Application of quasi-Monte Carlo methods to PDEs with random coefficients -- an overview and tutorial

This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an accompanying software package which is also briefly discussed here. Embedded in this article is a step-by-step tutorial of the required analysis for the setting known as the uniform case with first order QMC rules. The aim of this article is to provide an easy entry point for QMC experts wanting to start research in this direction and for PDE analysts and practitioners wanting to tap into contemporary QMC theory and methods.Comment: arXiv admin note: text overlap with arXiv:1606.0661

Hot new directions for quasi-Monte Carlo research in step with applications

This article provides an overview of some interfaces between the theory of quasi-Monte Carlo (QMC) methods and applications. We summarize three QMC theoretical settings: first order QMC methods in the unit cube $[0,1]^s$ and in $\mathbb{R}^s$, and higher order QMC methods in the unit cube. One important feature is that their error bounds can be independent of the dimension $s$ under appropriate conditions on the function spaces. Another important feature is that good parameters for these QMC methods can be obtained by fast efficient algorithms even when $s$ is large. We outline three different applications and explain how they can tap into the different QMC theory. We also discuss three cost saving strategies that can be combined with QMC in these applications. Many of these recent QMC theory and methods are developed not in isolation, but in close connection with applications

Constraints on Three-Neutrino Mixing from Atmospheric and Reactor Data

Observations of atmospheric neutrinos are usually analyzed using the simplifying approximation that either $\nu_\mu \leftrightarrow \nu_\tau$ or $\nu_e \leftrightarrow \nu_\mu$ two-flavor mixing is relevant. Here we instead consider the data using the simplifying approximation that only one neutrino mass scale is relevant. This approximation is the minimal three-flavor notation that includes the two relevant two-flavor approximations. The constraints in the parameter space orthogonal to the usual, two-flavor analyses are studied.Comment: 15 pages, preprint IUHET-26

Solar and atmospheric neutrino oscillations with three flavours

We analyze the solar and the atmospheric neutrino problems in the context of three flavour neutrino oscillations. We assume a mass hierarchy in the vacuum mass eigenvalues $\mu_3^2 \gg \mu_2^2 \geq \mu_1^2$, but make no approximation regarding the magnitudes of the mixing angles. We find that there are small but continuous bands in the parameter space where the constraints imposed by the current measurements of $\ {}^{71} Ga$, ${}^{37} Cl$ and Kamiokande experiments are satisfied at $1 \sigma$ level. The allowed parameter space increases dramatically if the error bars are enlarged to $1.6 \sigma$. The electron neutrino survival probability has different energy dependence in different regions of the parameter space. Measurement of the recoil electron energy spectrum in detectors that use $\nu - e$ scattering may distinguish between some of the allowed regions of parameter space. Finally we use the results for the parameter space admitted by the solar neutrinos as an input for the atmospheric neutrino problem and show that there exists a substantial region of parameter space in which both problems can be solved.Comment: 25 pages plus eight figures. Uses Revtex. Postcript files for figures sent separately as a uuencoded fil

Comparative Analysis of Gene Content Evolution in Phytoplasmas and Mycoplasmas

Phytoplasmas and mycoplasmas are two groups of important pathogens in the bacterial class Mollicutes. Because of their economical and clinical importance, these obligate pathogens have attracted much research attention. However, difficulties involved in the empirical study of these bacteria, particularly the fact that phytoplasmas have not yet been successfully cultivated outside of their hosts despite decades of attempts, have greatly hampered research progress. With the rapid advancements in genome sequencing, comparative genome analysis provides a new approach to facilitate our understanding of these bacteria. In this study, our main focus is to investigate the evolution of gene content in phytoplasmas, mycoplasmas, and their common ancestor. By using a phylogenetic framework for comparative analysis of 12 complete genome sequences, we characterized the putative gains and losses of genes in these obligate parasites. Our results demonstrated that the degradation of metabolic capacities in these bacteria has occurred predominantly in the common ancestor of Mollicutes, prior to the evolutionary split of phytoplasmas and mycoplasmas. Furthermore, we identified a list of genes that are acquired by the common ancestor of phytoplasmas and are conserved across all strains with complete genome sequences available. These genes include several putative effectors for the interactions with hosts and may be good candidates for future functional characterization

