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The stochastic Hodgkin-Huxley neurons considered in this paper replace time-constant deterministic input $a dt$ of the classical deterministic model by increments $\vartheta dt + dX_t$ of a stochastic process: $X$ is Ornstein-Uhlenbeck with…
We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on…
Buckling instabilities driven by tissue growth underpin key developmental events such as the folding of the brain. Tissue growth is disordered due to cell-to-cell variability, but the effects of this variability on buckling are unknown.…
The goal of this paper is to outline a scenario of emerging stochasticity in high-dimensional highly nonlinear systems, such as genetic regulatory networks (GRN). We focus attention on the fact that in such systems confluence of all the…
Neural quantum states have recently demonstrated significant potential for simulating quantum dynamics beyond the capabilities of existing variational ans\"{a}tze. However, studying strongly driven quantum dynamics with neural networks has…
The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…
Evolution is simultaneously driven by a number of processes such as mutation, competition and random sampling. Understanding which of these processes is dominating the collective evolutionary dynamics in dependence on system properties is a…
We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under1 quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady…
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
Localized persistent cortical neural activity is a validated neural substrate of parametric working memory. Such activity `bumps' represent the continuous location of a cue over several seconds. Pyramidal (excitatory) and interneuronal…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
Consider first a memoryless population model described by the usual branching process with a given mean reproduction matrix on a finite space of types. Motivated by the consequences of atavism in Evolutionary Biology, we are interested in a…
Identifying and quantifying memory are often critical steps in developing a mechanistic understanding of stochastic processes. These are particularly challenging and necessary when exploring processes that exhibit long-range correlations.…
Active tissues exhibit tension fluctuations that are correlated in space and time. We study a minimal overdamped surface model in which such fluctuations enter as a zero-mean, multiplicative modulation of the local surface tension. Although…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
We investigate long and short memory in $\alpha$-stable moving averages and max-stable processes with $\alpha$-Fr\'echet marginal distributions. As these processes are heavy-tailed, we rely on the notion of long range dependence suggested…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…