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Interaction between network dynamics and network structure.

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Interaction between network dynamics and network structure.

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    1. Interaction between network dynamics and network structure. Michal Zochowski Dept. of Physics and Biophysics Res. Div. , Neuroscience Prog. University of Michigan Ann Arbor, MI

    2. What are neurons, and what they do (physicist view)?

    3. What are the temporal interdependencies between weakly coupled non-identical oscillators?

    4. Spatio-temporal patterning: coincidence vs. causal temporal structure

    5. Causal Entropies – monitoring evolving temporal interdependencies

    6. Adaptive updating

    7. Difference in causal Entropy detects temporal asymmetries

    8. Changes of the lag as a function of a parameter mismatch

    9. Classes of temporal interdependencies detectable by CEs

    10. Measurement of relative lags in the network

    11. Expectivity – global measure of temporal ordering

    12. Detection of hippocampal rewiring

    13. Learning novel hippocampal task

    14. Detection of coincidence vs. asymmetric interdependence

    15. Coincidence vs causality

    16. Network rewiring?

    17. Network dynamics and network structure

    18. Network topology determines temporal interdependencies during network dynamics

    19. Temporal ordering as a function of distance

    20. Dynamics near the transition point

    21. Changing network properties based on temporal signal structure Nodes are Rössler oscillators Frequencies ? are adapted towards that of driving nodes. I.e. Those for which CEij is low and CEji is high. Edges are weighted for coupling strength between nodes Coupling strength ? adapted such that low CEij leads to stronger connection.

    22. Network Reorganization Adaptation Control parameter of each oscillator adapted by ßw is adaptation speed, k is the in-degree Aggregation Coupling strength adapted by ßa is fragmentation speed, N is the number of oscillators

    23. Definitions Expectivity Measures to what extent time-ordering of oscillators measured by CEs matches that expected from frequencies Transitivity Measures the tendency for couplings to exist between oscillators that are both coupled to a third oscillator.

    24. Three types of network structure modulation Adaptation Only Aggregation turned off Coupling strengths remain constant through each simulation Aggregation Only Adaptation turned off Frequencies remain constant through each simulation Aggregation and Adaptation

    25. Adaptation Only Sample network Darker -> Higher Frequency

    26. Connectivity Connectivity = number neighbors / network size

    27. Rewiring Probability

    28. Aggregation Only Unidirectional coupling Faster (darker) -> Slower

    29. Asymmetric Aggregation Rate of coalescence ? fragmentation Optimum range established in which transitivity is bolstered, but selectivity is preserved

    30. Adaptation and (Symmetric) Aggregation Bidirectional coupling Highly similar oscillators in clusters

    31. Average Lifetime of Couplings For slow aggregation, network dissociates Similar timescales for aggregation and adaptation result in lack of regularity in lag Reveals optimum aggregation speed for coupling stability

    32. Local Frequency Variance Non-adaptive (??=0) selects ~30% of frequency range Adaptive systems make clusters more uniform

    33. Acknowledgements Lab Members: Rhonda Dzakpasu Benjamin Singer Jack Waddell Soyoun Kim Sarah Feldt Beth Percha Piotr Jablonski

    34. Application 2: seizure progression during seizure like activity

    35. Analysis

    36. CE significance

    37. Seizure evolution based on lag dynamics

    38. Modeling

    39. Characterization

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