Validating Sample Average Approximation Solutions with Negatively Dependent Batches

Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of scenarios. SAA can also be used to find estimates of a lower bound on the optimal objective value of the true problem which, when coupled with an upper bound, provides confidence intervals for the true optimal objective value and valuable information about the quality of the approximate solutions. Specifically, the lower bound can be estimated by solving multiple SAA problems (each obtained using a particular sampling method) and averaging the obtained objective values. State-of-the-art methods for lower-bound estimation generate batches of scenarios for the SAA problems independently. In this paper, we describe sampling methods that produce negatively dependent batches, thus reducing the variance of the sample-averaged lower bound estimator and increasing its usefulness in defining a confidence interval for the optimal objective value. We provide conditions under which the new sampling methods can reduce the variance of the lower bound estimator, and present computational results to verify that our scheme can reduce the variance significantly, by comparison with the traditional Latin hypercube approach

The Flexible Group Spatial Keyword Query

We present a new class of service for location based social networks, called the Flexible Group Spatial Keyword Query, which enables a group of users to collectively find a point of interest (POI) that optimizes an aggregate cost function combining both spatial distances and keyword similarities. In addition, our query service allows users to consider the tradeoffs between obtaining a sub-optimal solution for the entire group and obtaining an optimimized solution but only for a subgroup. We propose algorithms to process three variants of the query: (i) the group nearest neighbor with keywords query, which finds a POI that optimizes the aggregate cost function for the whole group of size n, (ii) the subgroup nearest neighbor with keywords query, which finds the optimal subgroup and a POI that optimizes the aggregate cost function for a given subgroup size m (m <= n), and (iii) the multiple subgroup nearest neighbor with keywords query, which finds optimal subgroups and corresponding POIs for each of the subgroup sizes in the range [m, n]. We design query processing algorithms based on branch-and-bound and best-first paradigms. Finally, we provide theoretical bounds and conduct extensive experiments with two real datasets which verify the effectiveness and efficiency of the proposed algorithms.Comment: 12 page

Classification of Arbitrary Multipartite Entangled States under Local Unitary Equivalence

We propose a practical method for finding the canonical forms of arbitrary dimensional multipartite entangled states, either pure or mixed. By extending the technique developed in one of our recent works, the canonical forms for the mixed $N$-partite entangled states are constructed where they have inherited local unitary symmetries from their corresponding $N+1$ pure state counterparts. A systematic scheme to express the local symmetries of the canonical form is also presented, which provides a feasible way of verifying the local unitary equivalence for two multipartite entangled states.Comment: 22 pages; published in J. Phys. A: Math. Theo

Semi-Parametric Joint Modeling of Survival and Longitudinal Data: The R Package JSM

This paper is devoted to the R package JSM which performs joint statistical modeling of survival and longitudinal data. In biomedical studies it has been increasingly common to collect both baseline and longitudinal covariates along with a possibly censored survival time. Instead of analyzing the survival and longitudinal outcomes separately, joint modeling approaches have attracted substantive attention in the recent literature and have been shown to correct biases from separate modeling approaches and enhance information. Most existing approaches adopt a linear mixed effects model for the longitudinal component and the Cox proportional hazards model for the survival component. We extend the Cox model to a more general class of transformation models for the survival process, where the baseline hazard function is completely unspecified leading to semiparametric survival models. We also offer a non-parametric multiplicative random effects model for the longitudinal process in JSM in addition to the linear mixed effects model. In this paper, we present the joint modeling framework that is implemented in JSM, as well as the standard error estimation methods, and illustrate the package with two real data examples: a liver cirrhosis data and a Mayo Clinic primary biliary cirrhosis data

Does evaporation paradox exist in China?

One expected consequence of global warming is the increase in evaporation. However, lots of observations show that the rate of evaporation from open pans of water has been steadily decreasing all over the world in the past 50 years. The contrast between expectation and observation is called &quot;evaporation paradox&quot;. Based on data from 317 weather stations in China from 1956 to 2005, the trends of pan evaporation and air temperature were obtained and evaporation paradox was analyzed. The conclusions include: (1) From 1956 to 2005, pan evaporation paradox existed in China as a whole while pan evaporation kept decreasing and air temperature became warmer and warmer, but it does not apply to Northeast and Southeast China; (2) From 1956 to 1985, pan evaporation paradox existed narrowly as a whole with unobvious climate warming trend, but it does not apply to Northeast China; (3) From 1986 to 2005, in the past 20 years, pan evaporation paradox did not exist for the whole period while pan evaporation kept increasing, although it existed in South China. Furthermore, the trend of other weather factors including sunshine duration, windspeed, humidity and vapor pressure deficit, and their relations with pan evaporation are discussed. As a result, it can be concluded that pan evaporation decreasing is caused by the decreasing in radiation and wind speed before 1985 and pan evaporation increasing is caused by the decreasing in vapor pressure deficit due to strong warming after 1986. With the Budyko curve, it can be concluded that the actual evaporation decreased in the former 30 years and increased in the latter 20 year for the whole China

Evidence for Two Gaps and Breakdown of the Uemura Plot in Ba0.6_{0.6}K0.4_{0.4}Fe2_2As2_2 Single Crystals

We report a detailed investigation on the lower critical field $H_{c1}$ of the superconducting Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ (FeAs-122) single crystals. A pronounced kink is observed on the $H_{c1}(T)$ curve, which is attributed to the existence of two superconducting gaps. By fitting the data $H_{c1}(T)$ to the two-gap BCS model in full temperature region, a small gap of $\Delta_a(0)=2.0\pm 0.3$ meV and a large gap of $\Delta_b(0)=8.9\pm 0.4$ meV are obtained. The in-plane penetration depth $\lambda_{ab}(0)$ is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in FeAs-122 superconductors.Comment: 5 pages, 4 figure

Critical Fields and Anisotropy of NdO0.82F0.18FeAs Single Crystals

The newly discovered iron-based superconductors have stimulated enormous interests in the field of superconductivity. Since the new superconductor is a layered system, the anisotropy is a parameter with the first priority to know. Meanwhile any relevant message about the critical fields (upper critical field and irreversibility line) are essentially important. By using flux method, we have successfully grown the single crystals NdO0.82F0.18FeAs at ambient pressure. Resistive measurements reveal a surprising discovery that the anisotropy \Gamma = (mc/mab)^{1/2} is below 5, which is much smaller than the theoretically calculated results. The data measured up to 400 K show a continuing curved feature which prevents a conjectured linear behavior for an unconventional metal. The upper critical fields determined based on the Werthamer-Helfand-Hohenberg formula are H_{c2}^{H||ab}(T=0 K) = 304 T and H_{c2}^{H||c}(T=0 K)=62-70 T, indicating a very encouraging application of the new superconductors.Comment: 12 pages, 4 figures, Submitted on 26 May, 200