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). |
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