(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.

Predictors of local recurrence after treatment of ductal carcinoma in situ - A meta-analysis

lBACKGROUND. Management of patients with ductal carcinoma in situ (DCIS) is a dilemma, as mastectomy provides nearly a 100% cure rate but at the expense of physical and psychologic morbidity. It would be helpful if we could predict which patients with DCIS are at sufficiently high risk of local recurrence after conservative surgery (CS) alone to warrant postoperative radiotherapy (RT) and which patients are at sufficient risk of local recurrence after CS + RT to warrant mastectomy. The authors reviewed the published studies and identified the factors that may be predictive of local recurrence after management by mastectomy, CS alone, or CS + RT. METHODS. The authors examined patient, tumor, and treatment factors as potential predictors for local recurrence and estimated the risks of recurrence based on a review of published studies. They examined the effects of patient factors (age at diagnosis and family history), tumor factors (sub-type of DCIS, grade, tumor size, necrosis, and margins), and treatment (mastectomy, CS alone, and CS + RT). The 95% confidence intervals (CI) of the recurrence rates for each of the studies were calculated for subtype, grade, and necrosis, using the exact binomial; the summary recurrence rate and 95% CI for each treatment category were calculated by quantitative meta-analysis using the fixed and random effects models applied to proportions. RESULTS, Meta-analysis yielded a summary recurrence rate of 22.5% (95% CI = 16.9-28.2) for studies employing CS alone, 8.9% (95% CI = 6.8-11.0) for CS + RT, and 1.4% (95% CI = 0.7-2.1) for studies involving mastectomy alone. These summary figures indicate a clear and statistically significant separation, and therefore outcome, between the recurrence rates of each treatment category, despite the likelihood that the patients who underwent CS alone were likely to have had smaller, possibly low grade lesions with clear margins. The patients with risk factors of presence of necrosis, high grade cytologic features, or comedo subtype were found to derive the greatest improvement in local control with the addition of RT to CS. Local recurrence among patients treated by CS alone is approximately 20%, and one-half of the recurrences are invasive cancers. For most patients, RT reduces the risk of recurrence after CS alone by at least 50%. The differences in local recurrence between CS alone and CS + RT are most apparent for those patients with high grade tumors or DCIS with necrosis, or of the comedo subtype, or DCIS with close or positive surgical margins. CONCLUSIONS, The authors recommend that radiation be added to CS if patients with DCIS who also have the risk factors for local recurrence choose breast conservation over mastectomy. The patients who may be suitable for CS alone outside of a clinical trial may be those who have low grade lesions with little or no necrosis, and with clear surgical margins. Use of the summary statistics when discussing outcomes with patients may help the patient make treatment decisions. Cancer 1999;85:616-28. (C) 1999 American Cancer Society.

Hysterectomy fractions in New South Wales, 1971-2006

Hysterectomy fractions by age group for particular periods are of interest for: estimating proper population denominators for calculation of disease and procedure rates affecting the cervix and uterus; estimating the target population for Pap test programs, and response rates; and as a way of displaying the cumulative consequences of hysterectomies in a population. Hysterectomy fractions for populations can be determined by direct inquiry via a representative sample survey, or, as in this study, from prior hysterectomy rates of the cohorts of women which compose each age bracket. Hysterectomy data 1979-93 were obtained from the hospital In-patients Statistics Collection (ISC) which covers both public and private hospitals in NSW. Annual population denominators of women were obtained from Census data. Data were modelled by Poisson regression, using five.-year age group (15-greater than or equal to 85 years), annual period, and five-year birth cohort (APC model). Forward- and back-projection of the period effects were undertaken. The resultant NSW hysterectomy fractions by age and period are consistent with fractions obtained from modelled hysterectomy rates for Western Australia (1980-84), and fractions from national representative sample surveys (1989/90 and 1995) for younger women, but not for women aged greater than or equal to 70 years in 1995, which revealed higher hysterectomy fractions than modelled hysterectomy data would suggest. Hysterectomy fractions for NSW women by five-year age group for quinquennia centred on 1971 to 2006 are provided.

