Related papers: Exact combinatorial approach to finite coagulating…
Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
In this paper we study the continuous coagulation and multiple fragmentation equation for the mean-field description of a system of particles taking into account the combined effect of the coagulation and the fragmentation processes in…
In this paper we prove the global in time solvability of the continuous growth--fragmentation--coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool…
We study the clustering problem for mixtures of bounded covariance distributions, under a fine-grained separation assumption. Specifically, given samples from a $k$-component mixture distribution $D = \sum_{i =1}^k w_i P_i$, where each $w_i…
We show that solutions to Smoluchowski's equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a self-similar profile. This convergence holds in…
Deep clustering as an important branch of unsupervised representation learning focuses on embedding semantically similar samples into the identical feature space. This core demand inspires the exploration of contrastive learning and…
Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process…
We propose a concise stochastic mechanics framework for chemical reaction systems that allows to formulate evolution equations for three general types of data: the probability generating functions, the exponential moment generating…
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Distributed data mining techniques and mainly distributed clustering are widely used in the last decade because they deal with very large and heterogeneous datasets which cannot be gathered centrally. Current distributed clustering…
In this work we demonstrate a surprising way of exploitation of the mosaic--skeleton approximations for efficient numerical solving of aggregation equations with many applied kinetic kernels. The complexity of the evaluation of the…
This paper applies conformal prediction techniques to compute simultaneous prediction bands and clustering trees for functional data. These tools can be used to detect outliers and clusters. Both our prediction bands and clustering trees…
Using exact computer arithmetic, it is possible to determine the (exact) solution of a numerical model without rounding error. For such purposes, a corresponding system of equations should be exactly defined, either directly or by…
Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional…
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…