarding its ability to detect actual code errors. It belongs to the class of computational problems which are undecidable [2]. For any such analysis, the major issues are: (1) the programming language of the source code where the analysis is applied (2) the type of errors to be detected (3) the effectiveness of the analysis and (4) the efficiency of the analysis.
George Chatzieleftheriou, Apostolos Chatzopoulos, Panagiotis Katsaros
### Construction of Abstract Domains for Heterogeneous Properties (Position Paper)
The aim of static analysis is to infer invariants about programs that are tight enough to establish semantic properties, like the absence of run-time errors. In the last decades, several branches of the static analysis of imperative programs have made significant progress, such as in the inference of numeric invariants or the computation of data structures properties (using pointer abstractions or shape analyzers). Although simultaneous inference of shape-numeric invariants is often needed, this case is especially challenging and less well explored. Notably, simultaneous shape-numeric inference raises complex issues in the design of the static analyzer itself. We study the modular construction of static analyzers, based on combinations of atomic abstract domains to describe several kinds of memory properties and value properties.
Xavier Rival, Antoine Toubhans, Bor-Yuh Evan Chang
### Verification of Polyhedral Optimizations with Constant Loop Bounds in Finite State Space Computations
As processors gain in complexity and heterogeneity, compilers are asked to perform program transformations of ever-increasing complexity to effectively map an input program to the target hardware. It is critical to develop methods and tools to automatically assert the correctness of programs generated by such modern optimizing compilers.
We present a framework to verify if two programs (one possibly being a transformed variant of the other) are semantically equivalent. We focus on scientific kernels and a state-of-the-art polyhedral compiler implemented in ROSE. We check the correctness of a set of polyhedral transformations by combining the computation of a state transition graph with a rewrite system to transform floating point computations and array update operations of one program such that we can match them as terms with those of the other program. We demonstrate our approach on a collection of benchmarks from the PolyBench/C suite.
Markus Schordan, Pei-Hung Lin, Dan Quinlan, Louis-Noël Pouchet
### The Guided System Development Framework: Modeling and Verifying Communication Systems
In a world that increasingly relies on the Internet to function, application developers rely on the implementations of protocols to guarantee the security of data transferred. Whether a chosen protocol gives the required guarantees, and whether the implementation does the same, is usually unclear. The Guided System Development framework contributes to more secure communication systems by aiding the development of such systems. The framework features a simple modelling language, step-wise refinement from models to implementation, interfaces to security verification tools, and code generation from the verified specification. The refinement process carries thus security properties from the model to the implementation. Our approach also supports verification of systems previously developed and deployed. Internally, the reasoning in our framework is based on the Beliefs and Knowledge tool, a verification tool based on belief logics and explicit attacker knowledge.
Jose Quaresma, Christian W. Probst, Flemming Nielson
### Processes and Data Integration in the Networked Healthcare
(Track Introduction)
Forward-looking issues in the Information and Communication Technology (ICT) for healthcare and medical applications include process integration, data annotation, ontologies and semantics, but also any automatization approach that is not imposed from the IT experts (in-house support or external consultants) but instead allows more flexibility and also a more direct ownership of the processes and data by the healthcare professionals themselves. In the ISoLA-Med workshop in Potsdam in June 2009 and in this track at ISoLA 2012 we showed that a set of innovative research topics related to the future of healthcare systems hinge on the notion of simplicity, for both the end users and the designer, developers, and to support change management and the agility of evolution.
Tiziana Margaria, Christoph Rasche
### Simple Management of High Assurance Data in Long-Lived Interdisciplinary Healthcare Research: A Proposal
Healthcare research data is typically produced, curated, and used by scientists, physicians, and other experts that have little or no professional affinity to programming and IT system design. In the context of evidence-based medicine or translational medicine, however the production, reliability, and long term availability of high quality and high assurance data is of paramount importance. In this paper we reflect on the data management needs we encountered in our experience as associated partners of a large interdisciplinary research project coordinated at the Cancer Metabolism Research Group, Institute of Biomedical Sciences at University of São Paulo in Brazil. Their research project involves extensive collection of detailed sample data within a complicated environment of clinical and research methods, medical, assessment, and measurement equipment and the regulatory requirements of maintaining privacy, data quality and security.
