Related papers: Towards Dead Time Inclusion in Neuronal Modeling

We study both analytically and numerically the effects of including refractory periods in the Hopfield model for associative memory. These periods are introduced in the dynamics of the network as thresholds that depend on the state of the…

The relationship between complex, brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize Maximum Caliber, a dynamical inference principle, to build a minimal, yet general model of the collective…

The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…

A neural field models the large scale behaviour of large groups of neurons. We extend results of van Gils et al. [2013] and Dijkstra et al. [2015] by including a diffusion term into the neural field, which models direct, electrical…

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found…

Networks of excitable nodes have recently attracted much attention particularly in regards to neuronal dynamics, where criticality has been argued to be a fundamental property. Refractory behavior, which limits the excitability of neurons…

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…

Long-time series of neuronal recordings are resulting from the activity of connected neuronal networks. Yet how neuronal properties can be extracted remains empirical. We review here the data analysis based on network models to recover…

We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…

The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these…

There are time series that are amenable to recurrent neural network (RNN) solutions when treated as sequences, but some series, e.g. asynchronous time series, provide a richer variation of feature types than current RNN cells take into…

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…

We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…

Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response…

In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of…

Training neural networks to perform different tasks is relevant across various disciplines. In particular, Recurrent Neural Networks (RNNs) are of great interest in Computational Neuroscience. Open-source frameworks dedicated to Machine…

Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis…

A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…

Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on the joint density of the first passage time of the first…