Related papers: Glauber Dynamics: An Approach in a Simple Physical…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…
This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms…
Dynamics is central to living systems. In the last two decades, experiments have revealed that the dynamics in diverse biological systems - from intracellular cytoplasm to cellular and organismal aggregates - are remarkably similar to that…
We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.
We study the dynamics of two particles that interact only when in contact. In this sense, although not in every particular, the interactions mimic those in granular materials. The detailed solution of the dynamics allows an analysis of the…
We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic,…
Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…
We introduce and apply a novel efficient method for the precise simulation of stochastic dynamical processes on locally tree-like graphs. Networks with cycles are treated in the framework of the cavity method. Such models correspond, for…
Case-Bsed Reasoning (CBR) is a recent theory for problem-solving and learning in computers and people.Broadly construed it is the process of solving new problems based on the solution of similar past problems. In the present paper we…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…
We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is…
The thermodynamic formalism, which was first developed for dynamical systems and then applied to discrete Markov processes, turns out to be well suited for continuous time Markov processes as well, provided the definitions are interpreted…
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems.…
Facilitated or kinetically constrained spin models (KCSM) are a class of interacting particle systems reversible w.r.t. to a simple product measure. Each dynamical variable (spin) is re-sampled from its equilibrium distribution only if the…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…
Various and ubiquitous information systems are being used in monitoring, exchanging, and collecting information. These systems are generating massive amount of event sequence logs that may help us understand underlying phenomenon. By…
This book covers a wide range of problems involving the applications of stochastic processes, stochastic calculus, large deviation theory, group representation theory and quantum statistics to diverse fields in dynamical systems,…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial…