Automating computations in the virtual Tokamak software system

We describe the concept, functional capabilities, graphic user interface (GUI), and operating technique of a specialized system for distributing the computational burden encountered in solving typical problems of controlled thermonuclear fusion. The system is employed in the Virtual Tokamak simulation modeling complex to automate the distribution of computing on a network of computers, making it possible to dramatically improve the productivity of a researcher??s work. The system is useful in various applications that require massive multivariate calculations using one or more application codes, and for supporting websites that provide computing services using locally stored science-intensive application software.     

A bi-objective weighted model for improving the discrimination power in MCDEA

Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.     

Comparisons of two commercial computational fluid dynamics codes in modelling pulverised coal combustion for a 2.5 MW burner

This paper reports an investigation into the performance of two commercial computational fluid dynamics (CFD) codes for pulverised coal combustion prediction. The two codes employed were FLUENT and FLOW3D 3.2 (now called CFX). The experimental case considered was a 2.5 MW Aerodynamically Air Staged Burner (AASB) fired in isolation into a rectangular furnace. Predictions were compared to velocity, temperature and species concentration experimental data. Some slight differences were noted between the two CFD codes predictions beyond one burner diameter downstream of the burner exit. Discrepancies between the predictions of the two CFD codes were concluded to be due to differences in the physical models used to describe devolatilisation and gaseous combustion. This paper therefore concludes that, for this case, the two commercial CFD codes were capable of predicting good `trend' answers.     

Implementation of a primal–dual method for SDP on a shared memory parallel architecture

Primal–dual interior point methods and the HKM method in particular have been implemented in a number of software packages for semidefinite programming. These methods have performed well in practice on small to medium sized SDPs. However, primal–dual codes have had some trouble in solving larger problems because of the storage requirements and required computational effort. In this paper we describe a parallel implementation of the primal–dual method on a shared memory system. Computational results are presented, including the solution of some large scale problems with over 50,000 constraints.     

Universal Hashing and Geometric Codes

We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield classes of universal hash functions which are substantially better than those known before.     

Parallel Asynchronous Algorithms for the K Shortest Paths Problem

We deal with the problem of computing in parallel the first K shortest paths from a single origin node to all other nodes of a directed graph. Our approach is based on a very easy way to introduce parallelism in the typical sequential label-correcting method. We describe formally an asynchronous method defined on a shared-memory parallel computational model, and we prove its theoretical correctness under very weak assumptions. According to different strategies used to implement the generic method, we propose several parallel label-correcting algorithms, and we analyze the numerical performance of the resulting codes on a nonuniform memory access multiprocessor via computational results collected on random generated networks. The advantage of parallelism is significant for very large-scale problems of practical interest.     

Eulerian tour algorithms for data visualization and the PairViz package

PairViz is an R package that produces orderings of statistical objects for visualization purposes. We abstract the ordering problem to one of constructing edge-traversals of (possibly weighted) graphs. PairViz implements various edge traversal algorithms which are based on Eulerian tours and Hamiltonian decompositions. We describe these algorithms, their PairViz implementation and discuss their properties and performance. We illustrate their application to two visualization problems, that of assessing rater agreement, and model comparison in regression.     

Cyclic Codes Over\mathbb{Z}_{4} of Even Length

We determine the structure of cyclic codes over for arbitrary even length giving the generator polynomial for these codes. We determine the number of cyclic codes for a given length. We describe the duals of the cyclic codes, describe the form of cyclic codes that are self-dual and give the number of these codes. We end by examining specific cases of cyclic codes, giving all cyclic self-dual codes of length less than or equal to 14. San Ling - The research of the second named author is partially supported by research Grants MOE-ARF R-146-000-029-112 and DSTA R-394-000-011-422.     

The steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.     

Higher support matroids

The purpose of this paper is to provide links between matroid theory and the theory of subcode weights and supports in linear codes. We describe such weights and supports in terms of certain matroids arising from the vector matroids associated to the linear codes. Our results generalize classical results by Whitney, Tutte, Crapo and Rota, Greene, and other authors. As an application of our results, we obtain a new and elegant dual correspondence between the bond union and cycle union cardinalities of a graph.     

