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Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. They amount to a generalization of series expansions from 2-point to point-link-point interactions. We outline…
Because of consuming energy to drive their motion, systems of active colloids are intrinsically out of equilibrium. In the past decade, a variety of intriguing dynamic patterns have been observed in systems of active colloids, and they…
Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the…
This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…
The general approach for the description of correlated hopping in the Dynamical Mean-Field Theory which is based on the expansion over electron hopping around the atomic limit is developed. It is formulated in terms of the local irreducible…
Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…
Often, experiments, observations or simulations generate large numbers of snapshots of the configurations of complex many-particle systems. It is important to find methods of extracting useful information from these ensembles of snapshots…
We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…
In Part I (G.Olshanski, math.RT/9804086) and Part II (A.Borodin, math.RT/9804087) we developed an approach to certain probability distributions on the Thoma simplex. The latter has infinite dimension and is a kind of dual object for the…
Identification of the clusters from an unlabeled data set is one of the most important problems in Unsupervised Machine Learning. The state of the art clustering algorithms are based on either the statistical properties or the geometric…
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…
With rapid growth in the amount of unstructured data produced by memory-intensive applications, large scale data analytics has recently attracted increasing interest. Processing, managing and analyzing this huge amount of data poses several…
We introduce a new clustering method for the classification of functional data sets by their probabilistic law, that is, a procedure that aims to assign data sets to the same cluster if and only if the data were generated with the same…
The dynamics and spontaneous organization of coupled particles is a classic problem in modeling and applied mathematics. Here we examine the behavior of particles coupled by the Ricker potential, exhibiting finite local repulsion…
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g.,…
Many clustering algorithms when the data are curves or functions have been recently proposed. However, the presence of contamination in the sample of curves can influence the performance of most of them. In this work we propose a robust,…
Peaks-over-threshold analysis using the generalized Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results.…
We present a theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system. Such higher-order correlation functions have attracted much interest recently in the…
We introduce a systematic expansion tailored to systems with strong local interactions and capable of computing response functions, including finite DC transport, analytically. The expansion is controlled by a small parameter $s^2$ that…