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.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Social identity and self-categorization processes in organizational contexts

Although aspects of social identity theory are familiar to organizational psychologists, its elaboration, through self-categorization theory, of how social categorization and prototype-based depersonalization actually produce social identity effects is less well known. We describe these processes, relate self-categorization theory to social identity theory, describe new theoretical developments in detail, and show how these developments can address a: range of organizational phenomena. We discuss cohesion and deviance, leadership, subgroup and sociodemographic structure, and mergers and acquisitions.

Effect of density on spatial distribution, pit formation and pit diameter of Myrmeleon acer Walker, (Neuroptera : Myrmeleontidae): patterns and processes

The effect of increasing population density on the formation of pits, their size and spatial distribution, and on levels of mortality was examined in the antlion Myrmeleon acer Walker. Antlions were kept at densities ranging from 0.4 to 12.8 individuals per 100 cm(2). The distribution of pits was regular or uniform across all densities, but antlions constructed proportionally fewer and smaller pits as density increased. Mortality through cannibalism was very low and only occurred at densities greater than five individuals per 100 cm(2). Antlions in artificially crowded situations frequently relocated their pits and when more space became available, individuals became more dispersed with time. Redistribution of this species results from active avoidance of other antlions and sand throwing associated with pit construction and maintenance, rather than any attempt to optimise prey capture per se.

Quantum measurement and stochastic processes in mesoscopic conductors

In quantum measurement theory it is necessary to show how a, quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of Buttiker and the Fermi quantum stochastic calculus for mesoscopic systems.

Dual processes in recognition: Does a focus on measurement operations provide a sufficient foundation?

Current theoretical thinking about dual processes in recognition relies heavily on the measurement operations embodied within the process dissociation procedure. We critically evaluate the ability of this procedure to support this theoretical enterprise. We show that there are alternative processes that would produce a rough invariance in familiarity (a key prediction of the dual-processing approach) and that the process dissociation procedure does not have the power to differentiate between these alternative possibilities. We also show that attempts to relate parameters estimated by the process dissociation procedure to subjective reports (remember-know judgments) cannot differentiate between alternative dual-processing models and that there are problems with some of the historical evidence and with obtaining converging evidence. Our conclusion is that more specific theories incorporating ideas about representation and process are required.

Long-distance signalling and a mutational analysis of branching in pea

Four ramosus mutants with increased branching at basal and aerial nodes have been used to investigate the genetic regulation of bud outgrowth in Pisum sativum L. (garden pea). Studies of long-distance signalling, xylem sap cytokinin concentrations, shoot auxin level, auxin transport and auxin response are discussed. A model of branching control is presented that encompasses two graft-transmissible signals in addition to auxin and cytokinin. Mutants rms1 through rms4 are not deficient in indole-3-acetic acid (IAA) or in the basipetal transport of this hormone. Three of the four mutants, rms1, rms3 and rms4, have very reduced cytokinin concentrations in xylem sap from roots. This reduction in xylem sap cytokinin concentration appears to be caused by a property of the shoot and may be part of a feedback mechanism induced by an aspect of bud outgrowth. The shoot-to-root feedback signal is unlikely to be auxin itself, as auxin levels and transport are not correlated with xylem sap cytokinin concentrations in various intact and grafted mutant and wild-type plants. Rms1 and Rms2 act in shoot and rootstock to regulate the level or transport of graft-transmissible signals. Various grafting studies and double mutant analyses have associated Rms2 with the regulation of the shoot-to-root feedback signal. Rms1 is associated with a second unknown graft-transmissible signal that is postulated to move in the direction of root-to-shoot. Exogenous auxin appears to interact with both of the signals regulated by Rms1 and Rms2 in the inhibition of branching after decapitation. The action of Rms3 and Rms4 is less apparent at this stage, although both appear to act largely in the shoot.

The relationship between radiation-induced chemical processes and transverse relaxation times in polymer gel dosimeters

The effects of ionizing radiation in different compositions of polymer gel dosimeters are investigated using FT-Raman spectroscopy and NMR T-2 relaxation times. The dosimeters are manufactured from different concentrations of comonomers (acrylamide and N,N'-methylene-bis-acrylamide) dispersed in different concentrations of an aqueous gelatin matrix. Results are analysed using a model of fast exchange of magnetization between three proton pools. The fraction of protons in each pool is determined using the known chemical composition of the dosimeter and FT-Raman spectroscopy. Based on these results, the physical and chemical processes in interplay in the dosimeters are examined in view of their effect on the changes in T-2 The precipitation of growing macroradicals and the scavenging of free radicals by gelatin are used to explain the rate of polymerization. The model describes the changes in T-2 as a function of the absorbed dose up to 50 Gy for the different compositions. This is expected to aid the theoretical design of new, more efficient dosimeters, since it was demonstrated that the optimum dosimeter (i.e, with the lowest dose resolution) must have a range of relaxation times which match the range of T-2 values which can be determined with the lowest uncertainty using an MRI scanner.

Developing qualitative career assessment processes

Assessment has been integral to career counseling since the early 1900s. During that time, the greatest amount of attention was focused on quantitative assessment. Thus, there is still very little to guide the development and conduct of qualitative assessment in career counseling. The authors present an overview of qualitative career assessment and its theoretical underpinnings and propose suggestions that could guide the development of qualitative career assessment instruments.

Mental rotation processes in mathematically gifted boys: An fMRI investigation

The functional brain organisation of mathematically gifted adolescents may be different from those of average mathematical ability. In this study we used fMRI to examine the neural circuitry that mediates the performance of mathematically gifted boys and average ability controls while engaged in mental rotation. Eight math gifted male adolescents and five average ability male adolescents were presented 18 control and 18 mental rotation trials in two separate blocks. Participants selected one of four test stimuli to match the target stimulus by pressing one of four fibreoptic buttons. The control task required a simple 'best match' for the target stimulus. EPI scans were acquired on a 3-T MR scanner and a fixed effects statistical analysis (SPM99) was used to identify areas of significant activation in the rotation tasks, for the two groups. The results indicate that during mental rotation both groups activate the parietal lobes bilaterally, though to different levels. Moreover, the math gifted are uniformly bilateral in their pattern of activation, and engage some anterior regions not found in those of average ability. These regions include bilateral prefrontal cortex and the right anterior cingulate, which may serve to heighten concentration, and to optimise the pre-planning of purposeful actions.

The effect of emotional and attentional processes on blink startle modulation and on electrodermal responses

Emotional accounts of startle modulation predict that startle is facilitated if elicited during aversive foreground stimuli. Attentional accounts hold that startle is enhanced if startle-eliciting stimulus and foreground stimulus are in the same modality. Visual and acoustic foreground stimuli and acoustic startle probes were employed in aversive differential conditioning and in a stimulus discrimination task. Differential conditioning was evident in electrodermal responses and blink latency shortening in both modalities, but effects on magnitude facilitation were found only for visual stimuli. In the discrimination task, skin conductance responses, blink latency shortening, and blink magnitude facilitation were larger during to-be-attended stimuli regardless of stimulus modality. The present results support the notion that attention and emotion can affect blink startle modulation during foreground stimuli.