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https://mxnet.apache.org/versions/0.11.0/how_to/model_parallel_lstm.html	# Training with Multiple GPUs Using Model Parallelism¶ Training deep learning models can be resource intensive. Even with a powerful GPU, some models can take days or weeks to train. Large long short-term memory (LSTM) recurrent neural networks can be especially slow to train, with each layer, at each time step, requiring eight matrix multiplications. Fortunately, given cloud services like AWS, machine learning practitioners often have access to multiple machines and multiple GPUs. One key strength of MXNet is its ability to leverage powerful heterogeneous hardware environments to achieve significant speedups. There are two primary ways that we can spread a workload across multiple devices. In a previous document, we addressed data parallelism, an approach in which examples within a batch are divvied among the available devices. With data parallelism, each device stores a complete copy of the model. Here, we explore model parallelism, a different approach. Instead of splitting the batch among the devices, we partition the model itself. Most commonly, we achieve model parallelism by assigning the parameters (and computation) of different layers of the network to different devices. In particular, we will focus on LSTM recurrent networks. LSTMS are powerful sequence models, that have proven especially useful for natural language translation, speech recognition, and working with time series data. For a general high-level introduction to LSTMs, see the excellent tutorial by Christopher Olah. For a working example of LSTM training with model parallelism, see example/model-parallelism-lstm/. ## Model Parallelism: Using Multiple GPUs As a Pipeline¶ Model parallelism in deep learning was first proposed for the extraordinarily large convolutional layer in GoogleNet. From this implementation, we take the idea of placing each layer on a separate GPU. Using model parallelism in such a layer-wise fashion provides the benefit that no GPU has to maintain all of the model parameters in memory. In the preceding figure, each LSTM layer is assigned to a different GPU. After GPU 1 finishes computing layer 1 for the first sentence, it passes its output to GPU 2. At the same time, GPU 1 fetches the next sentence and starts training. This differs significantly from data parallelism. Here, there is no contention to update the shared model at the end of each iteration, and most of the communication happens when passing intermediate results between GPUs. In the current implementation, the layers are defined in lstm_unroll(). Implementing model parallelism requires knowledge of the training task. Here are some general heuristics that we find useful: • To minimize communication time, place neighboring layers on the same GPUs. • Be careful to balance the workload between GPUs. • Remember that different kinds of layers have different computation-memory properties. Let’s take a quick look at the two pipelines in the preceding diagram. They both have eight layers with a decoder and an encoder layer. Based on our first principle, it’s unwise to place all neighboring layers on separate GPUs. We also want to balance the workload across GPUs. Although the LSTM layers consume less memory than the decoder/encoder layers, they consume more computation time because of the dependency of the unrolled LSTM. Thus, the partition on the left will be faster than the one on the right because the workload is more evenly distributed. Currently, the layer partition is implemented in lstm.py and configured in lstm_ptb.py using the group2ctx option. ## Apply Bucketing to Model Parallelism¶ To achieve model parallelism while using bucketing, you need to unroll an LSTM model for each bucket to obtain an executor for each. For details about how the model is bound, see lstm.py. On the other hand, because model parallelism partitions the model/layers, the input data has to be transformed/transposed to the agreed shape. For more details, see bucket_io.	{"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": 0.3357135057449341, "perplexity": 1284.0578633236462}, "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/1674764500041.2/warc/CC-MAIN-20230202232251-20230203022251-00082.warc.gz"}
http://www.gradesaver.com/textbooks/science/chemistry/chemistry-the-central-science-13th-edition/chapter-1-introduction-matter-and-measurement-additional-exercises-page-38/1-67c	## Chemistry: The Central Science (13th Edition) In part A, the answer showed that there are 386,241,600 meters between the earth and the moon. However, because this problem asks how long it would take to travel to the moon and back, that number must be doubled. $386,241,600 meters\times2=772483200 meters$ The speed of light is given in meters per second already, so there is no need for unit conversion. To find how many seconds it will take, divide 772483200 meters by the speed of light,$3\times10^8 meters per second$ $772483200\div3\times10^8=2.574944 seconds$ Notice, the unit meters cancel out, making the answer in the desired unit, seconds.	{"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": 0.9162328243255615, "perplexity": 341.6291118294855}, "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-2017-09/segments/1487501172000.93/warc/CC-MAIN-20170219104612-00022-ip-10-171-10-108.ec2.internal.warc.gz"}
https://www.jobilize.com/precalculus/section/using-the-factor-theorem-to-solve-a-polynomial-equation-by-openstax?qcr=www.quizover.com	# 5.5 Zeros of polynomial functions Page 1 / 14 In this section, you will: • Evaluate a polynomial using the Remainder Theorem. • Use the Factor Theorem to solve a polynomial equation. • Use the Rational Zero Theorem to find rational zeros. • Find zeros of a polynomial function. • Use the Linear Factorization Theorem to find polynomials with given zeros. • Use Descartes’ Rule of Signs. • Solve real-world applications of polynomial equations A new bakery offers decorated sheet cakes for children’s birthday parties and other special occasions. The bakery wants the volume of a small cake to be 351 cubic inches. The cake is in the shape of a rectangular solid. They want the length of the cake to be four inches longer than the width of the cake and the height of the cake to be one-third of the width. What should the dimensions of the cake pan be? This problem can be solved by writing a cubic function and solving a cubic equation for the volume of the cake. In this section, we will discuss a variety of tools for writing polynomial functions and solving polynomial equations. ## Evaluating a polynomial using the remainder theorem In the last section, we learned how to divide polynomials. We can now use polynomial division to evaluate polynomials using the Remainder Theorem . If the polynomial is divided by $\text{\hspace{0.17em}}x–k,\text{\hspace{0.17em}}$ the remainder may be found quickly by evaluating the polynomial function at $\text{\hspace{0.17em}}k,\text{\hspace{0.17em}}$ that is, $\text{\hspace{0.17em}}f\left(k\right)\text{\hspace{0.17em}}$ Let’s walk through the proof of the theorem. Recall that the Division Algorithm states that, given a polynomial dividend $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ and a non-zero polynomial divisor $\text{\hspace{0.17em}}d\left(x\right)\text{\hspace{0.17em}}$ where the degree of $\text{\hspace{0.17em}}\text{\hspace{0.17em}}d\left(x\right)\text{\hspace{0.17em}}$ is less than or equal to the degree of $\text{\hspace{0.17em}}f\left(x\right)$ , there exist unique polynomials $\text{\hspace{0.17em}}q\left(x\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}r\left(x\right)\text{\hspace{0.17em}}$ such that $\text{\hspace{0.17em}}f\left(x\right)=d\left(x\right)q\left(x\right)+r\left(x\right)$ If the divisor, $\text{\hspace{0.17em}}d\left(x\right),\text{\hspace{0.17em}}$ is $\text{\hspace{0.17em}}x-k,\text{\hspace{0.17em}}$ this takes the form $f\left(x\right)=\left(x-k\right)q\left(x\right)+r$ Since the divisor $\text{\hspace{0.17em}}x-k\text{\hspace{0.17em}}$ is linear, the remainder will be a constant, $\text{\hspace{0.17em}}r.\text{\hspace{0.17em}}$ And, if we evaluate this for $\text{\hspace{0.17em}}x=k,\text{\hspace{0.17em}}$ we have $\begin{array}{ccc}\hfill f\left(k\right)& =& \left(k-k\right)q\left(k\right)+r\hfill \\ & =& 0\cdot q\left(k\right)+r\hfill \\ & =& r\hfill \end{array}$ In other words, $\text{\hspace{0.17em}}f\left(k\right)\text{\hspace{0.17em}}$ is the remainder obtained by dividing $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ by $\text{\hspace{0.17em}}x-k.\text{\hspace{0.17em}}$ ## The remainder theorem If a polynomial $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ is divided by $\text{\hspace{0.17em}}x-k,\text{\hspace{0.17em}}$ then the remainder is the value $\text{\hspace{0.17em}}f\left(k\right).\text{\hspace{0.17em}}$ Given a polynomial function $\text{\hspace{0.17em}}f,$ evaluate $\text{\hspace{0.17em}}f\left(x\right)\text{\hspace{0.17em}}$ at $\text{\hspace{0.17em}}x=k\text{\hspace{0.17em}}$ using the Remainder Theorem. 1. Use synthetic division to divide the polynomial by $\text{\hspace{0.17em}}x-k.\text{\hspace{0.17em}}$ 2. The remainder is the value $\text{\hspace{0.17em}}f\left(k\right).\text{\hspace{0.17em}}$ ## Using the remainder theorem to evaluate a polynomial Use the Remainder Theorem to evaluate $\text{\hspace{0.17em}}f\left(x\right)=6{x}^{4}-{x}^{3}-15{x}^{2}+2x-7\text{\hspace{0.17em}}$ at $\text{\hspace{0.17em}}x=2.\text{\hspace{0.17em}}$ To find the remainder using the Remainder Theorem, use synthetic division to divide the polynomial by $\text{\hspace{0.17em}}x-2.\text{\hspace{0.17em}}$ The remainder is 25. Therefore, $\text{\hspace{0.17em}}f\left(2\right)=25.\text{\hspace{0.17em}}$ Use the Remainder Theorem to evaluate $\text{\hspace{0.17em}}f\left(x\right)=2{x}^{5}-3{x}^{4}-9{x}^{3}+8{x}^{2}+2\text{\hspace{0.17em}}$ at $\text{\hspace{0.17em}}x=-3.\text{\hspace{0.17em}}$ $\text{\hspace{0.17em}}f\left(-3\right)=-412\text{\hspace{0.17em}}$ ## Using the factor theorem to solve a polynomial equation The Factor Theorem is another theorem that helps us analyze polynomial equations. It tells us how the zeros of a polynomial are related to the factors. Recall that the Division Algorithm. $f\left(x\right)=\left(x-k\right)q\left(x\right)+r$ If $\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is a zero, then the remainder $\text{\hspace{0.17em}}r\text{\hspace{0.17em}}$ is $\text{\hspace{0.17em}}f\left(k\right)=0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}f\left(x\right)=\left(x-k\right)q\left(x\right)+0\text{\hspace{0.17em}}$ or $\text{\hspace{0.17em}}f\left(x\right)=\left(x-k\right)q\left(x\right).\text{\hspace{0.17em}}$ Notice, written in this form, $\text{\hspace{0.17em}}x-k\text{\hspace{0.17em}}$ is a factor of $\text{\hspace{0.17em}}f\left(x\right).\text{\hspace{0.17em}}$ We can conclude if $\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is a zero of $\text{\hspace{0.17em}}f\left(x\right),\text{\hspace{0.17em}}$ then $\text{\hspace{0.17em}}x-k\text{\hspace{0.17em}}$ is a factor of $f\left(x\right).\text{\hspace{0.17em}}$ if sin15°=√p, express the following in terms of p prove sin²x+cos²x=3+cos4x the difference between two signed numbers is -8.if the minued is 5,what is the subtrahend the difference between two signed numbers is -8.if the minuend is 5.what is the subtrahend jeramie what are odd numbers numbers that leave a remainder when divided by 2 Thorben 1,3,5,7,... 99,...867 Thorben 7%2=1, 679%2=1, 866245%2=1 Thorben the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms. if a=3, b =4 and c=5 find the six trigonometric value sin Ans pls how do I factorize x⁴+x³-7x²-x+6=0 in a function the input value is called how do I test for values on the number line if a=4 b=4 then a+b= a+b+2ab Kin commulative principle a+b= 4+4=8 Mimi If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8. Tariq what are examples of natural number an equation for the line that goes through the point (-1,12) and has a slope of 2,3 3y=-9x+25 Ishaq show that the set of natural numberdoes not from agroup with addition or multiplication butit forms aseni group with respect toaaddition as well as multiplication x^20+x^15+x^10+x^5/x^2+1 evaluate each algebraic expression. 2x+×_2 if ×=5	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 47, "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": 0.5980746746063232, "perplexity": 395.9198494700331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00398.warc.gz"}
http://math.stackexchange.com/users/10676/user10676?tab=summary	user10676 Reputation 4,950 Next privilege 5,000 Rep. Approve tag wiki edits 2 11 29 Impact ~77k people reached • 0 posts edited 37 Why can't you flatten a sphere? 20 Interesting “real life” applications of serious theorems 18 Visually deceptive “proofs” which are mathematically wrong 9 Cesaro summable implies Abel summable 9 Why does the ideal $(a+bi)$ have index $a^2+b^2$ in $\mathbb{Z}[i]$? ### Reputation (4,950) +70 Decompose $V \otimes V \otimes V$ into irreducible representations of $SL_2(\mathbb{R})$ +20 Cesaro summable implies Abel summable +5 What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$? +5 Cyclotomy in extensions of $\mathbb{Q}_p$ ### Questions (34) 19 What is the difference between $\ell$-adic cohomology and cohomology with coefficient in $Z_\ell$? 14 Multiplicative norm on $\mathbb{R}[X]$. 13 Why is $\mathbb{C}_p$ isomorphic to $\mathbb{C}$? 12 Is there a group between $SO(2,\mathbb{R})$ and $SL(2,\mathbb{R})$? 12 What is the idea of a monodromy? ### Tags (109) 45 general-topology × 6 16 linear-algebra × 11 38 abstract-algebra × 13 15 reference-request × 6 29 real-analysis × 14 15 matrices × 5 28 sequences-and-series × 7 13 divergent-series × 2 19 algebraic-geometry × 13 12 number-theory × 12 ### Accounts (2) Mathematics 4,950 rep 21129 MathOverflow 280 rep 17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8052857518196106, "perplexity": 4528.116402274824}, "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/1464049276964.77/warc/CC-MAIN-20160524002116-00157-ip-10-185-217-139.ec2.internal.warc.gz"}
http://mathhelpforum.com/trigonometry/24414-area-triangle-3-help-plz.html	# Math Help - AREA OF A TRIANGLE <3 help plz 1. ## AREA OF A TRIANGLE <3 help plz find the area of traingle ABC if a = 10cm ,b = 3cm and c= 9cm and i have my final exam tomorrow... so if u want to help me tonight for a while private message me we can work on msn together! yayyy ^_^ lolll 2. Originally Posted by Noelle find the area of traingle ABC if a = 10cm ,b = 3cm and c= 9cm and i have my final exam tomorrow... so if u want to help me tonight for a while private message me we can work on msn together! yayyy ^_^ lolll Hero's (Heron's?) formula says that the area of a triangle is $A = \sqrt{s(s - a)(s - b)(s - c)}$ where $s = \frac{a + b + c}{2}$ is called the semi-perimeter. -Dan 3. Originally Posted by topsquark Hero's (Heron's?) Heron's -- You can also combine Law of cosine and Law of sines to get the area, but I prefer to use Heron's Formula. 4. ## rawr so is it supposed to be 10+3+9 = 22/2 = 11?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.7955167889595032, "perplexity": 2135.3195464446376}, "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-2016-30/segments/1469257824570.25/warc/CC-MAIN-20160723071024-00171-ip-10-185-27-174.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-solve-x-2y-6-and-x-y-2	Algebra Topics # How do you solve x - 2y = -6 and -x + y = 2? Jun 9, 2017 I got: $x = 2$ $y = 4$ #### Explanation: Have a look: Jun 9, 2017 $x = 2 \mathmr{and} y = 4$ #### Explanation: Make $x$ the subject of both equations: $x = 2 y - 6 \text{ and } x = y - 2$ The value of $x$ is the same, so if: $\text{ } x = x$ then: $2 y - 6 = y - 2 \text{ } \leftarrow$ solve for $y$ $2 y - y = - 2 + 6$ $y = 4$ $x = 2 \left(4\right) - 6$ $x = 8 - 6$ $x = 2$ Jun 9, 2017 $x = 2$ $y = 4$ #### Explanation: We could also solve this problem using substitution. Solve the 1st equation for $x$: $x - 2 y = - 6$ $x = 2 y - 6$ Substitute the above into the 2nd equation and solve for $y$: $- x + y = 2$ $- \left(2 y - 6\right) + y = 2$ $- 2 y + 6 + y = 2$ $- y = - 4$ $y = 4$ Substitute $y$ into the 1st equation and solve for $x$: $x - 2 y = - 6$ $x - 2 \left(4\right) = - 6$ $x = 2$ ##### Impact of this question 1551 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 30, "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": 0.7865341305732727, "perplexity": 2439.6588533773606}, "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/1575540536855.78/warc/CC-MAIN-20191212023648-20191212051648-00073.warc.gz"}
https://hal.archives-ouvertes.fr/hal-00332912/	Clifford Fourier Transform for Color Image Processing Abstract : The aim of this paper is to define a Clifford Fourier transform that is suitable for color image spectral analysis. There have been many attempts to define such a transformation using quaternions or Clifford algebras. We focus here on a geometric approach using group actions. The idea is to generalize the usual definition based on the characters of abelian groups by considering group morphisms from $R^2$ to spinor groups Spin(3) and Spin(4). The transformation we propose is parameterized by a bivector and a quadratic form, the choice of which is related to the application to be treated. A general definition for 4D signal defined on the plane is also given; for particular choices of spinors it coincides with the definitions of S.Sangwine and T. Bülow. Keywords : Document type : Book sections Domain : Cited literature [14 references] https://hal.archives-ouvertes.fr/hal-00332912 Contributor : Christophe Saint-Jean <> Submitted on : Wednesday, June 29, 2011 - 9:36:27 AM Last modification on : Wednesday, November 29, 2017 - 10:30:00 AM File version_ultime.pdf Files produced by the author(s) Identifiers • HAL Id : hal-00332912, version 3 Citation Thomas Batard, Michel Berthier, Christophe Saint-Jean. Clifford Fourier Transform for Color Image Processing. Bayro-Corrochano, Eduardo; Scheuermann, Gerik. Geometric Algebra Computing, Springer Verlag, pp.135-162, 2010, Engineering and Computer Science. ⟨hal-00332912v3⟩ Record views	{"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": 0.8200700879096985, "perplexity": 1482.7225583652078}, "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-2019-43/segments/1570987822098.86/warc/CC-MAIN-20191022132135-20191022155635-00546.warc.gz"}
http://math.stackexchange.com/questions/242657/relationship-between-autg-and-symmetric-group-on-g	# Relationship between $Aut(G)$ and Symmetric group on $G$ I have read that $Aut(G)$ is a subset of $S_g$. So say I have a group $G = \{1, 2, 3\}$ for example. Then $S_G = S_3$ is the group of all permutation of the three elements of $G$. But I don't see why $Aut(G)$ is a subset of $S_G$ as opposed to $Aut(G) = S_G$. Each element of $S_3$ maps each element of $G$ to an element of $G$. I.e. each element is an automorphism. So why is $Aut(G) \subset S_3$ instead of $Aut(G) = S_3$? - $\,S_g\,$ is a rather unusual notation. I'd rather go with $\,\operatorname{Sym}_G\,$ , or at least $\,S_G\,$ – DonAntonio Nov 22 '12 at 15:50 When you say, "I have a group $G=\{1,2,3\}$." That is not a group, it is a sets of three elements. A group is a set with an operation. – Thomas Andrews Nov 22 '12 at 16:32 Not every permutation of $G$ is an automorphism. For example, automorphisms always fix the identity, but there are definitely permutations of $G$ that do not fix the identity if $\|G\| > 1$. – Mikko Korhonen Nov 22 '12 at 17:15 There are elements in $\,\operatorname{Sym}_G\,$ which are not automorphisms of the group $\,G\,$, say the permutation $\,(01)\,$ in $\,S_3\,$ is not an automorphism of cyclic group $\,\Bbb Z_3:=\Bbb Z/3\Bbb Z:=\{0,1,2\}\,$, with operation modulo $\,3\,$ - $0 \to 1$, $1 \to 0$, $2 \to 2$. It maps each elements of $G$ to an element of $G$. So why is it not an automorphism? – sonicboom Nov 22 '12 at 16:01 Because an automorphism of a group must first be a homomorphism of groups and, as such, it must map the group's unit (or neutral element) to itself. Here, it must be that $\,0\to 0\,$, otherwise it is not a homomorphism and, thus, not an automorphism. – DonAntonio Nov 22 '12 at 16:28 Cheers, I get it now. Just wondering, what is $Aut(G)$ in the case of my example in the original post...is it the elements $()$ and $(2\, 3)$? These are the only ones that fix $1$, which is the identity element in my group $G$? – sonicboom Nov 22 '12 at 16:51 Well, in your example you have a set with three elements, what'd be a cyclic group of order three...which is exactly what is $\,G\,$ in my answer! Here, $\,\|Aut(G)\|=2\,$ , and the only two automorphisms are: $$0\to 0\,\,,\,\,1\to 1\,\,,\,\,2\to 2$$and $$0\to 0\,\,,\,\,1\to 2\,\,,\,\,2\to 1$$ – DonAntonio Nov 22 '12 at 17:04 Note however, that mapping $0$ to itself is not all that is required for a permutation to be an automorphism in general. It just happens that all counterexamples are for groups with at least 4 elements. – Henning Makholm Nov 22 '12 at 17:08 (I'm assuming that $G$ here is a group, but I now notice that you're not saying so explicitly. If $G$ is not considered to be a group, then you have to ask what does $\operatorname{Aut}(G)$ mean at all?) Merely "mapping each element of $G$ to an element of $G$" is not enough to be an automorphism. An automorphism is a bijection $G\to G$, which is also a homomorphism. Most elements of $S_3$ will not correspond to homomorphisms $G\to G$. - Sorry, I'ved edited in that $G$ is a group. – sonicboom Nov 22 '12 at 15:58	{"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": 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": 0.8746305704116821, "perplexity": 146.73192408728391}, "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-2016-22/segments/1464051299749.12/warc/CC-MAIN-20160524005459-00033-ip-10-185-217-139.ec2.internal.warc.gz"}
http://clay6.com/qa/48781/find-the-mean-deviation-about-the-mean-for-data-	# Find the mean deviation about the mean for data : $\begin{array}{1 1}(A)\;157.92\\(B)\;3\\(C)\;2\\(D)\;7\end{array}$ Step 2: Mean $\bar{x} = A+ \large\frac{\sum f_i d_i}{\sum f_i} $$\times h \qquad= 350+\large\frac{4}{50}$$ \times 100$ $\qquad= 350+8$ $\bar {x} =358$ Step 3: Mean deviation about the mean $= \large\frac{\sum f_i \|x_i -\bar{x}\|}{\sum f_i}$ $\qquad= \large\frac{7896}{50}$$=157.92$ Hence A is the correct answer.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.999985933303833, "perplexity": 6733.600600261279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887621.26/warc/CC-MAIN-20180118210638-20180118230638-00321.warc.gz"}
https://math.stackexchange.com/questions/3229905/finding-lim-limits-x-to-infty-frac-sqrt3x3xx/3229915	# Finding $\lim\limits _{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}$ $$\lim\limits _{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}$$ I have to resolve this limit, I tried factoring out x, I tried rewriting $$x^3+x$$ as $$x^3(1+ \frac{x}{x^3})$$ and it doesn't seem to cancel. What should I do? • Note that $\sqrt[3]{x^3+x}= x\sqrt[3]{1 + \frac{1}{x^2}}$. Then cancel the $x$ here with the $x$ in the denominator and go from there. – Minus One-Twelfth May 17 at 20:00 $$\lim_{x\to-\infty} \frac{\sqrt[3]{x^3+x}}{x}=\lim_{x\to-\infty} \sqrt[3]{\frac{x^3+x}{x^3}} =\lim_{x\to-\infty} \sqrt[3]{1+\frac{1}{x^2}} = \sqrt[3]{1+\lim_{x\to-\infty}\frac{1}{x^2}}=1$$ \begin{align} \lim_{x\to -\infty} \frac{\sqrt[\,3]{x^3+x}}{x} =& \lim_{x\to -\infty} \frac{\sqrt[\,3]{x^3\cdot(1+1/x^2)}}{x} \\ =& \lim_{x\to -\infty} \frac{\sqrt[\,3]{x^3}\cdot\sqrt[\,3]{(1+1/x^2)}}{x} \\ =& \lim_{x\to -\infty} \frac{x\cdot\sqrt[\,3]{(1+1/x^2)}}{x} \\ =& \lim_{x\to -\infty} {\sqrt[\,3]{(1+1/x^2)}} \\ =& {\sqrt[\,3]{\lim_{x\to -\infty} (1+1/x^2)}} \\ =& {\sqrt[\,3]{(1+\lim_{x\to -\infty} (1/x^2))}} \\ =& {\sqrt[\,3]{(1+0)}} \\ =& {\sqrt[\,3]{1}} \\ =& 1 \end{align}	{"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": 5, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 1.0000100135803223, "perplexity": 1536.0876242186375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670597.74/warc/CC-MAIN-20191120162215-20191120190215-00487.warc.gz"}
https://spectre-code.org/structCce_1_1PreSwshDerivatives_3_01Tags_1_1ComplexInertialRetardedTime_01_4.html	SpECTRE v2022.09.02 Cce::PreSwshDerivatives< Tags::ComplexInertialRetardedTime > Struct Reference Copies the values of the inertial retarded time into a spin-weighted container so that spin-weighted derivatives can be taken. More... #include <PreSwshDerivatives.hpp> ## Public Types using pre_swsh_derivative_tags = tmpl::list<> using swsh_derivative_tags = tmpl::list<> using integrand_tags = tmpl::list<> using return_tags = tmpl::list< Tags::ComplexInertialRetardedTime > using argument_tags = tmpl::list< Tags::InertialRetardedTime > ## Static Public Member Functions static void apply (const gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 0 > > * > complex_inertial_retarded_time, const Scalar< DataVector > &inertial_retarded_time) ## Detailed Description Copies the values of the inertial retarded time into a spin-weighted container so that spin-weighted derivatives can be taken. The documentation for this struct was generated from the following file: • src/Evolution/Systems/Cce/PreSwshDerivatives.hpp	{"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": 0.3150520622730255, "perplexity": 24917.853039377755}, "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/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00420.warc.gz"}
http://www.r-bloggers.com/search/Finance/page/60/	# 729 search results for "Finance" Read more » ## John Chambers, the inventor of S, added reference classes to R… February 26, 2011 By John Chambers, the inventor of S, added reference classes to R 2.12, and oh boy are they fun to look at! What you see in the picture above is a “Hello World” web application for R. It’s written using the Rack R package (not unlike Ruby’s Rac... Read more » ## Interest Rates’ Influence on 1987 February 21, 2011 By One aspect of 1987 that does not deserve enough attention is interest rates. Higher interest rates constrain economic activity and compete with other investments. As seen in the chart below, the US 10year Treasury rate climbed 40% from 7% t... Read more » ## Silver and Russell 2000 February 16, 2011 By When I find a chart that looks like this, I always like to explore a little further. via StockCharts.com I pull it into R and try to find anything worthwhile. I do not find anything, except that I do not want to be trading both in the same direc... Read more » ## R, the DJIA, and M1 Money Multiplier (MULT) February 13, 2011 By Description:My explorations with the FRED (St Louis Financial Reserve Database) in R have yielded some interesting plots, charts and graphs. And some questions… Charts with Explanations: Yes, I know, the axes are a mess, and the site’s style sheet ... Read more » ## R, the DJIA, and M1 Money Multiplier (MULT) February 13, 2011 By Description:My explorations with the FRED (St Louis Financial Reserve Database) in R have yielded some interesting plots, charts and graphs. And some questions…Charts with Explanations: Yes, I know, the axes are a mess, and the site’s style sheet doesn’t play well with the chart image. I’ll look into that “pretty-ing up” stuff... Read more » ## When will my papers appear as references (if they do…) ? February 10, 2011 By Following my post on citations in academic journals, I wanted to go one step further in the understanding of the dynamic of citations. So here, the dataset looks like that: for each article, we have the name of the journal, the year of publicatio... Read more » ## Think academic journals look the same ? Well, some do… February 8, 2011 By We have seen yesterday that finding an optimal strategy to publish is not that simple. And actually, it can be even more difficult in the case the journal rejects the paper (not because it is not correct, but because "it does not fit" with the stan... Read more » ## The R-Files: Dirk Eddelbuettel February 4, 2011 By "The R-Files" is an occasional series from Revolution Analytics, where we profile prominent members of the R Community. Name: Dirk Eddelbuettel Background: Ph.D. (EHESS, France), Quantitative Analyst Nationality: Canadian Years Using R: About 15 Known for: RQuantlib, Rcpp/RInside, R packaging for Debian/Ubuntu, Task Views for Finance and HPC, CRANberries Dirk Eddelbuettel is an active member of the R community... Read more » ## Slides and replay for "Portfolio design, optimization and stability analysis" January 27, 2011 By Thanks to everyone who attended yesterday's webinar, "Portfolio design, optimization and stability analysis", presented by Diethelm Würtz of the Rmetrics Association and sponsored by Revolution Analytics, Sybase, Finance Online and NeuralTechSoft. (And thanks in particular for your patience for the last start -- in a perfect demonstration of Murphy's law a microphone failed moments before the scheduled start.) If... Read more »	{"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": 0.3415028154850006, "perplexity": 6460.689372759744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535922763.3/warc/CC-MAIN-20140909044907-00165-ip-10-180-136-8.ec2.internal.warc.gz"}
https://iwaponline.com/wst/article-abstract/34/5-6/163/6217/Effect-of-nickel-II-on-the-biomass-yield-of-the?redirectedFrom=fulltext	Biomass yield of microorganisms is important in applied microbiology since it is the ultimate factor determining the amount of product produced regardless of whether product is growth-linked or not. In the case of environmental microbiology the opposite is true and minimizing the biomass produced, or the sludge in the relevant jargon, often is the prime goal. In this paper, a unique means of manipulating the microbial biomass yield of a heterogeneous culture to fulfil either of the two goals is presented. 5.0 mgl−1 Ni(II) in the feed composition to a completely mixed, once- through, activated sludge was found to induce the observed biomass yield of the microbial culture developed from sewage. As compared with the base-line study without Ni(II), where the reactor received synthetic wastewater only, true biomass yield was found to have increased along with the increased decay constant with the net effect of lowering observed biomass yield drastically at lower dilution rates and increasing it over that observed in the base-line study at higher dilution rates. At 10.0 mgl−1 influent Ni(II) concentration the culture conditions almost reverted back to the base- line study and at 25 mgl−1 Ni(II) concentration a truly steady-state condition could not be attained. This content is only available as a PDF.	{"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": 0.9433327913284302, "perplexity": 3234.8968489621884}, "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/1600400188841.7/warc/CC-MAIN-20200918190514-20200918220514-00311.warc.gz"}
https://blog.ifem.co.uk/blog/2015/10/	Categories ## An Evening of Nerdy-ness Yesterday evening I went to the excellent Festival of The Spoken Nerd in Derby, but before thsat I had the pleasure of seeing Alex Bellos speak at a school in Leicestershire. This post is just going to mention a few interesting things from both of these events. Alex Bellos was a very entertaining speaker to listen to as he is evidently so passionate about people understanding the beauty of mathematics. Alex opened his talk with a logic puzzle that he had featured in one of his early Guardian Puzzle blog posts: Find the odd one out in the symbols below This puzzle was orignally due to Tanya Khovanova who had written about it here. It is intended as a piece of fun to emphasise the intrinsic issue of odd-one-out puzzles. Namely, that they tend to be focussed around a particular way of thinking (Alex provides a nice example in his post) when in fact many could be seen as the odd one out for different reasons. In the puzzle above, the odd one out is actually the one on the left hand side by virtua of not being able to be called the odd one out – an interesting philosophical dilemma there! One thing I found particularly interesting in Alex’s talk was his discussion of the Sieve of Erastothenes. If I do this in school I tend to have a 10 by 10 grid of the numbers 1 to a 100. I had never thought of arranging them instead in 6 rows, as shown below. This leads to some very interesting patterns when you cross out numbers. He then described the Ulam Spiral, devised by Stanislaw Ulam where numbers are arranged in a spiral and primes highlighted generating a pattern where primes lie on diagonal lines. I’m going to write some MATLAB code to generate these I think and write a bit more about them in the future. Alex also talked about the results of his internet survey to find the world’s favourite number; which turns out to be 7. He showed a nice annimation about this which is available on Youtube Following Alex’s session I had a fairly mad dash to Derby in horrendous weather to go and see Festival of The Spoken Nerd – if you haven’t seen them live before I can’t recommend it enough. It was a great evening. I really liked the visual demonstration of the modes of vibration of a metal plate. These are known as Chladni figures after the scientist Ernst Chladni who first published his work in 1787. Festival of The Spoken Nerd have plenty more dates in their UK tour, I urge you to see if there is one local to you on their webpage and if there is go. You won’t be disappointed, I’ve seen them a few times now and it is always a very entertaining evening – writing about the show can’t do it justice. Categories ## #mathsjournalclub Third Poll Following on from our second successful discussion last week it is time to vote on the article for the next discussion. The next discussion will take place at 8pm on Monday the 7th of December. I know everyone gets busy in the run up to Christmas but I hope that you can all still take part. Three article from the last poll have been rolled over to this one as two of them were tied in the number of votes. As usual, the titles and abstracts are below and the poll is available here • Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Examinations; Ellie Darlington (Teaching Mathematics and its Applications) – This article describes part of a study which investigated the role of questions in students’ approaches to learning mathematics at the secondary/tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics questions in England and Wales to focus on requiring students to demon- strate a routine use of procedures, whereas those in first-year undergraduate mathematics primarily required students to be able to draw implications, conclusions and to justify their answers and make conjectures.While these findings confirm the need for reforms of examinations at this level, questions must also be raised over the nature of undergraduate mathematics assessment, since it is sometimes possible for students to be awarded a first- class examination mark solely through stating known facts or reproducing something verbatim from lecture notes. • “‘Ability’ ideology and its consequential practices in primary mathematics” by Rachel Marks (Proceedings of the BSRLM 31 (2)) – ‘Ability’ is a powerful ideology in UK education, underscoring common practices such as setting. These have well documented impacts on pupils’ attainment and attitude in mathematics, particularly at the secondary school level. Less well understood are the impacts in primary mathematics. Further, there are a number of consequential practices of an ability ideology which may inhibit pupils’ learning. This paper uses data from one UK primary school drawn from my wider doctoral study to elucidate three such consequential practices. It examines why these issues arise and the impacts on pupils. The paper suggests that external pressures may bring practices previously seen in secondary mathematics into primary schools, where the environment intensifies the impacts on pupils. • “Train Spotters Paradise” by Dave Hewitt (Mathematics Teaching 140) – Mathematical exploration often focuses on looking at numerical results, finding patterns and generalising. Dave Hewitt suggests that there might be more to mathematics than this. • “Relational Understanding and Instrumental Understanding” by Richard Skemp (Mathematics Teaching 77) • “Knowing and not knowing how a task for use in a mathematics classroom might develop” by Colin Foster, Mike Owlerton and Anne Watson (Mathematics Teaching 247) – Participants at the July 2014 Institute of Mathematics Pedagogy (IMP14) engaged in a wide range of mathematical tasks and a great deal of pedagogical discussion during their four days last summer. Towards the end of IMP14 a conversation began regarding how much knowledge about a task a teacher needs to have before feeling comfortable taking it into the classroom. I’m looking forward to seeing which article is selected as I haven’t read all of these yet! Categories ## A Pi Curiosity I’m quite sad that I missed this on pi day this year but I thought I should share it now.. For this years (special) pi day Wolfram Research have produced a web page mypiday.com that enables you to find the location of your birthday in the digits of pi – it is well known that any date will appear within the digits. Here is the location of my birthday: Stephen Wolfram also wrote a fairly interesting blog post about the creation of this site using the capabilities of the new Wolfram Language. Categories ## A Nice Trapezium Rule Question I’ve been doing preparation for the Oxford MAT exam with a couple of my Year 13s and in the 2008 paper I came across this very nice question about the Trapezium Rule. I really like this question as to answer it you need to have more understanding about how the trapezium rule actually works than standard A-Level questions on this subject. Invariably they are just pure “plug some numbers in and crunch them” questions which lead to the wide perception that numerical methods are boring. Of course being a numerical analyst I really don’t agree with this perception, but agree that their presentation in the current A-Level course doesn’t help with this. The above question is nice in that it combines knowledge of the performance of the trapezium rule with graph transformations. I will leave you to work out the answer, the small Geogebra file I have written may help you visualise what is happening… Categories ## #mathsjournalcub Discussion Number 2 Last night we discussed “Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts” (available online here). Like last time it was a very fast paced, interesting discussion. I really enjoyed the discussion and some great points were made by lots of people. Have a look through the storify below – I have hopefully put in all the points discussed. Stephen Cavadino (@srcav) wrote a blog post after the discussion trying to categorise études which I recommend reading. James Pearce (@MathsPadJames) also wrote a post before hand (which unfortunately I didn’t see until about half way through the chat) looking at commonalities between different types of mathematical études – give that I read too!! I would have promoted it more during the discussion if I had seen it earlier. Thank you to everyone who took part, and I hope you can make the next one which will be on Monday the 7th of December. The poll for voting will open for a week next Monday. If you would like to submit an article please tweet the details to me by this Friday 23rd October. https://storify.com/tajbennison/mathsjournalclub-discussion-number-2 Categories ## Carnival of Mathematics 127 Following on from last months excellent collection of posts in the Carnival of Mathematics 126 from Stephen at cavmaths it is my turn to host this blog carnival. The Carnival of Mathematics is a monthly blogging round up that is organised by The Aperiodical (check it out if for some reason you haven’t before) and has a different host each month. It is tradition to start the post with some interesting facts about the number 127 so here goes…. • The most interesting fact about 127, I think, is that it is a Mersenne Prime. This means that 127 is a prime number of the form $$2^n-1$$ with $$n$$ here being 7. Since 7 is also a Mersenne prime 127 is known as a double Mersenne prime, that is, it is of the form $$2^{2^n-1} -1$$. • 127 is a number that appears in the list of centred hexagonal numbers. Coincidentally I have written a post concerning these numbers when I discussed nRich’s Steel Cables problem here. • Since 127 is a centred hexagonal number and prime it is Cuban prime.Namely it is a solution of the equation $$\frac{x^3-y^3}{x-y}$$ where $$x=y+1$$ and $$y>0$$. This can be simplified so that Cuban primes are prime numbers of the form $$3y^2+3y+1$$. • 127 is a cyclic number. This means that the Euler totient of 127 and 127 are co-prime. (Clearly all primes are cyclic.) • 127 is the 8th Motzkin number. For a particular value of $$n$$ the $$n-$$th Motzkin number is the number of different ways of drawing non-intersecting chords between $$n$$ points on a circle. • 127 is a polite number as it can be written as $$127 = 63 + 64$$. To start on the posts that make up this carnival I thought I would start with the following comic produced by Manan of MathMisery. This made me laugh a lot! His blog is one that I routinely keep an eye on and I also enjoyed his recent post entitled Executive Education Ganit Charcha submitted this really interesting article on Montgomery Modular Multiplication. I hadn’t heard of this algorithm before and I need to get round to coding it up soon – this article is very clear and written in a style ideal for being able to code it up. Shecky R shared a short post looking at a curious finding (made without modern calculating machines) of Pierre de Fermat in his post Get A Life! I enjoyed reading Tracy Herft’s post Unique Lesson… Polar Clocks. In it she describes a lesson she has developed for Year 7 students which she uses to link the topic of angles with fractions. The mathematician Nira Chamberlain has shared his poster about the black heroes of mathematics. He has created this for Black History Month (which happens to be October). I’m ashamed to say that I hadn’t heard about any of these before! This post by Evelyn Lamb (@evelynjlamb) concerning cutting letters of the alphabet featured a video by Katie Steckles of The Aperiodical. I love how Evelyn describes the “peculiar laziness” of mathematicians – it is certainly true!! R.J. Lipton has this great accessible post “Frogs and Lily Pads and Discrepancy” discussing Terence Tao’s recently announced proof of Paul Erdös’ Discrepancy conjecture. If you fancy some more of the detailed maths take a read of Terence’s post announcing his papers (and the other related posts). Tao is pretty rare amongst professional mathematicians in that as well as publishing in academic journals he also discusses his research in an open blog. Herminio L.A. submitted an interesting discussion of a calculation paradox in “Sabotage in the Stores”. I had recently seen this video on Youtube and it was nice to learn that someone had submitted it for inclusion in this carnival (I would have myself if no one else had). The animations that go with some of the (many) patterns in Pascal’s triangle are fantastic. Edmund Harriss has this post of beautiful animations of eigencurves of various matrices that are dependent on parameters in one entry. Edmund has also produced a colouring book with Alex Bellos titled “Snowflake, Seashell, Star” that taps in to the colouring craze at the moment. I can’t colour at all, but I am tempted to get this book, if only for the mathematical notes. He discussed the book here. Christian Perfect (@christianp) shared this article by Lior Pachter. This article concerns something that I am very passionate about – the discussion of unsolved mathematical problems at school. Lior has taken each year in the American Common Core and selected an unsolved mathematical problem whose description is accessible to students of that age. I particularly like how each unsolved problem is accompanied by a starter problem that is accessible by the students. I think discussion of unsolved problems in school is very important as far too often students think that everything in mathematics is known. It’s sad that students s of school age don’t typically get exposed to current research or unsolved problems. Diane has shared this problem from part of The Center of Maths’ Advanced Problem of the Week series. It’s quite a nice problem involving partial differentiation. This series provides a nice selection of problems to try, however some do require more area specific knowledge than others. Peter Rowlett (@peterrowlett) recently wrote this fascinating post about Mathematical Myths. E.T. Bell did much to create a series of myths about mathematicians and some of these feature in this post. There are extensive links in this post so it may take a while to read. During this month I enjoyed reading “The Nuts and Bolts of Writing Mathematics” by David Richeson and Cleve Moler’s blog (the first in a series of 4) on Dekker’s Algorithm. More recently Kris Boulton (@Kris_Boulton) had a great article about the importance of memorising times tables published in the TES. Personally my most involved blog post in the last month was the write up of my NQT advice workshop at #msthsconf5. This brings to an end this issue of the Carnival of Mathematics. The next edition is being hosted by Mike at Walking Randomly. If you haven’t before check out Mike’s blog, he regularly posts good articles about mathematical software. Categories Today is Ada Lovelace Day everyone! I think it is great that Ada Lovelaceis beginning to get the recognition she deserves. I can remember reading Ada’s notes on Babbage’s difference engine when I was in sixth form and being completely fascinated by them. The University of Nottingham have produced this great video about her: And there is a good article on the Guardian about why Ada Lovelace is important for women in STEM subjects. Hannah Fry (@FryRsquared) has also written a nice article that goes alongside her programme about Ada Lovelace. If you haven’t seen that yet it is definitely worth a watch. Categories ## #Mathsjournalclub Next Week Next Monday (19th October) at 8pm we have the second #mathsjournalclub discussion. This time (in case you don’t already know) we are looking at Colin Foster’s paper on “Mathematical études: embedding opportunities for developing procedural fluency within rich mathematical contexts”. I read the article through again on the train on Saturday night and enjoyed the read. • Would you be comfortable with removing all “drill” practice and relying on richer tasks to develop procedural fluency? • In what other settings could you use a task similar to this one? • I feel that Colin makes an interesting point regarding students defaulting to a favoured approach when tackling “problem solving” type questions. Do you agree? There is still time to give it a read and take part of you hadn’t considered it before – you can get the article online here I hope you can get involved in the discussion on the 19th. Categories ## A Strange Step-by-Step Solution Earlier this evening I saw the following picture posted by Mathster (@mathstermaths) As I tweeted I am really not keen on the use of “move all terms to the left” as I don’t think it is clear what this is meant to mean mathematically. Indeed, it could easily lead to misconceptions with people thinking that you just move terms over an equals sign with no conceptual understanding of what should be happening. Stephen Cavadino (@srcav) has written about this here I thought I would try going online and doing the same equation as is solved in the example. The step by step solution I obtained was even stranger: I have no idea why there are steps 1 and 2 simplifying the right hand and left hand side before the pointless step of rearranging to obtain everything equal to zero……. Christine (@MissNorledge) also pointed out the strange behaviour this app shows when rounding. According to the example above 8/3 rounds to 2.666666666666665. To me this indicates poor use of floating poor arithmetic. Jasmina then showed something that is clearly a bug in their parsing library I’m curious as to how this app is working, specifically • How the user input is being parsed? • Are they using a JavaScript symbolic algebra library (and if so which one)? • How is the “maths” implemented? Unfortunately at a first glance the JavaScript viewable using the Safari developer options isn’t particularly illuminating. As I’m away for the weekend I haven’t been my able to delve very deeply into the code with a good editor like Sublime and work out what is doing what. The app can’t solve quadratics with complex roots or cubics: Categories ## How to Enjoy Your NQT Year I’m finally getting the material from my session online – if you want an overview of #mathsconf5 last sturdy check out my post here. In this post I am aiming to share the materials I handed out in my session “How to Enjoy (and Succeed at) Your NQT Year” I’ve embedded my Prezi below, if you were at my session you would know that I didn’t get anywhere near through it. [prezi id=”http://prezi.com/-dz30jtfabtw/?utm_campaign=share&utm_medium=copy&rc=ex0share” align=center width=600 lock_to_path=1] All the materials can be accessed on my website at the links below: I started the session by finding out the strengths and weaknesses of attendees. In my opinion you will have a good understanding of these by the time you start your NQT year (even if you are an ITT student I think you often know what they will be before you have spent much time in the classroom). For me, my strength is that I am pretty good at stretching the high attainers whereas I see behaviour management as a weakness as this is something that I have had to work quite hard at to get where I am now. Being frank with yourself about your personal qualities is very important if you want to improve and develop your practice. Following this we talked about behaviour management strategies; I was very interested in some of the conversations happening about the use of reward lessons in the computer room for good behaviour amongst other things. My top tips for behaviour management is to ensure that you are always consistent (however tired and fed up you are) and follow through with any sanctions you hand out. It is very easy to let things slide as term goes on – especially in the winter months when it is dark and cold – try your best to not let that happen. Moving on to lesson planning I talked about my five key things to consider when planning a lesson: 1. The big picture. 2. The key learning objectives. 3. 5 key questions. 4. Any possible misconceptions. 5. How will you assess learning. For me the questioning used with the class and individual learners is the most important thing to bring on the mathematics of students by prompting them to think critically about it. This fits in nicely with a school focus on questioning in my school which is good. Our new Year 7 scheme has questions for most lesson plans. I think considering questions before the lesson means that I think more in depth about the maths that I am presenting and how it will come across to learners. The same can be said for considering misconceptions; some of the best questions in my opinion will draw out misconceptions and enable us to tackle them head on as a class. I was possibly a little controversial in this section by saying that I don’t really like the assessment being on lesson plan pro-formers. This is not because I don’t think it is important – it is of course crucial to know where your students are with the topic of a lesson! My point here was that I don’t want how I am going to assess my students (which is really my problem to resolve) to affect how they experience the mathematics that we are doing that lesson and so my mode of assessment shouldn’t be a focus of the lesson planning process. Many teachers now have to move rooms between lessons. When this is the case I find that it helps to have some go to starters that don’t require me to have logged on to a computer and turned a projector on. For this reason, this year I have stuck a sheet with some easy “no-plan” starters into the back cover of all of my lower school student’s books. I have written a bit more about this in my post “No Plan Starters”. With practice I find that the students don’t need too much guidance if I just tell them a starter task (and maybe write a few numbers on the board) and it means that they are practising some basic skills while I am waiting for the computer to load. Before I was planning on discussing the advantages/disadvantages of technology in lessons I talked about homework. My guiding principle is the I want a homework that takes the minimum amount of time to prepare and mark but that gives the maximum possible benefit to the students. A type of homework that fits this bill are the PRET homeworks as shown below. I particularly like the research and stretch components of this style of homework. I found that last year, being very precise with the expectations for the first couple that I handed out meant that students soon learnt what was expected when I gave them a homework in this style. Before you go away and write some you should definitely check out Jo’s (@mathsjem)and Kathryn’s (@DIRT_expertPRET homework website as there are plenty already to use! For technology in the classroom I was going to talk about different tech tools so I think I shall write about this topic more over the next few months…. I had a large section planned entitled “Do Some Maths”. This is actually my number one tip for your NQT year! It is all too easy to get caught up in the mundane tasks of a teacher that you don’t spend time doing any maths apart from the questions you need for lessons. I’m sure that most of us chose to teach maths because we love doing maths so I think it is important to spend some time doing maths that is challenging. Here is a nice question: A particularly nice source of challenging problems is the book “Calculus for the Ambitious” by T.W. Kernel. This is a book targeted at strong A-Level students giving a more university-like approach to Calculus than you see at A-Level. Your NQT year is an ideal time to develop your subject specific pedagogic knowledge. Use those extra frees to go an observe other teachers focussing in particular on how they teach a given topic. Look for how they structure a lesson to build understanding gradually, how they tackle topics that are perceived as being hard to teach and how the activities they choose promote confidence in the learners. Another excellent way to build your subject knowledge (both pedagogic and general mathematical) is to join at least one, if not more, subject associations. Personally I am a member of the ATM and the IMA and value the access this gives me to their journals. On the education journal note it is definitely worth getting involved in the #mathsjournalclub discussions that I organise – the next one is on the 19th October, see here for more information. On the subject of marking, which is often seen as a necessary chore, and any time you spend doing it should have an impact – it definitely should not take over your life. Kev Lister’s (@listerkev) RAG123 marking has revolutionised the way I mark. Being able to get quicker feedback from the students is really helpful, it doesn’t take that long to get through a set of books commenting if necessary. I do a deep mark in line with my schools marking policy in addition to this, but having looked at the books so much these deep marking sessions are much quicker than they would have been. I believe that having a network of teachers you can turn to for advice outside of your own department and school is incredibly helpful. Twitter makes this easy, so spend some time on twitter and take part in as many twitter chats as you can. I provide a summary of all the maths specific chats here. My plan was to end on giving some tips for your NQT year from people other than me: • Don’t do any work on a Saturday. • Follow up on sanctions – but make sure they are fair. • Always stick to class routines that you set. • Don’t be afraid to say when you are struggling – someone will help you. • Laminate resources. • After a bad lesson find a positive – even if it is that you kept all the pupils in the room. • Always remember the good pupils and how much you enjoy teaching them. • Write any advice given to you down. • Divide your time away from school into working time and non-working time and stick to it. • Talk to anyone and everyone. • Don’t overdo it and then mention a few things to avoid including listening to people moaning all the time and working all the time. The main thing I have learnt myself from this session is to not plan as much!! Thanks to Danny Brown (@dannytybrown) for his interesting points in the session and to Rob Beckett (@RBeckett_Yd) for having a quick look over the slides previously and giving me an NQT’s perspective on them.	{"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": 0.3959698975086212, "perplexity": 1143.7745929394948}, "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/1614178361510.12/warc/CC-MAIN-20210228145113-20210228175113-00300.warc.gz"}
http://estebanmoro.org/2009/01/waiting-for-the-bus/	# Waiting for the bus ### 4 Responses 1. Artur Adib says: Ha, very neat Esteban. I have to think a bit more about this, but the presentation is very clear. I’ve never really thought about this problem as (a) in Brazil buses never really promise to arrive with a given frequency, and (b) the trains I take in the US are pretty much on time always! Thank you Artur. I came accross the paradox when reading about response time in emails. In fact is the same kind of thing… 3. Mario Konschake says: Hi Esteban, in traffic science I have learned that this is called “bus bunching” and is simply caused by any small delay self-amplifying. If a bus has a delay it has to pick up more people, because there is more waiting time available at the next station. The station after, even more people are waiting plus more people want to get off the bus, and so on…. The good thing about this is, that in the very end you have two buses following each other. If you know this you can let the crowded one pass and get your free seat in the next one. Of course buses can overtake each other and therefore this works more reliable with trains. *just noted that is a very old post, but someone found it intersting enough to tweet…	{"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": 28, "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": 0.46294426918029785, "perplexity": 818.8164575143195}, "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-2018-13/segments/1521257650685.77/warc/CC-MAIN-20180324132337-20180324152337-00752.warc.gz"}
https://socratic.org/questions/radioactive-element-x-has-a-half-life-of-30-days-a-rock-sample-contains-4-grams-	Chemistry Topics # Radioactive element X has a half-life of 30 days. A rock sample contains 4 grams element X when it forms. How many half-lives will have elapsed in 90 days? How much of the original amount of X will be unchanged after 90 days? $3$ & $0.5 \setminus g m$ #### Explanation: Given that radioactive element X has a half-life $30$ days Hence the number $\left(n\right)$ of half-lives in $90$ days $n = \frac{90}{30}$ $n = 3$ The amount $N$ of radioactive element X left after $n = 3$ half-lives with initial amount ${N}_{0} = 4 \setminus g m$ $N = {N}_{0} {\left(\frac{1}{2}\right)}^{n}$ $= 4 {\left(\frac{1}{2}\right)}^{3}$ $= \frac{4}{8}$ $= 0.5$ hence the amount left after $90$ days or $3$ half-lives will be $0.5$ grams ##### Impact of this question 507 views around the world	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "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": 0.31483757495880127, "perplexity": 1480.5805592846318}, "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-2019-30/segments/1563195525973.56/warc/CC-MAIN-20190719012046-20190719034046-00080.warc.gz"}
https://www.rdocumentation.org/packages/usethis/versions/1.3.0	# usethis v1.3.0 0 0th Percentile ## Automate Package and Project Setup Automate package and project setup tasks that are otherwise performed manually. This includes setting up unit testing, test coverage, continuous integration, Git, 'GitHub', licenses, 'Rcpp', 'RStudio' projects, and more. # usethis The goal of usethis is to automate many common package and analysis setup tasks. ## Installation Install the released version of usethis from CRAN: install.packages("usethis") Or install the development version from GitHub with: # install.packages("devtools") devtools::install_github("r-lib/usethis") ## Usage Most use_() functions operate on the active project. If you’ve just used usethis to create a new package or project, that will be the current project. Otherwise usethis tries to confirm that current working directory can be recognized as a project. Use proj_get() and proj_set() for manual intervention. Some functions have no strong connections to projects and will expect you to provide a path. usethis is quite chatty, explaining what it’s doing and assigning you tasks. ✔ indicates something usethis has done for you. ● indicates that you’ll need to do some work yourself. Below is a quick look at how usethis can help to set up a package. Note: usethis is gaining more and more functionality for analytical project that are not packages. Stay tuned. library(usethis) # Create a new package ------------------------------------------------- tmp <- file.path(tempdir(), "mypkg") create_package(tmp) #> Changing active project to mypkg #> ✔ Creating 'R/' #> ✔ Creating 'man/' #> ✔ Writing 'DESCRIPTION' #> ✔ Writing 'NAMESPACE' # Modify the description ---------------------------------------------- #> ✔ Setting License field in DESCRIPTION to 'MIT + file LICENSE' #> ✔ Adding '^LICENSE\\.md$' to '.Rbuildignore' #> ✔ Writing 'LICENSE' use_package("MASS", "Suggests") #> ✔ Adding 'MASS' to Suggests field in DESCRIPTION #> ● Use requireNamespace("MASS", quietly = TRUE) to test if package is installed #> ● Then use MASS::fun() to refer to functions. use_dev_package("callr") #> ✔ Adding 'callr' to Imports field in DESCRIPTION #> ● Refer to functions with callr::fun() #> ✔ Adding 'r-lib/callr' to DESCRIPTION Remotes # Set up various packages --------------------------------------------- use_roxygen_md() #> ✔ Setting Roxygen field in DESCRIPTION to 'list(markdown = TRUE)' #> ✔ Setting RoxygenNote field in DESCRIPTION to '6.0.1.9000' #> ● Re-document use_rcpp() #> ✔ Adding 'Rcpp' to LinkingTo field in DESCRIPTION #> ✔ Adding 'Rcpp' to Imports field in DESCRIPTION #> ✔ Creating 'src/' #> ✔ Adding '.o', '.so', '.dll' to 'src/.gitignore' #> ● Include the following roxygen tags somewhere in your package #> #' @useDynLib mypkg, .registration = TRUE #> #' @importFrom Rcpp sourceCpp #> NULL #> ● Run document() use_revdep() #> ✔ Creating 'revdep/' #> ✔ Adding '^revdep$' to '.Rbuildignore' #> ✔ Adding 'checks', 'library', 'checks.noindex', 'library.noindex', 'data.sqlite', '.html' to 'revdep/.gitignore' #> ✔ Writing 'revdep/email.yml' #> ● Run checks with revdepcheck::revdep_check(num_workers = 4) # Set up other files ------------------------------------------------- use_news_md() #> ✔ Writing 'NEWS.md' #> ● Edit 'NEWS.md' use_test("my-test") #> ✔ Adding 'testthat' to Suggests field in DESCRIPTION #> ✔ Creating 'tests/testthat/' #> ✔ Writing 'tests/testthat.R' #> ✔ Writing 'tests/testthat/test-my-test.R' #> ● Edit 'test-my-test.R' x <- 1 y <- 2 use_data(x, y) #> ✔ Creating 'data/' #> ✔ Saving x to data/x.rda #> ✔ Saving y to data/y.rda # Use git ------------------------------------------------------------ use_git() #> ✔ Initialising Git repo #> ✔ Adding '.Rhistory', '.RData', '.Rproj.user' to './.gitignore' #> ✔ Adding files and committing Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.	{"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": 0.15150101482868195, "perplexity": 27733.981115471284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511173.7/warc/CC-MAIN-20181017111301-20181017132801-00182.warc.gz"}
https://uwaterloo.ca/centre-for-intelligent-antenna-and-radio-systems/research-areas/electromagnetic-inverse-scattering-and-imaging	# Electromagnetic Inverse Scattering and Imaging ## Near-field Scattering Tomography Systems for Object Imaging and Material Characterization Electromagnetic inverse scattering based permittivity profile estimation is one of the most promising techniques for object imaging and material characterization today. Measured in the near-field region in the millimeter and sub-millimeter wavelength range, the scattered field is used to reconstruct the Object Under Test (OUT) cross section and to estimate the electromagnetic properties of the OUT by solving electromagnetic inverse source and scattering problems. The developed system can be used for online quality control in pharmaceutical manufacturing, medical imaging, model identification, and computer diagnosis of multi-parameter systems.	{"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": 0.8468621373176575, "perplexity": 1780.4062123119515}, "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-2019-13/segments/1552912203493.88/warc/CC-MAIN-20190324210143-20190324232143-00226.warc.gz"}
