We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Betaand Gam...

We investigate relaxation and correlations in a class of mean-reverting models for stochastic variances. derive closed-form expressions the correlation functions leverage general form term. also discuss three specific models— multiplicative, Heston (Cox-Ingersoll-Ross) combined multiplicative-Heston—whose steady-state probability density are Gamma, Inverse Gamma Beta Prime respectively, latter ...

There have been intense debates about the decomposition of regional diversity (gamma) into its within-community component (alpha) and between-community component (beta). Although a recent Ecology Forum achieved consensus in the use of "numbers equivalents" (Hill numbers) as the proper choice of diversity measure, three related major issues were still left unresolved. (1) What is the precise mea...

Wheeling: A Diagrammatic Analogue of the Duflo Isomorphism We construct and prove a diagrammatic version of the Duflo isomorphism between the invariant subalgebra of the symmetric algebra of a Lie algebra and the center of the universal enveloping algebra. This version implies the original for metrized Lie algebras (Lie algebras with an invariant non-degenerate bilinear form). As an application...

Given a finite group [Formula: see text], we study certain regular subgroups of the permutations which occur in classification theories two types algebraic objects: skew left braces with multiplicative isomorphic to text] and Hopf–Galois structures admitted by Galois extension fields text]. We questions when such yield or involving Hopf algebras. In particular, show that some cases isomorphism ...

there are several kinds of hyperrings, for example, krasnerhyperrings, multiplicative hyperring, general hyperrings and$h_v$-rings. in a multiplicative hyperring, the multiplication isa hyperoperation, while the addition is a binary operation. in this paper, the notion of derivation on multiplicative hyperrings is introduced and some related properties are investigated. {bf keywords:} multiplic...

We introduce and analyze a novel type of coalescent processes called cross-multiplicative that models system with two types particles, $A$ $B$. The bonds are formed only between the pairs particles opposite same rate for each bond, producing connected components made both types. solve Smoluchowski coagulation equations obtained as hydrodynamic limit corresponding Marcus-Lushnikov process. estab...

We present a construction of symmetry plane-groups for quasiperiodic point-sets in the plane, named beta-lattices. The algebraic framework is issued from counting systems called beta-integers, determined by Pisot-Vijayaraghavan (PV) algebraic integers β > 1. The beta-integer sets can be equipped with abelian group structures and internal multiplicative laws. These arithmetic structures lead to ...

Consistency is an important issue that causes wide public concern of decision makers in the decision-making process. The lack consistency preference relations results a vague solution. main goal this paper to achieve consistent intuitionistic multiplicative relation using graphical approach. We have proposed two different approaches for (IMPR). In first approach, we propose algorithm IMPR by cy...