Identification of functional information subgraphs in complex networks

Abstract

We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of information quantities involving a growing number of correlated variables at other nodes. We demonstrate that each term in this sum is generated by successively conditioning mutual informations on new measured variables, in a way analogous to a discrete differential calculus. The analogy to a Taylor series suggests efficient search algorithms for determining the state of a target variable in terms of functional groups of other degrees of freedom. We apply this methodology to electrophysiological recordings of networks of cortical neurons grown it in vitro. Despite strong stochasticity, we show that each cell's patterns of firing are generally explained by the activity of a small number of other neurons. We identify these neuronal subgraphs in terms of their mutually redundant or synergetic character and reconstruct neuronal circuits that account for the state of each target cell.

4 pages, 4 figures

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• Conditional Decoupling of Quantum Information
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• Entropy and its discontents: A note on definitions
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• Density-dependence of functional development in spiking cortical networks grown in vitro
• Cooperative searching for stochastic targets
• Spontaneous coordinated activity in cultured networks: Analysis of multiple ignition sites, primary circuits, burst phase delay distributions and functional structures
• Comparison of different spike train synchrony measures regarding their robustness to erroneous data from bicuculline induced epileptiform activity