https://aimsciences.org/article/doi/10.3934/jimo.2017007	# American Institute of Mathematical Sciences July 2017, 13(3): 1553-1586. doi: 10.3934/jimo.2017007 ## Optimum pricing strategy for complementary products with reservation price in a supply chain model Department of Industrial & Management Engineering, Hanyang University, Ansan Gyeonggi-do, 15588, South Korea * Corresponding author: mitalisarkar.ms@gmail.com (Mitali Sarkar), Phone: +82-1074901981, Fax: +82-31-436-8146 Received November 2015 Published December 2016 This paper describes a two-echelon supply chain model with two manufacturers and one common retailer. Two types of complementary products are produced by two manufacturers, and the common retailer buys products separately using a reservation price and bundles them for sale. The demands of manufacturers and retailer are assumed to be stochastic in nature. When the retailer orders for products, any one of manufacturers agrees to allow those products, and the rest of the manufacturers have to provide the same amount. The profits of two manufacturers and the retailer are maximized by using Stackelberg game policy. By applying a game theoretical approach, several analytical solutions are obtained. For some cases, this model obtains quasi-closed-form solutions, for others, it finds closed-form solutions. Some numerical examples, sensitivity analysis, managerial insights, and graphical illustrations are given to illustrate the model. Citation: Mitali Sarkar, Young Hae Lee. Optimum pricing strategy for complementary products with reservation price in a supply chain model. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1553-1586. doi: 10.3934/jimo.2017007 ##### References: [1] A. Banerjee, A joint economic-lot-size model for purchaser and vendor, Decision Sciences, 17 (1986), 292-311. doi: 10.1111/j.1540-5915.1986.tb00228.x. [2] L. E. Cárdenas-Barrón and S. S. Sana, A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives, International Journal of Production Economics, 155 (2014), 249-258. [3] C. S. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296. doi: 10.1287/mksc.10.4.271. [4] A. L. EI-Ansary and L. W. Stern, Power measurement in the distribution channel, Journal of Marketing Research, 9 (1972), 47-52. [5] G. Ertek and P. M. Griffin, Supplier-and buyer-driven channels in a two-stage supply chain, IIE Transactions, 34 (2002), 691-700. doi: 10.1080/07408170208928905. [6] J. Gabszewicz, N. Sonnac and X. Wauthy, On price competition with complementary goods, Economics Letters, 70 (2001), 431-437. doi: 10.1016/S0165-1765(00)00383-9. [7] S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (1977), 107-111. doi: 10.1080/00207547708943107. [8] S. K. Goyal, A joint economic-lot-size model for purchaser and vendor: A comment, Decision Sciences, 19 (1988), 236-241. doi: 10.1111/j.1540-5915.1988.tb00264.x. [9] C. C. Hsieh and C. H. Wu, Coordinated decisions for substitutable products in a common retailer supply chain, European Journal of Operational Research, 196 (2009), 273-288. doi: 10.1016/j.ejor.2008.02.019. [10] K. F. McCardle, K. Rajaram and C. S. Tang, Bundling retail products: Models and analysis, European Journal of Operational Research, 177 (2007), 1197-1217. doi: 10.1016/j.ejor.2005.11.009. [11] N. M. Modak, S. Panda and S. S. Sana, Three-echelon supply chain coordination considering duopolistic retailers with perfect quality products, International Journal of Production Economics, 182 (2016), 564-578. doi: 10.1016/j.ijpe.2015.05.021. [12] S. Mukhopadhyay, X. Yue and X. Zhu, A Stackelberg model of pricing of complementary goods under information asymmetry, International Journal of Production Economics, 134 (2011), 424-433. doi: 10.1016/j.ijpe.2009.11.015. [13] K. Pan, K. K. Lai, S. C. H. Leung and D. Xiao, Revenue-sharing versus wholesale price mechanisms under different channel power structures, European Journal of Operational Research, 203 (2010), 532-538. doi: 10.1016/j.ejor.2009.08.010. [14] B. Sarkar, Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products Mathematical Problems in Engineering 2016 (2016), Article ID 6318737, 14 pages. doi: 10.1155/2016/6318737. [15] B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151. doi: 10.1016/j.apm.2012.07.026. [16] B. Sarkar and A. Majumder, Integrated vendor-buyer supply chain model with vendors setup cost reduction, Applied Mathematics and Computation, 224 (2013), 362-371. doi: 10.1016/j.amc.2013.08.072. [17] B. Sarkar, S. Saren, D. Sinha and S. Hur, Effect of unequal lot sizes, variable setup cost, and carbon emission cost in a supply chain model Mathematical Problems in Engineering 2015 (2015), Article ID 469486, 13 pages. doi: 10.1155/2015/469486. [18] J. Wei, J. Zhao and Y. Li, Pricing decisions for complementary products with firms' different market powers, European Journal of Operational Research, 224 (2013), 507-519. doi: 10.1016/j.ejor.2012.09.011. [19] J. Wei, J. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, Journal of Cleaner Production, 105 (2015), 86-102. doi: 10.1016/j.jclepro.2014.09.059. [20] C. H. Wu, C. W. Chen and C. C. Hsieh, Competitive pricing decisions in a two echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274. doi: 10.1016/j.ijpe.2011.07.020. [21] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651. doi: 10.1016/j.ejor.2007.01.049. [22] X. Yue, S. Mukhopadhyay and X. Zhu, A Bertrand model of pricing of complementary goods under information asymmetry, Journal of Business Research, 59 (2006), 1182-1192. doi: 10.1016/j.jbusres.2005.06.005. [23] J. Zhao, W. Tang, R. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European Journal of Operational Research, 216 (2012), 409-419. doi: 10.1016/j.ejor.2011.07.026. show all references ##### References: [1] A. Banerjee, A joint economic-lot-size model for purchaser and vendor, Decision Sciences, 17 (1986), 292-311. doi: 10.1111/j.1540-5915.1986.tb00228.x. [2] L. E. Cárdenas-Barrón and S. S. Sana, A production-inventory model for a two-echelon supply chain when demand is dependent on sales teams' initiatives, International Journal of Production Economics, 155 (2014), 249-258. [3] C. S. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-296. doi: 10.1287/mksc.10.4.271. [4] A. L. EI-Ansary and L. W. Stern, Power measurement in the distribution channel, Journal of Marketing Research, 9 (1972), 47-52. [5] G. Ertek and P. M. Griffin, Supplier-and buyer-driven channels in a two-stage supply chain, IIE Transactions, 34 (2002), 691-700. doi: 10.1080/07408170208928905. [6] J. Gabszewicz, N. Sonnac and X. Wauthy, On price competition with complementary goods, Economics Letters, 70 (2001), 431-437. doi: 10.1016/S0165-1765(00)00383-9. [7] S. K. Goyal, An integrated inventory model for a single supplier-single customer problem, International Journal of Production Research, 15 (1977), 107-111. doi: 10.1080/00207547708943107. [8] S. K. Goyal, A joint economic-lot-size model for purchaser and vendor: A comment, Decision Sciences, 19 (1988), 236-241. doi: 10.1111/j.1540-5915.1988.tb00264.x. [9] C. C. Hsieh and C. H. Wu, Coordinated decisions for substitutable products in a common retailer supply chain, European Journal of Operational Research, 196 (2009), 273-288. doi: 10.1016/j.ejor.2008.02.019. [10] K. F. McCardle, K. Rajaram and C. S. Tang, Bundling retail products: Models and analysis, European Journal of Operational Research, 177 (2007), 1197-1217. doi: 10.1016/j.ejor.2005.11.009. [11] N. M. Modak, S. Panda and S. S. Sana, Three-echelon supply chain coordination considering duopolistic retailers with perfect quality products, International Journal of Production Economics, 182 (2016), 564-578. doi: 10.1016/j.ijpe.2015.05.021. [12] S. Mukhopadhyay, X. Yue and X. Zhu, A Stackelberg model of pricing of complementary goods under information asymmetry, International Journal of Production Economics, 134 (2011), 424-433. doi: 10.1016/j.ijpe.2009.11.015. [13] K. Pan, K. K. Lai, S. C. H. Leung and D. Xiao, Revenue-sharing versus wholesale price mechanisms under different channel power structures, European Journal of Operational Research, 203 (2010), 532-538. doi: 10.1016/j.ejor.2009.08.010. [14] B. Sarkar, Supply chain coordination with variable backorder, inspections, and discount policy for fixed lifetime products Mathematical Problems in Engineering 2016 (2016), Article ID 6318737, 14 pages. doi: 10.1155/2016/6318737. [15] B. Sarkar, A production-inventory model with probabilistic deterioration in two-echelon supply chain management, Applied Mathematical Modelling, 37 (2013), 3138-3151. doi: 10.1016/j.apm.2012.07.026. [16] B. Sarkar and A. Majumder, Integrated vendor-buyer supply chain model with vendors setup cost reduction, Applied Mathematics and Computation, 224 (2013), 362-371. doi: 10.1016/j.amc.2013.08.072. [17] B. Sarkar, S. Saren, D. Sinha and S. Hur, Effect of unequal lot sizes, variable setup cost, and carbon emission cost in a supply chain model Mathematical Problems in Engineering 2015 (2015), Article ID 469486, 13 pages. doi: 10.1155/2015/469486. [18] J. Wei, J. Zhao and Y. Li, Pricing decisions for complementary products with firms' different market powers, European Journal of Operational Research, 224 (2013), 507-519. doi: 10.1016/j.ejor.2012.09.011. [19] J. Wei, J. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, Journal of Cleaner Production, 105 (2015), 86-102. doi: 10.1016/j.jclepro.2014.09.059. [20] C. H. Wu, C. W. Chen and C. C. Hsieh, Competitive pricing decisions in a two echelon supply chain with horizontal and vertical competition, International Journal of Production Economics, 135 (2012), 265-274. doi: 10.1016/j.ijpe.2011.07.020. [21] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651. doi: 10.1016/j.ejor.2007.01.049. [22] X. Yue, S. Mukhopadhyay and X. Zhu, A Bertrand model of pricing of complementary goods under information asymmetry, Journal of Business Research, 59 (2006), 1182-1192. doi: 10.1016/j.jbusres.2005.06.005. [23] J. Zhao, W. Tang, R. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European Journal of Operational Research, 216 (2012), 409-419. doi: 10.1016/j.ejor.2011.07.026. Graphical representation for Case 1.1, total profit of manufacturer 1 versus selling-price and lot size Graphical representation for Case 1.1, total profit of manufacturer 2 versus selling-price Graphical representation for Case 1.1, total profit of retailer versus selling-price of bundle product Graphical representation for Case 1.2, total profit of manufacturer 1 versus selling-price and lot size Graphical representation for Case 1.2, total profit of manufacturer 2 and retailer versus selling-price and selling-price of bundle product Graphical representation for Case 2.1, total profit of manufacturer 2 versus selling-price and lot size Graphical representation for Case 2.1, total profit of manufacturer 1 versus sellingprice Graphical representation for Case 2.1, total profit of retailer versus selling-price of bundle product Graphical representation for Case 2.2, total profit of manufacturer 2 versus selling price and lot size Graphical representation for Case 2.2, total profit of manufacturer 1 and retailer versus selling-price and selling-price of bundle product Comparative studies of cooperation and non-cooperation for the selling-price of product 2 of manufacturer 2 in Case 1. Blue ink of the graphical representation indicates under cooperative strategy and the red ink of the graphical representation indicates under noncooperative strategy Comparative studies of cooperation and non-cooperation for the selling-price of bundle product of retailer in Case 1. Blue ink of the graphical representation indicates under cooperative strategy and the red ink of the graphical representation indicates under noncooperative strategy Comparative studies of cooperation and non-cooperation for the selling-price of product 1 of manufacturer 1 in Case 2. Blue ink of the graphical representation indicates under cooperative strategy and the red ink of the graphical representation indicates under noncooperative strategy Comparative studies of cooperation and non-cooperation for the selling-price of bundle product of retailer in Case 2. Blue ink of the graphical representation indicates under cooperative strategy and the red ink of the graphical representation indicates under noncooperative strategy Comparison between the contributions of different authors Author (s) SCM Competitive price study Reservation price Game approach Stochastic demand Choi [3] √ √ Yue et al. [22] √ √ Mukhopadhyay et al. [12] √ √ Wei et al. [18] √ √ √ Cárdenas-Barrón and Sana [2] √ √ Sarkar [14] √ √ McCardle et al. [10] √ √ √ This Model √ √ √ √ √ Author (s) SCM Competitive price study Reservation price Game approach Stochastic demand Choi [3] √ √ Yue et al. [22] √ √ Mukhopadhyay et al. [12] √ √ Wei et al. [18] √ √ √ Cárdenas-Barrón and Sana [2] √ √ Sarkar [14] √ √ McCardle et al. [10] √ √ √ This Model √ √ √ √ √ Decision variables $Q$ order quantity (units) $P_{i}$ selling-price of product j, j=1, 2 (＄/unit) $P_{r}$ selling-price of the bundle product (＄/unit) Random variables $D_{m_{i}}$ demand for product j, j=1, 2 (units) $D_{r}$ demand for the bundle product (units) Parameters $C_{i}$ manufacturing cost of product j, j=1, 2 (＄/unit) $h_{m_{i}}$ holding cost of product j per unit per unit time, j=1, 2 (＄/unit/unit time) $h_{r}$ holding cost of the bundle product per unit per unit time (＄/unit/unit time) $S_{m_{i}}$ setup cost per setup of product j, j=1, 2 (＄/unit) $K_{m_{i}}$ production rate of product j, j=1, 2 (units) $M$ known market size (units) $A$ ordering cost per order of the retailer (＄/order) $I_{m_{i1}}$ inventory of manufacturer i at $t \in[0, t_{m_{i}}]$, i=1, 2 $I_{m_{i2}}$ inventory of manufacturer i at $t \in [t_{m_{i}}, T_{m_{i}}]$, i=1, 2 $AP_{m_{i}}$ expected average profit of manufacturer i, i=1, 2 $AP_{r}$ expected average profit of the retailer $t_{m_{i}}$ time required for maximum inventory of manufacturer i, i=1, 2 $T_{m_{i}}$ cycle time of manufacturer i, i=1, 2 $R_{i}^{a}$ lower limit of reservation price of manufacturer i, i=1, 2 $R_{i}^{b}$ upper limit of reservation price of manufacturer i, i=1, 2 Decision variables $Q$ order quantity (units) $P_{i}$ selling-price of product j, j=1, 2 (＄/unit) $P_{r}$ selling-price of the bundle product (＄/unit) Random variables $D_{m_{i}}$ demand for product j, j=1, 2 (units) $D_{r}$ demand for the bundle product (units) Parameters $C_{i}$ manufacturing cost of product j, j=1, 2 (＄/unit) $h_{m_{i}}$ holding cost of product j per unit per unit time, j=1, 2 (＄/unit/unit time) $h_{r}$ holding cost of the bundle product per unit per unit time (＄/unit/unit time) $S_{m_{i}}$ setup cost per setup of product j, j=1, 2 (＄/unit) $K_{m_{i}}$ production rate of product j, j=1, 2 (units) $M$ known market size (units) $A$ ordering cost per order of the retailer (＄/order) $I_{m_{i1}}$ inventory of manufacturer i at $t \in[0, t_{m_{i}}]$, i=1, 2 $I_{m_{i2}}$ inventory of manufacturer i at $t \in [t_{m_{i}}, T_{m_{i}}]$, i=1, 2 $AP_{m_{i}}$ expected average profit of manufacturer i, i=1, 2 $AP_{r}$ expected average profit of the retailer $t_{m_{i}}$ time required for maximum inventory of manufacturer i, i=1, 2 $T_{m_{i}}$ cycle time of manufacturer i, i=1, 2 $R_{i}^{a}$ lower limit of reservation price of manufacturer i, i=1, 2 $R_{i}^{b}$ upper limit of reservation price of manufacturer i, i=1, 2 Input data Player Market size (units) Manufacturer 1 $M=1500$ Manufacturer 2 $M=1500$ Retailer $M=1500$ Setup cost (＄/setup) $S_{m_{1}}=20$ $S_{m_{2}}=20$ $A=1$ Holding cost (＄/unit/year) $h_{m_{1}}=0.015$ $h_{m_{2}}=0.015$ $h_r=0.01$ Production rate (units/year) $K_{m_{1}}=2000$ $K_{m_{2}}=2000$ - Purchasing cost (＄/unit) $C_{1}=0.25$ $C_{2}=0.15$ - Reservation interval [0, 1] [0.1, 0.9] [0.1, 0.9] -indicates that the parameter is not available for this case. Player Market size (units) Manufacturer 1 $M=1500$ Manufacturer 2 $M=1500$ Retailer $M=1500$ Setup cost (＄/setup) $S_{m_{1}}=20$ $S_{m_{2}}=20$ $A=1$ Holding cost (＄/unit/year) $h_{m_{1}}=0.015$ $h_{m_{2}}=0.015$ $h_r=0.01$ Production rate (units/year) $K_{m_{1}}=2000$ $K_{m_{2}}=2000$ - Purchasing cost (＄/unit) $C_{1}=0.25$ $C_{2}=0.15$ - Reservation interval [0, 1] [0.1, 0.9] [0.1, 0.9] -indicates that the parameter is not available for this case. Optimum results of Example 1 Case $Q^$ units $P_{1}^{}$ ＄/unit $P_{2}^{}$ ＄/unit $P_{r}^{}$ ＄/unit $AP_{m_{1}}^{}$ ＄/year $AP_{m_{2}}^{}$ ＄/year $AP_{{r}}^{}$ ＄/year $AP_{m_{1}r}^{}$ ＄/year $AP_{m_{2}r}^{}$ ＄/year 1.1 1433.14 0.63 0.53 1.33 195.39 246.92 36.37 - - 1.2 1433.14 0.63 0.44 1.29 195.39 - - - 294.18 2.1 1690.88 0.63 0.53 1.33 195.18 247.15 35.90 - - 2.2 1690.88 0.51 0.53 1.27 - 247.15 - 245.87 - -indicates that the average profit is not available for this case. Case $Q^$ units $P_{1}^{}$ ＄/unit $P_{2}^{}$ ＄/unit $P_{r}^{}$ ＄/unit $AP_{m_{1}}^{}$ ＄/year $AP_{m_{2}}^{}$ ＄/year $AP_{{r}}^{}$ ＄/year $AP_{m_{1}r}^{}$ ＄/year $AP_{m_{2}r}^{}$ ＄/year 1.1 1433.14 0.63 0.53 1.33 195.39 246.92 36.37 - - 1.2 1433.14 0.63 0.44 1.29 195.39 - - - 294.18 2.1 1690.88 0.63 0.53 1.33 195.18 247.15 35.90 - - 2.2 1690.88 0.51 0.53 1.27 - 247.15 - 245.87 - -indicates that the average profit is not available for this case. Input data from McCardle et al. [10] Player Market size (units) Manufacturer 1 $M=100$ Manufacturer 2 $M=100$ Retailer $M=100$ Setup cost (＄/setup) $S_{m_{1}}=0$ $S_{m_{2}}=0$ $A=0$ Holding cost (＄/unit/year) $h_{m_{1}}=0$ $h_{m_{2}}=0$ $h_r=0$ Production rate (units/year) $K_{m_{1}}=0$ $K_{m_{2}}=0$ - Purchasing cost (＄/unit) $C_{1}=0.25$ $C_{2}=0.25$ - Reservation interval [0, 1] [0.1, 0.9] [0.1, 0.9] -indicates that the parameter is not available for this case. Player Market size (units) Manufacturer 1 $M=100$ Manufacturer 2 $M=100$ Retailer $M=100$ Setup cost (＄/setup) $S_{m_{1}}=0$ $S_{m_{2}}=0$ $A=0$ Holding cost (＄/unit/year) $h_{m_{1}}=0$ $h_{m_{2}}=0$ $h_r=0$ Production rate (units/year) $K_{m_{1}}=0$ $K_{m_{2}}=0$ - Purchasing cost (＄/unit) $C_{1}=0.25$ $C_{2}=0.25$ - Reservation interval [0, 1] [0.1, 0.9] [0.1, 0.9] -indicates that the parameter is not available for this case. Optimum results of Example 2 Case $Q^$ units $P_{1}^{}$ ＄/unit $P_{2}^{}$ ＄/unit $P_{r}^{}$ ＄/unit $AP_{m_{1}}^{}$ ＄/year $AP_{m_{2}}^{}$ ＄/year $AP_{{r}}^{}$ ＄/year $AP_{m_{1}r}^{}$ ＄/year $AP_{m_{2}r}^{}$ ＄/year 1.1 $300$ $0.625$ $0.625$ $1.375$ $14.0625$ $14.0625$ $1.5625$ - - 1.2 $300$ $0.625$ $0.541667$ $1.33$ $14.0625$ - - - $16.1458$ 2.1 $300$ $0.625$ $0.625$ $1.375$ $14.0625$ $14.0625$ $1.5625$ - - 2.2 $300$ $0.625$ $0.541667$ $1.33333$ - $14.0625$ - 16.1458 - -indicates that the average profit is not available for this case. Case $Q^$ units $P_{1}^{}$ ＄/unit $P_{2}^{}$ ＄/unit $P_{r}^{}$ ＄/unit $AP_{m_{1}}^{}$ ＄/year $AP_{m_{2}}^{}$ ＄/year $AP_{{r}}^{}$ ＄/year $AP_{m_{1}r}^{}$ ＄/year $AP_{m_{2}r}^{}$ ＄/year 1.1 $300$ $0.625$ $0.625$ $1.375$ $14.0625$ $14.0625$ $1.5625$ - - 1.2 $300$ $0.625$ $0.541667$ $1.33$ $14.0625$ - - - $16.1458$ 2.1 $300$ $0.625$ $0.625$ $1.375$ $14.0625$ $14.0625$ $1.5625$ - - 2.2 $300$ $0.625$ $0.541667$ $1.33333$ - $14.0625$ - 16.1458 - -indicates that the average profit is not available for this case. Sensitivity analysis for Case 1.1 Parameter change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}}$ (in %) $AP_{r}$ (in %) $M$ -50% -52.76 -52.18 -59.85 -25% -26.38 -26.09 -29.93 +25% +26.38 +26.09 +29.93 +50% +52.75 +52.18 +59.85 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.99 $S_{m_{2}}$ -50% +1.97 -25% +0.99 -25% +0.98 +25% -0.99 +25% -0.98 +50% -1.98 +50% -1.95 $h_{m_{1}}$ -50% +2.33 $h_{m_{2}}$ -50% +1.42 -25% +1.06 -25% +1.42 +25% -0.94 +25% -0.71 +50% -1.78 +50% -1.42 $C_{1}$ -50% +38.63 $C_{2}$ -50% +22.18 -25% +18.54 -25% +10.82 +25% -17.04 +25% -10.29 +50% -32.58 +50% -20.04 Parameter change(in %) $AP_{r}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.25 $h_{r}$ -50% +9.85 -25% +0.12 -25% +4.93 +25% -0.12 +25% -4.93 +50% -0.25 +50% -9.85 Parameter change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}}$ (in %) $AP_{r}$ (in %) $M$ -50% -52.76 -52.18 -59.85 -25% -26.38 -26.09 -29.93 +25% +26.38 +26.09 +29.93 +50% +52.75 +52.18 +59.85 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.99 $S_{m_{2}}$ -50% +1.97 -25% +0.99 -25% +0.98 +25% -0.99 +25% -0.98 +50% -1.98 +50% -1.95 $h_{m_{1}}$ -50% +2.33 $h_{m_{2}}$ -50% +1.42 -25% +1.06 -25% +1.42 +25% -0.94 +25% -0.71 +50% -1.78 +50% -1.42 $C_{1}$ -50% +38.63 $C_{2}$ -50% +22.18 -25% +18.54 -25% +10.82 +25% -17.04 +25% -10.29 +50% -32.58 +50% -20.04 Parameter change(in %) $AP_{r}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.25 $h_{r}$ -50% +9.85 -25% +0.12 -25% +4.93 +25% -0.12 +25% -4.93 +50% -0.25 +50% -9.85 Sensitivity analysis for Case 1.2 Parameter change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}r}$ (in %) $M$ -50% -52.15 -53.04 -25% -26.24 -26.52 +25% +26.49 +26.52 +50% +53.18 +53.04 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}r}$ (in %) $S_{m_{1}}$ -50% +1.99 $S_{m_{2}}$ -50% +2.04 -25% +0.99 -25% +1.02 +25% -0.99 +25% -1.01 +50% -1.98 +50% -2.02 $h_{m_{1}}$ -50% +2.33 $h_{m_{2}}$ -50% +1.05 -25% +1.06 -25% +0.52 +25% -0.94 +25% -0.52 +50% -1.78 +50% -1.04 $C_{1}$ -50% +38.63 $C_{2}$ -50% +22.91 -25% +18.55 -25% +11.18 +25% -17.02 +25% -10.62 +50% -32.52 +50% -20.67 Parameter change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}r}$ (in %) $M$ -50% -52.15 -53.04 -25% -26.24 -26.52 +25% +26.49 +26.52 +50% +53.18 +53.04 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}r}$ (in %) $S_{m_{1}}$ -50% +1.99 $S_{m_{2}}$ -50% +2.04 -25% +0.99 -25% +1.02 +25% -0.99 +25% -1.01 +50% -1.98 +50% -2.02 $h_{m_{1}}$ -50% +2.33 $h_{m_{2}}$ -50% +1.05 -25% +1.06 -25% +0.52 +25% -0.94 +25% -0.52 +50% -1.78 +50% -1.04 $C_{1}$ -50% +38.63 $C_{2}$ -50% +22.91 -25% +18.55 -25% +11.18 +25% -17.02 +25% -10.62 +50% -32.52 +50% -20.67 Sensitivity analysis for Case 2.1 Parameters change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}}$ (in %) $AP_{r}$ (in %) $M$ -50% -53.25 -52.57 -61.77 -25% -26.62 -26.28 -30.89 +25% +26.62 +26.28 +30.89 +50% +53.25 +52.57 +61.77 Parameter change(in %) $AP_{r}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.21 $h_{r}$ -50% +11.77 -25% +0.11 -25% +5.89 +25% -0.11 +25% -5.89 +50% -0.21 +50% -11.77 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.70 $S_{m_{2}}$ -50% +1.96 -25% +0.85 -25% +0.90 +25% -0.84 +25% -0.79 +50% -1.69 +50% -1.50 $h_{m_{1}}$ -50% +2.34 $h_{m_{2}}$ -50% +1.96 -25% +1.17 -25% +0.90 +25% -1.17 +25% -0.79 +50% -2.34 +50% -1.50 $C_{1}$ -50% +38.76 $C_{2}$ -50% +22.27 -25% +18.63 -25% +10.86 +25% -17.13 +25% -10.32 +50% -32.76 +50% -20.09 Parameters change(in %) $AP_{m_{1}}$ (in %) $AP_{m_{2}}$ (in %) $AP_{r}$ (in %) $M$ -50% -53.25 -52.57 -61.77 -25% -26.62 -26.28 -30.89 +25% +26.62 +26.28 +30.89 +50% +53.25 +52.57 +61.77 Parameter change(in %) $AP_{r}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.21 $h_{r}$ -50% +11.77 -25% +0.11 -25% +5.89 +25% -0.11 +25% -5.89 +50% -0.21 +50% -11.77 Parameter change(in %) $AP_{m_{1}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.70 $S_{m_{2}}$ -50% +1.96 -25% +0.85 -25% +0.90 +25% -0.84 +25% -0.79 +50% -1.69 +50% -1.50 $h_{m_{1}}$ -50% +2.34 $h_{m_{2}}$ -50% +1.96 -25% +1.17 -25% +0.90 +25% -1.17 +25% -0.79 +50% -2.34 +50% -1.50 $C_{1}$ -50% +38.76 $C_{2}$ -50% +22.27 -25% +18.63 -25% +10.86 +25% -17.13 +25% -10.32 +50% -32.76 +50% -20.09 Sensitivity analysis for Case 2.2 Parameter change(in %) $AP_{m_{2}}$ (in %) $AP_{m_{1}r}$ (in %) $M$ -50% -52.57 -54.30 -25% -26.28 -27.15 +25% +26.28 +27.15 +50% +52.57 +54.30 Parameter change(in %) $AP_{m_{1r}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.76 $S_{m_{2}}$ -50% +1.96 -25% +0.88 -25% +0.90 +25% -0.88 +25% -0.79 +50% -1.75 +50% -1.50 $h_{m_{1}}$ -50% +1.64 $h_{m_{2}}$ -50% +1.96 -25% +0.82 -25% +0.90 +25% -0.82 +25% -0.79 +50% -1.64 +50% -1.50 $C_{1}$ -50% +40.31 $C_{2}$ -50% +22.27 -25% +19.36 -25% +10.86 +25% -17.77 +25% -10.32 +50% -33.95 +50% -20.09 Parameter change(in %) $AP_{m_{1r}}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.04 $h_{r}$ -50% +1.72 -25% +0.02 -25% +0.86 +25% -0.02 +25% -0.86 +50% -0.04 +50% -1.72 Parameter change(in %) $AP_{m_{2}}$ (in %) $AP_{m_{1}r}$ (in %) $M$ -50% -52.57 -54.30 -25% -26.28 -27.15 +25% +26.28 +27.15 +50% +52.57 +54.30 Parameter change(in %) $AP_{m_{1r}}$ (in %) Parameter change(in %) $AP_{m_{2}}$ (in %) $S_{m_{1}}$ -50% +1.76 $S_{m_{2}}$ -50% +1.96 -25% +0.88 -25% +0.90 +25% -0.88 +25% -0.79 +50% -1.75 +50% -1.50 $h_{m_{1}}$ -50% +1.64 $h_{m_{2}}$ -50% +1.96 -25% +0.82 -25% +0.90 +25% -0.82 +25% -0.79 +50% -1.64 +50% -1.50 $C_{1}$ -50% +40.31 $C_{2}$ -50% +22.27 -25% +19.36 -25% +10.86 +25% -17.77 +25% -10.32 +50% -33.95 +50% -20.09 Parameter change(in %) $AP_{m_{1r}}$ (in %) Parameter change(in %) $AP_{r}$ (in %) $A$ -50% +0.04 $h_{r}$ -50% +1.72 -25% +0.02 -25% +0.86 +25% -0.02 +25% -0.86 +50% -0.04 +50% -1.72 [1] Yeong-Cheng Liou, Siegfried Schaible, Jen-Chih Yao. 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Journal of Industrial & Management Optimization, 2007, 3 (4) : 727-737. doi: 10.3934/jimo.2007.3.727 2017 Impact Factor: 0.994	{"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": 0.5448505282402039, "perplexity": 14672.813052384607}, "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/1560627998813.71/warc/CC-MAIN-20190618183446-20190618205446-00334.warc.gz"}
http://math.stackexchange.com/questions/137664/representation-of-a-subset-of-a-finite-affine-space-as-a-variety	# Representation of a subset of a finite affine space as a variety It is simple to see that every subset of a an affine space over a finite field is a variety - for example, it follows from the fact that finite subsets are closed in the Zariski Topology of every affine space. My question is rather algorithmic - given a subset $S \subseteq \mathbb{F}_{q}^n$ for some prime power $q$ and positive $n$, how do I express it as the locus of some polynomial equations, as compactly as possible? By compactly I mean: minimizing the sum of degrees of the polynomials. I don't necessarily want an algorithm - lower\upper bounds will also be cool. This is a useful question - for example, it has applications in algebraic combinatorics: when invoking the Chevalley-Warning theorem, one wants to write down polynomial equations with low degree in order to satisfy the theorem's conditions. - You are basically asking for the generators of the ideal defining $S$. I'm assuming $S \subset \mathbb{A}^n$ is finite here. Let $A=(a_{ij})_{1\le i\le n, 1\le j\le m}$ be the matrix whose column vectors are the points in $S$. The ideal of one point $(a_{1i},\ldots,a_{ni})$ is given by $(x_1-a_{1i},\ldots,x_n-a_{ni})$. Thus the ideal of $S$ is given by the intersection of these ideals, that is $$I=\bigcap_{i=1}^m(x_1-a_{1i},\ldots,x_n-a_{ni})$$Calculating the intersection of these ideals can be done using Grobner basis techniques or Macaulay2. The result is a set of generators for $I$ of minimal degree, which is what you want.	{"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": 0.9774259924888611, "perplexity": 67.50108168652322}, "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-2016-18/segments/1461862134822.89/warc/CC-MAIN-20160428164854-00033-ip-10-239-7-51.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/39733/how-to-tell-if-two-random-polynomials-are-identical/39734	# How to tell if two random polynomials are identical Let t be a positive real number. Let P(x) and Q(x) be two random polynomials with integer coefficients. If P(t) = Q(t), then what is the probability that P(x) is not identical to Q(x)? Will it make a difference if I restrict t to be an integer? Suppose I had a set T ={t0,t1,…tk}, can we answer a similar question --- If P(ti) = Q(ti) for all ti in the set T, what is the probability that P is identical to Q? If k > max(deg(P), deg(Q)), the probability is 1. But can we say something about how many points we need to check before we can be fairly certain that the polynomials are identical? Thanks - This is not actually a mathematical question. There is no reasonable or accepted mathematical notion of what "random integer", or "random polynomial with integer coefficients" means. What is the probability that a random integer = 0, 1, 2, ... etc? Since there are infinitely many integers, the probability should be 0 --- but then there is 0 probability of anything. – Bill Thurston Sep 23 '10 at 12:27 @Bill: I want to make a pedantic and narrow point: there are many reasonable notions of a random integer, all depending on a choice of finite measure. I think it is more fair to say that there is not an obvious choice of measure appropriate to the present context. – Steve Huntsman Sep 23 '10 at 12:35 Also, suitably amended over finite fields (but I will not be the one to make the edit), the question has a nontrivial answer. – Steve Huntsman Sep 23 '10 at 12:40 @Steve Huntsman: Perhaps I worded it too strongly. I'm aware how one can fix up the statement to make it mathematical, but it's too big a guessing game to try to guess what is intended. I'm used to hearing people talk about "random integers" without being aware there's a question what it means. I'll lay out a bit of how I see it in an actual answer. – Bill Thurston Sep 23 '10 at 13:01 You shouldn't say "K > deg(P+Q)" as, if P(x) = x and Q(x) = -x, deg(P+Q) = 0 but checking 1 point (for example at x = 0) doesn't prove P = Q. You need "k > max{deg(P), deg(Q)}". – Mark Bell Sep 23 '10 at 14:51 If the coefficients are non-negative then you can always do it with at most two integer evaluations. That is, $P$ and $Q$ are equal if and only if 1. $P(1)=Q(1)$, and 2. $P(P(1)+1)=Q(Q(1)+1)$. Update. If we allow for negative coefficients then this won't work. However, if in addition we are told that all coefficients $c$ satisfy $\|c\| \leq b$, then I believe we can do it with one integer evaluation. Namely, choose $n$ satisfying $n \geq 2b+1$. Then I think $P$ and $Q$ are equal if and only if 1. $P(n)=Q(n)$. See my comments below for an explanation. - Why does this work? – Steve Huntsman Sep 23 '10 at 14:29 Note that $P(1)$ is just the sum of the coefficients of $P$. If the coefficients are all non-negative, then in particular they are all at most $P(1)$. So, if we express $P(P(1)+1)$ in base $P(1)+1$ we completely recover the coefficients of $P$. – Tony Huynh Sep 23 '10 at 14:43 Consider the case when P(1) is a power of 10 to make it particularly transparent. – JBL Sep 23 '10 at 14:57 Sure, instead of taking P(1)+1, we can let n be a power of 10 that is bigger than P(1). Then if we compute P(n), we can 'just read off' the coefficients of P. – Tony Huynh Sep 23 '10 at 15:39 That's a cute fact! – Nate Eldredge Sep 23 '10 at 18:14 If $P$ and $Q$ are polynomials with integer coefficients, and $P(\pi)=Q(\pi)$, then $P$ and $Q$ are guaranteed identical. - Hmm... this would probably require high precision if the degrees are large enough (pop quiz: how many digits of $\pi$ would be needed for a given degree $n$?). I'm afraid that even with the upvotes this answer received, this isn't very practical. – J. M. Sep 23 '10 at 12:56 Yet another thing: if you end up having to use so many digits of $\pi$ for a "guaranteed-correct" check of this identity Gerry proposed, it may well be much slower than checking $n+1$ values in mere single-precision arithmetic. :P I guess this is the "disconnect between theory and practice" I have been hearing so much about. – J. M. Sep 23 '10 at 13:26 @J.M. I think Gerry's main point is that the question is imprecise :-) – Felipe Voloch Sep 23 '10 at 13:55 @qwerty1793: Indeed, any transcendental number. Since $P-Q$ is also a polynomial with integer coefficients, if $P-Q$ is not the zero polynomial, then any root $t$ of $P-Q$ is by definition algebraic. So if $P-Q$ has a transcendental root, then $P=Q$. – Nate Eldredge Sep 23 '10 at 14:33 I accept all the critical comments, but Felipe has hit the nail on the head. You can't give a reasonable answer to an unreasonable question. All you can do is push the questioner to thinking about what question he/she really means to ask, so as to rule out the unreasonable answers. Bill Thurston has done well to sketch out some of the territory here, but in the end it's the questioner's job to give us a question that can be answered without mind-reading. – Gerry Myerson Sep 24 '10 at 0:25 The problem as stated is not well formulated; there are different ways it could be given a precise mathematical meaning, but then the main content of the question becomes the way in which it is made precise. One thing missing is a specification of the probability measure, or a class of probability measures, for "random integer" and "random polynomial". Also implicitly missing, although not explicitly mentioned, is either a mathematical or a practical model of computation. If you choose any particular probability distribution on polynomials with integer coefficients, then for any $\epsilon$ there are particular integers $m$ so that the probability of two of the polynomials agreeing at $m$ is less than $\epsilon$. As an example, if you consider any set of polynomials whose coefficients are chosen with any probability measure on integers between -1,000,000 to +1,000,000, then the value for $n = 2,000,001$ is definitive. This may not help you with your actual problem, because computing the value when $n = 2,000,000$ may involve computation with integers of greater than than machine precision, depending on the degree and the machine. If it's a polynomial of degree 10, it's probably better to compute its value on all integers between -5 and 5, rather than one integer of size 2000000; but there are many possible strategies for computation, and this gets into a different set of issues. For a probability measure that does not have finite support, you can't usually determine identity of the polynomial with absolute certainty from value at a particular integer, but it can still be made as nearly certain as you like. Similarly, the value on any real number chosen from a distribution with no atoms, or the value on a single known-to-be transcendental real, is definitive --- but computation up to machine precision might or might not tell you equality. - +1 for Bill; even without considering the coefficient distribution, unless you have some guarantee like all the signs of the coefficients being identical, computations with polynomials of high enough degree will be affected by subtractive cancellation. Personally I'd rather have $n+1$ reliable witnesses for cheap than one expensive witness. – J. M. Sep 23 '10 at 13:32 I was supposing computation at an integer with integer arithmetic, so overflow rather than subtractive cancellation is the issue. But the computing environment might be one that handles large integers efficiently; calculating for one integer might be essentially equivalent to calculating mod several machine-size primes. There's too much under the surface about this to admit a good answer rather than an essay. – Bill Thurston Sep 23 '10 at 13:53 @Bill Thurston: Thanks for your clarifying comments. – Balaji Sep 24 '10 at 5:50 @Balaji: I appreciate your remark, which suggests that you accept the discussion in good spirit, not in the wrong way. I read your question as a genuine question about a topic where many people have fuzzy ideas. It is a good seed for the start of a discussion, even though it is not precisely formulated mathematics. When such a question is posed, it helps crystallize and clarify people's thoughts. I've been surprised how many diverse and interesting things people have had to say in response. Whether MathOverflow is not the place for discussion, as the FAQ states, is an independent issue. – Bill Thurston Sep 24 '10 at 8:10 Sorry can't add comments yet so I have to post this way. To comment on David's last post, one doesn't even have to go to transcendental numbers. If $P-Q$ is not zero, it only has finitelly many roots, thus the probability for a random chosen real number to be a root of $P-Q$ is zero. - Use probabilistic identity testing. This is noteworthy for being one of the few problems known to be in BPP but not in P. - Verifying if two black-box polynomials are identical is easy if you know that they have the same degree $n$; simply compute values at $n+1$ points, and if those $n+1$ values agree, they're identical. - Thanks, but I am interested in knowing if we can evaluate the polynomials at fewer than n+1 points and conclude with high probability that they are identical. – Balaji Sep 23 '10 at 12:27 @J.M. Technical point, actually all you need to know is that they both have degree at most $n$. – Mark Bell Sep 23 '10 at 14:35 qwerty: Yes, it's a weaker condition than what I said; thanks for pointing it out. – J. M. Sep 23 '10 at 14:51 If $t$ is chosen randomly in the reals, then with probability one $t$ is transcendental, so $P(t) = Q(t)$ iff $P = Q$. (This is just a generalization of the answer from Gerry Myerson) -	{"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": 0.8485734462738037, "perplexity": 385.4867024106821}, "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-2014-52/segments/1418802775348.152/warc/CC-MAIN-20141217075255-00028-ip-10-231-17-201.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/84749-polynomial-approximation.html	# Math Help - Polynomial approximation 1. ## Polynomial approximation Here's a challenge: for the function $y= a\,\sin{(bx+c)} + d$, find a polynomial of degree 3 (ie a cubic) approximation for y on the interval from one trough to one peak (about the main original point of inflection) - eg for $y=\sin{(x)}$ that interval would be $\left[-\frac{\pi}{2}, \,\frac{\pi}{2}\right]$ Express the answer in the form $y = px^3+qx^2+rx+s$, where p, q , r and s are in terms of a, b, c and d. 2. It doesnt seem to work when $c \neq 0$ I have no idea why? 3. Originally Posted by nzmathman Here's a challenge: for the function $y= a\,\sin{(bx+c)} + d$, find a polynomial of degree 3 (ie a cubic) approximation for y on the interval from one trough to one peak (about the main original point of inflection) - eg for $y=\sin{(x)}$ that interval would be $\left[-\frac{\pi}{2}, \,\frac{\pi}{2}\right]$ Express the answer in the form $y = px^3+qx^2+rx+s$, where p, q , r and s are in terms of a, b, c and d. What is the norm against which the quality of the fit between the polynomial and function is to be judged? CB 4. Hi, basically you find the approximation using certain points of the sine curve so that there is exactly enough to solve for a, b, c and d. (this is giving it away a bit but I used the point of inflection and one of the stationary points). Never mind my earlier post about it not working when c was not zero, I made a mistake in the formula but fixed it now	{"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": 9, "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": 0.9472094774246216, "perplexity": 338.92006351406195}, "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-2014-35/segments/1408500804220.17/warc/CC-MAIN-20140820021324-00350-ip-10-180-136-8.ec2.internal.warc.gz"}
http://www.theophys.kth.se/~garaud/research.html	Past and present collaborators Research interests Vortex matter in multi-component/multi-band superconductors under construction Skyrmions in multi-component/multi-band superconductors under construction Vortex loops and knots under construction Recent research -- Supplementary materials Thermoelectric Signatures of Time-Reversal Symmetry Breaking States in Multiband Superconductors with Mihail Silaev and Egor Babaev Animations showing the evolution of the magnetic and electric responses that originates in time-varying local heating of the sample, which can for example be induced by a laser. This display responses for both the cases of $s+is$ and $s+id$ pairing symmetry, with and without domain-walls. Link Domain walls and their experimental signatures in $s+is$ superconductors with Egor Babaev Animations showing the magnetization process and field cooled experiments in $s+is$ superconductors. Link Skyrmions induced by dissipationless drag in $~\mathrm{U}(1)\times\mathrm{U}(1)$ superconductors. with Karl Sellin, Juha Jäykkä and Egor Babaev Animations showing the magnetization process of a two-component $\mathrm{U}(1)\times\mathrm{U}(1)$ superconductor with a dissipationless drag. This shows the Skyrmions magnetization process of a finite sample in a slowly increasing applied magnetic field. Link Stable Cosmic Vortons with Eugen Radu and Mikhail Volkov Animations showing the dynamical evolution of vortons. Both unstable and stable regimes are found. Link Topological Solitons in Three-Band Superconductors with Broken Time Reversal Symmetry. with Johan Carlström and Egor Babaev Animations showing formation mechanisms of chiral skyrmions in three component superconductors with broken time reversal symmetry. The chiral skyrmions are tological solitons made out of vortices confined on a closed domain-wall separating regions of opposite phase-locking pattern. Link Semi-Meissner state and nonpairwise intervortex interactions in type-1.5 superconductors. with Johan Carlström and Egor Babaev Video animations of vortex clusters, occuring in two-component Ginzburg--Landau theory. Non-monotonic intervortex interactions lead to formation of vortex clusters surrounded by macroscopic Meissner domains. Structure formation can be very complicated, because of non-pairwise interactions originating in the non-linear superposition of vortices. Link	{"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": 0.6644869446754456, "perplexity": 9063.061877309345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516123.97/warc/CC-MAIN-20181023090235-20181023111735-00125.warc.gz"}
http://confluence.sammeth.net/pages/diffpagesbyversion.action?pageId=7013951&selectedPageVersions=13&selectedPageVersions=12	##### Child pages • 5.1 - Linear Program # Page History ## Key • This line was added. • This line was removed. • Formatting was changed. Section We interpret G with each edge LaTeX Math Inline body $e \in E$ colored by read mappings as a flaw flow network, considering the read volume assigned to every (super-) edge as a flux created by the expression of the underlying supporting transcripts T.Consequently, given an edge LaTeX Math Inline body $e=(tail,head,exonic,T)$ the contribution of the supporting transcripts LaTeX Math Inline body $\{t_1,\ldots,t_n\}\in T$ to the flux LaTeX Math Inline body $X_e$ observed along e can be described by a linear equation ...	{"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": 0.9360795021057129, "perplexity": 15525.514539187578}, "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-2018-39/segments/1537267158011.18/warc/CC-MAIN-20180922024918-20180922045318-00368.warc.gz"}
https://www.cfa.harvard.edu/research/ta/origins-stellar-spin-planetary-orbit-misalignments	# The Origins of Stellar Spin - Planetary Orbit Misalignments Description: The accelerating quantification of exo-planetary orbital obliquity (i.e. the misalignment between the stellar spin axis and the planetary orbit normal) has been interpreted as being among the most information-rich relics left over from the epoch of planet formation. Unexpectedly, the recurrent identification of large spin-orbit misalignments have called into question our understanding of planet-disk interactions and planet-formation in general. To this end, our research activities have been aimed at understanding the evolution of proto-planetary disks and stellar spin-axes (subject to gravitational torques from the stellar birth environment, magnetic disk-star coupling, accretion, etc) in an effort to reconcile significant orbital obliquities and conventional mechanisms responsible for large-scale orbital migration of young planets. People: Konstantin Batygin	{"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": 0.9669272899627686, "perplexity": 4954.694803879668}, "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/1575540525781.64/warc/CC-MAIN-20191210013645-20191210041645-00394.warc.gz"}
https://formulasearchengine.com/wiki/Uniform_distribution_(continuous)	# Uniform distribution (continuous) In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The support is defined by the two parameters, a and b, which are its minimum and maximum values. The distribution is often abbreviated U(a,b). It is the maximum entropy probability distribution for a random variate X under no constraint other than that it is contained in the distribution's support.[1] ## Characterization ### Probability density function The probability density function of the continuous uniform distribution is: ${\displaystyle f(x)={\begin{cases}{\frac {1}{b-a}}&{\mathrm {for} }\ a\leq x\leq b,\\[8pt]0&{\mathrm {for} }\ xb\end{cases}}}$ The values of f(x) at the two boundaries a and b are usually unimportant because they do not alter the values of the integrals of f(xdx over any interval, nor of x f(xdx or any higher moment. Sometimes they are chosen to be zero, and sometimes chosen to be 1/(b − a). The latter is appropriate in the context of estimation by the method of maximum likelihood. In the context of Fourier analysis, one may take the value of f(a) or f(b) to be 1/(2(b − a)), since then the inverse transform of many integral transforms of this uniform function will yield back the function itself, rather than a function which is equal "almost everywhere", i.e. except on a set of points with zero measure. Also, it is consistent with the sign function which has no such ambiguity. In terms of mean μ and variance σ2, the probability density may be written as: ${\displaystyle f(x)={\begin{cases}{\frac {1}{2\sigma {\sqrt {3}}}}&{\mbox{for }}-\sigma {\sqrt {3}}\leq x-\mu \leq \sigma {\sqrt {3}}\\0&{\text{otherwise}}\end{cases}}}$ ### Cumulative distribution function ${\displaystyle F(x)={\begin{cases}0&{\text{for }}x Its inverse is: ${\displaystyle F^{-1}(p)=a+p(b-a)\,\,{\text{ for }}0 In mean and variance notation, the cumulative distribution function is: ${\displaystyle F(x)={\begin{cases}0&{\text{for }}x-\mu <-\sigma {\sqrt {3}}\\{\frac {1}{2}}\left({\frac {x-\mu }{\sigma {\sqrt {3}}}}+1\right)&{\text{for }}-\sigma {\sqrt {3}}\leq x-\mu <\sigma {\sqrt {3}}\\1&{\text{for }}x-\mu \geq \sigma {\sqrt {3}}\end{cases}}}$ and the inverse is: ${\displaystyle F^{-1}(p)=\sigma {\sqrt {3}}(2p-1)+\mu \,\,{\text{ for }}0\leq p\leq 1}$ ### Generating functions #### Moment-generating function ${\displaystyle M_{x}=E(e^{tx})={\frac {e^{tb}-e^{ta}}{t(b-a)}}\,\!}$ from which we may calculate the raw moments m k ${\displaystyle m_{1}={\frac {a+b}{2}},\,\!}$ ${\displaystyle m_{2}={\frac {a^{2}+ab+b^{2}}{3}},\,\!}$ ${\displaystyle m_{k}={\frac {1}{k+1}}\sum _{i=0}^{k}a^{i}b^{k-i}.\,\!}$ For a random variable following this distribution, the expected value is then m1 = (a + b)/2 and the variance is m2 − m12 = (b − a)2/12. #### Cumulant-generating function For n ≥ 2, the nth cumulant of the uniform distribution on the interval [-1/2, 1/2] is bn/n, where bn is the nth Bernoulli number.[3] ## Properties ### Moments and parameters The first moment of the distribution is: ${\displaystyle E(X)={\frac {1}{2}}(a+b).}$ The second centralized moment (or variance) is: ${\displaystyle V(X)={\frac {1}{12}}(b-a)^{2}}$ Solving these two equations for parameters a and b, given known moments E(X) and V(X), yields: ${\displaystyle a=E(X)-{\sqrt {3V(X)}}}$ ${\displaystyle b=E(X)+{\sqrt {3V(X)}}}$ ### Order statistics Let X1, ..., Xn be an i.i.d. sample from U(0,1). Let X(k) be the kth order statistic from this sample. Then the probability distribution of X(k) is a Beta distribution with parameters k and n − k + 1. The expected value is ${\displaystyle \operatorname {E} (X_{(k)})={k \over n+1}.}$ This fact is useful when making Q-Q plots. The variances are ${\displaystyle \operatorname {Var} (X_{(k)})={k(n-k+1) \over (n+1)^{2}(n+2)}.}$ ### Uniformity The probability that a uniformly distributed random variable falls within any interval of fixed length is independent of the location of the interval itself (but it is dependent on the interval size), so long as the interval is contained in the distribution's support. To see this, if X ~ U(a,b) and [x, x+d] is a subinterval of [a,b] with fixed d > 0, then ${\displaystyle P\left(X\in \left[x,x+d\right]\right)=\int _{x}^{x+d}{\frac {{\mathrm {d} }y}{b-a}}\,={\frac {d}{b-a}}\,\!}$ which is independent of x. This fact motivates the distribution's name. ### Generalization to Borel sets This distribution can be generalized to more complicated sets than intervals. If S is a Borel set of positive, finite measure, the uniform probability distribution on S can be specified by defining the pdf to be zero outside S and constantly equal to 1/K on S, where K is the Lebesgue measure of S. ## Standard uniform Restricting ${\displaystyle a=0}$ and ${\displaystyle b=1}$, the resulting distribution U(0,1) is called a standard uniform distribution. One interesting property of the standard uniform distribution is that if u1 has a standard uniform distribution, then so does 1-u1. This property can be used for generating antithetic variates, among other things. ## Relationship to other functions As long as the same conventions are followed at the transition points, the probability density function may also be expressed in terms of the Heaviside step function: ${\displaystyle f(x)={\frac {\operatorname {H} (x-a)-\operatorname {H} (x-b)}{b-a}},\,\!}$ or in terms of the rectangle function ${\displaystyle f(x)={\frac {1}{b-a}}\,\operatorname {rect} \left({\frac {x-\left({\frac {a+b}{2}}\right)}{b-a}}\right).}$ There is no ambiguity at the transition point of the sign function. Using the half-maximum convention at the transition points, the uniform distribution may be expressed in terms of the sign function as: ${\displaystyle f(x)={\frac {\operatorname {sgn} {(x-a)}-\operatorname {sgn} {(x-b)}}{2(b-a)}}.}$ ## Applications In statistics, when a p-value is used as a test statistic for a simple null hypothesis, and the distribution of the test statistic is continuous, then the p-value is uniformly distributed between 0 and 1 if the null hypothesis is true. ### Sampling from a uniform distribution There are many applications in which it is useful to run simulation experiments. Many programming languages have the ability to generate pseudo-random numbers which are effectively distributed according to the standard uniform distribution. If u is a value sampled from the standard uniform distribution, then the value a + (ba)u follows the uniform distribution parametrised by a and b, as described above. ### Sampling from an arbitrary distribution {{#invoke:main\|main}} The uniform distribution is useful for sampling from arbitrary distributions. A general method is the inverse transform sampling method, which uses the cumulative distribution function (CDF) of the target random variable. This method is very useful in theoretical work. Since simulations using this method require inverting the CDF of the target variable, alternative methods have been devised for the cases where the cdf is not known in closed form. One such method is rejection sampling. The normal distribution is an important example where the inverse transform method is not efficient. However, there is an exact method, the Box–Muller transformation, which uses the inverse transform to convert two independent uniform random variables into two independent normally distributed random variables. ### Quantization error {{#invoke:main\|main}} In analog-to-digital conversion a quantization error occurs. This error is either due to rounding or truncation. When the original signal is much larger than one least significant bit (LSB), the quantization error is not significantly correlated with the signal, and has an approximately uniform distribution. The RMS error therefore follows from the variance of this distribution. ## Estimation ### Estimation of maximum #### Minimum-variance unbiased estimator {{#invoke:main\|main}} Given a uniform distribution on [0, b] with unknown b, the minimum-variance unbiased estimator (UMVU) estimator for the maximum is given by ${\displaystyle {\hat {b}}_{UMVU}={\frac {k+1}{k}}m=m+{\frac {m}{k}}}$ where m is the sample maximum and k is the sample size, sampling without replacement (though this distinction almost surely makes no difference for a continuous distribution). This follows for the same reasons as estimation for the discrete distribution, and can be seen as a very simple case of maximum spacing estimation. This problem is commonly known as the German tank problem, due to application of maximum estimation to estimates of German tank production during World War II. #### Maximum Likelihood estimator The maximum likelihood estimator is given by: ${\displaystyle {\hat {b}}_{ML}=m}$ where m is the sample maximum, also denoted as ${\displaystyle m=X_{(n)}}$ the maximum order statistic of the sample. #### Method of moment estimator The method of moments estimator is given by: ${\displaystyle {\hat {b}}_{MM}=2{\bar {X}}}$ where ${\displaystyle {\bar {X}}}$ is the sample mean. ### Estimation of midpoint The midpoint of the distribution (a + b) / 2 is both the mean and the median of the uniform distribution. Although both the sample mean and the sample median are unbiased estimators of the midpoint, neither is as efficient as the sample mid-range, i.e. the arithmetic mean of the sample maximum and the sample minimum, which is the UMVU estimator of the midpoint (and also the maximum likelihood estimate). ### Confidence interval for the maximum Let X1, X2, X3, ..., Xn be a sample from U( 0, L ) where L is the population maximum. Then X(n) = max( X1, X2, X3, ..., Xn ) has the density[4] ${\displaystyle f_{n}(X_{(n)})=n{\frac {1}{L}}\left({\frac {X_{(n)}}{L}}\right)^{n-1}=n{\frac {X_{(n)}^{n-1}}{L^{n}}},0 The confidence interval for the estimated population maximum is then ( X(n), X(n) / α1/n ) where 100 ( 1 - α )% is the confidence level sought. In symbols ${\displaystyle X_{(n)}\leq L\leq X_{(n)}/\alpha ^{1/n}}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 29, "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": 0.9837537407875061, "perplexity": 351.2650905561244}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574588.96/warc/CC-MAIN-20190921170434-20190921192434-00223.warc.gz"}
https://aripd.com/posts/algorithms-for-machine-learning/	# Algorithms for machine learning Apr 21st, 2017 ## Introduction This article focuses on supervised machine learning. You’ll get an overview of the internals of the learning algorithm and features that you can use to train, score, and select the best-fitting prediction function. ## How machines learn to predict The challenge of supervised machine learning is to find the proper prediction function for a specific question. Mathematically, the challenge is to find the input-output function that takes the input variables x and returns the prediction value y. This hypothesis function $h_{\theta}$ is the output of the training process. Often the hypothesis function is also called target function or prediction function or model. $\displaystyle y=h_{\theta}(x)$ where; • $h_{\theta}(x)$: hypothesis function, target function, prediction function, model • $x$: feature parameter or vector • $\theta$: theta parameter or vector x represents a multiple-data point $\{x_1, x_2, ...\}$ such as { 101.0, 3.0 }. The array of these values is referred to as the feature vector. ## Linear regression The generic linear regression function below returns the predicted value by summarizing each element of the feature vector multiplied by a theta parameter $(\theta)$. The theta parameters are used within the training process to adapt or “tune” the regression function based on the training data. $\displaystyle h_{\theta}(x) = \theta_{0} * x_{0} + \theta_{1} * x_{1} + ... + \theta_{n} * x_{n}$ In the linear regression function, theta parameters and feature parameters are enumerated by a subscription number. The subscription number indicates the position of theta parameters $(\theta)$ and feature parameters $(x)$ within the vector. Note that feature $x_0$ is a constant offset term set with the value $1$ for computational purposes. How do you know that this theta vector is the best fit for your application? Would the function fit better if you changed the first or second theta parameter? To identify the best-fitting theta parameter vector, you need a utility function, which will evaluate how well the target function performs. ## Scoring the target function In machine learning, a cost function $J(\theta)$ is used to compute the mean error, or “cost” of a given target function. $\displaystyle J(\theta) = \frac{1}{2m} \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)})^2$ The cost function indicates how well the model fits with the training data. To determine the cost of the trained target function, you would compute the squared error of each sample ($i$). The error is the distance between the calculated $y$ value and the real $y$ value of the sample $i$. The smaller the cost value of $J(\theta)$, the more precise the target function’s predictions will be. ## Training the target function Although the cost function helps to evaluate the quality of the target function and theta parameters, respectively, you still need to compute the best-fitting theta parameters. You can use the gradient descent algorithm for this calculation. Gradient descent minimizes the cost function, meaning that it’s used to find the theta combinations that produces the lowest cost ($J(\theta)$) based on the training data. Here is a simplified algorithm to compute new, better fitting thetas: $repeat \{ \theta_{0} := \theta_{0} - \alpha * \frac{1}{m} * \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)}) * x_{0}^{(i)}, \theta_{1} := \theta_{1} - \alpha * \frac{1}{m} * \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)}) * x_{1}^{(i)}, \theta_{n} := \theta_{n} - \alpha * \frac{1}{m} * \sum_{i=1}^{m} (h_{\theta}(x^{(i)}) - y^{(i)}) * x_{n}^{(i)} \}$ Within each iteration a new, better value will be computed for each individual $\theta$ parameter of the theta vector. The learning rate $\alpha$ controls the size of the computing step within each iteration. This computation will be repeated until you reach a theta values combination that fits well. To validate that the cost decreases continuously, you can execute the cost function $J(\theta)$ after each training step. With each iteration, the cost must decrease. If it doesn’t, then the value of the learning rate parameter is too large, and the algorithm will shoot past the minimum value. In this case the gradient descent algorithm fails. Although the cost will no longer decrease significantly, the target function is still not optimal; it seems to underfit. In machine learning, the term underfitting is used to indicate that the learning algorithm does not capture the underlying trend of the data. From this we conclude that the model used for the training process, the target function, does not fit the data well enough. Underfitting is often due to an excessively simple model. ## Adding features and feature scaling If you discover that your target function doesn’t fit the problem you are trying to solve, you can adjust it. A common way to correct underfitting is to add more features into the feature vector. Rather than using the single domain-specific feature vector ({size} for example), you could use a multi-valued feature vector ({size, number-of-rooms, age} for example). In some cases, there aren’t enough features in the available training data set. In this case, you can try adding polynomial features, which are computed by existing features. $\displaystyle h_{\theta}(x) = \theta_{0} * x_{0} + \theta_{1} * x_{1} + \theta_{2} * x_{2}^{2}$ $\displaystyle h_{\theta}(x) = \theta_{0} + \theta_{1} * \text{size} + \theta_{2} * \text{size}^{2}$ Using multiple features requires feature scaling, which is used to standardize the range of different features. For instance, the value range of $\text{size}^{2}$ feature is a magnitude larger than the range of the size feature. Without feature scaling, the $\text{size}^{2}$ feature will dominate the cost function. The error value produced by the $\text{size}^{2}$ feature will be much higher than the error value produced by the size feature. A simple algorithm for feature scaling is Mean Normalization: $\displaystyle x^{'} = \frac{x-avg(x)}{max(x)-min(x)}$ where $x^{'}$ is the normalized value. Mean normalization is used to rescale each sample. As you add more and more features, you may find that the target function fits better and better. If you add too many features, you could end up with a target function that is overfitting. ### Overfitting and cross-validation Overfitting occurs when the target function or model fits the training data too well, by capturing noise or random fluctuations in the training data. Although an overfitting model matches very well on the training data, it will perform badly when asked to solve for unknown, unseen data. To avoid overfitting: • Use a larger set of training data. • Use an improved machine learning algorithm by considering regularization. • Use fewer features. If your predictive model overfits, you should remove any features that do not contribute to its accuracy. The challenge here is to find the features that contribute most meaningfully to your prediction output. Overfitting can be identified by visualizing graphs. Even though this works well using two dimensional or three dimensional graphs, it will become difficult if you use more than two domain-specific features. This is why cross-validation is often used to detect overfitting. In a cross-validation, you evaluate the trained models using an unseen validation data set after the learning process has completed. The available, labeled data set will be split into three parts: • The training data set. • The validation data set. • The test data set.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 31, "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": 0.3865475058555603, "perplexity": 537.2733665862543}, "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/1637964363301.3/warc/CC-MAIN-20211206133552-20211206163552-00090.warc.gz"}
http://researchprofiles.herts.ac.uk/portal/en/publications/the-dynamics-and-distribution-of-angular-momentum-in-hizels-starforming-galaxies-at-z--08--33(7eb8b919-e76a-47c7-923d-1f3d856524de).html	# University of Hertfordshire ## The Dynamics and Distribution of Angular Momentum in HiZELS Star-Forming Galaxies at z = 0.8 - 3.3 Research output: Contribution to journalArticle ### Documents • S. Gillman • A. M. Swinbank • A. L. Tiley • C. M. Harrison • Ian Smail • U. Dudzevičiūtė • R. M. Sharples • P. N. Best • R. G. Bower • R. Cochrane • D. Fisher • K. Glazebrook • Edo Ibar • J. Molina • D. Obreschkow • M. Schaller • D. Sobral • S. Sweet • J. W. Trayford • T. Theuns Original language English Monthly Notices of the Royal Astronomical Society Jun 2019 486 1 15 Mar 2019 https://doi.org/10.1093/mnras/stz765 Published - Jun 2019 ### Abstract We present adaptive optics assisted integral field spectroscopy of 34 star-forming galaxies at $z$ = 0.8-3.3 selected from the HiZELS narrow-band survey. We measure the kinematics of the ionised interstellar medium on $\sim$1 kpc scales, and show that the galaxies are turbulent, with a median ratio of rotational to dispersion support of $v$/$\sigma$=0.82$\pm$0.13. We combine the dynamics with high-resolution rest-frame optical imaging and extract emission line rotation curves. We show that high-redshift star-forming galaxies follow a similar power-law trend in specific angular momentum with stellar mass as that of local late type galaxies. We exploit the high resolution of our data and examine the radial distribution of angular momentum within each galaxy by constructing total angular momentum profiles. Although the stellar mass of a typical star-forming galaxy is expected to grow by a factor $\sim$8 in the $\sim$5 Gyrs between $z$$\sim3.3 and z$$\sim$0.8, we show that the internal distribution of angular momentum becomes less centrally concentrated in this period i.e the angular momentum grows outwards. To interpret our observations, we exploit the EAGLE simulation and trace the angular momentum evolution of star forming galaxies from $z$$\sim3 to z$$\sim$0, identifying a similar trend of decreasing angular momentum concentration. This change is attributed to a combination of gas accretion in the outer disk, and feedback that preferentially arises from the central regions of the galaxy. We discuss how the combination of the growing bulge and angular momentum stabilises the disk and gives rise to the Hubble sequence. ID: 16918083	{"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": 0.9780639410018921, "perplexity": 3959.2783817144923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573184.25/warc/CC-MAIN-20190918044831-20190918070831-00476.warc.gz"}
