Plasticity of synaptic connections plays an important role in the temporal development of neural networks which are the basis of memory and behavior. The conditions for successful functional performance of these nerve nets have to be either guaranteed genetically or developed during ontogenesis. In the latter case, a general law of this development may be… (More)
We prove a generalization of Brouwer's famous xed point theorem to discontinuous maps. The main result shows that for discontinuous functions on a compact convex domain X one can always nd a point x 2 X such that kx ? f(x)k is less than a certain measure of discontinuity. Applications to artiicial neural nets, economic equilibria, and analysis are given.