tag:blogger.com,1999:blog-73791109607960141702017-08-17T14:07:13.770-04:00Clueless FundatmaA random walk through a subset of things I care about. Science, math, computing, higher education, open source software, economics, food etc.Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.comBlogger697125tag:blogger.com,1999:blog-7379110960796014170.post-69677843180920213992017-08-15T12:49:00.002-04:002017-08-15T12:49:40.166-04:00Diffusion: A Historical Perspective<div dir="ltr" style="text-align: left;" trbidi="on">The paper (<a href="https://pdfs.semanticscholar.org/24c0/5e77599f7ec211b9c0bbf326138607889415.pdf">pdf</a>) "One and a half century of diffusion: Fick, Einstein, Before and Beyond" by Jean Philibert traces the history of diffusion phenomena.<br /><br />It starts with <a href="https://en.wikipedia.org/wiki/Thomas_Graham_(chemist)">Thomas Graham</a> (of dialysis fame) who perhaps made the first systematic observations, which were integrated into phenomenological law by German physiologist <a href="https://en.wikipedia.org/wiki/Adolf_Eugen_Fick">Adolf Fick</a> in 1855, at the age of 26.<br /><br />Fick observed the analogy between mass diffusion and heat conduction (now considered obvious), and piggy-backed on Fourier's law of conduction (1822). The paper cites the opening lines of Fick's work:<br /><blockquote class="tr_bq">A few years ago, Graham published an extensive investigation on the diffusion of salts in water, in which he more especially compared the diffusibility of different salts. It appears to me a matter of regret, however, that in such an exceedingly valuable and extensive investigation, the development of a fundamental law, for the operation of diffusion in a single element of space, was neglected, and I have therefore endeavoured to supply this omission.</blockquote>Next, the paper talks about the contributions of W. C. Roberts-Austen (an assistant to Thomas Graham, and successor as Master of the Mint) to quantification of diffusion in solids.<br /><br />In 1905, Einstein integrated Robert Brown's observations of random zig-zag trajectories and Fick's phenomenological laws, with the crucial observation that it was the mean-squared displacement, and not the mean displacement that was related to diffusion.<br /><br />Following Einstein's paper, the experimental work of Perrin was responsible helping the world accept the link between the microscopic (MSD is proportional to diffusivity and time) and macroscopic worlds (flux is proportional to concentration gradient).<br /><br />It is always interesting to look at the chronological development of (now familiar) ideas. These uncontroversial ideas were once strongly wrestled with. It took centuries for scientists to come up with a comprehensive understanding, and to develop interesting applications based off of it.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/RlwSUOuAfIg" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com2http://sachinashanbhag.blogspot.com/2017/08/diffusion-historical-perspective.htmltag:blogger.com,1999:blog-7379110960796014170.post-67709878068357351832017-08-12T14:30:00.000-04:002017-08-12T14:31:00.383-04:00Exam Question on Fitting Sums of Exponentials to Data<div dir="ltr" style="text-align: left;" trbidi="on">I wrote the question below for our PhD qualifiers. It addresses a problem I have been thinking about for over a decade now - starting from my time as a graduate student: how to fit a sum of decaying exponentials to data?<br /><br />The question explores a method called the <a href="https://en.wikipedia.org/wiki/Prony%27s_method">Prony</a> method. Here is the question:<br /><br />A classical problem in data analysis involves fitting a sum of exponentials to a time series of uniformly sampled observations. Here, let us suppose we are given N observations \((t_i, f_i)\), where \(t_i = i \Delta t\) for \(i = 0, 1, ..., N-1\).<br /><br />We want to fit the data to a sum of two exponentials. The <b>model equation</b> is, \[\hat{f}(t) = a_1 e^{b_1 t} + a_2 e^{b_2 t}.\] The general nonlinear regression problem to determine \(\{a_j, b_j\}\) becomes difficult as the number of exponentials in the sum increases. A number of quasi-linear methods have been developed to address this. In the question, we will explore one of these methods, and determine the fitting parameters.<br /><div><br />(a) First, generate a synthetic dataset \((t_i, f_i)\) with true \(a_1^* = a_2^* = 1.0\), \(b_1^* = -2.0\), \(b_2^* = -0.2\). Use \(t_0 = 0\), \(\Delta t = 1\), and N = 20. Attach a plot of the synthetic dataset. Use this dataset for numerical calculations below.<br /><br />(b) If \(b_1\) and \(b_2\) are known, then we can determine \(a_1\) and \(a_2\) by linear least squares. Set \(u_1 = e^{b_1 \Delta t}\) and \(u_2 = e^{b_2 \Delta t}\). Recognize that \(e^{b_i t_j} = e^{b_i j \Delta t} = u_i^j\). Hence from the model eqn, we can get a <b>linear system</b>:<br />\begin{align}<br />f_0 & = a_1 u_1^0 + a_2 u_2^0 \nonumber\\<br />f_1 & = a_1 u_1^1 + a_2 u_2^1 \nonumber\\<br />\vdots & = \vdots \nonumber\\<br />f_{N-1} & = a_1 u_1^{N-1} + a_2 u_2^{N-1}<br />\end{align}<br />Write a program to determine \(a_1\) and \(a_2\), given the data, \(b_1\) and \(b_2\).<br /><br />(c) Consider the polynomial \(p(z)\), which has \(u_1\) and \(u_2\) as its roots, \(p(z) = (z-u_1)(z-u_2) = z^2 - d_1 z -d_2 = 0\). Express \(u_1\) and \(u_2\) in terms of \(d_1\) and \(d_2\).<br /><br />(d) Now we seek to take linear combinations equations in the linear system above with the goal of eliminating \(a_j\). For example, consider the first three equations. If we multiply the first eqn by \(d_2\), the next by \(d_1\), and the third by -1 and sum them up.<br />\begin{align*}<br />d_2 f_0 & = a_1 d_2 + a_2 d_2\\<br />d_1 f_1 & = a_1 u_1 d_1 + a_2 u_2 d_1 \\<br />-1 f_2 & = -a_1 u_1^2 - a_2 u_2^2.