相关论文: Partitioning Composite Finite Systems

Partitioning is a well studied research problem in the area of VLSI physical design automation. In this problem, input is an integrated circuit and output is a set of almost equal disjoint blocks. The main objective of partitioning is to…

Any Hilbert space with composite dimension can be factorized into a tensor product of smaller Hilbert spaces. This allows to decompose a quantum system into subsystems. We propose a simple tractable model for a constructive study of…

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…

The surface partition of large fragments is derived analytically within a simple statistical model by the Laplace-Fourier transformation method. In the limit of small amplitude deformations, a suggested Hills and Dales Model reproduces the…

This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

We propose locally stable sparse hard-disk packings, as introduced by B\"or\"oczky, as a model for the analysis and benchmarking of Markov-chain Monte Carlo (MCMC) algorithms. We first generate such packings in a square box with periodic…

Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…

Given an undirected graph representing similarities between a set of items and an additive measure evaluating the items, we treat the position of a special subset of items in an ordinal ranking through a collection of combinatorial…

Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…

A model of a geometric algorithm is introduced and methodology of its operation is presented for the dynamic partitioning of data spaces.

Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…

Researchers and legislators alike continue the search for methods of drawing fair districting plans. A districting plan is a partition of a state's subdivisions (e.g. counties, voting precincts, etc.). By modeling these districting plans as…

There are two main approximations of mining big data in memory. One is to partition a big dataset to several subsets, so as to mine each subset in memory. By this way, global patterns can be obtained by synthesizing all local patterns…