Related papers: Partitioning Composite Finite Systems
We introduce Markov chain Monte Carlo (MCMC) algorithms based on numerical approximations of piecewise-deterministic Markov processes obtained with the framework of splitting schemes. We present unadjusted as well as adjusted algorithms,…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps…
We learn the structure of a Markov Network between two groups of random variables from joint observations. Since modelling and learning the full MN structure may be hard, learning the links between two groups directly may be a preferable…
A randomized algorithm for finding sparse cuts is given which is based on constructing a dual markov chain called multiscale rings process(MRP) and a new concept of entropy. It is shown how the time to absorption of the dual process…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we proof a pivotal convergence theorem for finite Markov chains and a minimal version of the…
An important objective for analyzing real-world graphs is to achieve scalable performance on large, streaming graphs. A challenging and relevant example is the graph partition problem. As a combinatorial problem, graph partition is NP-hard,…
Set partitions are arrangements of distinct objects into groups. The problem of listing all set partitions arises in a variety of settings, in particular in combinatorial optimization tasks. After a brief review, we give practical…
We present a Markov-chain analysis of blockwise-stochastic algorithms for solving partially block-separable optimization problems. Our main contributions to the extensive literature on these methods are statements about the Markov operators…
We present a new multiple-try Metropolis-Hastings algorithm designed to be especially beneficial when a tailored proposal distribution is available. The algorithm is based on a given acyclic graph $G$, where one of the nodes in $G$, $k$…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
In dynamic Monte Carlo simulations, using for example the Metropolis dynamic, it is often required to simulate for long times and to simulate large systems. We present an overview of advanced algorithms to simulate for larger times and to…
A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the…
This paper presents an algorithm for sampling random variables that allows to separation of the sampling process into subproblems by dividing the sample space into overlapping parts. The subproblems can be solved independently of each other…
We present several implementations of the Metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The Metropolis technique…
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…