<br />\end{align*}<br />We get \(-F_2 +d_1 F_1 + d_2 F_0 = -a_1(u_1^2 - d_1 u_1 - d_2) -\) \( a_2(u_2^2 -d_1 u_2 - d_2) = 0\), since \(p(u_i) = 0\).</div><div><br />We can pick the next set of three equations, and repeat the process (multiply by \(d_2\), \(d_1\), and -1 before summing up). Show that we end up with the following linear system:<br />\[\begin{bmatrix} f_{1} & f_0 \\ f_2 & f_1 \\ <br />\vdots & \vdots \\<br />f_{N-2} & f_{N-3} \\<br />\end{bmatrix} \begin{bmatrix} d_1 \\ d_2 \end{bmatrix} = \begin{bmatrix} f_2 \\ f_{3} \\ \vdots \\ f_{N-1} \end{bmatrix}\]<br />Determine \(d_1\) and \(d_2\), and hence \(u_1\) and \(u_2\). From this, find the estimated \(b_1\) and \(b_2\).<br /><br />(e) Once you know \(b_1\) and \(b_2\) find \(a_1\) and \(a_2\) by linear least squares solution of linear system.<br /><br /></div></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/tTNGdIInFrM" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/08/exam-question-on-fitting-sums-of.htmltag:blogger.com,1999:blog-7379110960796014170.post-10001900818720983522017-08-09T16:35:00.000-04:002017-08-09T23:05:02.175-04:00Complex Numbers<div dir="ltr" style="text-align: left;" trbidi="on">1. What really are <a href="http://robjlow.blogspot.com/2017/06/what-is-this-thing-called-i.html?m=1">complex numbers</a>?<br /><br />2. The joy of <a href="https://mathwithbaddrawings.com/2017/05/17/the-joy-of-slightly-fishy-proofs/">slightly fishy proofs</a>.<br /><br />3. This <a href="https://math.stackexchange.com/questions/4961/interesting-results-easily-achieved-using-complex-numbers">discussion</a> on MathOverflow</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/DWrFECnrRo4" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com1http://sachinashanbhag.blogspot.com/2017/08/complex-numbers.htmltag:blogger.com,1999:blog-7379110960796014170.post-24432746365791598692017-08-02T15:52:00.000-04:002017-08-02T15:52:04.594-04:00NumPy and Matlab<div dir="ltr" style="text-align: left;" trbidi="on">This post bookmarks two sites that provide handy cheat sheets of numpy equivalents for Matlab/Octave commands.<br /><br />The ones for linear algebra are particularly handy, because that is one subdomain where Matlab's notation is more natural.<br /><br />1. Numpy for Matlab users (<a href="http://mathesaurus.sourceforge.net/matlab-numpy.html">Mathesaurus</a>)<br /><br />2. Cheatsheets for Numpy, Matlab, and Julia (<a href="https://cheatsheets.quantecon.org/">quantecon</a>)</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/vcft0PJS-hs" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/08/numpy-and-matlab.htmltag:blogger.com,1999:blog-7379110960796014170.post-49677357244099734842017-07-28T21:19:00.000-04:002017-07-24T08:59:15.425-04:00Interesting Scaling Laws<div dir="ltr" style="text-align: left;" trbidi="on">I recently read Geoffrey West's book "<a href="https://www.amazon.com/Scale-Universal-Innovation-Sustainability-Organisms/dp/1594205582">Scale</a>", and thought it was really great. Here are some resources to prime you for the subject.<br /><br />1. <a href="https://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations">TED Talk</a><br /><br />2. Talk <a href="https://www.youtube.com/watch?v=GoHD1ROPiUc">@ Google</a><br /><br />3. Essay at the <a href="https://www.edge.org/conversation/geoffrey_west-why-cities-keep-growing-corporations-and-people-always-die-and-life-gets">Edge</a><br /><br />4. Essay on <a href="https://medium.com/sfi-30-foundations-frontiers/scaling-the-surprising-mathematics-of-life-and-civilization-49ee18640a8">Medium</a></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/vZqgD0Jj11I" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/interesting-scaling-laws.htmltag:blogger.com,1999:blog-7379110960796014170.post-41031123725894969792017-07-25T10:44:00.000-04:002017-07-25T10:44:00.167-04:00Russell's paradox<div dir="ltr" style="text-align: left;" trbidi="on"><div class="tr_bq">I came across this interesting paradox on a recent podcast. According to <a href="https://en.wikipedia.org/wiki/Russell%27s_paradox">wikipedia</a>:</div><blockquote>According to naive set theory, any definable collection is a set. Let ''R'' be the set of <b>all</b> sets that are not members of themselves. If ''R'' is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves. This contradiction is Russell's paradox. </blockquote><blockquote>Symbolically:<br />\[\text{Let } R = \{ x \mid x \not \in x \} \text{, then } R \in R \iff R \not \in R\]</blockquote>There is a nice commentary on the paradox in <a href="https://www.scientificamerican.com/article/what-is-russells-paradox/">SciAm</a>, and a superb entry on the <a href="https://plato.stanford.edu/entries/russell-paradox/">Stanford Encyclopedia of Philosophy</a></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/y5s1tE1Vc8o" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/07/russells-paradox.htmltag:blogger.com,1999:blog-7379110960796014170.post-38426202088200803172017-07-19T10:48:00.000-04:002017-07-19T10:48:20.013-04:00Questions Kids Ask<div dir="ltr" style="text-align: left;" trbidi="on">Between my curious 4- and 8-year olds, I got asked the following questions in the past month.<br /><br />I found all of them fascinating.<br /><br />1. Why are our front milk teeth (incisors) the first to fall out?<br />2. Why is "infinity minus infinity" not equal to zero?<br />3. Why don't you get a rainbow when you shine a flashlight on rain in the night?<br />4. How are Cheerios and donuts made (into tori)?<br />5. His, hers, ours, yours. Then why not "mines"?<br /><br />PS: I also learned from my 4-year old that <a href="http://spiders.ucr.edu/daddylonglegs.html">daddy long legs aren't really spiders</a> and don't spin webs, and that <a href="https://www.google.com/search?q=sea+turtles+jellyfish&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiPobTbg47VAhVEOSYKHckgB9kQ_AUICigB&biw=1920&bih=963">sea turtles feed on jellyfish</a>.