I have learned a lot more about Kuramoto oscillators since I wrote my blog post three weeks ago. I am working with Indika Rajapakse at the University of Michigan and Stephen Smale at the University of California, Berkeley. They are interested in the Kuramoto model because they are studying the beating of human heart cells. At this point we have some interesting results and some unanswered questions.... 更多内容 >>

Fireflies on a summer evening, pacemaker cells, neurons in the brain, a flock of starlings in flight, pendulum clocks mounted on a common wall, bizarre chemical reactions, alternating currents in a power grid, oscillations in SQUIDs (superconducting quantum interference devices). These are all examples of synchronized oscillators.... 更多内容 >>

(This is a reprint of the second ever Cleve's Corner from the Winter 1990 MathWorks Newsletter).The other day at lunch with a couple of other MathWorks people, I posed the following... 更多内容 >>

We will have a two-part minisymposium on "Bohemian Matrices" at ICIAM2019, the International Congress on Industrial and Applied Mathematics in Valencia, Spain, July 15-19. This is an outline of my talk.... 更多内容 >>

This is a summary of my talk at the conference Celebrating the Centenary of James H. Wilkinson's Birth at the University of Manchester, May 29.... 更多内容 >>

Why are manhole covers round? It is so they won't fall through the hole they are intended to cover. They have the same diameter regardless of where it is measured. If the hole has a slightly smaller diameter, it is not possible to orient the cover so that it will fall through. A square or rectangular cover can be turned slightly and it will easily fit through the hole.... 更多内容 >>

In a comment following my post about half-precision arithmetic, "Raj C" asked how the parameters for IEEE Standard 754 floating point arithmetic were chosen. I replied that I didn't know but would try to find out. I called emeritus U. C. Berkeley Professor W. (Velvel) Kahan, who was the principle architect of 754. Here is what I learned.... 更多内容 >>

As the degree of an interpolating polynomial increases, does the polynomial converge to the underlying function? The short answer is maybe. I want to describe a visual tool to help you investigate this question yourself.... 更多内容 >>

Two months ago I wrote a blog post about Teaching Calculus to a Deep Learner. We wrote the code for that post in one afternoon in the MathWorks booth at the SIAM Annual Meeting. Earlier that day, during his invited talk, MIT Professor Gil Strang had spontaneously wondered if it would possible to teach calculus to a deep learning computer program. None of us in the booth were experts in deep learning.... 更多内容 >>

I probably first saw this matrix in 1960 in John Todd's class at Caltech. But I forgot about it until Tahar Loulou jogged my memory with a comment following my blog post in late May. It deserves a place in our gallery of interesting matrices.... 更多内容 >>