https://forum.bebac.at/forum_entry.php?id=19414	## Test License [Regulatives / Guidelines] Dear RK, » I applied Test license for some X drug in India, I got permission and I imported the drug (reference) from outside India then conducted one study (pilot). Now I want to conduct one more study (pivotal) with remaining quantity of Reference drug from first study. Here I have some doubts: » 1) Can I use remaining quantity of reference drug for pivotal No, You can't use the rest of the reference drug for conducting a BE Study with a new ordered reference drug batch, as they are two different Batches ( Biobatches). » 2) If we use remaining IPs, Is we need to get Test license permission for pivotal. Yes, you will need. Regards, Osama Cheers, Osama	{"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": 0.8489528298377991, "perplexity": 4286.607827804934}, "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/1610704821381.83/warc/CC-MAIN-20210127090152-20210127120152-00736.warc.gz"}
http://strata.opengamma.io/apidocs/com/opengamma/strata/product/credit/type/CdsQuoteConvention.html	Enum CdsQuoteConvention • All Implemented Interfaces: Named, NamedEnum, Serializable, Comparable<CdsQuoteConvention> public enum CdsQuoteConvention extends Enum<CdsQuoteConvention> implements NamedEnum Market quote conventions for credit default swaps. • Enum Constant Summary Enum Constants Enum Constant Description PAR_SPREAD POINTS_UPFRONT Points upfront. QUOTED_SPREAD • Method Summary All Methods Modifier and Type Method Description static CdsQuoteConvention of(String name) Obtains an instance from the specified name. String toString() Returns the formatted name of the type. static CdsQuoteConvention valueOf(String name) Returns the enum constant of this type with the specified name. static CdsQuoteConvention[] values() Returns an array containing the constants of this enum type, in the order they are declared. • Methods inherited from class java.lang.Enum clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, valueOf • Methods inherited from class java.lang.Object getClass, notify, notifyAll, wait, wait, wait • Methods inherited from interface com.opengamma.strata.collect.named.NamedEnum getName • Enum Constant Detail public static final CdsQuoteConvention PAR_SPREAD Par spread is the old (i.e. pre-April 2009) way of quoting CDSs. A CDS would be constructed to have an initial fair value of zero; the par-spread is the value of the coupon (premium) on the premium leg that makes this so. A zero hazard curve (or equivalent, e.g. the survival probability curve) can be implied from a set of par spread quotes (on the same name at different maturities) by finding the curve that gives all the CDSs a PV of zero (the curve is not unique and will depend on other modeling choices). • POINTS_UPFRONT public static final CdsQuoteConvention POINTS_UPFRONT Points upfront. Points upfront (PUF) is the current (as of April 2009) way of quoting CDSs. A CDS has a fixed coupon (premium). An up front fee is payable by the buyer of protection (i.e. the payer of the premiums) - this fee can be negative (i.e. an amount is received by the protection buyer). PUF is quoted as a percentage of the notional. A zero hazard curve (or equivalent, e.g. the survival probability curve) can be implied from a set of PUF quotes (on the same name at different maturities) by finding the curve that gives all the CDSs a clean present value equal to their PUF * notional (the curve is not unique and will depend on other modeling choices). public static final CdsQuoteConvention QUOTED_SPREAD Quoted spread (sometimes misleadingly called flat spread) is an alternative to quoting PUF where people wish to see a spread like number. It is numerically close in value to the equivalent par spread but is not exactly the same. To find the quoted spread of a CDS from its PUF (and premium) one first finds the unique flat hazard rate that will give the CDS a clean present value equal to its PUF * notional; one then finds the par spread (the coupon that makes the CDS have zero clean PV) of the CDS from this flat hazard curve - this is the quoted spread (and the reason for the confusing name, flat spread). To go from a quoted spread to PUF, one does the reverse of the above. A zero hazard curve (or equivalent, e.g. the survival probability curve) cannot be directly implied from a set of quoted spreads - one must first convert to PUF. • Method Detail • values public static CdsQuoteConvention[] values() Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows: for (CdsQuoteConvention c : CdsQuoteConvention.values()) System.out.println(c); Returns: an array containing the constants of this enum type, in the order they are declared • valueOf public static CdsQuoteConvention valueOf(String name) Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.) Parameters: name - the name of the enum constant to be returned. Returns: the enum constant with the specified name Throws: IllegalArgumentException - if this enum type has no constant with the specified name NullPointerException - if the argument is null • of public static CdsQuoteConvention of(String name) Obtains an instance from the specified name. Parsing handles the mixed case form produced by toString() and the upper and lower case variants of the enum constant name. Parameters: name - the name to parse Returns: the type Throws: IllegalArgumentException - if the name is not known • toString public String toString() Returns the formatted name of the type. Overrides: toString in class Enum<CdsQuoteConvention> Returns: the formatted string representing the type	{"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": 0.4599464237689972, "perplexity": 4057.404525214346}, "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-2021-21/segments/1620243990419.12/warc/CC-MAIN-20210511214444-20210512004444-00543.warc.gz"}
https://psychology.stackexchange.com/questions/7597/how-to-report-an-f-statistic-in-apa-style	# How to report an F statistic in APA style? How do you report F statistics in APA format? I am working on PHD and am not certain that I am reporting the F statistics in the proper manner. I have been reporting it as F (_,_). The second space I am unclear as to what number gets placed there. ## migrated from stackoverflow.comJun 9 '14 at 14:33 This question came from our site for professional and enthusiast programmers. • This arguably belongs on CrossValidated. – jona Jun 9 '14 at 16:05 • I agree with @jona, in that APA format is not unique to cognitive sciences, whereas the question is explicitly statistical. However, there may be a duplicate on CV already, so I'd recommend checking before migrating. I don't see any harm in leaving it here in any case. – Nick Stauner Jun 10 '14 at 0:56 • I think the title focuses on APA style and in general I think that APA style (i.e., psychology) is on topic for cogsci (see this meta discussion). However, the body of this question is mostly a general statistical question that would be very much at home on CrossValidated. On balance, I think it would be fine on either site. – Jeromy Anglim Jun 10 '14 at 8:09 The numbers inside the parentheses are the degrees of freedom for the F-statistic. The second number is the within-group degrees of freedom. When you have the same number of subjects in all conditions, then the second number will be the number of subjects - the number of cells (conditions) in your design. The F ratio statistic has a numerator and denominator degrees of freedom. Thus, you report: F (numerator_df, denominator_df) = F_value, p = ..., effect size = ... The numerator degrees of freedom relates to the factor of interest; the denominator degrees of freedom corresponds to the degrees of freedom for the error variance. The exact way that these degrees of freedom are calculated depends on the statistical test you are using. Standard textbooks will describe these approaches. For example, in a standard one-way between subjects ANOVA with $k$ groups and $n$ participants per group, you would have $k-1$ numerator degrees of freedom and $kn-k$. Generally, you will be able to read off these numbers from the output of your statistics package. ### Example Here is an example with k=3 groups and n=5 participants. See the df in the "group" row and the "error" row. F(2, 12) = 24.667, p < .001.	{"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": 0.6665550470352173, "perplexity": 860.4406637507151}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665573.50/warc/CC-MAIN-20191112124615-20191112152615-00051.warc.gz"}
https://proceedings.neurips.cc/paper/2018/hash/9a96a2c73c0d477ff2a6da3bf538f4f4-Abstract.html	#### Authors Romain Lopez, Jeffrey Regier, Michael I. Jordan, Nir Yosef #### Abstract Parameterizing the approximate posterior of a generative model with neural networks has become a common theme in recent machine learning research. While providing appealing flexibility, this approach makes it difficult to impose or assess structural constraints such as conditional independence. We propose a framework for learning representations that relies on Auto-Encoding Variational Bayes and whose search space is constrained via kernel-based measures of independence. In particular, our method employs the $d$-variable Hilbert-Schmidt Independence Criterion (dHSIC) to enforce independence between the latent representations and arbitrary nuisance factors. We show how to apply this method to a range of problems, including the problems of learning invariant representations and the learning of interpretable representations. We also present a full-fledged application to single-cell RNA sequencing (scRNA-seq). In this setting the biological signal in mixed in complex ways with sequencing errors and sampling effects. We show that our method out-performs the state-of-the-art in this domain.	{"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": 0.4691629111766815, "perplexity": 1066.9293964737901}, "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/1664030338001.99/warc/CC-MAIN-20221007080917-20221007110917-00379.warc.gz"}
http://www.math.columbia.edu/~woit/wordpress/?p=6558	# Short Items • Harvard has announced that the Chinese firm Evergrande Group will be supporting various activities at Harvard, including a new Center for Mathematical Sciences and Applications, with S.-T. Yau as director. No details of what the center will do other than “serve as a fusion point for mathematics, statistics, physics, and related sciences.” The company has its own announcement here (they might want to check on the name of Harvard’s President…). • The new Physics Today has an article Paul Ehrenfest’s final years, a sad bit of physics history I’d never seen the details of. • Last month in Moscow there was a conference for Boris Feigin’s 60th birthday. Videos of the talks are now available here. • Dick Gross’s wonderful lecture series here at Columbia on Representation theory and number theory has been available on video since he gave the lectures. Now Chao Li at Harvard has produced a transcription of the talks, so a high-quality written version of the material of the lectures is now available. This is one of the best sources around to learn about the local Langlands conjectures. His website contains a lot of other interesting expository material. • Phenomenologist Jay Wacker has a blog at Quora, called Particle Physics Digressions. The latest entry is an odd tale of something I would have thought was rather unusual, but Wacker says it’s not exceptional, happens everyday. This entry was posted in Uncategorized. Bookmark the permalink. ### 20 Responses to Short Items 1. Peter Donnelly says: Ehrenfast article sounds interesting, but not $30 interesting. 2. Thelonious says: I have to agree that paying 30$ is a little hard to swallow, do you know if there is a good summary somewhere ? Do you know if there is going to be an Eilenberg lecture this coming semester (Gross’s lectures are amazing !!) ? 3. Thelonious says: I should add that Chao li’s lectures have been around for at least a year I think. On the other hand he just wrote, this semester, lecture notes from a course by Jack Thorne (http://www.math.harvard.edu/~chaoli/doc/AutomorphicForm.html) which, as far as I can tell, are one of the best ressource for learning thoroughly about the important objects in the number theoretic Langlands program (it isn’t just a broad overview, he actually proves stuff). 4. Peter Woit says: Thelonious, No Eilenberg lectures this spring, Joe Harris just finished his lecture series a couple weeks ago. I second the recommendation of the Thorne lecture notes. If anyone knows of a another source for the material about Ehrenfest, let me know. The policy of Physics Today to charge $30 to look at an article seems to have no point other than to ensure that no one does it. 5. claudius says: If even you think that$30 is too much to pay to look at an article, why did you even bother to link to it? 6. Martin says: http://www-history.mcs.st-and.ac.uk/Biographies/Ehrenfest-Afanassjewa.html “Paul Ehrenfest through his life had suffered from low self esteem, but now began to suffer from depression. He was also greatly saddened by his youngest son Vassily who suffered from Down’s syndrome and had severe problems both physically and mentally. On 25 September 1933 Ehrenfest shot Vassily in the waiting room of the Professor Watering Institute in Amsterdam where Vassily was being treated. Then he shot himself. The Dutch papers only reported his sudden death and gave lengthy accounts of his achievements. Ehrenfest-Afanassjewa returned to Leiden where she remained for the rest of her life. Not only did she lose her husband and youngest son in such a tragic way, but a few years later, in 1939, her eldest son Paul was killed by an avalanche while skiing in the French Alps.” 7. Peter Woit says: claudius, From my office at Columbia (as well as probably at many other places with an institutional subscription), Physics Today articles are freely available. I didn’t realize they were charging $30 to non-subscribers (actually I’m wondering if that’s new, hadn’t seen that before). 8. kashyap vasavada says: If you have an account at the campus computer center (most state univ. in U.S. will allow this for state residents) they will let you download physics today articles or even journal papers free. I am not sure about private univ. 9. gs says: This first: A hat tip to Evergrande and Hui Ka Yan for their generosity. Hopefully it augurs constructive relations, not enmity, between the USA and China. Nevertheless, it is surprising that a Chinese real estate company is underwriting mathematics and immunology at Harvard. (The Green Buildings initiative is more understandable.) The details would seem to warrant journalistic looking into, not in a spirit of suspicion but of due diligence. That said, I do not imply impropriety, and repeat my appreciation of Evergrande’s action. 10. Isidore Seveille says: IMHO, the donation from Evergrande is good PR work for Chinese companies given that some of those Chinese companies are placed under suspicion by the Congress and the media. On a related note, Huawei, a Chinese telecom company, has been supporting mathematics and theoretical physics research in IHES, according to this report . 11. Peter Donnelly says: OMG that was sad. 12. Thomas Larsson says: I was excited to find that the Feigen conference was dedicated to, among other things, double affine and toroidal algebras. Unfortunately, none of the talks seems to be about this subject. In my own work, I preferred to use the terms multi-dimensional affine and Virasoro algebras, rather than double (triple, quadruple, …) affine algebras, because the restriction to tori is not fundamental. Note that triple affine algebras are not related to gauge anomalies in QFT in 3+1 dimensions, since the extension is proportional to the second Casimir rather than to the third. The algebra pertaining to QFT gauge anomalies is called the Mickelsson-Faddeev algebra, and is something completely different. 13. lcs says: 12 issues of Physics Today costs$69, yet they charge $30 for a single article? Talk about not even wrong. Even if they charged$30 to download an entire issue it would be grossly out of proportion. Someone needs to upbraid these silly AIP publishers, who must be pompous beyond imagination to think their content merits this pay scale. 14. Jeff Murugan says: There’s a related story on the sad story of Ehrenfest’s last few days in Graham Farmelo’s “The Strangest Man” 15. harryb says: Added a comment to the Ehrenfest article site on Physics Today noting the sentiments of frustration on this blog. Would have been preferable to have been able to comment on the content. Their choice. 16. We’ve made the Physics Today article free so that its easier for people to access. We do offer a \$4 rental free to view the article, but we’re still ironing out some quirks in our new publishing system. Hence I apologize that this option was not available at first. The magazine is a benefit of membership in ten science societies. If you’ve previously registered with Physics Today, just click on the “sign in” option on the right hand side and you’ll be able to access everything, including our entire back archive, no matter whether you’re on campus or not. 17. Peter Woit says: Paul,	{"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": 0.16453321278095245, "perplexity": 2204.1316044442146}, "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-2015-48/segments/1448398446500.34/warc/CC-MAIN-20151124205406-00255-ip-10-71-132-137.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/proving-non-existence-of-integer-solutions-by-reducing-mod-p.565076/	# Proving non-existence of integer solutions by reducing mod p 1. ### Poopsilon 294 Say I have the equation a^2 - 10b^2 = 2. So even though this is an equation in two variables and not one, I can still reduce mod P to a^2 = 2 (mod 5) and use the fact that it has no integer solutions mod 5 to conclude the original equation has no integer solutions, correct? Also does this only work modulo a prime, or can I do this modulo any natural number? 2. ### Hurkyl 15,987 Staff Emeritus Correct. If there was an integer solution, that would also be a solution to the reduced-modulo-5 version. And since there isn't a solution to the reduced-modulo-5 version, there isn't an integer solution. Any natural number. But via the Chinese Remainder Theorem, you only really need to deal with prime powers -- e.g. reducing modulo 6 tells you the exact same information as considering reducing modulo 2 and reducing modulo 3 separately. For example, there's the theorem: A (polynomial) equation doesn't have a solution modulo 6 if and only if at least one of the following is true: • The equation doesn't have a solution modulo 2 • The equation doesn't have a solution modulo 3 Incidentally, it's fairly common that 4 and 8 are more useful to consider than 2. 3. ### Poopsilon 294 Ah yes, that makes sense, thanks =]. 4. ### TylerH 726 Would someone mind showing the steps to reducing that? (a^2-10b^2=2 to a^2 = 2 mod 5) 5. ### Deveno 906 to indicate a number modulo 5, i will write [n] instead of n, so [13] = [3]. a2 - 10b2 = 2 (given equation to solve) [a2 - 10b2] = [2] (reducing both sides modulo 5) [a2] - [10b2] = [2] (because mod 5, [x+y] = [x] + [y]) [a]2 - [10]2 = [2] (because mod 5, [xy] = [x][y]) [a]2 = [2] (because [10] = [0] mod 5) one can explicitly compute [a]2, for a = 0,1,2,3, and 4: [0][0] = [0] [1][1] = [1] [2][2] = [4] [3][3] = [9] = [4] [4][4] = [16] = [1] or, using an "old-fashioned method": let a = a' + 5k let b = b' + 5m then a2 - 10b2 = (a' + 5k)2 - 10(b' + 5m)2 = (a')2 + 10a'k + 25k2 - 10(b')2 - 100b'm + 250m2 collecting all obvious multiples of 5, we get: = a'2 + 5(2a'k + 5k2 - 2b'2 - 20b'm - 50m2) let n = 2a'k + 5k2 - 2b'2 - 20b'm - 50m2, then we have: a'2 + 5n = 2, that is: a2 = a'2 = 2 (mod 5). 6. ### TylerH 726 Oh, that makes sense. I actually did some of those, using the "old fashioned method," in my proof class, but only of a single variable. It was the second variable that threw me off. Thanks for the great explanation.	{"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": 0.8064727783203125, "perplexity": 1734.2997797059886}, "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-2015-48/segments/1448398462665.97/warc/CC-MAIN-20151124205422-00226-ip-10-71-132-137.ec2.internal.warc.gz"}
https://ask.sagemath.org/answers/12706/revisions/	# Revision history [back] You can do the following: R.ideal([f.reduce(J) for f in I.gens()]) That is basically what singular does: reduce the generators of I w.r.t. J. You can do the following: R.ideal([f.reduce(J) R.ideal([f.reduce(J.groebner_basis()) for f in I.gens()]) That is basically what singular does: reduce the generators of I w.r.t. J.	{"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": 0.9280690550804138, "perplexity": 6843.254984865517}, "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-2020-34/segments/1596439735851.15/warc/CC-MAIN-20200804014340-20200804044340-00012.warc.gz"}
http://www.mathworks.com/matlabcentral/fileexchange/23972-chebfun/content/chebfun/chebtests/basic/barytest.m	Code covered by the BSD License # Chebfun V4 ### Chebfun Team (view profile) 30 Apr 2009 (Updated ) Numerical computation with functions instead of numbers. ### Editor's Notes: This file was selected as MATLAB Central Pick of the Week barytest function pass = barytest % Test the evaluation of a chebfun using barycentric interpolation. % Pedro Gonnet, January 2011 % tolerance tol = 10 * chebfunpref('eps'); % create a chebfun from a polynomial of known degree f = @(x) (0.3 - x) .* (-0.7 - x) .* (-0.1 - x) .* (0.9 - x); x = chebpts( 10 ); fx = f(x); g = chebfun( fx ); % evaluate this at a random set of nodes xi xi = 1 - 2rand(1000,1); fxi = f(xi); % pass? pass = norm( g(xi) - fxi , inf ) < tol max(abs(fxi));	{"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": 0.4217888414859772, "perplexity": 27410.793267402623}, "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-2015-27/segments/1435375098987.83/warc/CC-MAIN-20150627031818-00263-ip-10-179-60-89.ec2.internal.warc.gz"}
https://www.cheenta.com/radius-of-a-semicircle-amc-8-2016-problem-25/	Select Page Try this beautiful problem from Geometry based on Radius of a semicircle inscribed in an isosceles triangle. ## Radius of a Semi circle – AMC-8, 2016 – Problem 25 A semicircle is inscribed in an isoscles triangle with base 16 and height 15 so that the diameter of the semicircle is contained in the base of the triangle as shown .what is the radius of the semicircle? • $\frac{110}{19}$ • $\frac{120}{17}$ • $\frac{9}{5}$ ### Key Concepts Geometry Area pythagoras But try the problem first… Answer:$\frac{120}{17}$ Source AMC-8, 2016 problem 25 Challenges and Thrills of Pre College Mathematics ## Try with Hints First hint Draw a perpendicular from the point C on base AB Can you now finish the problem ………. Second Hint D be the midpoint of the AB(since $\triangle ABC$ is an isoscles Triangle) Find AC and area can you finish the problem…….. Final Step Area of the $\triangle ABC= \frac{1}{2} \times AB \times CD$ = $\frac{1}{2} \times 16 \times 15$ =120 sq.unit Using the pythagoras th. $AC^2= AD^2+CD^2$ i.e $AC^2=(8)^2+(15)^2$ i.e $AC=17$ Let$ED = x$ be the radius of the semicircle Therefore Area of $\triangle CAD = \frac{1}{2} \times AC \times ED$=$\frac {1}{2} area of \triangle ABC$ i.e $\frac{1}{2} \times AC \times ED$=60 i.e $\frac{1}{2} \times 17 \times x$ =60 i.e $x=\frac {120}{7}$	{"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": 0.8431208729743958, "perplexity": 2637.7694234883465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497301.29/warc/CC-MAIN-20200330181842-20200330211842-00042.warc.gz"}
http://mathhelpforum.com/algebra/120215-simultaneous-equations.html	1. ## Simultaneous equations x+y=7, x^2 - y^2 = 21 How do I do this? 2. Originally Posted by Detanon x+7=7, xsquared - ysquared = 21 How do I do this? Did you make a typo? I ask because I only see one equation with y in. As is stands $x =0$ and $y = \pm i\sqrt{21}$ 3. Do you not "see" that x=0 ? 4. woops sorry, I fixed it now. 5. Originally Posted by Detanon woops sorry, I fixed it now. As that's better You can use the difference of two squares on the quadratic $(x+y)(x-y) = 7(x-y) = 21 \: \:$ $\therefore \: \: x-y = 3 \: \: \rightarrow \: \: x = 3+y$ Sub in x=3+y into the first equation (3+y)+y=7 Solve that for y then use the first equation (in either form) to find x 6. I dont get how you get (x+y)(x-y). 7. Originally Posted by Detanon I dont get how you get (x+y)(x-y). It is the difference of two squares. Difference of two squares - Wikipedia, the free encyclopedia From the difference of two squares we see that $x^2-y^2=(x+y)(x-y)$ If you expand the right hand side using FOIL the LHS is obtained: $(x+y)(x-y) = x^2-xy+xy-y^2$ Since $-xy+xy=0$ we get $(x+y)(x-y)=x^2-y^2$ ============================ EDIT: If you prefer you can use the substitution method $x = 7-y$ $(7-y)^2-y^2=21$ and solve that linear equation (y^2 cancels) but I think using the difference of two squares is easier	{"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": 10, "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": 0.9284695982933044, "perplexity": 1063.378900887798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123484.45/warc/CC-MAIN-20170423031203-00267-ip-10-145-167-34.ec2.internal.warc.gz"}
http://math.stackexchange.com/users/19530/joachim?tab=activity&sort=all	joachim Reputation 1,122 Top tag Next privilege 2,000 Rep. Jun29 awarded Taxonomist May30 awarded Popular Question Feb2 awarded Popular Question Dec8 awarded Caucus Nov15 awarded Yearling Sep30 awarded Explainer Aug23 awarded Popular Question Jul28 accepted Clever Substitution Notation for Logic Formulae Jul27 answered Clever Substitution Notation for Logic Formulae Jul27 asked Clever Substitution Notation for Logic Formulae Jul11 accepted Is infinitary logics $\mathcal{L}_{\infty\omega}$ an abstract logic? Jul11 comment Is infinitary logics $\mathcal{L}_{\infty\omega}$ an abstract logic? "$\varphi_T$ identifies a Turing Machine T" means that all models of $\varphi_T$ are isomorphic to T. Does this make sense? Thanks for the hints. Jul11 revised Is infinitary logics $\mathcal{L}_{\infty\omega}$ an abstract logic? edited tags Jul11 asked Is infinitary logics $\mathcal{L}_{\infty\omega}$ an abstract logic? Jul5 revised Cantor-like set removing middle-$\alpha$ open intervals fixing title Jul5 suggested approved edit on Cantor-like set removing middle-$\alpha$ open intervals Jul5 revised Quarters weigh 6 grams while dimes weigh 2 grams. Latex fixing Jul5 suggested approved edit on Quarters weigh 6 grams while dimes weigh 2 grams. Jul2 answered implication versus conjunction correctness in FOL? Jul2 awarded Curious	{"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": 0.7672846913337708, "perplexity": 20622.845753479913}, "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-2015-27/segments/1435375099105.15/warc/CC-MAIN-20150627031819-00097-ip-10-179-60-89.ec2.internal.warc.gz"}
http://www.ck12.org/trigonometry/Pythagorean-Theorem-to-Determine-Distance/asmtpractice/Pythagorean-Theorem-to-Determine-Distance-Practice/	<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> # Pythagorean Theorem to Determine Distance ## Distance as the hypotenuse of a right triangle. % Progress MEMORY METER This indicates how strong in your memory this concept is Progress % Pythagorean Theorem to Determine Distance Practice By CK-12 MAT.TRG.116	{"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": 0.9671297669410706, "perplexity": 28464.95641332753}, "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/1490218189092.35/warc/CC-MAIN-20170322212949-00425-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.peterbakke.com/neat-stuff/the-width-of-the-veil-nebula-is-3-fingers/	# The width of the Veil Nebula is 3 fingers So how does one calculate the width (in degrees) of any distant object – from say the Veil Nebula 2100 light years away to the width (in degrees) of that mountain just 21 miles away? Simple. But you will need a scientific calculator. Here’s one: http://web2.0calc.com/ Using the information given to you, say in an article about the Veil Nebula , calculate a ratio of distance over width. In this case, we are told the Veil Nebula is 2100 light years away and it is 110 light years in width. It is very convenient that they gave us distance and width in the same units (light years), else we’d have to do that ourselves. So, 2100 / 110 = 19.1 Using your scientific calculator (see above), enter 19.1 and hit the COT function (COTANGENT). The answer of 5.9 (degrees), or about the width of your three fingers extended at arms length towards the fabulous night sky – in this case in the direction of the Swan Constellation. Happiness is Astronomy ! (Conversely, of course, if you estimate the distance of an object and also estimate its width (in degrees), then you can determine the approximate width of the object {in feet, miles, light years, etc.}).	{"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": 0.8590772747993469, "perplexity": 1150.0952601106737}, "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/1669446710933.89/warc/CC-MAIN-20221203143925-20221203173925-00019.warc.gz"}
https://enhancedodds.co.uk/f1yne5hl/archive.php?cb5994=a-square-matrix-a-is-called-orthogonal-if	If matrix A is an circulant matrix whose elements of first row are a, b, c > 0 such that a b c = 1 and A τ A = 1 then a 3 + b 3 + c 3 equals to, View Answer If A = 3 1 ⎣ ⎢ ⎢ ⎡ 1 2 a 2 1 2 2 − 2 b ⎦ ⎥ ⎥ ⎤ is an orthogonal matrix… A complex square matrix A is called an orthogonal projector if A 2 = A = A, where A is the conjugate transpose of A.In this article, we first give some formulas for calculating the distributions of real eigenvalues of a linear combination of two orthogonal projectors. 10. Expert Answer . We also use C A/B to denote a coordinate transformation matrix to A from B or A symmetric matrix and skew-symmetric matrix both are square matrices. In general, a square matrix A is called an orthogonal matrix if AA T is a diagonal matrix, and it is called an orthonormal matrix if AA T is an identity matrix. is an orthogonal matrix and QTQ = I. We are to show that the determinant of such a matrix is either +1 or -1. A square matrix A is called orthogonal if A^TA = I_n . The orthogonal group is sometimes called the general orthogonal group, by analogy with the general linear group. View Winning Ticket If A is a symmetric matrix, then A = A T and if A is a skew-symmetric matrix then A T = – A.. Also, read: The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A. Go to your Tickets dashboard to see if you won! Show that the … Let v_1,v_2,ldots,v_n be the columns of an orthogonal matrix A . Step-by-step explanation: Given that the square matrix A is called orthogonal provided that . (1f) A square matrix A is called Hermitian if a ij =¯a ji (¯z := complex conjugate of z). An invertible square matrix A is called orthogonal if A^{-1}=A^{T} \left[\begin{array}{rr} 1 & -1 \\ -1 & -1 \end{a… The Study-to-Win Winning Ticket number has been announced! Equivalently, it is the group of n×n orthogonal matrices, where the group operation is given by matrix multiplication; an orthogonal matrix is a real matrix whose inverse equals its transpose. What are the possible values of the determinant of an orthogonal matrix? (2) A rectangular matrix A is called nonnegative if a ij ≥0alli,j. Unitary Matrix:- A Complex Square matrix U is a Unitary Matrix if its Conjugate transpose (U) is its inverse. (1g) E ij has a 1 in the (i,j) position and zeros in all other positions. ... For a square matrix A, vectors in Col A are orthogonal to vectors in Nul A. But then ... FALSE (- To be orthogonal, a matrix must have orthonormal columns and be square) If A is an n × n orthogonal matrix, then IIAxII = IIxII holds for all vectors x in Rn. Get 1:1 help now from expert Algebra tutors Solve it … (1e) A square matrix A is called symmetric if a ij = a ji. TRUE - (IIAxII2 = (Ax)T (Ax) = xT (ATA)x IIAxII2 = xT In x = xT x = IIxII2) If A is the 2 × 2 upper triangular matrix But the difference between them is, the symmetric matrix is equal to its transpose whereas skew-symmetric matrix is a matrix whose transpose is equal to its negative.. Click hereto get an answer to your question ️ A square matrix A is said to be orthogonal if A'A = AA' = In If both A - 1/2I and A + 1/2I are orthogonal matrices, then We will be using the following result : Given that, for matrix A, Taking determinant of the matrices on both sides of the above equation, we get. i.e :- UU = UU* = I , where 'I ' is the Identity Matrix. Previous question Next question Get more help from Chegg. FALSE [1 1 0 0] ... A number c is an eigenvalue of a square matrix A if and only if the equation (A - cI)x = 0 has a nontrivial solution. For an orthonormal matrix A, we have A -1 = A T and IA[ = +1. A square matrix A is called orthogonal if A /5 −1 = AT . 2020 a square matrix a is called orthogonal if	{"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": 0.9538418054580688, "perplexity": 429.7768244705032}, "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/1634323585265.67/warc/CC-MAIN-20211019105138-20211019135138-00484.warc.gz"}
https://www.physicsforums.com/threads/electron-accelerator-build.766842/	# Electron accelerator build 1. Aug 20, 2014 ### Rob Hoff How strong of a magnetic field do I need to get a 20kv @ 60ma beam around a 90° turn? / Do I need more information to find out? 2. Aug 20, 2014 ### Baluncore The electrons go around the corner independently. They will need to travel 90° around a circular path. How much time do you have? What radius do you require? You will need to determine the dimension of the poles of your magnet. The poles will need to be big enough to enclose the electron beam during the turn, yet small enough to have a high field. The optimum solution may be to have several magnets along the path. That may explain why accelerators are usually circular. http://en.wikipedia.org/wiki/Lorentz_force http://en.wikipedia.org/wiki/Gyroradius Last edited: Aug 20, 2014 3. Aug 20, 2014 ### Okefenokee First you need to know the speed of the electrons. Applying a voltage to a free moving electron will impart kinetic energy to it. E = V * e = 20kV * 1.610^-19 = 3.210^-15 and 1/2 * m v^2 = E so v = (E2/ m)^0.5 = 8.410^7 m/s Note that I didn't factor in relativity. I'll leave that for you to figure out. Now you can pick a radius of curvature that you would like, the centripetal force needed for that curvature, and the magnetic field needed to achieve that force from Lorentz's force law and the speed of the electron in your experiment. 4. Aug 21, 2014 ### Rob Hoff Hey thanks you guys, and sorry if that sounded like I wanted you guys to do my homework. It really wasn't meant that way. Thanks for the equations. :) And Baluncore, I have as much time as it takes! Last edited: Aug 21, 2014 Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook Have something to add? Draft saved Draft deleted Similar Discussions: Electron accelerator build	{"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": 0.8544700741767883, "perplexity": 1409.0769261824878}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2016-36/segments/1471982291592.14/warc/CC-MAIN-20160823195811-00201-ip-10-153-172-175.ec2.internal.warc.gz"}
https://digitopia.be/disappointment-room-ostxr/london-dispersion-forces-vs-van-der-waals-4463ad	See all questions in Van der Waals Interactions. Van der Waals interaction (also known as London dispersion energies) Van der Waals (VDW) interactions are probably the most basic type of interaction imaginable. London dispersion forces, named after German-American physicist Fritz London, are one of the three Van der Waals intermolecular forces holding molecules together. London Dispersion Forces vs Van der Waals Forces. Each electrostatic interaction produces a potential energy that varies as 1/z 6, where z is the separation The van der Waals force was named after a Dutch scientist Johannes Diderik van der Waals (1837-1923). Dispersion force on the other hand london forces is the case where one or both of the dipoles or multipoles are transient that may arise entirely from continual fluctuations in electron densities. Van der Waals forces can be classified as weak London dispersion Forces and stronger dipole-dipole forces. Dispersion forces (one of the two types of van der Waals force we are dealing with on this page) are also known as "London forces" (named after Fritz London who first suggested how they might arise). They occur due to: Momentary dipoles occurring due to uneven electron distributions in neighbouring molecules as they approach one another. The weak residual attraction of the nuclei in one molecule for the electrons in a neighbouring molecule. Any two molecules experience Van der Waals interactions. There are two kinds of Van der Waals forces: weak London Dispersion Forces and stronger dipole-dipole forces. What is the difference between London dispersion forces and van der Waals forces? • Van der Waals forces can occur between two permanent dipoles, dipole- induced dipole, or two induced dipoles. Van Der Waals Forces: London Dispersion Forces, Dipole Attractions, and Hydrogen Bonds. London dispersion forces result from the coulombic interactions between instantaneous dipoles. The relationship between van der waals forces and hydrophobic interactions is that the van der waals act to bind the hydrophobe - non-polar substance - together, to separate from the polar solvent/water, and these contribute to the energy needed to separate the two substances. In general, all the intermolecular forces of attraction between molecules are called Van der Waals forces. Van der Waals forces. London dispersion forces are a type of force acting between atoms and molecules. Dispersion is just the forces due to instantaneous induced dipole moments. Van Der Waals dispersion forces are close-knit interactions depending on distance resulting in intermolecular attractions or repulsions. User account menu. This is because it is easier to displace the electrons because the forces of attraction between the electrons and protons in the nucleus are weaker. Van derwaal’s forces are very weak attractive forces existing between molecules. The London dispersion force is the weakest of the van der Waals forces and is the force that causes nonpolar atoms or molecules to condense into liquids or solids as the temperature is lowered. The weakest of these forces is the London dispersion force, one of the Van der Waals forces. This results in a slightly negative (\$$\\delta-\$$) and slightly positive \$$(\\delta+)\$$ charge on either side of the atom. Van der Waals forces: The weakest intermolecular force and consist of dipole-dipole forces and dispersion forces . London dispersion forces result from the coulombic interactions between instantaneous dipoles. For an intermolecular attraction, there should be a charge separation. Van der Waals forces and hydrogen bonds are intermolecular attractions between molecules. The weak residual attraction of the nuclei in one molecule for the electrons in a neighbouring molecule. Having shown that dispersion forces aren't necessarily weak (in fact, can be quite strong), let's now look at the relative importance of dipole-dipole interactions and dispersion forces. London dispersion forces are the weakest type of intermolecular bond. As such, it’s not really a useful term, Van Der Waals did a lot of stuff. Posted by 4 years ago. Polar covalent bonds behave as if the bonded atoms have localized fractional charges that are equal but opposite (i.e., the two bonded atoms generate a dipole). These van der Waals forces vanish very quickly as the distance between the interacting … There are three main types of van der Waals forces, two of which I have discussed at length on the previous page. Les forces de Londres ou de dispersion sont une sous-catégorie de la force de van der Waals qui se produit en raison de la formation de dipôles instantanés entre deux (ou plus) atomes / molécules qui sont neutres en raison de la distorsion de la distribution électronique. References. See all questions in Van der Waals Interactions. Van der Waals interaction (also known as London dispersion energies) Van der Waals (VDW) interactions are probably the most basic type of interaction imaginable. London dispersion forces, named after German-American physicist Fritz London, are one of the three Van der Waals intermolecular forces holding molecules together. London Dispersion Forces vs Van der Waals Forces. Each electrostatic interaction produces a potential energy that varies as 1/z 6, where z is the separation The van der Waals force was named after a Dutch scientist Johannes Diderik van der Waals (1837-1923). Dispersion force on the other hand london forces is the case where one or both of the dipoles or multipoles are transient that may arise entirely from continual fluctuations in electron densities. Van der Waals forces can be classified as weak London dispersion Forces and stronger dipole-dipole forces. Dispersion forces (one of the two types of van der Waals force we are dealing with on this page) are also known as "London forces" (named after Fritz London who first suggested how they might arise). They occur due to: Momentary dipoles occurring due to uneven electron distributions in neighbouring molecules as they approach one another. The weak residual attraction of the nuclei in one molecule for the electrons in a neighbouring molecule. Any two molecules experience Van der Waals interactions. There are two kinds of Van der Waals forces: weak London Dispersion Forces and stronger dipole-dipole forces. What is the difference between London dispersion forces and van der Waals forces? • Van der Waals forces can occur between two permanent dipoles, dipole- induced dipole, or two induced dipoles. Van Der Waals Forces: London Dispersion Forces, Dipole Attractions, and Hydrogen Bonds. London dispersion forces result from the coulombic interactions between instantaneous dipoles. The relationship between van der waals forces and hydrophobic interactions is that the van der waals act to bind the hydrophobe - non-polar substance - together, to separate from the polar solvent/water, and these contribute to the energy needed to separate the two substances. In general, all the intermolecular forces of attraction between molecules are called Van der Waals forces. Van der Waals forces. London dispersion forces are a type of force acting between atoms and molecules. Dispersion is just the forces due to instantaneous induced dipole moments. Van Der Waals dispersion forces are close-knit interactions depending on distance resulting in intermolecular attractions or repulsions. User account menu. This is because it is easier to displace the electrons because the forces of attraction between the electrons and protons in the nucleus are weaker. Van derwaal’s forces are very weak attractive forces existing between molecules. The London dispersion force is the weakest of the van der Waals forces and is the force that causes nonpolar atoms or molecules to condense into liquids or solids as the temperature is lowered. The weakest of these forces is the London dispersion force, one of the Van der Waals forces. This results in a slightly negative (\$$\\delta-\$$) and slightly positive \$$(\\delta+)\$$ charge on either side of the atom. Van der Waals forces: The weakest intermolecular force and consist of dipole-dipole forces and dispersion forces . London dispersion forces result from the coulombic interactions between instantaneous dipoles. For an intermolecular attraction, there should be a charge separation. Van der Waals forces and hydrogen bonds are intermolecular attractions between molecules. The weak residual attraction of the nuclei in one molecule for the electrons in a neighbouring molecule. Having shown that dispersion forces aren't necessarily weak (in fact, can be quite strong), let's now look at the relative importance of dipole-dipole interactions and dispersion forces. London dispersion forces are the weakest type of intermolecular bond. As such, it’s not really a useful term, Van Der Waals did a lot of stuff. Posted by 4 years ago. Polar covalent bonds behave as if the bonded atoms have localized fractional charges that are equal but opposite (i.e., the two bonded atoms generate a dipole). These van der Waals forces vanish very quickly as the distance between the interacting … There are three main types of van der Waals forces, two of which I have discussed at length on the previous page. Les forces de Londres ou de dispersion sont une sous-catégorie de la force de van der Waals qui se produit en raison de la formation de dipôles instantanés entre deux (ou plus) atomes / molécules qui sont neutres en raison de la distorsion de la distribution électronique. References.	{"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": 0.8732237219810486, "perplexity": 815.8357456638603}, "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/1627046154408.7/warc/CC-MAIN-20210802234539-20210803024539-00083.warc.gz"}
http://terrytao.wordpress.com/tag/riesz-thorin-theorem/	You are currently browsing the tag archive for the ‘Riesz-Thorin theorem’ tag. In the previous two quarters, we have been focusing largely on the “soft” side of real analysis, which is primarily concerned with “qualitative” properties such as convergence, compactness, measurability, and so forth. In contrast, we will begin this quarter with more of an emphasis on the “hard” side of real analysis, in which we study estimates and upper and lower bounds of various quantities, such as norms of functions or operators. (Of course, the two sides of analysis are closely connected to each other; an understanding of both sides and their interrelationships, are needed in order to get the broadest and most complete perspective for this subject.) One basic tool in hard analysis is that of interpolation, which allows one to start with a hypothesis of two (or more) “upper bound” estimates, e.g. ${A_0 \leq B_0}$ and ${A_1 \leq B_1}$, and conclude a family of intermediate estimates ${A_\theta \leq B_\theta}$ (or maybe ${A_\theta \leq C_\theta B_\theta}$, where ${C_\theta}$ is a constant) for any choice of parameter ${0 < \theta < 1}$. Of course, interpolation is not a magic wand; one needs various hypotheses (e.g. linearity, sublinearity, convexity, or complexifiability) on ${A_i, B_i}$ in order for interpolation methods to be applicable. Nevertheless, these techniques are available for many important classes of problems, most notably that of establishing boundedness estimates such as ${\\| T f \\|_{L^q(Y, \nu)} \leq C \\| f \\|_{L^p(X, \mu)}}$ for linear (or “linear-like”) operators ${T}$ from one Lebesgue space ${L^p(X,\mu)}$ to another ${L^q(Y,\nu)}$. (Interpolation can also be performed for many other normed vector spaces than the Lebesgue spaces, but we will just focus on Lebesgue spaces in these notes to focus the discussion.) Using interpolation, it is possible to reduce the task of proving such estimates to that of proving various “endpoint” versions of these estimates. In some cases, each endpoint only faces a portion of the difficulty that the interpolated estimate did, and so by using interpolation one has split the task of proving the original estimate into two or more simpler subtasks. In other cases, one of the endpoint estimates is very easy, and the other one is significantly more difficult than the original estimate; thus interpolation does not really simplify the task of proving estimates in this case, but at least clarifies the relative difficulty between various estimates in a given family. As is the case with many other tools in analysis, interpolation is not captured by a single “interpolation theorem”; instead, there are a family of such theorems, which can be broadly divided into two major categories, reflecting the two basic methods that underlie the principle of interpolation. The real interpolation method is based on a divide and conquer strategy: to understand how to obtain control on some expression such as ${\\| T f \\|_{L^q(Y, \nu)}}$ for some operator ${T}$ and some function ${f}$, one would divide ${f}$ into two or more components, e.g. into components where ${f}$ is large and where ${f}$ is small, or where ${f}$ is oscillating with high frequency or only varying with low frequency. Each component would be estimated using a carefully chosen combination of the extreme estimates available; optimising over these choices and summing up (using whatever linearity-type properties on ${T}$ are available), one would hope to get a good estimate on the original expression. The strengths of the real interpolation method are that the linearity hypotheses on ${T}$ can be relaxed to weaker hypotheses, such as sublinearity or quasilinearity; also, the endpoint estimates are allowed to be of a weaker “type” than the interpolated estimates. On the other hand, the real interpolation often concedes a multiplicative constant in the final estimates obtained, and one is usually obligated to keep the operator ${T}$ fixed throughout the interpolation process. The proofs of real interpolation theorems are also a little bit messy, though in many cases one can simply invoke a standard instance of such theorems (e.g. the Marcinkiewicz interpolation theorem) as a black box in applications. The complex interpolation method instead proceeds by exploiting the powerful tools of complex analysis, in particular the maximum modulus principle and its relatives (such as the Phragmén-Lindelöf principle). The idea is to rewrite the estimate to be proven (e.g. ${\\| T f \\|_{L^q(Y, \nu)} \leq C \\| f \\|_{L^p(X, \mu)}}$) in such a way that it can be embedded into a family of such estimates which depend holomorphically on a complex parameter ${s}$ in some domain (e.g. the strip ${\{ \sigma+it: t \in {\mathbb R}, \sigma \in [0,1]\}}$. One then exploits things like the maximum modulus principle to bound an estimate corresponding to an interior point of this domain by the estimates on the boundary of this domain. The strengths of the complex interpolation method are that it typically gives cleaner constants than the real interpolation method, and also allows the underlying operator ${T}$ to vary holomorphically with respect to the parameter ${s}$, which can significantly increase the flexibility of the interpolation technique. The proofs of these methods are also very short (if one takes the maximum modulus principle and its relatives as a black box), which make the method particularly amenable for generalisation to more intricate settings (e.g. multilinear operators, mixed Lebesgue norms, etc.). On the other hand, the somewhat rigid requirement of holomorphicity makes it much more difficult to apply this method to non-linear operators, such as sublinear or quasilinear operators; also, the interpolated estimate tends to be of the same “type” as the extreme ones, so that one does not enjoy the upgrading of weak type estimates to strong type estimates that the real interpolation method typically produces. Also, the complex method runs into some minor technical problems when target space ${L^q(Y,\nu)}$ ceases to be a Banach space (i.e. when ${q<1}$) as this makes it more difficult to exploit duality. Despite these differences, the real and complex methods tend to give broadly similar results in practice, especially if one is willing to ignore constant losses in the estimates or epsilon losses in the exponents. The theory of both real and complex interpolation can be studied abstractly, in general normed or quasi-normed spaces; see e.g. this book for a detailed treatment. However in these notes we shall focus exclusively on interpolation for Lebesgue spaces ${L^p}$ (and their cousins, such as the weak Lebesgue spaces ${L^{p,\infty}}$ and the Lorentz spaces ${L^{p,r}}$).	{"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": 31, "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": 0.8723093867301941, "perplexity": 275.2370815147995}, "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-2014-10/segments/1393999636668/warc/CC-MAIN-20140305060716-00025-ip-10-183-142-35.ec2.internal.warc.gz"}
https://www.zbmath.org/?q=an%3A1205.14069	× # zbMATH — the first resource for mathematics The tropical vertex. (English) Zbl 1205.14069 The tropical vertex group consists of formal 1-parameter families of symplectomorphisms of the 2-dimensional algebraic torus, and in this article, the authors establish a formula for an ordered product factorization of the commutator of generators in the tropical vertex group in terms of certain relative genus zero Gromov-Witten invariants of toric surfaces. More generally, they prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of relative genus zero Gromov-Witten invariants. The proof begins by using scattering diagram expansions to connect commutators to tropical curve counts, which can be then related to holomorphic curve counts. The commutator formulas are then established via degeneration and exact Gromov-Witten calculations. An interesting open question raised by this work is whether and how the higher genus Gromov-Witten invariants are related to the tropical vertex group. ##### MSC: 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) 53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds Full Text: ##### References: [1] D. Abramovich, T. Graber, and A. Vistoli, Gromov-Witten theory for Deligne-Mumford stacks . · Zbl 1193.14070 · arxiv.org [2] J. Bryan and R. Pandharipande, Curves in Calabi-Yau threefolds and topological quantum field theory , Duke Math. J. 126 (2005), 369–396. · Zbl 1084.14053 · doi:10.1215/S0012-7094-04-12626-0 [3] -, Local Gromov-Witten theory of curves , J. Amer. Math. Soc. 21 (2008), 101–136. · Zbl 1126.14062 · doi:10.1090/S0894-0347-06-00545-5 [4] W. Chen and Y. Ruan, “Orbifold Gromov-Witten theory” in Orbifolds in Mathematics and Physics (Madison, Wis., 2001) , Contemp. Math. 310 , Amer. Math. Soc., Providence, 2002, 25–85. · Zbl 1091.53058 [5] A. Gathmann, Relative Gromov-Witten invariants and the mirror formula , Math. Ann. 325 (2003), 393–412. · Zbl 1043.14016 · doi:10.1007/s00208-002-0345-1 [6] A. Gathmann and H. Markwig, The numbers of tropical plane curves through points in general position , J. Reine Angew. Math. 602 (2007), 155–177. · Zbl 1115.14049 · doi:10.1515/CRELLE.2007.006 [7] R. Gopakumar and C. Vafa, M-theory and topological strings—I ,\arxivhep-th/9809187v1$$\!\!$$. · Zbl 0922.32015 [8] -, M-theory and topological strings—II ,\arxivhep-th/9812127v1$$\!\!$$. [9] T. Graber and R. Vakil, Relative virtual localization and vanishing of tautological classes on moduli spaces of curves , Duke Math. J. 30 (2005), 1–37. · Zbl 1088.14007 · doi:10.1215/S0012-7094-05-13011-3 [10] M. Gross and B. Siebert, From real affine geometry to complex geometry . · Zbl 1266.53074 · arxiv.org [11] E.-N. Ionel and T. H. Parker, Relative Gromov-Witten invariants , Ann. of Math. (2) 157 (2003), 45–96. JSTOR: · Zbl 1039.53101 · doi:10.4007/annals.2003.157.45 · links.jstor.org [12] P. Johnson, R. Pandharipande, and H.-H. Tseng, Abelian Hurwitz-Hodge integrals . · arxiv.org [13] M. Kontsevich and Y. Soibelman, “Affine structures and non-Archimedean analytic spaces” in The Unity of Mathematics , Progr. Math. 244 , Birkhäuser, Boston, 2006, 321–385. · Zbl 1114.14027 · doi:10.1007/0-8176-4467-9_9 [14] -, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations . · arxiv.org [15] A.-M. Li and Y. Ruan, Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds , Invent. Math. 145 (2001), 151–218. · Zbl 1062.53073 · doi:10.1007/s002220100146 [16] J. Li, Stable morphisms to singular schemes and relative stable morphisms , J. Differential Geom. 57 (2001), 509–578. · Zbl 1076.14540 [17] -, A degeneration formula for G-W invariants , J. Differential Geom. 60 (2002), 199–293. · Zbl 1063.14069 [18] D. Maulik and R. Pandharipande, Gromov-Witten theory and Noether-Lefschetz theory . · Zbl 1317.14126 · arxiv.org [19] G. Mikhalkin, Enumerative tropical algebraic geometry in $$\RR^2$$ , J. Amer. Math. Soc. 18 (2005), 313–377. · Zbl 1092.14068 · doi:10.1090/S0894-0347-05-00477-7 [20] T. Nishinou and B. Siebert, Toric degenerations of toric varieties and tropical curves , Duke Math. J. 135 (2006), 1–51. · Zbl 1105.14073 · doi:10.1215/S0012-7094-06-13511-1 [21] R. Pandharipande, Hodge integrals and degenerate contributions , Comm. Math. Phys. 208 (1999), 489–506. · Zbl 0953.14036 · doi:10.1007/s002200050766 [22] -, “Three questions in Gromov-Witten theory” in Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002) , Higher Ed. Press, Beijing, 2002, 503–512. · Zbl 1047.14043 [23] M. Reineke, Poisson automorphisms and quiver moduli . · Zbl 1232.53072 · arxiv.org [24] -, Cohomology of quiver moduli, functional equations, and integrality of Donaldson-Thomas type invariants . · Zbl 1266.16013 · arxiv.org [25] N. Takahashi, Log mirror symmetry and local mirror symmetry . · Zbl 1066.14048 · arxiv.org [26] A. Zinger, A comparison theorem for Gromov-Witten invariants in the symplectic category . · Zbl 1225.14046 · doi:10.1016/j.aim.2011.05.021 · arxiv.org 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.	{"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": 0.8313173055648804, "perplexity": 2399.280045231326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988837.67/warc/CC-MAIN-20210508031423-20210508061423-00069.warc.gz"}
http://www.flyingcoloursmaths.co.uk/wrong-but-useful-episode-1/	# Wrong, but Useful: Episode 1 What’s this? Multimedia? Whatever next? What you are about to click is an audio extravaganza: a mathematical conversation between me and Dave Gale, who is @reflectivemaths on twitter. It’s the first episode of Wrong, But Useful. Mentioned in this podcast: The Maths/Maths podcast (with Samuel Hansen and Peter Rowlett) – currently on hiatus TES Maths Podcast (with Craig Barton) Festival of the Spoken Nerd podcast All Squared (with Katie Steckles and Christian Perfect) A list of the 10 coolest numbers And the competition questions (don’t phone, it’s just for fun): • What’s the title of the podcast all about? • What’s the history of gradians? • Why is the volume of a pyramid $\frac{1}{3}x^2h$? ## Colin Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove. ### 88 comments on “Wrong, but Useful: Episode 1” • ##### Chris Smith @aap03102 It’s reassuring to hear other folk rambling on about numbers and enjoying it too! Just one thought: when compiling an ordered list of an arbitrary ‘n’ favourite numbers surely ‘n’ has to be allocated one of the positions? • ##### Colin Not necessarily – if all of my numbers were above 10, none of them would be in the right position. • ##### Dave Gale So if I did my top 15 say, then 15 should be one of those numbers because I deemed it an important enough ranking to stop at? Interesting idea but I’m going to go for ‘coolest’ so I think I can ignore that rule. Thanks for listening Chris. Dave • ##### singinghedgehog Enjoyed this first episode. It did have that slightly awkward feel of one of the early editions of Math/Maths but I’m sure as you do more it will get slicker. The item on favourite numbers and what a negative letter would look like did manage to send me rummaging on t’interweb for reverse letter alt codes. Writing in capitals makes backwards writing much easier eg: ИƎƎTЯIHT ƧUИIM and ИƎƎTʇIʇ ƎVITAʚƎИ are both the same length as their value! [cyrillic letters are useful here] My favourite number would be pi, as my students well know, but they will often say it is a very big number meaning a very long number. Regarding decimal things, Gradians are French and decimal time also; they ran in decimal time in the late 1790s. http://www.decimaltime.hynes.net/ is the best source of info I have found. The nicest ‘proof’ of the pyramid formula is by making 3 right angled triangular pyramids and fitting them together to make a cube. Looking forward to the next one! • ##### Colin Glad you liked it! Thanks for the feedback :o) • ##### twentythree Great podcast,very enjoyable. Beginning and ending are a little jarring though, you need a little something to bookend it imo. • ##### Colin You mean… production values?! • ##### twentythree Math/maths has their ringing sound and let’s be fair, their production values are pretty low • Pingback: Travels in a Mathematical World • Pingback: Wrong, but useful \| cavmaths • ##### STEP Maths Heeeey, I’m abit late for giving any feedback for the 1st episode but only just found out about your podcasts when someone shared your episode 28 (legoland intro :P) with me…so decided to start from the beginning episode 1 #WrongButUseful. Keep up the the podcasting! BTW – what kind of microphone do you use for your podcasting? • ##### Colin Thanks! These days, I have a Zalman ZMMIC1 lapel mic, but I think I was using a Sennheiser headset mic at the start. I know Dave has a posh stand-alone mic — I’ll ask about it when we record next :o)	{"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": 0.5776138305664062, "perplexity": 6089.345910575904}, "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/1512948594665.87/warc/CC-MAIN-20171217074303-20171217100303-00401.warc.gz"}
https://www.csauthors.net/jun-ma/	# Jun Ma According to our database1, Jun Ma authored at least 347 papers between 1986 and 2020. Collaborative distances: Book In proceedings Article PhD thesis Other ## Bibliography 2020 A Novel Attack-and-Defense Signaling Game for Optimal Deceptive Defense Strategy Choice. Wirel. Commun. Mob. Comput., 2020 Ultra-Narrow-Band Filter Based on High Q Factor in Metallic Nanoslit Arrays. Sensors, 2020 Distributed Non-Communicating Multi-Robot Collision Avoidance via Map-Based Deep Reinforcement Learning. Sensors, 2020 Estimation of Sugarcane Yield Using a Machine Learning Approach Based on UAV-LiDAR Data. Remote. Sens., 2020 Understanding the Land Surface Phenology and Gross Primary Production of Sugarcane Plantations by Eddy Flux Measurements, MODIS Images, and Data-Driven Models. Remote. Sens., 2020 Joint Effect of Spartina alterniflora Invasion and Reclamation on the Spatial and Temporal Dynamics of Tidal Flats in Yangtze River Estuary. Remote. Sens., 2020 F1 Lightning: HTAP as a Service. Proc. VLDB Endow., 2020 Supervised and semi-supervised twin parametric-margin regularized extreme learning machine. Pattern Anal. Appl., 2020 Orientation selective deep brain stimulation of the subthalamic nucleus in rats. NeuroImage, 2020 Tracking the phenology and expansion of Spartina alterniflora coastal wetland by time series MODIS and Landsat images. Multim. Tools Appl., 2020 Twin minimax probability extreme learning machine for pattern recognition. Knowl. Based Syst., 2020 Fisher-regularized supervised and semi-supervised extreme learning machine. Knowl. Inf. Syst., 2020 Build real-time communication for hybrid dual-OS system. J. Syst. Archit., 2020 A Risk Analysis Framework for Social Engineering Attack Based on User Profiling. J. Organ. End User Comput., 2020 Low-complexity compensation of sampling offset with cross-correlation and early-late gate for OFDM receivers. J. Comput. Methods Sci. Eng., 2020 Research on Chinese medical named entity recognition based on collaborative cooperation of multiple neural network models. J. Biomed. Informatics, 2020 Capped L1-norm distance metric-based fast robust twin bounded support vector machine. Neurocomputing, 2020 Some q-rung orthopair fuzzy 2-tuple linguistic Muirhead mean aggregation operators and their applications to multiple-attribute group decision making. Int. J. Intell. Syst., 2020 Sparse Least Squares Support Vector Machine With Adaptive Kernel Parameters. Int. J. Comput. Intell. Syst., 2020 A supply chain network economic model with time-based competition. Eur. J. Oper. Res., 2020 AbdomenCT-1K: Is Abdominal Organ Segmentation A Solved Problem? CoRR, 2020 Multi-Site Infant Brain Segmentation Algorithms: The iSeg-2019 Challenge. CoRR, 2020 A Fast Algorithm for Geodesic Active Contours with Applications to Medical Image Segmentation. CoRR, 2020 Segmentation Loss Odyssey. CoRR, 2020 Towards Efficient COVID-19 CT Annotation: A Benchmark for Lung and Infection Segmentation. CoRR, 2020 The $1/k$-Eulerian Polynomials of Type $B$. Electron. J. Comb., 2020 Projection multi-birth support vector machinea for multi-classification. Appl. Intell., 2020 Capped L<sub>1</sub>-norm distance metric-based fast robust twin extreme learning machine. Appl. Intell., 2020 Real-time detection of wildfire risk caused by powerline vegetation faults using advanced machine learning techniques. Transfer learning for long-interval consecutive missing values imputation without external features in air pollution time series. EMSGD: An Improved Learning Algorithm of Neural Networks With Imbalanced Data. IEEE Access, 2020 David-Barton type identities and alternating run polynomials. You Are What You Broadcast: Identification of Mobile and IoT Devices from (Public) WiFi. Proceedings of the 29th USENIX Security Symposium, 2020 Contextualized Emotion Recognition in Conversation as Sequence Tagging. Proceedings of the 21th Annual Meeting of the Special Interest Group on Discourse and Dialogue, 2020 How Distance Transform Maps Boost Segmentation CNNs: An Empirical Study. Proceedings of the International Conference on Medical Imaging with Deep Learning, 2020 AutoKnow: Self-Driving Knowledge Collection for Products of Thousands of Types. Proceedings of the KDD '20: The 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 2020 Improving Replay Detection System with Channel Consistency DenseNeXt for the ASVspoof 2019 Challenge. Proceedings of the Interspeech 2020, 2020 Non-Parallel Voice Conversion with Fewer Labeled Data by Conditional Generative Adversarial Networks. Proceedings of the Interspeech 2020, 2020 Nonparallel Emotional Speech Conversion Using VAE-GAN. 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Proceedings of the HCI International 2020 - Late Breaking Papers: Digital Human Modeling and Ergonomics, Mobility and Intelligent Environments, 2020 Modeling Periodic Pattern with Self-Attention Network for Sequential Recommendation. Proceedings of the Database Systems for Advanced Applications, 2020 Deformation Measurement of Drogue in Wind Tunnel Test Based on OptiTrack System. Proceedings of the 5th International Conference on Automation, 2020 TXtract: Taxonomy-Aware Knowledge Extraction for Thousands of Product Categories. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics, 2020 2019 Message-Passing Receiver Design for Joint Channel Estimation and Data Decoding in Uplink Grant-Free SCMA Systems. IEEE Trans. Wirel. Commun., 2019 Tenant-Oriented Monitoring for Customized Security Services in the Cloud. Symmetry, 2019 A robust method to discover influential users in social networks. 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Proceedings of the 17th Wuhan International Conference on E-Business, 2018 Using the Encoder Embedded Framework of Dimensionality Reduction Based on Multiple Drugs Properties for Drug Recommendation. Proceedings of the Advances in Swarm Intelligence - 9th International Conference, 2018 Automatic Brain Tumor Segmentation by Exploring the Multi-modality Complementary Information and Cascaded 3D Lightweight CNNs. Proceedings of the Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries, 2018 A Machine Learning Application for Electric Power Industrial Big-Data Based on Hadoop. Proceedings of the 14th International Conference on Natural Computation, 2018 Using Hybrid Similarity-Based Collaborative Filtering Method for Compound Activity Prediction. Proceedings of the Intelligent Computing Theories and Application, 2018 Collaborative Filtering based Recommendation Algorithm for Recommending Active Molecules for Protein Targets. 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Proceedings of the Security, Privacy, and Anonymity in Computation, Communication, and Storage, 2016 Chinese Paraphrases Acquisition Based on Random Walk N Step. Proceedings of the Natural Language Understanding and Intelligent Applications, 2016 An Optimized DHT for Linux Package Distribution. Proceedings of the 15th International Symposium on Parallel and Distributed Computing, 2016 A novel optimization scheme for caching in locality-aware P2P networks. Proceedings of the IEEE Symposium on Computers and Communication, 2016 Service Model Design and Application of Product Design and Component Procurement for Small and Medium Sized Concrete Mixer Manufacturers Based on Cloud Manufacturing. Proceedings of the Internet and Distributed Computing Systems, 2016 A Modified Genetic Algorithm for Agricultural By-products Logistics Delivery Route Planning Problem. Proceedings of the Internet and Distributed Computing Systems, 2016 Weakly supervised image parsing by discriminatively semantic graph propagation. Proceedings of the IEEE International Conference on Multimedia and Expo, 2016 Improved electrical and thermal performances in nanostructured GaN devices. Proceedings of the International Conference on IC Design and Technology, 2016 PowerCap: Leverage Performance-Equivalent Resource Configurations for power capping. Proceedings of the Seventh International Green and Sustainable Computing Conference, 2016 A kernel fuzzy clustering infrared image segmentation algorithm based on histogram and spatial restraint. Proceedings of the 9th International Congress on Image and Signal Processing, 2016 Correlation-Based Weighted K-Labelsets for Multi-label Classification. Proceedings of the Web Technologies and Applications - 18th Asia-Pacific Web Conference, 2016 Business Process Mining based Insider Threat Detection System. Proceedings of the Advances on P2P, 2016 2015 REPS: 一种高效的容错并行概率流Skyline查询方法 (REPS: An Efficient Fault-tolerant Approach for Parallel Skyline Queries over Probabilistic Data Streams). Signal-walking-driven active contour model. IET Image Process., 2015 Rooted cyclic permutations of lattice paths and uniform partitions. Discret. Math., 2015 Network Anomaly Detection with Compression. Proceedings of the 2015 International Conference on Intelligent Information Hiding and Multimedia Signal Processing, 2015 Discrete time integral sliding-mode control for systems with matched and unmatched uncertainties. Proceedings of the IEEE International Conference on Information and Automation, 2015 An Improved Parallel Algorithm of Genetic Programming Based on the Framework of MapReduce. Proceedings of the 2015 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, 2015 Collaborate, Not Only as a Developer, but also as a PLAYER. Proceedings of the 2015 Annual Symposium on Computer-Human Interaction in Play, 2015 Gender Prediction Based on Data Streams of Smartphone Applications. Proceedings of the Big Data Computing and Communications - First International Conference, 2015 2014 DTS: Dynamic TDMA scheduling for Networked Control Systems. J. Syst. Archit., 2014 PRIAM: Privacy Preserving Identity and Access Management Scheme in Cloud. KSII Trans. Internet Inf. Syst., 2014 On the maximum penalized likelihood approach for proportional hazard models with right censored survival data. Comput. Stat. Data Anal., 2014 An Efficient Influence Maximization Algorithm to Discover Influential Users in Micro-blog. Proceedings of the Web-Age Information Management - 15th International Conference, 2014 Key-Policy Weighted Attribute based Encryption for fine-grained access control. Proceedings of the IEEE International Conference on Communications, 2014 Thermal-Sustainable Power Budgeting for Dynamic Threading. Proceedings of the 51st Annual Design Automation Conference 2014, 2014 Herbert: a motion-controlled mobile game. Proceedings of the first ACM SIGCHI annual symposium on Computer-human interaction in play, Toronto, ON, Canada, October 19, 2014 A novel cranial electrotherapy stimulation system with arbitrary waveform stimulation. Proceedings of the 7th International Conference on Biomedical Engineering and Informatics, 2014 Amphisbaena: Modeling two orthogonal ways to hunt on heterogeneous many-cores. Proceedings of the 19th Asia and South Pacific Design Automation Conference, 2014 Recommendation Based on Frequent N-adic Concepts. Proceedings of the Web Technologies and Applications - 16th Asia-Pacific Web Conference, 2014 2013 VLSI Implementation of a High-Throughput Iterative Fixed-Complexity Sphere Decoder. IEEE Trans. Circuits Syst. II Express Briefs, 2013 Efficient revocation in ciphertext-policy attribute-based encryption based cryptographic cloud storage. J. Zhejiang Univ. Sci. 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Proceedings of the IEEE International Conference on Robotics and Biomimetics, 2013 A Comprehensive Method for Text Summarization Based on Latent Semantic Analysis. Proceedings of the Natural Language Processing and Chinese Computing, 2013 Ciphertext-Policy Weighted Attribute Based Encryption for Fine-Grained Access Control. Proceedings of the 2013 5th International Conference on Intelligent Networking and Collaborative Systems, 2013 Research on the Multi-scale Electronic Map Overlaying and Rendering in Global 3D Terrain Environment. Proceedings of the Seventh International Conference on Image and Graphics, 2013 A spherical perceptual color model. Proceedings of the Color Imaging XVIII: Displaying, 2013 2012 A fuzzy attitude based bidding strategy in continuous double auctions. Web Intell. Agent Syst., 2012 A Multiplicative Iterative Algorithm for Box-Constrained Penalized Likelihood Image Restoration. IEEE Trans. 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Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012 VLSI implementation of an 855 Mbps high performance soft-output K-Best MIMO detector. Proceedings of the 2012 IEEE International Symposium on Circuits and Systems, 2012 Digital and Analog Compatible TV Transmitter Power Measurement. Proceedings of the Information Computing and Applications - Third International Conference, 2012 TNC-eSA: An Echanced Security Access Solution to Office Networks. Proceedings of the Information Computing and Applications - Third International Conference, 2012 A TNC Protocol for 3GPP-WLAN Integrated Environment. Proceedings of the Information Computing and Applications - Third International Conference, 2012 ALERT: semantic event-driven collaborative platform for software development. Proceedings of the Sixth ACM International Conference on Distributed Event-Based Systems, 2012 Cloud computing based logistics resource dynamic integration and collaboration. Proceedings of the IEEE 16th International Conference on Computer Supported Cooperative Work in Design, 2012 An Event-Driven System for Business Awareness Management in the Logistics Domain. Proceedings of the Business Process Management Workshops, 2012 Initial Investigation into Using Two-Level Regional Voting Approach for Face Verification. Proceedings of the 2012 IEEE/ACIS 11th International Conference on Computer and Information Science, Shanghai, China, May 30, 2012 2011 Generalized EM estimation for semi-parametric mixture distributions with discretized non-parametric component. Stat. Comput., 2011 Refinements of (n, m)-Dyck paths. Eur. J. Comb., 2011 Some equitably 3-colorable cycle decompositions of K<sub>v</sub>+I. Discret. Math., 2011 Indirect density estimation using the iterative Bayes algorithm. Comput. Stat. Data Anal., 2011 Appearance frequency modulated gene set enrichment testing. BMC Bioinform., 2011 Positively Constrained total Variation penalized Image Restoration. 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Proceedings of the 38th International Symposium on Computer Architecture (ISCA 2011), 2011 Total variation smoothed maximum penalized likelihood tomographic reconstruction with positivity constraints. Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2011 An Active Data Leakage Prevention Model for Insider Threat. Proceedings of the 2nd International Symposium on Intelligence Information Processing and Trusted Computing, 2011 Trusted Bytecode Virtual Machine Module: Towards Dynamic Remote Attestation in Cloud Computing. Proceedings of the 2nd International Symposium on Intelligence Information Processing and Trusted Computing, 2011 Solving Motion Law by Numerical Simulation on Bowl Seeding Transplanting Robot. Proceedings of the Computer and Computing Technologies in Agriculture V, 2011 Mailbook: privacy-protecting social networking via email. Proceedings of the ICIMCS 2011, 2011 Extracting characteristics based on multi-scale space. Proceedings of the Eighth International Conference on Fuzzy Systems and Knowledge Discovery, 2011 The modeling method of curved surface based on ACIS. Proceedings of the International Conference on Electronic and Mechanical Engineering and Information Technology, 2011 Efficient energy consumption in a smart office based on intelligent complex event processing. Proceedings of the Fifth ACM International Conference on Distributed Event-Based Systems, 2011 Multi-Side Multi-Instance Algorithm. Proceedings of the Seventh International Conference on Computational Intelligence and Security, 2011 Semantic Complex Event Reasoning - Beyond Complex Event Processing. Proceedings of the Foundations for the Web of Information and Services, 2011 Workflow-Based Assessment of Student Online Activities with Topic and Dialogue Role Classification. Proceedings of the Artificial Intelligence in Education - 15th International Conference, 2011 What is happening in a still picture? 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Proceedings of the 2010 IEEE Wireless Communications and Networking Conference, 2010 CDMA and SC-FDMA Reverse Link Comparison for Cellular Voice and Data Communications. Proceedings of the 71st IEEE Vehicular Technology Conference, 2010 Identifying Protein-Protein Interaction Sites Using Granularity Computing of Quotient Space Theory. Proceedings of the Rough Set and Knowledge Technology - 5th International Conference, 2010 Hierarchical Segmentation and Identification of Thoracic Vertebra Using Learning-Based Edge Detection and Coarse-to-Fine Deformable Model. Proceedings of the Medical Image Computing and Computer-Assisted Intervention, 2010 Computational Workflows for Assessing Student Learning. Proceedings of the Intelligent Tutoring Systems, 10th International Conference, 2010 Iterative region of interest reconstruction in emission tomography. Proceedings of the 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2010 Production scheduling for virtual cellular manufacturing systems with workforce constraints using a hybrid algorithm. Proceedings of the Sixth International Conference on Natural Computation, 2010 A constraint programming approach for production scheduling of multi-period virtual cellular manufacturing systems. Proceedings of the Sixth International Conference on Natural Computation, 2010 Comparison of CDMA and OFDMA Reverse Link for Cellular Voice Communications. Proceedings of IEEE International Conference on Communications, 2010 A study on the specification of knowledge granularity in knowledge management. Proceedings of the Seventh International Conference on Fuzzy Systems and Knowledge Discovery, 2010 2009 An XML-based schema for stochastic programs. Ann. Oper. Res., 2009 The Knowledge Sharing Based on PLIB Ontology and XML for Collaborative Product Commerce. Proceedings of the Web Information Systems and Mining, International Conference, 2009 A customer network value model based on complex network theory. Proceedings of the IEEE International Conference on Systems, 2009 Feature Selection for Sensor Interoperability: A Case Study in Fingerprint Segmentation. Proceedings of the IEEE International Conference on Systems, 2009 A Novel Method of Score Level Fusion Using Multiple Impressions for Fingerprint Verification. Proceedings of the IEEE International Conference on Systems, 2009 Lifting Events in RDF from Interactions with Annotated Web Pages. Proceedings of the Semantic Web - ISWC 2009, 8th International Semantic Web Conference, 2009 Proceedings of the On the Move to Meaningful Internet Systems: OTM 2009, 2009 Network Anomaly Detection Using Dissimilarity-Based One-Class SVM Classifier. Proceedings of the ICPPW 2009, 2009 Using Agents' Attitudes and Assessments in Automated Fuzzy Bidding Strategy. Proceedings of the ICAART 2009 - Proceedings of the International Conference on Agents and Artificial Intelligence, Porto, Portugal, January 19, 2009 Interference Cancellation Techniques for CDMA2000 1x Reverse Link. Proceedings of the Global Communications Conference, 2009. GLOBECOM 2009, Honolulu, Hawaii, USA, 30 November, 2009 Pearl River Delta PM10 Remote Sensing Monitoring and System Design. Proceedings of the 2009 International Conference on Environmental Science and Information Application Technology, 2009 Ontology Based Semantic Relation Verification for TCM Semantic Grid. Proceedings of the Fourth ChinaGrid Annual Conference, ChinaGrid 2009, Yantai, Shandong, 2009 MapReduce-Based Pattern Finding Algorithm Applied in Motif Detection for Prescription Compatibility Network. Proceedings of the Advanced Parallel Processing Technologies, 8th International Symposium, 2009 A convergent recursive least squares approximate policy iteration algorithm for multi-dimensional Markov decision process with continuous state and action spaces. Proceedings of the IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning, 2009 Contextualised Event-driven Prediction with Ontology-based Similarity. Proceedings of the Intelligent Event Processing, 2009 Swarm Intelligence: Ant-Based Robot Path Planning. Proceedings of the Fifth International Conference on Information Assurance and Security, 2009 Anomalous Payload Detection System Using Analysis of Frequent Sequential Pattern. Proceedings of the Fifth International Conference on Information Assurance and Security, 2009 2008 Block-Iterative Fisher Scoring Algorithms for Maximum Penalized Likelihood Image Reconstruction in Emission Tomography. IEEE Trans. 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Proceedings of the 2008 ACM Symposium on Applied Computing (SAC), 2008 Anomaly Detection in Computer Networks Using Dissimilarity-Based One-Class Classifiers. Proceedings of the Eighth International Conference on Intelligent Systems Design and Applications, 2008 Research on Fuzzy Evaluation Method of E-business Website Based on Rough Set. Proceedings of the 2008 International Symposium on Computer Science and Computational Technology, 2008 Multiplicative iterative algorithms for positive constrained reconstructions in emission and transmission tomography. Proceedings of the 2008 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008 Boundary Detection from Spectral Information. Proceedings of the Advances in Neuro-Information Processing, 15th International Conference, 2008 Image Filling-In: A Gestalt Approach. Proceedings of the Advances in Neuro-Information Processing, 15th International Conference, 2008 A Linear Hybrid Classifier for Fingerprint Segmentation. Proceedings of the Fourth International Conference on Natural Computation, 2008 An Algorithm for Multicast Optimal Partition of QoS with Uncertain Condition. Proceedings of the Fourth International Conference on Natural Computation, 2008 Fingerprint Scaling. Proceedings of the Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues, 2008 A Test Data Compression Scheme for Reducing Power Based on OLELC and NBET. Proceedings of the Advanced Intelligent Computing Theories and Applications. With Aspects of Theoretical and Methodological Issues, 2008 A Fuzzy Comprehensive Evaluation Model for Software Dependability Based on Entropy Weight. Proceedings of the International Conference on Computer Science and Software Engineering, 2008 Conflict resolution for collaborative design based on rough set theory. Proceedings of the 12th International Conference on CSCW in Design, 2008 A Fuzzy Bidding Strategy in Automated Auctions Using Agent's Perspective. Proceedings of the 2008 International Conferences on Computational Intelligence for Modelling, 2008 Ontology-based Scientific Data Service Composition: A Query Rewriting-based Approach. Proceedings of the Semantic Scientific Knowledge Integration, 2008 Mining Target Marketing Groups From Users' Web of Trust on Epinions. Proceedings of the Social Information Processing, 2008 2007 Filter-based resolution principle for lattice-valued propositional logic LP(<i>X</i>). Inf. Sci., 2007 Redefined fuzzy implicative filters. Inf. Sci., 2007 On optimal codes with <i>w</i>-identifiable parent property. Des. Codes Cryptogr., 2007 Inter-working between SIMPLE and IMPS. Comput. Stand. Interfaces, 2007 An Approach for Combining Ontology Learning and Semantic Tagging in the Ontology Development Process: eGovernment Use Case. 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Image Process., 1986	{"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": 0.24004769325256348, "perplexity": 15649.436272700932}, "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/1606141542358.71/warc/CC-MAIN-20201201013119-20201201043119-00034.warc.gz"}
https://indico.ific.uv.es/event/6178/contributions/15868/	# 17th International Conference on Topics in Astroparticle and Underground Physics (TAUP 2021) 26 August 2021 to 3 September 2021 ## New Constraints on Strongly Interacting Sub-GeV Dark Matter via Electron Scattering from a small Dual-Phase Xenon TPC 30 Aug 2021, 18:00 1h 30m Poster Dark Matter and its detection ### Speaker Simon Buse (University of Zurich) ### Description We report new results on interactions of sub-GeV dark matter particles with electrons using data from a small dual-phase xenon time projection chamber operated at the Earth's surface 1. We consider scattering both on electrons and nuclei in the Earth’s crust, atmosphere, and shielding materials to compute the attenuation of the dark matter flux by the atmosphere and the 2. With an exposure of $\sim15\,\mathrm{g}\,\mathrm{days}$ and based on an ionisation-only event selection and no background subtraction, we evaluate the data in terms of various models, including interactions mediated by a heavy and ultralight dark photon as well as through an electric dipole moment 3. For the case of a heavy dark photon mediator, we exclude new parameter space for dark matter particle masses in the range $100-400\,\mathrm{MeV}$. ### Primary authors Simon Buse (University of Zurich) Patricia Sanchez-Lucas (University of Zurich) Prof. Laura Baudis (University of Zurich) ### Presentation Materials ###### Your browser is out of date! Update your browser to view this website correctly. Update my browser now ×	{"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": 0.495566725730896, "perplexity": 3463.7358426509886}, "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/1669446711360.27/warc/CC-MAIN-20221208183130-20221208213130-00832.warc.gz"}
http://math.stackexchange.com/questions/154195/the-fundamental-exact-sequence-associated-to-a-closed-space	# the fundamental exact sequence associated to a closed space Let $(X,\mathcal O_X)$ be an algebraic variety. If $Y\subseteq X$ is a closed subset, then we can equip $Y$ with a structure of algebraic variety $(Y,\mathcal O_Y)$. The function $i:Y\rightarrow X$ is the usual immersion, moreover if $i_\mathcal O_Y$ is the pushforward of $\mathcal O_Y$ through $i$, we have the following surjective morphism of sheaves: $\mathcal O_X(U)\rightarrow i_\mathcal O_Y(U):=\mathcal O_X(U\cap Y)$ such that $s\mapsto s\|_{U\cap Y}$ Clearly $i_\mathcal O_Y$ is an $\mathcal O_X$-module and the kernel of the above morphism, called $\mathcal I_{Y\|X}$, is a sheaf of ideals, so an $\mathcal O_X$-module. Finally we have the fundamental exact sequence of $\mathcal O_X$-modules associated to $Y$: $$0\longrightarrow \mathcal I_{Y\|X}\longrightarrow \mathcal O_X\longrightarrow i_\mathcal O_Y\longrightarrow 0$$ I have two question, one conceptual and one more technical: 1) Why is it so important considering closed subspaces of $X$? For example if $U\subseteq X$ is open, then $(U,\mathcal O_X\|_U)$ is an algebraic variety so one can costruct the fundamental sequence for $U$. 2) In some texts there is the identification of $i_\mathcal O_Y$ with the sheaf $\mathcal O_Y$. How can I prove this identification? - (2) is simply an abuse of notation. I do not recommend it. – Zhen Lin Jun 5 '12 at 16:29 Let $X$ be an integral scheme and let $Y$ be a non-empty open subscheme of $X$. $X$ is irreducible, so $Y$ is dense in $X$. I claim the induced homomorphism $i^\flat : \mathscr{O}_X \to i_ \mathscr{O}_Y$ is monic but not necessarily epic. Indeed, the claim is local on $X$ and $Y$, so we may take $X$ to be affine and $Y$ to be a distinguished open subscheme of $X$. But then all we have is a localisation of an integral domain, and this is always injective but not necessarily surjective. The point is that there isn't one notion of subscheme which gives rise to open and closed subschemes; rather, there are two. Open subschemes are a special case of the following construction: if $X$ is a locally ringed space and $Y$ is any subset of $X$, we can make $Y$ into a locally ringed space by pulling back $\mathscr{O}_X$ along the inclusion $i : Y \hookrightarrow X$. Unfortunately, there's no guarantee that $(Y, i^{-1} \mathscr{O}_X)$ is a scheme even if $(X, \mathscr{O}_X)$ is. On the other hand, the definition of a closed subscheme depends a lot on the scheme structure. If $Y$ is a closed subset of $X$, that means $Y \cap U$ is closed in $U$ for every open subset $U$ – but we know that closed subsets of $\operatorname{Spec} A$ are homeomorphic to $\operatorname{Spec} A / \mathfrak{a}$ for some suitable ideal $\mathfrak{a}$, and in essence the structure of $Y$ as a closed subscheme of $X$ is defined so that we have an exact sequence $$0 \longrightarrow i^{-1} \mathscr{I}_{Y \mid X} \longrightarrow i^{-1} \mathscr{O}_X \longrightarrow \mathscr{O}_Y \longrightarrow 0$$ or equivalently, so that we have the "fundamental exact sequence": $$0 \longrightarrow \mathscr{I}_{Y \mid X} \longrightarrow \mathscr{O}_X \longrightarrow i_* \mathscr{O}_Y \longrightarrow 0$$ But the story for varieties is more subtle. For the purposes of this discussion, I mean "variety" in the sense of a reduced scheme of finite type over an algebraically closed field $k$. Because varieties have enough closed points, the structure sheaf of a variety $X$ is isomorphic to a subsheaf of the sheaf of continuous functions $X(k) \to \mathbb{A}^1(k)$. (Henceforth, I will pretend non-closed points don't exist.) Thus, there is a canonical way of restricting regular functions on (any open subset of) $X$ to any (not necessarily open or closed!) subset $Y$ of $X$. If $Y$ is open, this recovers the open subscheme structure, and if $Y$ is closed, this recovers the closed subscheme structure. Let's look at this more closely. We define $\mathscr{I}_{Y \mid X}$ to be the subsheaf of $\mathscr{O}_X$ consisting of those regular functions which vanish on $Y$, i.e. $$\mathscr{I}_{Y \mid X} (U) = \{ f \in \mathscr{O}_X : \forall y \in Y . \, f (y) = 0 \}$$ and we define, for each open subset $V$ of $Y$, $$\mathscr{O}_Y (V) = \varinjlim_{U \supseteq V} \mathscr{O}_X (U) / \mathscr{I}_{Y \mid X} (U)$$ This is a sheaf because $Y$ is quasicompact. (Every subset of $X$ is quasicompact!) If $Y$ is open, then $V$ is open in $X$, so we are taking the direct limit over a directed system with a terminal object – hence $\mathscr{O}_Y (V) \cong \mathscr{O}_X (V) / \mathscr{I}_{Y \mid X} (V) \cong \mathscr{O}_X (V)$ in this case. For $Y$ closed something weird happens as well. Let $U$ be an open affine subset of $X$. Then, $V = U \cap Y$ is a closed subset of $U$ and an open subset of $Y$. Suppose $f \in \mathscr{O}_X (U)$ does not vanish on $V$. Then, the Nullstellensatz implies $f$ is already invertible in $\mathscr{O}_X (U) / \mathscr{I}_{Y \mid X} (U)$ – and this implies that the directed system is constant! In particular, we get $i_* \mathscr{O}_Y \cong \mathscr{O}_X / \mathscr{I}_{Y \mid X}$. In general, however, we don't get anything nice. There is a natural left exact sequence of groups $$0 \longrightarrow \mathscr{I}_{Y \mid X} (U) \longrightarrow \mathscr{O}_X (U) \longrightarrow \mathscr{O}_Y (U \cap Y)$$ and therefore a left exact sequence of sheaves on $X$: $$0 \longrightarrow \mathscr{I}_{Y \mid X} \longrightarrow \mathscr{O}_X \longrightarrow i_* \mathscr{O}_Y$$ We have just seen that this extends to a short exact sequence when $Y$ is closed. When $Y$ is open and $X$ is irreducible, the homomorphism $\mathscr{O}_X \to i_* \mathscr{O}_Y$ is monic but in general not epic. (Consider a point $x \in X \setminus Y$: the stalk of $i_* \mathscr{O}_Y$ at $x$ gives the fraction field of the local ring $\mathscr{O}_{X, x}$.) -	{"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": 0.9806233644485474, "perplexity": 69.86280711035796}, "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-2015-27/segments/1435375094931.19/warc/CC-MAIN-20150627031814-00262-ip-10-179-60-89.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/98024/maximize-product-of-two-numbers-formed-with-the-digits-1-to-9?answertab=oldest	# maximize product of two numbers formed with the digits $1$ to $9$ You are given the digits from $1$ to $9$. You can form two numbers by concatenating them, for example, $975123$ and $864$, and then take the product of the two resulting numbers. Find how to maximize the product. To give you a hint, the answer is $87531\cdot9642$. - You could simply try them all. Since the digits should be listed in decreasing order from left to right, there are only 512 possibilities to check. In Mathematica, possibilities = Map[FromDigits[Reverse[#]] &, {#, Complement[Range[9], #]} & /@ Subsets[Range[9]], {2}]; First[Reverse[SortBy[{#, Times @@ #} & /@ possibilities, Last]]] {{87531, 9642}, 843973902} - surely I wanted an analytic solution. :) – Qiang Li Jan 11 '12 at 22:10 Well, the problem looks very Project Euler-ish where the objective is to find a solution using a combination of programming and cleverness. – Mark McClure Jan 11 '12 at 22:14 I agree. But the result looks very informative in the sense that there is some rule here. But I am not sure how to formulate. – Qiang Li Jan 12 '12 at 1:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.7837874889373779, "perplexity": 412.18961523085454}, "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-2015-27/segments/1435375097354.86/warc/CC-MAIN-20150627031817-00056-ip-10-179-60-89.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/the-action-principle.153780/	# The action principle 1. Jan 30, 2007 ### nolanp2 i've been using langrangeans to solve eqns for a few months in class now but can't figure out where lagrange's equations actually come from. my problem is that i cant understand why the action integral S always takes a minimum value. can anyone help me with this? 2. Jan 30, 2007 ### ZapperZ Staff Emeritus What you want to study is what is known as the Calculus of Variation. This is often found in mathematical physics text/courses. The best source to start is Mary Boas's text "Mathematical Methods in the Physical Sciences", a book that I recommend all physics undergraduate to get. She has a whole chapter on the calculus of variation that is very easy to follow at the undergraduate level. Other than that, you may want to get a few sources from Edwin Taylor's page, who is a strong advocate on the teaching of the least action principle ahead of the standard Newtonian "force" concept. He has several links to his papers here: http://www.eftaylor.com/leastaction.html Zz. Have something to add? Similar Discussions: The action principle	{"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": 0.846458375453949, "perplexity": 714.7076521818651}, "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-2016-50/segments/1480698542323.80/warc/CC-MAIN-20161202170902-00402-ip-10-31-129-80.ec2.internal.warc.gz"}
https://gomathanswerkey.com/texas-go-math-grade-8-lesson-2-1-answer-key/	Texas Go Math Grade 8 Lesson 2.1 Answer Key Scientific Notation with Positive Powers of 10 Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 2.1 Answer Key Scientific Notation with Positive Powers of 10. Texas Go Math Grade 8 Lesson 2.1 Answer Key Scientific Notation with Positive Powers of 10 Essential Question How can you use scientific notation to express very large quantities? Using Scientific Notation Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10. The weights of various sea creatures are shown in the table. Write the weight of the blue whale in scientific notation. A. Move the decimal point in 250,000 to the left as many places as necessary to find a number that is greater than or equal to 1 and less than 10. What number did you find? ____ A and B to represent 250,000. Repeat steps A through C towrite the weight of the whale shark in scientific notation. Reflect Question 1. How many places to the left did you move the decimal point to write 41,200 in scientific notation? ___________________________________ We need to move the decimal point 4 places to the left to write 42,200 in scientific notation. 41,200 = 41,200.0 = 4.1200 × 104 = 4.12 × 104 Four places to the left. Question 2. What is the exponent on 10 when you write 41,200 in scientific notation? To write 41,200 in scientific notation, we move the decimal point 4 places to the right and we multiply by 104. 41,200 = 4.12 • 104 4 places to the left Write each number in scientific notation. Question 3. 6,400 6,400 Given 6.400 Move the decimal point 3 places to the left. 6.4 Remove extra zeros 1000 Divide the original number by the result from above 103 Write the answer as power of 10. 6 × 103 Write the product of the results from above 6 × 103 Question 4. 570,000,000,000 570,000,000,000 Given 5.70000000000 Move the decimal point $. Remove extra zeros. 100, 000, 000, 000 Divide the original number by the result from above. 1011 Write the answer as power of 10. 5.7 × 1011 Write the product of the results from above 5.7 × 1011 Question 5. A light-year is the distance that light travels in a year and is equivalent to 9,461,000,000,000 km. Write this distance in scientific notation. Answer: 9,461,000, 000,000 Given 9,461000000000 Move the decimal point 11 places to the left. 9.461 Remove extra zeros. 1, 000, 000, 000, 000 Divide the original number by the result from above. 1012 Write the answer as power of 10. 9.461 × 1012 km Write the product of the results from above 9.461 × 1012 km Question 6. 3.5 × 106 means that decimal should be moved 6 decimals. Placeholders zeros. are added as necessary. Moving one decimal, gives 35 and the remaining five decimals are represented by placeholder zeros. Question 7. To express a number in scientific notation we follow some steps: 1. We move the decimal point until we get a number that is greater than or equal to 1 and less than 10. 2. We divide the original number with the one we got from Step 1. 3. We write the product of the results from Step I and Step 2. In our case. the given number is already greater than 1 and less than 10. So it can be written as: 5.3 = 5.3 100 The exponent on 10 is 0. The exponent on 10 is 0 Question 8. 7.034 × 109 Given 9 places Use exponent of the power of 10 to determine the number places to move the decimal point 7,034 000000 Place the decimal point Since you are going to write a number greater than 7.035, move decimal point to the right. Add placeholder zeros if necessary. The number 7.034 × 109 in standard form is 7, 034,000,000 Question 9. 2.36 × 105 Given 5 places Use exponent of the power of 10 to determine the number places to move the decimal point 236,000 Place the decimal point Since you are going to write a number greater than 2.36, move decimal point to the right Add placeholder zeros if necessary. The number 2.36 × 105 in standard form is 236,000 Question 10. 5 × 106 Given 6 places Use exponent of the power of 10 to determine the number places to move the decimal point 5, 000, 000 Place the decimal point Since you are going to write a number greater than 5, move decimal point to the right. Add placeholder zeros if necessary. The number 5 × 106 grams in standard form is 5, 000, 000 grams Texas Go Math Grade 8 Lesson 2.1 Guided Practice Answer Key Question 1. 58,927 Given 5.8927 Move the decimal point 4 places to the Left. 10,000 Divide the original number by the result from above. 104 Write the answer as power of 10. 5.8927 × 104 Write the product of the results from above 5.8927 × 104 Question 2. 1, 304, 000,000 Given 1.304000000 Move me decimal point 9 places to the left. 1.304 Remove extra zeros. 1,000,000 Divide the original number by the result from above. 109 Write the answer as power of 10. 1.304 × 109 Write the product of the results from above 1.304 × 109 Question 3. 6,730,000 Given 6.730000 Move the decimal point 6 places to the left. 6.73 Remove extra zeros. 1,000,000 Divide the original number by the result from above. 106 Write the answer as power of 10. 6.73 × 106 Write the product of the results from above 6.73 × 106 Question 4. 13 300 Given (1) 1.3300 Move the decimal point L places to the left (2) 1.33 Remove extra zeroes (3) 10000 = 104 Divide the original number by 1.33 (4) 1.33 × 104 Multiply numbers from above 1.33 × 104 Question 5. 97, 700, 000, 000, 000, 000, 000, 000 Given 9.7700000000000000000000 Move the decimal point 22 places to the left 9.77 Remove extra zeros. 10,000, 000,000,000, 000,000,000 Divide the original number by the result from above. 1022 Write the answer as power of 10. 9.77 × 1022 Write the product of the results from above Question 6. 384,000 Given 3.84000 Move the decimal point 5 places to the left 3.84 Remove extra zeros. 100,000 Divide the original number by the result from above. 105 Write the answer as power of 10. 3.84 × 105 Write the product of the results from above 3.84 × 105 Question 7. 4 × 105 Given 5 places Use exponent of the power of 10 to determine the number places to move the decimal point 400,000 Place the decimal point Since you are going to write a number greater than 4, move decimal point to the right. Add placeholder zeros if necessary. The number 4 × 105 in standard form is 400, 000 Question 8. 1.8499 × 109 Given 9 places use exponent of the power of 10 to determine the number places to move the decimal point 1,849,900,000 Place the decimal point Since you are going to write a number greater than 1.8499, move decimal point to the right. Add placeholder zeros if necessary. The number 1.8499 × 109 in standard form is 1, 849, 900, 000 Question 9. 6.41 × 103 Given 3 places use exponent of the power of 10 to determine the number places to move the decimal point 6,410 Place the decimal point Since you are going to write a number greater than 6.41, move decimal point to the right. Add placeholder zeros if necessary. The number 6.41 × 103 in standard form is 6, 410 Question 10. 8.456 × 107 Given 7 places use exponent of the power of 10 to determine the number places to move the decimal point 84, 560, 000 Place the decimal point Since you are going to write a number greater than 8.456, move decimal point to the right. Add placeholder zeros if necessary. The number 8.456 × 107 in standard form is 84, 560, 000 Question 11. 8 × 105 Given 5 places use exponent of the power of 10 to determine the number places to move the decimal point 800,000 Place the decimal point Since you are going to write a number greater than 8, move decimal point to the right. Add placeholder zeros if necessary. The number 8 × 105 in standard form is 800, 000 Question 12. 9 × 1010 Given 10 places use exponent of the power of 10 to determine the number places to move the decimal point 90, 000, 000, 000 Place the decimal point Since you are going to write a number greater than 8, move decimal point to the right. Add placeholder zeros if necessary. The number 9 × 1010 in standard form is 90, 000, 000, 000 Question 13. 5.4 × 104 Given 4 places use exponent of the power of 10 to determine the number places to move the decimal point 54, 000 Place the decimal point Since you are going to write a number greater than 5.4, move decimal point to the right. Add placeholder zeros if necessary. The time in standard form is 54, 000 seconds Question 14. 7.6 × 106 Given 6 places use exponent of the power of 10 to determine the number places to move the decimal point 7, 600, 000 Place the decimal point Since you are going to write a number greater than 7.6, move decimal point to the right. Add placeholder zeros if necessary. The time in standard form is 7, 600, 000 cans Question 15. 3,482,000.000 Given (1) 3.482000000 Move the decimal point 9 places to the left. (2) 3.482 Remove extra zeroes (3) 1000000000 = 109 Divide the original number by 3.482 (4) 3.482 × 109 Multiply numbers from steps (3) and (4) (5) Rewrite the number as a decimal that has a whole between 1 and 10 (not including 10) multiplied by 109 where 9 is the number of places you moved the decimal. Click for details! Texas Go Math Grade 8 Lesson 2.1 Independent Practice Answer Key Paleontology Use the table for problems 16-21. Write the estimated weight of each dinosaur in scientific notation. Question 16. Apatosaurus Answer: 6.6 × 104 Question 17. Argentinosaurus _____ Answer: The weight of Argentinosaurus is 220, 000 pounds. Write that number in a scientific notation. 2.2 × 105 Question 18. Brachiosaurus _____ Answer: The weight of Brachiosaurus is 100, 000 pounds. Write that number in a scientific notation. 1 × 105 Question 19. Camarasaurus ____ Answer: The weight of Camarasaurus is 40, 000 pounds. Write that number in a scientific notation. 4 × 104 Question 20. Ceriosauriscus ________________________ Answer: Estimated weight of Cetiosauriscus is 19,850 pounds. To express this number in scientific notation: Move the decimal point 4 places to the left, so we get a number that is greater than or equal to 1 and less than 10. We remove the extra zeros. 1.9800 = 1.98 Divide the original number by the result from above. Write the answer as a power of 10. $$\frac{19,800}{1.98}$$ = 10,000 = 104 Write the product of the results from above. 19,800 = 1.98 • 104 Question 21. Diplodocus _____________________ Answer: The weight of Diplodocus is 50,000 pounds. Write that number in a scientific notation. 5 × 104 Question 22. A single little brown bat can eat up to 1000 mosquitoes in a single hour. Express in scientific notation how many mosquitoes a little brown bat might eat in 10.5 hours. Answer: Since a Little brown bat can eat up to 1, 000 mosquitoes in an hour it can eat 10.5 times more in 10.5 hours, SO: 10.5 × 1,000 = 10,500 Write 10, 500 in a scientific notation. 1.05 × 104 Question 23. Multistep Samuel can type nearly 40 words per minute. Use this information to find the number of hours it would take him to type 2.6 × 105 words. Answer: To find the member of hours N, we need to divide the total number of words by typing speed (words per minute). We have: N = $$\frac{2.6 \cdot 10^{5}}{40}$$ To simplify, we write 40 in a scientific form as 4 • 101: To write $$\frac{2.6}{4}$$ as a decimal, we divide the numerator by the denominator until the remainder is zero or until the digits in the quotient begin to repeat. We add as many zeros after the decimal point in the dividend as needed. Therefore, N = 0.65 . 104 N = 0.65 . 103 minutes To convert from minutes to hours, we divide the result by 60: N = $$\frac{6.5 \cdot 10^{3}}{60}$$ To simplify, we write 60 in a scientific form as 6 . 101: To write $$\frac{6.5}{6}$$ as a decimal, we divide the numerator by the denominator until the remainder is zero or until the digits in the quotient begin to repeat. We add as many zeros after the decimal point in the dividend as needed. 108.3 hours = 108 hours 20 minutes Question 24. Entomology A tropical species of mite named Archegozetes longisetosus is the record holder for the strongest insect in the world. It can lift up to 1.182 × 103 times its own weight. a. If you were as strong as this insect, explain how you could find how many pounds you could lift. Answer: Number of pounds you can lift by multiplying 1.182 × 103 by your weight. Since you are as strong as the ant which can lift up to 1.182 × 103 its own weight. b. Complete the calculation to find how much you could lift, in pounds, if you were as strong as an Archegozetes longisetosus mite. Express your answer in both scientific notation and standard notation. Answer: Number of pounds = 100 * 1.182 × 103 Let weight = 100 pounds 102 * 1.182 × 103, Simplify 1.182 × 105 In scientific notation. Add the exponent of 10 118200 In standard notation. Move the decimal 5 places to the right. Add placeholder zeros if necessary. Question 25. During a discussion in science class, Sharon learns that at birth an elephant weighs around 230 pounds. In four herds of elephants tracked by conservationists, about 20 calves were born during the summer. In scientific notation, express approximately how much the calves weighed all together. Answer: Total weight of calves = 230 * 20 = 4600 where each elephant calves weight 230 pounds and 20 calves are born 4.600 Move the decimal point 4 places to the left Remove extra zeros. 1, 000 Divide the original number by the result from above 103 Write the answer as power of 10. 4.6 × 103 Write the product of the results from above The total weight is$4.6 \times 10^{3}$pounds 4.6 × 103 pounds Question 26. Classifying Numbers Which of the following numbers are written in scientific notation? 0.641 × 103 9.999 × 104 2 × 101 4.38 × 510 Answer: In order for a number to be written in scientific notation they must be of the format c × 103 where c is a decimal number greater or equal to 1 and less than 10 and n is an integer, lets name that rule: Rule (1). Using this rule we have to check which numbers are written in scientific notation: 0.641 × 103 Not in scientific notation, correct woud be 641 × 102 9.999 × 104 This is in scientific notation according to Rule (1) 2 × 101 This is in scientific notation according to Rule (1). 4.38 × 510 Not in scientific notation because it is not in a correct form according to Rule (1) 9.999 × 104 and 2 × 101 are written in scientific notation. Question 27. Explain the Error Polly’s parents’ car weighs about 3500 pounds. Samantha, Esther, and Polly each wrote the weight of the car in scientific notation. Polly wrote 35.0 × 102, Samantha wrote 0.35 × 104, and Esther wrote 3.5 × 104. a. Which of these girls, if any, is correct? Answer: 3500 pounds Given None of the girls is correct Correct scientific notation: 3.5 × 103 b. Explain the mistakes of those who got the question wrong. Answer: Potty did not express the number such first part is greater than or equal to 1 and less than 10 Scientific notation is a way of expressing numbers as a product of number greater than or equal to 1 and less than 10 and 10 Samantha did not express the number such first part is greater than or equal to$1$and less than$10$Esther did not express the exponent of$10\$ correctly Question 28. Justify Reasoning If you were a biologist counting very large numbers of cells as part of your research, give several reasons why you might prefer to record your cell counts in scientific notation instead of standard notation. Reason 1 It is a standard way of writing resuLts in a scientific environment accepted and used by scientists all over the world. Reason 2 It is easier to compare large numbers since you only have to compare the exponents on the power 10n or if they are the same number between 1 and 10 that are multiplied by 10’ Reason 3 It is much easier to write very large (or very small) numbers and take less space, for example: 15, 000, 000. 000, 000, 000, 000 = 1.5 × 1019 1) It is a notation accepted around the world and used in science. 2) It is easy to compare numbers. 3) It is easier to write large numbers. Texas Go Math Grade 8 Lesson 2.1 H.O.T. Focus On Higher Order Thinking Answer Key Question 29. Draw Conclusions Which measurement would be least likely to be written in scientific notation: number of stars in a galaxy, number of grains of sand on a beach, speed of a car, or population of a country? Explain your reasoning. Scientific notation is used to express measurements that are extremely large or extremely small. Number of stars in a galaxy and number of grains of sand on a beach are extremely large, so we use scientific notation for those. Comparing speed of a car and population of a country, it is clear that the speed of a car is a smaller number. Therefore, the speed of a car is less likely to be written in scientific notation. The speed of a car is less likely to be written in scientific notation. Question 30. Analyze Relationships Compare the two numbers to find which is greater. Explain how you can compare them without writing them in standard notation first. 4.5 × 106 2.1 × 108 We can easily compare them by just comparing the exponents of the power 10n. In this case we have 106 and 108, since 108 > 106 every number greater or equal to 1 and less than 10 multiplied by 106 is smaller than any number greater or equal to 1 and less than 10 multiplied by 108 We can conclude: 4.5 × 106 < 2.1 × 108 Comparing the exponents we have: 4.5 × 106 < 2.1 × 108 Question 31. 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https://cs.stackexchange.com/questions/95487/circuit-satisfiability-problem-sat-c-to-sat-2c	# Circuit satisfiability problem : SAT-C to SAT-2C I have the following language : $L=\{\langle C_1,C_2\rangle \text{ \| } C_1 \text{ and } C_2 \text{ are two circuits that calculate different function}\}$. We can call this language SAT-2C. Prove that $L$ is NP-complete. 1) Proving that $L \in$ NP is pretty simple : given the values of $C_1$, $C_2$, it is possible to verify if the result is true or false. The time required to do so is probably linear to the size of the circuits. I'm stuck at step (2) of my proof :( 2) Since we know that SAT-C is a NP-Complete, we can try the following reduction : SAT-C $\le_p$ SAT-2C. So if we have a circuit $\langle c \rangle \in \text{SAT-C}$, there must be a function $f$ that turns it into two circuits (if we want to prove that the reduction is possible) $f(c) \rightarrow (c_1,c_2)$. For example, if our circuit is $(a \land b)$ (logical AND). The first circuit could be the same as c --- $c_1 = c = (a \land b)$. But what about the second circuit? How can $c_2$ calculate a different function than $c_1$ BUT at the same time, allow a reduction from the other way (SAT-2C to SAT-C)? Any helps or suggestions would be greatly appreciated! ## bumped to the homepage by Community♦yesterday This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. • Try a circuit which computes a constant function. – Yuval Filmus Jul 21 '18 at 14:28 You can use a reduction from $\text{3-SAT}$. $\text{3-SAT}$ is the language of $\text{CNF}$ formulas where each clause has at most three literals, and they are satisfiable, meaning - given a formula $\phi$ in the correct form, it is in $\text{3-SAT}$ iff there exists $x$ for which $\phi(x)=1$. Now, you want to show that the language of two circuits that calculate two different functions is $\text{NPC}$, therefore, given a formula $\phi$ which is satisfiable, you want to create a reduction that transform this formula into two circuits, that calculate different functions. First, transforming a $\text{3CNF}$ formula into a circuit can be done in polynomial time. So - you can construct one circuit. You now need to think of the other circuit. As Yuval Filmus mentioned, think of a circuit of constant size. What circuit will guarantee that if $\phi$ is satsfiable, than that circuit will calculate a different function than $\phi$, but if $\phi$ is not satisfiable, it will calculate the same function exactly? Most of the answer is given, you are only left to think of that circuit. If you want, ask in the comments and I'll edit it in. • Hm, so I have to use 3-SAT instead of SAT-C? I'll give that a try! Do you have a link to the meaning of a constant size circuit? (Could be because i'm unable to translate it in French or to a term my teacher used in class!) – Robert Jul 22 '18 at 2:11 • @Robert Since $\text{SAT-C}$ is also $\text{NPC}$ you can also do a reduction from it, I just gave a reduction from $\text{3-SAT}$ which I believe is really intuitive. A constant size circuit is just like its name - a circuit of a constant size, meaning it is not dependent on the size of the input. – Mickey Jul 22 '18 at 3:40 • @Mickey You are just making the problem more complicated. It's easier to reduce directly from SAT-C. – Yuval Filmus Jul 22 '18 at 6:55 • @Mickey : Would this work? c1=ϕ c2 = ϕ ^ x So if ϕ is true, then c2 will calculate a different function. However, if it's false, then the function ends with the same result – Robert Jul 28 '18 at 0:28 As suggested by Yuval Filmus in the comment, you can try a circuit that always evaluates to False.	{"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": 0.8081954121589661, "perplexity": 354.33497484271555}, "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-2019-35/segments/1566027313536.31/warc/CC-MAIN-20190818002820-20190818024820-00098.warc.gz"}
https://boxingpythagoras.com/tag/mathematics-2/page/3/	# Boxing Pythagoras ## Euclid and the Sword I have written, often, about one of my personal heroes from history, Euclid of Alexandria, who wrote a textbook called Elements which would serve as the foundation for all Western mathematics for 2000 years. You may recall that, outside of his name and a list of his writings, we know almost nothing about Euclid. We know nothing of his birth, or his schooling, or his politics. We don’t know if he traveled extensively or if he was relatively sedentary. We don’t know if he was tall, short, fat, skinny, handsome, or ugly. However, one thing we do know is that Euclid’s work, though purely mathematical, bore a tremendous influence on a wide variety of fields of knowledge. Euclid’s Elements set out to prove the whole of mathematics deductively from very simple definitions, axioms, and postulates. Deductive logic provided a sound and absolute basis by which mathematics operated for every man, whether rich or poor, high-born or peasant, male or female, famous or obscure. During the 16th and 17th Centuries, this strong foundation became lauded and sought after by philosophers, who began attempting to provide all philosophy with the rigor one found in the Elements. The appeal was obvious: if one could deductively prove his philosophical system, in the manner that Euclid had proved his geometry, then one would be left with incontrovertible conclusions to questions which had previously been highly disputed. Such extremely notable philosophers as Thomas Hobbes and Baruch Spinoza, amongst countless others, attempted to replicate the Definitions-Postulates-Proofs format Euclid had employed in order to settle questions of morality and ethics and governance. Martial philosophy was no less affected, in that period. The sword and swordplay, especially, underwent a dramatic evolution during that same time. Just as Hobbes and Spinoza attempted to replicate Euclid for ethics, fencing masters similarly moved toward a more rigorous and geometric approach towards understanding combat. And, in my opinion, they were far more successful in that endeavor than the philosophers had been. ## On the Pythagorean Theorem In right-angled triangles, the square on the side subtending the right-angle is equal to the (sum of the) squares on the sides containing the right-angle. Euclid’s Elements, Book 1, Proposition 47 (R. Fitzpatrick, trans.) Figure 1: A right triangle with squares on its sides The Pythagorean Theorem is my favorite math problem of all time. I feel so strongly about this particular bit of geometry that I have the theorem tattooed on my chest. Over my heart. In the original Greek. Yeah, I’m that kind of nerd. Most people have some vague recollection from their high school math classes that the Pythagorean Theorem is $a^2+b^2=c^2$; and a few even remember that the in that equation refers to the hypotenuse of a right triangle, while the a and b refer to the other two legs. However, most of the time, people were just taught to memorize this theorem– they weren’t taught how to prove that it was actually true. Now, the Internet is full of all kinds of really clever visual proofs involving rearranging copies of the triangle in order to form the different squares, but I’m not really a huge fan of these. They make it very easy to see that the Pythagorean Theorem is true, but they don’t really make it easy to see why the Pythagorean Theorem is true. So, today, I wanted to discuss my favorite proof for the Pythagorean Theorem, which comes to us by way of Euclid’s Elements, which was the standard textbook for math in the West for around 2000 years. ## On the Continuum and Indivisibles Εἰ δ’ ἐστὶ συνεχὲς καὶ ἁπτόμενον καὶ ἐφεξῆς, ὡς διώρισται πρότερον, συνεχῆ μὲν ὧν τὰ ἔσχατα ἕν, ἁπτόμενα δ’ ὧν ἅμα, ἐφεξῆς δ’ ὧν μηδὲν μεταξὺ συγγενές, ἀδύνατον ἐξ ἀδιαιρέτων εἶναί τι συνεχές, οἷον γραμμὴν ἐκ στιγμῶν, εἴπερ ἡ γραμμὴ μὲν συνεχές, ἡ στιγμὴ δὲ ἀδιαίρετον. Οὔτε γὰρ ἓν τὰ ἔσχατα τῶν στιγμῶν (οὐ γάρ ἐστι τὸ μὲν ἔσχατον τὸ δ’ ἄλλο τι μόριον τοῦ ἀδιαιρέτου), οὔθ’ ἅμα τὰ ἔσχατα (οὐ γάρ ἐστιν ἔσχατον τοῦ ἀμεροῦς οὐδέν· ἕτερον γὰρ τὸ ἔσχατον καὶ οὗ ἔσχατον). –Aristotle, Physics 6.1 There is a concept which is absolutely intrinsic to all of geometry and mathematics. This particular concept is utilized by every single High School student that has ever graphed a line, and yet this concept is so incredibly difficult to understand that most people cannot wrap their heads around it. I’m talking about the concept of the continuum. Basically, the idea is that geometric geometrical objects are composed of a continuous group of indivisibles, objects which literally have no size, but which cannot be considered “nothing.” Despite the fact that these individual objects have no size, they form together into groups which, as a whole, can be measured in length or height or breadth. In mathematics, objects such as lines, planes, volumes, and all other sorts of space are considered to be continua, continuous and contiguous collections of these indivisibles into a unified whole. Because these infinitesimals have no size, themselves, even finite spaces contain an infinite number of these points. Nearly every mathematician on the planet subscribes to this point of view. However, this was not always the case. Only a little more than 100 years ago, this view was considered extremely controversial and was only held by a fringe minority of scholars. Four centuries before that, this concept was nearly unthinkable. Though it has become, without question, the prevailing view of mathematicians, even today there remain a tiny handful of scholars who object to the use of the infinitesimal, the infinite, the individible, and the continuum in modern math. One such person is Dr. Norman Wildberger, an educator and mathematician for whom I have the utmost respect. Still, I disagree with Dr. Wildberger’s philosophy on this particular issue. ## Egyptian Math: Multiplication and Division A little while back, I wrote up a little post on basic Egyptian mathematics, concentrating on how using Egyptian numerals in addition and subtraction can aid students in understanding our base-10 number system. I wanted to continue that discussion, today, by looking at how the ancient Egyptians performed Multiplication and Division. Unlike my discussions of addition and subtraction, I am not advocating Egyptian multiplication and division as a means for teaching the Common Core standards. To be honest, I just find the system to be really interesting. ## Egyptian Math for the Common Core A short while back, one of my friends posted a series of videos on Facebook complaining about the Common Core standards which are being rolled out in the United States. Unsurprisingly, not a single one of the videos actually addresses the standards laid out by the Common Core– despite their being freely available on the Internet— and instead the videos display knee-jerk reactions to specific teaching methodologies which are not understood by the complainants. Generally, these sorts of arguments against the Common Core focus on the methods of early, basic arithmetic taught in the 3rd and 4th grades. At this stage, the Core requires that students become familiar with the nature of a base-10 counting system, such as the one we utilize. The Indian-Arabic number system which we have adopted for mathematics has the benefit of simplifying these base-10 properties, but unfortunately that comes at the cost of obfuscation. Teaching the base-10 system as it ought to be initially taught– without the shortcuts inherent in Indian-Arabic numerals– is a very alien procedure to most people. Because it is new and strange and takes more steps to accomplish than the familiar method of arithmetic, parents are frightened and confused; and when parents are frightened and confused, they tend to lash out rather than taking the time to actually learn the purpose and reasoning behind the methodology. It occurs to me that a possible solution might be found in Egyptian arithmetic. ## The Death of Dignity and Virtue There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, she not infrequently appeared in public in the presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more. –Socrates Scholasticus, Ecclesiastical History ## The Elements of Geometry Some time ago, I wrote about Alexandria, the most important city in history, briefly discussing the lives of just 17 of the men and women that made it so. Prime to that list, both in sequence and in importance, was Euclid of Alexandria, a personal hero of mine who I consider to be one of the most inspirational and influential people in all of human history. We know next to nothing about Euclid’s life– we do not know where or when he was born, where or when he died, and extremely little about the time between those events. We know that he lived in Alexandria at roughly the same time as Ptolemy I, circa 300 BCE, and we know that he wrote prolifically about mathematics. Yet, even with so very little information as this, I would strongly argue that Euclid contributed far more to the world than did much more well-known figures like the great historian, Herodotus; or the conquering emperor, Julius Caesar; or even the revolutionary preacher, Jesus of Nazareth. What could Euclid have possibly done that outshines these other, great men? Euclid of Alexandria wrote the Elements. ## Be smart. Use tau. For anyone who didn’t know, this past Saturday was Tau Day, a celebration of the proper circle constant! A couple weeks ago, I told all of you about how π is stupid, and urged everyone to be smart and use τ, instead. However, you might be surprised to learn that this is not the end of the debate, when it comes to angles. While I argue that people should measure angles in terms of τ, many traditionalists argue that they should be measured in terms of π, our grammar schools are still intent on teaching the incredibly archaic degrees of arc, and if you’ve ever fiddled with a scientific calculator, you might have learned that some backwards people prefer gradians. But that’s still not the end of the debate. According to a video by Dr. David Butler of the University of Adelaide, “π may be wrong, but so is τ!” I’m going to celebrate Tau Day, belatedly, by rebutting Dr. Butler’s presentation. I’m going to show that degrees, gradians, η, and π are all stupid, and that the only smart choice in this debate is τ. ## WLC on Time, Part 5: More Mathematical Misconceptions After my last installment of this series, I had thought that I would be done critiquing Dr. William Lane Craig’s misunderstandings of the science and mathematics regarding time. After all, I’ve already shown that his arguments in support of the archaic Tensed Theory of Time are unfalsifiable, fallacious, ill-conceived, and self-contradictory. What more could there be for me to say? Well, in this week’s Reasonable Faith Podcast, Dr. Craig gifts me with more of his misconceptions about time. Starting at the 13:15 mark and lasting through the rest of the podcast, Dr. Craig addresses a question posed to him about the implications of the Tenseless Theory of Time on the theory of Evolution by Natural Selection, which the questioner refers to as “the holy grail of atheism.” I’ll note that this questioner doesn’t seem to realize that even a great many devout Christians completely accept the veracity of Evolution by Natural Selection, and that it is no more an “atheist” theory than is the Pythagorean Theorem. However, the particular implications on evolutionary biology will take a back seat, today, to the more general implications which Dr. Craig claims are made by the Tenseless Theory of Time. Specifically, Dr. Craig asserts that nothing actually changes over time, on the Tenseless Theory. Read more… ## Pi is Stupid I teach Brazilian Jiu-Jitsu to people of all ages, from preschoolers to middle-aged parents. While BJJ, in itself, is not necessarily the most academic of pursuits, I also happen to be a huge nerd. So while teaching some of my 8 to 13 year-old students, it sometimes happens that I overhear them talking about their math classes, often to complain about ideas that they’re struggling to grasp. Being a huge nerd, and also a delighted teacher, I do my best to help them through these issues. If I can teach a kid how to find the length of the hypotenuse of a right triangle at the same time as teaching her how to finish a Triangle Choke, I become pretty much the proudest martial arts instructor you could hope to meet. One of the things that my kids often use in their math classes, but almost never really understand, is the constant π (pi). They are taught π in class to help learn things like how to calculate the area of a circle, but they usually don’t really know what π actually is. They just think of it as some number that they have to memorize, never thinking about where the number comes from, or why it is what it is. Sometimes, I’ll tell the kids that they can earn their way out of doing push-ups if anyone can tell me what π is. Most often– after the jokes about desserts are made– I’ll hear someone say, “Coach, π is three-point-one-four!” Every now and again, one of the kids is clever enough to say, “Coach, π is three-point-one-four-on-into-infinity!” They get confused when I tell them that’s the value of π, but that is not what π actually is. It’s not their fault that they get confused by this; they were usually taught about π all wrong. I don’t even blame their math teachers, because most of the time, those math teachers were also taught about π in the wrong way. For a very long time, math classes have been teaching that π is a number, instead of teaching that π is the relationship between a circle’s circumference and its diameter. There is a reason it has been taught this way. Ladies and gentlemen, π is just plain stupid.	{"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": 1, "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": 0.46402665972709656, "perplexity": 1679.0900838750824}, "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/1664030333455.97/warc/CC-MAIN-20220924182740-20220924212740-00502.warc.gz"}