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/ecIMR2JPj8g" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/07/questions-kids-ask.htmltag:blogger.com,1999:blog-7379110960796014170.post-73248781229028323952017-07-16T10:37:00.000-04:002017-07-16T10:37:02.284-04:00Matplotlib: Subplots, Inset Plots, and Twin Y-axes<div dir="ltr" style="text-align: left;" trbidi="on">This <a href="https://gist.github.com/shane5ul/9e8dbade9f9f9f4de5c8b00a41b53f20">jupyter notebook</a> highlights ways in which matplotlib gives you control over the layout of your charts. This is intended as a personal cheatsheet.<br /><div><br /></div><script src="https://gist.github.com/shane5ul/9e8dbade9f9f9f4de5c8b00a41b53f20.js"></script> <br /><div><br /></div></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/ibswlrsV8fY" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com1http://sachinashanbhag.blogspot.com/2017/07/matplotlib-subplots-inset-plots-and.htmltag:blogger.com,1999:blog-7379110960796014170.post-84514712745093005092017-07-07T16:34:00.002-04:002017-07-07T16:34:16.832-04:00John Roberts Commencement Speech<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: left;">This part of the address is really nice and timeless.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/pavcM8VGtX0/0.jpg" src="https://www.youtube.com/embed/pavcM8VGtX0?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div><br />The transcript of the full speech is available <a href="http://time.com/4845150/chief-justice-john-roberts-commencement-speech-transcript/">here</a>.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/7spx4ii8BcI" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/07/john-roberts-commencement-speech.htmltag:blogger.com,1999:blog-7379110960796014170.post-84717300133956368502017-07-05T16:20:00.001-04:002017-07-05T16:20:07.674-04:00Joints from Marginals: Compilation<div dir="ltr" style="text-align: left;" trbidi="on">For convenience, here is a link to the three blogs in this series in one place.<div><br /></div><div>1. A <a href="https://sachinashanbhag.blogspot.com/2017/06/joint-distribution-from-marginals.html">technique</a> for solving the problem in a special case</div><div><br /></div><div>2. The <a href="https://sachinashanbhag.blogspot.com/2017/06/joint-from-marginals-why.html">reason</a> this technique works</div><div><br /></div><div>3. The <a href="https://sachinashanbhag.blogspot.com/2017/07/joint-from-marginals-non-gaussian.html">corners/edges</a> of this technique, or how it fails for non-Gaussian marginals</div></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/kek9wb_HrT4" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/07/joints-from-marginals-compilation.htmltag:blogger.com,1999:blog-7379110960796014170.post-50122949468697229432017-07-02T09:32:00.001-04:002017-07-02T09:32:09.644-04:00Joint from Marginals: non-Gaussian Marginals<div dir="ltr" style="text-align: left;" trbidi="on">In a <a href="http://sachinashanbhag.blogspot.com/2017/06/joint-from-marginals-why.html">previous</a> post, I asked the question if the method described here can be used with non-Gaussian distributions.<br /><br />Let us explore that by considering two independent zero mean, unit variance distributions that are not Gaussian. Let us sample \(x_1\) from a <a href="https://en.wikipedia.org/wiki/Triangular_distribution">triangular distribution</a>, and \(x_2\) from a <a href="https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)">uniform distribution</a>.<br /><br />We consider a triangular distribution with zero mean and unit variance, which is symmetric about zero (spans -sqrt(6) to +sqrt(6)). Similarly, we consider a symmetric uniform distribution, which spans -sqrt(3) to +sqrt(3).<br /><br />Samples from these independent random variables are shown below.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-pNLDuhtXQ5Q/WRyrwnETwYI/AAAAAAAADCM/pUpMWJIS4Lk-lt8_NU8mW6-v-H2pPpd3gCLcB/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-pNLDuhtXQ5Q/WRyrwnETwYI/AAAAAAAADCM/pUpMWJIS4Lk-lt8_NU8mW6-v-H2pPpd3gCLcB/s400/1.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">When we use a correlation coefficient of 0.2, and use the previous recipe, we get correlated random variables with zero mean and the same covariance matrix, but ...</div><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/--bINPDVldFQ/WRysK_14TvI/AAAAAAAADCQ/eaKLJTfyNxkH5_QBSP3sfULOUPgnsa91gCLcB/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/--bINPDVldFQ/WRysK_14TvI/AAAAAAAADCQ/eaKLJTfyNxkH5_QBSP3sfULOUPgnsa91gCLcB/s400/2.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">... the marginals are not exactly the same!</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">This is evident when we increase the correlation coefficient to say 0.5.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-4dm9JM45UO4/WRysg793OmI/AAAAAAAADCU/8jZMoOYiNs0jLXr8g7nQYdpAC5lZYnRzACLcB/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://2.bp.blogspot.com/-4dm9JM45UO4/WRysg793OmI/AAAAAAAADCU/8jZMoOYiNs0jLXr8g7nQYdpAC5lZYnRzACLcB/s400/2.png" width="400" /></a></div><div class="separator" style="clear: both; text-align: left;">The sharp edges of the uniform distribution get smoothened out.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Did the method fail?