The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

We discuss inequalities between the values of \emph{homotopical and cohomological Poincar\'e polynomials} self-products rationally elliptic spaces. For quasi-projective varieties, we prove generating functions for ranks graded pieces weight Hodge filtrations canonical mixed structures on homotopy cohomology groups. Several examples such polynomials related algebraic varieties are presented. One...

Let $\overrightarrow{G}$ be a directed graph with no component of orderless than~$3$, and let $\Gamma$ finite Abelian group such that $|\Gamma|\geq 4|V(\overrightarrow{G})|$ or if $|V(\overrightarrow{G})|$ is large enough respect to an arbitrarily fixed $\varepsilon>0$ then (1+\varepsilon)|V(\overrightarrow{G})|$. We show there exists injective mapping $\varphi$ from $V(\overrightarrow{G})$ the...

Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs both convex and nonconvex cases. Most them require a large number samples in some all iterations improved SGMs. In this paper, we propose new SGM, named PStorm, nonsmooth With moment...

Given a stable SISO LTI system $G$, we investigate the problem of estimating the $\mathcal{H}_\infty$-norm of $G$, denoted $||G||_\infty$, when $G$ is only accessible via noisy observations. Wahlberg et al. recently proposed a nonparametric algorithm based on the power method for estimating the top eigenvalue of a matrix. In particular, by applying a clever time-reversal trick, Wahlberg et al. ...