Beta is found to be a function of several leading economic indicators and government policy variables within the context of the Variable Beta Model which incorporates economic characteristics in the single index model in a multiplicative manner. When contemporaneous macroeconomic descriptors are replaced with reporting-period-lagged macroeconomic descriptors, in the Lagged Variable Beta Model, ...

Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as product two smaller matrices, $W$ and $H$. In this paper, we introduce a general framework to design multiplicative updates (MU) for NMF based on $\beta$-divergences ($\beta$-NMF) with disjoint equality constraints, penalty terms in objective function. By disjoint, mean that each variable...

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...

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 ...

in this paper, we study a coupled system of nonlinear fractional differential equations with multi-point boundary condi- tions. the differential operator is taken in the riemann-liouville sense. applying the schauder fixed-point theorem and the contrac- tion mapping principle, two existence results are obtained for the following system d^{alpha}_{0+}x(t)=fleft(t,y(t),d^{p}_{0+}y(t)right), t in (0,...