Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

Reconciling Horse Welfare, Worker Safety, and Public Expectations: Horse Event Incident Management Systems in Australia

Human-horse interactions have a rich tradition and can be highly rewarding, particularly within sport and recreation pursuits, but they can also be dangerous or even life-threatening. In parallel, sport and recreation pursuits involving animals, including horses, are facing an increased level of public scrutiny in relation to the use of animals for these purposes. However, the challenge lies with event organisers to reconcile the expectations of the public, the need to meet legal requirements to reduce or eliminate risks to paid and volunteer workers, and address horse welfare. In this article we explore incident management at horse events as an example of a situation where volunteers and horses can be placed at risk during a rescue. We introduce large animal rescue skills as a solution to improving worker safety and improving horse welfare outcomes. Whilst there are government and horse industry initiatives to improve safety and address animal welfare, there remains a pressing need to invest in a strong communication plan which will improve the safety of workplaces in which humans and horses interact

A Framework for the Exploration of The Evolution of Electronic Meeting Systems in Multinational Corporations

The purpose of this paper is to identify an important development in videoconferencing and present a framework for future research and understanding of this technology. Video-conferencing is a rich medium that provides multiple cues through reoccurring channels of communication with immediate feedback capabilities supporting different languages and a high degree of personalization. The Information Technology (IT) infrastructure necessary to support the large bandwidth for video-conferencing is being expanded around the globe. Organizations dealing across national boundaries will be faced with additional equivocality in making decisions because of diverse cultural perspectives. Equivocality is reduced by allowing decision makers to communicate their individual understanding to each other in an attempt to develop a shared vision or interpretation of the circumstance. Desktop video-conferencing has the potential to be an important new tool for the coordination of multinational corporation

Reconciling Horse Welfare, Worker Safety, and Public Expectations: Horse Event Incident Management Systems in Australia

Human-horse interactions have a rich tradition and can be highly rewarding, particularly within sport and recreation pursuits, but they can also be dangerous or even life-threatening. In parallel, sport and recreation pursuits involving animals, including horses, are facing an increased level of public scrutiny in relation to the use of animals for these purposes. However, the challenge lies with event organisers to reconcile the expectations of the public, the need to meet legal requirements to reduce or eliminate risks to paid and volunteer workers, and address horse welfare. In this article we explore incident management at horse events as an example of a situation where volunteers and horses can be placed at risk during a rescue. We introduce large animal rescue skills as a solution to improving worker safety and improving horse welfare outcomes. Whilst there are government and horse industry initiatives to improve safety and address animal welfare, there remains a pressing need to invest in a strong communication plan which will improve the safety of workplaces in which humans and horses interact

On-chip high-speed sorting of micron-sized particles for high-throughput analysis

A new design of particle sorting chip is presented. The device employs a dielectrophoretic gate that deflects particles into one of two microfluidic channels at high speed. The device operates by focussing particles into the central streamline of the main flow channel using dielectrophoretic focussing. At the sorting junction (T- or Y-junction) two sets of electrodes produce a small dielectrophoretic force that pushes the particle into one or other of the outlet channels, where they are carried under the pressure-driven fluid flow to the outlet. For a 40mm wide and high channel, it is shown that 6micron diameter particles can be deflected at a rate of 300particles/s. The principle of a fully automated sorting device is demonstrated by separating fluorescent from non-fluorescent latex beads

Electric field representation of pulsar intensity spectra

Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we consider the possibility of decomposing pulsar dynamic spectra -- which are intensity measurements -- into their constituent scattered waves, i.e. electric field components. We describe an iterative method of achieving this decomposition and show how the algorithm performs on data from the pulsar B0834+06. The match between model and observations is good, although not formally acceptable as a representation of the data. Scattered wave components derived in this way are immediately useful for qualitative insights into the scattering geometry. With some further development this approach can be put to a variety of uses, including: imaging the scattering and refracting structures in the interstellar medium; interstellar interferometric imaging of pulsars at very high angular resolution; and mitigating pulse arrival time fluctuations due to interstellar scattering.Comment: 7 Pages, 2 Figures, revised version, accepted by MNRA

Random Walks Along the Streets and Canals in Compact Cities: Spectral analysis, Dynamical Modularity, Information, and Statistical Mechanics

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random walkers is developed. The complexity of city modularity can be measured by an information-like parameter which plays the role of an individual fingerprint of {\it Genius loci}. Global structural properties of a city can be characterized by the thermodynamical parameters calculated in the random walks problem.Comment: 44 pages, 22 figures, 2 table