Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Domestic violence in the urban fringe

Police call data for domestic violence incidents in the city of Brisbane were used to further explore the locational disadvantage thesis. It was hypothesised that the supposed additional burdens and stresses on disadvantaged families living in the outer suburbs may be reflected in significantly higher rates of reported domestic violence. Using an index of relative socioeconomic disadvantage and employing Analysis of Variance (ANOVA), this research shows that significantly higher rates of reported domestic violence occur in the inner suburbs relative to the middle or outer suburbs of Brisbane. This finding adds further doubt as to the magnitude of locational disadvantage impacts on outer suburban low income family households.

Exploratory spatial data analysis techniques for examining urban crime

Regional planners, policy makers and policing agencies all recognize the importance of better understanding the dynamics of crime. Theoretical and application-oriented approaches which provide insights into why and where crimes take place are much sought after. Geographic information systems and spatial analysis techniques, in particular, are proving to be essential or studying criminal activity. However, the capabilities of these quantitative methods continue to evolve. This paper explores the use of geographic information systems and spatial analysis approaches for examining crime occurrence in Brisbane, Australia. The analysis highlights novel capabilities for the analysis of crime in urban regions.

A randomized controlled trial assessing the health economics of realtime teledermatology compared with conventional care: an urban versus rural perspective

A randomized controlled trial was carried out to measure the cost-effectiveness of realtime teledermatology compared with conventional outpatient dermatology care for patients from urban and rural areas. One urban and one rural health centre were linked to a regional hospital in Northern Ireland by ISDN at 128 kbit/s. Over two years, 274 patients required a hospital outpatient dermatology referral -126 patients (46%) were randomized to a telemedicine consultation and 148 (54%) to a conventional hospital outpatient consultation. Of those seen by telemedicine, 61% were registered with an urban practice, compared with 71% of those seen conventionally. The clinical outcomes of the two types of consultation were similar - almost half the patients were managed after a single consultation with the dermatologist. The observed marginal cost per patient of the initial realtime teledermatology consultation was f52.85 for those in urban areas and f59.93 per patient for those from rural areas. The observed marginal cost of the initial conventional consultation was f47.13 for urban patients and f48.77 for rural patients. The total observed costs of teledermatology were higher than the costs of conventional care in both urban and rural areas, mainly because of the fixed equipment costs. Sensitivity analysis using a real-world scenario showed that in urban areas the average costs of the telemedicine and conventional consultations were about equal, while in rural areas the average cost of the telemedicine consultation was less than that of the conventional consultation.

Urban birth and migrant status as risk factors for psychosis: An Australian case-control study

Background Urban birth and migrant status have been identified as risk factors for psychosis in North American and European studies. The aim of this study was to explore these variables in an Australian case-control study. Method Country of birth of subjects and their parents, and place of birth of Australian-born subjects, were examined in individuals with psychosis drawn from a prevalence study (n = 310) and well controls recruited from the same catchment area (n = 303). Results Migrant status was associated with a significantly decreased odds of having a psychotic disorder. For those born in Australia, neither migrant status of parents nor urban birth was associated with having a psychotic disorder. Conclusions The lack of effect for urban birth and second-generation migrant status may help generate candidate environmental risk factors that operate in Europe but not in Australia.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

Monitoring the composition and form of urban environments based on the vegetation-impervious surface-soil (VIS) model by sub-pixel analysis techniques

The majority of the world's population now resides in urban environments and information on the internal composition and dynamics of these environments is essential to enable preservation of certain standards of living. Remotely sensed data, especially the global coverage of moderate spatial resolution satellites such as Landsat, Indian Resource Satellite and Systeme Pour I'Observation de la Terre (SPOT), offer a highly useful data source for mapping the composition of these cities and examining their changes over time. The utility and range of applications for remotely sensed data in urban environments could be improved with a more appropriate conceptual model relating urban environments to the sampling resolutions of imaging sensors and processing routines. Hence, the aim of this work was to take the Vegetation-Impervious surface-Soil (VIS) model of urban composition and match it with the most appropriate image processing methodology to deliver information on VIS composition for urban environments. Several approaches were evaluated for mapping the urban composition of Brisbane city (south-cast Queensland, Australia) using Landsat 5 Thematic Mapper data and 1:5000 aerial photographs. The methods evaluated were: image classification; interpretation of aerial photographs; and constrained linear mixture analysis. Over 900 reference sample points on four transects were extracted from the aerial photographs and used as a basis to check output of the classification and mixture analysis. Distinctive zonations of VIS related to urban composition were found in the per-pixel classification and aggregated air-photo interpretation; however, significant spectral confusion also resulted between classes. In contrast, the VIS fraction images produced from the mixture analysis enabled distinctive densities of commercial, industrial and residential zones within the city to be clearly defined, based on their relative amount of vegetation cover. The soil fraction image served as an index for areas being (re)developed. The logical match of a low (L)-resolution, spectral mixture analysis approach with the moderate spatial resolution image data, ensured the processing model matched the spectrally heterogeneous nature of the urban environments at the scale of Landsat Thematic Mapper data.