Theoretical Computer Modeling Research Articles

SOLVING SPARSE LEAST SQUARES PROBLEMS WITH PRECONDITIONED CGLS METHOD ON PARALLEL DISTRIBUTED MEMORY COMPUTERS

In this paper we study the parallel aspects of PCGLS, a basic iterative method based on the conjugate gradient method with preconditioner applied to normal equations and Incomplete Modified Gram-Schmidt (IMGS) preconditioner, for solving sparse least squares problems on massively parallel distributed memory computers. The performance of these methods on this kind of architecture is usually limited because of the global communication required for the inner products. We will describe the parallelization of PCGLS and IMGS preconditioner by two ways of improvement. One is to accumulate the results of a number of inner products collectively and the other is to create situations where communication can be overlapped with computation. A theoretical model of computation and communication phases is presented which allows us to determine the optimal number of processors that minimizes the runtime. Several numerical experiments on the Parsytec GC/PowerPlus are presented.

Theoretical modelling of arteriovenous malformation rupture risk: a feasibility and validation study

Purpose: To explore the feasibility of using a theoretical computational model to simulate the risk of spontaneous arteriovenous malformation (AVM) haemorrhage. Methods: Data from 12 patients were collected from a prospective databank which documented the angioarchitecture and morphological characteristics of the AVM and the feeding mean arterial pressure (FMAP) measured during initial superselective angiography prior to any treatment. Using the data, a computational model of the cerebral circulation and the AVM was constructed for each patient (patient-specific model). Two model risk (Risk model) calculations (haemodynamic- and structural-weighted estimates) were performed by using the patient-specific models. In our previously developed method of haemodynamic-weighted estimate, Risk model was calculated with the simulated intranidal pressures related to its maximal and minimal values. In the method of structural-weighted estimate developed and described in this paper, the vessel mechanical properties and probability calculation were considered in more detail than in the haemodynamic-weighted estimate. Risk model was then compared to experimentally determined risk which was calculated using a statistical method for determining the relative risk of having initially presented with AVM haemorrhage, termed Risk exp. Results: The Risk model calculated by both haemodynamic- and structural-weighted estimates correlated with experimental risks with χ 2=6.0 and 0.64, respectively. The risks of the structural-weighted estimate were more correlated to experimental risks. Conclusions: Using two different approaches to the calculation of AVM haemorrhage risk, we found a general agreement with independent statistical estimates of haemorrhagic risk based on patient data. Computational approaches are feasible; future work can focus on specific pathomechanistic questions. Detailed patient-specific computational models can also be developed as an adjunct to individual patient risk assessment for risk-stratification purposes.

Ultimate theoretical models of nanocomputers

Although a complete nanotechnology does not yet exist, we can already foresee some new directions in theoretical computer science that will be required to help us design maximally efficient computers using nanoscale components. In particular, we can devise novel theoretical models of computation that are intended to faithfully reflect the computational capabilities of physics at the nanoscale, in order to serve as a basis for the most powerful possible future nanocomputer architectures. In this paper we present arguments that a reversible 3D mesh of processors is an optimal physically realistic model for scalable computers. We show that any physical architecture based on irreversible logic devices would be asymptotically slower than realizations of our model, and we argue that no physical realization of computation aside from quantum computation could be asymptotically faster. We also calculate, using parameters from a variety of different existing and hypothetical technologies, how large a reversible computer would need to be in order to be faster than an irreversible machine. We find that using current technology, a reversible machine containing only a few hundred layers of circuits could outperform any existing machine, and that a reversible computer based on nanotechnology would only need to be a few microns across in order to outperform any possible irreversible technology. We argue that a silicon implementation of the reversible 3D mesh could be valuable today for speeding up certain scientific and engineering computations, and propose that the model should become a focus of future study in the theory of parallel algorithms for a wide range of problems.

Theoretical Model for Computation of the Energy Release of an Electron Beam in a Magnetized Plasma

Physical and mathematical models for computation of the energy release of an electron beam in a homogeneous magnetized plasma are developed. Profiles of the energy release in a carbon plasma as functions of various parameters of the beam and the plasma state are obtained.

