E-Courant algebroids

In this paper, we introduce the notion of $E$-Courant algebroids, where $E$ is a vector bundle. It is a kind of generalized Courant algebroid and contains Courant algebroids, Courant-Jacobi algebroids and omni-Lie algebroids as its special cases. We explore novel phenomena exhibited by $E$-Courant algebroids and provide many examples. We study the automorphism groups of omni-Lie algebroids and classify the isomorphism classes of exact $E$-Courant algebroids. In addition, we introduce the concepts of $E$-Lie bialgebroids and Manin triples.Comment: 29 pages, no figur

Dirac structures of omni-Lie algebroids

Omni-Lie algebroids are generalizations of Alan Weinstein's omni-Lie algebras. A Dirac structure in an omni-Lie algebroid \dev E\oplus \jet E is necessarily a Lie algebroid together with a representation on $E$. We study the geometry underlying these Dirac structures in the light of reduction theory. In particular, we prove that there is a one-to-one correspondence between reducible Dirac structures and projective Lie algebroids in \huaT=TM\oplus E; we establish the relation between the normalizer $N_{L}$ of a reducible Dirac structure $L$ and the derivation algebra \Der(\pomnib (L)) of the projective Lie algebroid \pomnib (L); we study the cohomology group $\mathrm{H}^\bullet(L,\rho_{L})$ and the relation between $N_{L}$ and $\mathrm{H}^1(L,\rho_{L})$; we describe Lie bialgebroids using the adjoint representation; we study the deformation of a Dirac structure $L$, which is related with $\mathrm{H}^2(L,\rho_{L})$.Comment: 23 pages, no figure, to appear in International Journal of Mathematic

Order-statistics-based inferences for censored lifetime data and financial risk analysis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis focuses on applying order-statistics-based inferences on lifetime analysis and financial risk measurement. The first problem is raised from fitting the Weibull distribution to progressively censored and accelerated life-test data. A new orderstatistics- based inference is proposed for both parameter and con dence interval estimation. The second problem can be summarised as adopting the inference used in the first problem for fitting the generalised Pareto distribution, especially when sample size is small. With some modifications, the proposed inference is compared with classical methods and several relatively new methods emerged from recent literature. The third problem studies a distribution free approach for forecasting financial volatility, which is essentially the standard deviation of financial returns. Classical models of this approach use the interval between two symmetric extreme quantiles of the return distribution as a proxy of volatility. Two new models are proposed, which use intervals of expected shortfalls and expectiles, instead of interval of quantiles. Different models are compared with empirical stock indices data. Finally, attentions are drawn towards the heteroskedasticity quantile regression. The proposed joint modelling approach, which makes use of the parametric link between the quantile regression and the asymmetric Laplace distribution, can provide estimations of the regression quantile and of the log linear heteroskedastic scale simultaneously. Furthermore, the use of the expectation of the check function as a measure of quantile deviation is discussed

An atomic test of higher-order interference

Canonical quantum formalism predicts that the interference pattern registered in multi-slit experiments should be a simple combination of patterns observed in two-slit experiments. This has been linked to the validity of Born's rule and verified in precise experiments with photons as well as molecules via nuclear magnetic resonance. Due to the expected universal validity of Born rule, it is instructive to conduct similar tests with yet other physical systems. Here we discuss analogs of triple-slit experiment using atoms allowing tripod energy level configuration, as realisable e.g. with alkaline-earth-like atoms. We cover all the stages of the setup including various ways of implementing analogs of slit blockers. The precision of the final setup is estimated and offers improvement over the previous experiments.Comment: 7 pages, 4 figure

Inwardly rectifying potassium channels in Drosophila

Inwardly rectifying potassium channels (Kir) are a special subset of potassium selective ion channels which pass potassium more easily into rather than out of the cell. These channels mediate a variety of cellular functions, including control of membrane resting potential, maintenance of potassium homeostasis and regulation of cellular metabolism. Given the existence of fifteen Kir genes in mammals, current genetic studies using mutant animals that lack a single channel may have missed many important physiological functions of these channels due to gene redundancy. This issue can be circumvented by using a simple model organism like Drosophila, whose genome encodes only 3 Kir proteins. The sophisticated genetic approaches of Drosophila may also provide powerful tools to identify additional regulation mechanisms of Kir channels. Here we provide an overview of the progress made in elucidating the function of Drosophila Kir channels. The knowledge of Drosophila Kir channels may lead us to uncover novel functions and regulation mechanisms of human Kir channels and help on pathological studies of related diseases

Whither the roads lead to? estimating association between urbanization and primary healthcare service use with Chinese prefecture-level data in 2014

With the rapid economic development across China over recent decades, examining how urbanization may affect healthcare service use and its implications is more than urgent. This study estimates the association between urbanization and primary healthcare services use in China. We construct a prefecture-level dataset on healthcare services utilization and urbanization. We regress the proportion of residents using healthcare services in primary healthcare centers versus secondary or tertiary hospitals on a set of prefecture-level control variables. Results suggest that use of primary healthcare centers outpatient service is positively associated with being in the proximity of a provincial capital, but negatively correlated with the percentage of the urban population and the availability of public transportation. Higher likelihood of seeking care in major hospitals instead of primary healthcare centers is associated with urbanization, justifying a need for primary care physicians as gatekeepers in China’s healthcare delivery system