Automatic Integral Reduction for Higher Order Perturbative Calculations

We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.Comment: 23 page

General Algorithm For Improved Lattice Actions on Parallel Computing Architectures

Quantum field theories underlie all of our understanding of the fundamental forces of nature. The are relatively few first principles approaches to the study of quantum field theories [such as quantum chromodynamics (QCD) relevant to the strong interaction] away from the perturbative (i.e., weak-coupling) regime. Currently the most common method is the use of Monte Carlo methods on a hypercubic space-time lattice. These methods consume enormous computing power for large lattices and it is essential that increasingly efficient algorithms be developed to perform standard tasks in these lattice calculations. Here we present a general algorithm for QCD that allows one to put any planar improved gluonic lattice action onto a parallel computing architecture. High performance masks for specific actions (including non-planar actions) are also presented. These algorithms have been successfully employed by us in a variety of lattice QCD calculations using improved lattice actions on a 128 node Thinking Machines CM-5. {\underline{Keywords}}: quantum field theory; quantum chromodynamics; improved actions; parallel computing algorithms

Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.

Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets

Assessing the disclosure protection provided by misclassification for survey microdata

Government statistical agencies often apply statistical disclosure limitation techniques to survey microdata to protect confidentiality. There is a need for ways to assess the protection provided. This paper develops some simple methods for disclosure limitation techniques which perturb the values of categorical identifying variables. The methods are applied in numerical experiments based upon census data from the United Kingdom which are subject to two perturbation techniques: data swapping and the post randomisation method. Some simplifying approximations to the measure of risk are found to work well in capturing the impacts of these techniques. These approximations provide simple extensions of existing risk assessment methods based upon Poisson log-linear models. A numerical experiment is also undertaken to assess the impact of multivariate misclassification with an increasing number of identifying variables. The methods developed in this paper may also be used to obtain more realistic assessments of risk which take account of the kinds of measurement and other non-sampling errors commonly arising in surveys