Showing papers on "Computation published in 1990"

Mathematical Analysis and Numerical Methods for Science and Technology

Abstract: These six volumes - the result of a ten year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the Methoden der mathematischen Physik by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to caluclate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every fact of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences. Volumes 5 and 6 cover problems of Transport and Evolution.

Computation of component image velocity from local phase information

Abstract: We present a technique for the computation of 2D component velocity from image sequences. Initially, the image sequence is represented by a family of spatiotemporal velocity-tuned linear filters. Component velocity, computed from spatiotemporal responses of identically tuned filters, is expressed in terms of the local first-order behavior of surfaces of constant phase. Justification for this definition is discussed from the perspectives of both 2D image translation and deviations from translation that are typical in perspective projections of 3D scenes. The resulting technique is predominantly linear, efficient, and suitable for parallel processing. Moreover, it is local in space-time, robust with respect to noise, and permits multiple estimates within a single neighborhood. Promising quantiative results are reported from experiments with realistic image sequences, including cases with sizeable perspective deformation.

Optimal network reconfigurations in distribution systems. II. Solution algorithms and numerical results

Abstract: Using a two-stage solution methodology and a modified simulated annealing technique, the authors develop a solution algorithm to the network reconfiguration problem, which is a constrained, multiobjective, nondifferentiable, optimization problem. This solution algorithm allows the designer to obtain a desirable, global noninferior point in a reasonable computation time. Also, given a desired number of switch-on/switch-off operations involved in the network configuration, the solution algorithm can identify the most effective operations. In order to reduce the computation time required, the idea of approximate calculations is explored and incorporated into the solution algorithm, where two efficient load-flow methods are employed; one for high temperature and the other for low temperature. The solution algorithm has been implemented in a software package and tested on a 69-bus system with very promising results. >

Efficient computation on oblivious RAMs

Abstract: A machine is oblivious if the sequence in which it accesses memory locations is equivalent for any two programs with the same running time. For example, an oblivious Turing Machine is one for which the movement of the heads on the tapes is identical for each computation. (Thus, it is independent of the actual input.) What is the slowdown in the running time of any machine, if it is required to be oblivious? In 1979 Pippenger and Fischer [PF] showed how a twotape oblivious Turing Machine can simulate, on-line, a onetape Turing Machine, with a logarithmic slowdown in the running time. We show a similar result for the randomaccess machine (RAM) model of computation, solving an open problem posed by Goldreich [G]. In particular, we show how to do an on-line simulation of an arbitrary RAM program by a probabilistic RAM whose memory access pattern is independent of the program which is being executed, and with a poly-logarithmic slowdown in the running time. Our proof yields a technique of efficiently hiding (through randomization) the access pattern into any composite datastructure. As one of the applications, we exhibit a simple and efficient software protection scheme for a generic oneprocessor RAM model of computation.

Logic and computation : interactive proof with Cambridge LCF

Abstract: From the Publisher: This study of techniques for formal theorem-proving focuses on the applications of Cambridge LCF (Logic for Computable Functions), a computer program for reasoning about computation.

MSLiP: a computer code for the multistage stochastic linear programming problem

Abstract: This paper describes an efficient implementation of a nested decomposition algorithm for the multistage stochastic linear programming problem. Many of the computational tricks developed for deterministic staircase problems are adapted to the stochastic setting and their effect on computation times is investigated. The computer code supports an arbitrary number of time periods and various types of random structures for the input data. Numerical results compare the performance of the algorithm to MINOS 5.0.

Parallel algorithms for dense linear algebra computations

Abstract: Scientific and engineering research is becoming increasingly dependent upon the development and implementation of efficient parallel algorithms on modern high-performance computers. Numerical linear algebra is an indispensable tool in such research and this paper attempts to collect and describe a selection of some of its more important parallel algorithms. The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers. A major emphasis is given here to certain computational primitives whose efficient execution on parallel and vector computers is essential in order to obtain high performance algorithms.

