赢家通吃随机神经网络的谱
Spectra of winner-take-all stochastic neural networks
摘要：
在最近几年中，为了响应经验发现，表明无标度自组织现象在中尺度水平上出现在复杂的神经系统中，在神经科学文献中一直在寻找合适的模型和理论解释，参见Bullmore和Sporns最近的调查（2009）。在Piekniewski和Schreiber（2008）中，我们开发了一个简单易行的数学模型，对上述现象中的一类特殊现象，即功能性脑网络在功能性磁共振成像下的介观水平自组织，提供了一些启示，我们在其中与现有的经验报告取得了高度一致。针对神经科学界，我们的工作Piekniewski和Schreiber（2008）依赖于对一类递归神经网络中信息流结构的半严格研究，这些网络表现出渐近无标度行为，并允许用所谓的赢家通吃动力学来描述。本论文的目的是定义和研究这些赢家通吃网络与充分的数学严谨性的背景下，其渐近谱特性，众所周知是感兴趣的神经科学界。我们的主要结果是一个极限定理的频谱的尖峰流图诱导的赢家通吃的动力学。我们提供了一个明确的表征的极限谱测度表示的贝塞尔的J-函数的零点。
英文摘要：
During the recent few years, in response to empirical findings suggesting scale-free self-organisation phenomena emerging in complex nervous systems at a mesoscale level, there has been significant search for suitable models and theoretical explanations in neuroscientific literature, see the recent survey by Bullmore and Sporns (2009). In Piekniewski and Schreiber (2008) we have developed a simple and tractable mathematical model shedding some light on a particular class of the afore-mentioned phenomena, namely on mesoscopic level self-organisation of functional brain networks under fMRI imaging, where we have achieved a high degree of agreement with existing empirical reports. Being addressed to the neuroscientific community, our work Piekniewski and Schreiber (2008) relied on semi-rigorous study of information flow structure in a class of recurrent neural networks exhibiting asymptotic scale-free behaviour and admitting a description in terms of the so-called winner-take-all dynamics. The purpose of the present paper is to define and study these winner-take-all networks with full mathematical rigour in context of their asymptotic spectral properties, well known to be of interest for neuroscientific community. Our main result is a limit theorem for spectra of the spike-flow graphs induced by the winner-take-all dynamics. We provide an explicit characterisation of the limit spectral measure expressed in terms of zeros of Bessel's J-function.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
