# Flagging a Specific Variable Value

A recent question on a web forum, one I’ve seen asked elsewhere, was the following: in a mathematical programming model, how does one constrain a binary variable to take the value 1 if another variable takes a specific (predefined) value, and 0 otherwise? If the binary variable is , the other variable is , and …

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# Making Math Fun

I was a math major from undergrad to doctorate, so obviously I think math is fun. Equally obvious to me (especially after teaching a variety of mathematical topics to college students), not everyone shares that opinion, which is too bad. Recently, though, I came across an organization devoted to making math fun for small children, …

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# Analogies between Analogies

As reported by Stan Ulam in Adventures of a Mathematician: “A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between …

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# Gender differences in preferences, choices, and outcomes: SMPY longitudinal study

The recent SMPY paper below describes a group of mathematically gifted (top 1% ability) individuals who have been followed for 40 years. This is precisely the pool from which one would hope to draw STEM and technological leadership talent. There are 1037 men and 613 women in the study. The figures show significant gender …

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# On quantum measurement (Part 5: Quantum Venn diagrams)

Here’s what you missed, in case you have stumbled into this series midway. As you are wont to do, of course. Part 1 had me reminiscing about how I got interested in the quantum measurement problem, even though my Ph.D. was in theoretical nuclear physics, not “foundational” stuff, and introduced the incomparable Hans Bethe, who …

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# Linearize That!

For whatever reason, I’ve seen a bunch of questions posted on various fora boiling down to “How do I linearize <insert grossly nonlinear function>?” Whether by coincidence or due to some virtual viral epidemic, I’ve seen three or four in the past week that involved logarithms. So, without further ado, here is the quick solution: …

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# The Reciprocal Normal Distribution

A recent question on OR-Exchange dealt with the reciprocal normal distribution. Specifically, if k is a constant and X is a Gaussian random variable, the distribution of Y=k/X is reciprocal normal. The poster had questions about approximating the distribution of Y with a Gaussian (normal) distribution. This gave me a reason (excuse?) to tackle something …

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# Nifty papers I wrote that nobody knows about (Part 4: Complex Langevin equation)

This is the last installment of the “Nifty Papers” series. Here are the links to Part1, Part2, and Part 3. For those outside the computational physics community, the following words don’t mean anything: “The Sign Problem“ For those others that have encountered the problem, these words elicit terror. They stand for sleepless nights. They spell despair. They make grown men …

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# Happy Teacher’s Day (new ambigrams)

September 5 is Teacher’s Day in India. It is celebrated on the birthdate of Sarvepalli Radhakrishnan, Indian philosopher and statesman who was also the first Vice-President and the second President of India. He famously said, “teachers should be the best minds in the country.” To celebrate this day, here are three new ambigram designs (see image below). …

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# A Musical Random Walk

I just read a blog post here at MSU about The Infinite Jukebox, a web tool that will analyze a song (either one you upload or one from their library) and map out links between segments of the song that have approximately the same beat. You then see a visualization of the song as a …

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# Why math ed sucks (not just in India)

My friend Hartosh Bal (author of A Certain Ambiguity, a mathematical novel) has a piece in Caravan Magazine titled “Why Fields medalists are unlikely to emerge from the Indian educational system.” He mentions the fact that of the three winners of the Field’s medal (the highest accolade in mathematics) are Brazilian, Iranian and Canadian respectively. The …

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# Vijay Iyer, polymath & a fantastic example of trans-disciplinary creativity

Vijay Iyer,  (http://vijay-iyer.com/) is an Indian-American jazz pianist and composer. He is a MacArthur Genius grant winner and is currently Franklin and Florence Rosenblatt Professor of the Arts at Harvard University and is widely regarded as being one of the most innovative composers and musicians today. His music transcends national boundaries through creatively bringing together traditional …

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# Self-similarity in math & ambigrams, article 3 in series

Self-similarity in geometry is the idea of repeating a similar shape (often at a different scale) over and over again. In other words, a self-similar image contains copies of itself at smaller and smaller scales, such as the image below of the word “zoom.” Self-similarity is a rich mathematical idea and connects to other powerful concepts such …

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# Fewer Zeros

A question I saw online not too long ago caused me a flashback to my days teaching linear programming (LP) to masters students. The poster had developed an optimization model — I can’t recall if it was an LP, a quadratic program (QP) or a mixed-integer program (MIP) — and had no problem solving it. …

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# On quantum measurement (Part 4: Born’s rule)

Let me briefly recap parts 1-3 for those of you who like to jump into the middle of a series, convinced that they’ll get the hang of it anyway. You might, but a recap is nice anyway. Remember these posts use MathJax to render equations. Your browser can handle this, so if you see a bunch …

