Related papers: On the Relationship between Mutual Information and…
A subthreshold signal is transmitted through a channel and may be detected when some noise -- with known structure and proportional to some level -- is added to the data. There is an optimal noise level, called stochastic resonance, that…
We identify a unifying measure for stochastic resonance (SR) in voltage dependent ion channels which comprises periodic (conventional), aperiodic and nonstationary SR. Within a simplest setting, the gating dynamics is governed by two-state…
Stochastic representation for interaction of quantum systems is formulated which allows to replace some of them by equivalent but purely commutative random sources. The formalism is applied to two-level systems interacting with Gaussian…
The dichotomy spectrum is introduced for linear mean-square random dynamical systems, and it is shown that for finite-dimensional mean-field stochastic differential equations, the dichotomy spectrum consists of finitely many compact…
The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…
A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For…
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The…
We study the tradeoff between the statistical error and communication cost of distributed statistical estimation problems in high dimensions. In the distributed sparse Gaussian mean estimation problem, each of the $m$ machines receives $n$…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
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…
This brief note considers the problem of estimating temporal synergy and integrated information in dyadic dynamical processes. One of the standard estimators of dynamic synergy is based on the minimal mutual information between sets of…
In this thesis we aim to analyze and quantify the energetic and information contents that can be extracted from a dynamical system subject to the external environment. The latter is usually assumed to be deleterious for the feasibility of…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
Quantum Gaussian channels play a key role in quantum information theory. In particular, the attenuation and amplification channels are useful to describe noise and decoherence effects on continuous variables systems. They are directly…
Causal inference seeks to identify cause-and-effect interactions in coupled systems. A recently proposed method by Liang detects causal relations by quantifying the direction and magnitude of information flow between time series. The…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
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…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
We consider multiscale stochastic dynamical systems. In this article an \emph{intermediate} reduced model is obtained for a slow-fast system with fast mode driven by white noise. First, the reduced stochastic system on exponentially…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…