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In Equation 8b, ρ μ (w ij = ω) is a mean field derived change to the probability distribution of the locally optimized parameter, towards minimizing the model error (CSSE(W)).
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Spatial patterns registered by Terasawa and coworkers could possibly be understood in a mean field model derived from our network system.
Moreover, the oscillatory and chaotic properties we observed in the small coupled network will also be observed had our mean field been derived in terms of the weight and the analyses been done with the synaptic weights.
In order to identify the attractors accessible to the network and to study their stability as a function of the parameters of the model, we used the mean field approximation derived in [16] (see s for a summary).
Moreover, even the mean diurnal variation of electric field derived for 10 fine weather days in April 1998 turned out to be inconsistent with the mean diurnal variation of the lightning flashes for the same days.
Results are presented as the means ± SD of eight fields derived from two wells.
Explicit results are obtained in a mean field approach which is derived by writing the equations for the extrema of the free energy.
The interest in deriving mean field equations from stochastic microscopic model has been revived recently as it contains the possibility to derive deterministic 'corrections' to the mean field equations, also called second-order approximations.
We present DPD simulations of linear polyethylene melts with force fields derived from microscopic simulations using the concept of potential of mean force.
We derive the averaged mean field equations and show that there are changes in the stability as the homeostatic time constant changes.
This equation was derived recently for describing the mean field dynamics of boson stars.
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