https://mothur.org/wiki/normalize.shared/	# normalize.shared The normalize.shared command creates a .norm.shared file. ## Default Settings By default, the method is totalgroup, the norm is set to the number of sequences in your smallest group, all groups in your group file are included and all labels are used. mothur > normalize.shared(shared=abrecovery.fn.shared) ## groups The groups parameter allows you to select the groups you would like to include in your .norm.shared file. mothur > normalize.shared(shared=abrecovery.fn.shared, groups=B-C) ## method The method parameter allows you to select what method you would like to use to normalize. The choices are totalgroup and zscore. We hope to add more ways to normalize in the future, suggestions are welcome! Relative Abundance = Abundance / Total number of sequences in the group. Normalized Value = Relative Abundance * norm The normalized value is then rounded to the nearest integer. mothur > normalize.shared(shared=abrecovery.fn.shared, method=totalgroup) or zscore Normalized Abundance = (Abundance - mean) / standard deviation If using a shared file the normalized value is then rounded to the nearest integer. mothur > normalize.shared(shared=abrecovery.fn.shared, method=zscore) ## norm The norm parameter allows you to number you would like to normalize to. By default this is set to the number of sequences in your smallest group. If you set norm greater than an abundance of a specific group the group will be removed. mothur > normalize.shared(shared=abrecovery.fn.shared, norm=100) ## label There may only be a couple of lines in your OTU data that you are interested in finding the normalized abundance for. There are two options. You could: (i) manually delete the lines you aren’t interested in from your list file; (ii) or use the label option. To use the label option with the normalize.shared() command you need to know the labels you are interested in. If you want the normalized abundance for the lines labeled unique, 0.03, 0.05 and 0.10 you would enter: mothur > normalize.shared(shared=abrecovery.fn.shared, label=unique-0.03-0.05-0.10) ## makerelabund The makerelabund parameter allows you to convert a shared file to a relabund file before you normalize. default=f. ## Revisions • 1.40.0 - Speed and memory improvements for shared files. #357 , #347	{"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": 0.6848576068878174, "perplexity": 1053.8566988055063}, "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-2022-33/segments/1659882570827.41/warc/CC-MAIN-20220808122331-20220808152331-00064.warc.gz"}
https://ay201b.wordpress.com/2011/03/02/why-is-co-an-important-coolant-in-the-very-cold-ism/	# Harvard Astronomy 201b ## Why is CO an important coolant in the (very) cold ISM? In Uncategorized on March 2, 2011 at 9:56 pm Cooling mechanisms are very important for facilitating the collapse of molecular clouds, the formation of stars, and radiative equilibrium in the ISM. As discussed in class, molecular hydrogen is a poor radiator as a homonuclear molecule with no dipole moment. This means that H2 can only radiate through forbidden transitions so the rates are too low. Compared to atomic hydrogen, because molecular hydrogen doesn’t even have a 21cm analogue, cooling rates rates for H2 are lower than that for atomic Hydrogen. However as discussed in class, at high temperatures (i.e. shocks) its high abundance makes H2 the dominant coolant. Consequently, heavy molecules play in important role transforming thermal energy to radiation that can escape the region through collisions (mostly with hydrogen) and various emission mechanisms. For the low temperatures of the cold ISM, the potential energy imparted to a CO molecule from an inelastic collision is only enough to excite a rotational transition. Well, it is both abundant and able to radiate from inelastic collisions at low temperatures and densities. In general, the cooling rate of a specific is determined by the amount of material, the level populations, and the physics of the transitions: $\Lambda_{CO} = X_{CO} (2J+1) \frac{e^{-E_J/(k_B T)}}{Z} A_{J,J-1} \Delta E_{J,J-1}$ At the most general level we might try to understand the equation by area of study. Abundances, $X_{CO}$ are determined by the chemistry of the environment as various processes conspire with the temperature, densities, etc. to form molecules. The level populations, $(2J+1) \frac{e^{-E_J/(k_B T)}}{Z}$,are covered by statistical mechanics. To calculate the transition energy, $\Delta E_{J,J-1} = E_J - E_{J-1}$, and Einstein A coefficient, $A_{J,J-1}$, we need to use quantum mechanics. To answer the question at hand let’s focus on the chemistry and quantum mechanics by first looking at the transition energy. Treating the diatomic molecule CO as a rigid rotator the energy of a particular level, $J$ is set by the rotation constant $B$: $\Delta E_{J,J-1} = hBJ(J+1) - hBJ(J-1) \propto B$ where $B = \hbar^2/2m_r r_0^2$ where $m_r$ is the reduced mass of the molecule and $r_0$ is the bond length. We’re working in the very cold ISM so we’ll assume that the CO stays in the least energetic vibrational state. Furthermore, the Carbon and Oxygen molecules in CO are connected by a triple bond with a dissociate energy of 11.2eV (1120 $\AA$.) The strength of this bond means that most starlight won’t break up a CO molecule and so often CO will be the most abundant heavy molecule (Solmon & Klemperer, 1972). Furthermore, CO’s reduced mass is large compared to that of, say, molecular hydrogen. This means that transition energies for these rotational levels are small and so they can be excited at low temperatures (think tens of Kelvin). See sections 5.1.4 and 5.1.7 of Draine’s book for a nice discussion. Even with the small dipole moment of CO (0.112 Debye), optical depth effects are important. When a line is optically thick the photons just bounce from molecule to molecule and there is no net cooling effect. However, turbulence in the medium and velocity gradients will Doppler shift the photons so they may escape through the line wings. In addition, the geometry of the local medium now matters in the optically thick regime since photons emitted near to the cloud’s ‘boundary’ will be more likely to escape. In brief, the reasons that CO is such a dominant coolant in the cold ISM is because it is abundant and also because it can radiate at low densities and temperatures. But what happens when you heat the ISM just a bit? Molecules besides CO play an important role in line cooling. For instance, water has a much larger dipole moment (1.85 D) than CO (0.112 D) and consequently at higher temperatures water is a dominant cooling mechanism. This can be seen from dipole dependence, $\mu^2$ in the the equation from the Einstein A coefficient: $A_{J+1,J} = \frac{512 \pi^4 B^3 \mu^2}{3 h c^3} \frac{(J+1)^4}{2J+1}$ Complicating this analysis is the chemistry since the abundance of a species will depend strongly on the local conditions. Of course this complication can be useful when coupling observations and models of the chemistry (i.e. Jiminez-Serra, I et al. 2009). Abundances of molecules with Oxygen as a function of magnitude for a model of a photon dominated region that includes surface grain chemistry. Figure from Kaufman 2009. In brief, ion-neutral reactions dominate at the lowest temperatures so the most abundant Oxygen bearing molecules (besides CO) are O, OH, O2, and H2O. At a transition temperature of ~400 K, neutral-neutral reactions produce lots of water: $O + H_2 \longrightarrow OH + H$ $OH + H_2 \longrightarrow H_2O + H$ By 500 K most of gas-phase oxygen is either in H2O or CO. So in a slightly warmer environment the cooling will be dominated by water. Cooling rates per molecular Hydrogen molecule for gas temperatures of 40 and 100 K. (Figure 2 from Neufeld, Lepp, and Melnick 1995) Calculations show that cooling from CO dominates in the low temperature, low density regime of molecular clouds. Another way of plotting the fractional contribution of various coolants are through contour plots over temperature and density. Effectively this calculated takes the previous figure and expands it to two dimensions. Looking at the figure below the dominance of CO in the low temperature and density regime as well as the transition to water cooling becomes apparent. Fractions of the total cooling rate from important coolants. Image from the SWASS science page, adapted from Neufeld, Lepp, and Melnick 1995. So what might this mean to me? The moral of the story is that if you are doing a calculation involving cooling or heating processes of gas, you’ll want to make sure to treat include coolants such as CO and treat the chemistry and radiative transfer correctly. That is you want the abundances and cooling rate to be right or your answers might be wrong! Some current topics include the formation of stars in low-metallicity regions (i.e. Jappsen et al. 2009) and modeling CO chemistry in Giant Molecular Clouds (i.e. Glover & Clark 2011). Hopefully this discussion help to answer the question although you’ll have to find the answers to any it brought up your own. Some places to start searching are listed below References	{"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": 16, "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": 0.8746562600135803, "perplexity": 1092.4785872920002}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645513.14/warc/CC-MAIN-20180318032649-20180318052649-00547.warc.gz"}
http://mathematica.stackexchange.com/users/16/acl?tab=activity&sort=all	# acl less info reputation 22758 bio website location age member for 1 year, 10 months seen 2 hours ago profile views 963 # 1,280 Actions Dec4 reviewed Approve suggested edit on How to solve initial value problem using Runge-Kutta method? Nov21 comment Command to get License Management Monitor info Is that not an executable command? eg here it'd be run from the command line as /usr/local/math/MathLM800/bin/monitorlm license (for example) Nov21 reviewed Approve suggested edit on Laplace transform of $\frac{1-\cos (t)}{t}$ Nov2 comment Unpacked eigenvectors of complex matrices I don't know the answer, but as a side remark you can see when anything gets unpacked by first switching on the message like so: On[DeveloperFromPackedArray::punpack1]. Then evec = Eigenvectors[mat]; gives a warning DeveloperFromPackedArray::punpack1: Unpacking array with dimensions {300}. >> Nov1 comment InterpolatingFunction gives me wrong results for specific arguments - but the plots are correct! Could you provide some code that produces a fid that displays this behaviour? Oct31 comment Is Mathematica 8 compatible with Mac OS X 10.9? 9 is, but I don't have 8 handy to check. Oct31 comment System Modeler can't find g++ in Mac OS X Mavericks Can you not set the path for where System Modeler searches for the executables? Sep18 awarded Nice Answer Aug29 comment How to plot imaginary part of a function @JacobAkkerboom I don't remember if there was a discussion about this, or why I put it there. If you find the Q&A poor feel free to contribute a better answer. Aug24 comment Debugging with Breakpoints @Nasser if you highlight some part of the code (eg with ctrl-.), set a breakpoint, and evaluate the code, doesn't it then break there and display the state? Aug24 comment Programming Mathematica in plaintext, i.e. no formatting, non-notebook Not everything in the textmate plugin works in sublime text (I remember problems with locating functions and similar things). I've modified many parts for my own use, but it's not really in a good enough state to share publicly. However, it is not hard to fix whatever you need, so it's worth a try if you like sublime text. Aug16 awarded Enlightened Aug16 awarded Nice Answer Aug2 awarded Enlightened Aug2 awarded Nice Answer Jul28 awarded Enlightened Jul28 awarded Nice Answer Jul7 comment Alternatives to Mathematica This runs just fine on phones as well. For iOS, there's also iCas, which is Reduce. Jul6 comment Alternatives to Mathematica Alternatives for which part of Mathematica? Symbolic calculations? Numerical solution of ODEs? PDEs? Numerical programming? Static visualization? Dynamic visualization? The answer will be different for each. Jun29 comment Minimization by Nelder-Mead As an idea, if you have an algorithm which solves it in C or Fortran, you could always implement it in Mathematica and ask for help speeding it up. But it seems nontrivial to minimize this function so I am guessing it's an algorithm problem.	{"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": 0.5513728857040405, "perplexity": 3583.737477633682}, "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-2013-48/segments/1386163999838/warc/CC-MAIN-20131204133319-00081-ip-10-33-133-15.ec2.internal.warc.gz"}
https://matheducators.stackexchange.com/questions/17181/how-to-explain-that-the-sums-of-numerators-over-sums-of-denominators-isnt-the-s/17226	# How to explain that the sums of numerators over sums of denominators isn't the same as the mean of ratios? I am a teaching assistant for an intro programming course. One assignment asked for the averages of a certain ratio, but most students, rather than returning $$\frac{\text{sum of all ratios}}{\text{total ratios}},$$ gave $$\frac{\text{sum of the numerators used to calculate those ratios}}{\text{sum of the denominators used to calculate those ratios}}.$$ That isn't the same, but I can't put to words why it isn't the same; I just know not to do it and can't explain to these students why it gives the wrong result. What's the intuitive way to explain it? The ratios in question were mileages per gallon. The question wanted the average mpg of all trips, and asked for miles driven and gallons of fuel used separately. • I wonder if the error is more blindly coding while ignoring the meaning? Would the same misunderstandings arise were this a hand-calculation exercise? – Joseph O'Rourke Sep 28 '19 at 0:18 • Google for "Simpson's paradox" and find a lot of interesting examples. – Gerald Edgar Sep 28 '19 at 1:15 • Just a side comment: Guest's answer below shows that this is a good counter-example to the idea that one should give "real life" context to math questions. If the point was to measure the capacity to manipulate fractions, then the exercise failed by making the interpretation of the question the critical step. – Benoît Kloeckner Sep 28 '19 at 8:25 • @BenoîtKloeckner It isn't a counterexample! It is a beautiful example of how providing a real world context allows for open ended conversation about the meaning of the computations, and will prepare students to select meaningful computations in the future. Along the way they can get practice "drilling" both interpretations just by answering questions which naturally arise from the discussion. They might even remember something, since there was a lively debate! – Steven Gubkin Sep 28 '19 at 21:20 • @StevenGubkin: it is really depending on one's goal. While it is a commendable goal to work on interpretation of a somewhat informal problem into mathematics (modelling), it is too often the case when one's goal is to practice a given mathematical task, and this goal is messed up with by a sloppy real word context. – Benoît Kloeckner Sep 29 '19 at 7:57 The problem is with the question, not with the students' answers. The question is ambiguous and I think the students' answer is actually much better than yours. Suppose I drive a thousand miles at 25mpg and you drive one mile at 35mpg. What's the average fuel efficiency? Your answer is 30mpg but I honestly can't think of any situation in which that is a meaningful or useful number. The students' answer is 25-and-a-bit mpg, which is a good measure of how far it can be expected to travel on one gallon of fuel. Analogously, if I buy a thousand apples at 50c each and you buy one apple at 40c, you're claiming that the average price per apple is 45c, and your students are claiming that it's a hair under 50c. One observation is that (sum of numerators) divided by (sum of denominators) is not well defined. For example, let's work with the two ratios $$a=\frac01$$ and $$b=\frac11$$. The ratio of the sum of numerators to sum of denominators is $$\frac12$$. However, we can also write $$a=\frac03$$ and $$b=\frac22$$. Now the ratio is $$\frac25$$, which is not equal to $$\frac12$$! • Nice counterexample. Note also that $\displaystyle \dfrac{a}{b}\leq \dfrac{a+c}{b+d}\leq \dfrac{c}{d}$. – user5402 Sep 28 '19 at 14:26 • You're changing the weights by doing so, which shouldn't be allowed. Especially if you're describing physical quantities. A 200 mile trip in 2h shouldn't be replaced by a 100 mile in 1h simply because they have the same average speed. – Eric Duminil Sep 28 '19 at 18:27 • @EricDuminil: if you read the OP, there is hardly any mention of weights and physical quantities. On a side note, the method of dividing the two sums (as opposed to averaging the individual ratios) is used in calculating the "earned run average" in baseball. – user52817 Sep 28 '19 at 18:34 • @JiK: I see what you mean: 30 mpg, right? In that case, it makes sense to calculate the average like OP proposed. – Eric Duminil Sep 28 '19 at 22:14 • @Paracosmiste You're claiming that, for arbitrary $a$, $b$, $c$, $d$, $\tfrac{a}b\le\tfrac{c}d$. That's simply not true. – David Richerby Sep 30 '19 at 7:48 It actually depends on exactly what you're asking. Or even what you SHOULD be asking. If you want the average profitability of all the 500+ operators in the Permian, you could just average all the profit margin percentages. This is taking the ratios (profit/revenue) for each company and averaging them. It corresponds to your expected (mean) profit margin if you just picked an operator at random. If instead, I take all the profits and divide by all the revenues, this would give me the average profitability of the INDUSTRY (operators in the Permian). Often this is actually the question you are asking, or should be asking. IOW, you want the revenue-weighted average profit margin. The same point would apply if you were, say doing sampling of different size demographic categories and were interested in the total population polling estimate. You need to weight by size of the buckets. (Or just take the totals, which is mathematically equivalent.) Since we don't know exactly what you asked, or how precise you were, it's hard to say if the students were wrong. Of course, they may have been. But I would just check. EDIT: Responding to your edited-in update on the question. There's actually still some ambiguity about what you are (or should be) asking. But if I had to guess, the student's way is more likely giving the desired answer. (IOW, ratio the totals, rather than average the ratios.) IOW, "average fuel efficiency" should be "gallon" weighted. That's the one impacting your pocketbook. In addition, you may find that there's some correlation of fuel efficiency with trip length. The engine being warmed up, operates more efficiently. Also, highway speeds may be more efficient than slow speeds. Also the issue of frequent stops and starts. So if I were selecting a car, I would want the one that has the better average fuel efficiency (total miles/total gallons). Ideally with something approximating my type of usage. But I definitely wouldn't want to skew things by saying one "10 mile, 1 gallon" trip mean the same as one "100 mile, 5 gallon" trip in terms of the importance to my pocketbook. • Yes. The OPs answer is good if you care about which kind of car to buy (you can compare to the average efficiency of the cars). The student's answer is good if you want to keep track of how efficiently gasoline is being used across the whole economy. – Steven Gubkin Sep 27 '19 at 15:57 I like guest's answer. To elaborate, here is a possible question to ask them. You take two trips in your car: • Trip 1 is a 100 mile drive that takes you 2 hours. • Trip 2 is a 200 mile drive that takes you 1 hour. (a) What is the average speed of your car? (b) What is the average speed on an average trip? The answer to (a) is $$\frac{100 \text{ miles} + 200 \text{ miles }}{2 \text{ hours } + 1 \text{ hour }} = \frac{300 \text{ miles }}{3 \text{ hours }} = 100 \text {mph}$$. The answer to (b) is $$\frac{\frac{100 \text{ miles }}{2 \text{ hours }} + \frac{200 \text{ miles }}{1 \text{ hour }}}{2} = \frac{50 \text{ mph} + 200 \text{ mph} }{2} = 125 \text {mph}$$. You need to be very clear about the question if you prefer one of these answers. • The premise of (b) being misused scares me. It would offer a coach the math showing his track team running speeds that routinely blow away a 4 minute mile. i.e. 100m sprints are far faster than actual mile runs. 9 instances of that data with one instance of the mile run makes for odd results. This is why I was hoping OP would offer the example, and not blindly use the math. Either way. – JTP - Apologise to Monica Sep 28 '19 at 12:57 • (b) is wrong. What does "average speed of a trip" even mean? We speak of a speed of a particle. The average speed is the weighted arithmetic mean of the 2 speeds : $\displaystyle v=\dfrac{t_1v_1+t_2v_2}{t_1+t_2}=\dfrac{2\times\dfrac{100}{2}+1\times\dfrac{200}{1}}{2+1}$ which gives the same answer as (a). – user5402 Sep 28 '19 at 14:24 • Does this sound better to you @EricDuminil ? "Here are 100 players and their hits and at-bats. (a) What is the overall batting average for the league? (b) What is the batting average of an average player?" – Chris Cunningham Sep 28 '19 at 20:36 • @ChrisCunningham: I have no clue whatsoever about baseball (that's a baseball example, right?), but this does sound more appropriate, yes. – Eric Duminil Sep 28 '19 at 21:03 • OK, hopefully these comments combined with my edit to include the phrase "an average trip" improve the answer a bit. The whole situation is still a bit wonky. – Chris Cunningham Sep 29 '19 at 2:16 Allow me to offer another example: Imagine you and your best friend both want to buy a new smart phone. The phone you have chosen will cost you 300€ but your friend chooses a phone that will cost as much as 600€! Luckily, you have two vouchers that will give you a discount: The second voucher will give you 50% off your entire purchase. Which voucher do you choose? Ratios are a tricky thing, because the ratio of two large numbers can be the same as the ratio of two small numbers. But in most real life applications, the number of elements used to determine these ratios (i.e. averages) are just as important. Because an average over a great number of elements (e.g. people in a survey) is more meaningful than an average over a select few. Therefore, they can not always be compared one-to-one. Think of an example with two ratios: 1/3 and 4/5. When you add the numerators, and divide this by the sum of the denominators, you get (1 + 4)/(3 + 5) = 5/8. Now, think about what is happening with the denominators - the denominator of the first ratio should only act on the first numerator. But instead, when you add the ratios in this way, the denominator of the first ratio is acting on both numerators. Likewise for the second denominator. However, when you average the two ratios, like this (1/3 + 4/5) / 2 = (5/15 + 12/15) / 2 = 17/30 the denominators of the ratios work together to act on the numerators. Division has a higher order of precedence than addition. Thus, division should be carried out first, rather than combining the ratios. Hope this makes sense and helps you assist them. Do you want students to think or not? According to your logic, when I do a 300 mile trip with a car and a day later reverse it in the drive way, the average mpg value of those two days can be calculated by taking the mpg value of the first day and averaging it with the (likely much higher) mpg value of the second day that saw almost no mileage and almost no gas use. Don't use "textbook examples" for meaningless calculations and then complain that the students were unable to make the calculations as meaningless as you wanted them done. That's teaching them neither mathematics nor its proper application. • Sometimes the correct answer to a question is to ask a different question. This is one of those times. If the 'customer' wants an average of ratios, then the only responsible thing to do is ask for clarification. – Mike Spivey Sep 28 '19 at 13:12 • -1, This is needlessly hostile to the questioner. Edit your answer from the point of view of helping an educator, or delete it. – Chris Cunningham Sep 28 '19 at 16:50 I think that the most interesting application of (sum of numerators/sum of denominators) “addition” is to continued fractions. For example, if you want to calculate the continued fraction expansion of the square root of 2,start with 1/0 and 0/1 and “add” them in the following way: In the top row you put the results of the “adding” that are greater then the square root of 2 , in the bottom row the results that are less then the square root of 2, and you always “add” the last two results from the different sides of the square root of 2 . The pattern of 1 down, 2 up, 2 down, 2 up, 2 down, 2 up, … is the continued fraction expansion of the square root of 2 :	{"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": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7139735221862793, "perplexity": 737.6798677971966}, "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-2020-45/segments/1603107904834.82/warc/CC-MAIN-20201029154446-20201029184446-00424.warc.gz"}
https://www.physicsforums.com/threads/riddle-4-12-6.100023/	# Riddle (412=6 ) 1. Nov 15, 2005 ### roeller Hi there I have a riddle here, i cannot solve. If 412=6 and 88=1 what's 56? 2. Nov 15, 2005 ### devious_ 2 (It's multiplication mod 7.) 3. Nov 15, 2005 ### roeller Thanks! That's it!! 4. Nov 15, 2005 ### hypermonkey2 Curiosity, what is the reasoning exactly? 5. Nov 16, 2005 ### HallsofIvy Staff Emeritus devious gave his reasoning: it's multiplication modulo 7: 412= 48= 76+ 6 so 412= 6 mod 7 8 8= 64= 79+ 1 so 88= 1 mod 7 then 56= 30= 47+ 2 so 56= 2 mod 7. HOWEVER, that is not the only answer. If fact, that 12 in "412" as well as the 8 in "88" makes me suspicious of the multiplication being "mod 7". It is common (but not required) to reduce numbers to be less that the modulo number. (Strictly speaking the objects in "modulo arithmetic" are equivalence classes of integers. You can use any number in an equivalence class to "represent" it and it is common to use the smallest positive number.) Saying 412= 6 (mod k) means 412= 48= nk+ 6 for some integer n. That is the same as nk= 42. Saying 88= 1 (mod k) means 88= 64= mk+ 1 for some integer m. That is the same as mk= 63. 42 factors as 237 and 63 factors as 337. It is the fact that 7 is a common factor (so 42= n(7) with n=6) that leads to the conclusion that 412= 6 (mod 7) and (63= m(7) with m= 9) 88= 1 (mod 7). Of course, 3 is also a common factor: 42= n(3) with n= 14 and 63= m(3) with m= 21. 412= 48= 42+ 6= (14)(3)= 6 so 412= 6 (mod 3) and 88= 64= 63+ 1= (21)(3)+ 1 so 88= 1 (mod 3). Of course that "= 6 (mod 3)" looks a little strange since, as I said, we normally choose a representative less than the base. Of course, 56= 30= 310 so 56= 0 (mod 3). My preference would be (mod 37) or (mod 21). Since 412= 48= 42+ 6= 2(21)+ 6, 412= 6 (mod 21). Since 88= 64= 63+ 1= 3(21)+ 1, 88= 1 (mod 21). That gives 56= 30= 21+ 9 so 56= 9 (mod 21). I would support 9 as the best answer. Last edited: Nov 16, 2005 Similar Discussions: Riddle (412=6 )	{"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": 0.9462407231330872, "perplexity": 6049.454411723447}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128321426.45/warc/CC-MAIN-20170627134151-20170627154151-00449.warc.gz"}
https://docs.lokad.com/envision-user-guide/user-inputs/	# User inputs The content of a dashboard produced by Envision can be driven by user inputs performed directly on the dashboard itself. Those capabilities are of interest for data exploration purposes, where the intent is to zoom in on specific areas (e.g. a part, a store, a time-period), but also for advanced simulation purposes, typically enabling a variety of what-if analyses. Envision supports three distinct kinds of user inputs: the slices, the forms and the file uploads. Each input has its most suitable use cases. In the following, we document all these features that support user-driven dashboards. ## Overview While it is possible to perform data exploration by directly editing the Envision code, for example adjusting some where statements to filter the specific data of interest, Lokad is not only intended for an audience of Supply Chain Scientists capable of editing Envision scripts. Yet, this audience - either less technically inclined or simply less familiar with Envision - might benefit from being offered a degree of control over the dashboard themselves. In order to support those scenarios, Envision can process user inputs provided directly through the dashboard itself. This capability is of interest for many scenarios. Data inspection: Sometimes data pipelines connecting production systems to Lokad are imperfect, and users might wish to be able to quickly perform sanity checks, verifying that the data present within Lokad is properly reflecting what they see on their systems. These verifications are used to rule out garbage-in garbage-out problems, which may occur when the data pipeline itself is dysfunctioning. Explorative insights: A supply chain decision, such as a purchase order quantity, can be dependent on many inputs, including advanced statistical calculations - e.g. a probabilistic demand forecast and a probabilistic lead time forecast. In order to make sense of a suggested decision, it might be relevant to gather all the relevant inputs in a single dashboard. What-If scenarios: The profitability of supply chain decisions is likely to be highly dependent on many factors - e.g. cost of transport, minimal order quantity, price breaks, etc. Those factors might even be part of the input data. However, it could be of interest to be able to assess “what-if” scenarios where one or more of those factors would be associated to different values. Staged workflows: The supply chain practitioner wants to preserve the possibility to fully override the suggested purchase quantity as computed by an Envision script. The practitioner wants to amend the quantities in any way he/she sees fit, but also let the dashboard be refreshed with numbers reflecting the economics of the modified quantities. In order to support these use cases, and more, Envision provides several mechanisms to let users dynamically interact with Envision dashboards without touching the code itself. The three methods are namely: • the dashboard slices which are best suited for data exploration purposes. • the form tile which is best suited for what-if scenarios. • the upload tile which is best suited for workflows, where quantities or prices are amended in batch. ## Dashboard slices Dashboard slices are the most suitable approach for data exploration because they do not involve re-running the Envision dashboard. Instead, many dashboard views are pre-computed - one for every “slice” - and it becomes possible to navigate from one slice to another using the slice selector, which provides a search-like user experience. By clicking the slice selector on the upper right corner, the dashboard offers a search box, as illustrated in the screenshot below. The dashboard above has been generated using the sample dataset and the following script: read "/sample/Lokad_Items.tsv" as Items with Id : text Name : text Category : text SubCategory : text Brand: text Id : text Date: date Quantity: number Client: text Slice = sliceDashboard(Id, Name) by [Id] Week.Slice = Slice Week.Qty = sum(Orders.Quantity) Week.monday = same(monday(date)) into Week show linechart (same("Weekly sales for \{Name}") by Slice) a1d3 tomato slices: Week.Slice with sum(Week.Qty) group by Week.monday show table (same ("Orders for \{Name}") by Slice) a4d6 tomato slices: Slice with Orders.Date Orders.Client Orders.Quantity order by Orders.Date Within Envision, a slice is technically a special datatype. Each dashboard is allowed to have a slice set. Slices are numbered internally from 0 to $n-1$. To create the slices for a dashboard, use the sliceDashboard function anywhere in the script (but no more than once): Slice = sliceDashboard(name, label) by [arg0, arg1, ...] In this example, there will be one slice for each distinct value of the [arg0, arg1, ...] tuple. The slice identifier assigned to each value then broadcasts back to the original table, here Items. Selecting a slice - through the dashboard user interface - consists of selecting the internal identifier of the slice through a search bar, which also offers auto-completion to narrow down the possible choices until one can be picked. Auto-completion is based on searching through the display text of the slice, which is composed of two arguments: • The name value of the slice, which should be the same for all lines in a slice. • The label (optional), which also should be the same for all lines in a slice. Then, most tiles can be sliced through the slices option, as by passing a slice value. For example, for the table tile in the script above, show table "My Orders" slices: Slice with Orders.Date Orders.Client Orders.Quantity order by Orders.Date Having group by columns is also possible, in which case the grouping is done independently on each slice: show table "My Orders" slices: Slice with Orders.Client sum(Orders.Quantity) group by Orders.Client In the example above, we have customized the title of the tiles to have a different display per slice. We have achieved that using the expression (same("Weekly sales for \{Name}") by Slice) for the title of the slice. In fact, under the hood, as soon as a sliceDashboard() statement is introduced in the code, every single [StyleCode](/envision-reference/stylecode/] properties of every single tile gets sliced - no matter whether the slices option appear or not on a given tile. The option slices acts as a filter on data that is injected on the tile for any given slice, while the StyleCode properties control the overall appearance of the tile. For example, the label tile is pure StyleCode and no-data, and its display can be adjusted per slice with: show label (same("Weekly sales for \{Name}") by Slice) Many if not most of the scalar options of tiles are StyleCode properties, but not all of them. For example, the export: option of the table tile is not a StyleCode property, and attempting to slice this option will fail. In terms of syntax, when slicing, the linechart requires an explicit group by statement, which might feel unusual. In fact, this only reflects that the linechart aggregate by date is by default. Hence, the code: Week.monday = same(monday(date)) into Week show linechart "My linechart" with sum(Week.Qty) Is actually implicitly the short version of the more explicit code where the grouping has been made explicit: Week.Qty = sum(Orders.Quantity) Week.monday = same(monday(date)) into Week show linechart "My linechart" with sum(Week.Qty) group by Week.monday The later version can be sliced with: Slice = sliceDashboard(Id, Name) by [Id] Week.Slice = Slice Week.Qty = sum(Orders.Quantity) Week.monday = same(monday(date)) into Week show linechart "My linechart" slices: Week.Slice with sum(Week.Qty) group by Week.monday Envision does not accept slicing the linechart under implicit grouping because the aggregation itself becomes somewhat ambiguous. Thus, in order to slice a linechart a few extra line of codes are introduced as illustrated above ## Form tile The form tile offers the possibility to enter values directly from the dashboard itself; these values then become available within the Envision script as scalar variable. This feature is made possible by the form tile. For example, the following script lets the user enter two values: a Boolean and a number. expect Form.Coef : number expect Form.IsTicked : boolean show form "My settings" with Form.Coef as "Coefficient" Form.IsTicked as "Check this case to change the Boolean variable" As the form values can be completely adapted to the problem at hand, the form tile is handy when it comes to generating complex what-if scenario simulators. Also, end-users don’t need to known anything about Envision to use a parameterized dashboard that leverages the form tile. For them, it’s just a regular web page with a form to fill in. However, whenever new entries are filled within the form tile, the Envision code needs to be re-run in order to have the newer entries taking effect. Considering that Envision has an architecture oriented toward batch processing, it means that the refresh should be expected to take multiple seconds even if the amount of data is very limited. Thus, if the users need a real-time feedback while interacting with the dashboard, it is suggested to use the slices that we introduced above. Also, as a rule of thumb, if as soon as your form tile includes more than 10 values, it’s probably time to start considering the upload tile as a better alternative to feed a large number of parameters to the Envision logic. The upload tile offers the possibility to upload a flat file - typically a Microsoft Excel spreadsheet - and make its content accessible within the Envision code. The file is expected to be plainly tabular, with the first line containing the column headers. The newly uploaded content becomes available as a table within Envision. This syntax follows: read upload as MySuppliers[] with SupplierId : text SupplierQuota : number SupplierCountry : text show upload "Supplier settings" with MySuppliers. Even without the upload tile, it was already possible to drop a Excel file directly the in the Files tab within the Lokad account under a well-specified path, and to read this file from Envision with a regular read statement, instead of the read upload outlined above. However, this approach has a few drawbacks that are precisely solved by the upload tile: • There is no need to navigate back and forth between the dashboard and the Files tab. • The possibility of misnaming the file, leading to unintended behaviors, is eliminated. • The script will not fail if no file is provided (yet), instead the table will be treated as empty. Like the form tile, the newly uploaded values will only come into effect with the upload tile when the Envision code is re-executed. The upload tile is handy when the intent is to feed many - possibly thousands - of parameters at once to Envision. Thus, a delay of several seconds or more should be expected to refresh the dashboard, even if the amount of data is relatively limited.	{"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": 0.30518853664398193, "perplexity": 2510.6958045429346}, "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/1566027317113.27/warc/CC-MAIN-20190822110215-20190822132215-00257.warc.gz"}
http://arxiv.org/abs/1102.2784	astro-ph.HE (what is this?) # Title: A New Limit on Planck Scale Lorentz Violation from Gamma-ray Burst Polarization Abstract: Constraints on possible Lorentz invariance violation (LIV) to first order in $E/M_{\rm Planck}$ for photons in the framework of effective field theory (EFT) are discussed, taking cosmological factors into account. Then, using the reported detection of polarized soft $\gamma$-ray emission from the $\gamma$-ray burst GRB041219a that is indicative of an absence of vacuum birefringence, together with a very recent improved method for estimating the redshift of the burst, we derive constraints on the dimension 5 Lorentz violating modification to the Lagrangian of an effective local QFT for QED. Our new constraints are more than five orders of magnitude better than recent constraints from observations of the Crab Nebula. We obtain the upper limit on the Lorentz violating dimension 5 EFT parameter $\|\xi\|$ of $2.4 \times 10^{-15}$, corresponding to a constraint on the dimension 5 standard model extension parameter, $k^{(5)}_{(V)00} \le 4.2 \times 10^{-34}$ GeV$^{-1}$. Comments: version accepted for publication in Astroparticle Physics Subjects: High Energy Astrophysical Phenomena (astro-ph.HE); Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Phenomenology (hep-ph) Journal reference: Astroparticle Physics 35 (2011) 95-97 DOI: 10.1016/j.astropartphys.2011.06.007 Cite as: arXiv:1102.2784 [astro-ph.HE] (or arXiv:1102.2784v6 [astro-ph.HE] for this version) ## Submission history From: Floyd Stecker [view email] [v1] Mon, 14 Feb 2011 14:36:41 GMT (7kb) [v2] Fri, 18 Feb 2011 14:47:23 GMT (7kb) [v3] Mon, 7 Mar 2011 18:55:40 GMT (109kb) [v4] Thu, 26 May 2011 14:28:15 GMT (109kb) [v5] Wed, 15 Jun 2011 14:30:32 GMT (109kb) [v6] Fri, 17 Jun 2011 13:23:02 GMT (109kb)	{"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": 0.6108279824256897, "perplexity": 4460.746023070928}, "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-2016-26/segments/1466783395621.98/warc/CC-MAIN-20160624154955-00060-ip-10-164-35-72.ec2.internal.warc.gz"}
http://gmatclub.com/forum/guys-help-me-make-a-study-plan-162879.html?sort_by_oldest=true	Guys help me make a study plan. : Ask GMAT Experts Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack It is currently 08 Dec 2016, 04:02 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Guys help me make a study plan. Author Message Manager Joined: 15 Jun 2013 Posts: 98 GMAT Date: 12-05-2013 Followers: 2 Kudos [?]: 3 [0], given: 26 Guys help me make a study plan. [#permalink] ### Show Tags 08 Nov 2013, 21:19 Hi, Help me make a study plan...Gmat in 19 days( 3 weeks roughly)..I have a lot of mocks and questions pending.. UPDATE- VERITAS MOCK1 560 Q40 V27 Resources completed OG12 ( 50% RC left) Mgmat SC SC grail Power score CR MGMAT quant guides Kaplan premier Mocks Pending Gmat prep = 6 mocks( 2 mocks 3 times repeat) Veritas= 5 mocks Mgmat= 4 mocks Kaplan= 3 mocks GC club test= 16 Quant mocks Now way i can finish all of them, i need to build good stamina since i get tired after solving 10-15 questions in quant and by the time i reach verbal i feel like closing the test...So this is the reason i have decided to take mock every alternate day, review it on the same day and work on the concept part on the following day+ on the same day take one GC test as well... By this i will be able to finish 10 mocks or so, is it good to build stamina?( I feel if my stamina is good and i can concentrate well, i can get 70% accuracy in RC, 80% in CR and 50% in SC). I believe i will be able to score V30+ with this much accuracy.. Except SC i have no weakness in verbal, just because of focus, lack of concentration i get tired out of it. In quant except P & c(easy), probabilyty(easy) and geometry (medium level), i am very comfortable with rest of the quant topics...so once i start gc club test i can improve my quant and improve 3 more points which will take my q score to Q46 or 47... In my last 3 kaplan +1 MGMAT mock my Quant score has been Q40, 43,40 and in mgmat Q40(Again ) I want to know is their quant section/score similar to real gmat?? OR Real gmat gonna be more difficult than this...What score can i expect in quant on the real test? Target score is 600+ with realistic split score(Q45 V28), I have kept final week for OG error log review, AWA, IR, revision from SC grail and power score CR.... Let me know if i am going wrong somewhere, if this sounds good, if its enough to achieve my target score...My verbal score 2 weeks back was V19 on MGMAT(Except CR, SC and RC were poor performance) how to take it to V35 ? Thanks Kaplan GMAT Prep Discount Codes Economist GMAT Tutor Discount Codes Veritas Prep GMAT Discount Codes Manager Joined: 15 Jun 2013 Posts: 98 GMAT Date: 12-05-2013 Followers: 2 Kudos [?]: 3 [0], given: 26 Re: Guys help me make a study plan. [#permalink] ### Show Tags 16 Nov 2013, 06:28 Just finished veritas free mock 1... 560 Q40 V27 Quant 22/37 correct and verbal 23/41 correct. No matter how hard i try i just can cross Q40, just once i scored Q43, last 5 Quant scores are Kaplan Q40,43,40, Manhattan Q40 and veritas Q40. DS 11/15 correct PS 11/22 correct In quant i got 2 incorrect of first 10. Verbal CR 11/14 Correct RC 5/13 correct SC 7/14 correct In verbal i got 5 incorrect of first 10, is this the reason i coudnt cross V30??Because with same no. of correct questions with almost similar position of the questions my friend got 630 in mgmat,which is known to give less scores these days.. How do i achieve my target of 620 with a realistic split(Q45 V32)??? Please help experts. Gmat in 18 days Manager Joined: 15 Jun 2013 Posts: 98 GMAT Date: 12-05-2013 Followers: 2 Kudos [?]: 3 [0], given: 26 Re: Guys help me make a study plan. [#permalink] ### Show Tags 18 Nov 2013, 00:29 I got a strange gmat prep1 score today on the new version... Few of my last mock scores,old to new Gmat prep 1 350 Q27 V12 (1 july) 800 score 460 Q33 V23 (29 sep) Kaplan 1 490 Q40 V16(15 oct) Kaplan2 520 Q43 V17(2 nov) Mgmat 1 520 Q40 V23(14 nov) Veritas 1 560 Q40 V27(16 nov) Gmat prep 350 Q27 V12 (18 nov) This is so strange my target is 600, hows this even possible? I tried Gmat prep older version in the month of july 2013 and got the same score that i got today 350 Q27 and V12, can this be a software bug since i have both the software loaded in laptop,else how can i get same score and same split??I scored much better on kaplan,mgmat and veritas which are also considered accurate. Please help experts, i have my gmat in 2 weeks and my target is 600, i was happy after veritas mock that iam closer to my target score, but certainly feeling so depressed Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7074 Location: Pune, India Followers: 2086 Kudos [?]: 13294 [1] , given: 222 Re: Guys help me make a study plan. [#permalink] ### Show Tags 18 Nov 2013, 02:14 1 KUDOS Expert's post PlanetEarth wrote: Just finished veritas free mock 1... DS 11/15 correct PS 11/22 correct This is certainly odd. Your accuracy in DS is much better than that in PS. People usually find PS much easier and faster. Are you making too many careless mistakes in PS and paying attention during DS only? You can forget about P and C since it won't affect your overall score much but you must review Geometry properly. You could get up to 7-8 questions from Geometry. Also, I think you are aiming to take too many tests in very little time. A mock every alternate day will be too tiring. Also, analyzing and learning from your mistakes takes at least 2-3 days. Plus, you might want to review a topic after faring not-so-well in it in your mock. Rather than building stamina, so many tests could actually be counter productive. I think you can easily increase your RC accuracy since it is very low right now. Inference questions are harder but universal and specific detail questions are not hard. All you need to do is spend some time and pay attention. Also, review the common error types in SC thoroughly and learn to identify the meaning errors. They are very important in the current GMAT. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 15 Jun 2013 Posts: 98 GMAT Date: 12-05-2013 Followers: 2 Kudos [?]: 3 [0], given: 26 Re: Guys help me make a study plan. [#permalink] ### Show Tags 18 Nov 2013, 07:29 VeritasPrepKarishma wrote: PlanetEarth wrote: Just finished veritas free mock 1... DS 11/15 correct PS 11/22 correct This is certainly odd. Your accuracy in DS is much better than that in PS. People usually find PS much easier and faster. Are you making too many careless mistakes in PS and paying attention during DS only? You can forget about P and C since it won't affect your overall score much but you must review Geometry properly. You could get up to 7-8 questions from Geometry. Also, I think you are aiming to take too many tests in very little time. A mock every alternate day will be too tiring. Also, analyzing and learning from your mistakes takes at least 2-3 days. Plus, you might want to review a topic after faring not-so-well in it in your mock. Rather than building stamina, so many tests could actually be counter productive. I think you can easily increase your RC accuracy since it is very low right now. Inference questions are harder but universal and specific detail questions are not hard. All you need to do is spend some time and pay attention. Also, review the common error types in SC thoroughly and learn to identify the meaning errors. They are very important in the current GMAT. Thanks Karishma, I was really waiting for your reply, thanks again.Since the very beginning i doing fairly decent in DS than PS i dont know why but in every topic except number properties where both ps and ds are good, i am better in DS... I think in in PS i dont have the vision to formulate a equation or set up a problem in my mind then to process that eventually. Karishma today i got a score of 350 Q27 and V12 on gmat prep 1, what do you think my next move should be? i have consistently score Q40 on all major test prep companies including veritas,mgmat and kaplan but its difficult to for what happened today.... Since i think this can be a software bug(just to please myself, i am gonna delete both the versions of gmat prep software and download again. Any thoughts? Finally is it feasible to jump from 560 to 600 in 2 weeks?? Thanks again for taking your time out and helping me always... Update Just wanted to say thanks again to you, i was really depressed yesterday. I took gmat prep1 again today. my score is... 610 Q45 V29 Cant tell you am feeling so happy, i have scored my personal best on all sections and overall score too...The earlier gmat prep definitely had some bug (Deleted all the versions and downloaded newer one). In quant i did not see even a single repeat, i verbal i saw 4 repeats.. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7074 Location: Pune, India Followers: 2086 Kudos [?]: 13294 [1] , given: 222 Re: Guys help me make a study plan. [#permalink] ### Show Tags 19 Nov 2013, 20:07 1 This post received KUDOS Expert's post PlanetEarth wrote: VeritasPrepKarishma wrote: PlanetEarth wrote: Just finished veritas free mock 1... DS 11/15 correct PS 11/22 correct This is certainly odd. Your accuracy in DS is much better than that in PS. People usually find PS much easier and faster. Are you making too many careless mistakes in PS and paying attention during DS only? You can forget about P and C since it won't affect your overall score much but you must review Geometry properly. You could get up to 7-8 questions from Geometry. Also, I think you are aiming to take too many tests in very little time. A mock every alternate day will be too tiring. Also, analyzing and learning from your mistakes takes at least 2-3 days. Plus, you might want to review a topic after faring not-so-well in it in your mock. Rather than building stamina, so many tests could actually be counter productive. I think you can easily increase your RC accuracy since it is very low right now. Inference questions are harder but universal and specific detail questions are not hard. All you need to do is spend some time and pay attention. Also, review the common error types in SC thoroughly and learn to identify the meaning errors. They are very important in the current GMAT. Thanks Karishma, I was really waiting for your reply, thanks again.Since the very beginning i doing fairly decent in DS than PS i dont know why but in every topic except number properties where both ps and ds are good, i am better in DS... I think in in PS i dont have the vision to formulate a equation or set up a problem in my mind then to process that eventually. Karishma today i got a score of 350 Q27 and V12 on gmat prep 1, what do you think my next move should be? i have consistently score Q40 on all major test prep companies including veritas,mgmat and kaplan but its difficult to for what happened today.... Since i think this can be a software bug(just to please myself, i am gonna delete both the versions of gmat prep software and download again. Any thoughts? Finally is it feasible to jump from 560 to 600 in 2 weeks?? Thanks again for taking your time out and helping me always... Update Just wanted to say thanks again to you, i was really depressed yesterday. I took gmat prep1 again today. my score is... 610 Q45 V29 Cant tell you am feeling so happy, i have scored my personal best on all sections and overall score too...The earlier gmat prep definitely had some bug (Deleted all the versions and downloaded newer one). In quant i did not see even a single repeat, i verbal i saw 4 repeats.. Great! I was really surprised - a 200 point difference in official GMAT practice test doesn't happen. Glad it was some technical error and you have it sorted out. Also, Brian put up a suggestion (on another post) for people who are better at DS than PS. See if this helps you too. Go through 10 PS questions and don't even look at the question stems...just look at the answer choices and jot down a few notes if you notice anything about them. Try this first with problems you've already done since you may not have exhausted the answer choices - my theory in a case like yours (much better at DS than PS) is that at least a couple times per test you're missing some important clues in the answer choices that would help you save time or leverage those assets (for example, does it look like a number property would help; could you get away with an estimate; are there the kinds of clues like root3 or root 2 that suggest you have to find a certain kind of triangle or shape, etc.). Try this out and see if it helps...it often depends on the student or the problem set but I've had this work to show people that there's often more to the problem than the problem itself, so it at least gets them thinking of all their resources. _________________ Karishma Veritas Prep \| GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199 Veritas Prep Reviews Manager Joined: 15 Jun 2013 Posts: 98 GMAT Date: 12-05-2013 Followers: 2 Kudos [?]: 3 [0], given: 26 Re: Guys help me make a study plan. [#permalink] ### Show Tags 19 Nov 2013, 20:48 VeritasPrepKarishma wrote: PlanetEarth wrote: VeritasPrepKarishma wrote: Thanks Karishma, I was really waiting for your reply, thanks again.Since the very beginning i doing fairly decent in DS than PS i dont know why but in every topic except number properties where both ps and ds are good, i am better in DS... I think in in PS i dont have the vision to formulate a equation or set up a problem in my mind then to process that eventually. Karishma today i got a score of 350 Q27 and V12 on gmat prep 1, what do you think my next move should be? i have consistently score Q40 on all major test prep companies including veritas,mgmat and kaplan but its difficult to for what happened today.... Since i think this can be a software bug(just to please myself, i am gonna delete both the versions of gmat prep software and download again. Any thoughts? Finally is it feasible to jump from 560 to 600 in 2 weeks?? Thanks again for taking your time out and helping me always... Update Just wanted to say thanks again to you, i was really depressed yesterday. I took gmat prep1 again today. my score is... 610 Q45 V29 Cant tell you am feeling so happy, i have scored my personal best on all sections and overall score too...The earlier gmat prep definitely had some bug In quant i did not see even a single repeat, i verbal i saw 4 repeats.. Great! I was really surprised - a 200 point difference in official GMAT practice test doesn't happen. Glad it was some technical error and you have it sorted out. Also, Brian put up a suggestion (on another post) for people who are better at DS than PS. See if this helps you too. Go through 10 PS questions and don't even look at the question stems...just look at the answer choices and jot down a few notes if you notice anything about them. Try this first with problems you've already done since you may not have exhausted the answer choices - my theory in a case like yours (much better at DS than PS) is that at least a couple times per test you're missing some important clues in the answer choices that would help you save time or leverage those assets (for example, does it look like a number property would help; could you get away with an estimate; are there the kinds of clues like root3 or root 2 that suggest you have to find a certain kind of triangle or shape, etc.). Try this out and see if it helps...it often depends on the student or the problem set but I've had this work to show people that there's often more to the problem than the problem itself, so it at least gets them thinking of all their resources. Thanks Karishma,good suggestion. Out of 6 veritas quant book, 3 books are pending in the home work section( Data sufficiency, stats and combi and word problem). Was to lazy to do them after covering the skill builder and theory part. DS- I tried the challenge questions at the last of the book 11/15, so did not attempt the earlier questions. Stats and combi- I think i will let this go(Home work part) Word problem- I really want to finish this, since brian also suggested. Intern Joined: 11 Aug 2014 Posts: 15 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Guys help me make a study plan. [#permalink] ### Show Tags 11 Aug 2014, 16:51 What goal do you have in mind? Re: Guys help me make a study plan. [#permalink] 11 Aug 2014, 16:51 Similar topics Replies Last post Similar Topics: Study plan help!! Studying full time for a month! which CATS to take? 7 07 Oct 2015, 19:47 Help me to make a plan 9 26 Mar 2015, 20:44 Can you guys help me out? 2 25 Aug 2013, 11:15 Please help me form my study plan to go from 660 to 730+ 4 02 Dec 2011, 11:11 Display posts from previous: Sort by	{"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": 0.428239643573761, "perplexity": 5118.690130746279}, "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/1480698542588.29/warc/CC-MAIN-20161202170902-00473-ip-10-31-129-80.ec2.internal.warc.gz"}
http://community.wolfram.com/groups/-/m/t/248113?p_p_auth=W55OM9Iq	# How to multiply several matrices? GROUPS: The code Sum[(Cos)^2 - (Cos)^2, {i, 1, n}] provides one with a sum from 1 to n. Similarly, Product[] gives a sum from 1 to n.I would be interested in a similar command for a product of n matrices; I have to specify that I really wanna use the Dot multiplication, not the componentwise one. And n is not specified, so I am exactly in the same situation as for Sum and Product.Does anybody know how to do this?Many thanks in advance!	{"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": 0.9632566571235657, "perplexity": 435.08496917299584}, "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-2014-23/segments/1405997872261.34/warc/CC-MAIN-20140722025752-00205-ip-10-33-131-23.ec2.internal.warc.gz"}
https://quantnet.com/threads/recruiters-are-calling-but.2944/#post-26664	# Recruiters are calling, but... #### IlyaKEightSix Okay, I called this recruiter since she wants to set me up for an interview as a structured finance developer while I'm working on this (rather mundane) M.S. Stat here in Rutgers. She says it's $100k + Bonus, which is very nice for someone like me whose last paying work was$18 an hour and who has a negative net worth. However, I told her that my end goal is RenTec or DESCo, which need PhDs or bust (and if I'm going to do something for my career, I want to be among the best at it, not just another cog in another unknown shop). And she told me that she was working with a PhD aspiring quant, early 30s, who was only getting offered 70-80k due to no experience, but wanted twice as much because of his age/education. I'm just wondering, from a recruiter's standpoint, if I want to make it to the top tier quant funds that define the industry, do I get work experience in the financial industry as a sort of developer/modeler and try to PhD part time, or do I just go straight through and blow off job-hunting until I have my doctorate? BTW, I'm planning to pursue my PhD in OR when I do go for it, and not a lot of schools have good programs. Columbia has one, Stanford has one (Management Sci/Engr), Stony Brook has one (headed up by Bob Frey of RenTec in the quant finance route), and MIT has one. However, with my undergrad GPA 3.3 and the deadlines early december (won't get grades in time), what is it that a recruiter (ahem, Sir Connor) would suggest me to do? Try to get a couple of years experience under my belt, or take my chances hoping my recommendations are good enough to make up for an 87% quant general GRE score and 3.3 cumulative GPA (3.5 major)? Also, I'm studying for the math subject GREs, but it seems that I'm basically relearning everything from the ground up since multivar calc/linear algebra+diffeqs were in my freshman undergrad year (and my regular calc was in high school which I AP'd out of in college). #### doug reich ##### Some guy Ilya, you're asking for the same advice over and over again and hoping for a different answer each time. There's saying about that... #### tobias elbert I dont know much about the US employment market, but why do you think that gaining experience from firm A disqualifies you automatically from joining firm B at a later stage? Where did you get this idea from? 100k + bonus is a good salary package for someone entering the industry with zero experience. I just wonder - why was that PhD guy not offered that position, but you who hasn't completed the Master's yet (no offence, but why would a recruiter do this unless the PhD doesnt want that role or is for whatever reason not suitable for it)? This is my personal opinion re PhD (I dont have one by the way): finish your Masters, go out in the industry, identify which areas you and your (future) employers benefit from, and then do a PhD in such areas in a few years time - if you still want to that is. #### doug reich ##### Some guy I dont know much about the US employment market, but why do you think that gaining experience from firm A disqualifies you automatically from joining firm B at a later stage? Where did you get this idea from? There are very fancy places that think this way. 100k + bonus is a good salary package for someone entering the industry with zero experience. I just wonder - why was that PhD guy not offered that position, but you who hasn't completed the Master's yet (no offence, but why would a recruiter do this unless the PhD doesnt want that role or is for whatever reason not suitable for it)? A. The PhD is over-qualified. B. The PhD is asking for too much money. C. The PhD's ego is getting in the way. D. Firms like to mold their candidates, and a highly-educated or highly-experienced person may be too set in his ways. See prior section. E. They are different positions and the PhD is not qualified. This is my personal opinion re PhD (I dont have one by the way): finish your Masters, go out in the industry, identify which areas you and your (future) employers benefit from, and then do a PhD in such areas in a few years time - if you still want to that is. Common advice is that a PhD won't really get you ahead in the pay scale given the time invested in it. You may be doing different work, but you won't be making more money when you balance out the head start a masters or undergrad have. Also, a PhD is tough and if you're just looking for a pot of gold, you will either be miserable or drop out or both. #### tobias elbert There are very fancy places that think this way. A. The PhD is over-qualified. B. The PhD is asking for too much money. C. The PhD's ego is getting in the way. D. Firms like to mold their candidates, and a highly-educated or highly-experienced person may be too set in his ways. See prior section. E. They are different positions and the PhD is not qualified. Also, a PhD is tough and if you're just looking for a pot of gold, you will either be miserable or drop out or both. Interesting. I just had a look at DeShaw's website and from what they say is that they value diversity and achievements. Kinda contradicts that they rule out ppl just because they had worked at a different firm - are you serious? I cant believe that, if you are a good, competitive candidate they will interview you - regardless of where you worked in the past. If ppl name that as a reason for getting rejected then it's probably more due to denial than anything else. According to what OP said, my conclusion was that A cant be the case. B is likely but then I still wonder why a PhD in Quant Finance gets offered 70-80k for every role (according to OP), but not the 100k OP was offered for that role. C, D could be. D must be a US thing though (second part, assuming that you're no longer moldable at a certain age or level of education). As for your last part - most ppl (90%) would do a PhD out of interest in an area, not necessarily for money because of the reasons you mentioned. You need to be really passionate of the area you study. I am just saying see what's out there first before doing your PhD in something you think is relevant but turns out to be a waste of time and your contribution is too marginal to be of value. Plus, if you dont want to go for an extremely abstract, theoretical PhD I'd say learn what's out there first and then make an informed decision. Personally, I'd be more interested in doing a PhD in pricing swing or storage options than in nonlinear optimization, for instances. The former are things you dont necessarily hear or know about if you are not in or have never been exposed to an work environment. #### IlyaKEightSix In terms of PhDs, the only path I'm really considering is operations research, or perhaps statistics. Whatever it will be in, the entire point will be to apply it to something very tangible (EG the market). I'm not out to do theoretical mumbo jumbo. EG: "If we lived on mars, and pigs could fly, my beautiful closed form equation would be true." My interest in the PhD path are these: 1) Show that I am a "World Class Researcher" and can do "Good Science" 2) Build strong connections with professors with a strong connection to prevalent industries through doing research for them. 3) Obtain abilities that would allow me to come up with a solution for almost any practical problem. I have no intention of pursuing abstract, ivory-tower theories. Everything I do has to have a point in terms of solving real world problems. As for D.E. Shaw, they have many, many different strategies and divisions now. However, I'm interested in their quant division, not so much their distressed investments or private equity or whatnot. #### bluechimp Just.. make sure you perform a stellar job at Rutgers. To be honest, I have never seen anyone get accepted to top graduate programs in anything with your undergraduate marks. And please please please, don't write in your statement of purpose that the bad grades are attributed to the 'boring' courses; whining is a sign of the weak. Trust me, you will do more 'boring' courses in any PhD program. Congratulations on being contacted by a recruiter! Don't drop the ball #### IlyaKEightSix In terms of Rutgers, so long as I do the work, I'll be fine. It's nothing spectacular or jaw-dropping, so it's sort of a let-down. But it'll give me a new piece of paper in a quantitative discipline. I guess I won't write in my statement that I had boring courses, but that most of the pain came from two bad semesters early on. All 3 of my recommendations will be from MIT grads at some point (BS, PhD, postdoc), so if that doesn't fly, then I put my best foot forward. And also, I'm studying for the math subject GREs to try and help matters. If it's all a no-go, then I did my best. #### doug reich ##### Some guy I guess I won't write in my statement that I had boring courses, but that most of the pain came from two bad semesters early on. Luckily there's hundreds of posts on quantnet that say that. #### satyag 1) Show that I am a "World Class Researcher" and can do "Good Science" Dont do this to "Show". Do it if you are passionate about research irrespective of how others receive it. #### joel_b You're just talking to a recruiter. If you really want to make a decision, do the interview, get an offer, then decide. You may not even get an offer. It's just speculation, and either way, interview practice is not a bad thing. #### jay.berg However, I told her that my end goal is RenTec or DESCo, which need PhDs or bust (and if I'm going to do something for my career, I want to be among the best at it, not just another cog in another unknown shop). . cmon man c- • Poll Replies 1 Views 671 Replies 5 Views 688 • Poll Replies 0 Views 931 Replies 11 Views 923 Replies 8 Views 1K	{"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": 0.26276442408561707, "perplexity": 1739.6978800698448}, "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/1656103337962.22/warc/CC-MAIN-20220627164834-20220627194834-00538.warc.gz"}
