The RHMC algorithm for theories with unknown spectral bounds

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment ($dt$) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ($\chi$QCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.Comment: Latex(Revtex 4) 25 pages, 8 postscript figure

Genetic programming with context-sensitive grammars

This thesis presents Genetic Algorithm for Deriving Software (Gads), a new technique for genetic programming. Gads combines a conventional genetic algorithm with a context-sensitive grammar. The key to Gads is the onto genic mapping, which converts a genome from an array of integers to a correctly typed program in the phenotype language defined by the grammar. A new type of grammar, the reflective attribute grammar (rag), is introduced. The rag is an extension of the conventional attribute grammar, which is designed to produce valid sentences, not to recognize or parse them. Together, Gads and rags provide a scalable solution for evolving type-correct software in independently-chosen context-sensitive languages. The statistics of performance comparison is investigated. A method for representing a set of genetic programming systems or problems on a cladogram is presented. A method for comparing genetic programming systems or problems on a single rational scale is proposed

Computations of vector-valued Siegel modular forms

We carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. We highlight three experimental results: (1) we identify a rational eigenform in a three dimensional space of cusp forms, (2) we observe that non-cuspidal eigenforms of level one are not always rational and (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms.Comment: 18 pages, 2 table