Algorithm for the numerical proof of the existence of periodic trajectories in two-dimensional nonautonomous systems of ordinary differential equations

We suggest an algorithm that permits one to prove the existence of limit periodic trajectories (cycles) in two-dimensional nonautonomous dissipative systems with periodic coefficients with the use of computational methods alone. We prove a fixed point theorem for two-dimensional mappings and describe methods of its application to two-dimensional nonautonomous systems with the use of the Poincaré mapping and interval arithmetics.     

On maximal Spherical codes II

We consider spherical codes attaining the Levenshtein upper bounds on the cardinality of codes with prescribed maximal inner product. We prove that the even Levenshtein bounds can be attained only by codes which are tight spherical designs. For every fixed n ≥ 5, there exist only a finite number of codes attaining the odd bounds. We derive different expressions for the distance distribution of a maximal code. As a by-product, we obtain a result about its inner products. We describe the parameters of those codes meeting the third Levenshtein bound, which have a regular simplex as a derived code. Finally, we discuss a connection between the maximal codes attaining the third bound and strongly regular graphs. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 316–326, 1999     

The Language of Graphics

Abstract

We describe a system, called the Graphics Production Library (GPL), that implements a language for quantitative graphics. The structure of this system differs from existing statistical graphics, visualization, and mapping systems. Instead of treating a graphics display as a viewer for underlying data, GPL treats data as an accessory to viewing a graph. GPL is based on the mathematical definition of the graph of a function and uses that definition to organize data linked to the graph.     

Interactive Visualization of Hierarchically Structured Data

We introduce methods for visualization of data structured along trees, especially hierarchically structured collections of time series. To this end, we identify questions that often emerge when working with hierarchical data and provide an R package to simplify their investigation. Our key contribution is the adaptation of the visualization principles of focus-plus-context and linking to the study of tree-structured data. Our motivating application is to the analysis of bacterial time series, where an evolutionary tree relating bacteria is available a priori. However, we have identified common problem types where, if a tree is not directly available, it can be constructed from data and then studied using our techniques. We perform detailed case studies to describe the alternative use cases, interpretations, and utility of the proposed visualization methods.     

A collaboratory for radiation therapy treatment planning optimization research

Intensity modulated radiation therapy treatment planning (IMRTP) is a challenging application of optimization technology. We present software tools to facilitate IMRTP research by computational scientists who may not have convenient access to radiotherapy treatment planning systems. The tools, developed within Matlab and CERR (computational environment for radiotherapy research), allow convenient access, visualization, programmable manipulation, and sharing of patient treatment planning data, as well as convenient generation of dosimetric data needed as input for treatment plan optimization research. CERR/Matlab also provides a common framework for storing, reviewing, sharing, and comparing optimized dose distributions from multiple researchers.     

Virtual Tokamak library software

We describe the concept of the Virtual Tokamak library, its functionality, major components, and method of use. The library is designed to predict, support, and interpret experiments as well as handle measurements on tokamak instruments implementing the idea of energy production on the basis of controlled thermonuclear fusion. The library software consists of an interactive graphic shell and a number of interrelated computer codes simulating various processes in the tokamak plasma, its structural elements, diagnostics and control system. This is a specific implementation of advanced information technologies including Internet technologies and approaches of distributed computations in the field of the mathematical modeling of plasma. The Virtual Tokamak is unique in terms of combined application and system software.     

Materials by design and the exciting role of quantum computation/simulation

It is now well-recognized that we are witnessing a golden age of innovation with novel materials, with discoveries important for both basic science and device applications—some of which will be treated at this Workshop. In this talk, we discuss the role of computation and simulation in the dramatic advances of the past and those we are witnessing today. We will also describe the growing acceptance and impact of computational materials science as a major component of materials research and its import for the future. In the process, we will demonstrate how the well-recognized goal driving computational physics/computational materials science—simulations of ever-increasing complexity on more and more realistic models—has been brought into greater focus with the introduction of greater computing power that is readily available to run sophisticated and powerful software codes like our highly precise full-potential linearized augmented plane wave (FLAPW) method, now also running on massively parallel computer platforms.We will then describe some specific advances we are witnessing today, and computation and simulation as a major component of quantum materials design and its import for the future, with the goal—to synthesize materials with desired properties in a controlled way via materials engineering on the atomic scale. The theory continues to develop along with computing power. With the universality and applicability of these methods to essentially all materials and properties, these simulations are starting to fill the increasingly urgent demands of material scientists and engineers.