相关论文: Average Size of Implicational Bases

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…

We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…

Let $G$ be a graph on $[n]$ and $J_G$ be the binomial edge ideal of $G$ in the polynomial ring $S=\mathbb{K}[x_1,\ldots,x_n,y_1,\ldots,y_n]$. In this paper we investigate some topological properties of a poset associated to the minimal…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

In contrast to problems of interference in (exogenous) treatments, models of interference in unit-specific (endogenous) outcomes do not usually produce a reduced-form representation where outcomes depend on other units' treatment status…

In this paper, we give a sufficient condition for a set $\mathal G$ of polynomials to be a Gr\"obner basis with respect to a given term-order for the ideal $I$ that it generates. Our criterion depends on the linkage pattern of the ideal $I$…

An irredundant base of a group $G$ acting faithfully on a finite set $\Gamma$ is a sequence of points in $\Gamma$ that produces a strictly descending chain of pointwise stabiliser subgroups in $G$, terminating at the trivial subgroup.…

Parametric Gr\"obner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case…

Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…

We introduce the notion of Groebner S-basis of an ideal of the free associative algebra K<X> over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Groebner S-bases of the ideal…

In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…

In this paper, we investigate gravitational interactions of massive fields with arbitrary integer and half-integer spin, trying to construct a vertex that contains both standard minimal and non-minimal interaction terms necessary to make…

The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…

In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…

We introduce and investigate generalizations of interval and proper interval graphs to simplicial complexes, including strong interval, unit interval, and under closed variants. Through equivalent combinatorial and algebraic…

We identify the size of the largest connected component in a subcritical inhomogeneous random graph with a kernel of preferential attachment type. The component is polynomial in the graph size with an explicitly given exponent, which is…

Importance sampling approximates expectations with respect to a target measure by using samples from a proposal measure. The performance of the method over large classes of test functions depends heavily on the closeness between both…

A classical theorem of Balcar, Pelant, and Simon says that there is a base matrix of height h, where h is the distributivity number of P(omega)/fin. We show that if the continuum c is regular, then there is a base matrix of height c, and…

A base for a permutation group $G$ acting on a set $\Omega$ is a subset $\mathcal{B}$ of $\Omega$ such that the pointwise stabiliser $G_{(\mathcal{B})}$ is trivial. Let $n$ and $r$ be positive integers with $n>2r$. The symmetric and…

We investigate the problem of constructing unextendible product bases in the qubit case - that is, when each local dimension equals 2. The cardinality of the smallest unextendible product basis is known in all qubit cases except when the…