Weighted automata (WFAs) provide a general framework for the representation of functions mapping strings to real numbers. They include as special instances deterministic finite automata (DFAs), hidden Markov models (HMMs), and predictive states representations (PSRs). In recent years, there has been a renewed interest in weighted automata in machine learning due to the development of efficient ...

We introduce the weighted Yamabe flow{∂g∂t=(rϕm−Rϕm)g∂ϕ∂t=m2(Rϕm−rϕm) on a smooth metric measure space (Mn,g,e−ϕdvolg,m), where Rϕm denotes associated scalar curvature, and rϕm mean value of curvature. prove long-time existence convergence flow if dimension n satisfies n⩾3.

‎in this paper‎, ‎an approach based on statistical spline model (ssm) and collocation method is proposed to solve volterra-fredholm integral equations‎. ‎the set of collocation nodes is chosen so that the points yield minimal error in the nodal polynomials‎. ‎under some standard assumptions‎, ‎we establish the convergence property of this approach‎. ‎numerical results on some problems are given...

the purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $delta$ and give some inclusion relations.