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We consider an epidemic model of SIR type set on a homogeneous tree and investigate the spreading properties of the epidemic as a function of the degree of the tree, the intrinsic basic reproduction number and the strength of the…
Excitation waves are studied on trees and random networks of coupled active elements. Undamped propagation of such waves is observed in those networks. It represents an excursion from the resting state and a relaxation back to it for each…
Typically, contagion strength is modeled by a transmission rate $\lambda$, whereby all nodes in a network are treated uniformly in a mean-field approximation. However, local agents react differently to the same contagion based on their…
The interaction among spreading processes on a complex network is a nontrivial phenomenon of great importance. It has recently been realized that cooperative effects among infective diseases can give rise to qualitative changes in the…
We consider one-dimensional reaction-diffusion equations of Fisher-KPP type with random stationary ergodic coefficients. A classical result of Freidlin and Gartner [16] yields that the solutions of the initial value problems associated with…
Dynamics and function of neuronal networks are determined by their synaptic connectivity. Current experimental methods to analyze synaptic network structure on the cellular level, however, cover only small fractions of functional neuronal…
Neural-network processing in machine learning applications relies on layer synchronization. This is practiced even in artificial Spiking Neural Networks (SNNs), which are touted as consistent with neurobiology, in spite of processing in the…
We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a generalized linear model (kinetic Ising model), study their functional…
We study in this paper the effect of an unique initial stimulation on random recurrent networks of leaky integrate and fire neurons. Indeed given a stochastic connectivity this so-called spontaneous mode exhibits various non trivial…
The structure of a network dramatically affects the spreading phenomena unfolding upon it. The contact distribution of the nodes has long been recognized as the key ingredient in influencing the outbreak events. However, limited knowledge…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of…
In the present work, the discrete flame model [1] is augmented by introducing the thermal inertia of particles in the preheating zone. The effect of particle thermal inertia on flame speed, propagation limits, and near-limits dynamics of…
Results for estimating the convergence rate of non-stationary distributed consensus algorithms are provided, on the basis of qualitative (mainly topological) as well as basic quantitative information (lower-bounds on the matrix entries).…
We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at…
Rhythmic gait patterns in animal locomotion are widely believed to be produced by a central pattern generator (CPG), a network of neurons that drives the muscle groups. In previous papers we have discussed how phase-synchronous signals can…
We propose a solution to the weight transport problem, which questions the biological plausibility of the backpropagation algorithm. We derive our method based upon a theoretical analysis of the (approximate) dynamics of leaky…
The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects…