Final Report for Time Domain Boundary Element and Hybrid Finite Element Simulation for Maxwell's Equations

This report summarizes the work performed for Lawrence Livermore National Laboratory (LLNL) at the University of Washington between September 2004 and May 2006. This project studied fast solvers and stability for time domain integral equations (TDIE), especially as applied to radiating boundary for a massively parallel FEM solver

Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach

Shiga toxin 2-induced intestinal pathology in infant rabbits is A-subunit dependent and responsive to the tyrosine kinase and potential ZAK inhibitor imatinib

Shiga toxin producing Escherichia coli (STEC) are a major cause of food-borne illness worldwide. However, a consensus regarding the role Shiga toxins play in the onset of diarrhea and hemorrhagic colitis (HC) is lacking. One of the obstacles to understanding the role of Shiga toxins to STEC-mediated intestinal pathology is a deficit in small animal models that perfectly mimic human disease. Infant rabbits have been previously used to study STEC and/or Shiga toxin-mediated intestinal inflammation and diarrhea. We demonstrate using infant rabbits that Shiga toxin-mediated intestinal damage requires A-subunit activity, and like the human colon, that of the infant rabbit expresses the Shiga toxin receptor Gb3. We also demonstrate that Shiga toxin treatment of the infant rabbit results in apoptosis and activation of p38 within colonic tissues. Finally we demonstrate that the infant rabbit model may be used to test candidate therapeutics against Shiga toxin-mediated intestinal damage. While the p38 inhibitor SB203580 and the ZAK inhibitor DHP-2 were ineffective at preventing Shiga toxin-mediated damage to the colon, pretreatment of infant rabbits with the drug imatinib resulted in a decrease of Shiga toxin-mediated heterophil infiltration of the colon. Therefore, we propose that this model may be useful in elucidating mechanisms by which Shiga toxins could contribute to intestinal damage in the human

Recalcitrant generalized pustular eruption after diltiazem

Generalized pustular eruptions may occasionally present challenges both for diagnosis and treatment. A 55-year-old male was hospitalized with fever and a severe generalized pustular eruption after recent intake of diltiazem. A careful interpretation of history, clinical course and investigation findings and an active treatment intervention proved the key to management of the case

Eigenvalues Of A Fredholm Integral Operator And Applications To Problems Of Statistical Inference

. We determine the eigenvalues of a Fredholm integral operator of the second kind. The solution of the eigenvalue problem has applications to finding the distribution function of a stochastic integral. The stochastic integral itself represents the asymptotic form of a statistical test. Also discussed are related results for inference and applications. 1. Introduction. Applications of Fredholm integral operators in the areas of physical sciences and engineering are well known. Their applications to problems of statistical inference are probably less known among researchers in mathematics and other disciplines. The dynamic instability inherent in physical processes can often be statistically modelled by the change-point method. The change-point problem primarily consists of testing for a model with no change in the model parameters against a model where parameter changes occur after a certain unknown point of time. The problem has received wide attention among researchers in statistical ..