On (t,r) Broadcast Domination Numbers of Grids

The domination number of a graph $G = (V,E)$ is the minimum cardinality of any subset $S \subset V$ such that every vertex in $V$ is in $S$ or adjacent to an element of $S$. Finding the domination numbers of $m$ by $n$ grids was an open problem for nearly 30 years and was finally solved in 2011 by Goncalves, Pinlou, Rao, and Thomass\'e. Many variants of domination number on graphs have been defined and studied, but exact values have not yet been obtained for grids. We will define a family of domination theories parameterized by pairs of positive integers $(t,r)$ where $1 \leq r \leq t$ which generalize domination and distance domination theories for graphs. We call these domination numbers the $(t,r)$ broadcast domination numbers. We give the exact values of $(t,r)$ broadcast domination numbers for small grids, and we identify upper bounds for the $(t,r)$ broadcast domination numbers for large grids and conjecture that these bounds are tight for sufficiently large grids.Comment: 28 pages, 43 figure

The role of Melancholia in prostate cancer patients' depression

BACKGROUND: Although it is well established that prostate cancer (PCa) patients are more likely to experience clinical depression than their age-matched non-prostate cancer peers, and that such depression can have negative effects upon survival, little is known about the underlying nature of the depressive symptomatology that these men experience. In particular, the incidence of melancholic symptoms of depression, which are signs of increased risk of suicide and resistance to treatment, has not previously been reported in PCa patients. The present study aimed to measure the incidence and nature of Melancholia in PCa depression. METHOD: A sample of 507 PCa patients in Queensland, Australia, completed anonymous and confidential questionnaires about their background, treatment status, and depression. Data were analysed to select depressive symptoms that were part of the definition of Melancholia vs those which were not. Regression was used to determine the links between Melancholia and overall depressive status, and factor analysis revealed the underlying components of Melancholia, which were mapped over time since diagnosis for 3 years. RESULTS: Psychometric data were satisfactory. Melancholia significantly predicted depressive status for the most depressed subset of patients, but not for the total sample. Melancholia was factored into its components of Anhedonia and Agitation, and the first of these was more powerful in predicting Melancholia. Variability over the 3 years following diagnosis was noted for each of these two components of Melancholia. CONCLUSIONS: The strong presence of Melancholia in the depressive symptomatology of this sample of PCa patients suggests that some forms of treatment for depression may be more likely to succeed than others. The dominance of Anhedonia and Agitation over other symptoms of Melancholia also holds implications for treatment options when assisting these men to cope with their depression

Collaboration: ideas from the construction industry?

During the current difficult period faced by the UKCS oil and gas industry, collaboration between the various parties in the offshore industry has been identified as one of the key factors in ensuring that the oil and gas output from the UKCS is maximised

Pushing the boundaries: the impact of the changing nature of the professions in construction law.

The way in which the role of the professions is understood in society is changing. One of the traditional effects of being a profession was that the relevant group was regarded as having a virtual monopoly over the provision of services in the area in which it operated. As the understanding of what a 'profession' is has been put under pressure and changed, there is increasing scope for competition between the professions in the provision of particular services. There is increasing scope for 'turf wars' between professions as the boundaries between them are tested through competition for work. This is particularly apparent in the construction industry where there are number of traditional professions operating in similar fields - and in conjunction with other roles which have many 'profession-like' features. Much of this requires commercial and sociological consideration. These will be discussed briefly but the focus of this paper will be on the emerging legal issues in this area. This article looks at recent cases where the courts have looked at issues which arise when professions encroach upon each other's areas of operation. Moreover, in Scotland, a new 'profession' drawing on those with construction industry experience has been granted rights to essentially compete with the legal profession in presenting cases in court. Following discussion of these developments, the lessons this might have for the future coexistence of the professions will be discussed

How can the use of 'mutual trust and cooperation' in the NEC 3 suite of contracts help collaboration?

The NEC 3 standard form of construction contract aims to promote collaboration. It hinges on the use of a particular phrase 'mutual trust and understanding' which is largely undefined. Linking that to notions of good faith in contract, this paper explores how that meaning might be ascertained

The elephant in the dispute resolution room: problems with the definition of arbitration in Scots law.

Considers the implications of the absence of a precise definition of arbitration in Scots law, particularly for distinguishing an expert determination from a judicial pronouncement. Examines options for resolving the uncertainty, including the lessons offered by the hybrid role of adjudicators

The Iron Ore, Coal and Gas Sectors

The industrialisation of Asia – particularly China and India – has led to a strong increase in global demand for key resource commodities. The associated sharp rise in the prices of these commodities has underpinned a significant increase in the levels of Australia’s resource investment, production and exports over the past five years, especially for iron ore, coal and liquefied natural gas (LNG). This article outlines some key features and recent developments in these three commodity sectors within Australia.Resource exports; resource capacity; iron ore; coal; LNG

Factor structure of the Gotland Scale of male depression in two samples of men with prostate cancer:Implications for treating male depression

Up to a quarter of all prostate cancer (PCa) patients suffer from clinically significant depression but treatments are inconsistent and short-lived in their efficacy. One possible reason could be that 'male depression' is not adequately diagnosed by the criteria for major depressive disorder (MDD) used in many clinical settings.In response to this limitation, the Gotland Scale of Male Depression (GSMD) was developed to identify the extra symptoms of MDD in men. Although the factor structure of the GSMD has been reported in non-PCa samples, it has not been determined for this group of men. Two samples of PCa patients were recruited, 191 from Australia and 138 from the United Kingdom and all patients received the GSMD individually, plus a background questionnaire. Two-factor solutions were identified for each of the two samples. The Australian sample was characterized by changes in emotional and somatic function, followed by depressed mood. The U.K. sample exhibited the same two-factor solution but in reverse order of weighting. Targeted treatments for depression in PCa patients may benefit from identification of the loadings that individual patients have on these two GSMD factors so that specific clinical profiles and treatment needs may be based on this information about their depression

Long-Term Structural Price Relationships in Real Estate Markets

This study investigates the long-run stochastic properties of real estate assets by geographical breakdown. We also study their linkages with financial assets. The initial tests find that almost all property types exhibit the presence of nonstationarity. Thus, cointegrated methodologies are used. Structural breakpoints identified in the literature are used as a guide to divide the data into two windows, 1983-1989 and 1990-1996. The results show that real estate in the different regions exhibit a closer relationship with each other in the second period, compared with the first. Also, strong linkages between real estate regions and financial assets are noted in the second period. The South is the only region to exhibit segmentation in both periods. Overall, the information derived from our analysis sheds light on linkages among real estate assets and between real estate and financial assets and also provides a framework for creating diversified portfolios.