Self-Organized Criticality: A Fundamental Property of Neural Systems

1. Self-organized criticality as a fundamental property of neural systems 20153124 Su Hyun Kim Department of Bio and Brain Engineering KAIST

2. Table of Contents • 1. Self-organized Criticality • 2. Criticality Hypothesis • 3. Implications • 4. Further Studies • 5. Conclusion

3. 1. Self-organized Criticality • Criticality & Phase transition • Self-organization • Examples and properties

4. Self-organized Criticality: Criticality • Defined as a specific type of behavior observed when a system undergoes a phase transition

5. Self-organized Criticality: Criticality • Macroscopic measurable properties (order parameters) • Ambient property (control parameter) • The change in ambient property yields dramatic change in order parameters: Phase transition • Critical state is the state on the edge between two qualitatively different types of behaviors • Edge of Chaos

6. Self-organized Criticality: Criticality Quantum Critical point Percolation Theory • Boiling of a liquid to a gas • Quantum Critical point • Percolation • Boolean networks • Liquid state machine • Neuronal networks

7. Self-organized Criticality: Self-organization • Self-organization a process where some form of overall order or coordination arises out of the local interactions between the components of an initially disordered system.(wikipedia) • It is often triggered by random fluctuations that are amplified bypositive feedback. • The resulting organization is wholly decentralized or distributed over all the components of the system.  • It gives the whole system resiliency and robustness.

8. Self-organized Criticality: Self-organization

9. Self-organized Criticality (SOC) • Systems tuning themselves to critical states through active decentralized process

10. Self-organized Criticality:Properties • Power law distribution • Scale independence • Self-similarity • Emergent properties

11. 2. Hypothesis: Criticality Hypothesis • Criticality Hypothesis • Toy Model • Evidences • Experiments: neural avalanches • Theoretical Models

12. How are the brain and criticality related?

13. Criticality Hypothesis: The Brain operates in a critical state because optimal computational capabilities should be selected for.

14. Criticality Hypothesis:Toy Model z outgoing linkswith prob. p of activating post-synaptic node during time interval τ A mean proportion of activated nodes at time t =

15. Criticality Hypothesis:Evidences (How to detect?) • Phase diagram… accessible control parameter needed • Branching parameter • Sensitivity to inputs • Critical slowing down • 1/f-noise (

16. Experimental evidence:Neural Avalanches

17. Experimental evidence:Neural Avalanches (John M. Beggs et al., J Neurosci 2003) (Thomas Petermann et al., 2009)

18. In Modeling De Arcangelis et al., 2006

19. 3. Implications • -Information transmission. • -Information storage. • -Computational power • -Stability.

20. Applications • Disease detection (diagnostic tools & treatments) • Insights into other phenomena (sleep, learning, root-causes of certain diseases) • Prerequisite for efficient information processing in unstructured systems. (swarm intelligence)

21. 4. Further Studies • Experiments on low-input situations • Relation with learning and sleep • How do neuronal networks wire itself into a complex network?

22. 5. Conclusion • Self-organized criticalityishallmarks of complex network and nonlinear dynamics. • Properties of SOC include power-law dist., scale independence, and self-similarity(fractal). • Neural criticality hypothesis is motivated by the relationship between criticality and optimal computational properties. • The hypothesis is supported by experiments that observed hallmarks of criticality for a wide range of animals from leech to humans. • Self-organization is preferable over alternative explanations because it provides an evolutionary-motivated explanation.

23. Thank you!