Related papers: Complex systems under stochastic dynamics
We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…
The study of the physical properties of open quantum systems is at the heart of many present investigations which aim to describe their dynamical evolution, on theoretical ground and through physical realizations. Here we develop a…
This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…
In this thesis, we explore the use of complex systems to study learning and adaptation in natural and artificial systems. The goal is to develop autonomous systems that can learn without supervision, develop on their own, and become…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
The paper argues that attracting more economists and adopting a more-precise definition of dynamic complexity might help econophysics acquire more attention in the economics community and bring new lymph to economic research. It may be…
This paper deals with the analysis of stochastic systems which can be described by a Langevin equation. By the method presented in this paper drift and diffusion terms of the corresponding Fokker-Planck equation can be extracted from the…
In this paper, we investigate a special class of stochastic Markov processes, known as Glauber dynamics. Markov processes are importance, for example, in the study of complex systems. For this, we present the basic theory of Glauber…
We address the problem of learning linear system models from observing multiple trajectories from different system dynamics. This framework encompasses a collaborative scenario where several systems seeking to estimate their dynamics are…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multiple objectives, local constraints as well as local variables, and they are…
This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…
The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…
Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…
Identifying and understanding modular organizations is centrally important in the study of complex systems. Several approaches to this problem have been advanced, many framed in information-theoretic terms. Our treatment starts from the…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
Simulation has become the evaluation method of choice for many areas of distributing computing research. However, most existing simulation packages have several limitations on the size and complexity of the system being modeled. Fine…
This paper provides the analysis for structural and functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced, and local and global dynamic…