On Vertically Global, Horizontally Local Models for Astrophysical Disks

Disks with a barotropic equilibrium structure, for which the pressure is only a function of the density, rotate on cylinders in the presence of a gravitational potential, so that the angular frequency of such a disk is independent of height. Such disks with barotropic equilibria can be approximately modeled using the shearing box framework, representing a small disk volume with height-independent angular frequency. If the disk is in baroclinic equilibrium, the angular frequency does generally depend on height, and it is thus necessary to go beyond the standard shearing box approach. In this paper, we show that given a global disk model, it is possible to develop approximate models that are local in horizontal planes without an expansion in height with shearing-periodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be non-axisymmetric for globally barotropic equilibria but should be axisymmetric for globally baroclinic equilibria. We provide explicit equations for this VGSB which can be implemented in standard magnetohydrodynamic codes by generalizing the shearing-periodic boundary conditions to allow for a height-dependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose height-dependent shearing periodic boundary conditions. We illustrate the potential of this framework by studying a vertical shear instability and examining the modes associated with the magnetorotational instability.Comment: 24 pages, 8 figures, updated to match published versio

Maximising learning opportunities in handover

Handing over responsibility for patients has always been part of medical practice. Definitions emphasise transfer of responsibility to ensure patient safety and the available literature tends to follow this line (see box 1). Handover is much more than this, however. It is a key event where teams meet, have the opportunity to communicate, support each other and learn. This paper considers different ways of maximising learning opportunities in handover, with particular emphasis on the strengths and challenges of the paediatric environment. Alongside review of the best available evidence, many of the ideas discussed were generated from working with a group of 65 experienced paediatricians with particular experience and interest in medical education as part of the Royal College of Paediatrics and Child Health Paediatric Educators Programme. Formal handover has increased in importance and been embedded in practice with the transition from “on-calls” to “full-shift” rotas in an effort to comply with the European Working Time Directive1 in the United Kingdom (UK). Departments responsible for acute patient care have had to incorporate two or three handover sessions into every day to ensure patient problems and management plans are appreciated by the incoming medical team

The location of executive suites and business centers in the United States: an exploratory analysis

Increasingly, corporate occupiers seek more flexible ways of meeting their accommodation needs. One consequence of this process has been the growth of the executive suite, serviced office or business centre market. This paper, the final report of a research project funded by the Real Estate Research Institute, focuses upon the geographical distribution of business centers offering executive suites within the US. After a brief review of the development of the market, the paper examines the availability of data, provides basic descriptive statistics of the distribution of executive suites by state and by metropolitan statistical area and then attempts to model the distribution using demographic and socio-economic data at MSA level. The distribution reflects employment in key growth sectors and the position of the MSA in the urban hierarchy. An appendix presents a preliminary view of the global distribution of suites

Using somatic mutation data to test tumors for clonal relatedness

A major challenge for cancer pathologists is to determine whether a new tumor in a patient with cancer is a metastasis or an independent occurrence of the disease. In recent years numerous studies have evaluated pairs of tumor specimens to examine the similarity of the somatic characteristics of the tumors and to test for clonal relatedness. As the landscape of mutation testing has evolved, a number of statistical methods for determining clonality have developed, notably for comparing losses of heterozygosity at candidate markers, and for comparing copy number profiles. Increasingly tumors are being evaluated for point mutations in panels of candidate genes using gene sequencing technologies. Comparison of the mutational profiles of pairs of tumors presents unusual methodological challenges: mutations at some loci are much more common than others; knowledge of the marginal mutation probabilities is scanty for most loci at which mutations might occur; the sample space of potential mutational profiles is vast. We examine this problem and propose a test for clonal relatedness of a pair of tumors from a single patient. Using simulations, its properties are shown to be promising. The method is illustrated using several examples from the literature.Comment: Published at http://dx.doi.org/10.1214/15-AOAS836 in the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed