An SPDE Approach to Self-Excitatory Neuronal Models

自兴奋神经元模型的 SPDE 方法

基本信息

  • 批准号:
    2440959
  • 负责人:
  • 金额:
    --
  • 依托单位:
  • 依托单位国家:
    英国
  • 项目类别:
    Studentship
  • 财政年份:
    2020
  • 资助国家:
    英国
  • 起止时间:
    2020 至 无数据
  • 项目状态:
    未结题

项目摘要

This project falls within the EPSRC Statistics and Applied Probability research area. This project aims to study a system of interacting diffusions on the negative real line of the McKean-Vlasov type with a resetting component and all are influenced by an independent common source of noise. When one of the diffusions of the system hits zero, its value is reset and all other diffusions in the system will receive a continuous impulse to their value over a predetermined timescale. This system is a generalisation of noisy integrate-and-fire models in neuroscience that model the membrane potential of a neuron in biological systems. An important feature of these models is that when the membrane potential reaches a certain threshold it is instantly reset to some predetermined value and all other neurons in the system receive an impulse that affects their voltage. The primary hypothesis of noisy integrate-and-fire models is that the action potential threshold and shape are invariant from spike to spike, and thus a precise description of the spike can be omitted and simply sketched by a spiking threshold. The diffusion model captures solely spike generation and places the biological aspects of the neuron into the noise. It has been observed that neurons react in a predictable and reproducible manner to temporally structured stimuli. The main sources of stochasticity in the model arises from the innate stochasticity in the biological mechanisms which cause voltage changes in neurons and the neurons may receive inputs from other neurons in the system which are not being observed. The latter may be thought of as the common source of noise in the model.The main objective of this project is to show the existence and uniqueness of the mean-field limit to the system of diffusions described above. Moreover, as the interactions between diffusions occur over predefined time scales, this project will attempt to show that, as the time scales on which interactions occur approach zero, the models where the interaction between diffusions occur instantly are recovered. Aside from these aims, this project will also attempt to prove the convergence of an Euler-Maruyama type method for the numerical solution of the limiting system.A further novelty of this research project comes from there being a common noise source felt by all diffusions in the finite system which leads to showing well-posedness and solutions to an SPDE that describes the law of the representative particle in the limiting system with infinite diffusions. The SPDE approach which will be employed by this project leads to looking for solutions being elements of the càdlàg functions taking values in the space of tempered distributions endowed with the M1 topology. This approach differs from existing literature as generally solutions to large scale limits of systems interacting diffusions are looked for in the space of probability measures on the space of càdlàg functions endowed with the M1 topology.
该项目属于EPSRC统计和应用概率研究领域的福尔斯。本计画的目的是研究McKean-Vlasov型负真实的直线上的相互作用扩散系统,其中包含一个重置元件,且所有扩散都受到一个独立的共同噪声源的影响。当系统的一个扩散达到零时,其值被重置,并且系统中的所有其他扩散将在预定的时间尺度上接收到对其值的连续脉冲。该系统是神经科学中噪声集成和激发模型的概括,该模型模拟生物系统中神经元的膜电位。这些模型的一个重要特征是,当膜电位达到某个阈值时,它会立即重置为某个预定值,系统中的所有其他神经元都会收到一个影响其电压的脉冲。噪声积分激发模型的主要假设是动作电位阈值和形状从尖峰到尖峰是不变的,因此可以省略尖峰的精确描述,并简单地由尖峰阈值勾勒。扩散模型仅捕获尖峰生成,并将神经元的生物学方面置于噪声中。已经观察到,神经元以可预测和可再现的方式对时间结构化的刺激作出反应。模型中随机性的主要来源来自生物机制中的先天随机性,该生物机制导致神经元中的电压变化,并且神经元可以接收来自系统中未被观察到的其他神经元的输入。后者可以被认为是噪声的共同来源在model. This项目的主要目标是显示平均场极限的存在性和唯一性的上述扩散系统。此外,由于扩散之间的相互作用发生在预定义的时间尺度上,本项目将试图表明,随着相互作用发生的时间尺度接近零,扩散之间的相互作用立即发生的模型被恢复。除了这些目标之外,本研究的另一个新奇之处在于,在有限系统中,所有的扩散都能感觉到一个共同的噪声源,这导致了很好的显示,的适定性和解决方案的SPDE,描述了法律的代表性粒子在有限的系统与无限扩散。该项目将采用的SPDE方法导致寻找作为càdlàg函数的元素的解决方案,这些函数在具有M1拓扑的回火分布空间中取值。这种方法不同于现有的文献,因为通常在赋予M1拓扑的càdlàg函数空间上的概率测度空间中寻找系统相互作用扩散的大尺度极限的解。

项目成果

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其他文献

吉治仁志 他: "トランスジェニックマウスによるTIMP-1の線維化促進機序"最新医学. 55. 1781-1787 (2000)
Hitoshi Yoshiji 等:“转基因小鼠中 TIMP-1 的促纤维化机制”现代医学 55. 1781-1787 (2000)。
  • DOI:
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    0
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LiDAR Implementations for Autonomous Vehicle Applications
  • DOI:
  • 发表时间:
    2021
  • 期刊:
  • 影响因子:
    0
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  • 通讯作者:
生命分子工学・海洋生命工学研究室
生物分子工程/海洋生物技术实验室
  • DOI:
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    0
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吉治仁志 他: "イラスト医学&サイエンスシリーズ血管の分子医学"羊土社(渋谷正史編). 125 (2000)
Hitoshi Yoshiji 等人:“血管医学与科学系列分子医学图解”Yodosha(涉谷正志编辑)125(2000)。
  • DOI:
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    0
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Effect of manidipine hydrochloride,a calcium antagonist,on isoproterenol-induced left ventricular hypertrophy: "Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,K.,Teragaki,M.,Iwao,H.and Yoshikawa,J." Jpn Circ J. 62(1). 47-52 (1998)
钙拮抗剂盐酸马尼地平对异丙肾上腺素引起的左心室肥厚的影响:“Yoshiyama,M.,Takeuchi,K.,Kim,S.,Hanatani,A.,Omura,T.,Toda,I.,Akioka,
  • DOI:
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