THE ROLE OF FLUCTUATIONS IN COARSE-GRAINED DESCRIPTIONS OF NEURONAL   NETWORKS

CORC > 北京大学 > 生命科学学院

	THE ROLE OF FLUCTUATIONS IN COARSE-GRAINED DESCRIPTIONS OF NEURONAL NETWORKS
	Cai, David ; Tao, Louis ; Shkarayev, Maxim S. ; Rangan, Aaditya V. ; McLaughlin, David W. ; Kovacic, Gregor
刊名	communications in mathematical sciences
	2012
关键词	Integrate-and-fire neuronal network kinetic theory Fokker-Planck equation mean-driven limit PRIMARY VISUAL-CORTEX POPULATION-DENSITY APPROACH EXCITATORY NEURAL-NETWORKS MONKEY STRIATE CORTEX ORIENTATION SELECTIVITY FUNCTIONAL CONNECTIVITY CORTICAL-NEURONS COMPLEX NETWORKS PYRAMIDAL NEURONS SPIKING NEURONS
英文摘要	This paper reviews our recent work addressing the role of both synaptic-input and connectivity-architecture fluctuations in coarse-grained descriptions of integrate-and-fire (I&F) point-neuron network models. Beginning with the most basic coarse-grained description, the all-to-all coupled, mean-field model, which ignores all fluctuations, we add the effects of the two types of fluctuations one at a time. To study the effects of synaptic-input fluctuations, we derive a kinetic-theoretic description, first in the form of a Boltzmann equation in (2+1) dimensions, simplifying that to an advection-diffusion equation, and finally reducing the dimension to a system of two (1+1)-dimensional kinetic equations via the maximum entropy principle. In the limit of an infinitely-fast conductance relaxation time, we derive a Fokker-Planck equation which captures the bifurcation between a bistable, hysteretic operating regime of the network when the amount of synaptic-input fluctuations is small, and a stable regime when the amount of fluctuations increases. To study the effects of complex neuronal-network architecture, we incorporate the network connectivity statistics in the mean-field description, and investigate the dependence of these statistics on the statistical properties of the neuronal firing rates for three network examples with increasingly complex connectivity architecture.; Mathematics, Applied; SCI(E); 2; ARTICLE; 1,SI; 307-354; 10
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/393656]
专题	生命科学学院
推荐引用方式 GB/T 7714	Cai, David,Tao, Louis,Shkarayev, Maxim S.,et al. THE ROLE OF FLUCTUATIONS IN COARSE-GRAINED DESCRIPTIONS OF NEURONAL NETWORKS[J]. communications in mathematical sciences,2012.
APA	Cai, David,Tao, Louis,Shkarayev, Maxim S.,Rangan, Aaditya V.,McLaughlin, David W.,&Kovacic, Gregor.(2012).THE ROLE OF FLUCTUATIONS IN COARSE-GRAINED DESCRIPTIONS OF NEURONAL NETWORKS.communications in mathematical sciences.
MLA	Cai, David,et al."THE ROLE OF FLUCTUATIONS IN COARSE-GRAINED DESCRIPTIONS OF NEURONAL NETWORKS".communications in mathematical sciences (2012).