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To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…

The master equation and, more generally, Markov processes are routinely used as models for stochastic processes. They are often justified on the basis of randomization and coarse-graining assumptions. Here instead, we derive n-th order…

The identification of low-energy conformers for a given molecule is a fundamental problem in computational chemistry and cheminformatics. We assess here a conformer search that employs a genetic algorithm for sampling the low-energy segment…

While the structure of chromatin has been studied in great detail on length scales below 30 nm, amazingly little is known about the higher-order folding motifs of chromatin in interphase. Recent experiments give evidence that the folding…

Models for categorical sequences typically assume exchangeable or first-order dependent sequence elements. These are common assumptions, for example, in models of computer malware traces and protein sequences. Although such simplifying…

We describe general approach to classification of character sequences (texts, DNA) using relative entropy estimated by off-the-shelf compression and Markov Chains and find them precise enough. We also notice that the method for estimating…

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in enhancing phase space mixing of these protocols, thus…

Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power…

Order-preserving couplings are elegant tools for obtaining robust estimates of the time-dependent and stationary distributions of Markov processes that are too complex to be analyzed exactly. The starting point of this paper is to study…

Causal structure learning has long been the central task of inferring causal insights from data. Despite the abundance of real-world processes exhibiting higher-order mechanisms, however, an explicit treatment of interactions in causal…

Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…

We study the approximation of a Markov chain on a reduced state space, for both discrete- and continuous-time Markov chains. In this context, we extend the existing theory of formal error bounds for the approximated transient distributions.…

Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…

This paper establishes a Markov chain model as a unified framework for understanding information consumption processes in complex networks, with clear implications to the Internet and big-data technologies. In particular, the proposed model…

The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…

We present and implement a distance-based clustering of amino acids within the framework of a statistically derived interaction matrix and show that the resulting groups faithfully reproduce, for well-designed sequences, thermodynamic…

We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T…

In multi-state life insurance, an adequate balance between analytic tractability, computational efficiency, and statistical flexibility is of great importance. This might explain the popularity of Markov chain modelling, where matrix…

Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…