27 citations · 43 across the 4 of their papers we have counts for
5 papers
Global analysis of the Kuramoto flow
Daniel Burns, Gregorio Malajovich, Charles Pugh +2
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronizatio…
Emergence of Function
Indika Rajapakse, Steve Smale
This work gives a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, where the synthesis of the two gives rise to the emerge…
The Pitchfork Bifurcation
Indika Rajapakse, Steve Smale
We give development of a new theory of the Pitchfork bifurcation, which removes the perspective of the third derivative and a requirement of symmetry.
Mathematics of the Genome
Indika Rajapakse, Steve Smale
This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics we…
Hodge Theory on Metric Spaces
Laurent Bartholdi, Thomas Schick, Nat Smale +2
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, whi…