First, a process of building of the neural network for events forecasting is presented, that is the selection of networks’ architecture and parameters. Next, the effect of adding data calibrated by nonlinear input function to input data calibrated linearly is described. The nonlinear input function hyperbolic tangent was accepted. Hyperbolic tangent sigmoid transfer function and log sigmoid tra...

1. Notations and Assumptions 2 2. Error calculus 2 2.1. Ulp calculus 2 2.2. Relative error analysis 4 2.3. Generic error of addition/subtraction 4 2.4. Generic error of multiplication 5 2.5. Generic error of inverse 5 2.6. Generic error of division 6 2.7. Generic error of square root 7 2.8. Generic error of the exponential 7 2.9. Generic error of the logarithm 8 2.10. Ulp calculus vs relative e...

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...

1. Error calculus 2 1.1. Ulp calculus 2 1.2. Relative error analysis 4 1.3. Generic error of addition/subtraction 4 1.4. Generic error of multiplication 5 1.5. Generic error of inverse 5 1.6. Generic error of division 6 1.7. Generic error of square root 7 1.8. Generic error of the exponential 7 1.9. Generic error of the logarithm 8 1.10. Ulp calculus vs relative error 9 2. Low level functions 9...

Neural networks have a wide range of applications in analog and digital signal processing Nonlinear activation function is one of the main building blocks of artificial neural networks. Hyperbolic tangent and sigmoid are the most used nonlinear activation functions of NN.This project proposes a knowledge-based neural network (KBNN) modeling approach with new hyperbolic tangent function . The KB...

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...

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 ...

The aim of this short lecture course is to develop Selberg's trace formula for a compact hyperbolic surface M, and discuss some of its applications. The main motivation for our studies is quantum chaos: the Laplace-Beltrami operator −∆ on the surface M represents the quantum Hamiltonian of a particle, whose classical dynamics is governed by the (strongly chaotic) geodesic flow on the unit tange...