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  How to infer distributions in the brain from subsampled observations

Levina, A., & Priesemann, V. (2017). How to infer distributions in the brain from subsampled observations. Poster presented at Bernstein Conference 2017, Göttingen, Germany.

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Levina, A1, Author              
Priesemann, V, Author
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 Abstract: nferring the dynamics of a system from observations is a challenge, even if one can observe all system units or components. The same task becomes even more challenging if one can sample only a small fraction of the units at a time. As the prominent example, spiking activity in the brain can be accessed only for a very small fraction of all neurons in parallel. These limitations do not affect our ability to infer single neuron properties, but it influences our understanding of the global network dynamics or connectivity. Subsampling can hamper inferring whether a system shows scale-free topology or scale-free dynamics (criticality) [1,2]. Criticality is a dynamical state that maximizes information processing capacity in models, and therefore is a favorable candidate state for brain function. Experimental approaches to test for criticality extract spatio-temporal clusters of spiking activity, called avalanches, and test whether they followed power laws. These avalanches can propagate over the entire system, thus observations are strongly affected by subsampling. Therefore, we developed a formal ansatz to infer avalanche distributions in the full system from subsampling using both analytical approximation and numerical results. In the mathematical model subsampling from exponential (or, more generally, negative binomial distribution) does not change the class of distribution, but only its parameters. In contrast, power law distributions, do not manifest as power laws under subsampling [3]. We study changes in distributions to derive “subsampling scaling” that allows to extrapolate the results from subsampling to a full system: P ( s ) = p sub P sub ( s/p sub ) , where P ( s ) is an original distribution, P sub – distribution in the subsampled system, p sub probability to observe any particular event. In the model of critical avalanches subsampling scaling collapses distributions for all number of sampled units (Figure 1. B). However, for subcritical settings no distribution collapse is observed (Figure 1. D). With the help of this novel discovery we studied dissociated cortical cultures. We artificially subsampled recordings by considering only fraction of all electrodes. We observed that in the first days subsampling scaling does not collapse distributions well, whereas mature ( from day 21) allow for a good collapse, indicating development toward criticality (Figure 1. C, E) [4].

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 Dates: 2017-09
 Publication Status: Published online
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Title: Bernstein Conference 2017
Place of Event: Göttingen, Germany
Start-/End Date: 2017-09-13 - 2017-09-15

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Title: Bernstein Conference 2017
Source Genre: Proceedings
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Pages: - Volume / Issue: - Sequence Number: W 20 Start / End Page: 52 - 53 Identifier: -