Fringe analysis for parallel MacroSplit insertion algorithms in 2--3 trees

We extend the fringe analysis (used to study the expected behavior of balanced search trees under sequential insertions) to deal with synchronous parallel insertions on 2--3 trees. Given an insertion of k keys in a tree with n nodes, the fringe evolves following a transition matrix whose coefficients take care of the precise form of the algorithm but does not depend on k or n. The derivation of this matrix uses the binomial transform recently developed by P. Poblete, J. Munro and Th. Papadakis. Due to the complexity of the preceding exact analysis, we develop also two approximations. A first one based on a simplified parallel model, and a second one based on the sequential model. These two approximated analysis prove that the parallel insertions case does not differ significantly from the sequential case, namely on the terms O(1/n^2).Postprint (published version

B-urns

The fringe of a B-tree with parameter $m$ is considered as a particular P\'olya urn with $m$ colors. More precisely, the asymptotic behaviour of this fringe, when the number of stored keys tends to infinity, is studied through the composition vector of the fringe nodes. We establish its typical behaviour together with the fluctuations around it. The well known phase transition in P\'olya urns has the following effect on B-trees: for $m\leq 59$, the fluctuations are asymptotically Gaussian, though for $m\geq 60$, the composition vector is oscillating; after scaling, the fluctuations of such an urn strongly converge to a random variable $W$. This limit is $\mathbb C$-valued and it does not seem to follow any classical law. Several properties of $W$ are shown: existence of exponential moments, characterization of its distribution as the solution of a smoothing equation, existence of a density relatively to the Lebesgue measure on $\mathbb C$, support of $W$. Moreover, a few representations of the composition vector for various values of $m$ illustrate the different kinds of convergence

Developing young people's sense of self and place through sport

Previous research has recognized positive health implications, both physical and mental, as an outcome of participation in leisure pursuits. They provide opportunities for self-expression and stress reduction, as well as an environment in which people can socialize. Leisure activities, specifically sport activities, can play a significant role in young people's identity development. This paper explores the leisure activities in which young people in Adelaide, Australia participate. It examines the role of leisure activities in terms of young people's identity and feelings towards their hometown. This study consisted of semi-structured focus groups conducted with 24 senior high school students, followed by a survey resulting in 226 useable responses. Respondents were aged between 16 and 18 years of age. From the range of activities identified and explored, the results revealed sports activities to have the greatest impact on young people's lives. The results demonstrated that frequency of participation has a significant effect on young people's involvement levels and how they identify with the activity

Absolute Motion and Quantum Gravity

A new information-theoretic modelling of reality has given rise to a quantum-foam description of space, relative to which absolute motion is meaningful. In a previous paper (Cahill and Kitto) it was shown that in this new physics Michelson interferometers show absolute motion effects when operated in dielectric mode, as indeed such experiments had indicated, and analysis of the experimental data showed that the measured speeds were all consistent with the Cosmic Microwave Background (CMB) dipole-fit speed of 369km/s. Here the new physics is applied to the Michelson-Morley 1887 interferometer rotation curve data to demonstrate that the interferometer data is in excellent agreement with the CMB direction (RA, Dec)=(11.20h,-7.22deg) as well. This data also reveals a velocity component caused by the in-flow of the quantum foam past the Earth towards the Sun at 40+/-15km/s, while analysis of the Miller interferometer data of 1933 gives 49km/s, compared to the theoretical value of 42km/s. This observed in-flow is a signature of quantum gravity effects in the new physicsComment: 11 pages, Latex, 5 eps figure files Minor change

Why Do Non-Union Employees Want To Unionise? Evidence from Britain

The introduction of a statutory recognition procedure offers British unions the opportunity to reverse membership decline by organising non-union workers. The aim of this paper is to test theories of individual union joining in order to assess the likely impact of the new procedure on British union membership. Responses of a nationally representative sample of non-union employees to the question 'how willing would you be to join a union if one were available at your workplace?' are analysed. Results suggest that the new legislation will cause union membership to rise among manual employees, but that unions will face a much harder challenge organising non-manual employees. Unless unions can change their environment, or change themselves then long-term decline is likely.Trade Unions, employee attitudes, unionisation