Abstract
Patterns of biological activity with properties similar to critical states of statistical mechanics have received much attention, as they were mostly seen as indicators of computational optimality. Commonly, a single regime around an isolated critical point is expected. Our experimental data and our network simulations of developing neural cultures indicate the possibility of transitions between different critical regimes. In the latter, the addition of further fundamental neurophysiological principles to the standard neurodynamics branching model generates steeper power laws that have been observed in various experiments. Our analysis exhibits two populations of neurons, each composed of inhibitory and excitatory sites, that have distinct dynamical and topological properties. This generates a line of second order critical points, similar to what is known from the thermodynamics of two-component alloys. An analysis of two major critical regimes found in the experiments suggests that different critical regimes may express distinct computational roles.
Highlights
Patterns of biological activity with properties similar to critical states of statistical mechanics have received much attention, as they were mostly seen as indicators of computational optimality
Power laws from critical systems are robust in the following sense: they are a property of the system class considered, and independent of the microscopic details of an individual system
Direct demonstrations that real world power laws are the consequence of criticality are notoriously difficult, as the ideal matching would require to achieve the thermodynamic limit and observe a reliable divergence behavior at the critical point
Summary
Patterns of biological activity with properties similar to critical states of statistical mechanics have received much attention, as they were mostly seen as indicators of computational optimality. Our experimental data and our network simulations of developing neural cultures indicate the possibility of transitions between different critical regimes In the latter, the addition of further fundamental neurophysiological principles to the standard neurodynamics branching model generates steeper power laws that have been observed in various experiments. Our analysis exhibits two populations of neurons, each composed of inhibitory and excitatory sites, that have distinct dynamical and topological properties This generates a line of second order critical points, similar to what is known from the thermodynamics of two-component alloys. Due to the diverging correlation lengths at critical states, systems near criticality show a high susceptibility to external stimuli Seeing this as a favorable property of complex natural systems, it has been conjectured that neural systems operate preferentially in the close vicinity of a critical point[10,11,12,13,14].
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