Connectionist ideas and algorithms

Abstract: In our quest to build intelligent machines, we have but one naturally occurring model: the human brain. It follows that one natural idea for artificial intelligence (AI) is to simulate the functioning of the brain directly on a computer. Indeed, the idea of building an intelligent machine out of artificial neurons has been around for quite some time. Some early results on brain-line mechanisms were achieved by [18], and other researchers pursued this notion through the next two decades, e.g., [1, 4, 19, 21, 24]. Research in neural networks came to a virtual halt in the 1970s, however, when the networks under study were shown to be very weak computationally. Recently, there has been a resurgence of interest in neural networks. There are several reasons for this, including the appearance of faster digital computers on which to simulate larger networks, interest in building massively parallel computers, and most importantly, the discovery of powerful network learning algorithms.The new neural network architectures have been dubbed connectionist architectures. For the most part, these architectures are not meant to duplicate the operation of the human brain, but rather receive inspiration from known facts about how the brain works. They are characterized by Large numbers of very simple neuron-like processing elements;Large numbers of weighted connections between the elements—the weights on the connections encode the knowledge of a network;Highly parallel, distributed control; andEmphasis on learning internal representations automatically.Connectionist researchers conjecture that thinking about computation in terms of the brain metaphor rather than the digital computer metaphor will lead to insights into the nature of intelligent behavior.Computers are capable of amazing feats. They can effortlessly store vast quantities of information. Their circuits operate in nanoseconds. They can perform extensive arithmetic calculations without error. Humans cannot approach these capabilities. On the other hand, humans routinely perform simple tasks such as walking, talking, and commonsense reasoning. Current AI systems cannot do any of these things better than humans. Why not? Perhaps the structure of the brain is somehow suited to these tasks, and not suited to tasks like high-speed arithmetic calculation. Working under constraints suggested by the brain may make traditional computation more difficult, but it may lead to solutions to AI problems that would otherwise be overlooked.What constraints, then, does the brain offer us? First of all, individual neurons are extremely slow devices when compared to their counterparts in digital computers. Neurons operate in the millisecond range, an eternity to a VLSI designer. Yet, humans can perform extremely complex tasks, like interpreting a visual scene or understanding a sentence, in just a tenth of a second. In other words, we do in about a hundred steps what current computers cannot do in ten million steps. How can this be possible? Unlike a conventional computer, the brain contains a huge number of processing elements that act in parallel. This suggests that in our search for solutions, we look for massively parallel algorithms that require no more than 100 processing steps [9].Also, neurons are failure-prone devices. They are constantly dying (you have certainly lost a few since you began reading this article), and their firing patterns are irregular. Components in digital computers, on the other hand, must operate perfectly. Why? Such components store bits of information that are available nowhere else in the computer: the failure of one component means a loss of information. Suppose that we built AI programs that were not sensitive to the failure of a few components, perhaps by using redundancy and distributing information across a wide range of components? This would open the possibility of very large-scale implementations. With current technology, it is far easier to build a billion-component integrated circuit in which 95 percent of the components work correctly than it is to build a perfectly functioning million-component machine [8].Another thing people seem to be able to do better than computers is handle fuzzy situations. We have very large memories of visual, auditory, and problem-solving episodes, and one key operation in solving new problems is finding closest matches to old situations. Inexact matching is something brain-style models seem to be good at, because of the diffuse and fluid way in which knowledge is represented.The idea behind connectionism, then, is that we may see significant advances in AI if we approach problems from the point of view of brain-style computation rather than rule-based symbol manipulation. At the end of this article, we will look more closely at the relationship between connectionist and symbolic AI.

Secular perturbation theory and computation of asteroid proper elements

Abstract: A new theory for the calculation of proper elements is presented This theory defines an explicit algorithm applicable to any chosen set of orbits and accounts for the effect of shallow resonances on secular frequencies The proper elements are computed with an iterative algorithm and the behavior of the iteration can be used to define a quality code

Architecture-independent parallel computation

Abstract: The major parallel architecture classes are considered: single-instruction multiple-data (SIMD) computers, tightly coupled multiple-instruction multiple-data (MIMD) computers, hypercuboid computers and constant-valence MIMD computers. An argument that the PRAM model is universal over tightly coupled and hypercube systems, but not over constant-valence-topology, loosely coupled-system is reviewed, showing precisely how the PRAM model is too powerful to permit broad universality. Ways in which a model of computation can be restricted to become universal over less powerful architectures are discussed. The Bird-Meertens formalism (R.S. Bird, 1989), is introduced and it is shown how it is used to express computations in a compact way. It is also shown that the Bird-Meertens formalism is universal over all four architecture classes and that nontrivial restrictions of functional programming languages exist that can be efficiently executed on disparate architectures. The use of the Bird-Meertens formalism as the basis for a programming language is discussed, and it is shown that it is expressive enough to be used for general programming. Other models and programming languages with architecture-independent properties are reviewed. >