</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Not really. If you paid attention, the method is designed to preserve the mean and the covariance matrix (which is does). It doesn't really guarantee the preservation of the marginal distributions. </div><br /></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/ya05YBWZAU0" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/07/joint-from-marginals-non-gaussian.htmltag:blogger.com,1999:blog-7379110960796014170.post-7025669095900254742017-06-28T12:38:00.000-04:002017-06-28T12:38:33.872-04:00Printing webpages as PDFs<div dir="ltr" style="text-align: left;" trbidi="on"><a href="https://www.printfriendly.com/">PrintFriendly and PDF</a> has a useful browser extension (tested on Chrome) that creates more readable PDFs from web content.<br /><br />Here is a screenshot (click to enlarge) from a Matlab blog that I follow:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-JKuxK6ID6fg/WRXjeSwHWaI/AAAAAAAADA0/URIxezSfYH88BbvoEDI-8ikSmhXCJF9MwCEw/s1600/Screenshot%2Bfrom%2B2017-05-12%2B12-25-09.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-JKuxK6ID6fg/WRXjeSwHWaI/AAAAAAAADA0/URIxezSfYH88BbvoEDI-8ikSmhXCJF9MwCEw/s400/Screenshot%2Bfrom%2B2017-05-12%2B12-25-09.png" width="400" /></a></div><br /><br /><div class="separator" style="clear: both; text-align: center;"></div>Notice that the webpage has lots of links, and a frame on the left.<br /><br />When I use the "Print to File" feature directly from my Chrome browser, I get a PDF which looks like this:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-6cvqkJ4aseg/WRXjhC5uYvI/AAAAAAAADBA/wvqXVdLx08kmeeJYCdGCC4_8PPUGCYMvwCEw/s1600/Screenshot%2Bfrom%2B2017-05-12%2B12-25-48.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="347" src="https://1.bp.blogspot.com/-6cvqkJ4aseg/WRXjhC5uYvI/AAAAAAAADBA/wvqXVdLx08kmeeJYCdGCC4_8PPUGCYMvwCEw/s400/Screenshot%2Bfrom%2B2017-05-12%2B12-25-48.png" width="400" /></a></div>It does the job, but it looks very amateurish. On more complicated websites, results can be horrendous.<br /><br />Here is the same webpage, now using PrintFriendly.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-CfnI9BC8rMk/WRXjrwdt01I/AAAAAAAADBA/7zEj50gbvO4KwYnK3ukdeSyHpY3pc5qLgCEw/s1600/Screenshot%2Bfrom%2B2017-05-12%2B12-26-57.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-CfnI9BC8rMk/WRXjrwdt01I/AAAAAAAADBA/7zEj50gbvO4KwYnK3ukdeSyHpY3pc5qLgCEw/s400/Screenshot%2Bfrom%2B2017-05-12%2B12-26-57.png" width="307" /></a></div>Notice that the PDF is much cleaner, is well formatted, and contains all the relevant information.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/xK-TqnptFVs" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/printing-webpages-as-pdfs.htmltag:blogger.com,1999:blog-7379110960796014170.post-83125201019034120102017-06-22T15:53:00.000-04:002017-06-22T15:53:20.650-04:00Joint from Marginals: Why?<div dir="ltr" style="text-align: left;" trbidi="on">In the <a href="http://sachinashanbhag.blogspot.com/2017/06/joint-distribution-from-marginals.html">previous</a> blog post, we saw a special example in which we were able to sample random variables from a joint 2D-Gaussian distribution from the marginals and the correlation coefficient.<br /><br />I listed a simple method, which seemed to work like magic. It had two simple steps:<br /><br /><ul style="text-align: left;"><li>Cholesky decomposition of the covariance matrix, C(Y)</li><li>Y = LX, where X are independent random variables</li></ul><br />The question is, why did the method work?<br /><br />Note that the covariance matrix of random variables with zero mean and unit standard deviation can be written as, \(C(Y) = E(Y Y')\), where \(E()\) denotes the expected value of a random variable. Thus, we can write the expected value of the Y generated by the method as, \[\begin{align*} E(Y Y') & = E\left(LX (LX)'\right)\\ & = L E(XX') L' \\ & = L I L'\\ & = LL' = C.\end{align*}.\] Here we used the fact that the covariance of X is an identity matrix by design.<br /><br />Note that this method preserves the covariance matrix (and hence the standard deviation of the marginals).<br /><br />Does it preserve the mean?<br /><br />Yes. \(E(Y) = E(LX) = L E(X) = 0.\)<br /><br />Do the marginals have to be normal for this method to work? Would this work for any distribution (with zero mean, and unit standard deviation)?<br /><br />We will explore this in a subsequent blog.<br /><br /></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/jIIUr8RAKio" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/joint-from-marginals-why.htmltag:blogger.com,1999:blog-7379110960796014170.post-75074865068231560232017-06-15T12:06:00.001-04:002017-06-15T12:06:48.930-04:00Joint Distribution From Marginals<div dir="ltr" style="text-align: left;" trbidi="on">Consider two dependent random variables, \(y_1\) and \(y_2\), with a correlation coefficient \(\rho\).<br /><br />Suppose you are given the marginal distributions \(\pi(y_1)\) and \(\pi(y_2)\) of the two random variables. Is it possible to construct the joint probability distribution \(\pi(y_1, y_2)\) from the marginals?<br /><div><br /></div>In general, the answer is no. There is no unique answer. The marginals are like shadows of a hill from two orthogonal angles. The shadows are not sufficient to specify the full 3D shape (joint distribution) of the hill.<br /><br />Let us simplify the problem a little, so that we can seek a solution.<br /><br />Let us assume \(y_1\) and \(y_2\) have zero mean and unit standard deviation. We can always generalize later by shifting (different mean) and scaling (different standard distribution). Let us also stack them into a single random vector \(Y = [y_1, y_2]\).<br /><br />The <a href="https://en.wikipedia.org/wiki/Covariance_matrix">covariance matrix</a> of two such random variables is given by, \[C(Y) = \begin{bmatrix} E(y_1 y_1) - \mu_1 \mu_1 & E(y_1 y_2) - \mu_1 \mu_2 \\ E(y_2 y_1) - \mu_2 \mu_1 & E(y_2 y_2) - \mu_2 \mu_2 \end{bmatrix} = \begin{bmatrix} 1 & \rho \\ \rho & 1 \end{bmatrix},\] where \(\mu\) and \(\sigma\) refer to the mean and standard deviation.