Echoes in correlated neural systems
Echoes in correlated neural systems
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DOI：
10.1088/1367-2630/15/2/023002
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发表时间：
2013-02-01
影响因子：
3.3
通讯作者：
Diesmann, M.
中科院分区：
文献类型：
--
作者：
Helias, M.;Tetzlaff, T.;Diesmann, M.
相关性在现代物理学中用于解释微观和宏观现象，如高温超导体和超冷原子中的分数量子霍尔效应和莫特绝缘体状态。同时探测完整大脑中的神经元揭示了它们的活动之间的相关性，这是研究大脑中信息处理的重要措施，也影响了神经活动的宏观信号，如脑电图（EEG）。尖峰神经元网络与大多数物理系统不同：元素之间的相互作用是定向的，时间延迟的，由短脉冲介导，每个神经元接收来自数千个神经元的事件。甚至网络的定态也不能用平衡统计力学来描述。在这里，我们开发了一个定量理论的成对相关性在有限大小的随机网络的尖峰神经元。我们推导出明确的人口平均互相关函数的解析表达式。我们的理论解释了为什么直观的平均场描述失败，单个动作电位的回声如何导致抑制相对于兴奋的明显滞后，以及网络的大小如何在保持其动态状态的同时进行缩放。最后，我们从时间演化传播子的谱中导出了一个新的集体振荡出现的判据。
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously probed neurons in the intact brain reveal correlations between their activity, an important measure to study information processing in the brain that also influences the macroscopic signals of neural activity, like the electroencephalogram (EEG). Networks of spiking neurons differ from most physical systems: the interaction between elements is directed, time delayed, mediated by short pulses and each neuron receives events from thousands of neurons. Even the stationary state of the network cannot be described by equilibrium statistical mechanics. Here we develop a quantitative theory of pairwise correlations in finite-sized random networks of spiking neurons. We derive explicit analytic expressions for the population-averaged cross correlation functions. Our theory explains why the intuitive mean field description fails, how the echo of single action potentials causes an apparent lag of inhibition with respect to excitation and how the size of the network can be scaled while maintaining its dynamical state. Finally, we derive a new criterion for the emergence of collective oscillations from the spectrum of the time-evolution propagator.