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Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…

Stochastic transitions between discrete microscopic states play an important role in many physical and biological systems. Often, these transitions lead to fluctuations on a macroscopic scale. A classic example from neuroscience is the…

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing…

We introduce a deep learning model for speech denoising, a long-standing challenge in audio analysis arising in numerous applications. Our approach is based on a key observation about human speech: there is often a short pause between each…

Polyhomeostatic adaption occurs when evolving systems try to achieve a target distribution function for certain dynamical parameters, a generalization of the notion of homeostasis. Here we consider a single rate encoding leaky integrator…

Linear thresholding systems have been used as a model of neural activation and have more recently been proposed as a model of gene activation. Deterministic linear thresholding systems can be turned into non-deterministic systems by the…

Predator-prey models have been shown to exhibit resonance-like behaviour, in which random fluctuations in the number of organisms (demographic noise) are amplified when their frequency is close to the natural oscillatory frequency of the…

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. To this purpose, we have considered two types of modulations; namely, variations of the resistance and oscillations of…

We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…

Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…

Coherence resonance can be explained using differential entropy and mutual information. This theory explores the role of external noise in stabilising chaotic circuits such as the uni-junction transistor relaxation oscillator.The phenomenon…

Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…

Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: the most…

We investigate a model where strong noise in a sub-population creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortex-like, and its persistence time grows exponentially with the…

We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomogeneous highly degenerate diffusion for…

We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…

We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification…

A system under constant observation is practically freezed to the measurement subspace. If the system driving is a random classical field, the survival probability of the system in the subspace becomes a random variable described by the…

We propose a new non-equilibrium model for spatial pattern formation on the basis of local information transfer. Unlike standard models of pattern formation it is not based on the Turing instability. Information is transmitted through the…