Groups with exponent six

Burnside asked questions about periodic groups in his influential paper of 1902. The study of groups with exponent six is a special case of the study of the Burnside questions on which there has been significant progress. It has contributed a number of worthwhile aspects to the theory of groups and in particular to computation related to groups. Finitely generated groups with exponent six are finite. We investigate the nature of relations required to provide proofs of finiteness for some groups with exponent six. We give upper and lower bounds for the number of sixth powers needed to define the largest 2-generator group with exponent six. We solve related questions about other groups with exponent sis using substantial computations which we explain.

Maintenance of cooperative and helping behaviors in reconstituted groups

The authors conducted a 1-year investigation of whether children, who had been trained in the previous school gear to cooperate, were able to use the skills they had been taught in reconstituted groups without additional training. Sixty-four 4th graders, who had participated in training in cooperative group behaviors in the previous gear, were assigned to the trained condition; 84 4th graders, who had not received any training, were assigned to the untrained condition. The children worked in mixed-ability (high, medium, low) gender-balanced groups (2 boys, 2 girls). Results indicate that the children in the trained groups were consistently more cooperative and helpful than their peers in the untrained groups, although they had not received refresher training in cooperative group behaviors.

Providing evidence-based answers to clinical questions - A pilot information service for general practitioners

Objective: To pilot a clinical information service for general practitioners. Methods: A representative sample of 31 GPs was invited to submit clinical questions to a local academic department of general practice. Their views on the service and the usefulness of the information were obtained by telephone interview. Results: Over one month, nine GPs (29% of the sample, 45% of those stating an interest), submitted 20 enquiries comprising 45 discrete clinical questions. The median time to search for evidence, appraise it and write answers to each enquiry was 2.5 hours (range, 1.0-7.4 hours). The median interval between receipt of questions and dispatch of answers was 3 clays (range, 1-12 days). Conclusions: The GPs found the answers useful in clinical decision making; in four out of 20 cases patient management was altered.

Diagnosis and treatment of mental disorders: a survey of Singapore mental health professionals

Background: A series of surveys of mental health literacy have been undertaken in Australia, involving members of the general public as well as general practitioners and mental health professionals, whereby respondents consider vignettes of depression and of schizophrenia, offer a diagnosis and rate a series of possible interventions for their judged helpfulness. A similar survey was undertaken in Singapore and is reported in this paper. Methods: The survey was undertaken at a large state psychiatric hospital with staff (psychiatrists, allied health professionals, psychiatrically and generally trained nursing staff) rating a vignette of mania, in addition to the vignettes derived in Australia for depression and schizophrenia, and with the Australian intervention options extended somewhat to respect Singapore facilities. Results: Responses of those in the four professional groups were compared. The psychiatrists were highly accurate in generating diagnoses, other staff somewhat less so for diagnosing depression (with a percentage instead choosing a diagnosis of stress) and mania (with a percentage instead diagnosing a schizophrenic condition). Reported helpfulness ratings identified those interventions judged consensually as likely to be helpful or harmful, as well as establishing some differences across the four professional groups. Conclusions: The consensus decisions of helpful treatments for depression and schizophrenia revealed very similar findings to judgements made by Australian professionals. The treated outcome of schizophrenia was judged as somewhat worse than that for mania and depression. While non-medical staff differed from psychiatrists in judging the comparative utility of some drug interventions and lifestyle issues, there was clear evidence of a relatively dominant 'medical model' to recommended treatments, while traditional healing practices and services were rated as distinctly unhelpful.

Accessibility to general practitioners in rural South Australia - A case study using geographic information system technology

Objective: To demonstrate the potential of GIS (geographic information system) technology and ARIA (Accessibility/Remoteness Index for Australia) as tools for medical workforce and health service planning in Australia. Design: ARIA is an index of remoteness derived by measuring road distance between populated localities and service centres. A continuous variable of remoteness from 0 to 12 is generated for any location in Australia. We created a GIS, with data on location of general practitioner services in non-metropolitan South Australia derived from the database of HUMPS (Rural Undergraduate Medical Placement System), and estimated, for the 1170 populated localities in South Australia, the accessibility/inaccessibility of the 109 identified GP services. Main outcome measures: Distance from populated locality to GP services. Results: Distance from populated locality to GP service ranged from 0 to 677 km (mean, 58 km). In all, 513 localities (43%) had a GP service within 20 km (for the majority this meant located within the town). However, for 173 populated localities (15%), the nearest GP service was more than 80 km away. There was a strong correlation between distance to GP service and ARIA value for each locality (0.69; P<0.05). Conclusions: GP services are relatively inaccessible to many rural South Australian communities. There is potential for GIS and for ARIA to contribute to rational medical workforce and health service planning. Adding measures of health need and more detailed data on types and extent of GP services provided will allow more sophisticated planning.

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.