Design of a phase/Doppler light-scattering system for measurement of small-diameter glass fibers during fiberglass manufacturing

We present fundamental studies examining the design of a phase/Doppler laser light-scattering system applicable to on-line measurements of small-diameter (<15 mum) fibers during fiberglass manufacturing. We first discuss off-line diameter measurement techniques currently used in the fiberglass industry and outline the limitations and problems associated with these methods. For the phase/Doppler design study we have developed a theoretical computer model for the response of the measurement system to cylindrical fibers, which is based on electromagnetic scattering theory. The model, valid for arbitrary fiber diameters and hardware configurations, generates simulated detector output as a function of time for a finite absorbing, cylindrical fiber oriented perpendicular to the two incident laser beams. Results of experimental measurements are presented, confirming predictions of the theoretical model. Parametric studies have also been conducted using the computer model to identify experimental arrangements that provide linear phase-diameter relationships for small-diameter fibers, within the measurement constraints imposed by the fiberglass production environment. The effect of variations in optical properties of the glass as well as fiber orientation effects are discussed. Through this research we have identified phase/Doppler arrangements that we expect to have future applications in the fiberglass industry for on-line diameter monitoring and process control.

Networks of spiking neurons can emulate arbitrary Hopfield nets in temporal coding

A theoretical model for analogue computation in networks of spiking neurons with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analogue computations via the timing of single spikes in networks of detailed compartmental neuron models.In this way, one arrives at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. We also show that it suffices to store these patterns in the efficacies of excitatory synapses.A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different stable firing patterns for different inputs.

A benchmark study based on the parallel computation of the vector outer-product A = uvT operation

In this paper we benchmark the performance of the Cray T3D, IBM 9076 SP/1 and Intel Paragon XP/S parallel computers, using implementations of parallel algorithms for the computation of the vector outer-product A = uvT operation. The vector outer-product operation, although very simple in nature, requires the computation of a large number of floating-point operations and its parallelization induces a great level of communication between the processors. It is thus suited to measure the relative speed of the processor, memory subsystem and network capabilities of a parallel computer. It should not be considered a ‘toy problem’, since it arises in numerical methods in the context of the solution of systems of non-linear equations – still a difficult problem to solve. We present algorithms for both the explicit shared-memory and message-passing programming models together with theoretical computation models for those algorithms. Actual experiments were run on those computers, using Fortran 77 implementations of the algorithms. The results obtained with these experiments show that due to the high degree of communication between the processors one needs a parallel computer with fast communications and carefully implemented data exchange routines. The theoretical computation model allows prediction of the speed-up to be obtained for some problem size on a given number of processors. © 1997 John Wiley & Sons, Ltd.

Networks of spiking neurons can emulate arbitrary Hopfield nets in temporal coding

A theoretical model for analogue computation in networks of spiking neurons with temporal coding is introduced and tested through simulations in GENESIS. It turns out that the use of multiple synapses yields very noise robust mechanisms for analogue computations via the timing of single spikes in networks of detailed compartmental neuron models.In this way, one arrives at a method for emulating arbitrary Hopfield nets with spiking neurons in temporal coding, yielding new models for associative recall of spatio-temporal firing patterns. We also show that it suffices to store these patterns in the efficacies of excitatory synapses.A corresponding layered architecture yields a refinement of the synfire-chain model that can assume a fairly large set of different stable firing patterns for different inputs.

The possibility of employing a calculable four-electrode conductance cell to substitute for the secondary standards of electrolytic conductivity

It appears that a four-electrode conductance cell designed and used according to the van der Pauw method can be applied for the absolute determination of the electrolytic conductivity of solutions with an accuracy comparable with that of the secondary standards for this quantity. Therefore there may be a possibility of avoiding the use of those standards in some cases. The results of the experimental investigation of a prototype model of the cell of this type, carried out by the authors, are consistent with the theoretical considerations and computer modeling. An absolute determination of electrolytic conductivity has been made for 0.01 and 0.1 M KCl solutions, with an overall uncertainty lower than 0.4%.