<br /><div style="text-align: left;"><br /></div><div style="text-align: left;"><b>Method</b></div><br />A particular method for sampling from the joint distribution of correlated random variables \(Y\) begins by drawing samples of independent random variables \(X = [x_1, x_2]\) which have the same distribution as the desired marginal distributions.<br /><br />Note that the covariance matrix in this case is an identity matrix, because the correlation between independent variables is zero \(C(X) = I\).<br /><br />Now we recognize that the covariance matrix \(C(Y)\) is symmetric and positive definite. We can use Cholesky decomposition \(C(Y) = LL^T\) to find the lower triangular matrix \(L\).<br /><br />The recipe then says that we can draw the correlated random variables with the desired marginal distribution by simply setting \(Y = L X\).<br /><br /><b>Example</b><br /><b><br /></b>Suppose we seek two random variables whose marginals are normal distributions (zero mean, unit standard deviation) with a correlation coefficient 0.2.<br /><br />The method above asks us to start with independent random variables \(X\) such as those below.<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-yc6SE7nazqM/WRylDZ7nDOI/AAAAAAAADBw/bOsSEhSFXjgPTN0N5AgypQ0xWBO4aceqwCLcB/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://4.bp.blogspot.com/-yc6SE7nazqM/WRylDZ7nDOI/AAAAAAAADBw/bOsSEhSFXjgPTN0N5AgypQ0xWBO4aceqwCLcB/s400/1.png" width="400" /></a></div>Cholesky decomposition with \(\rho\) = 0.2, gives us, \[L = \begin{bmatrix} 1 & 0 \\ 0.1 & 0.9797 \end{bmatrix}.\] If we generate \(Y = LX\) using the same data-points used to create the scatterplot above, we get,<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://3.bp.blogspot.com/-MB0nLXdDD9s/WRymodTmzmI/AAAAAAAADB8/lEaz4NaCekE9h8AQ7iL8BtNHLzgfZeSdACLcB/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://3.bp.blogspot.com/-MB0nLXdDD9s/WRymodTmzmI/AAAAAAAADB8/lEaz4NaCekE9h8AQ7iL8BtNHLzgfZeSdACLcB/s400/2.png" width="400" /></a></div>It has the same marginal distribution, and a non-zero correlation coefficient as is visible from the figure above.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/qPNg-uk_RDM" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com1http://sachinashanbhag.blogspot.com/2017/06/joint-distribution-from-marginals.htmltag:blogger.com,1999:blog-7379110960796014170.post-74729544682312987222017-06-10T13:58:00.000-04:002017-06-10T13:58:05.094-04:00Links<div dir="ltr" style="text-align: left;" trbidi="on">1. "<a href="http://theconversation.com/the-seven-deadly-sins-of-statistical-misinterpretation-and-how-to-avoid-them-74306">The seven deadly sins of statistical misinterpretation, and how to avoid them</a>" (H/T FlowingData)<div><br /></div><div>2. Desirability Bias (<a href="http://theness.com/neurologicablog/index.php/confirmation-bias-vs-desirability-bias/">Neurologica</a>)</div><blockquote class="tr_bq">[...] defined confirmation bias as a bias toward a belief we already hold, while desirability bias is a bias toward a belief we want to be true.</blockquote>3. <a href="https://www.johndcook.com/blog/2017/05/24/students-future-teachers-past/">H/T</a> John D. Cook<br /><blockquote>“Teachers should prepare the student for the student’s future, not for the teacher’s past.” — Richard Hamming</blockquote> 4. This <a href="https://xkcd.com/1827/">xkcd</a> cartoon on survivorship bias</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/ZEjhGkaNBbc" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/links.htmltag:blogger.com,1999:blog-7379110960796014170.post-81528537143362805292017-06-08T13:29:00.000-04:002017-06-08T13:29:15.276-04:00Matplotlib Styles<div dir="ltr" style="text-align: left;" trbidi="on">I created a <a href="https://gist.github.com/shane5ul/50eda39e43b46d89a78d5ad9f60152c3">jupyter notebook</a> demonstrating the use of built-in or customized styles in matplotlib, mostly as a bookmark for myself.<br /><br /><script src="https://gist.github.com/shane5ul/50eda39e43b46d89a78d5ad9f60152c3.js"></script></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/K3ubVN2kUDY" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/matplotlib-styles.htmltag:blogger.com,1999:blog-7379110960796014170.post-7933141617926705422017-06-05T14:54:00.000-04:002017-06-05T14:54:22.981-04:00Jupyter Notebook Tricks<div dir="ltr" style="text-align: left;" trbidi="on">Some cool Jupyter <a href="https://www.dataquest.io/blog/jupyter-notebook-tips-tricks-shortcuts/">notebook tricks</a> from <a href="http://arogozhnikov.github.io/">Alex Rogozhnikov</a>. Here are some that I did not know:<br /><div style="text-align: left;"><ul><li>%run can execute python code from .py files and <b>also execute other jupyter notebooks</b>, which can quite useful. (this is different from %load which imports external python code</li><li>The %store command lets you pass variables between two different notebooks.</li><li>%%writefile magic saves the contents of that cell to an external file.</li><li>%pycat does the opposite, and shows you (in a popup) the syntax highlighted contents of an external file.</li><li>#19 on using different kernels in the same notebook, and #22 on writing fortran code inside the notebook</li></ul></div><div style="text-align: left;"><br /></div><div><br /></div><div><br /></div><div><br /></div></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/vXyVJBh6Y84" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/jupyter-notebook-tricks.htmltag:blogger.com,1999:blog-7379110960796014170.post-69231932106851554662017-06-01T09:19:00.002-04:002017-06-01T09:20:05.774-04:00Annotating PDFs on Linux<div dir="ltr" style="text-align: left;" trbidi="on">Most of my working day is spent reading.<br /><br />Usually, this means poring over some PDF document, and scribbling my thoughts - preferably on the PDF itself. I find these markups extremely helpful, when I want to recall the gist, or when it is time to synthesize "knowledge" from multiple sources.