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A New Variable for Assessing Information in Networks

A New Variable for Assessing Information in Networks. Michael Hadley Matthew McGranaghan Grayson Sipe Justin Bruce. Elaine R. Reynolds Chun Wai Liew. http://www.colmanweb.com/Assets/Resources/ALevelFormulas.jpg. Neuron and Node. Dendrites. Input. Cell body. Processing. Axon. Output.

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A New Variable for Assessing Information in Networks

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  1. A New Variable for Assessing Information in Networks Michael Hadley Matthew McGranaghan Grayson Sipe Justin Bruce Elaine R. Reynolds Chun WaiLiew

  2. http://www.colmanweb.com/Assets/Resources/ALevelFormulas.jpg

  3. Neuron and Node Dendrites Input Cell body Processing Axon Output

  4. Modeling at the Neuronal Level

  5. Modeling Brain Areas

  6. Studying Consciousness

  7. So here’s the problem…

  8. Information integration model of consciousness (IIT) • Proposed a model of consciousness based on information theory • Defined consciousness as “the capacity to integrate information” • Model is based on entropy Guilio Tononi, University of Wisconsin, Madison Olaf Sporns, Indiana University, Bloomington

  9. Whole greater than the sum of the parts Chuck Close

  10. The Phi Model Node 1 Node 2 Node 3 Node 4

  11. The Phi Model … … …

  12. Phi is a complicated metric EI(A B) = EI(A→B) + EI(B→A) EI(A→B) = MI(AHmax:B) MI(A:B) = H(A) + H(B) - H(AB) H(A) = (1/2) ln [ (2π e) n |COV(A)| ] • 15 nodes takes about 3 hours to run • The brain has billions of neurons

  13. A new metric: System Difference (SD) Compare the outputs from node 3 to node 4. No difference in outputs to node 2 Difference in outputs to node 1 Difference in outputs to node 3 No difference in outputs to node 4

  14. SD is significantly faster than Phi A 1200 node system can run in under 3 minutes This would literally take many, many millennia to run with the Phi model

  15. Correlation 10 Nodes, 24000 matrices, R = .87 10 Nodes, 12000 Matrices, r=0.8708

  16. Graph Theory • degree-fundamental measure, complex networks have nonGaussian function with • long tails towards high degrees • assortivity-positive assortivity means high degree nodes connect to each other • density-measure of cost of a system, want to balance efficiency with cost • clustering coefficient-high clustering property of complex systems • global efficiency (maybe need local efficiency measure) high global efficiency • average path length-low average path length, inversely related to efficiency

  17. Future

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