相关论文: The estimate of $\chi^2$ distance between binomial…

The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…

In this paper, we examine how far a polynomial in $\mathbb{F}_2[x]$ can be from a squarefree polynomial. For any $\epsilon>0$, we prove that for any polynomial $f(x)\in\mathbb{F}_2[x]$ with degree $n$, there exists a squarefree polynomial…

Distance transformation is an image processing technique used for many different applications. Related to a binary image, the general idea is to determine the distance of all background points to the nearest object point (or vice versa). In…

Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter…

The aim of this text is to extend the theory of generalized ordinary differential equations to the setting of metric spaces. We present existence and uniqueness theorems that significantly improve previous results even when restricted back…

The degree distribution is an important characteristic of complex networks. In many applications, quantification of degree distribution in the form of a fixed-length feature vector is a necessary step. On the other hand, we often need to…

This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…

We survey some basic results on the Gromov-Prohorov distance between metric measure spaces. (We do not claim any new results.) We give several different definitions and show the equivalence of them. We also show that convergence in the…

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…

The problem of estimating location (scale) parameters $\theta_1$ and $\theta_2$ of two distributions when the ordering between them is known apriori (say, $\theta_1\leq \theta_2$) has been extensively studied in the literature. Many of…

A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…

We use the bilocal method to derive the large $N$ solution of the most general $QCD_2$.

We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…

Dempster-Shafer theory of evidence (D-S theory) is widely used in uncertain information process. The basic probability assignment(BPA) is a key element in D-S theory. How to measure the distance between two BPAs is an open issue. In this…

We prove an equidistribution result for the zeros of polynomials with integer coefficients and simple zeros. Specifically, we show that the normalized zero measures associated with a sequence of such polynomials, having small height…

We study different ways of determining the mean distance $ < r_n >$ between a reference point and its $n$-th neighbour among random points distributed with uniform density in a $D$-dimensional Euclidean space. First we present a heuristic…

The generalized complex numbers can be realized in terms of $2\times2$ or higher-order matrices and can be exploited to get different ways of looking at the trigonometric functions. Since Chebyshev polynomials are linked to the power of…

Hayashi's Pinching Inequality, which establishes a matrix inequality between a semidefinite matrix and a multiple of its "pinched" version via a projective measurement, has found many applications in quantum information theory and beyond.…

We prove results on the decidability and complexity of computing the total variation distance (equivalently, the $L_1$-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between…

Motivated by putting empirical work based on (synthetic) election data on a more solid mathematical basis, we analyze six distances among elections, including, e.g., the challenging-to-compute but very precise swap distance and the distance…