Resolution of the 1D regularized Burgers equation using a spatial wavelet approximation

Abstract: The Burgers equation with a small viscosity term, initial and periodic boundary conditions is resolved using a spatial approximation constructed from an orthonormal basis of wavelets. The algorithm is directly derived from the notions of multiresolution analysis and tree algorithms. Before the numerical algorithm is described these notions are first recalled. The method uses extensively the localization properties of the wavelets in the physical and Fourier spaces. Moreover, the authors take advantage of the fact that the involved linear operators have constant coefficients. Finally, the algorithm can be considered as a time marching version of the tree algorithm. The most important point is that an adaptive version of the algorithm exists: it allows one to reduce in a significant way the number of degrees of freedom required for a good computation of the solution. Numerical results and description of the different elements of the algorithm are provided in combination with different mathematical comments on the method and some comparison with more classical numerical algorithms.

A framework for the parallel processing of Datalog queries

Abstract: This paper presents several complementary methods for the parallel, bottom-up evaluation of Datalog queries. We introduce the notion of a discriminating predicate, based on hash functions, that partitions the computation between the processors in order to achieve parallelism. A parallelization scheme with the property of non-redundant computation (no duplication of computation by processors) is then studied in detail. The mapping of Datalog programs onto a network of processors, such that the results is a non-redundant computation, is also studied. The methods reported in this paper clearly demonstrate the trade-offs between redundancy and interprocessor-communication for this class of problems.

Computation of synthetic seismograms for stratified azimuthally anisotropic media

Abstract: We outline a method of computing synthetic seismograms for stratified, azimuthally anisotropic, viscoelastic earth models. This method is an extended form of the Kennett algorithm that is efficient for multioffset vertical seismic profiling. The model consists of a stack of homogeneous plane layers, and the response is computed iteratively by successive inclusion of deeper layers. In each layer, the 6×6 system matrix A is diagonalized numerically; this permits treatment of triclinic materials, i.e., those with the lowest possible symmetry. Jacobi iteration is an efficient way to diagonalize A because the entries of A change little from one wavenumber to the next. When the material properties are frequency dependent, the wavenumber loops are inside the frequency loop, and the computation is slow even on a supercomputer. When the material parameters are frequency independent, it is better to make frequency the deepest loop, with diagonalization of A outside the loop, in which case vectorization gives a relatively rapid computation. Temporal wraparound is avoided by making use of complex frequencies, and spatial aliasing is avoided by using a generalized Filon's method to evaluate both the wavenumber integrals. Various methods of generating anisotropic elastic constants from microlayers, cracks, and fractures and joints are discussed. Example computations are given for azimuthally isotropic and azimuthally anisotropic (AA) earth models. Comparison of computations using single and double wavenumber integrations for a realistic AA model shows that single wave-number integration often gives incorrect answers especially at near offsets. Errors due to use of a single wavenumber integration are explained heuristically by use of wave front diagrams for point and line sources.

Computing the arc length of parametric curves

Abstract: Specifying constraints on motion is simpler if the curve is parameterized by arc length, but many parametric curves of practical interest cannot be parameterized by arc length. An approximate numerical reparameterization technique that improves on a previous algorithm by using a different numerical integration procedure that recursively subdivides the curve and creates a table of the subdivision points is presented. The use of the table greatly reduces the computation required for subsequent arc length calculations. After table construction, the algorithm takes nearly constant time for each arc length calculation. A linear increase in the number of control points can result in a more than linear increase in computation. Examples of this type of behavior are shown. >

