In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... 続きを読む >>

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... 続きを読む >>

I have always been fascinated by the names that are used to describe colors. There are dozens of web sites with lists of color names. I was surprised to discover that the shade of blue we use in MathWorks logo is almost the same as the one used by the United States Air Force Academy.... 続きを読む >>

Inspired by Patsy and https://www.amazon.com/gp/product/B075JDVR53. type xmas_2019.m function xmas_2019 % Christmas greetings. set(gcf,'pos',[800 200 420 315]) clf ... 続きを読む >>

My colleagues are looking for a matrix to be used in a new benchmark. They've come to the right place.... 続きを読む >>

Line plots with a color order from one of our color maps are useful, and pretty.... 続きを読む >>

I am working with Indika Rajapakse and Steve Smale to investigate the stability of the dynamic system describing Kuramoto oscillators. Indika and Steve are interested in Kuramoto oscillators for two reasons; the self synchronization provides a model of the cells in a beating heart and the dynamic system is an example for Morse-Smale theory. I am personally interested in the Kuramoto model as it relates to deep brain stimulation (DBS) for open-loop control of human movement disorders. My kuramoto program demonstrates both stable and unstable critical points. Roundoff error may destabilize an unstable critical point.... 続きを読む >>

Today's post was inspired by a YouTube video, Why do prime numbers make these spirals?, on the channel 3Blue1Brown, created by Grant Sanderson. In my opinion this is the best math channel on YouTube. He has beautiful graphics and superb exposition. I recommend you take a look, if you haven't already.... 続きを読む >>

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.... 続きを読む >>

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.... 続きを読む >>