Minimal Potentials with Very Many Minima

Minimal potentials with very many minima

We demonstrate, by construction, that simple renormalizable matrix potentials with S(N), as opposed to O(N), symmetry can exhibit an exponentially large number of inequivalent deep local minima.

Parallel deterministic and stochastic global minimization of functions with very many minima

The optimization of three problems with high dimensionality and many local minima are investigated under five different optimization algorithms: DIRECT, simulated annealing, Spall’s SPSA algorithm, the KNITRO package, and QNSTOP, a new algorithm developed at Indiana University.

Exponentially many local minima for single neurons

We show that for a single neuron with the logistic function as the transfer function the number of local minima of the error function based on the square loss can grow exponentially in the dimension.

treatment of patients with hcv related cirrhosis: many rewards with very few risks

Local Minima of the Gauss Curvature of a Minimal Surface

Let D be a domain in the complex in-plane and let as: D —• R be a regular minimal surface. Let M(K) be the set of points tu 0. The components of M(K) are of three types: isolated points; simple analytic arcs terminating nowhere in D; analytic Jordan curves in D. Components of the third type are r...