Related papers: Exclusion statistics: A resolution of the problem …
In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be…
New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical…
The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two…
We propose a new method, probabilistic divide-and-conquer, for improving the success probability in rejection sampling. For the example of integer partitions, there is an ideal recursive scheme which improves the rejection cost from…
We propose a simple approach for studying systems of compressed matter based on the Thomas-Fermi statistical model of single atom. The central point of our work is the development of the concept of ``statistical ionization'' by compression;…
This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density…
This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
We propose a new approximate method for counting the number of the solutions for constraint satisfaction problem (CSP). The method derives from the partition function based on introducing the free energy and capturing the relationship of…
Negative probabilities arise primarily in physics, statistical quantum mechanics and quantum computing. Negative probabilities arise as mixing distributions of unobserved latent variables in Bayesian modeling. Our goal is to provide a link…
In the number partitioning problem (NPP) one aims to partition a given set of $N$ real numbers into two subsets with approximately equal sum. The NPP is a well-studied optimization problem and is famous for possessing a…
We first reobtain in a simpler way the Haldane fractional statistics at thermal equilibrium using an interpolation argument. We then show that the mean occupation number for fractional statistics is invariant to a group of duality…
The exact solution of the asymmetric exclusion problem with N distinct classes of particles (c = 1,2,...,N), with hierarchical order is presented. In this model the particles (size 1) are located at lattice points, and diffuse with equal…
We prove the existence of solutions of a cross-diffusion parabolic population problem. The system of partial differential equations is deduced as the limit equations satisfied by the densities corresponding to an interacting particles…
We investigate a class of chance-constrained combinatorial optimization problems. Given a pre-specified risk level $\epsilon \in [0,1]$, the chance-constrained program aims to find the minimum cost selection of a vector of binary decisions…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
Using the subdivision schemes theory, we develop a criterion to check if any natural number has at most one representation in the $n$-ary number system with a set of non-negative integer digits $A=\{a_1, a_2,\ldots, a_n\}$ that contains…
We study the asymmetric exclusion process with open boundaries and derive the exact form of the joint probability function for the occupation number and the current through the system. We further consider the thermodynamic limit, showing…
As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in…