Weight discretization paradigm for optical neural networks

Abstract: Neural networks are a primary candidate architecture for optical computing. One of the major problems in using neural networks for optical computers is that the information holders: the interconnection strengths (or weights) are normally real valued (continuous), whereas optics (light) is only capable of representing a few distinguishable intensity levels (discrete). In this paper a weight discretization paradigm is presented for back(ward error) propagation neural networks which can work with a very limited number of discretization levels. The number of interconnections in a (fully connected) neural network grows quadratically with the number of neurons of the network. Optics can handle a large number of interconnections because of the fact that light beams do not interfere with each other. A vast amount of light beams can therefore be used per unit of area. However the number of different values one can represent in a light beam is very limited. A flexible, portable (machine independent) neural network software package which is capable of weight discretization, is presented. The development of the software and some experiments have been done on personal computers. The major part of the testing, which requires a lot of computation, has been done using a CRAY X-MP/24 super computer.

Speculative computation in multilisp

Abstract: We present experimental evidence that performing computations in parallel before their results are known to be required can yield performance improvements over conventional approaches to parallel computing. We call such eager computation of expressions speculative computation, as opposed to conventional mandatory computation that is used in almost all contemporary parallel programming languages and systems. The two major requirements for speculative computation are: 1) a means to control computation to favor the most promising computations and 2) a means to abort computation and reclaim computation resources.We discuss these requirements in the parallel symbolic language Multilisp and present a sponsor model for speculative computation in Multilisp which handles control and reclamation of computation in a single, elegant framework. We outline an implementation of this sponsor model and present performance results for several applications of speculative computation. The results demonstrate that our support for speculative computation adds expressive and computational power to Multilisp, with observed performance improvement as great as 26 times over conventional approaches to parallel computation.

Computation of irreducible generalized state-space realizations

Abstract: In this paper, an efficient, numerically stable procedure is presented for the computation of irreducible generalized state-space realizations from non-minimal ones. The order reduction is performed by removing successively the uncontrollable and the unobservable parts of the system. Each reduction is accomplished by the same basic algorithm which deflates the uncontrollable part of the system using orthogonal similarity transformations. Applications of the proposed procedure are also presented.

Rapid computation of configuration space obstacles

Abstract: Mathematical properties of configuration space are presented, and algorithms invoking those properties for efficient computation of obstacles in configuration space are described. Simple elements in Cartesian space which can be transformed into configuration space rapidly are identified. Transformations of complex workspace shapes into configuration space are described in terms of multiple transformations of such simpler primitives. Computational considerations and examples are presented for the first three degrees of freedom of an industrial robot. >

A parallel-vector algorithm for rapid structural analysis on high-performance computers

Abstract: A fast, accurate Choleski method for the solution of symmetric systems of linear equations is presented. This direct method is based on a variable-band storage scheme and takes advantage of column heights to reduce the number of operations in the Choleski factorization. The method employs parallel computation in the outermost DO-loop and vector computation via the 'loop unrolling' technique in the innermost DO-loop. The method avoids computations with zeros outside the column heights, and as an option, zeros inside the band. The close relationship between Choleski and Gauss elimination methods is examined. The minor changes required to convert the Choleski code to a Gauss code to solve non-positive-definite symmetric systems of equations are identified. The results for two large-scale structural analyses performed on supercomputers, demonstrate the accuracy and speed of the method.

A time-stepping algorithm for parallel computers

Abstract: Parabolic and hyperbolic differential equations are often solved numerically by time-stepping algorithms. These algorithms have been regarded as sequential in time; that is, the solution on a time level must be known before the computation of the solution at subsequent time levels can start. While this remains true in principle, it is demonstrated that it is possible for processors to perform useful work on many time levels simultaneously. Specifically, it is possible for processors assigned to “later” time levels to compute a very good initial guess for the solution based on partial solutions from previous time levels, thus reducing the time required for solution. The reduction in the solution time can be measured as parallel speedup.This algorithm is demonstrated for both linear and nonlinear problems. In addition, the convergence properties of the method based on the convergence properties of the underlying iterative method are discussed, and an accurate performance model from which the speedup and oth...

Uniform random number generators for parallel computers

Abstract: Almost all simulational computations require uniformly distributed random numbers. Generators of uniform random numbers are considered and assessed with respect to their possible use on parallel computers. Two recent, commercially available computers are given special attention: the Connection Machine and the T Series. Feedback shift register type generators with a large Mersenne prime are recommended for implementation on these computers.