Jurisdictional trends in opioid overdose deaths, 1988-96

This report analysed data on opioid overdose mortality between 1988 and 1996 to: examine differences between jurisdictions in the rate of fatal opioid overdose and the rate of increase in overdose; and estimate the proportion of all deaths which were attributed to opioid overdose. Australian Bureau of Statistics (ABS) data were obtained on the number of deaths attributed to opioid dependence (ICD 9 codes 304.0, 304.7) and accidental opioid poisoning (ICD 9 codes E850.0, E850.1). The highest rate of fatal overdose occurred in NSW, followed by Victoria. The standardised mortality rate among other jurisdictions fluctuated quite markedly. While the rate of opioid overdose has increased throughout Australia, the rate of increase has been greater in some of the less-populous states and territories than it has in NSW or Victoria. In 1996, approximately 6.5% of all deaths among people aged 15-24 years and approximately 10% of all deaths among those aged 25-34 were due to opioid overdose. During the interval from 1988 to 1996, the proportion of deaths attributed to opioid overdose increased. From 1988 to 1996, the proportion of deaths attributed to opioid overdose among individuals aged 25-34 years was approximately one-third that attributed to suicide, but this proportion had increased to approximately one-half by 1996. The rate of increase in the proportion of deaths attributed to opioid overdose was higher than the rate of increase in the proportion of deaths attributed to suicide.

Quantum open-systems approach to current noise in resonant tunneling junctions

A quantum Markovian master equation is derived to describe the current noise in resonant tunneling devices. This equation includes both incoherent and coherent quantum tunneling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict subshot noise statistics for strong tunneling between the wells. The method is an alternative to Green's function methods and population master equations for very small coherently coupled quantum dots.

Opioid overdose mortality in Australia, 1964-1997: birth-cohort trends

Objective: To examine trends in rates of opioid overdose deaths from 1964 to 1997 in different birth cohorts. Design: Age-period-cohort analysis of national data from the Australian Bureau of Statistics. Main outcome measures: Annual population rates of death attributed to opioid dependence or accidental opioid poisoning in people aged 15-44 years, by sex and birth cohort tin five-year intervals, 1940-1944 to 1975-1979). Results: The rate of opioid overdose deaths increased 55-fold between 1964 and 1997, from 1.3 to 71.5 per million population aged 15-44 years. The rate of opioid overdose deaths also increased substantially over the eight birth cohorts, with an incidence rate ratio of 20.70 (95% confidence interval, 13.60-31.46) in the 1975-1979 cohort compared with the 1940-1944 cohort. The age at which the cumulative rate of opioid overdose deaths reached 300 per million fell in successive cohorts (for men, from 28 years among those born 1955-1959 to 22 years among those born 1965-1974; for women, from 33 years among those born 1955-1959 to 27 years among those born 1965-1969). Conclusions: Heroin use in Australia largely began in the early 1970s and rates of heroin use have markedly increased in birth cohorts born since 1950.

Protein fold recognition score functions: Unusual construction strategies

We describe two ways of optimizing score functions for protein sequence to structure threading. The first method adjusts parameters to improve sequence to structure alignment. The second adjusts parameters so as to improve a score function's ability to rank alignments calculated in the first score function. Unlike those functions known as knowledge-based force fields, the resulting parameter sets do not rely on Boltzmann statistics, have no claim to representing free energies and are purely constructions for recognizing protein folds. The methods give a small improvement, but suggest that functions can be profitably optimized for very specific aspects of protein fold recognition, Proteins 1999;36:454-461. (C) 1999 Wiley-Liss, Inc.

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.

Macropore sheath: quantification of plant root and soil macropore association

Plants require roots to supply water, nutrients and oxygen for growth. The spatial distribution of roots in relation to the macropore structure of the soil in which they are growing influences how effective they are at accessing these resources. A method for quantifying root-macropore associations from horizontal soil sections is illustrated using two black vertisols from the Darling Downs, Queensland, Australia. Two-dimensional digital images were obtained of the macropore structure and root distribution for an area 55 x 55 mm at a resolution of 64 mu m. The spatial distribution of roots was quantified over a range of distances using the K-function. In all specimens, roots were shown to be clustered at short distances (1-10 mm) becoming more random at longer distances. Root location in relation to macropores was estimated using the function describing the distance of each root to the nearest macropore. From this function, a summary variable, termed the macropore sheath, was defined. The macropore sheath is the distance from macropores within which 80% of roots are located. Measured root locations were compared to random simulations of root distribution to establish if there was a preferential association between roots and macropores. More roots were found in and around macropores than expected at random.

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.

