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  Subsampling affects the identification of critical, supercritical and subcritical states of brain function in vivo

Priesemann, V., Wibral, M., & Munk, M. (2008). Subsampling affects the identification of critical, supercritical and subcritical states of brain function in vivo. Poster presented at 38th Annual Meeting of the Society for Neuroscience (Neuroscience 2008), Washington, DC, USA.

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Priesemann, V, Author
Wibral, M, Author
Munk, MHJ1, 2, Author              
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1Department Physiology of Cognitive Processes, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497798              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: Self organized criticality (SOC) has been proposed to govern the dynamics of various complex systems in which cascades of events form “avalanches”. In the critical state, the frequency distribution f(s) of avalanche sizes s follows a power law and the branching parameter σ equals 1. Both have been described for neuronal activity in vitro (Beggs & Plenz 2003). When recording data in vivo, it is important to note that only a small part of the system can be sampled (e.g. a few local field potential (LFP) channels, each sampling a sphere with radius r<500μm). Subsampling effects make it difficult to identify the critical state based on f(s) alone. To understand subsampling effects in subcritical, critical and supercritical (SCS) systems, we simulated several models with different dynamics and topology known from the theory of SOC (Abelian sandpile - ASM; forest fire; random neighbor) in all 3 states and varied size, shape and location of the subarea from which we sampled activity. We compared f(s) and σ of the subsampled models with those of multielectrode LFP and spike data recorded in 3 macaque monkeys performing a short term memory task. All models exhibit the expected f(s) and σ when fully sampled: subcritical - few large avalanches, σ<1; critical - f(s)~s-τ, σ=1; supercritical - many large avalanches, σ>1. However, upon incomplete sampling, f(s) strongly depends on the state of the system, its local dynamics, its topology, on temporal scaling, and size, shape and location of the sampling area - less so σ. In all subsampled models we find σ<1 for critical and subcritical states, while σ>1 for supercritical states. Evaluating both, f(s) and σ calculated from subsampled models, increases the chance to determine the state of the whole model unambiguously. Only a subset of the investigated models exhibits f(s) and σ similar to those calculated from LFP or spike activity. In detail, the critical ASM reproduces best f(s) and σ observed for LFP activity, while spike activity is approximated best by subsampling the supercritical ASM. Our results show that subsampling can prevent the identification of the critical state if solely based on f(s). We suggest that upon subsampling both parameters, f(s) and σ, should be evaluated in order to decrease the probability of false classifications of SCS systems. In addition, the system specific scaling of f(s) and σ under subsampling conditions strongly suggests that f(s) and σ should be used to test physiologically plausible models of brain function. Models that do not reproduce f(s) and σ calculated from the corresponding physiological recordings should be discarded in favor of more promising ones.

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Title: 38th Annual Meeting of the Society for Neuroscience (Neuroscience 2008)
Place of Event: Washington, DC, USA
Start-/End Date: 2008-11-15 - 2008-11-19

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Title: 38th Annual Meeting of the Society for Neuroscience (Neuroscience 2008)
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: 683.20 Start / End Page: - Identifier: -