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The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present article is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.
We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since the last discharge, i.e., the refractory period. In this extension we incorporate the elapsed
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are soluti
Recently, FPGA has been increasingly applied to problems such as speech recognition, machine learning, and cloud computation such as the Bing search engine used by Microsoft. This is due to FPGAs great parallel computation capacity as well as low pow
In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an arbitrary confi
A developmental disorder that severely damages communicative and social functions, the Autism Spectrum Disorder (ASD) also presents aspects related to mental rigidity, repetitive behavior, and difficulty in abstract reasoning. More, imbalances betwee