The Bernstein Center Freiburg

Informal Seminar
Peter beim Graben

Berlin Bernstein Center for Computational Neuroscience Berlin
and Humboldt-Universität zu Berlin

Coarse Grainings in Neuroscience
Wednesday, February 23, 2011

14:00 h sharp
Lecture Hall (1st floor)
Bernstein Center
Hansastr. 9a
From a dynamical systems point of view, neural networks are complex dynamical systems with high-dimensional phase spaces spanned by the activations of all neurons together. A single point in such a phase space, e.g. a neural "microstate" would be addressed by measuring the actual activation values of every single neuron. Clearly, this is not feasible by means of neurophysiological measurements at all. By contrast, neurophysiological measurements either project the neural phase space upon some low-dimensional subspaces by means of single unit or multi-unit electrodes, or neurophysiological measurements yield average mass activity of neural populations by means of local field potentials, electrocorticograms, or electroencephalograms.

In both cases, neurophysiological observables introduce equivalence relations between microstates thereby partitioning the neural phase space into epistemic equivalence classes [1,2]. Referring to a class of epistemically equivalent microstates as to a neural "macrostate", poses the question of how nonlinear microstate dynamics is then mapped onto a coarse-grained macrostate dynamics obtained from a particular measurement. This question can be answered using symbolic dynamics [1,2,3] in case of finite partitions, where macrostates are treated as "symbols" and transitions between macrostates can be approximated by Markov chains. The dependence of a coarse-graining from a chosen measurement device makes partitions and the resulting macrostate dynamics contextually emergent if the corresponding Markov chains exhibit particular stability properties [1]. In a recent study [4], we have shown that Amari's original search for proper brain macrostates [5] can be rephrased in terms of contextual emergence from phase space partitions. Moreover, explicitly constructed partitions can be successfully deployed for analyzing neurophysiological data [2,6].

[1] Atmanspacher, H.& beim Graben, P. Contextual emergence of mental states from neurodynamics. Chaos and Complexity Letters, 2007, 2, 151 - 168.
[2] beim Graben, P.; Saddy, D.; Schlesewsky, M.& Kurths, J. Symbolic dynamics of event-related brain potentials. Physical Reviews E, 2000, 62, 5518 - 5541.
[3] Lind, D.& Marcus, B. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, 1995
[4] beim Graben, P.; Barrett, A.& Atmanspacher, H. Stability criteria for the contextual emergence of macrostates in neural networks. Network: Computation in Neural Systems, 2009, 20, 178 - 196.
[5] Amari, S.-I. A method of statistical neurodynamics. Kybernetik, 1974, 14, 201 - 215.
[6] Allefeld, C.; Atmanspacher, H.& Wackermann, J. Mental states as macrostates emerging from EEG dynamics. Chaos, 2009, 19, 015102.
The talk is open to the public. Guests are cordially invited!