The mincut graph of a graph

In this paper we introduce an intersection graph of a graph $G$, with vertex set the minimum edge-cuts of $G$. We find the minimum cut-set graphs of some well-known families of graphs and show that every graph is a minimum cut-set graph, henceforth called a \emph{mincut graph}. Furthermore, we show that non-isomorphic graphs can have isomorphic mincut graphs and ask the question whether there are sufficient conditions for two graphs to have isomorphic mincut graphs. We introduce the $r$-intersection number of a graph $G$, the smallest number of elements we need in $S$ in order to have a family $F=\{S_1, S_2 \ldots , S_i\}$ of subsets, such that $|S_i|=r$ for each subset. Finally we investigate the effect of certain graph operations on the mincut graphs of some families of graphs

Mortality patterns and the influence of antiretroviral therapy in medical patients at Chris Hani Baragwanath Academic Hospital

A research report submitted to the Faculty of Health Sciences, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Medicine in the branch of Internal Medicine Johannesburg, 2015South Africa has experienced an HIV epidemic that resulted in an increased population mortality rate and decreased life expectancy. Since 2007 these trends have reversed. Antiretroviral therapy has been shown to decrease mortality and increase life expectancy at a community and population level. The impact of antiretroviral therapy at a large healthcare facility level is unclear. Mortality patterns in South Africa are also changing however the method of data collection often underrepresents the burden of HIV. Aim To determine the mortality patterns of medical inpatients at CHBAH and to assess if improved access to antiretroviral therapy has decreased mortality and increased age at death over the period 2006 to 2009 when there was a rapid scale-up of antiretroviral therapy in the public sector. Methods This is a retrospective, cross-sectional study. Adult mortalities in the medical wards were reviewed between 2006 and 2009. Causes of death were ascertained by medical consultants who reviewed the patient records and results at the time of completing patient death certificates.. The annual mortality rates were determined and deaths were analysed with respect to age at death, sex and HIV-status. Results Data on 16020 deaths were available for analyses. The overall crude mortality rate fell significantly year on year from 113/100000 to 79/100000. The mean age at death for HIV-negative patients was 60in 2006 and showed no significant increase over the study period. The mean age at death of HIV-positive patients increased significantly year on year from 38 in 2006 to 40 years in 2009 . The peak age category of death for HIV-positive females moved from 30-34 to 35-39 years over the study period. Peak age category at time of death in males remained unchanged at 40-49 years An estimated total of 101478 years of life were lost to HIV disease in females and 65008 years were lost in HIV-positive males during the study period . HIV, tuberculosis and pneumonia were the top three causes of death and their proportional contribution to mortality remained unchanged over the study period. Diseased associated with advanced immunosuppression such as cryptococcal meningitis and infectious diarrhoea decreased over the study period. The mortality trends seen in this study are similar to those reported at population level. Increases in life expectancy occurred in the HIV-positive population and opportunistic infections as major contributors to death decreased, during the time that antiretroviral therapy was being escalated. Conclusion Improvement in mortality patterns within the HIV-positive group at the time that antiretroviral therapy was escalated suggest that cART roll-out had a positive impact on mortality at CHBAH

Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath

We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise non-thermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.Comment: 10 pages, 3 figure

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure