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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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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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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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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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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