Large deviation principles for the Ewens-Pitman sampling model

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large deviation principle and we characterize the corresponding rate function. A conditional counterpart of this large deviation principle is also presented. Specifically, given an initial sample of size $n$ from the Ewens-Pitman sampling model, we consider an additional sample of size $m$. For any fixed $n$ and as $m$ tends to infinity, we establish a large deviation principle for the conditional number of blocks with frequency $l$ in the enlarged sample, given the initial sample. Interestingly, the conditional and unconditional large deviation principles coincide, namely there is no long lasting impact of the given initial sample. Potential applications of our results are discussed in the context of Bayesian nonparametric inference for discovery probabilities.Comment: 30 pages, 2 figure

Mitigation of dynamical instabilities in laser arrays via non-Hermitian coupling

Arrays of coupled semiconductor lasers are systems possessing complex dynamical behavior that are of major interest in photonics and laser science. Dynamical instabilities, arising from supermode competition and slow carrier dynamics, are known to prevent stable phase locking in a wide range of parameter space, requiring special methods to realize stable laser operation. Inspired by recent concepts of parity-time ($\mathcal{PT}$) and non-Hermitian photonics, in this work we consider non-Hermitian coupling engineering in laser arrays in a ring geometry and show, both analytically and numerically, that non-Hermitian coupling can help to mitigate the onset of dynamical laser instabilities. In particular, we consider in details two kinds of nearest-neighbor non-Hermitian couplings: symmetric but complex mode coupling (type-I non-Hermitian coupling) and asymmetric mode coupling (type-II non-Hermitian coupling). Suppression of dynamical instabilities can be realized in both coupling schemes, resulting in stable phase-locking laser emission with the lasers emitting in phase (for type-I coupling) or with $\pi/2$ phase gradient (for type-II coupling), resulting in a vortex far-field beam. In type-II non-Hermitian coupling, chirality induced by asymmetric mode coupling enables laser phase locking even in presence of moderate disorder in the resonance frequencies of the lasers.Comment: revised version, changed title, added one figure and some reference

On an Open Problem by Feng Qi Regarding an Integral Inequality

In the article, a functional inequality in abstract spaces is established, which gives a new affirmative answer to an open problem posed by Feng Qi in Several integral inequalities which appeared in J. Inequal. Pure Appl. Math. 1 (2000), no. 2, Art. 19. Moreover, some integral inequalities and a discrete inequality involving sums are deduced

Gluon saturation and pseudo-rapidity distributions of charged hadrons at RHIC energy regions

We modified the gluon saturation model by rescaling the momentum fraction according to saturation momentum and introduced the Cooper-Frye hydrodynamic evolution to systematically study the pseudo-rapidity distributions of final charged hadrons at different energies and different centralities for Au-Au collisions in relativistic heavy-ion collisions at BNL Relativistic Heavy Ion Collider (RHIC). The features of both gluon saturation and hydrodynamic evolution at different energies and different centralities for Au-Au collisions are investigated in this paper.Comment: 14 pages, 4 figure

Superalgebra and Conservative Quantities in N=1 Self-dual Supergravity

The N=1 self-dual supergravity has SL(2,C) and the left-handed and right -handed local supersymmetries. These symmetries result in SU(2) charges as the angular-momentum and the supercharges. The model possesses also the invariance under the general translation transforms and this invariance leads to the energy-momentum. All the definitions are generally covariant . As the SU(2) charges and the energy-momentum we obtained previously constituting the 3-Poincare algebra in the Ashtekar's complex gravity, the SU(2) charges, the supercharges and the energy-momentum here also restore the super-Poincare algebra, and this serves to support the reasonableness of their interpretations.Comment: 18 pages, Latex, no figure

Asymptotic properties of the sequential empirical ROC, PPV and NPV curves under case-control sampling

The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries of the sequential empirical ROC, PPV and NPV curves.Comment: Published in at http://dx.doi.org/10.1214/11-AOS937 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Using Fuzzy Linguistic Representations to Provide Explanatory Semantics for Data Warehouses

A data warehouse integrates large amounts of extracted and summarized data from multiple sources for direct querying and analysis. While it provides decision makers with easy access to such historical and aggregate data, the real meaning of the data has been ignored. For example, "whether a total sales amount 1,000 items indicates a good or bad sales performance" is still unclear. From the decision makers' point of view, the semantics rather than raw numbers which convey the meaning of the data is very important. In this paper, we explore the use of fuzzy technology to provide this semantics for the summarizations and aggregates developed in data warehousing systems. A three layered data warehouse semantic model, consisting of quantitative (numerical) summarization, qualitative (categorical) summarization, and quantifier summarization, is proposed for capturing and explicating the semantics of warehoused data. Based on the model, several algebraic operators are defined. We also extend the SQL language to allow for flexible queries against such enhanced data warehouses

Doping and energy evolution of spin dynamics in the electron-doped cuprate superconductor Pr0.88_{0.88}LaCe0.12_{0.12}CuO4−δ_{4-\delta}

The doping and energy evolution of the magnetic excitations of the electron-doped cuprate superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ in the superconducting state is studied based on the kinetic energy driven superconducting mechanism. It is shown that there is a broad commensurate scattering peak at low energy, then the resonance energy is located among this low energy commensurate scattering range. This low energy commensurate scattering disperses outward into a continuous ring-like incommensurate scattering at high energy. The theory also predicts a dome shaped doping dependent resonance energy.Comment: 8 pages, 4 figures, added discussions, replotted figures, and updated references, accepted for publication in Phys. Rev.

Collective Flow Distributions and Nuclear Stopping in Heavy-ion Collisions at AGS, SPS and RHIC

We study the production of proton, antiproton and net-proton at \AGS, \SPS and \RHIC within the framework non-uniform flow model(NUFM) in this paper. It is found that the system of RHIC has stronger longitudinally non-uniform feature than AGS and SPS, which means that nuclei at RHIC energy region is much more transparent. The NUFM model provides a very good description of all proton rapidity at whole AGS, SPS and RHIC. It is shown that our analysis relates closely to the study of nuclear stopping and longitudinally non-uniform flow distribution of experiment. This comparison with AGS and SPS help us to understand the feature of particle stopping of thermal freeze-out at RHIC experiment.Comment: 16 pages,7 figure