Thermal conduction and thermal diffusion in dilute polyatomic gas mixtures

A novel theoretical basis for the evaluation of the thermal conductivity and the thermal diffusion ratios of dilute polyatomic gas mixtures is derived within the semi-classical isotropic kinetic theory. New expressions for species diffusion coefficients, thermal diffusion coefficients, and thermal diffusion ratios are also obtained by using an expansion vector based upon the total energy of the molecules. Finally, practical and accurate expressions for the thermal conductivity and the thermal diffusion ratios are derived by using the recent theory of iterative transport algorithms, as developed by the authors. The resulting expressions can be used in either theoretical calculations or computational models of multicomponent flows.

A Survey Of Parallel Algorithms For One-Dimensional Integer Knapsack Problems

This article surveys several methods that can be used to solve integer knapsack problems on a variety of parallel computing architectures. Parallel algorithms designed for a variety of one-dimensional knapsack problems on both theoretical PRAM models of computation and existing parallel architectures are examined. First, exact parallel algorithms for one-dimensional exact sum, unbounded, and 0/1 knapsack problems are reviewed. These algorithms were developed from sequential table-based approaches, dynamic programming formulations, and reduction to circuit-valued or prefix convolution problems. Next, greedy algorithms and approximation algorithms for the one-dimensional subset sum, subset product, and 0/1 knapsack problems are also discussed. Experimental results that have been reported in the literature are summarized throughout this report.

Data parallel computing for network-structured optimization problems

Data level parallelism is a type of parallelism whereby operations are performed on many data elements concurrently, by many processors. These operations are (more or less) identical, and are executed in a synchronous, orderly fashion. This type of parallelism is used by massively parallel SIMD (i.e., Single Instruction, Multiple Data) architectures, like the Connection Machine CM-2, the AMT DAP and Masspar, and MIMD (i.e., Multiple Instruction, Multiple Data) architectures, like the Connection Machine CM-5. Data parallelism can also be described by a theoretical model of computation: the Vector-Random Access Machine (V-RAM).

Localization of calcium signals by a mobile calcium buffer in frog saccular hair cells

A recent study (Roberts, 1993) of saccular hair cells from grass frogs (Rana pipiens) has suggested a mechanism by which the unusually high concentrations of calcium-binding proteins found in certain sensory receptors and neurons, particularly in the auditory system, can influence short-range intracellular calcium signaling. In frog saccular hair cells, the mechanism operates within arrays of calcium channels and calcium-activated potassium channels that are involved in the cells' electrical resonance and synaptic transmission. The present study tests the hypothesis that calbindin-D28k, one of the most abundant proteins in these cells, can serve as a mobile calcium buffer that reduces and localizes changes in the intracellular free-calcium concentration ([Ca2+]i) by shuttling calcium away from the channel arrays. Based upon theoretical analysis and computer modeling, it is shown that [Ca2+]i near one or more open channels quickly reaches a steady-state level determined primarily by two properties of the buffer, the mean time (tau c) before it captures a free-calcium ion and a replenishment factor (R), which are related to the buffer's diffusional mobility (DBu), association rate constant (kon), and concentration (Bo) by tau c = (konB0)-1 and R = B0DBu. Simulation of calcium entry through a channel array showed that approximately 1.5 mM of a molecule with the diffusional and binding properties expected for calbindin-D28k (Bo approximately 8 mM calcium-binding sites) is needed to reproduce the previous experimental results. A lower concentration (B0 = 2 mM) was almost completely depleted within the channel array by a modest calcium current (8 pA = 12% of calcium channels open), but still had two important effects: it caused [Ca2+]i to fall steeply with distance outside the array (space constant < 50 nm), and returned [Ca2+]i quickly to the resting level after the channels closed. A high concentration of calbindin-D28k can thus influence the cell's electrical resonance and synaptic transmission. Its most important functions may be to localize regions of high [Ca2+]i and speed the return of [Ca2+]i toward the resting level.

