Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used

Singularities and Gauge Theory Phases

Motivated by M-theory compactification on elliptic Calabi-Yau threefolds, we present a correspondence between networks of small resolutions for singular elliptic fibrations and Coulomb branches of five-dimensional N=1 gauge theories. While resolutions correspond to subchambers of the Coulomb branch, partial resolutions correspond to higher codimension loci at which the Coulomb branch intersects the Coulomb-Higgs branches. Flops between different resolutions are identified with reflections on the Coulomb branch. Physics aside, this correspondence provides an interesting link between elliptic fibrations and representation theory.Comment: 55 pages, 18 figures, section adde

Ideal filter approximation and synthesis

Several methods are currently used for approximating the ideal low pass filter. Generally, those approximations relate only to the amplitude or phase characteristic of the ideal filter. A class of filters has been proposed as approximating both the amplitude and phase characteristics of the ideal filter. The characteristics of the first ten members of the proposed class are considered in this paper. The results indicate a much improved approximation to the ideal filter has been achieved --Abstract, page ii

Survival mixture modelling of recurrent infections

Recurrent infections data are commonly encountered in biomedical applications, where the recurrent events are characterised by an acute phase followed by a stable phase after the index episode. Two-component survival mixture models, in both proportional hazards and accelerated failure time settings, are presented as a flexible method of analysing such data. To account for the inherent dependency of the recurrent observations, random effects are incorporated within the conditional hazard function. Assuming a Weibull or log-logistic baseline hazard in both mixture components of the survival mixture model, an EM algorithm is developed for the residual maximum quasi-likelihood estimation of fixed effect and variance components parameters. The methodology is implemented as a graphical user interface coded using Microsoft visual C++. Application to model recurrent urinary tract infections for elderly women is illustrated, where significant individual variations are evident at both acute and stable phases. The survival mixture methodology developed enable practitioners to identify pertinent risk factors affecting the recurrent times and to draw valid conclusions inferred from these correlated and heterogeneous survival data

The Magnetic Acoustic Change Complex and Mismatch Field:A Comparison of Neurophysiological Measures of Auditory Discrimination

The Acoustic Change Complex (ACC), a P1-N1-P2-like event-related response to changes in a continuous sound, has been suggested as a reliable, objective, and efficient test of auditory discrimination. We used magnetoencephalography to compare the magnetic ACC (mACC) to the more widely used mismatch field (MMF). Brain responses of 14 adults were recorded during mACC and MMF paradigms involving the same pitch and vowel changes in a synthetic vowel sound. Analyses of peak amplitudes revealed a significant interaction between stimulus and paradigm: for the MMF, the response was greater for vowel changes than for pitch changes, whereas, for the mACC, the pattern was reversed. A similar interaction was observed for the signal to noise ratio and single-trial analysis of individual participants’ responses showed that the MMF to Pitch changes was elicited less consistently than the other three responses. Results support the view that the ACC/mACC is a robust and efficient measure of simple auditory discrimination, particularly when researchers or clinicians are interested in the responses of individual listeners. However, the differential sensitivity of the two paradigms to the same acoustic changes indicates that the mACC and MMF are indices of different aspects of auditory processing and should, therefore, be seen as complementary rather than competing neurophysiological measures

Case study: auditory brain responses in a minimally verbal child with autism and cerebral palsy

An estimated 30% of individuals with autism spectrum disorders (ASD) remain minimally verbal into late childhood, but research on cognition and brain function in ASD focuses almost exclusively on those with good or only moderately impaired language. Here we present a case study investigating auditory processing of GM, a nonverbal child with ASD and cerebral palsy. At the age of 8 years, GM was tested using magnetoencephalography (MEG) whilst passively listening to speech sounds and complex tones. Where typically developing children and verbal autistic children all demonstrated similar brain responses to speech and nonspeech sounds, GM produced much stronger responses to nonspeech than speech, particularly in the 65–165 ms (M50/M100) time window post-stimulus onset. GM was retested aged 10 years using electroencephalography (EEG) whilst passively listening to pure tone stimuli. Consistent with her MEG response to complex tones, GM showed an unusually early and strong response to pure tones in her EEG responses. The consistency of the MEG and EEG data in this single case study demonstrate both the potential and the feasibility of these methods in the study of minimally verbal children with ASD. Further research is required to determine whether GM's atypical auditory responses are characteristic of other minimally verbal children with ASD or of other individuals with cerebral palsy