Duncan A. Buell

The Promise of High-Performance Reconfigurable Computing

Several high-performance computers now use field-programmable gate arrays as reconfigurable coprocessors. The authors describe the two major contemporary HPRC architectures and explore the pros and cons of each using representative applications from remote sensing, molecular dynamics, bioinformatics, and cryptanalysis.

Fuzzy sets and generalized Boolean retrieval systems

Substantial work has been done on the application of fuzzy subset theory to information retrieval. Boolean query processing has been generalized to allow for weights to be attached to individual terms, in either the document indexing or the query representation, or both. Problems with the generalized Boolean lattice structure have been noted, and an alternative approach using query thresholds and appropriate document evaluation functions has been suggested. Problems remain unsolved, however. Criteria generated for the query processing mechanism are inconsistent. The exact functional form and appropriate parameters for the query processing mechanism must be specified. Moreover, the generalized Boolean query model must be reconciled with the vector space approach, suggested new lattice structures for weighted retrieval, and probabilistic retrieval models. Finally, proper retrieval evaluation mechanisms reflecting the fuzzy nature of retrieval are needed.

Threshold values and Boolean retrieval systems

Several papers have appeared that have analyzed recent developments in the problem of processing, in a document retrieval system, queries expressed as Boolean expressions. The purpose of this paper is to continue that analysis. We shall show that the concept of threshold values resolves the problems inherent with relevance weights. Moreover, we shall explore possible evaluation mechanisms for retrieval of documents, based on fuzzy-set-theoretic considerations.

A model for a weighted retrieval system

There has been a good deal of work on information retrieval systems that have continuous weights assigned to the index terms that describe the records in the database, and/or to the query terms that describe the user queries. Recent articles have analyzed retrieval systems with continuous weights of either type and/or with a Boolean structure for the queries. They have also suggested criteria which such systems ought to satisfy and record evaluation mechanisms which partially satisfy these criteria. We offer a more careful analysis, based on a generalization of the discrete weights. We also look at the weights from an entirely different approach involving thresholds, and we generate an improved evaluation mechanism which seems to fulfill a larger subset of the desired criteria than previous mechanisms. This new mechanism allows the user to attach a “threshold” to the query term.

Binary quadratic forms : classical theory and modern computations

1 Elementary Concepts.- 2 Reduction of Positive Definite Forms.- 3 Indefinite Forms.- 3.1 Reduction, Cycles.- 3.2 Automorphs, Pells Equation.- 3.3 Continued Fractions and Indefinite Forms.- 4 The Class Group.- 4.1 Representation and Genera.- 4.2 Composition Algorithms.- 4.3 Generic Characters Revisited.- 4.4 Representation of Integers.- 5 Miscellaneous Facts.- 5.1 Class Number Computations.- 5.2 Extreme Cases and Asymptotic Results.- 6 Quadratic Number Fields.- 6.1 Basic Algebraic Definitions.- 6.2 Algebraic Numbers and Quadratic Fields.- 6.3 Ideals in Quadratic Fields.- 6.4 Binary Quadratic Forms and Classes of Ideals.- 6.5 History.- 7 Composition of Forms.- 7.1 Nonfundamental Discriminants.- 7.2 The General Problem of Composition.- 7.3 Composition in Different Orders.- 8 Miscellaneous Facts II.- 8.1 The Cohen-Lenstra Heuristics.- 8.2 Decomposing Class Groups.- 8.3 Specifying Subgroups of Class Groups.- 8.3.1 Congruence Conditions.- 8.3.2 Exact and Exotic Groups.- 9 The 2-Sylow Subgroup.- 9.1 Classical Results on the Pell Equation.- 9.2 Modern Results.- 9.3 Reciprocity Laws.- 9.4 Special References for Chapter 9.- 10 Factoring with Binary Quadratic Forms.- 10.1 Classical Methods.- 10.2 SQUFOF.- 10.3 CLASNO.- 10.4 SPAR.- 10.4.1 Pollard p - 1.- 10.4.2 SPAR.- 10.5 CFRAC.- 10.6 A General Analysis.- Appendix 1:Tables, Negative Discriminants.- Appendix 2:Tables, Positive Discriminants.

The Splash 2 processor and applications

Splash 2 is an attached parallel processor in which the computing elements are user-programmable FPGA devices. The architecture of Splash 2 is designed to accelerate the solution of problems which exhibit at least modest amounts of temporal or data parallelism. Applications are developed by writing descriptions of algorithms in VHDL, which are then iteratively refined and debugged within a simulator. Once an application is determined to be functionally correct in simulation, it is compiled to a gate list and optimized by logic synthesis. The gate list is then mapped onto the FPGA architecture by automatic placement and routing tools to form a loadable FPGA object module. A C language library and a symbolic debugger comprise the execution environment. The Splash 2 system has been shown to be effective on a variety of applications, including text searching, sequence analysis, and image processing.<<ETX>>

An analysis of some fuzzy subset applications to information retrieval systems

Abstract Several authors have attempted to improve the ability of an information retrieval system to process queries by allowing for a more general query and query-processing structure than standard Boolean expressions and ordinary set theory. The first step in generalization, from ordinary set theory to fuzzy subset theory, is both philosophically and mathematically straightforward. The next step, that of generalizing the use of fuzzy subset theory, has been more difficult. Of particular fundamental concern is the underlying lattice structure of the fuzzy subsets themselves and the possible loss of certain features of that structure in the second generalization step. This paper will show that the mathematical requirements placed on the generalization in order that the lattice structures be preserved are really quite minimal.

Guest Editors' Introduction: High-Performance Reconfigurable Computing

High-performance reconfigurable computers have the potential to exploit coarse-grained functional parallelism as well as fine-grained instruction-level parallelism through direct hardware execution on FPGAs.

Parallel algorithms for Bayesian phylogenetic inference

The combination of a Markov chain Monte Carlo (MCMC) method with likelihood-based assessment of phylogenies is becoming a popular alternative to direct likelihood optimization. However, MCMC, like maximum likelihood, is a computationally expensive method. To approximate the posterior distribution of phylogenies, a Markov chain is constructed, using the Metropolis algorithm, such that the chain has the posterior distribution of the parameters of phylogenies as its stationary distribution.This paper describes parallel algorithms and their MPI-based parallel implementation for MCMC-based Bayesian phylogenetic inference. Bayesian phylogenetic inference is computationally expensive both in time and in memory requirements. Our variations on MCMC and their implementation were done to permit the study of large phylogenetic problems. In our approach, we can distribute either entire chains or parts of a chain to different processors, since in current models the columns of the data are independent. Evaluations on a 32-node Beowulf cluster suggest the problem scales well. A number of important points are identified, including a superlinear speedup due to more effective cache usage and the point at which additional processors slow down the process due to communication overhead.

Custom computing machines: an introduction

We present a brief introduction to custom computing machines.