Graph Evolution: A Computational Approach Olaf Sporns, Department of Psychological and Brain Sciences Indiana University, Bloomington, IN Brain Connectivity Workshop “Nothing in biology makes sense except in the light of evolution” Problems: Linking biological structure to function – relating brain connectivity across multiple levels (structural, functional, effective). Propensity of connection patterns to support dynamic states and information integration. Linking brain connectivity to cognition and behavior – extensions of information processing that go beyond neurons. Functioning of neuronal networks in the context of body and environment. Approaches: Search for theoretical and computational principles. Modeling and building integrated systems and whole organisms (agents, robots). Evolution as a powerful algorithm that naturally connects structure and function in living systems.

Relation between Connectivity and Dynamics Relation between connectivity patterns and synchronicity stimulusneural model (connectivity)correlations / synchrony Sporns et al., 1991 Relation between small-world connectivity and synchrony Sporns and Rubinstein, in preparation

Graph Evolution population of graphs selection R.I.P. offspring mutation objective function “Macrostates”: Quantifying Information in Networks entropy: order/disorder/information mutual information: statistical dependence integration: global statistical dependence complexity: coexistence of local and global structure “multi-information” Candidate Objective Functions … Quantifying Structure of Networks small-world index: clustering and path length motifs: structural/functional building blocks Optimizing Features of the Graph Eigenspectrum causal network interactions: Granger “causality”, transfer entropy eigenvalues: algebraic connectivity (Fiedler value, λ 2 ) wiring: volume/length, conductance speed information integration (Φ): delineation of integrated complexes and of maximal capacity for information integration (in a causal network).

Graph Evolution Evolution for motif composition Evolution for “macrostates” maximize functional motif number Sporns and Kötter, 2004 Sporns and Tononi, 2002 Evolution for spectral graph properties and information integration Honey and Sporns, in progress λ 2 is an indicator of synchronizability, mixing time, and structural compactness of a graph. It is also related to the graph’s capacity for information integration (as measured by Φ) … Initial observations suggest that evolved networks can be used to predict unknown connections …

Evolving Agents, Information and Embodied Cognition Evolving Agents for Maximizing Information population of agents/robots selection R.I.P. offspring mutation objective function random agentevolved agent agents evolved for high complexity show coordinated behavior Sporns and Lungarella, 2006b Evolving Agents in a Computational Ecology Yaeger and Sporns, 2006 Mapping Causal Networks Sporns and Lungarella, 2006a