Related papers: Stochastic pattern formation and spontaneous polar…
We introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are infinite-dimensional and defined on a scale-invariant…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…
We present a review on the state-of-the-art of the mathematical framework known as stochastic inflation, paying special attention to its derivation and giving references for the readers interested on results coming from the application of…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
Markovian population models are suitable abstractions to describe well-mixed interacting particle systems in situation where stochastic fluctuations are significant due to the involvement of low copy particles. In molecular biology,…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Influence of mesoscopic channel noise on excitable dynamics of living cells became a hot subject within the last decade, and the traditional biophysical models of neuronal dynamics such as Hodgkin-Huxley model have been generalized to…
Robust oscillations play crucial roles in a wide variety of biological processes and are often generated by deterministic mechanisms. However, stochastic fluctuations often generate complex perturbations of these deterministic oscillations,…
It has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to…
We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a…
The transduction process that occurs in the inner ear of the auditory system is a complex mechanism which requires a non-linear dynamical description. In addition to this, the stochastic phenomena that naturally arise in the inner ear…
While generative methods have progressed rapidly in recent years, generating expressive prosody for an utterance remains a challenging task in text-to-speech synthesis. This is particularly true for systems that model prosody explicitly…
Randomness is an unavoidable feature of the intracellular environment due to chemical reactants being present in low copy number. That phenomenon, predicted by Delbr\"uck long ago \cite{delbruck40}, has been detected in both prokaryotic…
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
Conventional wisdom suggests that environmental noise drives populations toward extinction. In contrast, we report a paradoxical phenomenon in which stochasticity reverses a deterministic tipping point, thereby preventing collapse. Using a…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
We study the effect of extrinsic noise in metabolic networks. We introduce external random fluctuations at the kinetic level, and show how these lead to a stochastic generalization of standard Metabolic Control Analysis. While Summation and…