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# HKUST IAS

I have a new candidate for coolest research institute architecture. HKUST’s Institute for Advanced Study is housed in an amazing building with a view of Clearwater Bay in HK. The members of the institute will be mostly theoretical physicists and mathematicians :-) Stiff competition from Benasque’s Center and the Perimeter Institute, however. Also Caltech’s IQIM! …

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# On quantum measurement (Part 3: No cloning allowed)

In the previous two parts, I told you how I became interested in the quantum measurement problem (Part I), and provided a bit of historical background (Part 2). Now we’ll get to the heart of the matter. Note that I’m using MathJax to display equations in this blog. If your browser shows a bunch of dollar …

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# On quantum measurement (Part 2: Some history, and John von Neumann is confused)

This is Part 2 of the “On quantum measurement” series. Part 1: (Hans Bethe, the oracle) is here. Before we begin in earnest, I should warn you, (or ease your mind, whichever is your preference): this sequence has math in it. I’m not in it to dazzle you with math. It’s just that I know …

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# Physics and the Horizons of Truth

I came across a PDF version of this book online. It contains a number of fine essays, including the ones excerpted from below. A recurring question concerning Godel’s incompleteness results is whether they impact “interesting” mathematical questions. CHAPTER 21 The Godel Phenomenon in Mathematics: A Modern View: … Hilbert believed that all mathematical truths are …

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# Verizon’s new ad promotes encouraging girls’ interest in STEM

Bravo, Verizon, for making a very powerful ad about how parents may discourage their daughters from pursuing STEM (science, technology, engineering, and math) interests.  They teamed up with Makers and Girls Who Code to create this video, which although depressing, is receiving a lot of praise. I’m sure I received some similar comments about not …

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# Turning Bounds into Constraints in CPLEX

I had to delve into the CPLEX documentation today, and found something I had not seen before. As part of a (Java) program I’m writing, I need to use the conflict refiner to track down which upper and lower bounds on variables take a role in making a linear program infeasible. Of course, I could change the …

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# Strategic War (with cards)

War is a simple card game played by children. The most common version does not require decisions, so it’s totally deterministic (outcome is determined) once the card order in each deck is fixed. Nevertheless it can be entertaining to watch/play: there are enough fluctuations to engage observers, mainly due to the treatment of ties. The …

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# Modeling an On/Off Span

I may be ruining a perfectly good homework problem by posting this. :-) Occasionally someone needs to incorporate in an integer programming model the notion of something changing state for a predefined span of time. The typical characterization I’ve seen is as follows: we have a sequence of binary variables xi∈{0,1},i∈{1,…,N} that indicate the state …

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# Ridge Regression Revisited

I’ve been neglecting the blog a bit lately, partly because I haven’t had much to say and partly because I’ve been a bit busy with other things. One of the things keeping me occupied is the excellent Statistical Learning course offered by Stanford. (In one of those coming-full-cycle things, now that I’m retired from teaching, …

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# Of Math and Ambigrams, a new series of articles…

Mathematicians love puzzles—they love to play with numbers and shapes but often their love can turn to words and other areas that, at least on the surface, have little to do with mathematics. One form of visual wordplay with some deep connections to mathematics, and one that I have played with over they years, are called ambigrams. …

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# LP Cutting Planes in CPLEX

Cut generation, as used in what follows, refers to generating constraints for a mathematical program “on the fly” (based on intermediate solutions), rather than adding all relevant constraints at the outset of the problem. It is typically used when  there is an astronomical number of possible constraints, most of which will turn out not to …

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# Project Einstein

I met Jonathan Rothberg, a real pioneer in genetic sequencing technology, at Scifoo back in 2008 (see Gene machines). Jonathan’s foundation is now backing an effort similar to the BGI Cognitive Genomics project. He may not remember, but we had a long conversation about this topic on the bus from the hotel to the Googleplex. …

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# Number sense and math ability

This is consistent with my experience as a parent and educator: my guess is that number sense is a cognitive module, at least somewhat distinct from general intelligence, and somewhat hardwired. Number sense in infancy predicts mathematical abilities in childhood (PNAS) Abstract: Human infants in the first year of life possess an intuitive sense of …

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# Seeing mathematics everywhere…

Dame Kathleen Ollernshaw was deaf since the age of 8. Despite this she had an amazing life as a mathematician, amateur astronomer, politician (she served as mayor of Manchester as well as in the Thatcher administration) and mother. To learn more about her read this story on the Scientific American website, titled Centenarian Dame Kathleen Ollerenshaw—Conqueror of Magic …

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