<br /><br />I use Linux on both my desktops (home and work), and the usual applications (Evince, Okular, etc.) for marking up PDFs are inadequate in one form or another. Adobe Reader, while bloated, used to do the job. But they don't release a Linux version anymore.<br /><br />The solution that best fits my needs currently is <a href="https://www.foxitsoftware.com/products/pdf-reader/">Foxit Reader</a>. Although you can't use the standard software manager (ex. apt-get on Ubuntu) to get it, you can easily download a 32- or 64-bit version from their website.<br /><br />The "installation guide" tells you how to do the rest [unzip, cd, and run the executable installer].<br /><br />On my Linux Mint systems it was easy, peasy!<br /><br />The software itself is intuitive. You can highlight, add text, stick in comments, and draw basic shapes. The changes you make are permanently saved into the PDF, so that when you use another application to reopen, the changes persist.<br /><br />It is cross-platform, so you can get a version on any OS (including iOS) you want.</div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/6irYR-K1h6g" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/06/annotating-pdfs-on-linux.htmltag:blogger.com,1999:blog-7379110960796014170.post-16535837701963922242017-05-25T17:01:00.000-04:002017-05-25T17:01:02.389-04:00PyCon 2017 Talks<div dir="ltr" style="text-align: left;" trbidi="on">Some interesting Python talks (links to YouTube videos) from this year's PyCon.<br /><br />1. Jake Vanderplas: <a href="https://www.youtube.com/watch?v=FytuB8nFHPQ&t=1742s">The Python Visualization Landscape</a><br /><br />2. Chistopher Fonnesbeck: <a href="https://www.youtube.com/watch?v=5TyvJ6jXHYE">PyMC3</a><br /><br />3. Eric Ma: <a href="https://www.youtube.com/watch?v=p1IB4zWq9C8">Bayesian analysis</a><br /><br />4. Alex Orlov: <a href="https://www.youtube.com/watch?v=_1MSX7V28Po">Cython</a><br /><br />5. Bret Cannon: <a href="https://www.youtube.com/watch?v=c2rEbbGLPQc">What new is python 3.6</a>?<br /><br /><br /><br /></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/kFFnmK6v4Vg" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/pycon-2017-talks.htmltag:blogger.com,1999:blog-7379110960796014170.post-35926699358348750402017-05-23T09:48:00.002-04:002017-05-23T09:48:36.052-04:00Scott Galloway's Advice to Graduates<div dir="ltr" style="text-align: left;" trbidi="on">Let me start with a confession: I love commencement ceremonies.<div><br /></div><div>It's not the elaborate regalia, the tradition, or the choreographed deference that appeal to me - although those do add to the theater.</div><div><br /></div><div>What I enjoy most is the commencement address, seeing heartfelt hugs between students and their mentors, and cheers from family members in the galleries.</div><div><br /></div><div>Like Disney movies, they fill me with hope and optimism.</div><div><br /></div><div>I came across this speech "<a href="https://www.l2inc.com/no-mercy-no-malice/commence">No Mercy, no Malice</a>" by Prof. Scott Galloway, which condenses so much practical wisdom. It is short; I recommend reading it in its entirety. Here's a snippet to entice you.</div><div><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-uCLjAZNSSFQ/WSQ9FDusSUI/AAAAAAAADDA/oGcRqWZToLYuaXy6awNUoyd0mhPuCtTIACLcB/s1600/NMNM-week-26-10.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="267" src="https://3.bp.blogspot.com/-uCLjAZNSSFQ/WSQ9FDusSUI/AAAAAAAADDA/oGcRqWZToLYuaXy6awNUoyd0mhPuCtTIACLcB/s320/NMNM-week-26-10.png" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">from <a href="https://www.l2inc.com/no-mercy-no-malice/commence">L2</a></td></tr></tbody></table></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/mxeHnRwp5W0" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/scott-galloways-advice-to-graduates.htmltag:blogger.com,1999:blog-7379110960796014170.post-15054691816353307592017-05-21T14:41:00.000-04:002017-05-21T14:41:02.488-04:00Quotes<div dir="ltr" style="text-align: left;" trbidi="on"><blockquote class="tr_bq">Everything that irritates us about others can lead us to an understanding of ourselves.</blockquote><div style="text-align: right;">Carl Jung</div><blockquote class="tr_bq">The value of a prototype is in the education it gives you, not in the code itself.</blockquote><div><div style="text-align: right;"><div style="text-align: right;">Alan Cooper</div><br /><div style="text-align: center;">Saving money is a non-socially-rewarded, non-observable, 1 player game. Spending money is a socially rewarded, observable, multiplayer game</div><div style="text-align: center;"><br /></div><div style="text-align: right;">Eric Jorgenson</div><br /><div style="text-align: center;">Academic life is 10% what happens to you, and 99% making it count for multiple sections on your CV.</div><div style="text-align: center;"><br /></div><div style="text-align: right;">Shit Academics Say</div><div style="text-align: right;"><br /></div><div style="text-align: center;">"Most papers in computer science describe how their author learned what someone else already knew."</div></div><div style="text-align: right;"><div style="text-align: right;">Peter Landin</div><div style="text-align: center;"><br /></div><div style="text-align: center;">"Do I not destroy my enemies when I make them my friends?"</div></div><div style="text-align: right;">Abraham Lincoln</div><div style="text-align: right;"><br /></div><div style="text-align: left;"><br /></div><div style="text-align: right;"><br /></div></div></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/BvvjorAiy1w" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/quotes.htmltag:blogger.com,1999:blog-7379110960796014170.post-84239141795685835252017-05-19T13:46:00.000-04:002017-05-19T13:46:07.781-04:00Smart Machines, Complexity, and 42<div dir="ltr" style="text-align: left;" trbidi="on"><div class="tr_bq">In Hitchhiker's Guide to the Galaxy, there is a poignant moment when a machine is asked the answer to the ultimate question of life, the universe, and everything.