Implementing an accurate and fast activation function with low cost is a crucial aspect to the implementation of Deep Neural Networks (DNNs) on FPGAs. We propose a highaccuracy approximation approach for the hyperbolic tangent activation function of artificial neurons in DNNs. It is based on the Discrete Cosine Transform Interpolation Filter (DCTIF). The proposed architecture combines simple ar...

Abstract: From the approximate symmetry point of view, the perturbed burgers equation is investigated. The symmetry of a system of the corresponding PDEs which approximates the perturbed burgers equation is constructed and the corresponding general approximates symmetry reduction is derived, which enables infinite series solutions and general formulae. Study shows that the similarity solutions ...

We present a method to compute enclosures of the local invariant manifolds of a hyperbolic saddle of an analytic vector eld. By considering parametrisations of the invariant manifolds, instead of describing them as graphs of functions from the corresponding tangent spaces, we nd simple recursive formulae for their Taylor coe cients. In addition to this, we obtain rigorous bounds on the remainde...

These lecture notes were written to accompany a minicourse given at the School and Workshop on Dynamical Systems at IMPA (Rio de Janeiro), January 2006. Warning: These notes are unedited lecture notes and do contain errors! Proceed with caution... Let f : M → M be a (pointwise) partially hyperbolic diffeomor-phism. Recall what partially hyperbolic means. At every point in M , there exist tangen...

One of the most important problems in study geometric function theory is knowing how to obtain sharp bounds coefficients that appear Taylor–Maclaurin series univalent functions. In present investigation, our aim calculate some estimates involving for family convex functions with respect symmetric points and associated a hyperbolic tangent function. These include first four initial coefficients,...

The gradient fields v of nonsingular functions f on compact 3folds X with boundary are used to generate their spines K(f, v). We study the transformations of K(f, v) that are induced by deformations of the data (f, v). We link the Matveev complexity of c(X) with counting the trajectories of the v-flow that are tangent to the boundary ∂X at a pair of distinct points (call them double-tangent tra...

In arid and semi-arid environments, groundwater plays a significant role in the ecosystem. In the last decades, groundwater levels have decreased due to the increasing demand for water, weak irrigation management and soil damage. For the effective management of groundwater, it is important to model and predict fluctuations in groundwater levels. In this study, groundwater table in Kashan plain ...

In this article, we solve the Duffin--Kemmer--Petiau (DKP) equation in presence of hyperbolic tangent potential for spin-one particles. By partitioning spinor, show that DKP is equivalent to Klein--Gordon formalism. The scattering solutions are derived terms hypergeometric functions. reflection $R$ and transmission $T$ coefficients calculated Gamma results superradiance phenomenon when a specif...

There is a slight disparity in smooth ergodic theory, between Pesin theory and the Pugh-Shub partially hyperbolic theory. Both theories assume a weakened form of hyperbolicity and conclude ergodicity. While the two theories have considerable overlap, Pesin theory assumes a C hypothesis, whereas the Pugh-Shub stable ergodicity theorem assumes a C hypothesis. The purpose of this paper is to close...

In this paper, without assuming the boundedness, strict monotonicity and differentiability of the activation functions, we utilize a new Lyapunov function to analyze the global convergence of a class of neural networks models with time delays. A new sufficient condition guaranteeing the existence, uniqueness and global exponential stability of the equilibrium point is derived. This stability cr...