相关论文: A generatingfunctionology approach to a problem of…
Recently Richard Stanley initiated a study of the distribution of the length as(w) of the longest alternating subsequence in a random permutation w from the symmetric group $S_n$. Among other things he found an explicit formula for the…
We give an efficient algorithm to randomly generate finitely generated subgroups of a given size, in a finite rank free group. Here, the size of a subgroup is the number of vertices of its representation by a reduced graph such as can be…
We consider sequences of integers defined by a system of linear inequalities with integer coefficients. We show that when the constraints are strong enough to guarantee that all the entries are nonnegative, the generating function for the…
We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in…
The problem of estimating the multiplicity of the zero of a polynomial when restricted to the trajectory of a non-singular polynomial vector field, at one or several points, has been considered by authors in several different fields. The…
Existence of incomplete and imprecise data has moved the database paradigm from deterministic to proba- babilistic information. Probabilistic databases contain tuples that may or may not exist with some probability. As a result, the number…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
We study the asymptotic behavior of the maximal multiplicity $M_n=M_n(\sigma)$ of the blocks in a set partition of $[n]=\{1,2,...,n\}$, assuming that $\sigma$ is chosen uniformly at random from the set of all such partitions. Let $W=W(n)$…
Maximum entropy approach to classification is very well studied in applied statistics and machine learning and almost all the methods that exists in literature are discriminative in nature. In this paper, we introduce a maximum entropy…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
Due to the success of generative flows to model data distributions, they have been explored in inverse problems. Given a pre-trained generative flow, previous work proposed to minimize the 2-norm of the latent variables as a regularization…
This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…
Probability densities that are not uniquely determined by their moments are said to be "moment-indeterminate", or "M-indeterminate". Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is…
In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…
We propose a multivariate probability distribution for categorical and ordinal random variables. To this end, we use the Grassmann distribution in conjunction with dummy encoding of categorical and ordinal variables. To realize the…
This paper is concerned with the following fractional $p$-Kirchhoff equation \begin{eqnarray*} \varepsilon ^{sp}M\left( {\varepsilon ^{sp - N}}\iint_{\mathbb{R}^{2N}}\frac{{{{\left| {u(x) - u(y)} \right|}^p}}}{{{{\left| {x - y} \right|}^{N…
In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible…
We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the…