相关论文: Further Results for the Capacity Statistic Distrib…
This paper explores the distribution of indistinguishable balls into distinct urns with varying capacity constraints, a foundational issue in combinatorial mathematics with applications across various disciplines. We present a comprehensive…
This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known…
It is shown that in equilibrium a canonical ensemble of particles with two-particle interaction the Gibbs distribution function may be expressed uniquely through a pair distribution function. It means, that for given values of the particle…
The aim of this paper is to introduce a new technique for calculation of observables, in particular multiplicity distributions, in various statistical ensembles at finite volume. The method is based on Fourier analysis of the grand…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The probability distributions for charged particle numbers and their densities are derived in statistical ensembles with conservation laws. It is shown that if this limit is properly taken then the canonical and grand canonical ensembles…
Out-of-distribution generalization capabilities of sequence-to-sequence models can be studied from the lens of two crucial forms of generalization: length generalization -- the ability to generalize to longer sequences than ones seen during…
The semi-inclusive properties of the system of neutral and charged particles with net charge equal to zero are considered in the grand canonical, canonical and micro-canonical ensembles as well as in micro-canonical ensemble with scaling…
Designing neural network architectures is a task that lies somewhere between science and art. For a given task, some architectures are eventually preferred over others, based on a mix of intuition, experience, experimentation and luck. For…
Generalizing previous results, we introduce and study a new statistic on words, that we call rectangle capacity. For two fixed positive integers $r$ and $s$, this statistic counts the number of occurrences of a rectangle of size $r\times s$…
In "Reliable Communication in the Absence of a Common Clock" (Yeung et al., 2009), the authors introduce general run-length sets, which form a class of constrained systems that permit run-lengths from a countably infinite set. For a…
We continue to study the relationship between the size of the sum of a set and the common energy of its subsets. We find a rather sharp subexponential dependence between the doubling constant of a set $A$ and the minimal common energy taken…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
This article present a method of mutual transformation between count model and composition model. Offer the mathematical view of classical radio and log-radio in compositional data analysis and expand the idea of mixture model of counts…
We consider multiple access communication on a binary input additive white Gaussian noise channel using randomly spread code division. For a general class of symmetric distributions for spreading coefficients, in the limit of a large number…
In his influential work Choquet systematically studied capacities on Boolean algebras in a topological space, and gave a probabilistic interpretation for completely monotone (and completely alternating) capacities. Beyond complete…
We study pairs and m--tuples of compositions of a positive integer n with parts restricted to a subset P of positive integers. We obtain some exact enumeration results for the number of tuples of such compositions having the same number of…
We study some combinatorial statistics defined on the set $NC^{(mton)}(n)$ of monotonically ordered non-crossing partitions of {1,...,n}, and on the set $NC_2^{(mton)}(2n)$ of monotonically ordered non-crossing pair-partitions of…