A COMPUTER SIMULATION MODEL FOR ANALYSIS OF RISE IN SKIN TEMPERATURE FOLLOWING IRRADIATION WITH THE GaAlAs DIODE LASER

A popular benchmark for defining a laser therapy systcm is an output power of less than 100 mW, and low reactive-level laser therapy (LLLT) is commonly regarded as ‘safe’ for irradiating skin. However, with very small spot sizes in the order of 200 μm, the power density at tissue of a 100 mW laser therapy system is in the order of 318 W/cm2. If target tissue is painted with black ink or a similar pigment, this power density is quite capable of causing a burn injury. This has obvious implications in the use of such LLLT systems in treating dark-coloured naevi such as naevus cell naevus, or in LLLT on black patients. In order to examine this problem in detail, the authors designed a computer model with a program to calculate and analyze the temperature rise in an irradiated hemispherical block of homogeneous tissue at various powers in the range of 6 mW- 60 mW, and at spot sizes of 200 μm, 400 μm, 1.0 mm and 2.0 mm following 5 seconds irradiation with an 830 nm GaAlAs diode laser, after which the laser was ‘turned off’ The laser was deemed to be applied in the contact pressure mode, thereby compressing superficial blood vessels in the irradiated area so that blood flow cooling could be discounted. At maximum absorption, it was predicted that the 60 mW beam of the GaAlAs diode laser at 830 nm and a 200 μm spot size has the potential for causing thermal injury. The authors would like to stress that this is only a theoretical computer model, with hypothesized constants and a homogeneous target material. However, this model certainly demonstrates the error of applying arbitrary limits as to what constitutes the output power of an LLLT system, and would also appear to limit the application of LLLT at the above parameters on dark-colored naevi or for darker-skinned patients.

Die verluste wegen der reibung in Radial-Axial-Kugellagern bei hohen drehzahlen

A complex theoretical model for friction loss computation in high speed angular ball bearings has been presented. The theoretical model includes the dynamic and kinematic interactions in the angular ball bearings with numerical integration of the ball and cage motion equations. The shear stresses on the elliptical surfaces are determined by an original bidimensional Theological model in the elastohydrodynamic regime hypothesis and for the cage-race interactions an experimental model has been determined. Some theoretical elliptical sliding speeds, shear stresses and power losses have been determined for 7206 C angular contact ball bearings in the range from 5000 to 35000 rev min −1. Both theoretical and experimental outer-race torques have been determined and a good correlation between 5000 and 26000 rev min −1 is determined.

Air flow and turbulence over complex terrain: a colloquium and a computational workshop

The third Euromech Colloquium on this topic was held at FISBAT in Bologna in August 1990, in succession to those in 1979 at Munich (No. 113) and 1983 at Delphi (No. 173). About 30 participants came from 10 countries. At the Colloquium it became clear that there have been some significant developments since 1983 in theoretical analysis, computational modelling and field experiments, with new kinds of measurement. As well as papers on improvements in the quantification and understanding of the main, well-known features of these flows, there were also papers on phenomena that had not previously been studied; for example new computations of flows over undulating surfaces driven by buoyancy forces, caused by heating the surface, showed that secondary flows are produced with vorticity parallel to the undulations, while wind tunnel experiments on flows perpendicular to the crests showed secondary flow with vorticity perpendicular to the crests, and with a scale consistent with Craik's (1982) theory which predicted these novel kinds of Langmuir cells. The magnitude of the net drag force on undulating surfaces in neutrally stratified turbulent flows now appears to be moderately well established by different methods, including computations, laboratory experiments, and theoretical analyses. These have clarified the relative magnitudes of a number of contributing mechanisms. The role of Coriolis accelerations (f) in atmospheric flow over simple terrain features (lengthscale L, height H) on the mesoscale (order 30 km upwards) is now better understood. For stratified air flow impinging onto hills rising from a flat plain the Rossby radius (lR = HN/f) is the relevant lengthscale (where N is the buoyancy frequency), but in neutral or convective conditions, such as those which occur when southerly winds are channelled down the Rhine valley, the turning of the wind on a scale of the terrain less than the Rossby radius can also be significantly influenced by Coriolis accelerations.The recent field measurements by Doppler-sodar (which are installed in several French power stations) produce useful data for comparing with computational models; they also emphasize the need to solve the theoretical question of how best to combine model calculations and measurements within the flow field that exceed the number required to specify the flow in the model. Models of the mean flow and the turbulence have improved to the extent that they can be used in other scientific and practical problems, such as being incorporated into models of dispersion of pollutants, or in models of microphysics and chemical processes in polluted clouds over hills.Following the Colloquium an ERCOFTACt Workshop was held in which the computer codes of such models were presented and compared in detail. It was decided that i t is necessary to have a systematic intercomparison of such codes, and also detailed comparisons with the extensive sets of data now available from recent field and laboratory experiments.The wide range of scales that occur in these complex atmospheric flows (10−2 m to 105 m) all have to be considered and calculated in detail, because simple assumptions about the flow (such as that the mean velocity has a logarithmic profile up to a significant height above the surface) are erroneous. Computational models were described that range in complexity from those based on analytical solutions (at low computational cost) to those based on solving discretized equations with large variations in grid sizes to accommodate the range of scales. Novel interactive software was used that enables graphs from different models to be requested and then rapidly displayed simultaneously on a screen for comparisons to be made. This software opens out significant new possibilities for scientific meetings and workshops involving computational fluid dynamics.

