简介: |
Abstract: ?
The maximum entropy principle is
widely used in diverse fields. ?We address the issue of why the
second order maximum entropy model, by ?using only firing rates and
second order correlations of neurons as ?constraints, can well
capture the observed distribution of neuronal ?firing patterns in
many neuronal networks, thus, conferring its great ?advantage in that
the degree of complexity in the analysis of neuronal ?activity data
reduces drastically from O (2^n) to O(n^2), where n is ?the number of
neurons under consideration.
We first derive an ?expression for
the effective interactions of the n-th order maximum ?entropy model
using all orders of correlations of neurons as ?constraints and show
that there exists a recursive relation among the ?effective
interactions in the model.
Then, via a perturbative ?analysis,
we explore a possible dynamical state in which this ?recursive
relation gives rise to the strengths of higher order ?interactions
always smaller than the lower orders. Both numerical ?simulations and
experimental data demonstrate the existence of such ?dynamical state
in neuronal network dynamics.
Finally, we invoke ?this hierarchy
of effective interactions to provide a possible ?mechanism underlying
the success of the second order maximum entropy model.
?About speaker:
Professor Zhou’s research is
?mainly focusing on mathematical modeling and scientific computing for
?scientific problems in physical and biological sciences. In
?particular, he’s interested in understanding of the relation between
?structure and functions of biological neuronal networks, development
?of new efficient computational methods for modeling large-scale
?cortical networks, discovery of potential mechanisms underlying
?information processing in the brain, and investigation of new
?mathematical structures and tools to extract useful information from
?data measured in experiment.
?报告人简介:
?
周栋焯教授分别于2002和2007年在北京大学获学士和博士学位， 2007年至2009年，他在美国纽约大学库朗研究所从事博士后研究工作。周教授于2010年加入上海交通大学自然科学研究院、数学科学学院，2010年1月至2016年1月任特别研究员，2016年2月至今任教授。周栋焯博士目前的主要研究领域为生物及物理领域中的应用数学问题，如高分子流体的多尺度建模与计算、神经元网络动力学的数学性质与方法的研究、生物与物理系统中的非线性与混沌现象以及大尺度的视觉神经网络的建模与模拟的研究。 |