Season-specific directional movement in migratory Australian butterflies

Large numbers of adults of certain species of butterfly flying in an apparently 'purposeful' manner are often noted by entomologists and the general public. Occasionally, these are recorded in the literature. Using these records we summarise information regarding the direction of movement in Australian butterflies and test whether there are consistent patterns that could account for known seasonal shifts in geographical range. The data were analysed using contingency tables and directionality statistics. Vanessa itea, Vanessa kershawi, Danaus plexippus, Danaus chrysippus and Badamia exclamationis flew predominately south in the spring-summer and north in the autumn-winter. Tirumala hamata has a strong southern component to its flight in spring but, as in Euploea core, appears non-directional in the autumn. For many supposedly known migratory species, the number of literature records are few, particularly in one season (mainly autumn). Thus, for Appias paulina, four of seven records were south in the spring-summer, as were six of nine records for Catopsilia pomona, and three of five for Zizina labradus. For Belenois java, flight records were only available for the spring and these showed geographical differences; predominantly north-west in northern Australia (Queensland) and south-west in southern Australia (Victoria, New South Wales). There were too few records for Papilio demoleus in the literature (four only) to draw any conclusions. Major exceptions to the seasonal trend of south in the spring and north in the autumn were Junonia villida, which showed a predominant north-westward direction in both seasons, and Eurema smilax, with a predominant southern or western flight in both seasons. We discuss these species specific trends in migration direction in relation to seasonal shifts in suitable habitat conditions, possible cues used in orientation and in timing changes in direction.

Treads in opiate-related deaths in the United Kingdom and Australia, 1985-1995

This paper compares data on rates of opiate overdose mortality in the UK and Australia between 1985 and 1995. Data on rates of ICD 9-coded overdose mortality were obtained from the Office of National Statistics in the UK and from the Australian Bureau of Statistics mortality register. The proportion of all deaths attributed to opioid overdose increased in both countries between 1985 and 1995. The proportion of all deaths attributed to opioid overdose was substantially higher in Australia than in the UK, but methadone appeared to contribute to more opioid overdose deaths in the UK (50%) than in Australia (18%). Given deficiencies in the available data, the reasons for these differences between the two countries are uncertain but a plausible hypothesis is that the greater availability and ease of access to methadone maintenance in the UK contributes to both the lower rate of opioid overdose mortality and the greater apparent contribution that methadone makes to opioid overdose deaths in that country. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.

Gender and age-at-first-admission for schizophrenia: Data from Australia and Brazil

In order to examine whether different populations show the same pattern of onset in the Southern Hemisphere, we examined the age-at-first-admission distribution for schizophrenia based on mental health registers from Australia and Brazil. Data on age-at-first-admission for individuals with schizophrenia were extracted from two names-linked registers, (1) the Queensland Mental Health Statistics System, Australia (N=7651, F= 3293, M=4358), and (2) a psychiatric hospital register in Pelotas, Brazil (N=4428, F=2220, M=2208). Age distributions were derived for males and females for both datasets. The general population structure tbr both countries was also obtained. There were significantly more males in the Queensland dataset (gz = 56.9, df3, p < 0.0001 ). Both dataset distributions were skewed to the right. Onset rose steeply after puberty to reach a modal age group of 20-29 for men and women, with a more gradual tail toward the older age groups. In Queensland 68% of women with schizophrenia had their first admissions after age 30, while the proportion from Brazil was 58%. Compared to the Australian dataset, the Brazilian dataset had a slightly greater proportion of first admissions under the age 30 and a slightly smaller proportion over the age of 60 years. This reflects the underlying age distributions of the two populations. This study confirms the wide age range and gender differences in age-at-first-admission distributions for schizophrenia and identified a significant difference in the gender ratio between the two datasets. Given widely differing health services, cultural practices, ethic variability, and the different underlying population distributions, the age-at-first-admission in Queensland and Brazil showed more similarities than differences. Acknowledgments: The Stanley Foundation supported this project.

Age-at-first-admission of schizophrenia, bipolar disorder and major depression: Implications of heterogeneity

Age of onset is an important variable when considering the cause and course of mental illnesses. Given the debate about the relationship between psychotic disorders it would be useful to compare age-at-first-admission for ICD schizophrenia and for affective psychoses when the latter is differentiated into 'major depression' and 'bipolar disorder'. Data on age-at-first-admission for Australian-born individuals diagnosed with schizophrenia (ICD 295) or affective psychosis (ICD 296) were extracted from the Queensland Mental Health Statistics System -- a comprehensive, namelinked mental health register. Because the ICD 9 category 296.1 was used to code what is now called "major depressive episode', this group was differentiated from other 296 categorieswhich were considered bipolar disorders. Those receiving more than one diagnoses within these categories were excluded. All distributions show a wide age range of onset from early adolescence into the seventies and eighties. However the modal age-group for major depression ('60-69' for both sexes) is clearly different from bipolar disorder ('20-29' for males; '30- 39' for females), the latter distribution being more similar to the SCZ distribution (which had a model age-group of '20-29' for both sexes). While these distributions were similar for males and females, there were sex differences in the proportions within each diagnostic group: more males with schizophrenia, and more females with bipolar disorder and with major depression. Our results suggest heterogeneity within the affective psychoses as categorised by ICD 9, with bipolar disorder having an age-at-first-admission distribution more similar to schizophrenia than major depression. The Stanley Foundation supported this project.