Disjoint difference families and their applications

Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and allows a comparison of the similarities and disparities. We then focus on two constructions of disjoint difference families arising from frequency hopping sequences and showed that they are in fact the same. We conclude with a discussion of the notion of equivalence for frequency hopping sequences and for disjoint difference families

Implementation of the Crisis Resolution Team model in adult mental health settings: a systematic review.

Crisis Resolution Teams (CRTs) aim to offer an alternative to hospital admission during mental health crises, providing rapid assessment, home treatment, and facilitation of early discharge from hospital. CRTs were implemented nationally in England following the NHS Plan of 2000. Single centre studies suggest CRTs can reduce hospital admissions and increase service users' satisfaction: however, there is also evidence that model implementation and outcomes vary considerably. Evidence on crucial characteristics of effective CRTs is needed to allow team functioning to be optimised. This review aims to establish what evidence, if any, is available regarding the characteristics of effective and acceptable CRTs

Suprathermal plasma observed on STS-3 Mission by plasma diagnostics package

Artificially produced electron beams were used extensively during the past decade as a means of probing the magnetosphere, and more recently as a means of actively controlling spacecraft potential. Experimentation in these areas has proven valuable, yet at times confusing, due to the interaction of the electron beam with the ambient plasma. The OSS-1/STS-3 Mission in March 1982 provided a unique opportunity to study beam-plasma interactions at an altitude of 240 km. On board for this mission was a Fast Pulse Electron Generator (FPEG). Measurements made by the Plasma Diagnostics Package (PDP) while extended on the Orbiter RMS show modifications of the ion and electron energy distributions during electron beam injection. Observations made by charged particle detectors are discussed and related to measurements of Orbiter potential. Several of the PDP instruments, the joint PDP/FPEG experiment, and observations made during electron beam injection are described

Do Human Extraintestinal Escherichia coli Infections Resistant to Expanded-Spectrum Cephalosporins Originate From Food-Producing Animals? A Systematic Review

To find out whether food-producing animals (FPAs) are a source of extraintestinal expanded-spectrum cephalosporin-resistant Escherichia coli (ESCR-EC) infections in humans, Medline, Embase, and the Cochrane Database of Systematic Reviews were systematically reviewed. Thirty-four original, peer-reviewed publications were identified for inclusion. Six molecular epidemiology studies supported the transfer of resistance via whole bacterium transmission (WBT), which was best characterized among poultry in the Netherlands. Thirteen molecular epidemiology studies supported transmission of resistance via mobile genetic elements, which demonstrated greater diversity of geography and host FPA. Seventeen molecular epidemiology studies did not support WBT and two did not support mobile genetic element-mediated transmission. Four observational epidemiology studies were consistent with zoonotic transmission. Overall, there is evidence that a proportion of human extraintestinal ESCR-EC infections originate from FPAs. Poultry, in particular, is probably a source, but the quantitative and geographical extent of the problem is unclear and requires further investigation

Non-Hausdorff Symmetries of C*-algebras

Symmetry groups or groupoids of C*-algebras associated to non-Hausdorff spaces are often non-Hausdorff as well. We describe such symmetries using crossed modules of groupoids. We define actions of crossed modules on C*-algebras and crossed products for such actions, and justify these definitions with some basic general results and examples.Comment: very minor changes. To appear in Math. An

Diffusion Limited Aggregation with Power-Law Pinning

Using stochastic conformal mapping techniques we study the patterns emerging from Laplacian growth with a power-law decaying threshold for growth $R_N^{-\gamma}$ (where $R_N$ is the radius of the $N-$ particle cluster). For $\gamma > 1$ the growth pattern is in the same universality class as diffusion limited aggregation (DLA) growth, while for $\gamma < 1$ the resulting patterns have a lower fractal dimension $D(\gamma)$ than a DLA cluster due to the enhancement of growth at the hot tips of the developing pattern. Our results indicate that a pinning transition occurs at $\gamma = 1/2$, significantly smaller than might be expected from the lower bound $\alpha_{min} \simeq 0.67$ of multifractal spectrum of DLA. This limiting case shows that the most singular tips in the pruned cluster now correspond to those expected for a purely one-dimensional line. Using multifractal analysis, analytic expressions are established for $D(\gamma)$ both close to the breakdown of DLA universality class, i.e., $\gamma \lesssim 1$, and close to the pinning transition, i.e., $\gamma \gtrsim 1/2$.Comment: 5 pages, e figures, submitted to Phys. Rev.

New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at http://www.pik-potsdam.de/~ander

Functional repair codes: a view from projective geometry

Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to further repair failed nodes is preserved. There are two predominant approaches to repair codes: a coding theoretic approach and a vector space approach. We explore the relationship between the two and frame the later in terms of projective geometry. We find that many of the constructions proposed in the literature can be seen to arise from natural and well-studied geometric objects, and that this perspective gives a framework that provides opportunities for generalisations and new constructions that can lead to greater flexibility in trade-offs between various desirable properties. We also frame the cut-set bound obtained from network coding in terms of projective geometry. We explore the notion of strictly functional repair codes, for which there exist nodes that cannot be replaced exactly. Currently only one known example is given in the literature, due to Hollmann and Poh. We examine this phenomenon from a projective geometry point of view, and discuss how strict functionality can arise. Finally, we consider the issue that the view of a repair code as a collection of sets of vector/projective subspaces is recursive in nature and makes it hard to visualise what a collection of nodes looks like and how one might approach a construction. Here we provide another view of using directed graphs that gives us non-recursive criteria for determining whether a family of collections of subspaces constitutes a function, exact, or strictly functional repair code, which may be of use in searching for new codes with desirable properties