Conditional Estimation in Two-stage Adaptive Designs

We consider conditional estimation in two-stage sample size adjustable designs and the following bias. More specifically, we consider a design which permits raising the sample size when interim results look rather promising, and, which keeps the originally planned sample size when results look very promising. The estimation procedures reported comprise the unconditional maximum likelihood, the conditionally unbiased Rao-Blackwell estimator, the conditional median unbiased estimator, and the conditional maximum likelihood with and without bias correction. We compare these estimators based on analytical results and by a simulation study. We show in a real clinical trial setting how they can be applied

Photon Splitting in a Strong Magnetic Field: Recalculation and Comparison With Previous Calculations

We recalculate the amplitude for photon splitting in a strong magnetic field below the pair production threshold, using the worldline path integral variant of the Bern--Kosower formalism. Numerical comparison (using programs that we have made available for public access on the Internet) shows that the results of the recalculation are identical to the earlier calculations of Adler and later of Stoneham, and to the recent recalculation by Baier, Milstein, and Shaisultanov.Comment: Revtex, 9 pages, no figure

Annihilation of NMSSM neutralinos in the Sun and neutrino telescope limits

We investigate neutralino dark matter in the framework of NMSSM performing a scan over its parameter space and calculating neutralino capture and annihilation rates in the Sun. We discuss the prospects of searches for neutralino dark matter in neutrino experiments depending on neutralino content and its main annihilation channel. We recalculate the upper limits on neutralino-proton elastic cross sections directly from neutrino telescopes upper bounds on annihilation rates in the Sun. This procedure has advantages as compared with corresponding recalcalations from the limits on muon flux, namely, it is independent on details of the experiment and the recalculation coefficients are universal for any kind of WIMP dark matter models. We derive 90% c.l. upper limits on neutralino-proton cross sections from the results of the Baksan Underground Scintillator Telescope.Comment: 28 pages, 16 figures, accepted for publication in JCAP, references adde

The Maximum Traveling Salesman Problem with Submodular Rewards

In this paper, we look at the problem of finding the tour of maximum reward on an undirected graph where the reward is a submodular function, that has a curvature of $\kappa$, of the edges in the tour. This problem is known to be NP-hard. We analyze two simple algorithms for finding an approximate solution. Both algorithms require $O(|V|^3)$ oracle calls to the submodular function. The approximation factors are shown to be $\frac{1}{2+\kappa}$ and $\max\set{\frac{2}{3(2+\kappa)},2/3(1-\kappa)}$, respectively; so the second method has better bounds for low values of $\kappa$. We also look at how these algorithms perform for a directed graph and investigate a method to consider edge costs in addition to rewards. The problem has direct applications in monitoring an environment using autonomous mobile sensors where the sensing reward depends on the path taken. We provide simulation results to empirically evaluate the performance of the algorithms.Comment: Extended version of ACC 2013 submission (including p-system greedy bound with curvature

Use of shallow samples to estimate the total carbon storage in pastoral soils

Using data from pastoral soils sampled by horizon at 56 locations across New Zealand, we conducted a meta-analysis. On average, the total depth sampled was 0.93 ± 0.026 m (± SEM), and on a volumetric basis, the total C storage averaged 26.9 ± 1.8, 13.9 ± 0.6 and 9.2 ± 1.4 kg C m⁻² for allophanic (n=12), non-allophanic (n=40) and pumice soils (n=4), respectively. We estimated the total C storage, and quantified the uncertainty, using the data for samples taken from the uppermost A-horizon whose depth averaged 0.1 ± 0.003 m. For A-horizon samples of the allophanic soils, the mean C content was 108 ± 6 g C kg⁻¹ and the bulk density was 772 ± 29 kg m⁻³, for non-allophanic soils they were 51 ± 4 g C kg⁻¹ and 1055 ± 29 kg m⁻³, and for pumice soils they were 68 ± 9 g C kg⁻¹ and 715 ± 45 kg m⁻³. The C density —a product of the C content and bulk density —of the A-horizon samples was proportional to their air-dried water content, a proxy measure for the mineral surface area. By linear regression with C density of the A-horizon, the total C storage could be estimated with a standard error of 3.1 kg C m⁻², 19% of the overall mean

Rewriting High-Level Spreadsheet Structures into Higher-Order Functional Programs

Spreadsheets are used heavily in industry and academia. Often, spreadsheet models are developed for years and their complexity grows vastly beyond what the paradigm was originally conceived for. Such complexity often comes at the cost of recalculation performance. However, spreadsheet models usually have some high-level structure that can be used to improve performance by performing independent computation in parallel. In this paper, we devise rules for rewriting high-level spreadsheet structure in the form of so-called cell arrays into higher-order functional programs that can be easily parallelized on multicore processors. We implement our rule set for the experimental Funcalc spreadsheet engine which already implements parallelizable higher-order array functions as well as user-defined higher-order functions. Benchmarks show that our rewriting approach improves recalculation performance for spreadsheets that are dominated by cell arrays