50 citations · 265 across the 22 of their papers we have counts for
6 papers · 1 filter
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…
Geometric Aspects of Observability of Hypergraphs
Joshua Pickard, Cooper Stansbury, Amit Surana +2
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of g…
Kronecker Product of Tensors and Hypergraphs: Structure and Dynamics
Joshua Pickard, Can Chen, Cooper Stansbury +3
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the…
Observability of Hypergraphs
Joshua Pickard, Amit Surana, Anthony Bloch +1
In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguousl…
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…