Theory of population coupling and applications to describe high order correlations in large populations of interacting neurons
Abstract
To understand the collective spiking activity in neuronal populations, it is essential to reveal basic circuit variables responsible for these emergent functional states. Here, I develop a mean field theory for the population coupling recently proposed in the studies of the visual cortex of mouse and monkey, relating the individual neuron activity to the population activity, and extend the original form to the second order, relating neuronpair’s activity to the population activity, to explain the high order correlations observed in the neural data. I test the computational framework on the salamander retinal data and the cortical spiking data of behaving rats. For the retinal data, the original form of population coupling and its advanced form can explain a significant fraction of twocell correlations and threecell correlations, respectively. For the cortical data, the performance becomes much better, and the second order population coupling reveals nonlocal effects in local cortical circuits.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 March 2017
 DOI:
 10.1088/17425468/aa5dc8
 arXiv:
 arXiv:1602.08299
 Bibcode:
 2017JSMTE..03.3501H
 Keywords:

 Quantitative Biology  Neurons and Cognition;
 Physics  Biological Physics
 EPrint:
 14 pages, 8 figures, Journal of Statistical Mechanics: Theory and Experiment (in press)