A study of the stability of subcycling algorithms in structural dynamics

Algorithms for explicit integration of structural dynamics problems with multiple time steps (subcycling) are investigated. Only one such algorithm, due to Smolinski and Sleith has proved to be stable in a classical sense. A simplified version of this algorithm that retains its stability is presented. However, as with the original version, it can be shown to sacrifice accuracy to achieve stability. Another algorithm in use is shown to be only statistically stable, in that a probability of stability can be assigned if appropriate time step limits are observed. This probability improves rapidly with the number of degrees of freedom in a finite element model. The stability problems are shown to be a property of the central difference method itself, which is modified to give the subcycling algorithm. A related problem is shown to arise when a constraint equation in time is introduced into a time-continuous space-time finite element model. (C) 1998 Elsevier Science S.A.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

A mathematical model of HIV transmission in NSW prisons

A mathematical model was developed to estimate HIV incidence in NSW prisons. Data included: duration of imprisonment; number of inmates using each needle; lower and higher number of shared injections per IDU per week; proportion of IDUs using bleach; efficacy of bleach; HIV prevalence and probability of infection. HIV prevalence in IDUs in prison was estimated to have risen from 0.8 to 5.7% (12.2%) over 180 weeks when using lower (and higher) values for frequency of shared injections. The estimated minimum (and maximum) number of IDU inmates infected with HIV in NSW prisons was 38 (and 152) in 1993 according to the model. These figures require confirmation by seroincidence studies. (C) 1998 Published by Elsevier Science Ireland Ltd. All rights reserved.

Prediction of MHC class II-binding peptides using an evolutionary algorithm and artificial neural network

Motivation: Prediction methods for identifying binding peptides could minimize the number of peptides required to be synthesized and assayed, and thereby facilitate the identification of potential T-cell epitopes. We developed a bioinformatic method for the prediction of peptide binding to MHC class II molecules. Results: Experimental binding data and expert knowledge of anchor positions and binding motifs were combined with an evolutionary algorithm (EA) and an artificial neural network (ANN): binding data extraction --> peptide alignment --> ANN training and classification. This method, termed PERUN, was implemented for the prediction of peptides that bind to HLA-DR4(B1*0401). The respective positive predictive values of PERUN predictions of high-, moderate-, low- and zero-affinity binder-a were assessed as 0.8, 0.7, 0.5 and 0.8 by cross-validation, and 1.0, 0.8, 0.3 and 0.7 by experimental binding. This illustrates the synergy between experimentation and computer modeling, and its application to the identification of potential immunotheraaeutic peptides.

New techniques for biopsy and culture of human olfactory epithelial neurons

Objective: To improve the success of culturing olfactory neurons from human nasal mucosa by investigating the intranasal distribution of the olfactory epithelium and devising new techniques for growing human olfactory epithelium in vitro. Design: Ninety-seven biopsy specimens were obtained from 33 individuals, aged 21 to 74 years, collected from 6 regions of the nasal cavity. Each biopsy specimen was bisected, and 1 piece was processed for immunohistochemistry or electron microscopy while the other piece was dissected further for explant culture. Four culture techniques were performed, including whole explants and explanted biopsy slices. Five days after plating, neuronal differentiation was induced by means of a medium that contained basic fibroblast growth factor. After another 5 days, cultures were processed for immunocytochemical analysis. Results: The probability of finding olfactory epithelium in a biopsy specimen ranged from 30% to 76%, depending on its location. The dorsoposterior regions of the nasal septum and the superior turbinate provided the highest probability, but, surprisingly, olfactory epithelium was also found anteriorly and ventrally on both septum and turbinates. A new method of culturing the olfactory epithelium was devised. This slice culture technique improved the success rate for generating olfactory neurons from 10% to 90%. Conclusions: This study explains and overcomes most of the variability in the success in observing neurogenesis in cultures of adult human olfactory epithelium. The techniques presented here make the human olfactory epithelium a useful model for clinical research into certain olfactory dysfunctions and a model for the causes of neurodevelopmental and neurodegenerative diseases.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

5-cycle systems of K-v-F with a hole

Recently the problem of the existence of a 5-cycle system of K-v with a hole of size u was completely solved. In this paper we prove necessary and sufficient conditions on v and u for the existence of a 5-cycle system of K-v - F, with a hole of size u.

(m,n)-cycle systems

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.

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.

Relapse and mortality among HIV-infected and uninfected patients with tuberculosis successfully treated with twice weekly directly observed therapy in rural South Africa

Objective: To determine post-treatment relapse and mortality rates among HIV-infected and uninfected patients with tuberculosis treated with a twice-weekly drug regimen under direct observation (DOT). Setting: Hlabisa, South Africa. Patients: A group of 403 patients with tuberculosis (53% HIV infected) cured following treatment with isoniazid (H), rifampicin (R), pyrazinamide (Z) and ethambutol (E) given in hospital (median 17 days), followed by HRZE twice weekly to 2 months and HR twice weekly to 6 months in the community under DOT. Methods: Relapses were identified through hospital readmission and 6-monthly home visits. Relapse (culture for Mycobacterium tuberculosis) and mortality given as rates per 100 person-years observation (PYO) stratified by HIV status and history of previous tuberculosis treatment. Results: Mean (SD) post-treatment follow-up was 1.2 (0.4) years (total PYO = 499); 78 patients (19%) left the area, 58 (14%) died, 248 (62%) remained well and 19 (5%) relapsed. Relapse rates in HIV-infected and uninfected patients were 3.9 [95% confidence interval (CI) 1.5-6.3] and 3.6 (95% CI 1.1-6.1) per 100 PYO (P = 0.7). Probability of relapse at 18 months was estimated as 5% in each group. Mortality was four-fold higher among HIV-infected patients (17.8 and 4.4 deaths per 100 PYO for HIV-infected and uninfected patients, respectively; P < 0.0001). Probability of survival at 24 months was estimated as 59% and 81%, respectively. We observed no increase in relapse or mortality among previously treated patients compared with new patients. A positive smear at 2 months did not predict relapse or mortality. Conclusion: Relapse rates are acceptably low following successful DOT with a twice weekly rifampifin-containing regimen, irrespective of HIV status and previous treatment history. Mortality is substantially increased among HIV-infected patients even following successful DOT and this requires further attention. (C) 1999 Lippincott Williams & Wilkins.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

El Nino and arboviral disease prediction

Recent El Nino events have stimulated interest in the development of modeling techniques to forecast extremes of climate and related health events. Previous studies have documented associations between specific climate variables (particularly temperature and rainfall) and outbreaks of arboviral disease. In some countries, such diseases are sensitive to Fl Nino. Here we describe a climate-based model for the prediction of Ross River virus epidemics in Australia. From a literature search and data on case notifications, we determined in which years there were epidemics of Ross River virus in southern Australia between 1928 and 1998. Predictor variables were monthly Southern Oscillation index values for the year of an epidemic or lagged by 1 year. We found that in southeastern states, epidemic years were well predicted by monthly Southern Oscillation index values in January and September in the previous year. The model forecasts that there is a high probability of epidemic Ross River virus in the southern states of Australia in 1999. We conclude that epidemics of arboviral disease can, at least in principle, be predicted on the basis of climate relationships.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

Sausage: protein threading with flexible force fields

Sausage is a protein sequence threading program, but with remarkable run-time flexibility. Using different scripts, it can calculate protein sequence-structure alignments, search structure libraries, swap force fields, create models form alignments, convert file formats and analyse results. There are several different force fields which might be classed as knowledge-based, although they do not rely on Boltzmann statistics. Different force fields are used for alignment calculations and subsequent ranking of calculated models.

Applying the results of a systematic review in general practice

Objective: To assess how general practitioners might interpret and apply the results of a systematic review relevant to general practice. Design: Cross-sectional postal survey of general practitioners in August 1997. Participants: 51 general practitioners in the Southern Division of General Practice in Adelaide and 11 professors or heads of departments of general practice. Main outcome measures:Extent to which comments on the implications for practice and implications for research coincided with the evidence presented in a systematic review of antibiotics for the treatment of acute otitis media in children; and reported probability that respondents would prescribe antibiotics in three brief case scenarios. Results: There was considerable variation in the comments made by general practitioners on the implications of the review for clinical practice. After reading the review, respondents with training in critical appraisal were more likely to state that children with acute otitis media would usually recover spontaneously and reported a lower probability of prescribing antibiotics in two of the three case scenarios. Conclusions: Providing systematic reviews is not sufficient for the results of such evidence to be translated:into clinical practice. There is an association between critical appraisal skills and the application of evidence-based practice.