Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Applying autonomic computing concepts to parallel computing using intelligent agents

The work reported in this paper is motivated by the fact that there is a need to apply autonomic computing concepts to parallel computing systems. Advancing on prior work based on intelligent cores [36], a swarm-array computing approach, this paper focuses on ‘Intelligent agents’ another swarm-array computing approach in which the task to be executed on a parallel computing core is considered as a swarm of autonomous agents. A task is carried to a computing core by carrier agents and is seamlessly transferred between cores in the event of a predicted failure, thereby achieving self-ware objectives of autonomic computing. The feasibility of the proposed swarm-array computing approach is validated on a multi-agent simulator.

Towards self-ware via swarm-array computing

The work reported in this paper proposes Swarm-Array computing, a novel technique inspired by swarm robotics, and built on the foundations of autonomic and parallel computing. The approach aims to apply autonomic computing constructs to parallel computing systems and in effect achieve the self-ware objectives that describe self-managing systems. The constitution of swarm-array computing comprising four constituents, namely the computing system, the problem/task, the swarm and the landscape is considered. Approaches that bind these constituents together are proposed. Space applications employing FPGAs are identified as a potential area for applying swarm-array computing for building reliable systems. The feasibility of a proposed approach is validated on the SeSAm multi-agent simulator and landscapes are generated using the MATLAB toolkit.

Achieving intelligent agents and its feasibility in swarm-array computing

The work reported in this paper proposes ‘Intelligent Agents’, a Swarm-Array computing approach focused to apply autonomic computing concepts to parallel computing systems and build reliable systems for space applications. Swarm-array computing is a robotics a swarm robotics inspired novel computing approach considered as a path to achieve autonomy in parallel computing systems. In the intelligent agent approach, a task to be executed on parallel computing cores is considered as a swarm of autonomous agents. A task is carried to a computing core by carrier agents and can be seamlessly transferred between cores in the event of a predicted failure, thereby achieving self-* objectives of autonomic computing. The approach is validated on a multi-agent simulator.

Integrable quadratic Hamiltonians on the Euclidean group of motions

In this paper, we discuss the problem of globally computing sub-Riemannian curves on the Euclidean group of motions SE(3). In particular, we derive a global result for special sub-Riemannian curves whose Hamiltonian satisfies a particular condition. In this paper, sub-Riemannian curves are defined in the context of a constrained optimal control problem. The maximum principle is then applied to this problem to yield an appropriate left-invariant quadratic Hamiltonian. A number of integrable quadratic Hamiltonians are identified. We then proceed to derive convenient expressions for sub-Riemannian curves in SE(3) that correspond to particular extremal curves. These equations are then used to compute sub-Riemannian curves that could potentially be used for motion planning of underwater vehicles.

Exploring carrier agents in swarm-array computing

How can a bridge be built between autonomic computing approaches and parallel computing systems? The work reported in this paper is motivated towards bridging this gap by proposing a swarm-array computing approach based on ‘Intelligent Agents’ to achieve autonomy for distributed parallel computing systems. In the proposed approach, a task to be executed on parallel computing cores is carried onto a computing core by carrier agents that can seamlessly transfer between processing cores in the event of a predicted failure. The cognitive capabilities of the carrier agents on a parallel processing core serves in achieving the self-ware objectives of autonomic computing, hence applying autonomic computing concepts for the benefit of parallel computing systems. The feasibility of the proposed approach is validated by simulation studies using a multi-agent simulator on an FPGA (Field-Programmable Gate Array) and experimental studies using MPI (Message Passing Interface) on a computer cluster. Preliminary results confirm that applying autonomic computing principles to parallel computing systems is beneficial.

An MPI-based implementation of intelligent agents on clusters

Recent research in multi-agent systems incorporate fault tolerance concepts, but does not explore the extension and implementation of such ideas for large scale parallel computing systems. The work reported in this paper investigates a swarm array computing approach, namely 'Intelligent Agents'. A task to be executed on a parallel computing system is decomposed to sub-tasks and mapped onto agents that traverse an abstracted hardware layer. The agents intercommunicate across processors to share information during the event of a predicted core/processor failure and for successfully completing the task. The feasibility of the approach is validated by implementation of a parallel reduction algorithm on a computer cluster using the Message Passing Interface.

