Related papers: A Hypergeometric Formula Yielding Hilbert-Schmidt …

In this paper, we propose methods for computing the Hilbert series of multigraded right modules over the free associative algebra. In particular, we compute such series for noncommutative multigraded algebras. Using results from the theory…

A recent paper by the first and third authors together with Sabourin raised the question of what the possible Hilbert functions are for fat point subschemes of the form $2p_1+...+2p_r$, for all possible choices of $r$ distinct points in the…

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct new summation formulas…

The ability to compute the exact divergence between two high-dimensional distributions is useful in many applications but doing so naively is intractable. Computing the alpha-beta divergence -- a family of divergences that includes the…

The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute.…

In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…

The study is devoted to the construction of dynamical symmetry algebra of confluent hypergeometric function $_1F_1$ and $\Psi_2$-Humbert function and to derive some generating relations and reduction formulas for $_1F_1$ and $\Psi_2$…

The probabilities for gaps in the eigenvalue spectrum of the finite dimension $ N \times N $ random matrix Hermite and Jacobi unitary ensembles on some single and disconnected double intervals are found. These are cases where a reflection…

We first find an explicit formula for the square root of positive $2 \times 2$ operator matrices with commuting entries, and then use it to define and study semi-hyponormality for commuting pairs of Hilbert space operators. \ For the…

This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…

A complete description of the multitudinous ways in which quantum particles can be entangled requires the use of high-dimensional abstract mathematical spaces. We report here a particularly interesting feature of the nine-dimensional convex…

Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…

In the study of Hilbert schemes, the integer partition $\lambda$ helps researchers identify some geometric and combinatorial properties of the scheme in question. To aid researchers in extracting such information from a Hilbert polynomial,…

We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient…

By systematically applying ten inequivalent two-part relations between hypergeometric sums 3F2(1) to the published database of all such sums, 66 new sums are obtained. Many results extracted from the literature are shown to be special cases…

We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…

In this work some advances in the theory of curvature of two-dimensional probability manifolds corresponding to families of distributions are proposed. It is proved that location-scale distributions are hyperbolic in the Information…

In this paper, we derive closed-form exact expressions for the main statistics of the ratio of squared alpha-mu random variables, which are of interest in many scenarios for future wireless networks where generalized distributions are more…

The Hilbert class polynomial has as roots the j-invariants of elliptic curves whose endomorphism ring is a given imaginary quadratic order. It can be used to compute elliptic curves over finite fields with a prescribed number of points.…

Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_{\xi} s_{\eta}^*$…