Anomalous Lifshitz dimension in hierarchical networks of brain connectivity

Samaneh Esfandiary, A. Safari, Jakob Renner, P. Moretti, M. A. Muñoz
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引用次数: 2

Abstract

Network models of neural connectivity and function often invoke the ability of the brain to localize activity in distinct modules simultaneously. The propensity of a network to do the opposite instead, that is to transmit and diffuse information homogeneously, is measured by its spectral dimension, a quantity that is easily accessible through analyses of random walks, or equivalently diffusion processes. Here we show that diffusive dynamics in hierarchical modular network models, representing brain connectivity patterns, exhibit a strongly anomalous features, pointing to a global asymptotic slowdown at large times and to the emergence of localization phenomena. Using theoretical modeling and very-large-scale computer simulations, we demonstrate that the spectral dimension is not defined in such systems and that the observed anomalous dynamical features stem from the existence of Lifshitz tails in the lower spectral edge of the Laplacian matrix. We are able to derive the correct scaling laws relating the spectral density of states and anomalous dynamics, emphasizing the fundamental role played by the Lifshitz dimension. Our work contributes to establishing a theoretical framework for anomalous dynamical features, such as activity localization and frustrated synchronization in hierarchical and hierarchical-modular networks and helps contextualize previous observations of sub-diffusive behavior and rare-region effects in brain networks. More in general, our results, help shedding light on the relation between structure and function in biological information-processing complex networks.
脑连接层次网络中的异常Lifshitz维
神经连接和功能的网络模型经常调用大脑同时定位不同模块活动的能力。相反,网络倾向于做相反的事情,即均匀地传输和扩散信息,这是通过它的谱维来衡量的,这个量很容易通过分析随机游走或等效的扩散过程来获得。在这里,我们表明,代表大脑连接模式的分层模块化网络模型中的扩散动力学表现出强烈的异常特征,表明在大时间内全局渐近放缓和局部现象的出现。通过理论建模和大规模计算机模拟,我们证明了谱维在这样的系统中是没有定义的,并且观测到的异常动力学特征源于拉普拉斯矩阵下谱边缘的Lifshitz尾的存在。我们能够推导出与状态谱密度和异常动力学相关的正确标度定律,强调了Lifshitz维数所起的基本作用。我们的工作有助于建立异常动态特征的理论框架,例如分层和分层模块化网络中的活动定位和受挫同步,并有助于将先前对大脑网络中亚扩散行为和稀有区域效应的观察背景化。总的来说,我们的结果有助于揭示生物信息处理复杂网络中结构和功能之间的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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