We study the dynamics of an intriguing crossover from a chaotic to a power-law state as a function of strain rate within the context of a recently introduced model that reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power-law distribution of null exponents which also exhibits a power law. The slow-manifo...

This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses th...

Symmetry-breaking perturbations destabilize the critical points of the two-channel and two-impurity Kondo models, thereby leading to a crossover from non-Fermi liquid behavior to standard Fermi liquid physics. Here we use an analogy between this crossover and one occurring in the boundary Ising model to calculate the full crossover Green function analytically. In remarkable agreement with our n...

Crossover designs are efficient alternatives to parallel designs. Sample size reduction, comparing the 2x2 crossover to a two-arm parallel study, is approximately 4 to 1 in diabetes clinical trials. One challenge of using a crossover design is understanding and handling potential carryover effects. This paper will review the fundamentals of the crossover design, including design, model, and ana...

Pch2 is a widely conserved protein that is required in baker's yeast for the organization of meiotic chromosome axes into specific domains. We provide four lines of evidence suggesting that it regulates the formation and distribution of crossover events required to promote chromosome segregation at Meiosis I. First, pch2Delta mutants display wild-type crossover levels on a small (III) chromosom...

The dynamics of a genetic algorithm undergoing ranking selection, mutation, and two-point crossover for the ones-counting problem is studied using a statistical mechanics approach. This approach has been used previously to study this problem, but with uniform crossover. Two-point crossover induces additional linkage between nearby loci which changes the dynamics significantly. To account for th...

Genetic algorithms (GAs) are an optimization technique that has been successfully used on many real-world problems. There exist different approaches to their theoretical study. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Čech topologies) in two ways. First, we extend it to the case of n-points crossover. Then, we experimentally st...

A model of a hard optimization problem suggested in the literature is considered. The dynamics of a genetic algorithm (GA) using ranking selection, mutation, and uniform crossover are completely modeled on this problem and generalized to any symmetrical concave function of unitation. Full finite population effects are taken into account allowing a novel analytical comparison of roulette wheel a...

The apparatus of Generalized nets (GN) is here applied to a description of different techniques of crossover, which is one of the basic genetic algorithm operators. Presented here are GN models which describe three crossover techniques, namely one-point, two-point crossover as well as the “cut and splice” technique. The resulting GN models can be considered as separate modules, but they can als...