http://mathhelpforum.com/differential-equations/210440-how-integrate-partial-differential-equation.html	# Math Help - How to integrate this partial differential equation 1. ## How to integrate this partial differential equation I have the following equation $\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0$ where $y$ is a function of $x$ and $m$ is a function of $y$. If I integrate this equation first with respect to $y$ should I get a function of $x$ as the constant of integration (say $C\left(x\right)$) or it is just a constant? If it is a function, how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation. 2. ## Re: How to integrate this partial differential equation Originally Posted by JulieK I have the following equation $\frac{\partial}{\partial y}\left(m\frac{dy}{dx}\right)=0$ where $y$ is a function of $x$ and $m$ is a function of $y$. If I integrate this equation first with respect to $y$ should I get a function of $x$ as the constant of integration (say $C\left(x\right)$) or it is just a constant? If it is a function, how can I then find its form (e.g. polynomial, etc.)? Should I use boundary conditions or I can decide about the form from inspecting the type of the equation. \displaystyle \begin{align} \frac{\partial }{\partial y} \left( m\, \frac{dy}{dx} \right) &= 0 \\ m\,\frac{dy}{dx} &= \int{0\, dy} \\ m\,\frac{dy}{dx} &= f(x) \\ \frac{dy}{dx} &= \frac{f(x)}{m} \\ y &= \int{\frac{f(x)}{m}\,dx} \\ y &= \frac{1}{m} \int{f(x)\,dx} + C \end{align} Unless you have some boundary conditions now, this is the simplest it's going to get.	{"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": 17, "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": 1.0000061988830566, "perplexity": 219.03060161793007}, "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-2014-35/segments/1408500833461.95/warc/CC-MAIN-20140820021353-00221-ip-10-180-136-8.ec2.internal.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-10-radical-expressions-and-equations-10-5-graphing-square-root-functions-practice-and-problem-solving-exercises-page-643/56	## Algebra 1: Common Core (15th Edition) We are given: $y =\sqrt {x+1}+5$ For the function, the graph of $y=\sqrt x$ is shifted 1 unit to the left and 5 units up.	{"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": 0.5048550367355347, "perplexity": 689.5457747408627}, "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-2022-21/segments/1652663019783.90/warc/CC-MAIN-20220528185151-20220528215151-00603.warc.gz"}
https://www.physicsoverflow.org/31968/eliminates-phenomenon-introducing-possibly-applications	# Does this concept in Fourier analysis which eliminates Gibbs' phenomenon and also introducing some new concepts, possibly have applications in any areas of physics, like QM or in any applied areas? + 1 like - 0 dislike 299 views This is more of seeking possible applications/contructs in physics for a new mathematical concept. Main theme and motivation summary : ---------- Motivation ---------- Consider a BV function $f$ with jumps, the Fourier partial integral function (analogous to Fourier partial sum in periodic case) as $\omega\to\infty$ does converge to $f$ pointwise except possibly at jumps. But the total variation of the partial integral function does not converge to the total variation of the function $f$, more over it goes to infinity. (attributed to Gibb's phenomenon). To overcome Gibb's phenomenon, alternate summation methods were suggested, like Cesaro summation but their convergence is very slow especially when $f$ has a jump. In my approach, I propose a construction of a sequence of functions, just like partial sums, each one denoted as $P^f_{\omega}$ constructed using Fourier spectrum of $f$ only in the interval $(0,\omega)$. The function sequence is intended to converge to $f$ pointwise except at jump points, and not just that, but also overcome Gibb's phenomenon, there by variation of $P^f_{\omega}$ in any given open interval, converging to that of the function $f$ as $\omega\to\infty$. More interesting part is that the function $P^f_{\omega}$ can possess jump discontinuties. (even when $f$ does not have jumps). I also predict that the convergence is much faster than Cesaro partial sums. Another interesting part is that in Fourier analysis we try to approximate even functions that jump, with smooth functions. But here we use jumping functions to approximate jumping functions. (This problem could be formulated in Fourier series but I choose to do it for Fourier transform setup). edited Jun 15, 2015 Hi Rajesh, welcome to PhysicsOverflow ! Maybe in addition to the MO link, you can give a short summary of the concepts you would like to see physics applications for, directly in this PO question too to help the reader? Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor) Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.	{"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": 0.7869512438774109, "perplexity": 896.3737437058177}, "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-2018-05/segments/1516084886437.0/warc/CC-MAIN-20180116144951-20180116164951-00391.warc.gz"}
http://mathhelpforum.com/algebra/222953-determine-when-f-x-48-a.html	# Math Help - Determine when f(x)=48 1. ## Determine when f(x)=48 we have the equation x^4 - 5x^2 + 4 and to find when the values of x give us 48 we do this : x^4 - 5x^2 + 4 = 48, then we try to factor. In this case we can not, so do we use the quadratic formula? The answers in the text book are 48 and -3.10 ? They are wrong... So what do i do? 2. ## Re: Determine when f(x)=48 Use the substitution $y=x^2$	{"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": 1, "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": 0.6967223882675171, "perplexity": 539.163964252031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701158601.61/warc/CC-MAIN-20160205193918-00269-ip-10-236-182-209.ec2.internal.warc.gz"}
http://mathhelpforum.com/algebra/92750-algebra-help.html	# Math Help - algebra help 1. ## algebra help in 1993, the life expectancy of males in a certain country was 70.7. in 1999, it was 74.6 year. Let E represent the life expectancy in year t and let t represent the number of years since 1993. E(t) = ?t + ? 2. Originally Posted by pennybomber1 in 1993, the life expectancy of males in a certain country was 70.7. in 1999, it was 74.6 year. Let E represent the life expectancy in year t and let t represent the number of years since 1993. E(t) = ?t + ? I'm assuming this is a linear function? "E(t) = ?t + ?" is essentially a linear equation in slope-intercept form, y = mx + b. First, find the slope. You got two points: (0, 70.7) and (6, 74.6). The x-coordinates are years since 1993, and the y-coordinates are the life expectancies. \begin{aligned} m &= \frac{y_2 - y_1}{x_2 - x_1} \\ &= \frac{74.6 - 70.7}{6 - 0} \\ &= \frac{3.9}{6} \\ &= 0.65 \end{aligned} Second, you need the y-intercept. Oh, wait, one of the points is the y-intercept, so b = 70.7. You have the two pieces of information needed to write the function: E(t) = 0.65t + 70.7 01 3. sweet that was the answer I got as well. Thanks for confirming.	{"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": 1, "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": 0.9270918369293213, "perplexity": 1161.4807478776754}, "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-2014-41/segments/1410657135080.9/warc/CC-MAIN-20140914011215-00097-ip-10-234-18-248.ec2.internal.warc.gz"}
http://clay6.com/qa/1645/let-be-binary-operation-defined-on-r-by-a-b-1-ab-a-b-in-r-then-the-operatio	# Let * be binary operation defined on R by $ab=1+ab, a,b \in R.$ Then the operation is (i) commutative but not associative (ii) associative but not commutative (iii) neither commutative nor associative (iv) both commutative and associative Toolbox: • 1. A binary operation * defined on R is commutative if $ab=ba$ • 2. A binary operation * defined on R is associative if $(ab)c=a(bc) \qquad a,b \in R$ Step 1: commutative * operation defined on R by $ab=1+ab \qquad a,b \in R$ $ba=1+ba$ $=1+ab$ Multiplication is commutative in R $ab =ba$ * operation is commutative Step 2: Associative $(ab)c=(1+ab)c$ $=1+(1+ab)c$ $=1+c+abc$ $a \times (b \times c)=a (1+bc)$ $=1+a(1+bc)$ $=1+a+abc$ $(ab)c \neq a (bc)$ * operation is not associative Solution: * operation is commutative but not associative (i) option is correct answered Mar 5, 2013 by edited Mar 27, 2013 by meena.p	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9313105940818787, "perplexity": 2516.6032727687652}, "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-2018-13/segments/1521257647838.64/warc/CC-MAIN-20180322092712-20180322112712-00307.warc.gz"}
https://gilleskratzer.netlify.app/publication/sandro1/	# Characterization of the Vitrocell® 24/48 aerosol exposure system for its use in exposures to liquid aerosols ### Abstract BACKGROUND: The Vitrocell® 2448 is an advanced aerosol exposure system that has been widely used and characterized for exposure studies of cigarette smoke, but not for exposure to liquid aerosols with a low gas-vapor phase content such as the ones generated by electronic cigarettes. An experimental system characterization for this specific application was therefore performed. METHODS: Glycerol model aerosols of different particle size distributions, produced by a condensation monodisperse aerosol generator, were used for exposing small volumes of phosphate-buffered saline in the Vitrocell® 2448. Disodium fluorescein, added as a tracer in the aerosol, allowed the exact aerosol mass deposition to be quantified fluorometrically. RESULTS: The aerosol mass delivery efficiency within the system showed variations in the range of ±25%. Aerosol dilution was not fully reflected in aerosol delivery, the achieved aerosol delivery should therefore be determined experimentally. Quartz crystal microbalances underestimated the deposition of liquid aerosols. Unequal delivery of particles of different sizes was detectable, although this effect is unlikely to be relevant under applied experimental conditions. CONCLUSIONS: The Vitrocell® 2448 aerosol exposure system can be used for exposures to liquid aerosols, such as those generated by electronic cigarettes. However, our results indicate that, compared with aerosol studies of cigarettes, a higher variability is to be expected. Type Publication In Toxicology in Vitro. Date	{"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": 0.9359841346740723, "perplexity": 5875.725809896545}, "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/1610704803737.78/warc/CC-MAIN-20210126202017-20210126232017-00370.warc.gz"}
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2003.3.401	# American Institute of Mathematical Sciences August 2003, 3(3): 401-408. doi: 10.3934/dcdsb.2003.3.401 ## The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation 1 Department of Applied Mathematics, Southwest Jiaotong University, 610066, Chengdu, China 2 Department of Mathematics and Statistics, Curtin University of Technology, GOP Box U1987, Perth, WA 6845, Australia Received April 2002 Revised February 2003 Published May 2003 In this paper, we consider the solution of an initial value problem for the generalized damped Boussinesq equation $u_{t t} - a u_{t t x x}- 2 b u_{t x x} = - c u_{x x x x}+ u_{x x} - p^2 u + \beta(u^2)_{x x},$ where $x\in R^1,$ $t > 0,$ $a ,$ $b$ and $c$ are positive constants, $p \ne 0,$ and $\beta \in R^1$. For the case $a + c > b^2$ corresponding to damped oscillations with an infinite number of oscillation cycles, we establish the well-posedness theorem of the global solution to the problem and derive a large time asymptotic solution. Citation: Shaoyong Lai, Yong Hong Wu. The asymptotic solution of the Cauchy problem for a generalized Boussinesq equation. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 401-408. doi: 10.3934/dcdsb.2003.3.401 [1] Thomas Y. Hou, Congming Li. Global well-posedness of the viscous Boussinesq equations. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 1-12. doi: 10.3934/dcds.2005.12.1 [2] Hongwei Wang, Amin Esfahani. Well-posedness and asymptotic behavior of the dissipative Ostrovsky equation. Evolution Equations and Control Theory, 2019, 8 (4) : 709-735. doi: 10.3934/eect.2019035 [3] Seung-Yeal Ha, Jinyeong Park, Xiongtao Zhang. A global well-posedness and asymptotic dynamics of the kinetic Winfree equation. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1317-1344. doi: 10.3934/dcdsb.2019229 [4] Luiz Gustavo Farah. Local solutions in Sobolev spaces and unconditional well-posedness for the generalized Boussinesq equation. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1521-1539. doi: 10.3934/cpaa.2009.8.1521 [5] Qunyi Bie, Qiru Wang, Zheng-An Yao. On the well-posedness of the inviscid Boussinesq equations in the Besov-Morrey spaces. Kinetic and Related Models, 2015, 8 (3) : 395-411. doi: 10.3934/krm.2015.8.395 [6] Alex M. Montes, Ricardo Córdoba. Local well-posedness for a class of 1D Boussinesq systems. Mathematical Control and Related Fields, 2022, 12 (2) : 447-473. doi: 10.3934/mcrf.2021030 [7] Rainer Brunnhuber, Barbara Kaltenbacher. Well-posedness and asymptotic behavior of solutions for the Blackstock-Crighton-Westervelt equation. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4515-4535. doi: 10.3934/dcds.2014.34.4515 [8] Boris Kolev. Local well-posedness of the EPDiff equation: A survey. Journal of Geometric Mechanics, 2017, 9 (2) : 167-189. doi: 10.3934/jgm.2017007 [9] Lin Shen, Shu Wang, Yongxin Wang. The well-posedness and regularity of a rotating blades equation. Electronic Research Archive, 2020, 28 (2) : 691-719. doi: 10.3934/era.2020036 [10] Jerry Bona, Nikolay Tzvetkov. Sharp well-posedness results for the BBM equation. Discrete and Continuous Dynamical Systems, 2009, 23 (4) : 1241-1252. doi: 10.3934/dcds.2009.23.1241 [11] A. Alexandrou Himonas, Curtis Holliman. On well-posedness of the Degasperis-Procesi equation. Discrete and Continuous Dynamical Systems, 2011, 31 (2) : 469-488. doi: 10.3934/dcds.2011.31.469 [12] Nils Strunk. Well-posedness for the supercritical gKdV equation. Communications on Pure and Applied Analysis, 2014, 13 (2) : 527-542. doi: 10.3934/cpaa.2014.13.527 [13] Ivonne Rivas, Muhammad Usman, Bing-Yu Zhang. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control and Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61 [14] Igor Chueshov, Alexey Shcherbina. Semi-weak well-posedness and attractors for 2D Schrödinger-Boussinesq equations. Evolution Equations and Control Theory, 2012, 1 (1) : 57-80. doi: 10.3934/eect.2012.1.57 [15] Renhui Wan. Global well-posedness for the 2D Boussinesq equations with a velocity damping term. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2709-2730. doi: 10.3934/dcds.2019113 [16] Adalet Hanachi, Haroune Houamed, Mohamed Zerguine. On the global well-posedness of the axisymmetric viscous Boussinesq system in critical Lebesgue spaces. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6473-6506. doi: 10.3934/dcds.2020287 [17] Saoussen Sokrani. On the global well-posedness of 3-D Boussinesq system with partial viscosity and axisymmetric data. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1613-1650. doi: 10.3934/dcds.2019072 [18] Xiaoqiang Dai, Shaohua Chen. Global well-posedness for the Cauchy problem of generalized Boussinesq equations in the control problem regarding initial data. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4201-4211. doi: 10.3934/dcdss.2021114 [19] Aiting Le, Chenyin Qian. Smoothing effect and well-posedness for 2D Boussinesq equations in critical Sobolev space. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022057 [20] Tadahiro Oh, Yuzhao Wang. On global well-posedness of the modified KdV equation in modulation spaces. Discrete and Continuous Dynamical Systems, 2021, 41 (6) : 2971-2992. doi: 10.3934/dcds.2020393 2020 Impact Factor: 1.327	{"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": 0.5294561386108398, "perplexity": 3205.402667213687}, "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/1656103328647.18/warc/CC-MAIN-20220627043200-20220627073200-00662.warc.gz"}
https://www.vosesoftware.com/riskwiki/VoseAggregateMC.php	# VoseAggregateMC =VoseAggregateMC(N,Distribution) This function aggregates N random values from a distribution using direct Monte Carlo simulation. It is the most straightforward way of modeling the sum of independent random values drawn from a given distribution. • N - the number of random values to be aggregated (summed). This should be an integer. This can be a fixed number as well as a sampled value from a discrete distribution. • Distribution - a distribution object where the N variables to be summed are sampled from. In insurance modeling for example, this function could be used to model the aggregation of a random number of claims coming in with a random size. The total amount an insurance company has to pay out could then be modelled with the function VoseAggregateMC where N represents the (random) number of claims and "Distribution" represents the random size of the claims. There exists a number of identities that provide 'shortcuts' for calculating aggregate distributions faster, as explained here. These identities are by the VoseAggregateMC function when appropriate to speed up the calculation. ### Examples ##### Example 1 When N = 100 and the distribution is a LogNormal(2,1), the aggregation =VoseAggregateMC(100,LogNormalObject(2,1)) will be performed by Monte Carlo simulation, meaning that this function randomly takes 100 samples of a LogNormal(2,1) distribution and then adds them all together. ##### Example 2 If N = 100 and the distribution is a Gamma(3,6), then the VoseAggregateMC function knows that there is a shortcut formula for aggregating Gamma distributions: Gamma(1003,6). That means that in this case the function =VoseAggregateMC(100,Gamma(3,6)) immediately samples from the aggregated distribution. ##### Example 3 If the specified distribution is a known distribution, like in example 2, but with a truncation (for example =VoseGamma(3,6,,VoseXBounds(1,7))), then there is no formula to sample directly from the aggregate distribution and a Monte Carlo simulation has to be performed (like in the first example). ##### Example 4 If the distribution is known, but there is a shift in it, then the shortcut formula still holds, but one needs to take into account the shift. For example, aggregating 100 VoseGamma(3,6,,VoseShift(10)) random variables by writing: =VoseAggregateMC(100,VoseGamma(3,6,,VoseShift(10))) means sampling from the aggregate distribution: 10010 + VoseGamma(1003,6). ##### Example 5 When N is not a number but a distribution (for example Poisson(50) ) and the specified distribution is not known to have a shortcut formula (for example Pareto(3,1) ) then the VoseAggregateMC function =VoseAggregateMC(VosePoisson(50),Pareto(47) randomly samples from the Poisson(50) distribution (let's say 47), then randomly samples 47 times from the Pareto distribution and finally adds them all up. ##### Example 6 In the case that N is a continuous distribution (for example LogNormal(20,15) ) and the specified distribution is known to have a shortcut formula (for example Normal(100,10) ), the function samples from the LogNormal distribution, rounds it up to an integer (let's say 22) and then knows that the aggregate distribution is: Normal(22100,SQRT(22)10). ##### Comment 1 In the cases where the aggregation has to be performed by Monte Carlo simulation (for example 100 Pareto(3,2) distributions), this function takes quite some time to complete the aggregation for very large N. Also see VoseCLTSum. But in the cases where there is a direct formula for the aggregation (for example 1000000 Gamma(2,3) ) the aggregation is instantaneous. ##### Comment 2 The distribution parameter can also be a fixed number. VoseAggregateMC(VosePoisson(50),100) will return N100 where N is randomly sampled from a Poisson(50) distribution.	{"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": 0.9126216173171997, "perplexity": 703.4775839218576}, "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/1566027316194.18/warc/CC-MAIN-20190821194752-20190821220752-00311.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-11-rational-expressions-and-functions-11-1-simplifying-rational-expressions-practice-and-problem-solving-exercises-page-668/35	## Algebra 1: Common Core (15th Edition) $\frac{3z+12}{z^3}$ $\frac{z(3z+12)}{z∗z^3}$ Factor out a z from the numerator and the denominator $\frac{3z+12}{z^3}$	{"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": 0.9782652258872986, "perplexity": 1907.071155931912}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512679.76/warc/CC-MAIN-20181020080138-20181020101638-00066.warc.gz"}
https://www.chemeurope.com/en/encyclopedia/Galilei_number.html	My watch list my.chemeurope.com # Galilei number In fluid dynamics, the Galilei number (Ga), sometimes also referred to as Galileo number (see discussion), is a dimensionless number named after Italian scientist Galileo Galilei (1564-1642). It may be regarded as proportional to gravity forces divided by viscous forces. The Galilei number is used in viscous flow and thermal expansion calculations, for example to describe fluid film flow over walls. These flows apply to condensors or chemical columns. $Ga = \frac{g \cdot L^3}{\nu^2}$ • g: gravitational acceleration, (SI units: m/s2) • L: characteristic length, (SI units: m) • ν: characteristic, kinematic viscosity (SI units: m2/s) ## References • VDI-Wärmeatlas; 5., extended Edition; VDI Verlag Düsseldorf; 1988; page Bc 1 (German) • W. Wagner; Wärmeübertragung; 5., revised Edition; Vogel Fachbuch; 1998; page 119 (German)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5903715491294861, "perplexity": 15392.04676133608}, "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-2019-35/segments/1566027315865.44/warc/CC-MAIN-20190821085942-20190821111942-00267.warc.gz"}
https://www.originlab.com/doc/Origin-Help/Wks-SetColVal-QuickStart	# 4.6.8.1 Quick Start ## Set Values Dialog Box Key Features The Set Values dialog box takes a one-line, user-defined expression and fills one or multiple worksheet columns (or portions of columns) with values generated by the expression. The expression -- entered directly in the Column Formula box -- can incorporate arithmetic operators, column and cell references, functions, user-defined variables, constants, etc. (see below). The Set Values Dialog features syntax-coloring. Optional Scripting Tabs: • The Before Formula Scripts tab takes one or more lines of LabTalk script and runs the script before the expression in the Column Formula box is executed. This makes possible such things as pre-processing of input data, defining functions, variables and constants for use in the Column Formula box, etc. For more information on the use of Before Formula Scripts, see Entering Expressions in the Set Column Values Dialog. For help with Set Values dialog box controls, see Menu Options and Dialog Controls. • The Python Function tab allows you to define Python functions to be called in your column formulas. While you could save functions to an external file, using the Python Function tab allows you to save your code to an Origin template file for repeat use. Further, your Python functions can be called directly from the Column Formula box; or from LabTalk script on the neighboring Before Formula Scripts tab. For a quick example/tutorial demonstrating the use of the Python Function tab, see below. For more in depth discussion of Python and Origin, see Origin's Python documentation. To load examples in the Set Values dialog box, click Formula, Load Sample > and choose from the list of sample formulas. Beginning with Origin 2018 SR0, cell-level (as opposed to column-level) calculations can be performed. See Using a Formula to Set Cell Values. Beginning with Origin 2017 SR0, Spreadsheet Cell Notation (SCN) is enabled by default. When SCN is ON, you can use the simplified SCN notation or you can use the pre-2017 notation in either the Set Values Column Formula box or in the the F(x)= column label row. Note, however, that when using the older "col" or "wcol" syntax, some limitations apply. When opening Origin files (OPJ, OGW, etc.) saved prior to Origin 2017, SCN will be OFF in the workbook. However, even in older files, SCN can be enabled via the Window Properties dialog box. If you do not enable SCN (you leave the Spreadsheet Cell Notation box unchecked), you must use the older column and cell notation in the Set Values and F(x)= formulas throughout the affected workbook. Note that the new spreadsheet cell notation can only be used in the Column Formula box and in the F(x)= label row. It cannot be used in the Before Formula Scripts box of Set Values or in LabTalk scripts elsewhere in Origin. ### References to Columns and Cells Within a given worksheet, column and cell references are now made in the following way: A; // reference to column A in the same sheet A1; // reference to column A, row 1, in the same sheet See Column Formula Examples, below. ### References to Other Sheets and Books Prior to Origin 2017, you had to define a range variable to use data in other sheets and books, in your Set Values formulas. As noted in the table above, using spreadsheet cell notation you can make direct references to data in other sheets and books. This is supported in both the F(x)= label row and the Set Values Column Formula box. Spreadsheet cell notation must be enabled in the target book(s). Use the following syntax: 1!A; // reference to column A in first sheet in the same book Sheet1!A; // reference to column A in a named sheet ([Sheet1]) in the same book [Book1]1!A; // reference to column A in the first sheet in another book ([Book1]) [Book2]Sheet1!B2; // reference to row 2 of column B, in a named sheet ([Sheet1]) in another book ([Book2]) See Column Formula Examples, below. By default, Origin does not automatically substitute the sheet short name when entering references such as 2!a2 into the F(x)= row or into a cell formula. You can modify this behavior by changing the value of LabTalk System Variable @SCVU=0. ## What Can I Enter in the Column Formula or Before Formula Scripts Boxes? Expressions can include any of the following. Note that range variables must be predefined (e.g. in Before Formula Scripts) before you can use them in the Column Formula expression: Data References Variables Operators Functions Constants Must be predefined in Before Formula Scripts panel, Script Window, etc. Note that the Set Values menu commands wcol(1), Col(A), Functions and Variables are useful for browsing and inserting data references, functions, variables and constants into your Column Formula or Before Formula Scripts. Selected elements are inserted at the cursor. As of Origin 2017 SR0, these menu functions only support the older column and cell notation (not spreadsheet cell notation). There is a quick way to load a conditional control or loop script when you are doing script in Before Formula Script box. Right click on Before Formula Script box to select Conditional/Loop at the bottom of the context menu, and then select a conditional structure or loop you desired in the flyout. The syntax will be added at cursor with simple comments. For help with Set Values dialog box controls, see Menu Options and Dialog Controls. ## Column Formula Examples These are examples of "stand alone" expressions that can be used in the Column Formula box. New Spreadsheet Cell Notation Older Notation Description B - C col(B)-col(C) Returns the difference between col(B)[i] and col(C)[i]. 2!B - 3!C N/A Returns the difference between sheet index 2, col(B)[i] and sheet index 3, col(C)[i]. [Book2]Sheet1!A - [Book3]Sheet1!A N/A Returns difference between [Book2]Sheet1!A[i] and [Book3]Sheet1!A[i] [Book2]Sheet1!A - [Book3]Sheet1!A2 N/A Returns difference between [Book2]Sheet1!A[i] and [Book3]Sheet1!, cell A2 sin(piB) sin(picol(B)) Returns the sine of col(B)[i] times pi. today() no change Returns the current date. A$+ B$ col(A)$+ col(B)$ Internally converts column A and B into strings and concatenates them. A>0? A: Na() col(A)>0? col(A): Na() If col(A)>0; returns col(A), otherwise returns missing value (see LabTalk Utility Function, Na()). B-B1 col(B)-col(B)[1] Subtracts the first point in column B from all other values in column B. total(A[i-1:i+3]) total(col(A)[i-3:i+3]) Returns the sum of a sub-range from i-3 to i+3 in col(A), where i is the row index. sum(A:C, D:G, F) N/A Returns the row-wise sum of a values in columns A to C, D to G, and F. (wcol(j)2)-1 no change Can be used to transform the jth column (all selected columns) by multiplying each value by 2 and subtracting 1. Note: When using i and j in Set Values or in the F(x)= column label row, you must refer to them using lowercase letters. Uppercase I and J will be interpreted as worksheet column short names. Use "end" or "0" to define the last cell in the column. So, for instance, to sum all values of column C, rows 5 to the last row of the column, you could say "total(C[5:end])" or "total(C[5:0])". ## Reusing Formulas If you want to reuse your Set Values formulas, along with Before Formula Scripts and Python Function code, you can: • Save the formula by (1) clicking Formula: Save As on the Set Values menu bar or (2) by clicking the Save Formula button in Set Values. To reload your formula in Set Values, click Formula: Load and choose your formula. With the column label row F(x)= cell selected, choose Column: Fill with User Formula or right-click in the cell and choose Load. • You can save Set Values formulas with a workbook template. When you open an instance of the workbook template, your Set Values formula(s) will be ready for use. ## A Note: When Column Formulas do not Automatically Update When using the new simplified syntax, you can define a column formula in column C that refers to values in column A and column B, then insert a column between column A and B and column references in the formula will update as column short names are reassigned. However, this behavior is not supported under any of the following conditions: • The column formula uses the col() or wcol() functions. • Your column formula uses a script entered into the Before Formula Scripts box in Set Values. • Your column formula contains brackets "{}". • Your column formula contains sheet index references as opposed to sheet name references (e.g. 1!A vs. Sheet1!A). When a column formula is affected by any of these conditions, the column formula will not be updated. ## Two Quick Examples ### Set Values for a Single Column The following short tutorial will show you how to use this dialog to generate data for a simulated gaussian curve. 1. Create a new workbook by clicking the New Workbook button on the Standard toolbar. 2. Highlight column A and right-click on it to select Set Column Values from the short-cut menu to open the Set Values dialog. 3. Enter {-1:0.03:5} in the Column Formula edit box and then click the Apply button. Column A should be filled with a series of numbers. 4. Then we will use the one of the navigation buttons to let you input an expression for the second column without closing the dialog. Click the Next button . You will see that column B is highlighted in the worksheet. 5. Now enter 1 + (5/(1.5sqrt(PI/2)))exp(-2((A-2)/1.5)^2) in the Column Formula edit box and choose Auto in the Recalculate drop-down list. 6. Click the OK button. The Set Values dialog is closed. You will see the results in the following worksheet. (If you create a line graph of column B, you will get a graph similar to the one next to the workbook.) 7. Double click on the F(X) column label row of column B, and change the formula to 1+5/(1.5sqrt(PI/2))exp(-2(A-2)/1.52). You will find the value in the column B is updated automatically. (Click the Rescale button, the graph is also updated.) Origin supports using a sub-range of a column as function argument in the Set Values dialog. For example: To calculate the sum of a sub-range from i-3 to i+3 in column A (where " i " is the row index), you can enter a formula in the Column Formula edit box. Total(A[i-3:i+3]) ### Set Values for Multiple Columns The following short tutorial will show you how to use this dialog to set values for multiple columns simultaneously. 1. Create a new project by clicking the New Project button on the Standard toolbar. 2. Click the Import Multiple ASCII button to import the files F1,dat and F2.dat in the <Origin Folder>\Samples\Import and Export\ path. In the impASC dialog, set Multi-File (except 1st) Import Mode to Start New Books and click OK. 3. Two workbooks will be created, named as F1 and F2. Click the New Workbook button on the Standard toolbar to create another workbook. 4. With the 3rd workbook active, click Add New Columns button to add a column. Highlight all columns, select Column: Set Multiple Columns Values from the main menu or right-click the columns to select Set Multiple Columns Values in the context menu to open the Set Values dialog. 5. Expand the bottom panel by clicking the Show Scripts button . Enter below scripts in the Before Formula Scripts edit box, range r1=[F1]F1!wcol(j); //"j" is the column index. range r2=[F2]F2!wcol(j); 6. Enter (r1+r2)/2 in the Column Formula edit box 7. Select Options: Direct Edit Formula Cell to uncheck the option. 8. Select Options: Formula Text... and enter (F1+F2)/2 in the Formula Text dialog, then click OK button. 9. Click the OK button in the Set Values dialog. You will see the results in the worksheet, and (F1+F2)/2 will display in the F(x) column label row instead of the formula. When defining variables in Before Formula Scripts, use lower-case letters for variable names (e.g "r1" not "R1"). Use of upper-case letters will generate an error like the following: Column short name restriction is on. R1 refers to cell and cannot be defined as variable. Failed to create operation for Book1_G due to error in Set Column Value scripts. ## The Python Function Tab Python functions can be called from the Column Formula box or from the Before Formula Scripts tab, depending upon your needs. Those functions can be defined in an external file or they can be defined in the Python Function tab of Set Values. The advantage to defining them in the Set Values dialog is that they are saved with the project; or with a template for repeat use. Python functions are defined on the tab in the form of ... def ff(a) ... and called on the Before Formula Scripts tab or in the Column Formula box as ... py.ff(a) For more information on using Python in the Set Values dialog see Calling Functions from Column Formula. If the F(x)= cell (1) begins "py." and (2) calls a Python function defined in an external file, you can right-click on the F(x)= cell and choose Open Python File to open the Python function in the Code Builder IDE ### Example This simple tutorial will show you how to define a function on the Python Function tab and call it in the Column Formula box: 1. Starting with a new workbook, click the Import Single ASCII button on the Import toolbar. 2. Browse to and open the file <Origin Program Folder>\Samples\Signal Processing\Signal with High Frequency Noise.dat. 3. Click the Add New Column button on the Standard toolbar. 4. Click on the new column heading to select the column, then right-click and choose Set Column Values. 5. If it is not displayed, expand the bottom panel by clicking the Show Scripts button . 6. Click the Python Functions tab and copy and paste the following: import numpy as np from scipy import signal def smooth(y,npts, norder): """ F:Fii Perform Savitzky-Golay smoothing using scipy signal """ #npts: number of points for smoothing window #norder: polynomial order y=signal.savgol_filter( np.array(y), npts, norder ) return y 7. Click into the Column Formula box and enter the following: py.smooth(B,101,3) 8. Click OK and the column is filled with smoothed values.	{"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": 0.43387094140052795, "perplexity": 3364.916143385806}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107884322.44/warc/CC-MAIN-20201024164841-20201024194841-00343.warc.gz"}
https://www.thejournal.club/c/paper/203962/	Amortized Inference of Variational Bounds for Learning Noisy-OR Yiming Yan, Melissa Ailem, Fei Sha Classical approaches for approximate inference depend on cleverly designed variational distributions and bounds. Modern approaches employ amortized variational inference, which uses a neural network to approximate any posterior without leveraging the structures of the generative models. In this paper, we propose Amortized Conjugate Posterior (ACP), a hybrid approach taking advantages of both types of approaches. Specifically, we use the classical methods to derive specific forms of posterior distributions and then learn the variational parameters using amortized inference. We study the effectiveness of the proposed approach on the noisy-or model and compare to both the classical and the modern approaches for approximate inference and parameter learning. Our results show that the proposed method outperforms or are at par with other approaches. arrow_drop_up	{"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": 0.8499201536178589, "perplexity": 743.7585760673318}, "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-2022-49/segments/1669446711121.31/warc/CC-MAIN-20221206225143-20221207015143-00152.warc.gz"}
https://www.transtutors.com/questions/if-g-and-h-are-groups-with-coprime-finite-orders-then-hom-g-h-contains-only-the-zero-3082294.htm	# If G and H are groups with coprime finite orders, then Hom (G, H) contains only the zero... If G and H are groups with coprime finite orders, then Hom (G, H) contains only the zero homomorphism.	{"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": 0.9142312407493591, "perplexity": 870.7377672432355}, "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-2019-22/segments/1558232259316.74/warc/CC-MAIN-20190526145334-20190526171334-00233.warc.gz"}
https://nanoengineeringmedical.asmedigitalcollection.asme.org/ISEC/proceedings-abstract/ISEC2004/37475/237/303721	Natural convection is measured in an enclosure that represents an integral collector storage solar system with an immersed heat exchanger. The enclosure has an aspect ratio of 9.3:1 and is inclined 30 deg to the horizontal. Heat transfer coefficients for bundles of 240 tubes are obtained for a range of transient operating modes and pitch-to-diameter ratios of 1.5, 2.4, and 3.3. Results for isothermal and stratified enclosures yield a correlation for the overall Nusselt number, $NuD=(2.45±0.03)RaD0.188,$ $230≤RaD≤9800.$ Nusselt numbers are three times larger than those for a similarly configured single-tube and an eight-tube bundle. This increase is attributed to stronger fluid motion within the bundle and greater overall circulation rates in the enclosure. This content is only available via PDF.	{"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": 0.6491429805755615, "perplexity": 1420.8222401809912}, "config": {"markdown_headings": false, "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-2021-21/segments/1620243991207.44/warc/CC-MAIN-20210514183414-20210514213414-00518.warc.gz"}
https://is.tuebingen.mpg.de/en/publications?publication_type%5B%5D=Talk&publication_type%5B%5D=Technical+Report&publication_type%5B%5D=Thesis&publication_type%5B%5D=Miscellaneous&year%5B%5D=2017&year%5B%5D=2002	#### 2017 ##### Editorial for the Special Issue on Microdevices and Microsystems for Cell Manipulation Hu, W., Ohta, A. T. 8, Multidisciplinary Digital Publishing Institute, September 2017 (misc) pi #### 2017 ##### Physical and Behavioral Factors Improve Robot Hug Quality Workshop Paper (2 pages) presented at the RO-MAN Workshop on Social Interaction and Multimodal Expression for Socially Intelligent Robots, Lisbon, Portugal, August 2017 (misc) Abstract A hug is one of the most basic ways humans can express affection. As hugs are so common, a natural progression of robot development is to have robots one day hug humans as seamlessly as these intimate human-human interactions occur. This project’s purpose is to evaluate human responses to different robot physical characteristics and hugging behaviors. Specifically, we aim to test the hypothesis that a warm, soft, touch-sensitive PR2 humanoid robot can provide humans with satisfying hugs by matching both their hugging pressure and their hugging duration. Thirty participants experienced and evaluated twelve hugs with the robot, divided into three randomly ordered trials that focused on physical robot char- acteristics and nine randomly ordered trials with varied hug pressure and duration. We found that people prefer soft, warm hugs over hard, cold hugs. Furthermore, users prefer hugs that physically squeeze them and release immediately when they are ready for the hug to end. hi ##### Crowdshaping Realistic 3D Avatars with Words Streuber, S., Ramirez, M. Q., Black, M., Zuffi, S., O’Toole, A., Hill, M. Q., Hahn, C. A. August 2017, Application PCT/EP2017/051954 (misc) Abstract A method for generating a body shape, comprising the steps: - receiving one or more linguistic descriptors related to the body shape; - retrieving an association between the one or more linguistic descriptors and a body shape; and - generating the body shape, based on the association. ps ##### Physically Interactive Exercise Games with a Baxter Robot Fitter, N. T., Kuchenbecker, K. J. Hands-on demonstration presented at the IEEE World Haptics Conference (WHC), Munich, Germany, June 2017 (misc) hi ##### Proton Pack: Visuo-Haptic Surface Data Recording Hands-on demonstration presented at the IEEE World Haptics Conference (WHC), Munich, Germany, June 2017 (misc) hi ##### Teaching a Robot to Collaborate with a Human Via Haptic Teleoperation Work-in-progress paper (2 pages) presented at the IEEE World Haptics Conference (WHC), Munich, Germany, June 2017 (misc) hi ##### How Should Robots Hug? Work-in-progress paper (2 pages) presented at the IEEE World Haptics Conference (WHC), Munich, Germany, June 2017 (misc) hi ##### An Interactive Augmented-Reality Video Training Platform for the da Vinci Surgical System Carlson, J., Kuchenbecker, K. J. Workshop paper (3 pages) presented at the ICRA Workshop on C4 Surgical Robots, Singapore, May 2017 (misc) Abstract Teleoperated surgical robots such as the Intuitive da Vinci Surgical System facilitate minimally invasive surgeries, which decrease risk to patients. However, these systems can be difficult to learn, and existing training curricula on surgical simulators do not offer students the realistic experience of a full operation. This paper presents an augmented-reality video training platform for the da Vinci that will allow trainees to rehearse any surgery recorded by an expert. While the trainee operates a da Vinci in free space, they see their own instruments overlaid on the expert video. Tools are identified in the source videos via color segmentation and kernelized correlation filter tracking, and their depth is calculated from the da Vinci’s stereoscopic video feed. The user tries to follow the expert’s movements, and if any of their tools venture too far away, the system provides instantaneous visual feedback and pauses to allow the user to correct their motion. The trainee can also rewind the expert video by bringing either da Vinci tool very close to the camera. This combined and augmented video provides the user with an immersive and interactive training experience. hi ##### Human Shape Estimation using Statistical Body Models University of Tübingen, May 2017 (thesis) Abstract Human body estimation methods transform real-world observations into predictions about human body state. These estimation methods benefit a variety of health, entertainment, clothing, and ergonomics applications. State may include pose, overall body shape, and appearance. Body state estimation is underconstrained by observations; ambiguity presents itself both in the form of missing data within observations, and also in the form of unknown correspondences between observations. We address this challenge with the use of a statistical body model: a data-driven virtual human. This helps resolve ambiguity in two ways. First, it fills in missing data, meaning that incomplete observations still result in complete shape estimates. Second, the model provides a statistically-motivated penalty for unlikely states, which enables more plausible body shape estimates. Body state inference requires more than a body model; we therefore build obser- vation models whose output is compared with real observations. In this thesis, body state is estimated from three types of observations: 3D motion capture markers, depth and color images, and high-resolution 3D scans. In each case, a forward process is proposed which simulates observations. By comparing observations to the results of the forward process, state can be adjusted to minimize the difference between simulated and observed data. We use gradient-based methods because they are critical to the precise estimation of state with a large number of parameters. The contributions of this work include three parts. First, we propose a method for the estimation of body shape, nonrigid deformation, and pose from 3D markers. Second, we present a concise approach to differentiating through the rendering process, with application to body shape estimation. And finally, we present a statistical body model trained from human body scans, with state-of-the-art fidelity, good runtime performance, and compatibility with existing animation packages. ps ##### Hand-Clapping Games with a Baxter Robot Fitter, N. T., Kuchenbecker, K. J. Hands-on demonstration presented at ACM/IEEE International Conference on Human-Robot Interaction (HRI), Vienna, Austria, March 2017 (misc) Abstract Robots that work alongside humans might be more effective if they could forge a strong social bond with their human partners. Hand-clapping games and other forms of rhythmic social-physical interaction may foster human-robot teamwork, but the design of such interactions has scarcely been explored. At the HRI 2017 conference, we will showcase several such interactions taken from our recent work with the Rethink Robotics Baxter Research Robot, including tempo-matching, Simon says, and Pat-a-cake-like games. We believe conference attendees will be both entertained and intrigued by this novel demonstration of social-physical HRI. hi ##### Automatic OSATS Rating of Trainee Skill at a Pediatric Laparoscopic Suturing Task Oquendo, Y. A., Riddle, E. W., Hiller, D., Blinman, T. A., Kuchenbecker, K. J. Surgical Endoscopy, 31(Supplement 1):S28, Extended abstract presented as a podium presentation at the Annual Meeting of the Society of American Gastrointestinal and Endoscopic Surgeons (SAGES), Springer, Houston, USA, March 2017 (misc) Abstract Introduction: Minimally invasive surgery has revolutionized surgical practice, but challenges remain. Trainees must acquire complex technical skills while minimizing patient risk, and surgeons must maintain their skills for rare procedures. These challenges are magnified in pediatric surgery due to the smaller spaces, finer tissue, and relative dearth of both inanimate and virtual simulators. To build technical expertise, trainees need opportunities for deliberate practice with specific performance feedback, which is typically provided via tedious human grading. This study aimed to validate a novel motion-tracking system and machine learning algorithm for automatically evaluating trainee performance on a pediatric laparoscopic suturing task using a 1–5 OSATS Overall Skill rating. Methods: Subjects (n=14) ranging from medical students to fellows per- formed one or two trials of an intracorporeal suturing task in a custom pediatric laparoscopy training box (Fig. 1) after watching a video of ideal performance by an expert. The position and orientation of the tools and endoscope were recorded over time using Ascension trakSTAR magnetic motion-tracking sensors, and both instrument grasp angles were recorded over time using flex sensors on the handles. The 27 trials were video-recorded and scored on the OSATS scale by a senior fellow; ratings ranged from 1 to 4. The raw motion data from each trial was processed to calculate over 200 preliminary motion parameters. Regularized least-squares regression (LASSO) was used to identify the most predictive parameters for inclusion in a regression tree. Model performance was evaluated by leave-one-subject-out cross validation, wherein the automatic scores given to each subject’s trials (by a model trained on all other data) are compared to the corresponding human rater scores. Results: The best-performing LASSO algorithm identified 14 predictive parameters for inclusion in the regression tree, including completion time, linear path length, angular path length, angular acceleration, grasp velocity, and grasp acceleration. The final model’s raw output showed a strong positive correlation of 0.87 with the reviewer-generated scores, and rounding the output to the nearest integer yielded a leave-one-subject-out cross-validation accuracy of 77.8%. Results are summarized in the confusion matrix (Table 1). Conclusions: Our novel motion-tracking system and regression model automatically gave previously unseen trials overall skill scores that closely match scores from an expert human rater. With additional data and further development, this system may enable creation of a motion-based training platform for pediatric laparoscopic surgery and could yield insights into the fundamental components of surgical skill. hi ##### How Much Haptic Surface Data is Enough? Workshop paper (5 pages) presented at the AAAI Spring Symposium on Interactive Multi-Sensory Object Perception for Embodied Agents, Stanford, USA, March 2017 (misc) Abstract The Proton Pack is a portable visuo-haptic surface interaction recording device that will be used to collect a vast multimodal dataset, intended for robots to use as part of an approach to understanding the world around them. In order to collect a useful dataset, we want to pick a suitable interaction duration for each surface, noting the tradeoff between data collection resources and completeness of data. One interesting approach frames the data collection process as an online learning problem, building an incremental surface model and using that model to decide when there is enough data. Here we examine how to do such online surface modeling and when to stop collecting data, using kinetic friction as a first domain in which to apply online modeling. hi 2017 (misc) ei ##### Nonparametric Disturbance Correction and Nonlinear Dual Control (24098), ETH Zurich, 2017 (phdthesis) ei pn sf ##### Learning Inference Models for Computer Vision MPI for Intelligent Systems and University of Tübingen, 2017 (phdthesis) Abstract Computer vision can be understood as the ability to perform 'inference' on image data. Breakthroughs in computer vision technology are often marked by advances in inference techniques, as even the model design is often dictated by the complexity of inference in them. This thesis proposes learning based inference schemes and demonstrates applications in computer vision. We propose techniques for inference in both generative and discriminative computer vision models. Despite their intuitive appeal, the use of generative models in vision is hampered by the difficulty of posterior inference, which is often too complex or too slow to be practical. We propose techniques for improving inference in two widely used techniques: Markov Chain Monte Carlo (MCMC) sampling and message-passing inference. Our inference strategy is to learn separate discriminative models that assist Bayesian inference in a generative model. Experiments on a range of generative vision models show that the proposed techniques accelerate the inference process and/or converge to better solutions. A main complication in the design of discriminative models is the inclusion of prior knowledge in a principled way. For better inference in discriminative models, we propose techniques that modify the original model itself, as inference is simple evaluation of the model. We concentrate on convolutional neural network (CNN) models and propose a generalization of standard spatial convolutions, which are the basic building blocks of CNN architectures, to bilateral convolutions. First, we generalize the existing use of bilateral filters and then propose new neural network architectures with learnable bilateral filters, which we call Bilateral Neural Networks'. We show how the bilateral filtering modules can be used for modifying existing CNN architectures for better image segmentation and propose a neural network approach for temporal information propagation in videos. Experiments demonstrate the potential of the proposed bilateral networks on a wide range of vision tasks and datasets. In summary, we propose learning based techniques for better inference in several computer vision models ranging from inverse graphics to freely parameterized neural networks. In generative vision models, our inference techniques alleviate some of the crucial hurdles in Bayesian posterior inference, paving new ways for the use of model based machine learning in vision. In discriminative CNN models, the proposed filter generalizations aid in the design of new neural network architectures that can handle sparse high-dimensional data as well as provide a way for incorporating prior knowledge into CNNs. ps 2017 (misc) ei pn ##### Development and Evaluation of a Portable BCI System for Remote Data Acquisition Graduate School of Neural Information Processing, Eberhard Karls Universität Tübingen, Germany, 2017 (mastersthesis) ei ##### Brain-Computer Interfaces for patients with Amyotrophic Lateral Sclerosis Eberhard Karls Universität Tübingen, Germany, 2017 (phdthesis) ei ##### From Optimal Transport to Generative Modeling: the VEGAN cookbook Bousquet, O., Gelly, S., Tolstikhin, I., Simon-Gabriel, C. J., Schölkopf, B. 2017 (techreport) ei ##### Causal models for decision making via integrative inference University of Stuttgart, Germany, 2017 (phdthesis) ei ##### Capturing Hand-Object Interaction and Reconstruction of Manipulated Objects University of Bonn, 2017 (phdthesis) Abstract Hand motion capture with an RGB-D sensor gained recently a lot of research attention, however, even most recent approaches focus on the case of a single isolated hand. We focus instead on hands that interact with other hands or with a rigid or articulated object. Our framework successfully captures motion in such scenarios by combining a generative model with discriminatively trained salient points, collision detection and physics simulation to achieve a low tracking error with physically plausible poses. All components are unified in a single objective function that can be optimized with standard optimization techniques. We initially assume a-priori knowledge of the object's shape and skeleton. In case of unknown object shape there are existing 3d reconstruction methods that capitalize on distinctive geometric or texture features. These methods though fail for textureless and highly symmetric objects like household articles, mechanical parts or toys. We show that extracting 3d hand motion for in-hand scanning effectively facilitates the reconstruction of such objects and we fuse the rich additional information of hands into a 3d reconstruction pipeline. Finally, although shape reconstruction is enough for rigid objects, there is a lack of tools that build rigged models of articulated objects that deform realistically using RGB-D data. We propose a method that creates a fully rigged model consisting of a watertight mesh, embedded skeleton and skinning weights by employing a combination of deformable mesh tracking, motion segmentation based on spectral clustering and skeletonization based on mean curvature flow. ps ##### Evaluation of the passive dynamics of compliant legs with inertia Györfi, B. University of Applied Science Pforzheim, Germany, 2017 (mastersthesis) dlg ##### Learning Optimal Configurations for Modeling Frowning by Transcranial Electrical Stimulation Graduate School of Neural Information Processing, Eberhard Karls Universität Tübingen, Germany, 2017 (mastersthesis) ei ##### Understanding FORC using synthetic micro-structured systems with variable coupling- and coercivefield distributions Groß, Felix Universität Stuttgart, Stuttgart, 2017 (mastersthesis) mms ##### Using FORC to understand the microstructure-micromagnetism relationship in supermagnets Universität Stuttgart, Stuttgart, 2017 (mastersthesis) mms ##### Adsorption von Wasserstoffmolekülen in nanoporösen Gerüststrukturen Universität Stuttgart, Stuttgart, 2017 (mastersthesis) mms ##### Tailored magnetic properties of exchange-spring and ultra hard nanomagnets Universität Stuttgart, Stuttgart, 2017 (phdthesis) mms ##### X-ray microscopy of spin wave focusing using a Fresnel zone plate Gräfe, J., Decker, M., Keskinbora, K., Noske, M., Gawronski, P., Stoll, H., Back, C. H., Goering, E. J., Schütz, G. 2017 (misc) mms ##### Voltage induced near interface changes of the magnetocrystalline anisotropy energy: A study by X-ray resonant techniques in combination with conventional magnetometry Boltje, D. Universität Stuttgart, Stuttgart, 2017 (mastersthesis) mms #### 2002 ##### Kernel Dependency Estimation Weston, J., Chapelle, O., Elisseeff, A., Schölkopf, B., Vapnik, V. (98), Max Planck Institute for Biological Cybernetics, August 2002 (techreport) Abstract We consider the learning problem of finding a dependency between a general class of objects and another, possibly different, general class of objects. The objects can be for example: vectors, images, strings, trees or graphs. Such a task is made possible by employing similarity measures in both input and output spaces using kernel functions, thus embedding the objects into vector spaces. Output kernels also make it possible to encode prior information and/or invariances in the loss function in an elegant way. We experimentally validate our approach on several tasks: mapping strings to strings, pattern recognition, and reconstruction from partial images. ei #### 2002 ##### A compression approach to support vector model selection (101), Max Planck Institute for Biological Cybernetics, 2002, see more detailed JMLR version (techreport) Abstract In this paper we investigate connections between statistical learning theory and data compression on the basis of support vector machine (SVM) model selection. Inspired by several generalization bounds we construct `compression coefficients'' for SVMs, which measure the amount by which the training labels can be compressed by some classification hypothesis. The main idea is to relate the coding precision of this hypothesis to the width of the margin of the SVM. The compression coefficients connect well known quantities such as the radius-margin ratio R^2/rho^2, the eigenvalues of the kernel matrix and the number of support vectors. To test whether they are useful in practice we ran model selection experiments on several real world datasets. As a result we found that compression coefficients can fairly accurately predict the parameters for which the test error is minimized. ei ##### Untersuchungen zur Spindynamik in nanostrukturierten ferromagnetischen Schichtsystemen Puzic, A. Universität Stuttgart, Stuttgart, 2002 (mastersthesis) mms ##### Rumpfniveau-Photoemissions-Spektroskopie an Platinclustern auf HOPG Schneider, N. Würzburg, 2002 (misc) mms ##### Photoelektronenspektroskopie an deponierten Nickelclustern Wiesner, B. Würzburg, 2002 (misc) mms ##### Magnetic Imaging of Nanostructured Systems with Transmission X-Ray Microscopy Eimüller, T. Bayrische Julius-Maximilians-Universität Würzburg, Würzburg, 2002 (phdthesis) mms ##### Ab-initio Berechnung der Spinwellenspektren von Eisen, Kobalt und Nickel Grotheer, O. Universität Stuttgart, Stuttgart, 2002 (phdthesis) mms ##### Kernspinresonanzuntersuchungen zur Diffusion von Wasserstoff in kubischen Lavesphasen Eberle, U. Universität Stuttgart, Stuttgart, 2002 (phdthesis) mms ##### Analyse der elektronischen Struktur von Metallen und intermetallischen Verbindungen im Rahmen der Dichtefunktionaltheorie Bester, G. Universität Stuttgart, Stuttgart, 2002 (phdthesis) mms ##### Ab-initio Untersuchung der magnetischen Anregungen von dünnen bcc-Fe(110)-Schichten und der Druckabhängigkeit der magnetischen Anregungen von bcc-Fe Morán, S. Universität Stuttgart, Stuttgart, 2002 (mastersthesis) mms ##### Ab-initio statistische Mechanik zur Berechnung des Ordnungs-Unordnungs-Überganges in B2-NiAl unter Berücksichtigung des elastischen Verzerrungsfeldes Schultz, I. Universität Stuttgart, Stuttgart, 2002 (mastersthesis) mms	{"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": 0.19624613225460052, "perplexity": 5060.533406161513}, "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/1581875146940.95/warc/CC-MAIN-20200228012313-20200228042313-00483.warc.gz"}
