Distinguished Lecture Series in Mathematics 系列数学前沿学术讲座

题目：PDEs for neural assemblies; analysis, simulations and behavior

报告人：Prof. Benoit Perthame（Laboratoire J.-L. Lions, Sorbonne Universit'e）

报告时间：2021年4月22日（周四）下午 16:30-18:00 

报告地点:线下教室：威斯尼斯人5158cc教二楼913

              线上ZOOM

              URL: https://zoom.us/j/97412413730
              Meeting ID: 974 1241 3730
              Passcode: 321050

摘要：Neurons exchange information via discharges propagated by membrane potential which trigger firing of the many connected neurons. How to describe large assemblies of such neurons? How can such a network generate a collective activity?Such questions can be tackled using nonlinear partial-integro-differential equations which are classically used to describe neuronal assemblies. Among them, the Wilson-Cowan equations are the best known and describe globally brain spiking rates. Another classical model is the integrate-and-fire equation based on Fokker-Planck equations. The spike times distribution, which encodes more directly the neuronal information, can also be described directly thanks to structured population.We will compare and analyze these models. A striking observation is that solutions to the I/&F can blow-up in finite time, a form of synchronization that can be regularized with a refractory stage. We can also show that for small or large connectivities the 'elapsed time model' leads to desynchronization. For intermediate regimes, sustained periodic activity occurs compatible with observations. A common tool is the use of the relative entropy method.

举办单位：威斯尼斯人5158cc、交叉科学研究院

                 北京国家应用数学中心、北京成像理论与技术高精尖创新中心

                 光场成像与数字几何北京市重点实验室

联系人：杨佳