Echoes in correlated neural systems
Moritz Helias, Tom Tetzlaff, Markus Diesmann

TL;DR
This paper develops a quantitative theory for pairwise correlations in finite-sized random networks of spiking neurons, explaining complex neural dynamics and collective oscillations with explicit analytic expressions.
Contribution
It introduces a novel analytical framework for understanding correlations in directed, time-delayed neural networks, surpassing mean field limitations.
Findings
Derived explicit formulas for cross correlation functions.
Explained the impact of single action potentials on neural dynamics.
Provided criteria for the emergence of collective oscillations.
Abstract
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 macroscopic signals of neural activity, like the electro encephalogram (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…
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