<br /><br />It crunches numbers for millions of years, and returns the baffling answer "<a href="https://en.wikipedia.org/wiki/Phrases_from_The_Hitchhiker%27s_Guide_to_the_Galaxy">42</a>".</div><br />The scenario that Douglas Adams concocted might be amusing, but given our increasing reliance on machines, it has ripples in today's world.<br /><br />Computers can often provide answers, without providing insight. For meaning-seeking humans, this can be deeply unsatisfying. Witness <a href="http://math.stackexchange.com/questions/632705/why-are-mathematical-proofs-that-rely-on-computers-controversial">the unease</a> surrounding computer-assisted proofs.<br /><br />Machine learning can help us deduce models to navigate complex systems. Neural network models might start with simple rules for learning. But the models they "learn" or end up with, are anything but simple.<br /><br />To keep things specific, consider programming a self-driving car. The model may start simple ("keep between the lanes"), but get hellishly complicated as numerous edge cases ("dog jumps into the road", "many people don't check their blind spot", "the night is foggy") are subsumed.<br /><br />Even if the car works reasonably well, how it responds to a "black swan" situation (one it has never seen before) might be anybody's guess.<br /><br />Practical models for complex systems might be insanely complicated.<br /><br />A <a href="http://rationallyspeakingpodcast.org/show/rs-167-samuel-arbesman-on-why-technology-is-becoming-too-com.html">recent "Rationally Speaking"</a> podcast touched upon many of these issues. In particular, I found the discussion of "physics thinking", which emphasizes universal models by ignoring details, and "biological thinking", which celebrates the diversity of phenomenon by focusing on details, incredibly fascinating. From the transcript:<br /><blockquote>The physics approach, you see it embodied maybe in like an Isaac Newton. A simple set of equations explains a whole host of phenomena. So you write some equations to explain gravity, and it can explain everything from the orbits, the planets, the nature of the tides, to how a baseball arcs when you throw it. It has this incredibly explanatory power. It might not explain every detail, but it maybe it could explain the vast majority of what's going on within a system. That's the physics. The physics thinking approach, abstracting away details, deals with some very powerful insights.</blockquote><blockquote>On the other hand, you have biological thinking. Which is the recognition that oftentimes in other types of systems, in certain types of systems, the details not only are fun and enjoyable to focus on, but they're also extremely important. They might even actually make up the majority of the kinds of behavior that the system can exhibit. Therefore, if you sweep away the details and you try to create this abstracted notion of the system, you're actually missing the majority of what is going on. The biological approach should be that you recognize the details are actually very important. And therefore they need to be focused on. </blockquote><blockquote>I think when we think about technologies both approaches are actually very powerful. But oftentimes I think people in their haste to understand technology, oftentimes because technologies are engineered things, we often think of them as perhaps being more the physics thinking side of the spectrum. When in fact, because they need to mirror the extreme messiness of the real world, or there's a lot of exceptions, or they've grown and evolved over time, often it's a very organic, almost biological fashion. They actually end up having a great deal of affinity with biological systems. And systems that are amenable to biological thinking and biology approaches.</blockquote></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/SPWfttn8KE4" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/smart-machines-complexity-and-42.htmltag:blogger.com,1999:blog-7379110960796014170.post-56533070176694097802017-05-16T15:52:00.000-04:002017-05-16T15:52:16.051-04:00Purdue-Kaplan: Is Disruption Knocking?<div dir="ltr" style="text-align: left;" trbidi="on">Last month Purdue University <a href="https://www.purdue.edu/newsroom/releases/2017/Q2/purdue-to-acquire-kaplan-university,-increase-access-for-millions.html">announced</a> they were going to acquire Kaplan University, an online for-profit institution. The <a href="http://www.purduenewu.org/">NewU</a> ...<br /><blockquote class="tr_bq">... will be distinct from others in the Purdue system, relying only on tuition and fundraising to cover operating expenses. No state appropriations will be utilized. It will operate primarily online, but has 15 locations across the United States, including an existing facility in Indianapolis, with potential for growth throughout the state. Indiana resident students will receive a yet-to-be-determined tuition discount.</blockquote>The deal has the potential to bring down tuition costs, enhance access, and provide Purdue's solid brand name. Here are some reactions to news:<br /><br />1. <a href="https://www.purdue.edu/newsroom/releases/2017/Q2/purdue-to-acquire-kaplan-university,-increase-access-for-millions.html">Purdue's official statement</a> is, of course, positive.