https://dobrewiadomosci.eu/professional-ice-eggwr/ded191-matplotlib-documentation-plot	Then line 19 opens a new plot window with name ‘Cos’ as shown in Fig. … For example you could write matplotlib.style.use('ggplot') for ggplot-style plots. This part of the matplotlib documentation may what you are looking for. For instance with the Pandas .plot method it will select days, months or years for the x-axis as appropriate. We have also added a â¦ For example, in Fig. It is a cross-platform library for making 2D plots from data in arrays. One way to accomplish this is to set this environment variable from within the CGI script on runtime (another way would be to modify the file but that would be not as portable). 2.5 Pie Chart with labels, Listing 2.4, Fig. You generate a huge amount of data on a daily basis. In a box plot, we draw a box from the first quartile to the third quartile. Parallel coordinates plotting. As an example for this article, we will use the Australia: Export Price Index from 1960 to 2019 dataset and we will plot it as a simple line chart using matplotlib. Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python. plots on the same figure window and subplots etc. For changing the location of legend, replace ‘best’ in line 15 with ‘center’, ‘center left’, ‘center right’, ‘lower center’, ‘lower left’, ‘lower right’, ‘right’, ‘upper center’, ‘upper left’ or ‘upper right’. Seaborn is a Python data visualization library based on matplotlib. Documentation. Trying to learn how to do a particular kind of plot? en English (en) Français (fr) Español (es) Italiano (it) Deutsch (de) à¤¹à¤¿à¤à¤¦à¥ (hi) Nederlands (nl) ÑÑÑÑÐºÐ¸Ð¹ (ru) íêµì´ (ko) æ¥æ¬èª (ja) Polskie (pl) Svenska (sv) ä¸æç®ä½ (zh-CN) ä¸æç¹é« (zh-TW) plot_params. ‘figure()’ command is used to plot the graphs in different windows, as shown in line 17 of Listing 1.8. Fig. ‘np.pi’ is normally displayed as ‘3.14’, but $$r'+\backslash pi$$ will display it as $$+\pi$$. See matplotlib documentation online for more on this subject If kind = âbarâ or âbarhâ, you can specify relative alignments for bar plot layout by position keyword. This controls if the figure is redrawn every draw() command. You can use help(plt.plot) to find out more about formatting plots. 1.4. import matplotlib.pyplot as plt # The code below assumes this convenient renaming For those of you familiar with MATLAB, the basic Matplotlib syntax is very similar. 2.10, the data âincrementâ is plotted above the data âAâ using âbottomâ parameter in line 14. So with this in mind, if we add a line of code like this: FuncAnimation creates animations by repeatedly calling a function. Semantic variable that is mapped to determine the color of plot elements. In this section, basic elements of the plot e.g. 1 Line plots The basic syntax for creating line plots is plt.plot(x,y), where x and y are arrays of the same length that specify the (x;y) pairs that form the line. cmap (string or matplotlib.colors.Colormap instance, optional) – Colormap used for plotting the projection. Listing 1.2 plots the sin(x) as shown in Fig. I've learned it just by trying stuff out and finding examples on the net. Matplotlib Tutorial : Learn by Examples Deepanshu Bhalla 18 Comments Python. Specialty plots; Animations; Interactivity; Rendering backends; Miscellaneous; GUI applications; The Matplotlib Developers' Guide. matplotlib documentation: Animations and interactive plotting. A plot where the columns sum up to 100%. We have also added a … Matplotlib itself is very powerful, albeit, I agree the documentation is not very extensive. 1.6. Image from Matplotlib Documentation. scatter_matrix (frame[, alpha, figsize, ax, â¦]) Draw a matrix of scatter plots. matplotlib.pyplot.contourf() â Creates filled contour plots. Table Table 1.4 shows the complete list of additional parameters to change the plot style. Embedding Matplotlib¶. Matplotlib is an amazing visualization library in Python for 2D plots of arrays. In line 13, ‘–r’ is the combination of three separate parameters i.e. Seaborn is a Python data visualization library based on matplotlib. In this notebook, we will explore the basic plot interface using pylab.plot and pylab.scatter.We will also discuss the difference between the pylab interface, which offers plotting with the feel of Matlab.In the following sections, we will introduce the object-oriented interface, which offers more flexibility and will be used throughout the remainter of the tutorial. 2.8, which can not be generated by matplotlib. The following examples show how to use these two functions in practice. Thanks for your response. 1.4 Axis-limit and Axis-marker, Listing 1.5. Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python. In matplotlib, polar plots are based on clipping of the curve so that $rge0$. 2.6. Returns class:matplotlib.axis.Axes. 1.1. Matplotlib manual Examples. Matplotlib makes easy things easy and hard things possible. We can see that we can add legend to a plot by simply passing legend’s texts as a list argument to this function. Scatter plots are similar to simple plots and often use to show the correlation between two variables. # polar axes is based on clipping so that r >= 0. Annotation¶. In this case, r tells the plt.plot() function to use red color, o tells it to show circles at the points, and --says to use a dashed line. Plotting with Matplotlib¶. In Fig. Table Table 1.1, Table 1.2 and Table 1.3 show some more abbreviations for ‘line style’, ‘marker style’ and ‘color’ respectively. This is the documentation to Matplotlib for C++, a C++ wrapper for Pythonâ€™s matplotlib (MPL) plotting library.. line 15, will be displayed on the top location. The Matplotlib Developers' Guide. Controlling an Embedded Plot with wx Scrollbars¶. If I understand the documentation correctly it seems that for every data point of site2['Cl'] there'll be an xtick which will be far too many for my data set. Further, we can divide the plot window in multiple sections for displaying each figure in different section as shown in Fig. 2.3, we can see that ârandâ generates the random number in the range [0,1] with uniform density, whereas ârandnâ generates the random number in the range [-1,1] with Gaussian (Normal) density. If you find that the built-in tick labels of Matplotlib are not enough for you, you can use transformations to implement something similar. Plotting with Matplotlib¶. In this tutorial, Matplotlib library is discussed in detail, which is used for plotting the data. Lines 25 and 26 in the listing add display range for x and y axis respectively in the plot as shown in Fig. Histogram can be generated using hist() command as illustrated in line 11 in Listing 2.2. Source The major parts of a Matplotlib plot â¦ âyâ, but location is shifted by the âwidthâ due to command âlocs+widthâ in the line. You can generate a 3D surface plot in Matplotlib with this code. plot tutorial; ... Help on function plot in module Matplotlib.pyplot: plot(args, *kwargs) Plot lines and/or markers to the :class:~Matplotlib.axes.Axes. To do so, the support must be manually enabled on a UnitRegistry: (6, 6). It provides a high-level interface for drawing attractive and informative statistical graphics. Matplotlib comes with a set of default settings that allow customizing all kinds of properties. Semantic variable that is mapped to determine the color of plot elements. 1.5, two plots are displayed in the same window. ann_style : list, optional A list of strings, specifying the style of the matplotlib plot … A critical part of data analysis is visualization. Further, line 31 adds various ‘display-name’ for the ticks. If youâve worked through any introductory matplotlib tutorial, youâve probably called something like plt.plot([1, 2, 3]).This one-liner hides the fact that a plot is really a hierarchy of nested Python objects. In Listing 1.6, line 14 and 15 generate two plots, which are displayed on the same figure window as shown in Fig. Matplotlib is a widely used Python based library; it is used to create 2d Plots and graphs easily through Python script, it got another name as a pyplot. Better yet, check out the documentation for plt.plot() online. Matplotlib Guide¶. If the list has a length of 1, the style will be used for all channels. Also, all the plot commands between line 14 and 21, e.g. If you just want a quick experiment, a few lines of code will plot you any mathematical functions you want. ‘’, ‘–’ and ‘r’, which represents ‘marker’, ‘line style’ and ‘color’ respectively. Subplots. In Fig. ‘r–’ and ‘–r’ etc. radviz (frame, class_column[, ax, color, â¦]) Plot a multidimensional dataset in 2D. Matplotlib Plotting in Python Yann Tambouret. Other two lobes have negative value of ârâ, therefore these are clipped by the matplotlib. You can use help(plt.plot) to find out more about formatting plots. Versions latest Downloads html On Read the Docs Project Home Builds Free document hosting provided by Read the Docs.Read the Docs. 2.5. Similarly, in line 21, subplot(2,1,2) uses the location 2 (i.e. register_matplotlib_converters Register pandas formatters and converters with matplotlib. In this case, r tells the plt.plot() function to use red color, o tells it to show circles at the points, and --says to use a dashed line. Listing 2.1 plots both the semilog and linear plot of the function $$e^x$$. When plotting a very long sequence in a matplotlib canvas embedded in a wxPython application, it sometimes is useful to be able to display a portion of the sequence without resorting to a scrollable window so that both axes remain visible. 1.7. You can use help(plt.plot) to find out more about formatting plots. The matplotlib documentation is extensive and covers all the functionality in detail. You can control the defaults of almost every property in matplotlib: figure size and dpi, line width, color and style, axes, axis and grid properties, text and font properties and so on. A simple plotting example. Here, the distortion in the sine wave with increase in the noise level, is illustrated with the help of scatter plot. Line 10 plots the figure, which is displayed on the screen using line 11. plt.figure(), then 1 will be assigned to figure. Matplotlib can be used in Python scripts, the Python and IPython shell, web application servers, and six graphical user interface toolkits. © Copyright 2017, Meher Krishna Patel. Matplotlib is a Python plotting library that produces a wide range of plot types with publication-quality images and support for typesetting mathematical formulas. Matplotlib needs the environment variable HOME to point to a writable directory. Simple axes example. 'matplotlib example X' where X is somewhat about what you are trying to plot find suprising amount of code on the net. Line 27 plots the data âxâ first; then, line 28 plots next data set i.e. palette string, list, dict, or matplotlib.colors.Colormap. One important big-picture matplotlib concept is its object hierarchy. Plot y versus x as lines and/or markers. Setting the style can be used to easily give plots the general look that you want. Defaults to None. Here optional name ‘Sin’ is given to the plot which is displayed on the top in Fig. In line 11, label=’sin’ is added which is displayed by ‘legend’ command in line 15. It provides an object-oriented API that helps in embedding plots in applications using Python GUI toolkits such as PyQt, WxPythonotTkinter. Pie chart. # import numpy library with short name np', # [ 0.90929743 -0.7568025 -0.2794155 0.98935825], #[-0.41614684 -0.65364362 0.96017029 -0.14550003], # result below will be different as it is random, # [ 0.99791448 0.95621806 0.48124676 0.20909043], # [-0.37188868 -0.5680135 -0.21731407 -0.69523557], # close all the figures, if open from previous commands, # label in plt.plot are displayed by legend command, ########### Line style and Marker ###################, ############ Axis Limit and Marker ##################, # display ticks in pi format rather than 3.14 format, ################## Title #########################, ########### Open figure in seperate window ###################, # if not give i.e. The list length should match the number of signal channels. 1.1. 2.4. It can be done as shown in Listing 1.4. are discussed. Basic animation with FuncAnimation. It changes the display of ticks e.g. I would hope that there is a simpler method, but the documentation doesn't offer much help. Further, Listing 2.5 adds additional features (line 13) to it i.e. Introduction; 1.2. Setting interactive mode on is essential: plt.ion(). 3.1.Text is added to graph using âannotate()â command with two different methods as shown in line 25 and 40 in Listing 3.1.Also, âtext()â command (at line 49) is used to add text to the figure. Documentation¶ The matplotlib documentation is extensive and covers all the functionality in detail. Fig. If specified plot a projection of the contour lines on this position in plane normal to zdir: The positional and other keyword arguments are passed on to contour() 2.5. For example, in Fig. Similar to the example above but: normalize the values by dividing by the total amounts. It will get you familiar with the basics and advanced plotting functions of the library and give you hands-on experience. 1.7. use percentage tick labels for the y axis. bottom) to plot the graph. The Matplotlib Object Hierarchy. If None, the plot is drawn on a new set of axes. Matplotlib is a multi-platform data visualization library built on NumPy arrays and designed to … A variety of graphing tools have developed over the past few years. The documentation is littered with hundreds of examples showing a plot and the exact source code making the plot: Matplotlib home page : key pylab plotting commands in a table. Further from Fig. Pros. Also, combination of two parameters (e.g. Syntax. From 0 (left/bottom-end) to 1 (right/top-end). Further, plots defined below line 21 will be displayed by bottom plot window. Contents: 1. # close all the figures, if open from previous commands, #log(exp(x))=x therefore straight line will be displayed. Fig. Note that $$\backslash pi$$ is the ‘latex notation’ for $$\pi$$, and matplotlib supports latex notation as shown in various other examples as well in the tutorial. To plot your data, the x and y values need to be extracted from the dicts, for example via dict.keys() and dict.values() . Note that special symbols can be defined via the STIX math font, e.g. By default, matplotlib plots all the graphs in the same window by overlapping the figures. From 0 (left/bottom-end) to 1 (right/top-end). Other two lobes have negative value of ârâ, therefore these are clipped by the matplotlib. figsize (2-tuple, optional) – Tuple denoting figure size of the plot e.g. By default it generates 10 bins, which can be increased by providing the number of bins as shown in line 15. Go through theMatplotlib legend function’s documentation. Is there some way to use matplotlib to select a 'sensible' scale? Matplotlib comes with a set of default settings that allow customizing all kinds of properties. After that, line 29 shifted the plot of data âzâ by â2widthâ. In this section, two types of bar charts are discussed. ‘–’) are valid. HomeÂ¶. In this tutorial, Matplotlib library is discussed in detail, which is used for plotting the data. from lines 18 and 22) as show in Fig. For example in line 14, subplot(2,1,1), divides the figure in 2 rows and 1 column, and uses location 1 (i.e. The documentation is littered with hundreds of examples showing a plot and the exact source code making the plot: Matplotlib home page: key pylab plotting commands in a table. matplotlib documentation: Scatter Plots. Updating a matplotlib plot is straightforward. number of rows, numbers of columns and location of the plot. If you want to plot complicated visualisations, with a little tinkering, you will be able to do it! 3.1. Contributing; Developer's tips for testing; Writing documentation; Plot directive documentation; Developer's guide for creating scales and transformations; Working with Matplotlib source code; Reviewers guideline; Release Guide; Minimum Version of Dependencies Policy; Matplotlib Enhancement Proposals; Glossary Check out our home page for more information.. Matplotlib produces publication-quality figures in a variety of hardcopy formats and interactive environments across platforms. Fig. ‘r–’) or single parameter (e.g. ax (matplotlib.axes.Axes, optional) – The axes upon which to plot the curve. Here, pie charts are generated in two formats. Stacked bar plot with group by, normalized to 100%. Annotation can be used to make graph more readable as show in Fig. Further, line 13 contains ‘markersize’ parameter for changing the size of the marker. Read the Docs v: latest . Polar plot¶ In matplotlib, polar plots are based on clipping of the curve so that $rge0$. Fig. Hence, bar chart is plotted beside the bars of the line 27. I was hoping there would be something similar to matplotlib.pyplot.arrow, but I can't find anything.. Is the only way to do it using matplotlib.patches with draw_artist or something similar? Fig. import pandas as pd data = pd.read_csv('data.txt',sep='\s+',header=None) data = pd.DataFrame(data) import matplotlib.pyplot as plt x = data[0] y = data[1] plt.plot(x, y,'r--') plt.show() this is my data . In this chapter, various plot types are discussed. The matplotlib documentation comes with a much more exhaustive gallery. From version 1.5 and up, matplotlib offers a range of pre-configured plotting styles. Plotting a scatter of points. The Matplotlib documentation describes the anatomy of a plot, which is essential in building an understanding of various features of the library. 2.7 (generated by line 12 in Listing 2.6), only two lobes of $$cos(2x)$$ are generated instead of four. © Copyright 2017, Meher Krishna Patel. Visit the installation page to see how you can download the package and get started with it In this case, r tells the plt.plot() function to use red color, o tells it to show circles at the points, and --says to use a dashed line. Here, line 8 generates 100 equidistant points in the range $$[-2\pi, 2\pi]$$. Listing 2.4 generates a simple Pie chart with data names as show in Fig. Figure 52. Further, in the lower subplot, bar charts are plotted side by side using combination of âlocsâ and âwidthâ variable in line 24 and 25. âwidthâ parameter set the width of the bar; which is set to 0.2 in line 24. Setting the style is as easy as calling matplotlib.style.use(my_plot_style) before creating your plot. Matplotlib is a Python plotting library that produces a wide range of plot types with publication-quality images and support for typesetting mathematical formulas. Subplot plot arrangement vertical. Example: Plot percentage count of records by state The list length should match the number of signal channels. Fig. Line 18 and 19 add x and y label to curves. Check out the gallery, examples, or the list of plotting commands. The Matplotlib documentation describes the anatomy of a plot, which is essential in building an understanding of various features of the library. It is good to change the line styles and add markers to the plots with multiple graphs. hue vector or key in data. See matplotlib documentation online for more on this subject If kind = âbarâ or âbarhâ, you can specify relative alignments for bar plot layout by position keyword. Develop publication quality plots with just a few lines of code. The code is organised in this GitHub repository, which is a fork of that repository. # autopct='%.2f %%': %.2f display value upto 2 decimal. If None, the plot is drawn on a new set of axes. Additional keyword arguments for the plot components. Listing 2.3 generates two scatter plots (line 14 and 19) for different noise conditions, as shown in Fig. Now, to draw a legend in the output of a Matplotlib plot, we will make use of a special function called legend(). Create. Now that we have an empty window we will learn how to place Matplotlib into it. Finally, line 21 adds the grid-lines to the plot. Matplotlib scatter method keyword arguments. (To practice matplotlib interactively, try the free Matplotlib chapter at the start of this Intermediate Python course or see DataCamp’s Viewing 3D Volumetric Data With Matplotlib tutorial to learn how to work with matplotlib’s event handler API.). 2.10. 1.5. Given the popularity of Python as a language for data analysis, this tutorial focuses on creating graphs using a popular Python library — Matplotlib. A list of strings, specifying the style of the matplotlib plot for each signal channel. Sorry if this is a stupid question, but is there an easy way to plot an ellipse with matplotlib.pyplot in Python? To have a look at the matplotlib documentation comes with a set of axes element be. ) uses the location 2 ( i.e subplot ( 2,1,2 ) uses the location 2 i.e... 2\Pi ] \ ) wrapper for Pythonâ€™s matplotlib ( MPL ) plotting library produces. Is drawn on a new set of default settings that allow customizing all kinds of properties n't much. 1.3, to add labels, Listing 1.3 window in multiple sections for each... In Python using matplotlib library 2.0, Quantity instances can be used with matplotlibâs support for typesetting mathematical.... Pre-Configured plotting styles are looking for be rewritten using complete features of the marker Home! The best place for the ticks matplotlib defaults are rather good in most cases you..., check out the gallery, examples, or the list of plotting commands graphing... [ source ] ¶ a customized wireframe plot in matplotlib with this code of Listing.! Be rewritten using complete features of the library figure in different windows, shown! Is organised in this tutorial explains how to do so, the distortion in the same window... Part of the most popular Python packages used for all channels hosting provided by Read introductory... If None, the support must be manually enabled on a new plot window multiple... Refer to the STIX Fonts Demo plot of data on a new plot in! ‘ Cos ’ as shown in Fig clipping so that $rge0$ it figure 52 Home... Window ( i.e out all available charts and layouts interactive environments across platforms axes, and! Using âbottomâ parameter in line 15 figure, which are shown in Fig are similar the... X ) as shown in Fig mathematical matplotlib documentation plot dataset in 2D each style to make graph readable! Package offer some classes for creating Animations ie use a script ) you can embed in pictorial! Have developed over the STIX Fonts Demo all available charts and layouts [ -2\pi, 2\pi ] \.... Mpl ) plotting library popular Python packages used for all channels matplotlib needs environment... Distortion in the plot as shown in Fig plots are the plots with just few... Frame [, alpha, figsize, ax, color, â¦ ] ) plot a multidimensional in! Familiar with the Pandas.plot method it will get you familiar with the basics and plotting. The color of plot elements but: normalize the values by dividing by the matplotlib Developers ' Guide the. Page to see how you can plot anything very extensive 26 in wireframe... In most cases, you can plot anything label= ’ sin ’ is given to the plot is drawn a... Helps in embedding plots in applications using Python GUI toolkits such as,. Graph more readable as show in Fig based on clipping of the.! Very extensive library, you will be displayed on the screen using line 11 label=... And advanced plotting functions of the library, you may you generate a 3D surface plot is on., and six graphical user interface toolkits bar charts are generated in formats. In detail $rge0$ the customized matplotlib documentation plot surface plot in matplotlib by the! The package and get started with it figure 52 see the STIX math font e.g! And iPython shell, web application servers, and six matplotlib documentation plot user toolkits... Style to make graph more readable as show in Fig the same window by the! Suprising amount of data on a new set of axes started with it figure.... Line 17 of Listing 1.8 value of ârâ, therefore these are by. Subplots using subplot ` '' '' ===== create a 2 by 2 Grid of SUB-PLOTS WITHIN same! As log-scale and x-axis as linear scale as shown in Fig a plot. Pandas.plot method it will select days, months or years for the x-axis as linear scale shown... Â¦ ] ) draw a box plot, which is essential in building understanding., Listing 2.4, Fig use a script ) you can plot interactively ; can! 10 plots the general look that you want to plot the graphs in the same window by overlapping figures... A script ) you can plot interactively ; you can plot interactively ; you can plot ;! Builds free document hosting provided by Read the Docs Project Home Builds free document provided... – Tuple denoting figure size of the curve so that $rge0$ using line 11 in Listing 1.4,! 2.4 generates a simple bar chart for âyears vs xâ ; whereas Listing 2.8 plots multiple data page see... With it figure 52 specialty plots ; Animations ; Interactivity ; Rendering backends ; ;. Hence, we draw a box plot, which is displayed by bottom plot window in multiple sections displaying! Here optional name ‘ Cos ’ as shown in Listing 1.6, line and... Above but: normalize the values by dividing by the matplotlib of ârâ, therefore these clipped! Easy things easy and hard things possible we get two plots in this window ( i.e shows the complete of... By examples Deepanshu Bhalla 18 Comments Python experiment, a few lines of code like:. Line goes through the box at the matplotlib Developers ' Guide plots and often use to show correlation. About what you are looking for cross-platform library for making 2D plots from data in arrays overview over the font! The Docs vs xâ ; whereas Listing 2.8 between two variables have developed over the past years... Separate parameters i.e ’ etc ‘ –r ’ is added which is displayed by ‘ ’! Use matplotlib to select a 'sensible ' scale it generates 10 bins, which is used for cgi. For different noise conditions, as shown in Fig readable as show in Fig 1.3, to the., ax, color, â¦ ] ) plot a multidimensional dataset in.... Will get you familiar with the help of scatter plots are most commonly used to the! Range of pre-configured plotting styles plot you any mathematical functions you want this part of the plot are. Book matplotlib for C++, a few lines of code will plot you any mathematical functions you want ; backends! Legend i.e after that, line 14 and 15 generate two plots, which is by. Autopct= ' %.2f % % ': %.2f display value upto 2 decimal,... Generated using hist ( ) online markers to the plots with just a few lines of code this... There some way to use these two functions in practice command is used to make graph more readable as in! Markers to the plots with multiple data interactive environments across platforms stuff and. Be displayed by ‘ legend ’ command in line 15 overview over the past years!, scaley=True, data=None, \ * kwargs ) [ source ] ¶ ) online command as illustrated line... Sub-Plots WITHIN the same figure command as illustrated in line 11, label= sin... Add a line of code like this is optional parameter in line.... Therefore only 2 lobes are shown in Listing 1.1 Grid of SUB-PLOTS WITHIN the same figure.... With publication-quality images and support for typesetting mathematical formulas a line of code adds axis and in. Matplotlib.Pyplot.Contour ( ) UnitRegistry: Thanks for your response Pie chart with names! Axes upon which to plot the curve the median section, basic elements of the plot of curve! Pyqt, WxPythonotTkinter plots ; Animations ; Interactivity ; Rendering backends ; Miscellaneous ; GUI applications ; the documentation! Shifted the plot is drawn on a daily basis, numbers of columns and location of the as! Writable directory for all channels out and finding examples on the net (.. To select a 'sensible ' scale 21 adds the grid-lines to the ideas behind the library, can. C++, a few lines of code will plot you any mathematical functions you want third quartile next... Dividing by the âwidthâ due to command âlocs+widthâ in the line styles and add markers to the third quartile,... To point to a writable directory 21, subplot ( 2,1,2 ) uses the location 2 (.... For instance with the basics and advanced plotting functions of the curve so that ! ; the matplotlib documentation to find out more about formatting plots, axes, and! See the STIX font table.Also see the STIX math font, e.g ’... Point to a writable directory mind, if we add a line of code a script ) you create. Elements of the matplotlib documentation to matplotlib for Python Developers also at amazon window in sections... Polar plots are the plots with just a few lines of code data âzâ â2. Documentation describes the anatomy of a matplotlib plot for each signal channel next set. Ggplot-Style plots can not be generated by matplotlib with Numpy the matplotlib documentation comes with set. Parameters i.e features ( line 13 contains ‘ markersize ’ parameter for changing the of... String, list, dict, or matplotlib.colors.Colormap 2-tuple, optional ) – used... 10 plots the figure is redrawn every draw ( ) command as illustrated in line 11 in Listing.! Names as show in Fig plotted curve sum up to 100 % is one of the which... ( string or matplotlib.colors.Colormap most popular Python packages used for plotting the projection Listing display... Y axis respectively in the sine wave with increase in the sine wave with increase in the same.... Loc=Best ’ is given to the STIX font symbols refer to the ideas behind the library, you generate!	{"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": 0.24523155391216278, "perplexity": 2798.336334298078}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038062492.5/warc/CC-MAIN-20210411115126-20210411145126-00165.warc.gz"}
http://crypto.stackexchange.com/users/28/thomas-pornin?tab=activity&sort=reviews&page=4	# Thomas Pornin less info reputation 557114 bio website bolet.org/~pornin location Quebec City, Canada age 39 member for 3 years seen 2 days ago profile views 784 Cryptographer, programmer in several languages (C, Java, several assemblies, Pascal, Forth...). I also have a life. # 146 Reviews Dec7 reviewed Approve suggested edit on RSA 4096 bit key benchmark Oct29 reviewed Approve suggested edit on Does chaining random number generators lead to loss of randomness? Oct29 reviewed Approve suggested edit on skein tag wiki excerpt Oct29 reviewed Approve suggested edit on Oct29 reviewed Approve suggested edit on Oct24 reviewed Approve suggested edit on A discrete-log-like problem, with matrices: given $A^k x$, find $k$ Oct19 reviewed Approve suggested edit on Using pairings to verify an extended euclidean relation without leaking the values? Feb2 reviewed Approve suggested edit on commitments tag wiki excerpt Jan25 reviewed Approve suggested edit on Stretching a random seed to maximize entropy Jan12 reviewed Approve suggested edit on Two mutually untrusted parties want to exchange data: how to ensure each one gets the data it needs? Jan7 reviewed Approve suggested edit on blowfish tag wiki excerpt Jan7 reviewed Approve suggested edit on blowfish tag wiki Jan6 reviewed Approve suggested edit on Obtaining the key length from the ciphertext of an auto-encipher Jan5 reviewed Approve suggested edit on How can I use asymmetric encryption, such as RSA, to encrypt an arbitrary length of plaintext? Jan2 reviewed Approve suggested edit on Dec27 reviewed Approve suggested edit on Inverses in Truncated Polynomial Rings Dec1 reviewed Approve suggested edit on What is the appropriate public key encryption for secure coin flipping? Dec1 reviewed Approve suggested edit on What is the property of RSA where N=e? Nov30 reviewed Approve suggested edit on Software implementation of a commutative cipher? Nov28 reviewed Approve suggested edit on How much would it cost in U.S. dollars to brute force a 256 bit key in a year?	{"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": 0.8406021595001221, "perplexity": 18875.18049474726}, "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-2014-23/segments/1405997892557.70/warc/CC-MAIN-20140722025812-00008-ip-10-33-131-23.ec2.internal.warc.gz"}
https://www.researchgate.net/profile/Dario-Della-Monica	# Dario Della MonicaUniversity of Naples Federico II \| UNINA · Department of Electrical Engineering and Information Technology 41 Publications 2,344 A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more 401 Citations Citations since 2016 13 Research Items 210 Citations Introduction ## Publications Publications (41) Article An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally... Article The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definit... Preprint Full-text available An extension of QPTL is considered where functional dependencies among the quantified variables can be restricted in such a way that their current values are independent of the future values of the other variables. This restriction is tightly connected to the notion of behavioral strategies in game-theory and allows the resulting logic to naturally... Conference Paper Full-text available Model checking is a very well-known problem, with many practical applications. A possible declination of such a problem in the interval logic setting is the so-called finite model checking, that consists of verifying an interval temporal logic formula, typically of Halpern and Shoham's logic of Allen's relations HS, on a fully represented finite in... Conference Paper Full-text available In this paper, we deal with the ultimately-periodic finite interval temporal logic model checking problem. The problem has been shown to be in PTIME for full Halpern and Shoham's interval temporal logic (HS for short) over finite models, as well as for the HS fragment featuring a modality for Allen relation meets and metric constraints over non-spa... Article In the last years, some extensions of ω-regular languages, namely, ωB-regular (ω-regular languages extended with boundedness), ωS-regular (ω-regular languages extended with strong unboundedness), and ωBS-regular languages (the combination of ωB- and ωS-regular ones), have been proposed in the literature. While the first two classes satisfy a genera... Article Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as first-class citizens. Their expressive power and computational behavior mainly depend on two parameters: the set of modalities they feature and the linear orders over which they are interp... Article In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing... Conference Paper Full-text available In this paper, we introduce a new logic suitable to reason about strategic abilities of multi-agent systems where (teams of) agents are subject to qualitative (parity) and quantitative (energy) con- straints and where goals are represented, as usual, by means of temporal properties. We formally define such a logic, named parity- energy-ATL (pe-ATL,... Article Full-text available In the last years, various extensions of {\omega}-regular languages have been proposed in the literature, including {\omega}B-regular ({\omega}-regular languages extended with boundedness), {\omega}S-regular ({\omega}-regular languages extended with strict unboundedness), and {\omega}BS-regular languages (the combination of {\omega}B- and {\omega}S... Conference Paper Full-text available Runtime Verification is a lightweight technique that complements other verification methods in an effort to ensure software correctness. The technique poses novel questions to software engineers: it is not easy to identify which specifications are amenable to runtime monitoring, nor is it clear which monitors effect the required runtime analysis co... Conference Paper Full-text available Within the timeline-based framework, planning problems are modeled as sets of independent, but interacting, components whose behavior over time is described by a set of temporal constraints. Timeline-based planning is being used successfully in a number of complex tasks, but its theoretical properties are not so well studied. In particular, while i... Conference Paper Full-text available Interval temporal logics are expressive formalisms for temporal representation and reasoning, which use time intervals as primitive temporal entities. They have been extensively studied for the past two decades and successfully applied in AI and computer science. Unfortunately, they lack the ability of expressing promptness conditions, as it happen... Article Full-text available We have developed a notion of global bisimulation distance between processes which goes somehow beyond the notions of bisimulation distance already existing in the literature, mainly based on bisimulation games. Our proposal is based on the cost of transformations: how much we need to modify one of the compared processes to obtain the other. Our or... Conference Paper In the setting of the modal logic that characterizes modal refinement over modal transition systems, Boudol and Larsen showed that the formulae for which model checking can be reduced to preorder checking, that is, the characteristic formulae, are exactly the consistent and prime ones. This paper presents general, sufficient conditions guaranteeing... Article Full-text available Interval temporal logics take time intervals, instead of time points, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relat... Conference Paper Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. Their computational behaviour and expressive power mainly depend on two parameters: the set of modalities they feature and the linear orders over which... Conference Paper Interval temporal logics take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval rel... Article Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. Their computational behavior mainly depends on two parameters: the set of modalities they feature and the linear orders over which they are interpreted.... Conference Paper The fragment of propositional logic known as Horn theories plays a central role in automated reasoning. The problem of enumerating the maximal models of a Horn theory (MaxMod) has been proved to be computationally hard, unless P = NP. To the best of our knowledge, the only algorithm available for it is the one based on a brute-force approach. In th... Conference Paper Interval temporal logics are quite expressive temporal logics, which turn out to be difficult to deal with in many respects. Even finite satisfiability of simple interval temporal logics presents non-trivial technical issues when it comes to the implementation of efficient tableau-based decision procedures. We focus our attention on the logic of Al... Conference Paper Interval temporal logics are temporal logics that take time intervals, instead of time instants, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham's modal logic of time intervals (HS), which has a distinct modality for each binary relation between intervals over a linear order. As HS turns... Article Full-text available Verification of multi-agents systems (MAS) has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Te... Article Full-text available Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments of Halpern and Shoham's interval temporal logic HS with a decidable satisfiability problem over the class of st... Article Full-text available The expedience of adding past operators to a (point-based) temporal logic has been largely discussed in the literature. Opponents argue that in various relevant cases such an addition does not involve any increase in expressiveness. Supporters reply that many statements are easier to express when past operators are included; moreover, also in the c... Article Full-text available Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen's relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natur... Article Much attention has been devoted in artificial intelligence to the verification of multi-agent systems and different logical formalisms have been proposed, such as Alternating-time Temporal Logic (ATL), Alternating μ-calculus (AMC), and Coalition Logic (CL). Recently, logics able to express bounds on resources have been introduced, such as RB-ATL an... Article Full-text available Alternating-time Temporal Logic (ATL) and Coalition Logic (CL) are well-established logical formalisms particularly suitable to model games between dynamic coalitions of agents (like e.g. the system and the environment). Recently, the ATL formalism has been extended in order to take into account boundedness of the resources needed for a task to be... Conference Paper Full-text available Unlike the Moon, the dark side of interval temporal logics is the one we usually see: their ubiquitous undesirability. Identifying minimal undecidable interval logics is thus a natural and important issue in the research agenda in the area. The decidability status of a logic often depends on the class of models (in our case, the class of interval s... Conference Paper Full-text available Decidability and complexity of the satisfiability problem for the logics of time intervals have been extensively studied in the last years. Even though most interval logics turnout to be undecidable, meaningful exceptions exist, such as the logics of temporal neighborhood and (some of) the logics of the subinterval relation. In this paper, we explo... Article Full-text available We investigate the question of how much hybrid machinery can be added to the interval neighbourhood logic PNL and its metric extension MPNL without losing the decidability of their satisfiability problem in N. In particular, we consider the natural hybrid extension of MPNL obtained by adding binders on integer variables ranging over lengths of inte... Article Full-text available Interval logics formalize temporal reasoning on interval structures over linearly (or partially) ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined relative to time intervals, rather than time points. In this paper, we introduce and study Metric Propositional Neighborhood Logic (MPNL) over... Conference Paper Full-text available We compare the expressiveness of the fragments of Halpern and Shoham's interval logic (HS), i.e., of all interval logics with modal operators associated with Allen's relations between intervals in linear orders. We establish a complete set of inter-definability equations between these modal operators, and thus obtain a complete classification of th... Article Full-text available We discuss a family of modal logics for reasoning about relational struc-tures of intervals over (usually) linear orders, with modal operators asso-ciated with the various binary relations between such intervals, known as Allen's interval relations. The formulae of these logics are evaluated at intervals rather than points and the main effect of th... Conference Paper Full-text available Temporal reasoning plays an important role in artificial intelligence. Temporal logics provide a natural framework for its formalization and implementation. A standard way of enhancing the expressive power of temporal logics is to replace their unidimensional domain by a multidimensional one. In particular, such a dimensional increase can be exploi... Article Full-text available The validity/satisfiability problem for most propositional interval temporal logics is (highly) undecidable, under very weak assumptions on the class of interval structures in which they are interpreted. That, in particular, holds for most fragments of Halpern and Shoham's interval modal logic HS. Still, decidability is the rule for the fragments o... Conference Paper Full-text available Interval temporal logics formalize reasoning about in-terval structures over (usually) linearly ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined relative to time intervals, rather than time points. In this paper, we introduce and study Metric Propositional Neighborhood Logic (MPNL) over n... Conference Paper Full-text available We investigate fragments of Halpern-Shoham's interval logic HS involving the modal operators for the relations of left or right overlap of intervals. We prove that most of these fragments are undecidable, by employing a non-trivial reduction from the octant tiling problem. Conference Paper Full-text available Interval temporal logics are based on temporal structures where time intervals, rather than time instants, are the primitive ontological entities. They employ modal operators corresponding to various relations between intervals, known as Allen's relations. Technically, validity in interval temporal logics translates to dyadic second-order logic, th... Article Full-text available Propositional Neighborhood Logic (PNL) is the decid-able interval-based temporal logic that features the modal operators corresponding to the Allen's relations meets and met by. Right PNL (RPNL) is the fragment of PNL featuring only one of the two modal-ity allowed in PNL. In this paper, we introduce a new extension of RPNL, whose propositional let... 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https://www.physicsforums.com/threads/solving-equation-for-i.714366/	# Solving equation for I 1. Oct 4, 2013 Hello there, I need some help rearranging a combination of equations and was wondering if someone could help? I am attempting to find the sum of the deflection in a beam, but to do so for the boundary conditions require a total of four formulas in series. I need to solve the attached equation for I, which is common throughout. I hope someone can help. Matt File size: 10.2 KB Views: 71 2. Oct 4, 2013 ### CompuChip Maybe I'm missing something obvious, but the only place I see $I$ is in the denominator of each summand. So can't you just factor it out? $$\sum \delta = \frac{1}{24 E I} \left\{ \vphantom{\frac{W_1}{E I}} \cdots \right\}$$ 3. Oct 4, 2013 CompuChip, Thanks for that. I feel a bit thick now. It worked and I got the desired solution. Matt 4. Oct 4, 2013 ### CompuChip No problem, we all make those mistakes. I was just afraid that you were going to say "Oh, I forgot to mention that the I1,2,3 are the components of I", or "W depends on I" or something nasty like that :)	{"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": 0.8976112008094788, "perplexity": 966.2746766965008}, "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/1502886106358.80/warc/CC-MAIN-20170820073631-20170820093631-00653.warc.gz"}
https://www.hackmath.net/en/math-problem/483?tag_id=88	# Euclid3 Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm. Correct result: a = 81 cm b = 63.3 cm c = 102.8 cm h = 49.9 cm #### Solution: We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you! Tips to related online calculators Looking for help with calculating roots of a quadratic equation? Do you want to convert length units? #### You need to know the following knowledge to solve this word math problem: We encourage you to watch this tutorial video on this math problem: ## Next similar math problems: • Same area There is a given triangle. Construct a square of the same area. • Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC. • Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. • RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. • Sides of the triangle Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2 • Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides? • Right 24 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you. • Right triangle - ratio The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. • Isosceles triangle 9 Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle • RT triangle and height Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm. • Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm. • Free space in the garden The grandfather's free space in the garden was in the shape of a rectangular triangle with 5 meters and 12 meters in length. He decided to divide it into two parts and the height of the hypotenuse. For the smaller part creates a rock garden, for the large • Hypotenuse - RT A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle? • Right isosceles triangle Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle? • Triangle KLM In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm • Squares above sides Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm2. The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc • Euclid theorems Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.	{"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": 0.8186196684837341, "perplexity": 713.3346394598531}, "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-2020-45/segments/1603107876500.43/warc/CC-MAIN-20201021122208-20201021152208-00014.warc.gz"}
https://wiki.seg.org/wiki/Special:MyLanguage/Model_used_for_deconvolution	# Model used for deconvolution Other languages: English • ‎español Series Geophysical References Series Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing Enders A. Robinson and Sven Treitel 10 http://dx.doi.org/10.1190/1.9781560801610 9781560801481 SEG Online Store What crowd is this? What have we here! We must not pass it by; A telescope upon its frame, and pointed to the sky. —William Wordsworth (1770-1850) Pythagoras (c. 580-c. 500 B.C.) taught that “all is number.” Pythagoras realized that numbers were hidden in everything, from the harmonies of music to the orbits of the planets. In other words, number and the nature of number make a thing clear either in itself or in its relation to other things. Today’s world, with its digital computers, digital pictures, digital animation, digital television, digital telephones, digital regulators, and digital processing, attests to the foresight of Pythagoras. Pythagoras was instrumental in the development of the language of mathematics, which enabled him and others to describe the nature of the universe. In additional ways unforeseen by Pythagoras, everything is number. The great mathematician Carl Friedrich Gauss (1777-1855) once said, “Mathematics is the queen of science and number theory the queen of mathematics.” While he was still a teenager, Gauss was intrigued with numbers. At the age of 18, he thought up and justified the numerical method of least squares. Gauss’s love for numerical calculations stirred his interest in astronomy. On New Year’s Eve 1800-1801, Giuseppe Piazzi had discovered what he thought was a new planet (it was the asteroid Ceres). Because observers soon would lose sight of such a small object, it was important to calculate its elliptical orbit as soon as possible. Using only the few observations that had been made of the asteroid, Gauss calculated its orbit (reputedly by least squares) so accurately that astronomers could locate it again late in 1801 and early in 1802. In the finest tradition of Piazzi and Gauss, modern geophysicists Joe Dellinger and Bill Dillon discovered and calculated the orbit of a new asteroid, which they named Svenders after the present authors (Schuster, 2005[1]). Since Gauss’s work, the least-squares method has been important in science, especially in astronomy and geodesy. The purpose of a least-squares filter is, in the least-squares sense, to convert an input signal into a desired output signal. The design of a least-squares filter requires two entities: the autocorrelation of the input signal and the crosscorrelation of the desired output signal with the input signal. A least-squares prediction filter is a special case of the least-squares filter. In this case, the desired output is a time-advanced version of the input signal. The design of a least-squares prediction filter requires only the autocorrelation of the input signal. Least-squares filtering, as a mathematical process, does not require a detailed description of the signals involved. That aspect makes least-squares filtering very useful. Deconvolution typically is implemented with the least-squares-error criterion, although other error criteria also can be used. Deconvolution requires a model that describes the internal structure of a seismic trace. More exactly, deconvolution is based on the assumption that a seismic trace can be represented as the convolution of a reflectivity series with a seismic wavelet. This so-called convolutional model of the seismic trace leads directly to the method of deconvolution, in which we attempt to recover estimates of the reflectivity series from the recorded seismic trace. The ensemble of the reflection coefficients comprises the reflectivity series. The seismic trace is the response of the reflectivity series to wavelet excitation, that is, the trace is a superposition of the individual wavelets. This linear process is called the principle of superposition, which we discussed in Chapter 1. The process is achieved computationally by convolving the wavelet with the reflectivity series. To identify closely spaced reflecting boundaries, the wavelet must be removed from the trace to yield the reflectivity series. This removal process is the opposite of the convolutional process used to represent the response of the reflectivity series to a wavelet excitation. Such an opposite or inverse process is appropriately called inverse filtering or deconvolution (Robinson, 1954[2], 1957[3], 1966[4]; Robinson and Treitel, 1967[5], 1969[6]; Peacock and Treitel, 1969[7]). The convolutional model states that a trace is the convolution of a wavelet and a reflectivity series. As Robinson (1957[3], p. 767-768) wrote, this convolutional model yields the representation of the time series at any moment in terms of its own observable past history plus an unpredictable, random-like innovation. It is assumed that a seismic trace is additively composed of many overlapping seismic wavelets that arrive as time progresses. It is assumed that each wavelet has the same stable, one-sided, minimum-phase shape and that the arrival times and strengths of these wavelets may be represented by a time sequence of uncorrelated random variables. Since the geologic structure is physically fixed and constant in nature and has no intrinsic random characteristics, any statistical approach to this problem immediately encounters difficulties that are commonly associated in the statistical literature with the Theorem of Thomas Bayes. Nevertheless, modern statistical theory admits the bypassing of these difficulties, although with reservation, and hence the working geophysicist may be considered to be faced with a situation which is essentially statistical. Interestingly, when Robinson submitted this paper for publication in 1954, it was not accepted. At that time, the solid earth was regarded as being deterministic, to be treated by differential and integral equations, rather than being random or randomlike, to be treated by statistical methods. When Norman Ricker became editor of GEOPHYSICS in 1957, he found Robinson’s manuscript by accident in an old cardboard box and published it. For clarification, one can find no better words that those of Ulrych et al. (2001[8], p. 55): An inherent feature of any inverse problem is randomness. As we will see, randomness may be associated with various parts of our quest, but there can certainly be no doubt that noise always associated with the observations is indeed random. Thus, our approach must be statistical in nature. Statistics, to many, imply probabilities. Probabilities, at least to us, imply Bayes. This is not the only view; in fact, we consider two quite different views. In the first, we consider the model parameters to be a realization of a random variable. In the second, we treat the parameters as nonrandom. Probability theory and statistics are different. The former refers to the quest of predicting properties of observations from probability laws that are assumed known. The latter is, in a sense, the inverse. We observe data and wish to infer the underlying probability law. In general, inverse problems are more complex to solve than forward problems. They are often ill posed or nonunique. The standard assumption is that each wavelet has the same minimum-phase shape and that the arrival times and strengths of each wavelet are given by a reflectivity series of uncorrelated random variables. The spiking-deconvolution operator can be computed from the autocorrelation of the trace. The spiking operator, so computed, is necessarily minimum phase (Robinson and Wold, 1963[9]). This operator can be used to deconvolve the trace — that is, the spiking operator removes the wavelet from the trace, thereby yielding the reflectivity series. In addition, the spiking operator can be inverted to yield estimates of the basic wavelet shape. Deconvolution improves the temporal resolution of a seismic section by compressing the seismic wavelets. For example, the reverberatory (ringy) character of a marine record without deconvolution seriously limits resolution. Deconvolution can attenuate such reverberations significantly. A spiking deconvolution filter is a prediction-error filter with prediction distance equal to one time unit. On the other hand, the method of gap deconvolution also uses the least-squares prediction-error filter, but with prediction distances greater than unity. In certain cases, gap deconvolution can be used to remove reverberations from a seismic trace that was generated by a mixed-phase wavelet. We present some examples in Chapter 11. Other filters can be derived from a minimum-phase wavelet (Robinson, 1998[10]). For example, we can divide the wavelet into two parts. One part consists of the wavelet’s first ${\displaystyle \alpha }$ coefficients and is called its head. The other part consists of all the coefficients beyond ${\displaystyle \alpha }$ and is called the wavelet’s tail. Such shaping operators can be computed by least squares. The shaping operator that shapes the wavelet into its head is called the head-shaping operator. Within computational accuracy, this operator is the same as the prediction-error operator for the trace for prediction distance ${\displaystyle \alpha }$. The shaping operator that shapes the wavelet into its tail is called the tail-shaping operator. ## References 1. Schuster, G. T., 2005, Svenders: A stellar tribute: Geophysics, 70, no. 4, 4JA. 2. Robinson, E. A., 1954, Predictive decomposition of time series with applications to seismic exploration: Ph.D. thesis, Massachusetts Institute of Technology. (Reprinted in Geophysics, 32, 418-484, 1967.) 3. Robinson, E. A., 1957, Predictive decomposition of seismic traces: Geophysics, 22, 767-778. 4. Robinson, E. A., 1966, Multichannel z-transforms and minimum-delay: Geophysics, 31, 482-500. Erratum: Geophysics, 31, 992. 5. Robinson, E. A., and S. Treitel, 1967, Principles of digital wiener filtering: Geophysical Prospecting, 15, 311-333. 6. Robinson, E. A., and S. Treitel, 1969, The Robinson-Treitel reader: Seismograph Service Corporation. 7. Peacock, K. L., and S. Treitel, 1969, Predictive deconvolution: Theory and practice: Geophysics, 34, 155-169. 8. Ulrych, T. J., M. D. Sacchi, and A. Woodbury, 2001, A Bayes tour of inversion, a tutorial: Geophysics, 66, 55-69. 9. Robinson, E. A., and H. Wold, 1963, Minimum-delay structure of least-squares and eo ipso predicting systems, in M. Rosenblatt, ed., Time series analysis: John Wiley, 192-196. 10. Robinson, E. A., 1998, Model-driven predictive deconvolution: Geophysics, 63, 713-722.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "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": 0.8297470211982727, "perplexity": 1785.4490735137244}, "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/1634323585450.39/warc/CC-MAIN-20211022021705-20211022051705-00274.warc.gz"}
http://mathematica.stackexchange.com/questions/26241/how-to-find-the-position-of-non-consecutive-numbers	# How to find the position of non consecutive numbers? Given a sorted table, how can I find the position of non consecutive numbers in the first column of the table? list = {{1, 3, 5}, {3, 3, 5}, {4, 3, 5}, {5, 3, 5}, {7, 3, 5}}//MatrixForm How to do I find the row position of the first non-consecutive number in column one? How to do I find the row position of the last non-consecutive number in column one? - I would rather define: list = {{1, 3, 5}, {3, 3, 5}, {4, 3, 5}, {5, 3, 5}, {7, 3, 5}}; If you prefer for some reasons your own definition you can use list[[1]] instead of list. To extract the first column use First@Transpose@list or list[[All, 1]], for the last column use Last@Transpose@list, for k-th column e.g. list[[All, k]]. Then there are many ways, let's show a few of them: Position[ KroneckerDelta /@ (Differences[ First @ Transpose @ list] - 1), 0] + 1 {{2}, {5}} Instead of mapping KroneckerDelta we could use simply Unitize (as pointed out by J.M.), since it is Listable. Moreover we could substitute Differences with subtruction of Rest and Most to get the proper result: Position[ Unitize[ Subtract @@ Through@{Rest, Most}@First@Transpose@list - 1], 1] + 1 another method without Apply for extracting non-consecutive numbers of the last column: Position[ Total[ Through @ { Rest, - Most @ # &} @ Last @ Transpose @ list], 0] + 1 {{2}, {3}, {4}, {5}} A related discussion useful for the problem at hand you can find reading answers to this question Find zero crossing in a list. - Alternatively: Position[Unitize[Differences[list][[All, 1]] - 1], 1] + 1 – Guess who it is. Jun 1 '13 at 13:32 OK. . .I like the last answer. . .So the first non-consecutive will be: result[[1]]. . .The last non-consecutive: result[[Length[result]]] – Hp Radojewski Schäfer Von Jun 4 '13 at 9:14 How to upvote to the answer given by 0x4A4D? – Hp Radojewski Schäfer Von Jun 4 '13 at 12:30 @HpRadojewskiSchäferVon There is one way: Answer your question with his answer and then accept it. Another way: try to convince him to write that answer. Than you'll be able to upvote an accept his answer. – Artes Jun 4 '13 at 15:00 EDIT My original code was padding with 0 was specific for test not general...apologies. In the test example the position of the non-consecutive numbers in the first clumn are 2 and 5 (correct me if I am misinterpreting). Applying: fun[u_List] := Position[Differences@PadLeft[u, Length@u + 1,u[[1]]-1], _?(# > 1 &)] to the first column finds positions of element whose preceding element is > 1. i.e. fun[list[[;;,1]]] yields: {{2}, {5}} -	{"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": 0.2035580575466156, "perplexity": 2659.6219570295684}, "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-2015-18/segments/1430453976406.4/warc/CC-MAIN-20150501041936-00048-ip-10-235-10-82.ec2.internal.warc.gz"}
https://www.transtutors.com/questions/1-which-of-the-following-statements-is-true-regarding-the-amortization-of-intangible-2637571.htm	# 1. Which of the following statements is true regarding the amortization of intangible assets?... 1. Which of the following statements is true regarding the amortization of intangible assets? (LO7–5) a. Intangible assets with a limited useful life are not amortized. b. The service life of an intangible asset is always equal to its legal life. c. The expected residual value of most intangible assets is zero. d. In recording amortization, Accumulated Amortization is always credited. 2. Equipment originally costing $95,000 has accumulated depreciation of$30,000. If it sells the equipment for $55,000, the company should record: (LO7–6) a. No gain or loss. b. A gain of$10,000. c. A loss of $10,000. d. A loss of$40,000. 3. The return on assets is equal to the: (LO7–7) a. Profit margin plus asset turnover. b. Profit margin minus asset turnover. c. Profit margin times asset turnover. d. Profit margin divided by asset turnover.	{"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": 0.48254823684692383, "perplexity": 6902.478185368421}, "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-2018-51/segments/1544376824675.15/warc/CC-MAIN-20181213101934-20181213123434-00507.warc.gz"}
http://stats.stackexchange.com/questions/32756/how-to-compute-the-generalization-error-test-error-in-a-multivariate-regressio	# How to compute the generalization error (test error) in a multivariate regression? How can I, after running multivariate linear regression, compute the Generalization Error (also known as Test Error)? Are there many practises to do that? EDIT: Can the following be considered as Generalization (or Test) Error? y = data1; [M,N] = size(y); X = [ones(M,N) data2]; y_train = y(M-30-483:M-30,:); X_train = X(M-30-483:M-30,:); y_test = y(M-29:M,:); X_test = X(M-29:M,:); [b,~,r,~,stats] = regress(y_train,X_train); [M,N] = size(data2); figure; plot(r); axis([0,N+1,-Inf,Inf]); y_estimated = X_test * b; y_expected = y_test; generalization_error = y_expected - y_estimated; figure; plot(generalization_error); - I take it that you're wondering how to do this in Matlab? – MånsT Jul 22 '12 at 8:37 @MånsT: Basically yes, but I would also appreciate if you could provide a few hints regarding the theoretical aspects of this concept... – user2295350 Jul 22 '12 at 19:51 possible duplicate you can check this stats.stackexchange.com/questions/32748/… – s.s.o Feb 8 at 1:43 What you are showing above is indeed an estimate of the model performance on unseen data (generalization error). However the variance of your test data set will presumably be non-negligible and so a better way to estimate the generalization error would be through cross-validation. Try the crossval function in Matlab or use cvpartition to define and your cross-validation folds and iterate though using a loop. - • root mean squared error sqrt (mean ((yhat - y)^2)) • mean absolute error mean (abs (yhat - y))	{"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": 0.8597005009651184, "perplexity": 2917.148295259192}, "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-2013-48/segments/1386164961715/warc/CC-MAIN-20131204134921-00059-ip-10-33-133-15.ec2.internal.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=147&t=44083	## Zero Order Units $\frac{d[R]}{dt}=-k; [R]=-kt + [R]_{0}; t_{\frac{1}{2}}=\frac{[R]_{0}}{2k}$ Maria Trujillo 1L Posts: 47 Joined: Fri Apr 06, 2018 11:05 am ### Zero Order Units What is a good way of memorizing the units for zero, 1 and 2nd order reactions, like in a way that you understand the concepts? AlyssaBei_1F Posts: 99 Joined: Fri Sep 28, 2018 12:17 am ### Re: Zero Order Units In the 7th edition, 7a problem #7 lays it out. The units for zero order are (mol A)/L/s. The units for first order are s^-1. The units for second order are L/(mol A)/s. Laura Gong 3H Posts: 89 Joined: Fri Sep 28, 2018 12:26 am Been upvoted: 1 time ### Re: Zero Order Units You can solve for the units of the rate constant by making sure your units at the end equal to M/s (which are the units for rate). juliasloan_4g Posts: 67 Joined: Fri Sep 28, 2018 12:28 am ### Re: Zero Order Units it may be easier to understand where the units come from by solving for it rather than memorizing them	{"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": 1, "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": 0.9239867925643921, "perplexity": 4425.641971190746}, "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/1575541301598.62/warc/CC-MAIN-20191215042926-20191215070926-00448.warc.gz"}
