The viscosity subdifferential of the sum of two functions in Banach spaces. I: First order case.
The three space problem for smooth partitions of unity and C(K) spaces.
Almost classical solutions of Hamilton-Jacobi equations.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
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