We use this example as an illustrative case of a category of needs and a diversity of professional and skills profiles that is representative of what happens today in any large scale research endeavor. We derive a catalogue of requirements that an IT system for the definition and management of data and processes should have, how this relates to the IT development and XMDD philosophy, and we briefly sketch how the DyWA + jABC combination provides a foundation for meeting those needs.
Tiziana Margaria, Barry D. Floyd, Rodolfo Gonzalez Camargo, Anna-Lena Lamprecht, Johannes Neubauer, Marilia Seelaender
Discussing business models of companies and organizations based on graphical representations that emphasize essential factors has increased in recent years, particularly from a business perspective. However, feasible implementations of business modeling tools are rare, as they tend to be domain specific but at the same time tailored towards the requirements of a heterogeneous group of stakeholders. We present the Business Model Developer (BMD) and the underlying framework for the creation of domain-specific business models. The approach relies on the definition of a domain-specific library of model components as well as structured parameters with different scopes, i.e. declared areas of applicability. This setup forms the basis for the development of custom techniques for model analysis. We align the development process with the approach of Extreme Model Driven Development (XMDD) to keep it as simple as possible for domain experts to contribute in tailoring the tool towards specific needs. Furthermore, we present a practical application in the healthcare domain, as the BMD has been developed and applied in the course of a joint project in the area of Personalized Medicine.
Steve Boßelmann, Tiziana Margaria
### Dr. Watson? Balancing Automation and Human Expertise in Healthcare Delivery
IBM’s Watson, the supercomputer that beat two Jeopardy champions in a televised competition, has inevitably engendered speculation about what this surprising performance bodes for the role of computers in the workplace. How can Dr. Watson be best utilized in medicine and clinical support systems? This paper defines Computer Enhanced Medicine technology for healthcare as any medical application where the required tasks are split between a human being and a computer-controlled device.
Mark Gaynor, George Wyner, Amar Gupta
### Semantic Heterogeneity in the Formal Development of Complex Systems: An Introduction
System engineering is a complex discipline[1], which is becoming more and more complicated by the heterogeneity of the subsystem components[2] and of the models involved in their design. This complexity can be managed only through the use of formal methods[3]. However, in general the engineering of software in such systems leads to a need for a mix of modelling languages and semantics; and this often leads to unexpected and undesirable interactions between components at all levels of abstraction[4]. There are currently no generally applicable tools for dealing with this heterogeneity of interactions in the engineering of complex systems.
### Modelling and Verifying an Evolving Distributed Control System Using an Event-Based Approach
Evolving distributed systems are made of several physical devices distributed through a network and a set of functionalities or applications hosted by the physical devices. The configuration of the physical components may be modified through the time, hence the continuous evolving of the whole system. This should affect neither the hosted software components nor the global functionning of the whole system. The components of the systems are software components or physical components but their abstract models are considered with the aim of modelling and reasoning. We show that an event-based approach can be benefically used to model and verify this kind of evolving control systems. The proposed approach is first presented, then the CCTV case study is introduced and modelled. The resulting model is structured as a B abstract machine. The functional properties of the case study are captured, modelled and proved. The refinement technique of Event-B is used to introduce and prove some properties.
Christian Attiogbé
### Requirements Driven Data Warehouse Design: We Can Go Further
Data warehouses (
$\mathcal{D}\mathcal{W}$
) are defined as data integration systems constructed from a set of heterogeneous sources and user’s requirements. Heterogeneity is due to syntactic and semantic conflicts occurring between used concepts. Existing
$\mathcal{D}\mathcal{W}$
design methods associate heterogeneity only to data sources. We claim in this paper that heterogeneity is also associated to users’ requirements. Actually, requirements are collected from heterogeneous target users, which can cause semantic conflicts between concepts expressed. Besides, requirements can be analyzed by heterogeneous designers having different design skills, which can cause formalism heterogeneity. Integration is the process that manages heterogeneity in
$\mathcal{D}\mathcal{W}$
design. Ontologies are recognized as the key solution for ensuring an automatic integration process. We propose to extend the use of ontologies to resolve conflicts between requirements. A pivot model is proposed for integrating requirements schemas expressed in different formalisms. A
$\mathcal{D}\mathcal{W}$
design method is proposed for providing the target
$\mathcal{D}\mathcal{W}$
schema (star or snowflake schema) that meets a uniformed and consistent set of requirements.
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