Recommended
Recommended
More Related Content
Similar to SOC neunoral networks
Similar to SOC neunoral networks (20)
More from Osame Kinouchi
More from Osame Kinouchi (18)
Recently uploaded
Recently uploaded (20)
SOC neunoral networks
- 1. Self-Organized Criticality and Neuronal Avalanches in Networks with Dynamical Synapses Ariadne Costa, Mauro Copelli, Osame Kinouchi First Workshop of Young Researchers of NeuroMat, São Paulo, May 2015 University of São Paulo (USP), Ribeirão Preto, Brazil Federal University of Pernambuco (UFPE), Recife, Brazil
- 3. Size distribution of neuronal avalanches P(s) = c s-3/2
- 4. Quick historical background of SOC • Microscopically conservative models with true SOC (Bak, Tang & Wiesenfeld PRL 87, Jensen SOC 98) • Non-conservative models with after- avalanche (hard) loading, presenting pseudo-SOC (Drossel PRL 92, Kinouchi & Prado, PRE 99) • Non-conservative models with intra- avalanche (soft) loading, presenting SOqC (self-organized quase-criticality) (Levina, Herrmann & Geisel Nat Phys 07, Bonachela et al JSTAT 09, 10)
- 5. Self-Organized Criticality and Neuronal Avalanches in Networks with Dynamical Synapses • Microscopically non-conservative model with “soft” loading, but • Probabilistic cellular automata (larger system sizes & easier mean field) • Finite connectivity (random graph) • Stationary regime: conservative on average • Fluctuations vanish when N → ∞ Here:
- 6. Random network of excitable cellular automata Random graph with K outcoming synapses Kinouchi & Copelli, Nat. Phys. 06 Control parameter: Branching ratio: Order parameter: Mean firing rate: Mean-field equation: (I)
- 7. Directed-percolation phase transition at Kinouchi & Copelli, Nat. Phys. 06 Chialvo, Nat. Phys. 06
- 8. Directed-percolation phase transition at Kinouchi & Copelli, Nat. Phys. 2006 Chialvo, Nat. Phys. 2006 Can synaptic depression tune If so, is it SOC?
- 9. Synaptic Depression Levina et al, Nat. Phys. 07 (LHG) - Integrate and fire neurons (deterministic) - all-to-all coupling Synaptic depression: slow load Here - Cellular automata (probabilistic) - random graph Synaptic depression: slow load
- 10. Synaptic Depression: two variants Quenched Annealed (random neighbor)
- 11. Synaptic Depression: two variants Quenched Annealed (random neighbor)
- 12. Results • Analytical (mean-field theory) • Simulations
- 13. Mean-field theory Mean-field equation (I) Mean-field equation (II) Kinouchi & Copelli, Nat. Phys. 06
- 14. Mean-field theory Mean-field equation (I) Mean-field equation (II)
- 15. Results • Analytical (mean-field theory) • Simulations
- 16. Branching ratio converges to unity
- 17. Branching ratio converges to unity
- 18. Branching ratio converges to unity System becomes conservative, on average! Is on average good enough?
- 19. Our model Fluctuations decrease with system size Bonachela et al., JSTAT 10 LHG model
- 24. Pruessner-Jensen model: - Similar parameter dependence - Different cutoff exponent (Bonachela & Muñoz, JSTAT 09)
- 25. Conservative Bonachela & Muñoz, JSTAT 09 Non-Conservative
- 26. Bonachela & Muñoz, JSTAT 09 Conservative
- 27. Conclusions Costa, Copelli and Kinouchi – Can dynamical synapses produce true Self-organized criticality? accepted for publication in Journal of Statistical Mechanics (2015)
- 28. Perspectives • Study of neuronal interspike interval (ISI) probability distribution p(t) in the subcritical, critical and supercritical regime
- 29. PLoS Computational Biology Power-Law Inter-Spike Interval Distributions Infer a Conditional Maximization of Entropy in Cortical Neurons •Yasuhiro Tsubo , •Yoshikazu Isomura, •Tomoki Fukai •Published: April 12, 2012 •DOI: 10.1371/journal.pcbi.1002461 Study of neuronal interspike interval (ISI) probability distribution p(t) in the subcritical, critical and supercritical regime Perspectives ISI distributions (log-log graphs)
- 30. Interspike Intervals (ISI) distributions seems to have long (power laws) tails Collaboration with Lézio Soares Bueno Júnior started here!
- 31. Zipf plot for ISIs Rank of ISI interval
- 32. Thank you Come visit us in Ribeirão Preto!
- 33. Adaptation under constant input
- 34. Adaptation
- 35. Adaptation
- 36. Scaling with system size Mean-field equation (II) A similar scaling was found for the Pruessner- Jensen model (Bonachela & Muñoz, JSTAT 09)
Editor's Notes
- In 2006 Osame Kinouchi and I proposed a simple model an excitable network K random neighbors P_ij = probability that a spike in i causes a spike in j P_ij => control parameter sigma Order parameter F Self-consistent mean-field equation (I)
- Phase transition from quiescent (subcritical) to active (supercritical)
- - Cellular automata: allow larger system sizes [ up to O(10^5) ] - Ultra-slow load: dP/dt ~ O(1/N), but for FINITE CONNECTIVITY!
- Bad side: for fixed epsilon, varying N can take from subcritical, critical and supercritical (sigma = 1 might not necessarily be the critical value for finite N)
- Pruessner-Jensen model considered non-conservative by Bonachela & Muñoz 10