Graph Evolution: A Computational Approach

1. Brain Connectivity Workshop - 2006 Graph Evolution: A Computational Approach Olaf Sporns, Department of Psychological and Brain Sciences Indiana University, Bloomington, IN 47405 http://www.indiana.edu/~cortex , osporns@indiana.edu “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.

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

3. Graph Evolution mutation population of graphs objective function selection offspring R.I.P. Candidate Objective Functions … “Macrostates”: Quantifying Information in Networks entropy: order/disorder/information mutual information: statistical dependence integration: global statistical dependence “multi-information” complexity: coexistence of local and global structure Quantifying Structure of Networks information integration (Φ): delineation of integrated complexes and of maximal capacity for information integration (in a causal network). small-world index: clustering and path length motifs: structural/functional building blocks Optimizing Features of the Graph Eigenspectrum wiring: volume/length, conductance speed eigenvalues: algebraic connectivity (Fiedler value, λ2) causal network interactions: Granger “causality”, transfer entropy

4. Graph Evolution maximize functional motif number Evolution for “macrostates” Evolution for spectral graph properties and information integration Sporns and Tononi, 2002 λ2 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) … Evolution for motif composition Honey and Sporns, in progress Sporns and Kötter, 2004 Initial observations suggest that evolved networks can be used to predict unknown connections …

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