Related papers: Similarity Between Two Stochastic Differential Sys…
We present a full stochastic description of the pair approximation scheme to study binary-state dynamics on heterogeneous networks. Within this general approach, we obtain a set of equations for the dynamical correlations, fluctuations and…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
System identification and Koopman spectral analysis are crucial for uncovering physical laws and understanding the long-term behaviour of stochastic dynamical systems governed by stochastic differential equations (SDEs). In this work, we…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
The foundations of the Boltzmann-Gibbs (BG) distributions for describing equilibrium statistical mechanics of systems are examined. Broadly, they fall into: (i) probabilistic paaroaches based on the principle of equal a priori probability…
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex…
In this paper we use the master stability function (MSF) for nearly identical dynamical systems obtained in the previous paper to construct optimized networks (ONs) which show better synchronizability. Nearly identical nature is the result…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
We give a general unified method that can be used for $L_1$ {\em closeness testing} of a wide range of univariate structured distribution families. More specifically, we design a sample optimal and computationally efficient algorithm for…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
This paper investigates the relationship between Pontryagin's maximum principle and dynamic programming principle in the context of stochastic optimal control systems governed by stochastic evolution equations with random coefficients in…
Quantifying the similarity of two or more datasets has widespread applications in statistics and machine learning. The method choice is, however, difficult due to the abundance of proposed methods and the lack of neutral comparison studies,…
We present a scalable methodology to verify stochastic hybrid systems. Using the Mori-Zwanzig reduction method, we construct a finite state Markov chain reduction of a given stochastic hybrid system and prove that this reduced Markov chain…
We derive learning rules for finding the connections between units in stochastic dynamical networks from the recorded history of a ``visible'' subset of the units. We consider two models. In both of them, the visible units are binary and…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between…
A probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions.…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…