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The heterogeneous distributions of adsorbates on catalyst surfaces violate the mean field assumption and relevant macroscopic models.
We view this postulate as a more transparent assumption for the synaptic drive model than the mean field assumption.
However, given the immense dimensionality of the brain, in the first part of the paper we simplify our model using a mean field assumption.
Equations (11) and (12) represent the spatial average (mean) dynamics of the system given by (6) and (7), and they are predicated on a mean field assumption that reduces the complex (approximately (10^{11}times10^{11})) neuronal connectivity matrix to a (2times2) excitatory inhibitory system.
In the model of GPNP, a mean field assumption is utilized (by necessity, given the non-spatial nature of the model), and each cell is given one additional side per generation, arising from the fact that on average each cell receives a side from a dividing mother cell per generation.
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Furthermore, we address the more general question of synchronization and partial state equipartitioning of neural activity without mean field assumptions.
Finally, we investigate the synaptic drive model without mean field assumptions by postulating the existence of a subpopulation of inhibitory neurons that themselves do not receive inputs from other inhibitory neurons.
In the second part of the paper we have accordingly extended our analysis without mean field assumptions by postulating the existence of a subset of inhibitory neurons that themselves do not receive inhibitory inputs.
Typically, firing-rate models are simplified further by either mean field assumptions, which postulate that the brain is organized into a limited number of populations of identical neurons, or by assuming that the strength of connections between neurons have a specific (typically normal) distribution.
(1) The cooperators were always been excluded under mean-field assumption, showing that the coexistence of defective and cooperative behaviors is impossible in well-mixed population.
Differential models based on mean-field assumption and pair approximation and cellular automaton were built on metapopulation framework to reveal the effect of empty patches and multi-behavior strategies on persistence under habitat degradation.
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Justyna Jupowicz-Kozak
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