Time Integration Methods of Fundamental Solutions and Approximate Fundamental Solutions for Nonlinear Elliptic Partial Differential Equations

A time-dependent method is coupled with the Method of Approximate Particular Solutions (MAPS) of Delta-shaped basis functions, the Method of Fundamental Solutions (MFS), and the Method of Approximate Fundamental Solutions (MAFS) to solve a second order nonlinear elliptic partial differential equation (PDE) on regular and irregular shaped domains. The nonlinear PDE boundary value problem is first transformed into a time-dependent quasilinear problem by introducing a fictitious time. Forward Euler integration is then used to ultimately convert the problem into a sequence of time-dependent linear nonhomogeneous modified Helmholtz boundary value problems on which the superposition principle is applied to split the numerical solution at each time step into a homogeneous solution and an approximate particular solution. The Crank-Nicholson method is also examined as an option for the numerical integration as opposed to the forward Euler method. A Delta-shaped basis function, which can handle scattered data in various domains, is used to provide an approximation of the source function at each time step and allows for a derivation of an approximate particular solution of the associated nonhomogeneous equation using the MAPS. The corresponding homogeneous boundary value problem is solved using MFS or MAFS. Numerical results support the accuracy and validity of these computational methods. The proposed numerical methods are additionally applied in nonlinear thermal explosion to determine the steady state critical condition in explosive regimes

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Production of He-4 and (4) in Pb-Pb collisions at root(NN)-N-S=2.76 TeV at the LHC

Results on the production of He-4 and (4) nuclei in Pb-Pb collisions at root(NN)-N-S = 2.76 TeV in the rapidity range vertical bar y vertical bar <1, using the ALICE detector, are presented in this paper. The rapidity densities corresponding to 0-10% central events are found to be dN/dy4(He) = (0.8 +/- 0.4 (stat) +/- 0.3 (syst)) x 10(-6) and dN/dy4 = (1.1 +/- 0.4 (stat) +/- 0.2 (syst)) x 10(-6), respectively. This is in agreement with the statistical thermal model expectation assuming the same chemical freeze-out temperature (T-chem = 156 MeV) as for light hadrons. The measured ratio of (4)/He-4 is 1.4 +/- 0.8 (stat) +/- 0.5 (syst). (C) 2018 Published by Elsevier B.V.Peer reviewe

Association between the advanced glycosylation end product-specific receptor gene and cardiovascular death in older men

Advanced glycosylation end product-specific receptor (AGER) signaling has been implicated in atherosclerosis. The aim of this study was to evaluate whether a common genetic variation in the AGER gene is associated with cardiovascular (CV) death. We included 1304 older men who were genotyped for rs1035798:C>T, which is a single nucleotide polymorphism (SNP) mapped to the third intron of AGER. Cox proportional hazard analysis was used to estimate the association of rs1035798:C>T with CV death. In addition we analyzed total RNA extracted from carotid atherosclerosis biopsies of 18 patients that did or did not have recent symptoms of cerebral embolization by quantitative real-time reverse transcription PCR (qRT-PCR). The minor T-allele of rs1035798:C>T was found to be associated with CV death under dominant (HR = 1.43, 95% CI: 1.01–2.02, P = 0.04) and recessive (HR = 2.05, 95% CI: 1.11–3.81, P = 0.02) models of inheritance even after adjustment for traditional cardiovascular risk factors. No association was found between rs1035798:C>T and non-CV death. qRT-PCR results suggested that median relative expression of AGER isoform 1 and isoform 6 transcripts were approximately 6- (P = 0.01) and 2-fold (P = 0.02) greater, respectively, within carotid biopsies of symptomatic compared to asymptomatic patients. These data suggest that the minor (T) allele of rs1035798:C>T represents an independent susceptibility factor for CV death. The expression of AGER isoforms is different in atheroma from patients with recent symptoms. Further studies are needed to investigate if rs1035798:C>T influences the alternative splicing of AGER

Differential expression of <i>HMGB1</i> and <i>ARG1</i> in carotid atheroma biopsies of patients with and without symptoms of cerebral embolization.

<p>Increased expression of <i>HMGB1</i> (A; *P = 0.02) but not <i>ARG1</i> (B; P = 0.82) within carotid atheroma biopsies of symptomatic compared to asymptomatic patients. Data expressed as median and interquartile range with maximum and minimum data points (whiskers) for relative expression.</p

Association of rs1035798:C>T with death in HIMS subjects.

<p>N, number of individuals; MAF, observed minor allele frequency; HWE, Hardy-Weinberg equilibrium chi-squared test P value; HR, hazard ratio; 95% CI, 95% confidence interval. Adjusted for CHD, diabetes, dyslipidemia, hypertension, smoking, and WHR.</p><p>Association of rs1035798:C>T with death in HIMS subjects.</p

Differential expression of <i>AGER</i> isoforms in carotid atheroma biopsies from patients with and without symptoms of cerebral embolization.

<p>Expression of <i>AGER</i> isoform 1 (A; **P = 0.01) and <i>AGER</i> isoform 6 (B; *P = 0.02) was more than 6- and 2-fold greater within carotid atheroma biopsies of symptomatic compared to asymptomatic patients. Data expressed as median and interquartile range with maximum and minimum data points (whiskers) for relative expression.</p