Conformal Transformations of the Wigner Function and Solutions of the Quantum Corrected Vlasov Equation

We study conformal properties of the quantum kinetic equations in curved spacetime. A transformation law for the covariant Wigner function under conformal transformations of a spacetime is derived by using the formalism of tangent bundles. The conformal invariance of the quantum corrected Vlasov equation is proven. This provides a basis for generating new solutions of the quantum kinetic equations in the presence of gravitational and other external fields. We use our method to find explicit quantum corrections to the class of locally isotropic distributions, to which equilibrium distributions belong. We show that the quantum corrected stress--energy tensor for such distributions has, in general, a non--equilibrium structure. Local thermal equilibrium is possible in quantum systems only if an underlying spacetime is conformally static (not stationary). Possible applications of our results are discussed.Comment: 30 page

Next-to-Leading Order QCD Corrections to Jet Cross Sections and Jet Rates in Deeply Inelastic Electron Proton Scattering

Jet cross sections in deeply inelastic scattering in the case of transverse photon exchange for the production of (1+1) and (2+1) jets are calculated in next-to-leading order QCD (here the `+1' stands for the target remnant jet, which is included in the jet definition for reasons that will become clear in the main text). The jet definition scheme is based on a modified JADE cluster algorithm. The calculation of the (2+1) jet cross section is described in detail. Results for the virtual corrections as well as for the real initial- and final state corrections are given explicitly. Numerical results are stated for jet cross sections as well as for the ratio \sigma_{\mbox{\small (2+1) jet}}/\sigma_{\mbox{\small tot}} that can be expected at E665 and HERA. Furthermore the scale ambiguity of the calculated jet cross sections is studied and different parton density parametrizations are compared.Comment: 40 pages, LBL-34147 (Latex file). (figures available by mail on request (send e-mail to [email protected]), please include your address such that it can be used as an address label

Concomitant Active Tuberculosis Prolongs Survival in Non-Small Cell Lung Cancer: A Study in a Tuberculosis-Endemic Country

BACKGROUND: Adjuvant tumor cell vaccine with chemotherapy against non-small cell lung cancer (NSCLC) shows limited clinical response. Whether it provokes effective cellular immunity in tumor microenvironment is questionable. Concomitant active tuberculosis in NSCLC (TBLC) resembles locoregional immunotherapy of tumor cell vaccine; thus, maximally enriches effective anti-tumor immunity. This study compares the survival and immunological cell profile in TBLC over NSCLC alone. METHODS: Retrospective review of NSCLC patients within 1-year-period of 2007 and follow-up till 2010. RESULTS: A total 276 NSCLC patients were included. The median survival of TBLC is longer than those of NSCLC alone (11.6 vs. 8.8 month, p<0.01). Active tuberculosis is an independent predictor of better survival with HR of 0.68 (95% CI, 0.48 ~ 0.97). Squamous cell carcinoma (SCC) (55.8 vs. 31.7%, p<0.01) is a significant risk factor for NSCLC with active TB. The median survival of SCC with active tuberculosis is significantly longer than adenocarcinoma or undetermined NSCLC with TB (14.2 vs. 6.6 and 2.8 months, p<0.05). Active tuberculosis in SCC increases the expression of CD3 (46.4 ± 24.8 vs. 24.0 ± 16.0, p<0.05), CXCR3 (35.1 ± 16.4 vs. 19.2 ± 13.3, p<0.01) and IP-10 (63.5 ± 21.9 vs. 35.5 ± 21.0, p<0.01), while expression of FOXP3 is decreased (3.5 ± 0.5 vs. 13.3 ± 3.7 p<0.05, p<0.05). Survival of SCC with high expression of CD3 (12.1 vs. 3.6 month, p<0.05) and CXCR3 (12.1 vs. 4.4 month, p<0.05) is longer than that with low expression. CONCLUSIONS: Active tuberculosis in NSCLC shows better survival outcome. The effective T lymphocyte infiltration in tumor possibly underlies the mechanism. Locoregional immunotherapy of tumor cell vaccine may deserve further researches