Description of the inelastic collision of two solitary waves for the BBM equation

We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves).Comment: submitted for publication. Corrected typo in Theorem 1.

The Physics of Cluster Mergers

Clusters of galaxies generally form by the gravitational merger of smaller clusters and groups. Major cluster mergers are the most energetic events in the Universe since the Big Bang. Some of the basic physical properties of mergers will be discussed, with an emphasis on simple analytic arguments rather than numerical simulations. Semi-analytic estimates of merger rates are reviewed, and a simple treatment of the kinematics of binary mergers is given. Mergers drive shocks into the intracluster medium, and these shocks heat the gas and should also accelerate nonthermal relativistic particles. X-ray observations of shocks can be used to determine the geometry and kinematics of the merger. Many clusters contain cooling flow cores; the hydrodynamical interactions of these cores with the hotter, less dense gas during mergers are discussed. As a result of particle acceleration in shocks, clusters of galaxies should contain very large populations of relativistic electrons and ions. Electrons with Lorentz factors gamma~300 (energies E = gamma m_e c^2 ~ 150 MeV) are expected to be particularly common. Observations and models for the radio, extreme ultraviolet, hard X-ray, and gamma-ray emission from nonthermal particles accelerated in these mergers are described.Comment: 38 pages with 9 embedded Postscript figures. To appear in Merging Processes in Clusters of Galaxies, edited by L. Feretti, I. M. Gioia, and G. Giovannini (Dordrecht: Kluwer), in press (2001

Verified lifting of stencil computations

This paper demonstrates a novel combination of program synthesis and verification to lift stencil computations from low-level Fortran code to a high-level summary expressed using a predicate language. The technique is sound and mostly automated, and leverages counter-example guided inductive synthesis (CEGIS) to find provably correct translations. Lifting existing code to a high-performance description language has a number of benefits, including maintainability and performance portability. For example, our experiments show that the lifted summaries can enable domain specific compilers to do a better job of parallelization as compared to an off-the-shelf compiler working on the original code, and can even support fully automatic migration to hardware accelerators such as GPUs. We have implemented verified lifting in a system called STNG and have evaluated it using microbenchmarks, mini-apps, and real-world applications. We demonstrate the benefits of verified lifting by first automatically summarizing Fortran source code into a high-level predicate language, and subsequently translating the lifted summaries into Halide, with the translated code achieving median performance speedups of 4.1X and up to 24X for non-trivial stencils as compared to the original implementation.United States. Department of Energy. Office of Science (Award DE-SC0008923)United States. Department of Energy. Office of Science (Award DE-SC0005288

Using observational data to emulate a randomized trial of dynamic treatment switching strategies

BACKGROUND: When a clinical treatment fails or shows suboptimal results, the question of when to switch to another treatment arises. Treatment switching strategies are often dynamic because the time of switching depends on the evolution of an individual's time-varying covariates. Dynamic strategies can be directly compared in randomized trials. For example, HIV-infected individuals receiving antiretroviral therapy could be randomized to switching therapy within 90 days of HIV-1 RNA crossing above a threshold of either 400 copies/ml (tight-control strategy) or 1000 copies/ml (loose-control strategy).METHODS: We review an approach to emulate a randomized trial of dynamic switching strategies using observational data from the Antiretroviral Therapy Cohort Collaboration, the Centers for AIDS Research Network of Integrated Clinical Systems and the HIV-CAUSAL Collaboration. We estimated the comparative effect of tight-control vs. loose-control strategies on death and AIDS or death via inverse-probability weighting.RESULTS: Of 43 803 individuals who initiated an eligible antiretroviral therapy regimen in 2002 or later, 2001 met the baseline inclusion criteria for the mortality analysis and 1641 for the AIDS or death analysis. There were 21 deaths and 33 AIDS or death events in the tight-control group, and 28 deaths and 41 AIDS or death events in the loose-control group. Compared with tight control, the adjusted hazard ratios (95% confidence interval) for loose control were 1.10 (0.73, 1.66) for death, and 1.04 (0.86, 1.27) for AIDS or death.CONCLUSIONS: Although our effective sample sizes were small and our estimates imprecise, the described methodological approach can serve as an example for future analyses

Cosmology with clusters of galaxies

In this Chapter I review the role that galaxy clusters play as tools to constrain cosmological parameters. I will concentrate mostly on the application of the mass function of galaxy clusters, while other methods, such as that based on the baryon fraction, are covered by other Chapters of the book. Since most of the cosmological applications of galaxy clusters rely on precise measurements of their masses, a substantial part of my Lectures concentrates on the different methods that have been applied so far to weight galaxy clusters. I provide in Section 2 a short introduction to the basics of cosmic structure formation. In Section 3 I describe the Press--Schechter (PS) formalism to derive the cosmological mass function, then discussing extensions of the PS approach and the most recent calibrations from N--body simulations. In Section 4 I review the methods to build samples of galaxy clusters at different wavelengths. Section 5 is devoted to the discussion of different methods to derive cluster masses. In Section 6 I describe the cosmological constraints, which have been obtained so far by tracing the cluster mass function with a variety of methods. Finally, I describe in Section 7 the future perspectives for cosmology with galaxy clusters and the challenges for clusters to keep playing an important role in the era of precision cosmology.Comment: 49 pages, 19 figures, Lectures for 2005 Guillermo Haro Summer School on Clusters, to appear in "Lecture notes in Physics" (Springer

Modeling Host Genetic Regulation of Influenza Pathogenesis in the Collaborative Cross

Genetic variation contributes to host responses and outcomes following infection by influenza A virus or other viral infections. Yet narrow windows of disease symptoms and confounding environmental factors have made it difficult to identify polymorphic genes that contribute to differential disease outcomes in human populations. Therefore, to control for these confounding environmental variables in a system that models the levels of genetic diversity found in outbred populations such as humans, we used incipient lines of the highly genetically diverse Collaborative Cross (CC) recombinant inbred (RI) panel (the pre-CC population) to study how genetic variation impacts influenza associated disease across a genetically diverse population. A wide range of variation in influenza disease related phenotypes including virus replication, virus-induced inflammation, and weight loss was observed. Many of the disease associated phenotypes were correlated, with viral replication and virus-induced inflammation being predictors of virus-induced weight loss. Despite these correlations, pre-CC mice with unique and novel disease phenotype combinations were observed. We also identified sets of transcripts (modules) that were correlated with aspects of disease. In order to identify how host genetic polymorphisms contribute to the observed variation in disease, we conducted quantitative trait loci (QTL) mapping. We identified several QTL contributing to specific aspects of the host response including virus-induced weight loss, titer, pulmonary edema, neutrophil recruitment to the airways, and transcriptional expression. Existing whole-genome sequence data was applied to identify high priority candidate genes within QTL regions. A key host response QTL was located at the site of the known anti-influenza Mx1 gene. We sequenced the coding regions of Mx1 in the eight CC founder strains, and identified a novel Mx1 allele that showed reduced ability to inhibit viral replication, while maintaining protection from weight loss

Novel genetic loci associated with hippocampal volume

The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness