G. M. Prabhu

A random number generator for parallel computers

Abstract Running huge simulational computations on a system of parallel processors requires the generation of uniform random sequences on each processor. Various techniques useful for the generation of parallel random sequences are analyzed for their suitability to parallel architectures. An efficient parallelization of the Generalized Feedback Shift Register (GFSR) algorithm for generating pseudorandom numbers is presented. The algorithm works on any parallel computer where the number of processors is a power of two and requires the same amount of memory per processor as required by the sequential GFSR algorithm.

The Kappa network with fault-tolerant destination tag algorithm

The design of the Gamma network is analyzed in terms of block structure. The analysis reveals the asymmetry of its duplicate links, and an alternate design in the form of the Kappa network is proposed. Its novel feature is the symmetry of duplicate links at the block level. This symmetry results in a simple control algorithm and enhanced fault tolerance. The relationship between the Kappa network and other existing fault-tolerant networks is briefly discussed. >

Truly distribution-independent algorithms for the N-body problem

The N-body problem is to simulate the motion of N particles under the influence of mutual force fields based on an inverse square law. Greengards algorithm claims to compute the cumulative force on each particle in O(N) time for a fixed precision irrespective of the distribution of the particles. In this paper, we show that Greengards algorithm is distribution dependent and has a lower bound of /spl Omega/(N log/sup 2/ N) in two dimensions and /spl Omega/(N log/sup 4/ N) in three dimensions. We analyze the Greengard and Barnes-Hut algorithms and show that they are unbounded for arbitrary distributions. We also present a truly distribution independent algorithm for solving the N-body problem in O(N log N) time in two dimensions and in O(N log/sup 2/ N) time in three dimensions.<<ETX>>

A constructive formulation of the one-way speed of light

A formulation of the one-way speed of light in three-dimensional Euclidean space is derived by a constructive approach. This formulation is consistent with the result of the Michelson–Morley experiment in that the harmonic mean of the outward and return speeds is equal to c, the standard value for the speed of electromagnetic radiation in vacuum. It is also shown that a shift in synchronization, proportional to the distance along the line of motion, renders this speed a constant along all directions.

Reversal in the time order of interactive events: the collision of inclined rods

In the rod and hole paradox as described by Rindler (1961 Am. J. Phys. 29 365-6), a rigid rod moves at high speed over a table towards a hole of the same size. Observations from the inertial frames of the rod and slot are widely different. Rindler explains these differences by the concept of differing perceptions in rigidity. Gron and Johannesen (1993 Eur. J. Phys. 14 97-100) confirmed this aspect by computer simulation where the shapes of the rods are different as observed from the co-moving frames of the rod and slot. Lintel and Gruber (2005 Eur. J. Phys. 26 19-23) presented an approach based on retardation due to speed of stress propagation. In this paper we consider the situation when two parallel rods collide while approaching each other along a line at an inclination with their axis. The collisions of the top and bottom ends are reversed in time order as observed from the two co-moving frames. This result is explained by the concept of extended present derived from the principle of relativity of simultaneity.

Visualization of program performance on concurrent computers

A distributed memory concurrent computer (such as a hypercube computer) is inherently a complex system involving the collective and simultaneous interaction of many entities engaged in computation and communication activities. Program performance evaluation in concurrent computer systems requires methods and tools for observing, analyzing, and displaying system performance. This dissertation describes a methodology for collecting and displaying, via a unique graphical approach, performance measurement information from (possibly large) concurrent computer systems. Performance data are generated and collected via instrumentation. The data are then reduced via conventional cluster analysis techniques and converted into a pictorial form to highlight important aspects of program states during execution. Local and summary statistics are calculated. Included in the suite of defined metrics are measures for quantifying and comparing amounts of computation and communication. A novel kind of data plot is introduced to visually display both temporal and spatial information describing system activity. Phenomena such as hot spots of activity are easily observed, and in some cases, patterns inherent in the application algorithms being studied are highly visible. The approach also provides a framework for a visual solution to the problem of mapping a given parallel algorithm to an underlying parallel machine. A prototype implementation applied to several case studies is presented to demonstrate the feasibility and power of the approach.

Differing observations on the landing of the rod into the slot

In the usual rod and slot paradox a rod falls into a slot due to gravity. Many thought experiments have been conducted where the presence of gravity is eliminated with the rod and slot approaching each other along a line joining their centers. In these experiments the line of motion is not parallel to the axis of the rod or the slot. We consider the cases for which the rod falls into the slot and the rod does not fall into the slot, each from the perspective of the co-moving frames of the rod and the slot. We show that if the rod falls into the slot as determined by Galilean kinematics, the same conclusion is valid for relativistic kinematics. Our conclusion emphasizes that the passing (or crashing) of the rod is unaffected by relativistic kinematics. This determination does not depend on the magnitude of the velocity, but only on the proper lengths and the proper angles of the rod and slot with the line of motion.

Fuzzy multiobjective optimization with multivariate regression trees

We introduce a new methodology in which multiobjective optimization is formulated as unsupervised learning through induction of multivariate regression trees. In particular, it is shown that learning of Pareto-optimal solutions can be efficiently accomplished by using a number of fuzzy tree partitioning criteria. These include: a newly formulated fuzzy method based on Kendalls nonparametric measure of association (G. Simon, 1977), Bellman-Zadehs approach to multiobjective decision making utilized in an inductive framework (R.E. Bellman and L.A. Zadeh, 1970), and finally, multidimensional fuzzy entropy (B. Kosko, 1990). For purposes of comparison, the efficiency of learning with fuzzy partitioning criteria is compared with that of two conventional multivariate statistical techniques based on dispersion matrices. The widely used problem of design of a three bar truss is presented to highlight advantages of our new approach.<<ETX>>

Lorentz transformations with arbitrary line of motion

Sometimes it becomes a matter of natural choice for an observer (A) that he prefers a coordinate system of two-dimensional spatial x–y coordinates from which he observes another observer (B) who is moving at a uniform speed along a line of motion, which is not collinear with As chosen x- or y-axis. It becomes necessary in such cases to develop Lorentz transformations where the line of motion is not aligned with either the x- or the y-axis. In this paper we develop these transformations and show that under such transformations, two orthogonal systems (in their respective frames) appear non-orthogonal to each other. We also illustrate the usefulness of the transformation by applying it to three problems including the rod-slot problem.

A multi-path network with cross links

Abstract A fault-tolerant multistage interconnection network, called the H-network, and a fault-tolerant control algorithm for this network are introduced. The novel feature of this network lies in its design, which has connections not only between switching elements of successive stages but also between switching elements of the same stage. The control algorithm is a simple modification of the destination tag algorithm, but it provides for fault tolerance and is dynamic in nature. It is shown that this design technique is effective in reducing hardware, improving fault tolerance, and giving better performance than other fault-tolerant networks with comparable hardware cost.