Andrew A. Rawlinson

Source estimation is a fundamental ingredient of Full Waveform Inversion (FWI). In such seismic inversion methods wavelet intensity and phase spectra are usually estimated statistically although for the FWI formulation as a nonlinear least-squares optimization problem it can naturally be incorporated to the workflow. Modern approaches for source estimation consider robust misfit functions leading to the well known robust FWI method. The present work uses synthetic data generated from a high order spectral element forward solver to produce observed data which in turn are used to estimate the intensity and the location of the point seismic source term of the original elastic wave PDE. A min-max filter approach is used to convert the original source estimation problem into a state problem conditioned to the observations and a non-standard uncertainty description. The resulting numerical scheme uses an implicit midpoint method to solve, in parallel, the chosen 2D and 3D numerical examples running on an IBM Blue Gene/Q using a grid defined by approximately sixteen thousand 5^th order elements, resulting in a total of approximately 6.5 million degrees of freedom.

BACKGROUND AND PURPOSE: Prediction of the regions of the ischemic penumbra that are likely to progress to infarction is of great clinical interest. Whether lowered apparent diffusion coefficient (ADC) values were present in the ischemic penumbra of patients presenting with acute ischemic stroke and were specific to regions of the penumbra that proceeded to infarction was investigated.

We review why the Thomas rotation is a crucial facet of special relativity, that is just as fundamental, and just as “unintuitive” and “paradoxical,” as such traditional effects as length contraction, time dilation, and the ambiguity of simultaneity. We show how this phenomenon can be quite naturally introduced and investigated in the context of a typical introductory course on special relativity, in a way that is appropriate for, and completely accessible to, undergraduate students. We also demonstrate, in a more advanced section aimed at the graduate student studying the Dirac equation and relativistic quantum field theory, that careful consideration of the Thomas rotation will become vital as modern experiments in particle physics continue to move from unpolarized to polarized cross sections.

We present a procedure whereby the confocal laser scanning ophthalmoscope can be used to extract information about the three-dimensional structure of the central excavated area or the cup of the optic nerve head of the eye. The data are analyzed in terms of spherical harmonics. It is hypothesized that the shape of the cup of the optic nerve head for a normal eye can be parameterized by a specific set of spherical harmonic coefficients and is different from the set of coefficients describing a glaucomatous eye. The sets of coefficients are analyzed by using multivariate statistics and can in turn be used to classify new observations. Preliminary results indicate that there are significant differences in the coefficients and that the procedure might have potential as a diagnostic aid for the detection or the screening of glaucoma.

. We introduce the numerical technique of Mellin--Barnes integral regularization,which can be used to evaluate both convergent and divergent series. The technique is shownto be numerically equivalent to the corresponding results obtained by Borel summation. Bothtechniques are then applied to the Bender--Wu formula, which represents an asymptotic expansionfor the energy levels of the anharmonic oscillator. We find that this formula is unable to giveaccurate values for the ground-state...