The Optimal Confidence Region for a Random Parameter

Under a two-level hierarchical model, suppose that the distribution of the random parameter is known or can be estimated well. Data are generated via a fixed, but unobservable realization of this parameter. In this paper, we derive the smallest confidence region of the random parameter under a joint Bayesian/frequentist paradigm. On average this optimal region can be much smaller than the corresponding Bayesian highest posterior density region. The new estimation procedure is appealing when one deals with data generated under a highly parallel structure, for example, data from a trial with a large number of clinical centers involved or genome-wide gene-expession data for estimating individual gene- or center-specific parameters simultaneously. The new proposal is illustrated with a typical microarray data set and its performance is examined via a small simulation study

Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, for the difference of the precision measures between two competing rules can then be constructed. All the proposals are illustrated with two real examples and their finite sample properties are evaluated via a simulation study

Quantum algebra in the mixed light pseudoscalar meson states

In this paper, we investigate the entanglement degrees of pseudoscalar meson states via quantum algebra Y(su(3)). By making use of transition effect of generators J of Y(su(3)), we construct various transition operators in terms of J of Y(su(3)), and act them on eta-pion-eta mixing meson state. The entanglement degrees of both the initial state and final state are calculated with the help of entropy theory. The diagrams of entanglement degrees are presented. Our result shows that a state with desired entanglement degree can be achieved by acting proper chosen transition operator on an initial state. This sheds new light on the connect among quantum information, particle physics and Yangian algebra.Comment: 9 pages, 3 figure

Decoherence in elastic and polaronic transport via discrete quantum states

Here we study the effect of decoherence on elastic and polaronic transport via discrete quantum states. The calculations are performed with the help of nonperturbative computational scheme, based on the Green's function theory within the framework of polaron transformation (GFT-PT), where the many-body electron-phonon interaction problem is mapped exactly into a single-electron multi-channel scattering problem. In particular, the influence of dephasing and relaxation processes on the shape of the electrical current and shot noise curves is discussed in detail under the linear and nonlinear transport conditions.Comment: 11 pages, 3 figure

Mirror Manifolds in Higher Dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi--Yau manifolds. Our results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.Comment: 44 pages plus 3 tables using harvma

Phase separation and ferroelectric ordering in charge frustrated LuFe2O4-x

The transmission electron microscopy observations of the charge ordering (CO) which governs the electronic polarization in LuFe2O4-x clearly show the presence of a remarkable phase separation at low temperatures. Two CO ground states are found to adopt the charge modulations of Q1 = (1/3, 1/3, 0) and Q2 = (1/3 + y, 1/3 + y, 3/2), respectively. Our structural study demonstrates that the incommensurately Q2-modulated state is chiefly stable in samples with relatively lower oxygen contents. Data from theoretical simulations of the diffraction suggest that both Q1- and Q2-modulated phases have ferroelectric ordering. The effects of oxygen concentration on the phase separation and electric polarization in this layered system are discussed.Comment: 11 pages, 5 figure

Evolution and Flare Activity of Delta-Sunspots in Cycle 23

The emergence and magnetic evolution of solar active regions (ARs) of beta-gamma-delta type, which are known to be highly flare-productive, were studied with the SOHO/MDI data in Cycle 23. We selected 31 ARs that can be observed from their birth phase, as unbiased samples for our study. From the analysis of the magnetic topology (twist and writhe), we obtained the following results. i) Emerging beta-gamma-delta ARs can be classified into three topological types as "quasi-beta", "writhed" and "top-to-top". ii) Among them, the "writhed" and "top-to-top" types tend to show high flare activity. iii) As the signs of twist and writhe agree with each other in most cases of the "writhed" type (12 cases out of 13), we propose a magnetic model in which the emerging flux regions in a beta-gamma-delta AR are not separated but united as a single structure below the solar surface. iv) Almost all the "writhed"-type ARs have downward knotted structures in the mid portion of the magnetic flux tube. This, we believe, is the essential property of beta-gamma-delta ARs. v) The flare activity of beta-gamma-delta ARs is highly correlated not only with the sunspot area but also with the magnetic complexity. vi) We suggest that there is a possible scaling-law between the flare index and the maximum umbral area