Related papers: Equivalence between non-Markovian and Markovian dy…
The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme…
Since roughly a decade ago, network science has focused among others on the problem of how the spreading of diseases depends on structural patterns. Here, we contribute to further advance our understanding of epidemic spreading processes by…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
This paper introduces a theoretical framework for the analysis and control of the stochastic susceptible-infected-removed (SIR) spreading process over a network of heterogeneous agents. In our analysis, we analyze the exact networked Markov…
The static properties of the fundamental model for epidemics of diseases allowing immunity (susceptible-infected-removed model) are known to be derivable by an exact mapping to bond percolation. Yet when performing numerical simulations of…
We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
We present a computational modeling framework for data-driven simulations and analysis of infectious disease spread in large populations. For the purpose of efficient simulations, we devise a parallel solution algorithm targeting…
We study the mean-field limit and stationary distributions of a pulse-coupled network modeling the dynamics of a large neuronal assemblies. Our model takes into account explicitly the intrinsic randomness of firing times, contrasting with…
During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to…
We investigate measures of non-Markovianity in open quantum systems governed by Gaussian free fermionic dynamics. Standard indicators of non-Markovian behavior, such as the BLP and LFS measures, are revisited in this context. We show that…
We propose a Markovian stochastic approach to model the spread of a SARS-CoV-2-like infection within a closed group of humans. The model takes the form of a Partially Observable Markov Decision Process (POMDP), whose states are given by the…
This work introduces a new markovian stochastic model that can be described as a non-homogeneous Pure Birth process. We propose a functional form of birth rate that depends on the number of individuals in the population and on the elapsed…
The goal of this work is to formally abstract a Markov process evolving in discrete time over a general state space as a finite-state Markov chain, with the objective of precisely approximating its state probability distribution in time,…
Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational…
A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…
We observe n possibly dependent random variables, the distribution of which is presumed to be stationary even though this might not be true, and we aim at estimating the stationary distribution. We establish a non-asymptotic deviation bound…
In this survey paper, we review the recent advances in individual based non--Markovian epidemic models. They include epidemic models with a constant infectivity rate, varying infectivity rate or infection-age dependent infectivity,…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
Markov models are widely used to describe processes of stochastic dynamics. Here, we show that Markov models are a natural consequence of the dynamical principle of Maximum Caliber. First, we show that when there are different possible…