The aim of this paper is the study of problem of existence of Levitan almost periodic, almost automorphic, recurrent and Poisson stable solutions of seconde order differential equation (1) x′′ = f(σ(t, y), x, x′), (y ∈ Y ) where Y is a complete metric space and (Y,R, σ) is a dynamical system (driving system). For equation (1) with increasing (with respect to second variable) function f the exis...

Let ϕ:X×R→X be a continuous flow on compact metric space (X,d). In this article we constructively prove the existence of Lyapunov function for ϕ which is strictly decreasing outside SCRd(ϕ). Such result generalizes Conley's Fundamental Theorem Dynamical Systems strong chain recurrent set.

We propose a text-based recommendation engine that utilizes recurrent neural networks to flexibly map textual input into continuous vector representations tailored to the recommendation task. Here, the text objects are documents such as Wikipedia articles or question and answer pairs. As neural models require substantial training time, we introduce a sequential component so as to quickly adjust...

Neural network language models are often trained by optimizing likelihood, but we would prefer to optimize for a task specific metric, such as BLEU in machine translation. We show how a recurrent neural network language model can be optimized towards an expected BLEU loss instead of the usual cross-entropy criterion. Furthermore, we tackle the issue of directly integrating a recurrent network i...

BACKGROUND AND PURPOSE Minor stroke and transient ischemic attack portend a significant risk of disability. Three possible mechanisms for this include disability not captured by the National Institutes of Health Stroke Scale, symptom progression, or recurrent stroke. We sought to assess the relative impact of these mechanisms on disability in a population of patients with transient ischemic att...

This paper,  applies the concept  of KM-fuzzy metric spaces and  introduces a novel concept of KM-fuzzy metric  graphs based on KM-fuzzy metric spaces.  This study, investigates the finite KM-fuzzy metric spaces with respect to metrics and KM-fuzzy metrics and constructs KM-fuzzy metric spaces on any given non-empty sets. It tries to  extend   the concept of KM-fuzzy metric spaces to  a larger ...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...