Annealing schedule from population dynamics

We introduce a dynamical annealing schedule for population-based optimization algorithms with mutation. On the basis of a statistical mechanics formulation of the population dynamics, the mutation rate adapts to a value maximizing expected rewards at each time step. Thereby, the mutation rate is eliminated as a free parameter from the algorithm.Comment: 6 pages RevTeX, 4 figures PostScript; to be published in Phys. Rev.

Genetic algorithm dynamics on a rugged landscape

The genetic algorithm is an optimization procedure motivated by biological evolution and is successfully applied to optimization problems in different areas. A statistical mechanics model for its dynamics is proposed based on the parent-child fitness correlation of the genetic operators, making it applicable to general fitness landscapes. It is compared to a recent model based on a maximum entropy ansatz. Finally it is applied to modeling the dynamics of a genetic algorithm on the rugged fitness landscape of the NK model.Comment: 10 pages RevTeX, 4 figures PostScrip

Error threshold in finite populations

A simple analytical framework to study the molecular quasispecies evolution of finite populations is proposed, in which the population is assumed to be a random combination of the constiyuent molecules in each generation,i.e., linkage disequilibrium at the population level is neglected. In particular, for the single-sharp-peak replication landscape we investigate the dependence of the error threshold on the population size and find that the replication accuracy at threshold increases linearly with the reciprocal of the population size for sufficiently large populations. Furthermore, in the deterministic limit our formulation yields the exact steady-state of the quasispecies model, indicating then the population composition is a random combination of the molecules.Comment: 14 pages and 4 figure

Evolutionary Games with Affine Fitness Functions: Applications to Cancer

We analyze the dynamics of evolutionary games in which fitness is defined as an affine function of the expected payoff and a constant contribution. The resulting inhomogeneous replicator equation has an homogeneous equivalent with modified payoffs. The affine terms also influence the stochastic dynamics of a two-strategy Moran model of a finite population. We then apply the affine fitness function in a model for tumor-normal cell interactions to determine which are the most successful tumor strategies. In order to analyze the dynamics of concurrent strategies within a tumor population, we extend the model to a three-strategy game involving distinct tumor cell types as well as normal cells. In this model, interaction with normal cells, in combination with an increased constant fitness, is the most effective way of establishing a population of tumor cells in normal tissue.Comment: The final publication is available at http://www.springerlink.com, http://dx.doi.org/10.1007/s13235-011-0029-

Assessment of disease progression in dysferlinopathy: A 1-year cohort study

ObjectiveTo assess the ability of functional measures to detect disease progression in dysferlinopathy over 6 months and 1 year.MethodsOne hundred ninety-three patients with dysferlinopathy were recruited to the Jain Foundation's International Clinical Outcome Study for Dysferlinopathy. Baseline, 6-month, and 1-year assessments included adapted North Star Ambulatory Assessment (a-NSAA), Motor Function Measure (MFM-20), timed function tests, 6-minute walk test (6MWT), Brooke scale, Jebsen test, manual muscle testing, and hand-held dynamometry. Patients also completed the ACTIVLIM questionnaire. Change in each measure over 6 months and 1 year was calculated and compared between disease severity (ambulant [mild, moderate, or severe based on a-NSAA score] or nonambulant [unable to complete a 10-meter walk]) and clinical diagnosis.ResultsThe functional a-NSAA test was the most sensitive to deterioration for ambulant patients overall. The a-NSAA score was the most sensitive test in the mild and moderate groups, while the 6MWT was most sensitive in the severe group. The 10-meter walk test was the only test showing significant change across all ambulant severity groups. In nonambulant patients, the MFM domain 3, wrist flexion strength, and pinch grip were most sensitive. Progression rates did not differ by clinical diagnosis. Power calculations determined that 46 moderately affected patients are required to determine clinical effectiveness for a hypothetical 1-year clinical trial based on the a-NSAA as a clinical endpoint.ConclusionCertain functional outcome measures can detect changes over 6 months and 1 year in dysferlinopathy and potentially be useful in monitoring progression in clinical trials.ClinicalTrials.gov identifier:NCT01676077

An analysis of genetic algorithms using statistical mechanics.

A formalism is presented for modelling the evolutionary dynamics of a population of gene sequences. The formalism was originally developed for describing genetic algorithms. In this paper the formalism is elaborated by considering the evolution of an ensemble of populations. This allows the evolution to be modelled more accurately. To illustrate the formalism the problem of a population of gene sequences evolving in a multiplicative fitness landscape is considered. A comparison with simulations is made and shows very good agreement. More complicated problems have already been investigated including sexual recombination and evolution in a multi-valleyed fitness landscape. These results will be briefly reviewed