Microscopic approach of a time elapsed neural model
This work addresses the challenge of integrating microscopic and macroscopic neural models for researchers in computational neuroscience, but it appears incremental as it builds on existing frameworks without claiming major breakthroughs.
The paper tackles the problem of modeling spike trains in the brain by bridging point process models (Poisson, Wold, Hawkes) with age-structured partial differential equations, aiming to connect statistical fits of real data to macroscopic PDE approaches.
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.