Microscopic approach of a time elapsed neural model

TL;DR

This paper develops a novel framework connecting point process models of neural spike trains with age-structured PDE models, bridging microscopic and macroscopic approaches in neuroscience.

Contribution

It introduces a theoretical link between statistical point process models and PDE-based models for neural spike train analysis.

Findings

Established a mathematical connection between point processes and PDE models.

Provided a unified framework for modeling neural spike trains.

Enhanced understanding of neural information processing mechanisms.

Abstract

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.