Related papers: Exact combinatorial approach to finite coagulating…
In this thesis I discuss combinatorial optimization problems, from the statistical physics perspective. The starting point are the motivations which brought physicists together with computer scientists and mathematicians to work on this…
Mixture models, such as Gaussian mixture models, are widely used in machine learning to represent complex data distributions. A key challenge, especially in high-dimensional settings, is to determine the mixture order and estimate the…
In the usual Achlioptas processes the smallest clusters of a few randomly chosen ones are selected to merge together at each step. The resulting aggregation process leads to the delayed birth of a giant cluster and the so-called explosive…
In this paper we study the fundamental solution of the equation obtained by the linearisation of the Smoluchowski coagulation equation with the multiplicative kernel $(x y)^{\lambda/2}$ with $\lambda\in (1, 2)$ around the steady state…
The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…
We report a novel approach for the efficient computation of solutions of a broad class of large-scale systems of non-linear ordinary differential equations, describing aggregation kinetics. The method is based on a new take on the…
Consensus clustering aggregates partitions in order to find a better fit by reconciling clustering results from different sources/executions. In practice, there exist noise and outliers in clustering task, which, however, may significantly…
Cluster molecular field approximations represent a substantial progress over the simple Weiss theory where only one spin is considered in the molecular field resulting from all the other spins. In this work we discuss a systematic way of…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
In this work we study the stochastic process of two-species coagulation. This process consists in the aggregation dynamics taking place in a ring. Particles and clusters of particles are set in this ring and they can move either clockwise…
Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…
We describe an algorithm computing the exact value of the mean current, its variance, and higher order cumulants for stochastic driven systems. The method uses a Rayleigh-Schrodinger perturbation expansion of the generating function of the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
In this article a stochastic particle system approximation to the parametric sensitivity in the Smoluchowski coagulation equation is introduced. The parametric sensitivity is the derivative of the solution to the equation with respect to…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
We examine the interplay between anisotropy and percolation, i.e., the spontaneous formation of a system spanning cluster in an anisotropic model. We simulate an extension of a benchmark model of continuum percolation, the Boolean model,…
The cluster Gutzwiller method is widely used to study the strongly correlated bosonic systems, owing to its ability to provide a more precise description of quantum fluctuations. However, its utility is limited by the exponential increase…
Traditional machine learning approaches assume that data comes from a single generating mechanism, which may not hold for most real life data. In these cases, the single mechanism assumption can result in suboptimal performance. We…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…