90,894 research outputs found
Large deviation principles for the Ewens-Pitman sampling model
Let be the number of blocks with frequency in the exchangeable
random partition induced by a sample of size from the Ewens-Pitman sampling
model. We show that, as tends to infinity, 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 from the Ewens-Pitman
sampling model, we consider an additional sample of size . For any fixed
and as tends to infinity, we establish a large deviation principle for the
conditional number of blocks with frequency 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 () 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 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
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
Doping and energy evolution of spin dynamics in the electron-doped cuprate superconductor PrLaCeCuO
The doping and energy evolution of the magnetic excitations of the
electron-doped cuprate superconductor PrLaCeCuO
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.
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