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 >>

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.... read more >>

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.... read more >>

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.... read more >>

(This is a reprint of the second ever Cleve's Corner from the Winter 1990 MathWorks Newsletter).... read more >>

Let me tell you about MATLAB's controversial function rat.... read more >>

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.... read more >>

Sedona Arizona is a perfect site for the first MathWorks excursion into lifestyle products.... read more >>

My MATLAB® program, amaze, generates mazes by combining old friends, numgrid and delsq, with a new friend, the graph object. Let's see how we make this example maze.... read more >>

This is a short post to point to a web site in the Netherlands, VAXBARN. The site proprietor, Camiel Vanderhoeven, is assembling a collection of historically interesting computers.... read more >>