The continuum of quasi-psychotic beliefs and experiences in the Australian general public

When surveyed, many individuals without psychosis report a range of beliefs and experiences that are shared by patients with psychosis. This study aimed to examine quasi-psychotic beliefs and experiences in a sample of well Australians. 303 individuals were recruited from a defined catchment area as part of the Brisbane Psychosis Study. All subjects were screened with a modified SCAN in order to exclude psychoses. The Peters Delusional Inventory (PDI 40 items), items from the Chapmans' Psychosis Proneness Scale (PPS), the Communication Awareness Scale (CAS: a measure of awareness of thought disorder), items related to perceptions and beliefs from various schizotypy questionnaires and the Social Desirability (SD) items from the EPQ were administered. There was a significant negative correlation between age and total score on the PDI. There were significant positive correlations between the PDI, the PPS, the CAS and the items related to perception. There were no significant gender differences on any of the scores apart from SD (females had higher scores). Those with a positive family history of mental illness other than schizophrenia (n = 118) scored significantly higher on the PDI and scores related to perception, however they were no different on SD or the Psychosis Proneness items. There were no group differences on any of these items when those with a positive family history of schizophrenia (n = 27) were compared to the rest of the group. Well individuals who endorse delusional beliefs also tend to endorse items related to abnormal perceptions and awareness of thought disorder. The results of the study support the concept of a 'continuum of beliefs and experiences' in the general community that should inform our neurocognitive models of the symptoms of psychosis. The Stanley Foundation supported this project.

Inequitable distribution of general practitioners in Australia: estimating need through the Robin Hood Index

Objective: From Census data, to document the distribution of general practitioners in Australia and to estimate the number of general practitioners needed to achieve an equitable distribution accounting for community health need. Methods: Data on location of general practitioners, population size and crude mortality by statistical division (SD) were obtained from the Australian Bureau of Statistics. The number of patients per general practitioner by SD was calculated and plotted. Using crude mortality to estimate community health need, a ratio of the number of general practitioners per person:mortality was calculated for all Australia and for each SD (the Robin Hood Index). From this, the number of general practitioners needed to achieve equity was calculated. Results: In all, 26,290 general practitioners were identified in 57 SDs. The mean number of people per general practitioner is 707, ranging from 551 to 1887. Capital city SDs have most favourable ratios. The Robin Hood Index for Australia is 1, and ranges from 0.32 (relatively under-served) to 2.46 (relatively over-served). Twelve SDs (21%) including all capital cities and 65% of all Australians, have a Robin Hood Index > 1. To achieve equity per capita 2489 more general practitioners (10% of the current workforce) are needed. To achieve equity by the Robin Hood Index 3351 (13% of the current workforce) are needed. Conclusions: The distribution of general practitioners in Australia is skewed. Nonmetropolitan areas are relatively underserved. Census data and the Robin Hood Index could provide a simple means of identifying areas of need in Australia.

Community care and criminal offending in schizophrenia

Background The introduction of community care in psychiatry is widely thought to have resulted in more offending among the seriously mentally ill. This view affects public policy towards and public perceptions of such people. We investigated the association between the introduction of community care and the pattern of offending in patients with schizophrenia in Victoria, Australia. Methods We established patterns of offending from criminal records in two groups of patients with schizophrenia over their lifetime to date and in the 10 years after their first hospital admission. One group was first admitted in 1975 before major deinstitutionalisation in Victoria, the second group in 1985 when community care was becoming the norm. Each patient was matched to a control, by age, sex, and place of residence to allow for changing patterns of offending over time in the wider community. Findings Compared with controls, significantly more of those with schizophrenia were convicted at least once for ail categories of criminal offending except sexual offences (relative risk of offending in 1975=3.5 [95% CI 2.0-5.5), p=0.001, in 1985=3.0 [1.9-4.9], p=0.001). Among men, more offences were committed in the 1985 group than the 1975 group, but this was matched by a similar increase in convictions among the community controls. Those with schizophrenia who had also received treatment for substance abuse accounted for a disproportionate amount of offending. Analysis of admission data for the patients and the total population of admissions with schizophrenia showed that although there had been an increase of 74 days per annum spent in the community for each of the study population as a whole, first admissions spent only 1 more day in the community in 1985 compared with 1975. Interpretation Increased rates in criminal conviction for those with schizophrenia over the last 20 years are consistent with change in the pattern of offending in the general community. Deinstitutionalisation does not adequately explain such change. Mental-health services should aim to reduce the raised rates of criminal offending associated with schizophrenia, but turning the clock back on community care is unlikely to contribute towards any positive outcome.

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.

First-instar morphology and sexual dimorphism in the gall-inducing scale insect Apiomorpha Rubsaamen (Hemiptera : Coccoidea : Eriococcidae)

Sexual dimorphism among crawlers of the scale insect family Eriococcidae is reported for the first time. The general morphology of crawlers of the gall-inducing genus Apiomorpha (Eriococcidae) is presented and sexual dimorphism described. Sexual dimorphism appears to be associated with differential dispersal and settling-site preference of the sexes during the crawler stage. First-instar males of the A. pharetrata and A. munita species-groups settle only on the galls induced by their mothers or, in the case of A. munita, also galls of nearby females, whereas female crawlers disperse. Female crawlers of all species of Apiomorpha, and male crawlers of most species, are well suited for air-borne dispersal. It is suggested that sexual dimorphism among crawlers of Apiomorpha, and some other scale insects, is the result of loss or reduction of those morphological features associated with dispersal. In addition, male crawlers of some species of Apiomorpha have sensory structures which may assist in the detection of sex-specific settling sites.