Alternatives for parallel Krylov subspace basis computation

Numerical methods related to Krylov subspaces are widely used in large sparse numerical linear algebra. Vectors in these subspaces are manipulated via their representation onto orthonormal bases. Nowadays, on serial computers, the method of Arnoldi is considered as a reliable technique for constructing such bases. However, although easily parallelizable, this technique is not as scalable as expected for communications. In this work we examine alternative methods aimed at overcoming this drawback. Since they retrieve upon completion the same information as Arnoldi's algorithm does, they enable us to design a wide family of stable and scalable Krylov approximation methods for various parallel environments. We present timing results obtained from their implementation on two distributed-memory multiprocessor supercomputers: the Intel Paragon and the IBM Scalable POWERparallel SP2. (C) 1997 by John Wiley & Sons, Ltd.

Subspace wavepacket evolution with Newton polynomials

Time-dependent wavepacket evolution techniques demand the action of the propagator, exp(-iHt/(h)over-bar), on a suitable initial wavepacket. When a complex absorbing potential is added to the Hamiltonian for combating unwanted reflection effects, polynomial expansions of the propagator are selected on their ability to cope with non-Hermiticity. An efficient subspace implementation of the Newton polynomial expansion scheme that requires fewer dense matrix-vector multiplications than its grid-based counterpart has been devised. Performance improvements are illustrated with some benchmark one and two-dimensional examples. (C) 2001 Elsevier Science B.V. All rights reserved.

Research, knowledge and design

The discussion about relations between research and design has a number of strands, and presumably motivations. Putting aside the question whether or not design or “creative endeavour” should be counted as research, for reasons to do with institutional recognition or reward, the question remains how, if at all, is design research? This question is unlikely to have attracted much interest but for matters external to Architecture within the modern university. But Architecture as a discipline now needs to understand research much better than in the past when ‘research’ was whatever went on in building science, history or people/environment studies. In this paper, I begin with some common assumptions about design, considered in relation to research, and suggest how the former can constitute or be a mode of the latter. Central to this consideration is an understanding of research as the production of publicly available knowledge. The method is that of conceptual analysis which is much more fruitful than is usually appreciated. This work is part of a larger project in philosophy of design, in roughly the analytical tradition.

Popper's Explications of Ad hocness: Circularity, Empirical Content, and Scientific Practice

Popper's explications of 'ad hoc' in relation to hypotheses and explanations turn out to be either trivial, confused or mistaken. One such explication I discuss at length is circularity; another is reduction in empirical content. I argue that non-circularity is preferable to non-ad hocness for an acceptable explanation or explanans, and I isolate some persistent errors in his analysis. Second, Popper is barking up the wrong tree in proscribing reductions in empirical content in novel hypotheses. Such reductions may constitute scientific progress. He fails to show that ad hoc hypothesis are the threat to science he claims.

Popper and his Commentators on the Discovery of Neptune: a close shave for the Law of Gravitation?

Knowledge of residual perturbations in the orbit of Uranus in the early 1840s did not lead to the refutation of Newton's law of gravitation but instead to the discovery of Neptune in 1846. Karl Popper asserts that this case is atypical of science and that the law of gravitation was at least prima facie falsified by these perturbations. I argue that these assertions are the product of a false, a priori methodological position I call, 'Weak Popperian Falsificationism' (WPF). Further, on the evidence the law was not prima facie false and was not generally considered so by astronomers at the time. Many of Popper's commentators (Kuhn, Lakatos, Feyerabend and others) presuppose WPF and their views on this case and its implications for scientific rationality and method suffer from this same defect.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Jurors' responses to expert witness testimony: The effects of gender stereotypes

The present study investigated whether the impact of expert testimony was influenced by the congruency between the gender of the expert and the gender orientation of the case. Participants (N = 62) read a trial transcript involving a price-fixing allegation in either a male or female oriented domain. Within the case, the gender of the expert was manipulated. As predicted, the impact of the expert (e.g. damage awards) was greater when the gender of the expert and domain of the case were congruent as opposed to incongruent. Results also indicated that the impact of gender-domain congruency was particularly pronounced following group discussion. In addition, there was evidence that this effect was mediated through participants' evaluations of the expert witness.

Changes in inflammatory mediators following eccentric exercise of the elbow flexors

The aims of this study were to examine the plasma concentrations of inflammatory mediators including cytokines induced by a single bout of eccentric exercise and again 4 weeks later by a second bout of eccentric exercise of the same muscle group. Ten untrained male subjects performed two bouts of the eccentric exercise involving the elbow flexors (6 sets of 5 repetitions) separated by four weeks. Changes in muscle soreness, swelling, and function following exercise were compared between the bouts. Blood was sampled before, immediately after, 1 h, 3 h, 6 h, 24 h (1 d), 48 h (2 d), 72 h (3 d), 96 h (4 d) following exercise bout to measure plasma creatine kinase (CK) activity, plasma concentrations of myoglobin (Mb), interleukin (IL)-1 beta, IL-1 receptor antagonist (IL-1ra), IL-4, IL-6, IL-8, IL-10, IL-12p40, tumor necrosis factor (TNF)-alpha, granulocyte colony-stimulating factor (G-CSF), myeloperoxidase (MPO), prostaglandin E-2 (PGE(2)), heat shock protein (HSP) 60 and 70. After the first bout, muscle soreness increased significantly, and there was also significant increase in upper arm circumference; muscle function decreased and plasma CK activity and Mb concentration increased significantly. These changes were significantly smaller after the second bout compared to the first bout, indicating muscle adaptation to the repeated bouts of the eccentric exercise. Despite the evidence of greater muscle damage after the first bout, the changes in cytokines and other inflammatory mediators were quite minor, and considerably smaller than that following endurance exercise. These results suggest that eccentric exercise-induced muscle damage is not associated with the significant release of cytokines into the systemic circulation. After the first bout, plasma G-CSF concentration showed a small but significant increase, whereas TNF-alpha and IL-8 showed significant decreases compared to the pre-exercise values. After the second bout, there was a significant increase in IL-10, and a significant decrease in IL-8. In conclusion, although there was evidence of severe muscle damage after the eccentric exercise, this muscle damage was not accompanied by any large changes in plasma cytokine concentrations. The minor changes in systemic cytokine concentration found in this study might reflect more rapid clearance from the circulation, or a lack of any significant metabolic or oxidative demands during this particular mode of exercise. In relation to the adaptation to the muscle damage, the anti-inflammatory cytokine IL-10 might work as one of the underlying mechanisms of action.

Genetic association and cellular function of MC1R variant alleles in human pigmentation

We have examined MC1R variant allele frequencies in the general population of South East Queensland and in a collection of adolescent dizygotic and monozygotic twins and family members to define statistical associations with hair and skin color, freckling, and mole count. Results of these studies are consistent with a linear recessive allelic model with multiplicative penetrance in the inheritance of red hair. Four alleles, D84E, R151C, R160W, and D294H, are strongly associated with red hair and fair skin with multinomial regression analysis showing odds ratios of 63, 118, 50, and 94, respectively. An additional three low-penetrance alleles V60L, V92M, and R163Q have odds ratios 6, 5, and 2 relative to the wild-type allele. To address the cellular effects of MC1R variant alleles in signal transduction, we expressed these receptors in permanently transfected HEK293 cells. Measurement of receptor activity via induction of a cAMP-responsive luciferase reporter gene found that the R151C and R160W receptors were active in the presence of NDP-MSH ligand, but at much reduced levels compared with that seen with the wild-type receptor. The ability to stimulate phosphorylation of the cAMP response element binding protein (CREB) transcription factor was also apparent in all stimulated MC1R variant allele-expressing HEK293 cell extracts as assessed by immunoblotting. In contrast, human melanoma cell lines showed wide variation in the their ability to undergo cAMP-mediated CREB phosphorylation. Culture of human melanocytes of known MC1R genotype may provide the best experimental approach to examine the functional consequences for each MC1R variant allele. With this objective, we have established more than 300 melanocyte cell strains of defined MC1R genotype.

Human settlements: Australia state of the environment report, 2001

Australia’s transition to the 21st century has been marked by an extended period of economic prosperity unmatched for several decades, but one in which a series of question marks are being raised in three principal areas: in relation to the environment, the social well-being of the population, and the future path of economic development. The first concern, which is of primary interest in this report, relates to the physical environment of cities and their surrounding regions, and the range of pressures exerted by population and human activity. The report begins by noting the increasing divergence of the prime indicator of national economic performance—gross domestic product (GDP)—from the Genuine Progress Indicator (GPI). GPI is a new experimental measure of sustainable development that accommodates factors currently unaccounted for in GDP, such as income distribution, value of household work, cost of unemployment, and various other social and environmental costs. The divergence of these two indicators in recent decades suggests that Australia’s growth has been heavily dependent on the draw-down of the nation’s stocks of capital assets (its infrastructure), its human and social capital, and its natural capital (Hamilton 1997).