<br /><blockquote class="tr_bq">Former U.S. Secretary of Education Arne Duncan said, “I’ve always had great respect for Gov. Daniels, and I’m excited by this opportunity for a world-class university to expand its reach and help educate adult learners by acquiring a strong for-profit college. This is a first, and if successful, could help create a new model for what it means to be a land-grant institution.”</blockquote>2. However, questions are being raised (<a href="http://www.npr.org/sections/ed/2017/05/04/526748160/a-public-university-acquires-a-big-for-profit-and-raises-big-questions">NPR</a>).<br /><blockquote class="tr_bq">The deal is eye-catching, but also part of a trend. Over the past decade dozens of nonprofit universities have contracted with private companies to expand their online offerings. For example, Arizona State University works with Pearson, and the University of Southern California with a company called 2U. Florida A&M and South Carolina State, both historically black institutions, have partnered with the University of Phoenix. In an atmosphere of ever-skinnier state budgets, these programs enable universities to reach a global market, cater to working adults, and potentially increase revenue without expensive capital investment. </blockquote>3. The faculty at Purdue is not happy (<a href="https://www.insidehighered.com/news/2017/05/05/purdue-faculty-votes-against-kaplan-process">InsideHigherEd</a>)<br /><blockquote class="tr_bq">No faculty input was sought before the acquisition decision was made, and no assessment of its impact on Purdue’s academic quality was completed, according to the resolution. The resolution proceeded to fault a lack of transparency and a lack of an impact study on how the acquisition will affect faculty, curriculum, students and staff at Purdue. The resolution also wondered what will happen to faculty governance and academic freedom at Purdue’s newly acquired university. And it said previously Purdue’s administration has gone through University Senate structures -- which include faculty input -- when pursuing program restructuring or creation.</blockquote>4. An <a href="https://www.edsurge.com/news/2017-05-16-why-donald-graham-sold-kaplan-university-to-purdue-for-1">interview</a> with the seller, Donald Graham, chairman of Graham Holdings.<br /><blockquote class="tr_bq"><br />[<b>Q:</b>] I see what Purdue gets from the arrangement—a jumpstart into providing online courses. But what does Graham Holdings get out of this deal? </blockquote><blockquote class="tr_bq"><b>Graham</b>: [...] You asked about when Graham Holdings shareholders might be rewarded. The only way we would be rewarded, the only way we would get a growing stream of revenue, would be if Purdue continued over the years to add students. In other words if the university became a big success under Purdue's leadership, we'll be part of that success. But we will not be a participant in any profits. We're out of the for-profit education business here. We will be paid for our services, and the profits if any will go to Purdue, and hopefully back into the whole educational system.</blockquote>5. Some older links to universities, MOOCs and online education<br /><br /><ul style="text-align: left;"><li><a href="http://sachinashanbhag.blogspot.com/2012/12/worlds-got-talent-devlin-on-moocs.html">Devlin on MOOCs</a></li><li><a href="http://sachinashanbhag.blogspot.com/2012/11/kling-on-online-education.html">Kling on online education</a></li><li><a href="http://sachinashanbhag.blogspot.com/2014/01/universities-vs-moocs.html">Universities versus MOOCs</a> </li></ul></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/ZG42UyohA4Q" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/purdue-kaplan-is-disruption-knocking.htmltag:blogger.com,1999:blog-7379110960796014170.post-5023979513962062732017-05-12T09:57:00.000-04:002017-05-12T09:57:08.596-04:00Computational Thinking Classes<div dir="ltr" style="text-align: left;" trbidi="on">Here is a collection of "Computational Thinking for non-majors" type of classes:<br /><br />1. My department's very <a href="https://people.sc.fsu.edu/~jburkardt/classes/ct_2016/ct_2016.html">own</a><br /><br />2. Another <a href="https://www.cs.hmc.edu/~hadas/IntroCourses.html">list</a> which links to classes from <a href="http://inst.eecs.berkeley.edu/~cs10/fa10/">Berkeley</a>, and <a href="https://www.cs.hmc.edu/twiki/bin/view/CS5">Harvey Mudd</a>.<br /><br />3. A self-study <a href="https://computationalthinkingcourse.withgoogle.com/">course package</a><br /><br />4. This essay by Stephen Wolfram on how to teach <a href="http://blog.stephenwolfram.com/2016/09/how-to-teach-computational-thinking/">computational thinking</a> </div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/q20yvO8bxFU" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/computational-thinking-classes.htmltag:blogger.com,1999:blog-7379110960796014170.post-36754428087100519222017-05-09T10:00:00.000-04:002017-05-09T10:00:51.291-04:00Wait But Why<div dir="ltr" style="text-align: left;" trbidi="on">I first came across Tim Urban, through his interview with Julia Galef. The interview was one of my favorite episodes of Rationally Speaking.<br /><br />His website "<a href="http://waitbutwhy.com/">Wait But Why</a>" is an amazing resource. It is well thought out, and provides historical, scientific, and philosophical context to many contemporary issues.<br /><br />Listen to this TED talk for a quick introduction.<br /><br /><div class="separator" style="clear: both; text-align: center;"><iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/arj7oStGLkU/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/arj7oStGLkU?feature=player_embedded" width="320"></iframe></div><br /></div><img src="http://feeds.feedburner.com/~r/CluelessFundatma/~4/m9j0GQrqSO0" height="1" width="1" alt=""/>Sachin Shanbhaghttps://plus.google.com/115150474038005608083noreply@blogger.com0http://sachinashanbhag.blogspot.com/2017/05/wait-but-why.html