Related papers: A Cellular Automaton Model for the generation of B…
We study temporal oscillations, known as dynamical beats, developed by a propagating pulse due to its interaction with a near-resonant collective medium of $^{133}$Cs atoms randomly captured by a nanofiber-based optical lattice. A…
A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.
A model and analysis of the human sleep/wake system is presented. The model is derived using the known neuronal groups, and their various projections, involved with sleep and wake. Inherent in the derivation is the existence of a slow time…
We analyze the dynamics of the neural circuit of the lamprey central pattern generator (CPG). This analysis provides insights into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped…
We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a…
Nonlinear networks can host spatially compact time periodic solutions called compact breathers. Such solutions can exist accidentally (i.e. for specific nonlinear strength values) or parametrically (i.e. for any nonlinear strength). In this…
We consider suppression of macroscopic synchronized oscillations in mixed populations of active and inactive oscillators with local diffusive coupling, described by a lattice complex Ginzburg-Landau model with discrete Laplacian in general…
We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…
The heart is a vital organ that relies on the orchestrated propagation of electrical stimuli to coordinate each heart beat. Abnormalities in the heart's electrical behaviour can be managed with a cardiac pacemaker. Recently, the closed-loop…
We propose a generative model for single-channel EEG that incorporates the constraints experts actively enforce during visual scoring. The framework takes the form of a dynamic Bayesian network with depth in both the latent variables and…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us…
We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on two quickly alternating signals to engineer the appropriate…
It is shown, by means of numerical simulations, that intercellular spiral waves of calcium can be initiated in a network of coupled cells as a result of a de-synchronization between Ca2+ oscillations in two domains. No artificial…
We analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator-prey system. The individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired…
This paper presents a method for reproducing a simple central pattern generator (CPG) using a modified Echo State Network (ESN). Conventionally, the dynamical reservoir needs to be damped to stabilize and preserve memory. However, we find…
Consider a distributed network on a finite simple graph $G=(V,E)$ with diameter $d$ and maximum degree $\Delta$, where each node has a phase oscillator revolving on $S^{1}=\mathbb{R}/\mathbb{Z}$ with unit speed. Pulse-coupling is a class of…
Most models of biological pattern formation are simulated on continuous domains even though cells are discrete objects that provide internal boundaries to the diffusion of regulatory components. In our previous papers on simulating…