Adjusted empirical likelihood with high-order precision

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both problems. With a specific level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.Comment: Published in at http://dx.doi.org/10.1214/09-AOS750 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Hydro-Modeling Platform (HydroMP) - Enabling Cloud-Based Environmental Modeling Using Software-As-A-Service (SaaS) Cloud Computing

Hydro-model has become important tool for water resources management, with higher demand in simulation precision and speed of decision support, models designed for sectoral application becoming outmoded, and original mode that massive schemes are run sequentially cannot meet the real-time requirements, especially with the computation increase by finer discretization granularity and broader research range. Water management organizations are increasingly looking for new generation tools that allow integration across domains, and can provide extensible computing resources to assist their decision making processes. In response to this need, a hydro-modeling platform(HydroMP) based on cloud computing is designed and implemented, which can deployed in distributed HPC Cluster and center HPC Cluster use a resources balancer to manage load balancing. This platform integrates multi models and computing resources (i.e. blade computer) dynamically to assure models integrated in platform get extensible computing capacity. A server, hosting HydroMP Web Service and interfaces, is connected to the HPC Cluster and Internet constituting the gateway for registered users. Any terminal (i.e. decision making system) can reference library and Web service of HydroMP in their systems. Massive modeling schemes can be submitted by different users simultaneously, and terminal can get simulation results from HydroMP real-time. Some key approaches and techniques are utilized including: i) a standard model component wrapper communicating with platform by named pipe have developed. OpenMI-compliant model-components can be integrated to this wrapper; ii) API and Event-Handler interface provided by HPC Server, task scheduler and calculation management table is employed to dispatch computing resource, while controlling multiple concurrent scheme submitting; iii) Interface array(i.e. SchemesSubmit, StatusInquiry, GetResult) in the Web Service is supplied to make terminal communicate with platform; iv) Oracle database is used to manage massive model data, results and model-components. This paper describes the details of design and implementation, and gives a case presentation platform application

A Quadrillion Standard Models from F-theory

We present an explicit construction of ${\cal O}(10^{15})$ globally consistent string compactifications that realize the exact chiral spectrum of the Standard Model of particle physics with gauge coupling unification in the context of F-theory. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi--Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least ${\cal O}(10^{15})$ bases, each of which defines a distinct compactification.Comment: 7 pages, double column; v3: improved and expanded discussion, technical details deferred to an added appendi

Poopćena metoda razvoja po jacobijevim eliptičkim funkcijama i primjene na nelinearne valne jednadžbe

In this work an extended Jacobian elliptic function expansion method is applied to construct the exact periodic solutions of two nonlinear wave equations. The periodic solutions obtained by this method can be reduced to the solitary wave solutions under certain limiting conditions.Primijenili smo proširenu metodu razvoja po Jacobijevim eliptičkim funkcijama za izvod točnih periodičnih rješenja dviju nelinearnih valnih jednadžbi. Periodična rješenja koja smo izveli tom metodom svode se na solitonska rješenja u određenim graničnim uvjetima

Poopćena metoda razvoja po jacobijevim eliptičkim funkcijama i primjene na nelinearne valne jednadžbe

In this work an extended Jacobian elliptic function expansion method is applied to construct the exact periodic solutions of two nonlinear wave equations. The periodic solutions obtained by this method can be reduced to the solitary wave solutions under certain limiting conditions.Primijenili smo proširenu metodu razvoja po Jacobijevim eliptičkim funkcijama za izvod točnih periodičnih rješenja dviju nelinearnih valnih jednadžbi. Periodična rješenja koja smo izveli tom metodom svode se na solitonska rješenja u određenim graničnim uvjetima