The intersection problem for star designs

We determine those triples (m, II, k) of integers for which there are two m-star designs on the same n-set having exactly k stars in common.

Compact stellar systems in the Fornax Cluster: Super-massive star clusters or extremely compact dwarf galaxies?

We describe a population of compact objects in the centre of the Fornax Cluster which were discovered as part of our 2dF Fornax Spectroscopic Survey. These objects have spectra typical of old stellar systems, but are unresolved on photographic sky survey plates. They have absolute magnitudes - 13 < M-B

The evolution and star formation of dwarf galaxies in the Fornax Cluster

We present the results of a spectroscopic survey of 675 bright (16.5 < b(J) < 18) galaxies in a 6 degrees field centred on the Fornax cluster with the FLAIR-II spectrograph on the UK Schmidt Telescope. Three galaxy samples were observed: compact galaxies to search for new blue compact dwarfs, candidate M 32-like compact dwarf ellipticals, and a subset of the brightest known cluster members in order to study the cluster dynamics. We measured redshifts for 516 galaxies, of which 108 were members of the Fornax Cluster. Defining dwarf galaxies to be those with b(J) greater than or equal to 15 (M-B greater than or equal to - 16.5), there are a total of 62 dwarf cluster galaxies in our sample. Nine of these are new cluster members previously misidentified as background galaxies. The cluster dynamics show that the dwarf galaxies are still falling into the cluster whereas the giants are virialized. We classified the observed galaxies as late-type if we detected H alpha emission at an equivalent width greater than 1 Angstrom. The spectra were obtained through fixed apertures, so they reflect activity in the galaxy cores, but this does not significantly bias the classifications of the compact dwarfs in our sample. The new classifications reveal a higher rate of star formation among the dwarf galaxies than suggested by morphological classification: 35 per cent have significant H alpha emission indicative of star formations but only 19 per cent were morphologically classified as late-types. The star-forming dwarf galaxies span the full range of physical sizes and we find no evidence in our data for a distinct class of star-forming blue compact dwarf (BCD) galaxy. The distribution of scale sizes is consistent with evolutionary processes which transform late-type dwarfs to early-type dwarfs. The fraction of dwarfs with active star formation drops rapidly towards the cluster centre: this is the usual density-morphology relation confirmed here for dwarf galaxies. The star-forming dwarfs are concentrated in the outer regions of the cluster, the most extreme in an infalling subcluster. We estimate gas depletion time-scales for five dwarfs with detected Hi emission: these are long (of order 10(10) yr), indicating that an active gas removal process must be involved if they are transformed into gas-poor dwarfs as they fall further into the cluster. Finally, in agreement with our previous results, we find no compact dwarf elliptical (M 32-like) galaxies in the Fornax Cluster.

Age-at-first-registration for affective psychosis and schizophrenia

We compared the age-at-first-registration for patients with schizophrenia and affective psychosis in a statewide mental health register. After excluding those receiving (1) a diagnosis of both schizophrenia (ICD-9 295.x) and affective psychosis (ICD-9 296.x), or (2) a diagnosis of ICD-9 296.1 (which can cover major depressive episode), we adjusted the distributions for the age structure of the background general population. We found that all distributions showed a wide age range of onset, with a similar male modal age group of 20-24 for schizophrenia and 25-29 for affective psychosis. The female modal age group was 50-54 for both diagnoses. Although more individuals were diagnosed with schizophrenia (males = 2,434, females = 1,609) than with affective psychosis (males = 670, females = 913), the shape of the two distributions was similar. This finding suggests that factors influencing age-at-first-registration for schizophrenia and affective psychosis may be similar, especially for females.

Star decompositions of cubes

Let Sk denote the complete bipartite graph K-1k and let e,, denote the ii-cube. We prove that the obvious necessary conditions for the existence of an S-k-decomposition of Q(n) are sufficient.

Star factorizations of graph products

A k-star is the graph K-1,K-k. We prove a general theorem about k-star factorizations of Cayley graphs. This is used to give necessary and sufficient conditions for the existence of k-star factorizations of any power (K-q)(S) of a complete graph with prime power order q, products C-r1 x C-r2 x ... x C-rk of k cycles of arbitrary lengths, and any power (C-r)(S) of a cycle of arbitrary length. (C) 2001 John Wiley & Sons, Inc.

Long-term trends in sunshine duration and its association with schizophrenia birth rates and age at first registration - data from Australia and the Netherlands

Back ground. Based on the well-described excess of schizophrenia births in winter and spring, we hypothesised that individuals with schizophrenia (a) would be more likely to be born during periods of decreased perinatal sunshine, and (b) those born during periods of less sunshine would have an earlier age of first registration. Methods. We undertook an ecological analysis of long-term trends in perinatal sunshine duration and schizophrenia birth rates based on two mental health registers (Queensland. Australia n = 6630; The Netherlands n = 24, 474). For each of the 480 months between 1931 and 1970, the agreement between slopes of the trends in psychosis and long-term sunshine duration series were assessed. Age at first registration was assessed by quartiles of long-term trends in perinatal sunshine duration, Males and females were assessed separately. Results. Both the Dutch and Australian data showed a statistically significant association between falling long-term trends in sunshine duration around the time of birth and rising schizophrenia birth rates for males only. In both the Dutch and Australian data there were significant associations between earlier age of first registration and reduced long-term trends in sunshine duration around the time of birth for both males and females, Conclusions. A measure of long-term trends in perinatal sunshine duration was associated with two epidemiological features of schizophrenia in two separate data sets. Exposures related to sunshine duration warrant further consideration in schizophrenia research. (C) 2002 Elsevier Science B.V. All rights reserved.

Age-at-first-registration and heterogeneity in affective psychoses

Background: Previous research into age of onset in affective disorders has produced conflicting results. This paper examines the influence of heterogeneity on the age-at-first-registration distribution for the ICD-9 diagnostic group 'affective psychosis'. Method: For 1979-1991, data for age-at-first-registration for 4985 individuals diagnosed with affective psychosis (ICD-9 296.x) were extracted from a name-linked mental health register. These data were divided into (i) '296.1 only', a category used to code unipolar depression (males = 700; females = 1321); and (ii) '296 other', all 296 cases other than 296.1 (males = 1280; females = 1684). Inception rates for each 5-year age division were adjusted for the background population age-structure as a rate per 100 000 population. Results: The age-at-first-registration distribution for affective psychosis has a wide age range, with women outnumbering men. There is a near-linear increase in inception rates for both men and women with 296.1 only, while the bulk of those with affective psychoses (296 other) have an inverted U-shaped age distribution. Males have an earlier modal age-at-first-registration for 296 other compared to females. Conclusion: The heterogeneity in terms of subtypes and sex in affective psychosis clouds the interpretation of age-at-first-registration. Separating those with unipolar psychotic depression from other subclassifications and differentiating by sex may provide clues to factors that precipitate the onset of affective psychosis.