To my parents iii ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor, Prof. Edward J. Coyle, for his invaluable advice and persistent support during my Ph.D. study. Without his guidance, I would not have been able to successfully complete my dissertation. Moreover, his guidance in both my research and life has pretty much reshaped my way of thinking and working in the p...

We study large deviation events in the timing of disease recurrence. In particular, we are interested modeling cancer treatment failure due to mutation induced drug resistance. first present a two-type branching process model this phenomenon, where an initial population cells that sensitive therapy can produce mutants resistant therapy. investigate two random times, recurrence time and crossove...

This paper gives an introduction to the Random Field Ising Model (RFIM). Since its rst discussion in the paper by Imry and Ma 1] there has been great interest in this model, since Ising or Ising-like systems in random elds are a good representation of a large number of impure materials. These show features that can not be understood by studying ideal systems (i.e. Ising model). There are a lot ...

GP inherently is a technique for, and relies upon, exploration and exploitation of regularity. With ADFs, regularity translates into modularity. Regularity is explored both implicitly (evolution via crossover) and explicitly (as in ADFs). ACGP (Adaptable Constrained GP) offers a new way for GP to explore regularity of a different kind. It will have an impact on modularity as well. I will here b...

We consider numerically the crossover scaling behavior from the directed percolation universality class to the compact directed percolation universality class within the one-dimensional Domany-Kinzel cellular automaton. Our results are compared to those of a recently performed field theoretical approach. In particular, the value of the crossover exponent φ = 2 is confirmed.

This paper presents experimental results on the major benchmarking functions used for performance evaluation of Genetic Algorithms (GAs). Parameters considered include the e€ect of population size, crossover probability, mutation rate and pseudorandom generator. The general computational behavior of two basic GAs models, the Generational Replacement Model (GRM) and the Steady State Replacement ...

The long-range bond-percolation problem, on a linear chain (d = 1), in the presence of diluted sites (with an occupancy probability ps for an active site) is studied by means of a Monte Carlo simulation. The occupancy probability for a bond between two active sites i and j, separated by a distance rij is given by pij = p/r ij , where p represents the usual occupancy probability between nearest-...

We study the probability of formation of ferromagnetic string in the antiferromagnetic spin-1/2 XXZ chain. We show that in the limit of long strings with weak magnetization per site the bosonization technique can be used to address the problem. At zero temperature the obtained probability is Gaussian as a function of the length of the string. At finite but low temperature there is a crossover f...

We construct and investigate quantum fields induced on a d-dimensional dissipationless defect by bulk fields propagating in a d + 1dimensional space. All interactions are localized on the defect. We derive a unitary non-canonical quantum field theory on the defect, which is analyzed both in the continuum and on the lattice. The universal critical behavior of the underlying system is determined....

In studying within-chromosome recombination, Morgan proposed that the farther apart two genes were located on a chromosome, the more likely they would be to exhibit crossing-over. Alfred Sturtevant took this argument one step further and proposed that the probability of a cross-over occurring between two genes could be used as a measure of the chromosomal distances separating them. While this s...