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Mathematical study on coding and ergodicity in a model brain

模型脑中编码和遍历性的数学研究

基本信息

批准号：
15016023
负责人：
AIHARA Kazuyuki
金额：
$ 9.73万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15016023/
关键词：
neural network ergodicity rate coding spike coding synchronization learning reproducibility mathematical models

项目摘要

In most electrophysiological experiments, it is often the case that experimenters present the same stimulation repeatedly and investigates trial average of activities of one or a few neurons. One important research topic to understain the brain function mechanism from such experiments is the "physiological ergodicity problem", which pursues conditions that "trial average of a single neuron" and "ensemble average of the responses of neurons to a single input" are equivalent. In this research, we analyzed the spatio-temporal spike coding and the ergodicity with mathematical models.First, we analysed dynamics of network that models the cerebral cortex, to clarify nonlinear interactions of the neurons, which influence the reproducibility of neuronal responses. As a result, we should that the firing sequence is highly reproducible in cases of shorter internal memory and smaller influence of internal connections than external inputs. In addition, we studied dynamics of the cluster state betw … More een synchronous and asynchronous states the connection structure of the cluster generation, and dependency to synaptic learning.Next, we investigated relations among nonlinear spatio-temporal dynamics of the neural network model, noise, network structure, and learning. Based on the STDP (Spike Timing Dependent Plasticity) learning rule and the network architecture, we clarified that coexistence of various coding and cluster formation can be self-organized when there are two or more input sources. Further, by introducing Mexican-hat type connections to Synfire-Chain models, we showed the possibility of coding the stimulus strength into the size of the activated area and the existence of two non-trivial stable states of the isolated local excitation and the uniform excitation. We also studied the relation between the small-world network structure and spatio-temporal dynamics. In addition, we examined relations between ergodicity and noise in terms of synchronous firing and possible functions of depolarizing GABA in information coding. Less

在大多数电生理学实验中，实验者经常重复呈现相同的刺激，并调查一个或几个神经元的活动的试算平均值。从这类实验中揭示大脑功能机制的一个重要研究课题是“生理遍历问题”，它追求“单个神经元的试验平均值”和“神经元对单个输入的响应的集合平均值”相等的条件。在这项研究中，我们使用数学模型分析了时空脉冲编码和遍历性。首先，我们分析了模拟大脑皮层的网络的动力学，以阐明神经元之间的非线性相互作用，这些因素影响了神经元反应的重复性。因此，我们应该知道，在内部存储器较短且内部连接的影响比外部输入小的情况下，触发序列具有高度的重复性。此外，我们还研究了…之间团簇态的动力学接下来，我们研究了神经网络模型的非线性时空动力学、噪声、网络结构和学习之间的关系。基于STDP(Spike Timing Dependent Platform)学习规则和网络结构，我们阐明了当有两个或两个以上的输入源时，各种编码的共存和簇的形成可以自组织。此外，通过将墨西哥帽型连接引入Synfire链模型，我们证明了将刺激强度编码为激活区大小的可能性，以及孤立局部激发和均匀激发两个非平凡稳定态的存在。我们还研究了小世界网络结构与时空动力学的关系。此外，我们从同步激发的角度考察了遍历性和噪声之间的关系，以及在信息编码中去极化GABA的可能功能。较少