A cluster-based implementation of a fault-tolerant parallel reduction algorithm using swarm-array computing

Recent research in multi-agent systems incorporate fault tolerance concepts. However, the research does not explore the extension and implementation of such ideas for large scale parallel computing systems. The work reported in this paper investigates a swarm array computing approach, namely ‘Intelligent Agents’. In the approach considered a task to be executed on a parallel computing system is decomposed to sub-tasks and mapped onto agents that traverse an abstracted hardware layer. The agents intercommunicate across processors to share information during the event of a predicted core/processor failure and for successfully completing the task. The agents hence contribute towards fault tolerance and towards building reliable systems. The feasibility of the approach is validated by simulations on an FPGA using a multi-agent simulator and implementation of a parallel reduction algorithm on a computer cluster using the Message Passing Interface.

Quantitative evaluation of three reconfiguration strategies on FPGAs: a case study

Reconfigurable computing is becoming an important new alternative for implementing computations. Field programmable gate arrays (FPGAs) are the ideal integrated circuit technology to experiment with the potential benefits of using different strategies of circuit specialization by reconfiguration. The final form of the reconfiguration strategy is often non-trivial to determine. Consequently, in this paper, we examine strategies for reconfiguration and, based on our experience, propose general guidelines for the tradeoffs using an area-time metric called functional density. Three experiments are set up to explore different reconfiguration strategies for FPGAs applied to a systolic implementation of a scalar quantizer used as a case study. Quantitative results for each experiment are given. The regular nature of the example means that the results can be generalized to a wide class of industry-relevant problems based on arrays.

A cluster computing implementation of a Monte Carlo simulation of a particle growth mechanism

Clusters of computers can be used together to provide a powerful computing resource. Large Monte Carlo simulations, such as those used to model particle growth, are computationally intensive and take considerable time to execute on conventional workstations. By spreading the work of the simulation across a cluster of computers, the elapsed execution time can be greatly reduced. Thus a user has apparently the performance of a supercomputer by using the spare cycles on other workstations.

On the evaluation of temperature trends in the tropical troposphere

A series of model experiments with the coupled Max-Planck-Institute ECHAM5/OM climate model have been investigated and compared with microwave measurements from the Microwave Sounding Unit (MSU) and re-analysis data for the period 1979–2008. The evaluation is carried out by computing the Temperature in the Lower Troposphere (TLT) and Temperature in the Middle Troposphere (TMT) using the MSU weights from both University of Alabama (UAH) and Remote Sensing Systems (RSS) and restricting the study to primarily the tropical oceans. When forced by analysed sea surface temperature the model reproduces accurately the time-evolution of the mean outgoing tropospheric microwave radiation especially over tropical oceans but with a minor bias towards higher temperatures in the upper troposphere. The latest reanalyses data from the 25 year Japanese re-analysis (JRA25) and European Center for Medium Range Weather Forecasts Interim Reanalysis are in very close agreement with the time-evolution of the MSU data with a correlation of 0.98 and 0.96, respectively. The re-analysis trends are similar to the trends obtained from UAH but smaller than the trends from RSS. Comparison of TLT, computed from observations from UAH and RSS, with Sea Surface Temperature indicates that RSS has a warm bias after 1993. In order to identify the significance of the tropospheric linear temperature trends we determined the natural variability of 30-year trends from a 500 year control integration of the coupled ECHAM5 model. The model exhibits natural unforced variations of the 30 year tropospheric trend that vary within ±0.2 K/decade for the tropical oceans. This general result is supported by similar results from the Geophysical Fluid Dynamics Laboratory (GFDL) coupled climate model. Present MSU observations from UAH for the period 1979–2008 are well within this range but RSS is close to the upper positive limit of this variability. We have also compared the trend of the vertical lapse rate over the tropical oceans assuming that the difference between TLT and TMT is an approximate measure of the lapse rate. The TLT–TMT trend is larger in both the measurements and in the JRA25 than in the model runs by 0.04–0.06 K/decade. Furthermore, a calculation of all 30 year TLT–TMT trends of the unforced 500-year integration vary between ±0.03 K/decade suggesting that the models have a minor systematic warm bias in the upper troposphere.