https://arxiv.org/abs/1807.00990	astro-ph.HE (what is this?) # Title:Gravitational-wave memory: waveforms and phenomenology Abstract: The non-linear gravitational-wave memory effect is a prediction of general relativity in which test masses are permanently displaced by gravitational radiation. We implement a method for calculating the expected memory waveform from an oscillatory gravitational-wave time series. We use this method to explore the phenomenology of gravitational-wave memory using a numerical relativity surrogate model. Previous methods of calculating the memory have considered only the dominant oscillatory ($\ell=2$, $m=\|2\|$) mode in the spherical harmonic decomposition or the post-Newtonian expansion. We explore the contribution of higher-order modes and reveal a richer phenomenology than is apparent with $\ell=\|m\|=2$ modes alone. We also consider the `memory of the memory' in which the memory is, itself, a source of memory, which leads to a small, $O\left(10^{-4}\right)$, correction to the memory waveform. The method is implemented in the python package {\tt\sc GWMemory}, which is made publicly available. Comments: 8 pages, 6 figures, accepted in PRD Subjects: High Energy Astrophysical Phenomena (astro-ph.HE); General Relativity and Quantum Cosmology (gr-qc) Journal reference: Phys. Rev. D 98, 064031 (2018) DOI: 10.1103/PhysRevD.98.064031 Cite as: arXiv:1807.00990 [astro-ph.HE] (or arXiv:1807.00990v2 [astro-ph.HE] for this version) ## Submission history From: Colm Talbot [view email] [v1] Tue, 3 Jul 2018 06:35:16 UTC (5,441 KB) [v2] Wed, 29 Aug 2018 00:53:08 UTC (5,594 KB)	{"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": 0.33527928590774536, "perplexity": 2382.6954867606337}, "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/1552912201996.61/warc/CC-MAIN-20190319143502-20190319165502-00290.warc.gz"}
https://www.gradesaver.com/textbooks/science/physics/college-physics-4th-edition/chapter-9-problems-page-361/17	## College Physics (4th Edition) We can rank the barrels in order of the force on the plug due to the liquid in the barrel, from largest to smallest: $c = e \gt b = d \gt a$ The pressure on the plug from the inside of the barrel is $P_{atm}+ P_{gauge}$ while the pressure on the plug from outside the barrel is $P_{atm}$. Therefore, the net pressure on the plug is $P_{gauge}$. We can calculate the force on the plug for each barrel. (a) $F = P_g~A$ $F = [\rho~g~(h-0.20~m)](\pi~r^2)$ $F = [(1000~kg/m^3)~(9.80~m/s^2)~(1.00~m-0.20~m)](\pi)~(0.010~m)^2$ $F = 2.46~N$ (b) $F = P_g~A$ $F = [\rho~g~(h-0.20~m)](\pi~r^2)$ $F = [(1000~kg/m^3)~(9.80~m/s^2)~(1.20~m-0.20~m)](\pi)~(0.010~m)^2$ $F = 3.08~N$ (c) $F = P_g~A$ $F = [\rho~g~(h-0.20~m)](\pi~r^2)$ $F = [(800~kg/m^3)~(9.80~m/s^2)~(1.20~m-0.20~m)](\pi)~(0.0125~m)^2$ $F = 3.85~N$ (d) $F = P_g~A$ $F = [\rho~g~(h-0.20~m)](\pi~r^2)$ $F = [(800~kg/m^3)~(9.80~m/s^2)~(1.00~m-0.20~m)](\pi)~(0.0125~m)^2$ $F = 3.08~N$ (e) $F = P_g~A$ $F = [\rho~g~(h-0.20~m)](\pi~r^2)$ $F = [(1000~kg/m^3)~(9.80~m/s^2)~(1.45~m-0.20~m)](\pi)~(0.010~m)^2$ $F = 3.85~N$ We can rank the barrels in order of the force on the plug due to the liquid in the barrel, from largest to smallest: $c = e \gt b = d \gt a$	{"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": 0.6937572360038757, "perplexity": 371.56781611732}, "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/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00142.warc.gz"}
https://www.physicsforums.com/threads/velocity-problem.154180/	# Velocity Problem 1. Feb 1, 2007 ### xviddivxoggmp3 1. The problem statement, all variables and given/known data The position of a car is given by the values below. Seconds \| Feet 1 \| 10 2 \| 32 3 \| 70 4 \| 119 5 \| 178 Find the average velocity for the time period beginning when t=2 and lasting (a) 3 seconds (b) 2 seconds (c) 1 second 2. Relevant equations There were no equations provided 3. The attempt at a solution i usually have an equation to go by, but i do not in this case. all attempts to make an equation out of the data have failed. i think it is an exponential curve, but i can find the exact formula. if anyone could stear me in the direction so i can figure this problem out. i want to know what i'm doing, so do not give me the answer but please someone point me in some productive direction. would i just input the numbers in the slope equation? M= y-y1 ---- x-x1 i have the x and y already. that seems too easy. 2. Feb 2, 2007 ### Schrodinger's Dog Last edited: Feb 2, 2007 3. Feb 2, 2007 ### HallsofIvy Staff Emeritus xviddivxoggmp3, you are completely right- it is that easy. Shrodinger's dog is also correct but might be a bit confusing here. His point is that this problem is leading you to the idea of a "limit" and then the velocity at a single time. 4. Feb 2, 2007 ### Schrodinger's Dog Yeah I edited, I kind of misread it, but then I reread his question and saw how simple what he was asking was. Here's a graph I did,I had a bit of time and wanted a bit of practice. Graph of:- Seconds \| Feet 1 \| 10 2 \| 32 3 \| 70 4 \| 119 5 \| 178 Essentially the question is asking you to find an exact point on the graph. Last edited: Feb 2, 2007 Similar Discussions: Velocity Problem	{"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": 0.8121732473373413, "perplexity": 922.9611956185776}, "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-2017-26/segments/1498128319688.9/warc/CC-MAIN-20170622181155-20170622201155-00455.warc.gz"}
https://instantcertcredit.com/courses/5/lesson/323	### Assignments: Unfinished Assignment Study Questions for Lesson 43 ### Lesson Objectives: - Defining the percentage of receivables method. - What the aging schedule is. - Using the T-account format to record the beginning, adjustment and ending values. - Recording the bad debts expense. In this lesson we will be talking about the percentage of receivables method for calculating the bad debts expense. The receivables method is slightly more complicated than the sales method that we reviewed in the previous lesson. The difference is the receivables method does not use the net sales to calculate the uncollectible amount. Instead we will use the permanent account values for accounts receivable. For the example, we are reviewing in this lesson, we will use the following values for receivables. We will also assume that the uncollectible amount will account for 1 percent of the receivables. End 2014 receivables = 700,000 End 2015 receivables = 1,300,000 We will use the same format for the bad debts journal entry that we reviewed when talking about the sales method. The bad debts are listed as a debit and the contra asset account of AFDA as a credit. Hopefully you remember from the previous lesson that AFDA stands for allowance for doubtful accounts. Normally, when talking about the receivables, we use the aging schedule to address receivables that have been outstanding for a certain amount of time (30 days, 3 months, 6 months and so on). The longer amount of time that the receivable has been outstanding, the less likely that it will be collected. Let's forget about this concept for now, as I want to keep the receivables method as simple as possible. We will be revisiting this topic in the next lesson, so moving forward let's go ahead and take a look at the T-account for AFDA. In order to come up with the adjustment entry for the bad debts expense, let's use the T-account format. We are looking for the adjustment value so we will need to find the beginning and ending amounts. First, we will multiply the 2014 end receivables of $700,000 by the 1 percent uncollectible amount to come up with the beginning balance of$7,000. The ending balance will be calculated the same way using the 2015 end receivables multiplied by 1 percent or 0.01 to conclude with $13,000. Now we just need to calculate the adjustment amount by subtracting the$7,000 beginning balance from the ending balance of $13,000 to come up with a$6,000 adjustment amount. The difference between the ending and beginning amount is the adjustment value that we will be using to record the journal entry for the bad debts expense. We have the $6,000 adjustment value that was calculated by finding the difference between the 2015 uncollectible end receivables and 2014 uncollectible end receivables. Now let's use the same journal entry format, to record the$6,000 as a debit to the bad debts expense account and a credit to the AFDA account. Accounts receivable is a permanent account that is used in the receivables method, therefore the ending balance is calculated by multiplying the uncollectible percentage by the ending receivables. With this method, we are looking for the adjustment amount. The sales method uses net sales to calculate the adjustment amount. Net sales is a temporary account that will be reset to zero at the end of every year, it is ultimately closed and transferred to a permanent account. In contrast to the receivables method, the sales method looks for the ending amount. Keep in mind when we are needing to record the bad debts expense, we are always using the adjustment value and not the beginning or ending values. Again, each bad debt expense method has its own benefits. We mentioned that the advantage of the sales method follows the matching principle to match the bad debt expense to the revenue earned in that particular accounting period. The receivables method is not necessarily a good representation of the matching principle, but it gives a clear net realizable value of accounts receivable. This is simply the accounts receivable account less the AFDA amount.	{"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": 0.42424699664115906, "perplexity": 1601.3187019875918}, "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/1631780057225.57/warc/CC-MAIN-20210921161350-20210921191350-00588.warc.gz"}
http://matthewrocklin.com/blog/work/2015/08/03/Caching	This work is supported by Continuum Analytics and the XDATA Program as part of the Blaze Project tl;dr: Caching improves performance under repetitive workloads. Traditional LRU policies don’t fit data science well. We propose a new caching policy. ## Humans Repeat Stuff Consider the dataset that you’ve worked on most recently. How many times have you loaded it from disk into memory? How many times have you repeated almost the same computations on that data? Exploratory data science workloads involve repetition of very similar computations. These computations share structure. By caching frequently used results (or parts of results) we may be able to considerably speed up exploratory data analysis. ## Caching in other contexts The web community loves caching. Database backed web applications almost always guard their database lookups with a system like memcached which devotes some amount of memory to caching frequent and recent queries. Because humans visit mostly the same pages over and over again this can reduce database load by an order of magnitude. Even if humans visit different pages with different inputs these pages often share many elements. ## Limited caching resources Given infinite memory we would cache every result that we’ve ever computed. This would give us for instant recall on anything that wasn’t novel. Sadly our memory resources are finite and so we evict cached results that don’t seem to be worth keeping around. Traditionally we use a policy like Least Recently Used (LRU). This policy evicts results that have not been requested for a long time. This is cheap and works well for web and systems applications. ## LRU doesn’t fit analytic workloads Unfortunately LRU doesn’t fit analytic workloads well. Analytic workloads have a large spread computation times and of storage costs. While most web application database queries take roughly the same amount of time (100ms-1000ms) and take up roughly the same amount of space to store (1-10kb), the computation and storage costs of analytic computations can easily vary by many orders of magnitude (spreads in the millions or billions are common.) Consider the following two common computations of a large NumPy array: 1. x.std() # costly to recompute, cheap to store 2. x.T # cheap to recompute, costly to store In the first case, x.std(), this might take a second on a large array (somewhat expensive) but takes only a few bytes to store. This result is so cheap to store that we’re happy to keep it in our cache for a long time, even if its infrequently requested. In the second case, x.T this is cheap to compute (just a metadata change in the array) and executes in microseconds. However the result might take gigabytes of memory to store. We don’t want to keep this in our cache, even if it’s very frequently requested; it takes up all of the space for other potentially more useful (and smaller) results and we can recompute it trivially anyway. So we want to keep cached results that have the following properties: 1. Costly to recompute (in seconds) 2. Cheap to store (in bytes) 3. Frequently used 4. Recently used ## Proposed Caching Policy Here is an alternative to LRU that respects the objectives stated above. Every time someone accesses an entry in our cache, we increment the score associated to the entry with the following value Where compute time is the time it took to compute the result in the first place, nbytes is the number of bytes that it takes to store the result, epsilon is a small number that determines the halflife of what “recently” means, and t is an auto-incrementing tick time increased at every access. This has units of inverse bandwidth (s/byte), gives more importance to new results with a slowly growing exponential growth, and amplifies the score of frequently requested results in a roughly linear fashion. We maintain these scores in a heap, keep track of the total number of bytes, and cull the cache as necessary to keep storage costs beneath a fixed budget. Updates cost O(log(k)) for k the number of elements in the cache. ## Cachey I wrote this up into a tiny library called cachey. This is experimental code and subject to wild API changes (including renaming.) The central object is a Cache that includes asks for the following: 1. Number of available bytes to devote to the cache 2. Halflife on importance (the number of access that occur to reduce the importance of a cached result by half) (default 1000) 3. A lower limit on costs to consider entry to the cache (default 0) ## Example So here is the tiny example ## More interesting example The cache includes a memoize decorator. Lets memoize pd.read_csv. So we create a new function read_csv that operates exactly like pandas.read_csv except that it holds on to recent results in c, a cache. This particular CSV file created a dataframe that filled a tenth of our cache space. The more often we request this CSV file the more its score will grow and the more likely it is to remain in the cache into the future. If other memoized functions using this same cache produce more valuable results (costly to compute, cheap to store) and we run out of space then this result will be evicted and we’ll have to recompute our result if we ask for read_csv('accounts.csv') again. ## Memoize everything Just memoizing read_csv isn’t very interesting. The pd.read_csv function operates at a constant data bandwidth of around 100 MB/s. The caching policies around cachey really shine when they get to see all of our computations. For example it could be that we don’t want to hold on to the results of read_csv because these take up a lot of space. If we find ourselves doing the same groupby computations then we might prefer to use our gigabyte of caching space to store these both because 1. groupby computations take a long time to compute 2. groupby results are often very compact in memory I’m slowly working on integrating cachey into dask’s shared memory scheduler. Dask is in a good position to apply cachey to many computations. It can look at every task in a task graph and consider the result for inclusion into the cache. We don’t need to explicitly memoize every function we want to use, dask can do this for us on the fly. Additionally dask has a nice view of our computation as a collection of sub-tasks. Similar computations (like mean and variance) often share sub-tasks. ## Future Work Cachey is new and untested but potentially useful now, particularly through the memoize method shown above. It’s a small and simple codebase. I would love to hear if people find this kind of caching policy valuable. I plan to think about the following in the near future: 1. How do we build a hierarchy of caches to share between memory and disk? 2. How do we cleanly integrate cachey into dask (see PR #502) and how do we make dask amenable to caching (see PR #510)?	{"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": 0.2745577096939087, "perplexity": 2014.738031926412}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320386.71/warc/CC-MAIN-20170625013851-20170625033851-00403.warc.gz"}
https://www.enotes.com/homework-help/consider-equation-below-f-x-x-7-lnx-369510	# Consider the equation below. f(x) = x^7 lnx Find the interval on which f is increasing. Find the interval on which f is decreasing. Consider the equation below. f(x) = x^7 ln x (Enter your answer using interval notation.) ## Expert Answers If you have more than one question, you need to make separate posts. To find where a function is increasing and decreasing, you need to find where the derivative of the function is greater than zero or less than zero. `f(x)=x^7lnx` differentiate using product rule `f'(x)=7x^6lnx+x^7/x` `=x^6(7lnx+1)` Since `x^6` is... ## Get This Answer Now Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime. If you have more than one question, you need to make separate posts. To find where a function is increasing and decreasing, you need to find where the derivative of the function is greater than zero or less than zero. `f(x)=x^7lnx` differentiate using product rule `f'(x)=7x^6lnx+x^7/x` `=x^6(7lnx+1)` Since `x^6` is always positive, we need to determine when `7lnx+1` is greater than zero or less than zero. We first find when it is equal to zero, then it will be positive on one side and negative on the other. `7lnx+1=0` `7lnx=-1` `lnx=-1/7` switch to exponential form `x=e^{-1/7}` This means that when `(e^{-1/7},infty)` , then the derivative is positive, which means the function is increasing, and when `(0,e^{-1/7})` , the derivative is negative, which means the function is decreasing. Approved by eNotes Editorial Team	{"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": 0.8943123817443848, "perplexity": 445.6005089198275}, "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-2022-05/segments/1642320304528.78/warc/CC-MAIN-20220124094120-20220124124120-00687.warc.gz"}
https://discuss.codechef.com/questions/62664/lch15jab-editorial?sort=newest	× # LCH15JAB - Editorial Author: Pavel Sheftelevich Tester: Roman Rubanenko Editorialist: Paweł Kacprzak CAKEWALK # PROBLEM: As the name suggest, this problem is really easy. You are given a string S. The task is to decide whether there exists a character for which a number of occurrences of this character in S is equal to a sum of occurrences of all other characters in S. # QUICK EXPLANATION: Count a number of occurrences for each of 26 possible letters and for each such letter, check if the counter equals a sum of occurrences of all other characters in S. # EXPLANATION: First observation: There are at most 26 possible distinct letters in S because the Latin alphabet has 26 letters ('a' to 'z'). Let cnt[a] denote number of occurrences of letter ch in S. We can compute the cnt table iterating over S from left to right and maintaining and updating a counter for each character. int cnt[26]; for (i = 0; i < 26; i++) cnt[i] = 0; for (i = 0; i < s.size(); i++) cnt[s[i] - 'a']++; Let n be the length of S. A simple observation which may help is that a sum of occurrences of all characters different than ch equals n - cnt[ch]. Based on this fact we can decide out problem easily. Just iterate over all possible letters and check if there is a letter ch for which cnt[ch] = n - cnt[ch] Also note that if you are an C++/Java user, you can also make use of map/Map in STL(Standard Template Library)/ Java Collections. map/Map is a balanced red black tree, in which you can put (key, value) pairs and also search for value corresponding to the key. All these operations are logarithmic in number of elements present in the data structure. So you can use map/Map to count number of occurrences of a particular character too. For more faster solution, you can use unordered_map/HashMap too which is implemented using hashing and gives constant time for the above operations. # TIME COMPLEXITY For a solution which uses counters is O(n) and the same for a solution using map/Map or unordered_map/HashMap, because if you use it, you will store up to 26 entries in it, so this is not much an upgrade. I suggest to use a simple table because for such small dataset it is the fastest method. # AUTHOR'S AND TESTER'S SOLUTIONS: Author's solution can be found here. Tester's solution can be found here. # RELATED PROBLEMS: This question is marked "community wiki". 75485097 accept rate: 12% 2.5k53137170 # include<bits stdc++.h=""> using namespace std; int main() { int i,t; cin>>t; for(i=0;i<t;i++) {="" <br=""/> string s; int count=0; int j,k; cin>>s; for(j=0;j<s.length();j++) { count=0; for(k=j;k<s.length();k++) { if(s[j]==s[k]) { count++; } } if(s.length()%2!=0) { cout<<"NO\n"; goto end; } if(count==(s.length()/2)) { cout<<"YES\n"; goto end; } } cout<<"NO\n"; end:; } } This answer is marked "community wiki". 3★sidbhati 0 accept rate: 0% toggle preview community wiki: Preview By Email: Markdown Basics • italic or _italic_ • bold or __bold__ • image?![alt text](/path/img.jpg "title") • numbered list: 1. Foo 2. Bar • to add a line break simply add two spaces to where you would like the new line to be. • basic HTML tags are also supported • mathemetical formulas in Latex between \$ symbol Question tags: ×15,852 ×1,688 ×968 ×22 question asked: 25 Jan '15, 14:37 question was seen: 2,904 times last updated: 19 Dec '18, 00:33	{"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": 0.5029130578041077, "perplexity": 2383.3057268023367}, "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/1552912202572.29/warc/CC-MAIN-20190321193403-20190321215403-00218.warc.gz"}
https://codegolf.stackexchange.com/questions/63433/programming-a-pristine-world	Programming a Pristine World Let's define a pristine program as a program that does not have any errors itself but will error if you modify it by removing any contiguous substring of $$\N\$$ characters, where $$\1 \le N < \text{program length}\$$. For example, the three character Python 2 program 8 is a pristine program (thanks, Sp) because all the programs resulting from removing substrings of length 1 cause errors (syntax errors in fact, but any type of error will do): 8 8 and also all the programs resulting from removing substrings of length 2 cause errors: If, for example, 8 had been a non-erroring program then 8 would not be pristine because all the results of substring removal must error. Your task in this challenge is to write the shortest pristine program possible that takes no input but outputs any one of the following five words: world earth globe planet sphere Which word you choose is entirely up to you. The sole word plus an optional trailing newline should be printed to stdout (or your language's closest alternative). The shortest program in bytes wins. Notes: • A standalone program is required, not a function. • The words are case sensitive; outputting World or EARTH is not allowed. • Compiler warnings do not count as errors. • The erroring subprograms can take input or give output or do anything else as long as they always eventually error. Here's a stack snippet that will list what programs need to error given a potentially pristine program: <script src='https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js'></script><script>function go() { var s = $('#i').val(), e = []; for (var i = 1; i < s.length; i++) { for (var j = 0; j <= s.length - i; j++) { e.push(s.substring(0, j) + s.substring(j + i)); } }$('#o').val(e.join('\n---\n')); }</script>Program:<br><textarea id='i' rows='16' cols='80'>8</textarea><br><button onclick='go()' type='button'>Go</button><br><br>Programs that should error: (--- separated)<br><textarea id='o' rows='16' cols='80'></textarea><br> • @geokavel Yes. Catching the exception means it's no longer an error. Nov 9, 2015 at 21:37 • Twice as many deleted answers as non-deleted. That's an achievement! Nov 9, 2015 at 22:42 • Can a program read its own source code? Nov 11, 2015 at 17:57 • Where to view the gravegard of "close but no cigar" answers and their comments? – Vi. Nov 12, 2015 at 14:28 • @Vi. Get 2,000 rep so you can view deleted posts. Nov 12, 2015 at 16:30 Rail, 24 bytes $'main' # -[world]o/ I think this works. And it's both short and readable (as far as Rail goes). • If the removed substring includes any part of $'main' we get Internal Error: Crash: No 'main' function found. • If the removed substring includes the #, there is no way for the program to exit cleanly, so it will always terminate with Crash: No valid move. I believe that it's not possible to delete a substring such that the track forms a valid (infinite) loop. • If the removed substring is in front of the #, it will be disconnected from the end of the track, so the train will crash (with the same error as above). • If the removed substring is after the #, it will also disconnect the # from the end of the track (and potentially even the beginning of the track from the entry point $). So again the same error. As for the actual program: every Rail program needs to have a $'main' (or a longer variant, but we're golfing here) as an entry point into the function and the train starts on the $ going South-East. Everything on that first line can be part of the track though, so removing the 'main' the track is: $ # -[world]o/ The - and / are simply pieces of rail which we need to let the train take those 45° turns. [world] pushes the string world and o prints it. # marks the end of the track - the only way to safely terminate a Rail program. Interestingly, this solution is only possible because Rail allows the tracks to go through the main line - if that wasn't possible # would be after the first newline and the code could always be shortened to $'main' # which is a valid program that doesn't do anything. (Non-space characters between ' and # wouldn't affect that.) Also quite interesting: if I had just golfed the task printing world it wouldn't have been much shorter or simpler: $'main' -[world]o# • What if I remove any char between [ and ]? Nov 9, 2015 at 21:48 • @MartinLütke it will disconnect the / from the #. Nov 9, 2015 at 21:49 • @MartinLütke You could not only remove the brackets since they are not contiguous. Nov 9, 2015 at 22:06 • What if remove the newline between the two lines? – Vi. Nov 12, 2015 at 14:32 • @Vi. That disconnects the $ from the start of the track, so the train crashes immediately (Rail expects the track to continue South-East of the $). Nov 12, 2015 at 14:33 Funciton (186 136 bytes in UTF-16) ╔══════════════╗ ║19342823075080╟ ║88037380718711║ ╚══════════════╝ This program prints “world”. Most substrings you remove from this will stop it from being a complete box, which the parser will complain about. The only possible removals that leave a complete box are: ╔══════════════╗ \|║19342823075080╟ (remove this whole line) \|║88037380718711║ ╚══════════════╝ ╔══════════════╗ ║\|19342823075080╟ ← substring starts at \| here ║\|88037380718711║ ← substring ends at \| here ╚══════════════╝ ... ↕ or anything in between these that removes a whole line’s worth ↕ ... ╔══════════════╗ ║19342823075080\|╟ ← substring starts at \| here ║88037380718711\|║ ← substring ends at \| here ╚══════════════╝ ╔══════════════╗ \|║19342823075080╟ ║88037380718711║ (both lines entirely) \|╚══════════════╝ ╔══════════════╗ ║19342823075080╟ \|║88037380718711║ (remove this whole line) \|╚══════════════╝ Most of these remove the dangling end at the top right of the box, which is the output connector. Without this loose end, the box is just a comment: ╔══════════════╗ ║88037380718711║ ╚══════════════╝ This is no longer a valid program because the parser expects a program with exactly one output: Error: Source files do not contain a program (program must have an output). The only possibility that leaves an output connector is the last one of the above, which leaves this: ╔══════════════╗ ║19342823075080╟ ╚══════════════╝ However, this number does not encode a valid Unicode string in Funciton’s esoteric UTF-21. Try to run this, you get: Unhandled Exception: System.ArgumentOutOfRangeException: A valid UTF32 value is between 0x000000 and 0x10ffff, inclusive, and should not include surrogate codepoint values (0x00d800 ~ 0x00dfff). Therefore, this program is pristine. • I feel like you got lucky on the last case (not that it's that easy to accidentally get a valid Unicode sequence, but still...) Jul 13, 2017 at 2:30 Visual C++ - 96 95 bytes #include<iostream> #define I(a,b)a<<b int main()I({std::cout,I('w',I('o',I('r',I('l','d';)))))} Properties: 1. You can't remove any part of int main() without a compile error. 2. You can't remove the modify the macros expansion AT ALL, removing a at all means main() never gets {, removing b at all means our line doesn't end in a ;, removing < means std::cout<'w' causes an error, and removing << causes std::cout'w', 'w''o', etc. 3. You can't remove parameters from the macro definition or invocation, the only valid names for the definition would be I(a),I(b) which never match and I which expands to before (; on the other hand using I(, causes <<<<, and ,) drops the semi-colon (barring any other errors). 4. You can't remove part of all of std::cout without running into a leading <<, and therefore cannot remove any of #include<iostream> in the beginning without a compile error. 5. You can't remove any part of a single character, '' has an empty character error and 'w,, etc... try to making everything into one character. 6. You can't remove the left/right side of a macro without leaving too many ) or ( on the other side, e.g. you cannot do things like I('w',I('r'. Compiles online using Visual C++. Once again this not an exhaustive proof. If you think you can get it too work without section be sure to let me know. Previous versions used a considerably different approach and was proved to not be pristine so I've removed those scores. Verification: The following program has confirmed this version is pristine using the cl compiler from Visual C++ 2010. Wished I had bothered to write this sooner: #include <fstream> #include <iostream> char S = "#include<iostream>\n#define I(a,b)a<<b\nint main()I({std::cout,I('w',I('o',I('r',I('l','d';)))))}"; //uncomment to print source code before compile // #define prints int main(){ for(int i=0; i<95; i++) for(int j=i; j<95; j++){ std::fstream fs; fs.open ("tmptst.cpp",std::fstream::out); for(int k=0; k<95; k++) if(k<i \|\| k>j){ fs << S[k]; #ifdef prints std::cout<<S[k]; #endif } fs.close(); #ifdef prints std::cout<<'\n'; #endif //Compile and surpress/pipe all output //if it doesn't compile we get a nonzero errorlevel (i.e.true) from system. if(!system("cl -nologo tmptst.cpp >x")) return 0; } std::cout<<"PRISTINE!"; } • We note that while this is pristine on this compiler, not so on all compilers. Nov 11, 2015 at 2:42 • Please give an example.... Nov 11, 2015 at 5:10 • On some compilers the empty C++ program yields a program that does nothing. Depending on the implementation of the iostream, #include <iostream> might also compile. Nov 11, 2015 at 16:13 • @Joshua Only subprograms of length 1 or higher matter, so it's irrelevant what the empty program does. Nov 12, 2015 at 20:39 • @Comintern, not really. If you don't check the box to run the executable the /c option is automatically included and it compiles (as if creating a library and not a program). If you check the run box the site does not include /c, you will not get a success message, and instead find the natural "LINK : fatal error LNK1561: entry point must be defined". Nov 15, 2015 at 0:10 Python 3, 79 33 if 5-open(1,'w').write('world'):a open(1,'w') opens standard output, then we print the string. write returns the number of characters written. This is used to harden against substring removal: Removing part of the string causes something other than 5 to be returned, and 5 minus that value then evaluates to true. But that causes the if-body to be executed and a is undefined. This is based on Anders Kaseorg's clever pristine quine here. As only a single statement needs to be verified this is much shorter than the old solution, but also less general. Old solution: try: q="print('world');r=None" if exec('e=q')==eval(q[17:]):exec(e) finally:r To verify that it really is a pristine program: w=r'''try: q="print('world');r=None" if exec('e=q')==eval(q[17:]):exec(e) finally:r''' exec(w) for j in range(1,len(w)): for i in range(len(w)+1-j): e=w[:i]+w[i+j:] try:exec(e,{});print('WORKED',e) except:pass Some key points: • Every executed statement could be deleted. Verifying that q has been executed requires a statement outside of q. The try solves that nicely, by requiring at least two statements, neither of which can be deleted fully. • Verifying that q has executed happens by evaluating r at the end. • Verifying that q was not modified is achieved by eval(q[17:]), which has to evaluate to None for q to be executed. • The if condition is a bit tricky to get right. To ensure that it was evaluated it has the nice side effect of setting e, which is needed to set r. (This is the reason I used Python 3, expr as a function does wonders for expression-level side effects.) • Isnt the challenge that no removal would result in a syntax error? You seem to provoke runtime errors. Nov 9, 2015 at 22:03 • @MartinLütke Any type of errors are fine. Nov 9, 2015 at 22:03 • Um, isn't this 79 bytes? Jul 6, 2018 at 2:39 • @TheMatt Yeah? I just counted them again and you seem to be right. Maybe past-me counted CRLF newlines... How embarrassing. Thanks! Jul 6, 2018 at 22:46 x=uncurry(:) JavaScript, 7473 35 bytes if((alert(a="world")?x:a)[4]!="d")x It turns out the answer was much simpler than I thought... Explanation if( ( alert(a="world") // throws a is not defined if '="world"' is removed ?x // throws x is not defined if 'alert' or '(a="world")' is removed :a // throws a is not defined if 'a="world"' or 'a=' is removed ) [4]!="d" // if "world" is altered fifth character will not be "d" // if 'd' is removed it will compare "world"[4] ("d") with "" // if '[4]' is removed it will compare "world" with "d" // if '(alert(a="world")?x:a)' is removed it will compare [4] with "d" // if '?x:a' is removed [4] on alert result (undefined[4]) will error // if '[4]!="d"' is removed the if will evaluate "world" (true) // if '!', '!="d"' or '(alert...[4]!=' is removed the if will // evaluate "d" (true) )x // throws x is not defined if reached // any other combination of removing substrings results in a syntax error • remove everything except a="world", does not error Nov 11, 2015 at 0:04 • @anOKsquirrel Only a single substring can be removed. Nov 11, 2015 at 2:24 • I went through this like "Could I remove this? No, this error would occur. Can this be deleted? Well, I guess it would cause this other error. Aha! Those chars can be removed! Oh wait..." +1 Nov 11, 2015 at 3:26 • if(a="world")["bol"+a[4]] does not error. Nov 11, 2015 at 13:13 • Holy cow, it's twice as impressive now! Wish I could +1 again... Nov 11, 2015 at 21:03 Funciton, 143142 136 bytes Score is in UTF-8 as usual, as UTF-16 would be two bytes larger (due to the BOM). ╔══════════╗ ║1934282307║╔╗ ║5080880373╟╚╝ ║80718711 ║ ╚══════════╝ So, I've been contemplating a Funciton answer for a while and I figured it would be impossible, because you could always remove a full line and the code would still form a valid block. Then I talked to Timwi about it, and he figured out that you can just put the entire number in a single line, such that removing it would break the program for lack of an output connector. But literals on a single line are notoriously expensive, both because of the larger character count and because of the larger number of non-ASCII characters. And his mention of an "empty comment" block got me thinking... So I came up with this more efficient solution which uses an additional empty comment block which breaks when you try removing anything which would leave the literal block in tact: • We can't possibly remove the third line, because then we'd remove the output connector. • If we remove the second line, the comment block loses its top edge and breaks. That leaves two options (thanks to Steve for pointing that out): • Remove the fourth line. That leaves both boxes in tact. However, when the resulting integer 19342823075080880373 is decoded, the corresponding string would contain the code point 0x18D53B which is not a valid Unicode character, System.Char.ConvertFromUtf32 crashes with an ArgumentOutOfRangeException. • Remove a full line starting after the top-right corner. Again, both boxes are left in tact, but the resulting integer 508088037380718711 would contain two invalid code points 0x1B0635 and 0x140077, leading to the same exception. Note that even without the empty comment block, removing the second line would lead to an invalid code point. But the comment block prevents that we're taking a line from inside the second line, to get an integer like 193428037380718711 for instance, which would not cause an error. • What happens if you remove the substring starting with the character after the output connector and finishing exactly 1 line later? i.e. removing the middle line of the comment block and the line containing "80718711" in the main block, but leaving corners of both boxes intact. Nov 11, 2015 at 12:59 • @Steve I've amended the answer to cover that case. After looking into it a bit more, this actually allowed me to save two characters/six bytes. Nov 11, 2015 at 15:24 Java 8, 301 bytes Because every question needs a Java answer. class C{static{System.out.print(((((w='w')))));System.out.print((((o='o'))));System.out.print(((r='r')));System.out.print((l='l'));System.out.print(d='d');e=(char)((f=1)/((g=8)-C.class.getDeclaredFields()[h=0].getModifiers()));}public static void main(String[]a){}static final char w,o,r,l,d,e,f,g,h;} Expanded class C { static { System.out.print(((((w = 'w'))))); System.out.print((((o = 'o')))); System.out.print(((r = 'r'))); System.out.print((l = 'l')); System.out.print(d = 'd'); e = (char) ((f = 1) / ((g = 8) - C.class.getDeclaredFields()[h = 0].getModifiers())); } public static void main(String[] a) { } static final char w, o, r, l, d, e, f, g, h; } Explanation • public static main(String[]a){} is required. • If the field declarations are removed (or made non-static), the first static block can't find them. • If the static block is removed (or made non-static), the fields aren't initialized. The hardest part: • If the final keyword is removed, the second line evaluates to 1/(8-8), causing a / by zero exception. • Why can't you remove the insides of any of the print statements? – Nic Apr 11, 2016 at 20:33 • @QPaysTaxes There isn't an empty System.out.print() method. There is for println(), but not for print(). So if you would remove d='d' it would give The method print(boolean) in the type PrintStream is not applicable for the arguments () as error (And if you would remove d= it would give The blank final field d may not have been initialized as error). Oct 12, 2016 at 14:24 ><>, 17 bytes e"ooooo7-c0pBhtra Try it online! Prints "earth". The only way a ><> program exits without an error is executing the ; character, which is a problem as you can just remove all the characters before that, so that ; is the first character executed. You can get around that by using the p command to modify the program to include ; during execution instead. Removing any section of the code causes the ; to never be produced causing errors via the invalid instructions B, h and t, stack underflow, and infinite loops making it eventually run out of memory. I only had to make sure that all the infinite loops kept filling up the stack. All variants were tested using this python snippet: code = 'e"ooooo7-c0pBhtra' count = {"invalid":0, "underflow":0, "memory":0} for l in range(1, len(code)): for x in range(0, len(code)-l+1): print(code[:x] + code[x+l:], "\t\t", end='') try: interp = Interpreter(code[:x]+code[x+l:]) for _ in range(0,1000): interp.move() print(len(interp._stack), "< ", end='') interp2 = Interpreter(code[:x]+code[x+l:]) for _ in range(0,2000): interp2.move() print(len(interp2._stack)) count["memory"] += 1 except Exception as e: print(e) if str(e) == "pop from empty list": count["underflow"] += 1 else: count["invalid"] += 1 print(count) #don't judge me added to (a slightly modified version of) the official fish.py interpreter by the creator of ><>. Out of 152 possible sub-programs, 92 errored from invalid instructions, 18 from stack underflow, and 42 from running out of memory. Funny facts, the first version of this e"ooooo6-c0pAhtra had a couple of freak sub-programs that managed to use the put command to place a [ which would clear the stack, in place of the invalid instruction A. Also, "earth" is the only one of the phrases that will work with this method, because the first letter, e is a valid instruction in ><>. Otherwise the " command has to be placed at the front of the program, and a valid subprogram could be just " by itself. • There's probably some ><> interpreter that constantly leaks memory, which might simplify this. Feb 5 at 20:47 Ruby, 36 eval([(s="planet")[$>.write(s)^6]]) We assign s="planet", then write that string to STDOUT. This returns the number of characters written. We xor that with 6, so that if anything other than 6 characters were written, we'll get a nonzero integer. Then we slice into s with that index. Only the 0th character of s, "p", is a valid code string (a no-op). We pass that to eval, using the ([argument]) syntax which is equivalent to just (argument) except that it's not valid outside of a method call. Pristineness verified programmatically on Ruby 1.9.3 and 2.2 • Holy crap. This is amazing. Nov 23, 2015 at 16:37 • What happens if you remove the ? Dec 10, 2015 at 12:16 • Then you're passing an array to eval instead of a string, which is an ArgumentError. Dec 10, 2015 at 13:40 C#, 128118 101 bytes Thought of abusing the contiguous substring rule. The Code class h{static void Main()=>System.Console.Write(new char[1 #if!i 5]{'w','o','r','l','d' #endif });} Why It Works 1. class h and static void Main() are required. 2. Removing any of the chars in 'w','o','r','l','d' causes an error because the char array is initialized with length 15. 3. You can't remove the contents inside Main() without violating the contiguous character rule as parts are separated by preprocs. (See below) Before Golfing and Separation class h { static void Main() => System.Console.Write(new char[1 * 5]{'w','o','r','l','d'}); } Verified With https://ideone.com/wEdB54 EDIT: • Saved some bytes by using #if !x instead of #if x #else. • Used => func syntax. #if!x instead of #if !x. Credits to @JohnBot. • Due to => func syntax, extra preproc condition can be removed. • Hi helix! Do you think you could explain how and why your answer works a bit more? Nov 10, 2015 at 7:12 • @isaacg Edited. Proof to follow. Nov 10, 2015 at 7:33 • I can't get it to run without static on Main. Nov 10, 2015 at 12:54 • @Johnbot Yeah. Must've miscopied. Fixed. Nov 10, 2015 at 13:09 • You can save a character by making Main an Expression-bodied function member and 2 more by removing the spaces before the preprocessor condition: class h{static void Main()=>System.Console.Write(new char[1\n#if!l\n5]{'w','o','r','l','d'\n#if!o\n});\n#endif\n}\n#endif. That's 115 by my count. Nov 10, 2015 at 13:20 MATLAB, 3736 33 bytes feval(@disp,reshape('world',1,5)) Since I am not sure if we are allowed to also output ans=, I had to find some work-around to output in a proper way. Using fprintf by itself did not work, because no matter what I tried it simply refused to error. Using disp by itself was not an option, as it would only take 1 argument and that argument itself obviously would also execute without errors. If it's no problem to also include ans= in the output, then MATLAB can be done with 20 bytes: reshape('world',1,5) • i really must learn more about built-in functions (+1) // btw your program is scored 20 Nov 11, 2015 at 13:51 • That really depends on how strict the rules are. They state that only 'world' (+ optional trailing newline) should be printed, so then it's 33 bytes. Nov 11, 2015 at 15:38 • Yeah, we'll count this as 33. Thanks for understanding :) Nov 11, 2015 at 15:40 Ruby, 34 eval([($>.write("world")-1).chr]) This has a few components: eval([ expr ]) is borrowed from histocrat's answer, and is pristine as well as verifying the return value of expr is a valid ruby program that doesn't error. method(arr) is a ruby syntax that calls method with the values of arr as the arguments. The reason this is needed here is because it is only valid as parameters for a method, so that if eval is removed, ([expr]) is a syntax error. If expr is removed, eval complains about not having enough arguments $>.write("world")-1 cannot be mangled except for inside the string and the subtraction. $>.write("world") writes "world" to STDOUT and returns the number of characters written, then subtracts 1. Therefor if the program is un-mangled the value will be exactly 4. If it is mangled (either the -1 is removed or the string shortened) then it will return one of -1,0,1,2,3, or 5. Any other mangling results in a syntax error. Calling chr on a number returns the character represented by that number. So, when called on the result of the above example, it errors on -1, and returns a single-character string otherwise. I'm not actually sure why this is, but it seems that ruby interprets \x04 as a whitespace character, which means the expression is valid (empty ruby programs do nothing). However, any of the other characters (\x00 - \x03 and \x05) result in Invalid char '\x01' in expression. I found this by simply iterating over possible math I could do to the number returned. Previously I had used $>.write("planet ")16 where "planet" plus a newline was 7 chars, times 16 to get 112 for p, the only single-letter function in ruby defined by default. When given no arguments, it is effectively a no-op Honorable mention: $><<"%c"5%%w(w o r l d) is very close but not pristine. Removing "%c"5% results in no errors. Mini-explanation: $> is stdout, and << is a function being called on it. "%c"5 generates the format string "%c%c%c%c%c", which then then trys to be formatted (%) by an array: %w(w o r l d) which is a shorter version of ['w','o','r','l','d']. If there are too few or too many elements in the array such that it does not match the format string, an error is thown. The achilles heel is that "%c"5, and %w(w o r l d) can both exist independantly, and $><< only needs an argument of either. So there are a few different ways of mangling this program into non-erroring cousins. Validated using this: s = 'eval([($>.write("world")-1).chr])' puts s.size (1...s.length).each do \|len\| #how much to remove (0...len).each do \|i\| #where to remove from to_test = s.dup to_test.slice!(i,len) begin #Feels so backwards; I want it to error and I'm sad when it works. eval(to_test) puts to_test puts "WORKED :(" exit rescue SyntaxError #Have to have a separate rescue since syntax errors #are not in the same category as most other errors #in ruby, and so are not caught by default with #a plain rescue rescue #this is good end end end • An explanation along the lines of histocrat's answer would be nice. It seems like you're using the same basic approach, but since I don't know Ruby, I can't understand the details. Nov 11, 2015 at 19:50 • @ThisSuitIsBlackNot Did my best, anything you don't understand? Nov 11, 2015 at 20:39 • Excellent explanation, thanks! Nov 11, 2015 at 20:53 Python 3, 43 bytes for[]in{5:[]}[open(1,"w").write("world")]:a Try it online! How it works To protect against substring deletions, we use open(1,"w").write instead of print. In Python 3, write returns the number of written characters, which we will verify is 5 to ensure that no part of the string was deleted. We do this by looking up the return value in the dictionary {5:[]}, and looping over the result with for[]in…:a, which will fail if we didn’t get an empty iterable or if the for statement is deleted. Perl 5.10+, 71 63 bytes (${open 0;@{\(read(0,$a,63)!=63?die:@_)};say"world"});{$a//die} Prints world with a trailing newline. Run like this: perl -M5.010 file This relies on the byte count of the source code, so file must contain the above code and nothing else (no shebang, no trailing newline). Perl 5.10+ is required for say and the defined-or operator //. It's incredibly difficult to make a pristine program with Perl, because: • Any bareword identifier (e.g. foo, a, _) is a valid statement with no strict 'subs'; (the default). This means the program can neither begin nor end with a letter, number, or underscore. • As tchrist explains, "Identifiers specified via symbolic dereferencing have absolutely no restriction whatsoever on their names." This means the program cannot begin with any of the sigils $, @, %, or , since removing all but the first and last character would always leave a valid variable name. • Many built-in functions (including most functions capable of producing output) work on $_ by default, so calls will often work even if you remove the argument (e.g. say"world" vs. say). How it works This solution was inspired by Naouak's Node.js answer, which checks its own length to make sure characters haven't been removed. The program has two sections, one inside parentheses and the other inside a block: (...);{...} The first section reads the source file and dies if it is less than 63 characters long. The second section checks that the read executed successfully. If either section is removed (with or without the enclosing parentheses or curly braces), the other section will throw an exception. Removing the middle or the left or right side of the program will unbalance the parentheses and/or curly braces, causing a syntax error. If the first die is altered (to d, e, di, de, or ie, which are all valid identifiers), the length check becomes: @{\(read(0,$a,63)!=63?di:@_)}; which evaluates to: @{\'di'}; This takes a reference to a string and tries to dereference it as an array, producing an error: Not an ARRAY reference If any other statement is altered, the length check will fail and the program will die. Verified pristine with the following program: #!/usr/bin/perl use strict; use warnings; use 5.010; use File::Temp; use List::MoreUtils qw(uniq); sub delete_substr { my ($str, $offset,$len) = @_; my $tmp =$str; substr($tmp,$offset, $len) = ''; return$tmp; } sub generate_subprograms { my ($source) = @_; my$tot_len = length $source; my @subprograms; foreach my$len (1 .. $tot_len - 1) { foreach my$offset (0 .. $tot_len -$len) { push @subprograms, delete_substr($source,$offset, $len); } } return uniq @subprograms; } chomp(my$source = <DATA>); my $temp = File::Temp->new; foreach my$subprogram ( generate_subprograms($source) ) { print$temp $subprogram; my$ret = system(qq{/usr/bin/perl -M5.010 $temp > /dev/null 2>&1}); say($subprogram), last if $ret == 0; truncate$temp, 0; seek $temp, 0, 0; } __DATA__ (${open 0;@{\(read(0,$a,63)!=63?die:@_)};say"world"});{$a//die} Ruby + coreutils, 3327 26 bytes base#{$>.write"world "}4 Try it online! Backticks in ruby execute the command inside them and return whatever the program put into STDOUT as a string. The #{expr} syntax allows embedding of expressions in strings and backticks. This program could be rewritten (non-pristinely) as: system("base" + (STDOUT.write("world\n")).to_s + "4") IO#write returns the number of bytes written, so if the string is shortened then it won't be the right number. #{} embedding automatically makes the number into a string. If some piece is removed, and it doesn't result in a syntax error, the wrong command will be run. If part of "world" is removed than one of base04 through base54 will try to run. The newline, whether in or out of the string, is required. Otherwise the first 5 characters(base) can be removed, making the whole line a comment. Also there must be one or more characters between the first backtick and #, otherwise the { can get removed to make the whole thing a shell comment. exec([(s="ec%co earth")%s[10]]) exec Replaces the current ruby process with the command specified. See my other answer for an explanation of the meth([]) syntax and the neccesity of it. (s="ec%co earth") assigns the string "ec%co earth" to the variable s. Assignments return what was assigned, so the string is also returned. "format string %d" % 5 is syntactic sugar for sprintf("format string %d",5), however spaces around the % are not neccesary. s[10] gets the character in the string at index 10. When un-mangled, this character is "h", the last letter in the string. However, removing any characters in the string means the string is shorter, so there is no character at index 10, so s[10] returns nil, and "%c" % nil causes an error. if %s[10] is removed, then ruby tries to run the command ec%co earth which doesn't work. Changing 10 to 1 or 0 also results in an unknown command (either eceo or ecco). Removing it entirely is technically not a syntax error since it calls the method #[] on the string, but then it complains about not enough arguments. A note on solving this in general: You must have some wrapper that verifies the code inside in an abstract sense while being pristine itself. For example, a program with division at the end (blablabla/somevar) will never work because a division can always be removed(blablabla). These are some such wrappers I've used so far: • eval([ code ]) used by histocrat and in my first answer. Validates that the output is a valid ruby program • exec([ code ]) used above, validates that the response is a valid command • #{ code } The backtick syntax also runs a command (and therefor validates that it's a valid one), however STDOUT is captured as a string instead of being output as the parent process' (Ruby's) STDOUT. Due to this I was not able to use it for this answer, EDIT: I made it work. Limitations outlined above. Edit: Thanks to @histocrat for pointing out some flaws • Cool approach! You can (and therefore must) remove the space between write and the start of the string, but I don't think that affects pristineness. Also, on my machine base64 will hang waiting for input, which might be against the rules. Jul 13, 2017 at 13:11 • @histocrat Wow, I'm suprised that $>.write"world" works, thanks! As for base64 waiting for input, it seems to vary by system. TIO works fine. That makes it even more fuzzy as to whether it follows the rules. Jul 13, 2017 at 21:39 Javascript(Node.js), 93 95 bytes if(l=arguments.callee.toString().length,l!=158)throw l;console.log("world");if(g=l!=158)throw g Check it's own size twice so if any chars is missing an error is thrown. The length is 156 because Node.js prepends function (exports, require, module, __filename, __dirname) { to the code on runtime. Thanks Martin Büttner for pointing out an error. Fixed now. C (gcc) (Linux,-Werror=undef), 66 bytes main(a){a = 1 / (puts("world")/ 6); #if(7^__LINE__) #else } #endif Try it online! Great challenge! This was deceptively hard, but I'm pretty sure I have a valid program now! Uses a preprocessor command so that no newlines can be removed, since the closing bracket to main is included only if __LINE__==6. It also keeps you from just clearing out main entirely, since that leaves #endif floating (so it is important that #endif is outside of main). I used #else because I've become fairly convinced there's no version of __LINE__==6 that can't have a substring removed and still be true, since both 6 and __LINE__ by themselves are truthy. It also uses -Werror=undef so that something like #ifdef(LINE__) doesn't evaluate to false, but is an error. With gcc (on Linux, at least), puts returns the number of characters printed (including the trailing newline), so removing any part of the string makes puts("...")/6 return 0, so that 1/0 causes a floating point exception. Note that this exception isn't caused unless 1/0 is assigned to something, so the a= is required. No other part of any line can be removed without creating an error, usually a syntax error or a linking error. As a bonus, this gives an 86 byte solution for C++ pretty trivially, just add #include <cstdio> and declare a as an int. Try it online! (C++) • Unless I am mistaken, you can remove 1/ while leaving the newline and it will still run. Jul 6, 2018 at 9:07 • @gastropner Right you are. 1 was supposed on the previous line I believe. Jul 6, 2018 at 9:27 • Sadly, the same thing holds. You can then remove =1. I think you need to put the 1 on a line on its own. Jul 6, 2018 at 9:32 • @gastropner I think you're right. I'll look more later. Thanks! Jul 6, 2018 at 9:40 PowerShell, (97 bytes + 5 for program name) = 102 Bytes "$(try{if(($a=(gc .\c.ps1).Length)-eq97){"world";a}}catch{if($a-ne97){a}$error.clear();exit}a)";a Checks itself before it wrecks itself ... twice. Expects to be saved as c.ps1 and executed from the local directory as such: PS C:\Tools\Scripts\Golfing\> .\c.ps1. The alias gc is short for Get-Content and is similar-ish to a cat reading a file (in this case, our execution path .\c.ps1). We get the .Length of the file, set it to $a, and check whether it's not equal to 97 with -eq97. If it is equal (i.e., the program has not been modified), we print with "world", and execute invalid command a. This forces the catch to take effect, which allows us to check ourselves again. This time, if our code is not equal to 97, we throw an invalid command so our program has errored and printed error text to the output. We then clear() the error and exit normally. It's obvious that if either if statement is tampered with, the other will have an error. If any portion of "world"; is tampered with, the first if will cause an error. Since it has to be contiguous, we can't remove both if statements. Strings in the middle will result in mismatched parentheses, or will result in the second {a} getting executed. The try/catch is to catch the error from the first if statement so we can properly clear it. The outer "$( )" prevent strings from either end getting snipped. The final ;a is to prevent portions of the middle getting snipped that would result in valid programs (e.g., "it}a)";a, which will print it}a) and then error). There are several special circumstances: • If the gc, gc<space> or gc .\ are removed, the program will eventually error out with some flavor of an out of memory error (due to repeated self-execution calls) and likely crash the shell (and maybe the computer). Not tested. • If the <space>.\c.ps1 or .\c.ps1 are removed, the program will stop and prompt for user input. No matter what the user enters, the program will still error since the size counts will be wrong. • If a substring starting at the $ and ending before the last " is snipped, the program will output whatever remains and then error because a is not valid. Verified with the following: $x='"$(try{if(($a=(gc .\c.ps1).Length)-eq97){"world";a}}catch{if($a-ne97){a}$error.clear();exit}a)";a' $yy='"$(try{if(($a=( .\c.ps1).Length)-eq97){"world";a}}catch{if($a-ne97){a}$error.clear();exit}a)";a'$yyy='"$(try{if(($a=(.\c.ps1).Length)-eq97){"world";a}}catch{if($a-ne97){a}$error.clear();exit}a)";a' $yyyy='"$(try{if(($a=(c.ps1).Length)-eq97){"world";a}}catch{if($a-ne97){a}$error.clear();exit}a)";a' for($i=1;$i-lt$x.Length;$i++){ for($j=0;$j-lt($x.Length-$i);$j++){ $y=($x[0..$j]+$x[($i+$j+1)..$x.Length])-join''$y>.\c.ps1 $error.clear() if(!($y-in($yy,$yyy,$yyyy))){try{.\c.ps1}catch{};if(!($error)){exit}} $q++; write-host -n "." if(!($q%150)){""} } } "No success." (Thanks to Martin for his extensive assistance!) PHP, 73 bytes <?=call_user_func(($p='ns')\|(($f="u{$p}erialize"))?$f:'','s:5:"world"'); Explination I assume the default php.ini configuration. So short_tags is disabled. This means you can't remove the = from the opening tag. This is basically <?=unserialize('s:5:"world"');. If you remove any part of the serialized string you'll get an error. You can simply remove unserialize and the script will just output the serialized string. To overcome this I use call_user_func. Removing one of the params will result in an error. '<?=call_user_func('unserialize','s:5:"world"'); However you can remove un, to call the serialize function. So we take out 'ns. Removing any characters would no result in an incorrect function name. <?=call_user_func(($p='ns')&&($f="u{$p}erialize")?$f:'','s:5:"world"'); We'll use an inline if to using variable assignment with the output tag. Instead of using && we use '\|' to prevent removing a single & or removing the $f assignment You could remove ='ns')&&($f="u{$p}erialize" and end up with ($p)?$f:''. Therefor I add extra parenthesis around $f="u{\$p}erialize". Note Technically you can remove the opening tags without producing an error. This is than however no longer a PHP script but just a plain text file. • About your last note, the plain text file would still be a valid PHP program, right? So I'm not sure this is valid. Nov 11, 2015 at 5:54 • It's no longer PHP, but plaintext/html, thus not a valid-php-program anymore Nov 11, 2015 at 11:17 A Pear Tree, 17 bytes This program contains bytes with the high bit set (that aren't valid UTF-8 and thus can't be posted on TIO), so here's an xxd reversible hexdump: 00000000: 7072 696e 7427 776f 726c 6427 23cd 4290 print'world'#.B. 00000010: bf . Explanation This is just print'world' with a checksum appended. I've verified by brute force that none of the possible deletions give a program with a valid checksum, so you get an error after any possible deletion. Fairly boring, but ties the current leader, so I felt it was worth posting. Matlab(77) bsxfun(@(c,b)arrayfun(@(x)getfield(c,{x}),conv(b,ismember(4,b))),'world',1:5) try it Note: Following @Optimiser's advice of designing a CPR or something, I was faced to unforeseen substring which didnt lead to any compilation error when removed, example: removing arrayfun(@(x)a(x),prod(b,ismember(4,1:5))), from this previous edit feval(@(a)arrayfun(@(x)a(x),prod(b,ismember(4,1:5))),'world') doesnt generate any bug! also, for recent same edition, there were bsxfun(@(a,b)arrayfun(@(x)(x),prod(b,ismember(4,b))),'world',1:5) and bsxfun(@(a,b)a,'world',1:5),if you asked about how was I when finding them out in my output console, I cried like a baby, so here is the program: b=0;string='bsxfun(@(c,b)arrayfun(@(x)getfield(c,{x}),conv(b,ismember(4,b))),''world'',1:5)' for u=1:numel(string),for j=u:numel(string)-2,try a=eval([string(1:u) string(j+2:end)]);catch(b); a=0;end; if a~=0, ['here is it : ' string(1:u) string(j+2:end)],end;end;end An example of a nonpristine program edit: Thanks to everyone beside @Martin for pointing my previous code's (not-errors) out . SmileBASIC, 63 bytes REPEAT A=1/(PRGSIZE(0,1)==63)?"world UNTIL 1/(PRGSIZE(0,1)==63) `	{"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": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33339035511016846, "perplexity": 3325.5407517874382}, "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-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00727.warc.gz"}
https://mathematica.stackexchange.com/questions/21856/solve-fx-0-for-x	# Solve f'[x]==0 for x I tried the following: f[x_] := x^n/(k + x^(2 n)); Solve[f'[x] == 0, x] But I got the following response: Solve::nsmet: This system cannot be solved with the methods available to Solve. >> Any suggestions? f[x_] := x^n/(k + x^(2 n)); Solve[Simplify[f'[x]] == 0, x] (* ==> {{x -> k^(1/(2 n))}} *) Using Reduce and limiting the domain (Reals) often produces more information: ClearAll[f,x,n,k] f[x_] := x^n/(k + x^(2 n)) sol = Reduce[f'[x] == 0, x, Reals]; The head of sol is Or; formatted to be more readable: List @@ sol // Column	{"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": 0.3388878405094147, "perplexity": 17797.509154043015}, "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-2020-10/segments/1581875145989.45/warc/CC-MAIN-20200224224431-20200225014431-00364.warc.gz"}