Related papers: Statistical Enumeration of Groups by Double Cosets
We consider the problem of discovering subgroup $H$ of permutation group $S_{n}$. Unlike the traditional $H$-invariant networks wherein $H$ is assumed to be known, we present a method to discover the underlying subgroup, given that it…
Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is…
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary…
We investigate products of certain double cosets for the symmetric group and use the findings to derive some multiplication formulas for q-Schur superalgebras. This gives a combinatorialisation of the relative norm approach developed by the…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general $sl(2)$ embeddings into Lie (super)algebras, and in the case of general $osp(1|2)$ embeddings into Lie superalgebras. In another development…
Two concepts of symmetry for the distributions of positive random variables $Y$ are log-symmetry (symmetry of the distribution of $\log Y$) and R-symmetry [7]. In this paper, we characterise the distributions that have both properties,…
To address the computational issue in empirical likelihood methods with massive data, this paper proposes a grouped empirical likelihood (GEL) method. It divides $N$ observations into $n$ groups, and assigns the same probability weight to…
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…
Let $G$ be a finite group and let $H$ be a proper subgroup of $G$ of minimal index. By applying an old result of Y. Berkovich, we provide a polynomial algorithm for computing $|G : H|$ for a permutation group $G$. Moreover, we find $H$…
The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tessellation of its universal covering, the hyperbolic…
To every poset P, Stanley (1986) associated two polytopes, the order polytope and the chain polytope, whose geometric properties reflect the combinatorial qualities of P. This construction allows for deep insights into combinatorics by way…
In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality) between gauged Wess-Zumino-Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based…
We study the problem of distribution to real-value regression, where one aims to regress a mapping $f$ that takes in a distribution input covariate $P\in \mathcal{I}$ (for a non-parametric family of distributions $\mathcal{I}$) and outputs…
We introduce a notion of $k$-convexity and explore polygons in the plane that have this property. Polygons which are \mbox{$k$-convex} can be triangulated with fast yet simple algorithms. However, recognizing them in general is a 3SUM-hard…
These notes are an introduction to symplectic groupoids and the double structures associated with them. The treatment is intended to lie about midway between the original account of Coste, Dazord and Weinstein, which relied on effective use…
We study finitely generated pairs of groups $H \leq G$ such that the Schreier graph of $H$ has at least two ends and is \emph{narrow}. Examples of narrow Schreier graphs include those that are quasi-isometric to finitely ended trees or have…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…
The dualised formulation of the symmetric space sigma model is peformed for a general scalar coset G/K where G is a maximally non-compact group and K is it's maximal compact subgroup.By using the twisted self-duality condition the general…