Suppose we are given a system of coupled oscillators on an unknown graph along with the
trajectory of the system during some period. Can we predict whether the system will …

We propose a novel generalized cellular automaton (GCA) model for discrete-time pulse-
coupled oscillators and study the emergence of synchrony. Given a finite simple graph and …

Let T be the first return time to (−∞, 0] of sums of increments given by a functional of a
stationary Markov chain. We determine the asymptotic behavior of the survival probability, P …

Neural profiles of cellular automata provide a systematic, computational framework for
numerically and statistically characterizing seemingly disparate cellular automata transition …

We study the cyclic cellular automaton (CCA) and the Greenberg–Hastings model (GHM)
with κ≥ 3 colors and contact threshold θ≥ 2 on the infinite (d+ 1)-regular tree, T d. When the …

We study a one-parameter family of discrete dynamical systems called the κ-color firefly
cellular automata (FCAs), which were introduced recently by the author. At each discrete …

1.1. Motivation. In modern data analysis, a central step is to find a low-dimensional
representation to better understand, compress, or convey the key phenomena captured in …

1. Online Matrix/Tensor factorization+ MCMC sampling+ Networks. A central step in modern
data analysis is to find a low-dimensional representation to better understand, compress, or …

A prime example of complex systems is a population of\textit {coupled oscillators}, which is a
network of oscillatory units with local tendency to synchronize with their neighbors …

We study the end behavior of three different discrete-time processes on a variety of graphs.
The first is the cyclic particle system (CPS) on 3 colors with discordant voting,(Xt). Given a …