In this paper, we give some new coupled common  fixed point theorems for probabilistic $varphi$-contractions  in Menger probabilistic metric spaces.  As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...

In this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by George and Veeramani cite{Vee1}. Some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of ou...

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...

We consider random walks on the mapping class group that have finite first moment with respect to the word metric, whose support generates a non-elementary subgroup and contains a pseudo-Anosov map whose invariant Teichmüller geodesic is in the principal stratum of quadratic differentials. We show that a Teichmüller geodesic typical with respect to the harmonic measure for such random walks, is...

Many state-of-the-art Machine Translation (MT) evaluation metrics are complex, involve extensive external resources (e.g. for paraphrasing) and require tuning to achieve best results. We present a simple alternative approach based on dense vector spaces and recurrent neural networks (RNNs), in particular Long Short Term Memory (LSTM) networks. ForWMT-14, our new metric scores best for two out o...

A combination of satellite imagery, shipboard profiles, drifter tracks, and moored current observations reveals that an anticyclonic eddy off the coast of northern California transported plumes of suspended sediments from the continental shelf into the deep ocean. The horizontal scale of the eddy was about 90 kilometers, and the eddy remained over the continental shelf and slope for about 2 mon...

In this paper we show that a feedforward neural network with at leastone hiddenlayer can approximate the meaning function TP for an acceptable logic program P . This is found by using the property of acceptable logic programs that for this class of programs the meaning function TP is a contraction mapping on the complete metric space of the interpretations for P as shown by Fitting in [3]. Usin...

We propose the Recurrent Soft Attention Model, which integrates the visual attention from the original image to a LSTM memory cell through a down-sample network. The model recurrently transmits visual attention to the memory cells for glimpse mask generation, which is a more natural way for attention integration and exploitation in general object detection and recognition problem. We test our m...

We consider the dynamical behavior of Martin-Löf random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic model for the dynamics. Trough this construction we prove that such points have typical statistical behavior (the behavior which is typical in the Birkhoff ergodic...

A novel invariant pattern recognition approach is proposed based on a special gradient-type recurrent analog associative memory. The system exhibits stable equilibrium points in predefined positions specified by feature vectors extracted from the training set, while invariance to geometrical transformations is inferred by using the tangent distance. Experimental results for handwritten characte...