On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Software-based study of a non-sorting method for median calculation on a set of integer numbers

This paper presents a software-based study of a hardware-based non-sorting median calculation method on a set of integer numbers. The method divides the binary representation of each integer element in the set into bit slices in order to find the element located in the middle position. The method exhibits a linear complexity order and our analysis shows that the best performance in execution time is obtained when slices of 4-bit in size are used for 8-bit and 16-bit integers, in mostly any data set size. Results suggest that software implementation of bit slice method for median calculation outperforms sorting-based methods with increasing improvement for larger data set size. For data set sizes of N > 5, our simulations show an improvement of at least 40%.

On comparing two sequences of numbers and its applications to clustering analysis

A conceptual problem that appears in different contexts of clustering analysis is that of measuring the degree of compatibility between two sequences of numbers. This problem is usually addressed by means of numerical indexes referred to as sequence correlation indexes. This paper elaborates on why some specific sequence correlation indexes may not be good choices depending on the application scenario in hand. A variant of the Product-Moment correlation coefficient and a weighted formulation for the Goodman-Kruskal and Kendall`s indexes are derived that may be more appropriate for some particular application scenarios. The proposed and existing indexes are analyzed from different perspectives, such as their sensitivity to the ranks and magnitudes of the sequences under evaluation, among other relevant aspects of the problem. The results help suggesting scenarios within the context of clustering analysis that are possibly more appropriate for the application of each index. (C) 2008 Elsevier Inc. All rights reserved.

On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Undergraduate pre-registration nursing education in Australia: a longitudinal examination of enrolment and completion numbers with a focus on students from rural and remote campus locations

Introduction: There is much evidence to indicate a shortage of Registered Nurses (RNs) in Australia and to suggest that the shortage may be more pronounced in rural and remote locations. Attracting RNs to work in rural and remote areas may not be as simple as increasing the intake of students into university undergraduate pre-registration nursing courses. There is some evidence indicating that student nurses may be more likely to enter the nursing workforce in rural and remote locations if they have existing associations with rural and remote areas and/or their undergraduate education provides opportunities to undertake supported placements in rural and remote settings. Two important difficulties have been associated with measuring outcomes in relation to rural and remote pre-registration nursing students. One is defining what constitutes a rural or remote location and the other is suspect data on the number of nursing students enrolled in, and completing, nursing courses. The aims of this study were to provide a longitudinal profile of the number of domestic students studying and completing undergraduate pre-registration nursing courses in Australia, with a particular emphasis on identifying those at rural and remote university campuses, and to compare results across States and Territories.
Method: This study presents the combined findings from two investigative reports. Data on undergraduate pre-registration nursing student numbers were collected via electronic survey instruments completed by staff at all Australian educational institutions offering undergraduate pre-registration nursing education programs in 2001 and 2002. Australian domestic students were the focus of this study. Data included the total number of domestic students enrolled in undergraduate pre-registration nursing courses in 2001 and 2002, the number of domestic students who successfully completed courses in 1999, 2000 and 2001, and estimates for the number expected to complete in 2002. Surveys were sent to course coordinators or other staff nominated by heads of divisions of nursing at each institution.
Results: There was a 100% response rate. Twenty-four rural and remote campus locations were identified using an adjusted form of the Rural, Remote and Metropolitan Areas (RRMA) classification system. The Australian Capital Territory and the Northern Territory did not have any rural or remote campus locations. In contrast, undergraduate pre-registration nursing in Tasmania was offered at a rural campus only (for the first 2 years). From 2001 to 2002, there was an increase of just over 5% in the total number of domestic students enrolled in undergraduate pre-registration nursing courses in Australia (2002 total = 22 811 students). Rural and remote location students accounted for slightly more than 25% of these students in 2001, and almost 27% in 2002. The States Victoria, New South Wales and Queensland had the highest percentage of students enrolled at rural and remote campus locations, greater than the Australian average for both years. In contrast, South Australia and Western Australia had less than 11% of students enrolled at rural and remote campus locations for each year. Total undergraduate pre-registration course completions increased by approximately 16% across Australia between 1999 (n = 4868) and 2002 (n = 5667), although for 2002, the figure was projected. Of these total course completions, the percentage of students completing at rural and remote campus locations increased from almost 23% to nearly 28% during the same period. Of the States/Territories with both metropolitan and rural/remote campus locations, only Victoria and Queensland had more than 25% of their total student completions consisting of students enrolled at rural and remote campus locations for each year. In contrast, South Australia and Western Australia had approximately 6% of student completions consisting of students enrolled at rural and remote campus locations in 1999, increasing to approximately 12% projected for 2002.
Conclusion: In this study, the authors attempted to improve the accuracy of data collection in relation to the number of domestic undergraduate pre-registration nursing students in Australia, which is representative of the potentially new Australian domestic RN workforce. There was a trend towards an increasing number of students being enrolled in undergraduate pre-registration nursing courses, and also toward an increasing number of course completions. From the perspective of the rural and remote RN workforce, the percentage of students enrolled and completing courses at rural and remote campus locations was found to be increasing. However, there may be some areas of concern for education and workforce planners in States and Territories that are providing a smaller percentage of their undergraduate pre-registration nursing courses in rural and remote areas. Several study limitations are discussed and suggestions made for future research.

