From Euclidean to Lorentzian General Relativity: The Real Way

We study in this paper a new approach to the problem of relating solutions to the Einstein field equations with Riemannian and Lorentzian signatures. The procedure can be thought of as a "real Wick rotation". We give a modified action for general relativity, depending on two real parameters, that can be used to control the signature of the solutions to the field equations. We show how this procedure works for the Schwarzschild metric and discuss some possible applications of the formalism in the context of signature change, the problem of time, black hole thermodynamics...Comment: 20 pages uuencoded gzipped tar format. Accepted in Phys. Rev. D. Some references adde

When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

It has been shown in the past that a multistart hillclimbing strategy compares favourably to a standard genetic algorithm with respect to solving instances of the multimodal problem generator. We extend that work and verify if the utilization of diversity preservation techniques in the genetic algorithm changes the outcome of the comparison. We do so under two scenarios: (1) when the goal is to find the global optimum, (2) when the goal is to find all optima. A mathematical analysis is performed for the multistart hillclimbing algorithm and a through empirical study is conducted for solving instances of the multimodal problem generator with increasing number of optima, both with the hillclimbing strategy as well as with genetic algorithms with niching. Although niching improves the performance of the genetic algorithm, it is still inferior to the multistart hillclimbing strategy on this class of problems. An idealized niching strategy is also presented and it is argued that its performance should be close to a lower bound of what any evolutionary algorithm can do on this class of problems

Automorphisms of generalized Thompson groups

We look at the automorphisms of Thompson type groups of piecewise linear homeomorphisms of the real line or circle that use slopes that are integral powers of a fixed integer n with n>2. We show that large numbers of "exotic" automorphisms appear---automorphisms that are represented as conjugation by non-PL homeomorphisms of the real line or circle. This is in contrast to the n=2 case where no such automorphisms appear.Comment: DVI and Post-Script files onl