Information Dynamics in KC model

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XII Experimental Chaos and Complexity Conference talk, Michigan US. Related papers: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.88.012712 http://www.biomedcentral.com/1471-2202/14/S1/O18

Information dynamics
in the Kinouchi-Copelli model
T. S. Mosqueiro and Leonardo P. Maia
Instituto de F´ısica de S˜ao Carlos
Universidade de S˜ao Paulo
thiago.mosqueiro@gmail.com
lpmaia@ifsc.usp.br
May 16, 2012
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 1 / 13

Neuronal avalanches
* Experiments revealed power-law
distributions for both duration
and size of bursts of activity.
Beggs and Plenz. J. Neuroscience, v. 23 p. 11167 (2003)
Shew et al. J. Neuroscience, v. 31 p. 55 (2011)
Key questions:
Criticality in neurodynamics?
Critical optimization of information processing?
(“Edge of chaos”)
Psychophysics?
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 2 / 13

Criticality in neural systems
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 3 / 13

Our aim here
• Illustrate connections between neural dynamics and psychophysics
• Argue that information eﬃciency outperforms information capacity
• Discuss evidence of criticality w/o power-laws
• Preliminary results: quantify information ﬂow leading to psychophysics
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 4 / 13

$Kinouchi–Copelli model Optimal dynamic range → critical optimization • N neurons as nodes of a weighted undirected random graph • Weight matrix A • Average connectivity: K. • External stimulus r: rate of Poisson process Kinouchi and Copelli, Nature Physics, v. 2 p. 348-352 (2006) * Xj(t) = 0: quiescent state * Xj(t) = 1: excited state * 2 ≤ Xj(t) ≤ m − 1: refractory states • Mean activity = time average of excited fraction of the network • sj = k Akj: local branching ratio Average branching ratio: σ := sj Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 5 / 13$

Optimal channel eﬃciency
Preprint: arXiv:1204.0751v1 [physics.bio-ph]
Erd˝os-R´enyi topology Barab´asi-Albert topology
Dynamic range is optimized concomitantly with
information eﬃciency encoded in avalanche lifetimes
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 6 / 13

Order parameter: spontaneous activity
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 7 / 13

No power-laws?
• Dehghani et al: arxiv 1203.0738v2
• Friedman et al: to appear in PRL
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 8 / 13

Local information dynamics
Hamming distance
• Let A = (X1(0), X2(0), X3(0), . . .)
• Deﬁne B by ﬂipping a randomly chosen node
• δ =
1
N
N
j=1
|Aj − Bj |
Entropy rate
• Let’s deﬁne Hk(Xj ) =
−log [P {Xj (k), Xj (k − 1), . . . , Xj (0)}])
• H(X) = lim
k→∞
Hk(X)
k
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 9 / 13

Preliminary reports
• Performed simulations: N = 104
and K = 10
• Erd˝os-R´enyi and Barab´asi-Albert topologies
• Sampling ∼ 5 × 103
events with k ∼ 10.
• Criticality vs Local information dynamics?
Erd˝os-R´enyi topology Erd˝os-R´enyi topology
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 10 / 13

Dynamic range and the entropy rate
Preliminary reports
Reﬂects somehow the dynamic range optimization
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 11 / 13

Hamming distance and a transition
Preliminary reports
Erd˝os-R´enyi topology Barab´asi-Albert topology
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 12 / 13

The end?
Lots of work to characterize what optimizes information eﬃciency!
• This work is under ﬁnancial support of CAPES and FAPESP.
• Acknowledgements to John Beggs.
Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 13 / 13

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Information Dynamics in KC model

1. Information dynamics in the Kinouchi-Copelli model T. S. Mosqueiro and Leonardo P. Maia Instituto de F´ısica de S˜ao Carlos Universidade de S˜ao Paulo thiago.mosqueiro@gmail.com lpmaia@ifsc.usp.br May 16, 2012 Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 1 / 13

2. Neuronal avalanches * Experiments revealed power-law distributions for both duration and size of bursts of activity. Beggs and Plenz. J. Neuroscience, v. 23 p. 11167 (2003) Shew et al. J. Neuroscience, v. 31 p. 55 (2011) Key questions: Criticality in neurodynamics? Critical optimization of information processing? (“Edge of chaos”) Psychophysics? Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 2 / 13

3. Criticality in neural systems Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 3 / 13

4. Our aim here • Illustrate connections between neural dynamics and psychophysics • Argue that information eﬃciency outperforms information capacity • Discuss evidence of criticality w/o power-laws • Preliminary results: quantify information ﬂow leading to psychophysics Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 4 / 13

5. Kinouchi–Copelli model Optimal dynamic range → critical optimization • N neurons as nodes of a weighted undirected random graph • Weight matrix A • Average connectivity: K. • External stimulus r: rate of Poisson process Kinouchi and Copelli, Nature Physics, v. 2 p. 348-352 (2006) * Xj(t) = 0: quiescent state * Xj(t) = 1: excited state * 2 ≤ Xj(t) ≤ m − 1: refractory states • Mean activity = time average of excited fraction of the network • sj = k Akj: local branching ratio Average branching ratio: σ := sj Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 5 / 13

6. Kinouchi–Copelli model Optimal dynamic range → critical optimization • N neurons as nodes of a weighted undirected random graph • Weight matrix A • Average connectivity: K. • External stimulus r: rate of Poisson process Kinouchi and Copelli, Nature Physics, v. 2 p. 348-352 (2006) * Xj(t) = 0: quiescent state * Xj(t) = 1: excited state * 2 ≤ Xj(t) ≤ m − 1: refractory states • Mean activity = time average of excited fraction of the network • sj = k Akj: local branching ratio Average branching ratio: σ := sj Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 5 / 13

7. Optimal channel efficiency Preprint: arXiv:1204.0751v1 [physics.bio-ph] Erd˝os-Rényi topology Barabási-Albert topology Dynamic range is optimized concomitantly with information efficiency encoded in avalanche lifetimes Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 6 / 13

8. Order parameter: spontaneous activity Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 7 / 13

9. No power-laws? • Dehghani et al: arxiv 1203.0738v2 • Friedman et al: to appear in PRL Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 8 / 13

10. Local information dynamics Hamming distance • Let A = (X1(0), X2(0), X3(0), . . .) • Define B by flipping a randomly chosen node • δ = 1 N N j=1 |Aj − Bj | Entropy rate • Let’s define Hk(Xj ) = −log [P {Xj (k), Xj (k − 1), . . . , Xj (0)}]) • H(X) = lim k→∞ Hk(X) k Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 9 / 13

11. Preliminary reports • Performed simulations: N = 104 and K = 10 • Erd˝os-Rényi and Barabási-Albert topologies • Sampling ∼ 5 × 103 events with k ∼ 10. • Criticality vs Local information dynamics? Erd˝os-Rényi topology Erd˝os-Rényi topology Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 10 / 13

12. Dynamic range and the entropy rate Preliminary reports Reﬂects somehow the dynamic range optimization Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 11 / 13

13. Hamming distance and a transition Preliminary reports Erd˝os-R´enyi topology Barab´asi-Albert topology Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 12 / 13

14. The end? Lots of work to characterize what optimizes information eﬃciency! • This work is under ﬁnancial support of CAPES and FAPESP. • Acknowledgements to John Beggs. Mosqueiro and Maia (IFSC - USP) Information dynamics in KC model 12th ECC – Ann Arbor, 2012 13 / 13

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