I have added this section to my post a few weeks ago about using the SVD to measure partisanship in the United States Senate.... read more >>

I've blogged about this gem from Lothar Collatz (1910-1990) before, but it deserves to be repeated. Especially since it now provides an elegant example of singleton expansion.... read more >>

We are working on a paper about the Kuramoto model of self-synchronizing oscillators. This animation shows the different initial conditions where six oscillators fail to synchronize. I found it mesmerizing.... read more >>

Lots of tiny bubbles.... read more >>

I have completely rewritten the COVID-19 simulator that I described in last week's blog post and I now have a second version.... read more >>

Tomorrow, February 29, 2020 would be Gene Golub's 22nd birthday.... read more >>

While I was working on my posts about Pejorative Manifolds, I was pleased to discover the intriguing patterns created by the roundoff error in the computed eigenvalues of triple Kronecker products.... read more >>

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Line plots with a color order from one of our color maps are useful, and pretty.... read more >>

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.... read more >>