Northward migration of Afro-Siberian Knots Calidris canutus canutus : high variability in Red Knot numbers visiting staging sites on the French Atlantic coast, 1979–2009

The Afro–Siberian Red Knot subspecies, Calidris canutus canutus, winters mainly on Banc d’Arguin, Mauritania, West Africa. An International Wader Study Group project carried out in 1979 suggested that during northward migration Red Knots cover their migration between the wintering grounds and the Siberian breeding grounds in two long-distance non-stop flights, stopping only in the Wadden Sea in Schleswig-Holstein, Germany. Each year Red Knots also visit staging sites along the French Atlantic coast in addition to the German Wadden Sea. Ever since 1979, the French staging sites have been counted on a regular basis and here we present the count data from these 30 years. In some years more than 20% of the population used the French Atlantic coast as a staging site, but numbers are highly variable from one year to the next. We suggest that high numbers in France might occur when birds have to stop short of the Wadden Sea because of head-winds and/or a lack of tail-winds en route from West Africa.

More than mere numbers: the impact of lethal control on the social stability of a top-order predator

Population control of socially complex species may have profound ecological implications that remain largely invisible if only their abundance is considered. Here we discuss the effects of control on a socially complex top-order predator, the dingo (Canis lupus dingo). Since European occupation of Australia, dingoes have been controlled over much of the continent. Our aim was to investigate the effects of control on their abundance and social stability. We hypothesized that dingo abundance and social stability are not linearly related, and proposed a theoretical model in which dingo populations may fluctuate between three main states: (A) below carrying capacity and socially fractured, (B) above carrying capacity and socially fractured, or (C) at carrying capacity and socially stable. We predicted that lethal control would drive dingoes into the unstable states A or B, and that relaxation of control would allow recovery towards C. We tested our predictions by surveying relative abundance (track density) and indicators of social stability (scent-marking and howling) at seven sites in the arid zone subject to differing degrees of control. We also monitored changes in dingo abundance and social stability following relaxation and intensification of control. Sites where dingoes had been controlled within the previous two years were characterized by low scent-marking activity, but abundance was similar at sites with and without control. Signs of social stability steadily increased the longer an area was allowed to recover from control, but change in abundance did not follow a consistent path. Comparison of abundance and stability among all sites and years demonstrated that control severely fractures social groups, but that the effect of control on abundance was neither consistent nor predictable. Management decisions involving large social predators must therefore consider social stability to ensure their conservation and ecological functioning.

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chromosomal evolution in Pleurothallidinae (Orchidaceae: Epidendroideae) with an emphasis on the genus Acianthera: chromosome numbers and heterochromatin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.