Methods of theoretical analysis and computer modeling of the shaping of electrical pulses by nonlinear transmission lines and lumped-element delay lines

The mechanism by which high-power electrical pulses can be sharpened by propagation along nonlinear transmission lines and lumped-element delay lines is described with emphasis on the production of pulses with very fast leading or trailing edges. A survey of some of the mathematical techniques that have been applied to the propagation of electrical signals along nonlinear lines and ladder networks is presented, and the limitations of these techniques are discussed. The processes that both produce and limit pulse sharpening on nonlinear lumped-element delay lines are examined, and it is found that the wave equation, which describes the propagation of electrical signals along such networks, predicts that an electrical pulse will decompose into an array of solitons. An approximate formula for estimating the degree of pulse sharpening that can be produced on a delay line with a given number of sections is derived, and its accuracy is compared with experimental results. Numerical integration techniques for solving the nonlinear differential and difference equations that result from the mathematical analysis of nonlinear lines and networks are discussed, and the propagation of a voltage pulse along a lumped-element delay line containing nonlinear capacitors is simulated using a computer model based on an efficient algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A model of a Trombe wall

A theoretical computer model of a Trombe wall-room system is developed from first principles and empirical equations, such that the designer is free to change any of the variables, thus the wall-room properties can be changed to improve the performance. The effect of varying those properties is investigated. The model avoids the drawbacks of other empirical models in that it takes detailed system properties and hourly weather data, and gives the temperature profile of the heated enclosure over the day with the thermocirculation and the heat conducted across the wall being the only sources of heat.

OR Forum—Perspectives on Parallel Computing

Operations research is one problem domain that is likely to benefit from advances in parallel computing. We briefly review what has been achieved in recent years and try to sketch what may be expected in the near future. We argue that the lack of uniformity in available architectures is the main obstacle for the breakthrough of parallel computing. Also, formal techniques will have to be developed for the design and implementation of efficient parallel algorithms, and more realism will be required in theoretical models of parallel computation.

Stabilization of phage T4 lysozyme by engineered disulfide bonds.

Four different disulfide bridges (linking positions 9-164, 21-142, 90-122, and 127-154) were introduced into a cysteine-free phage T4 lysozyme at sites suggested by theoretical calculations and computer modeling. The new cysteines spontaneously formed disulfide bonds on exposure to air in vitro. In all cases the oxidized (crosslinked) lysozyme was more stable than the corresponding reduced (noncrosslinked) enzyme toward thermal denaturation. Relative to wild-type lysozyme, the melting temperatures of the 9-164 and 21-142 disulfide mutants were increased by 6.4 degrees C and 11.0 degrees C, whereas the other two mutants were either less stable or equally stable. Measurement of the equilibrium constants for the reduction of the engineered disulfide bonds by dithiothreitol indicates that the less thermostable mutants tend to have a less favorable crosslink in the native structure. The two disulfide bridges that are most effective in increasing the stability of T4 lysozyme have, in common, a large loop size and a location that includes a flexible part of the molecule. The results suggest that stabilization due to the effect of the crosslink on the entropy of the unfolded polypeptide is offset by the strain energy associated with formation of the disulfide bond in the folded protein. The design of disulfide bridges is discussed in terms of protein flexibility.