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Linear Stability of Spontaneously Active Local Cortical Circuits: Is There Criticality on Long Time Scales?

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The Functional Role of Critical Dynamics in Neural Systems

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 11))

Abstract

Self-organizing systems acquire their structures and functions without patterned input from the outside world. In the interconnected architectures of the neocortex, spontaneous activity—that is, activity that arises without external sensory or electrical stimulus—predominates over sensory-evoked activity. Thus, spontaneous neuronal activity provides a means to characterizing the structure, function and dynamics of neocortical networks. We have recorded spontaneous, asynchronous network activity from hundreds of neurons constituting local cortical circuits in mice with high-density microelectrode arrays (MEAs) in vitro. The spontaneous activity in the network displayed features of a system at criticality and scale-free structures, such as fluctuation scaling and multiple frequency bands. To investigate dynamical parameters, we have investigated the linear and nonlinear components of the network dynamics. The former allows us not only to define a linear measure of functional connectivity, but also to determine the linear stability of the system through its eigenvalues. Similarly, the latter allows us to define a measure of nonlinear functional connectivity. An important feature revealed by this approach is the large number of eigenvalues with positive real parts and the high density of eigenvalues near the imaginary axis, which demonstrate respectively that this high-dimensional system is linearly unstable and critical on long time scales (>1s). The function of critical dynamics in these networks is discussed with respect to exploratory behavior in rodents.

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH, 44106, USA

    Nathan X. Kodama & Roberto F. Galán

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  1. Nathan X. Kodama
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  2. Roberto F. Galán
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Correspondence to Roberto F. Galán .

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Editors and Affiliations

  1. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Nergis Tomen

  2. Institute of Perception, Action and Behaviour, University of Edinburgh, Edinburgh, UK

    J. Michael Herrmann

  3. Institute for Theoretical Physics, University of Bremen, Bremen, Germany

    Udo Ernst

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Kodama, N.X., Galán, R.F. (2019). Linear Stability of Spontaneously Active Local Cortical Circuits: Is There Criticality on Long Time Scales?. In: Tomen, N., Herrmann, J., Ernst, U. (eds) The Functional Role of Critical Dynamics in Neural Systems . Springer Series on Bio- and Neurosystems, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-030-20965-0_8

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