Spectro-Perfectionism: An Algorithmic Framework for Photon Noise-Limited Extraction of Optical Fiber Spectroscopy

We describe a new algorithm for the "perfect" extraction of one-dimensional spectra from two-dimensional (2D) digital images of optical fiber spectrographs, based on accurate 2D forward modeling of the raw pixel data. The algorithm is correct for arbitrarily complicated 2D point-spread functions (PSFs), as compared to the traditional optimal extraction algorithm, which is only correct for a limited class of separable PSFs. The algorithm results in statistically independent extracted samples in the 1D spectrum, and preserves the full native resolution of the 2D spectrograph without degradation. Both the statistical errors and the 1D resolution of the extracted spectrum are accurately determined, allowing a correct chi-squared comparison of any model spectrum with the data. Using a model PSF similar to that found in the red channel of the Sloan Digital Sky Survey spectrograph, we compare the performance of our algorithm to that of cross-section based optimal extraction, and also demonstrate that our method allows coaddition and foreground estimation to be carried out as an integral part of the extraction step. This work demonstrates the feasibility of current- and next-generation multi-fiber spectrographs for faint galaxy surveys even in the presence of strong night-sky foregrounds. We describe the handling of subtleties arising from fiber-to-fiber crosstalk, discuss some of the likely challenges in deploying our method to the analysis of a full-scale survey, and note that our algorithm could be generalized into an optimal method for the rectification and combination of astronomical imaging data.Comment: 9 pages, 4 figures, emulateapj; minor corrections and clarifications; to be published in the PAS

Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis

A numerical implementation of the eXtended Finite Element Method (X-FEM) to analyze crack propagation in a structure under dynamic loading is presented in this paper. The arbitrary crack is treated by the X-FEM method without re-meshing but using an enrichment of the classical displacement-based finite element approximation in the framework of the partition of unity method. Several algorithms have been implemented, within an Oriented Object framework in C++, in the home made explicit FEM code. The new module, called DynaCrack, included in the dynamic FEM code DynELA, evaluates the crack geometry, the propagation of the crack and allow the post-processing of the numerical results. The module solves the system of discrete equations using an explicit integration scheme. Some numerical examples illustrating the main features and the computational efficiency of the DynaCrack module for dynamic crack propagation are presented in the last section of the paper

Direct and Inverse Computational Methods for Electromagnetic Scattering in Biological Diagnostics

Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.Comment: 61 pages, 5 figure

The stellar populations of massive galaxies in the local Universe

I present a brief review of the stellar population properties of massive galaxies, focusing on early-type galaxies in particular, with emphasis on recent results from the ATLAS3D Survey. I discuss the occurrence of young stellar ages, cold gas, and ongoing star formation in early-type galaxies, the presence of which gives important clues to the evolutionary path of these galaxies. Consideration of empirical star formation histories gives a meaningful picture of galaxy stellar population properties, and allows accurate comparison of mass estimates from populations and dynamics. This has recently provided strong evidence of a non-universal IMF, as supported by other recent evidences. Spatially-resolved studies of stellar populations are also crucial to connect distinct components within galaxies to spatial structures seen in other wavelengths or parameters. Stellar populations in the faint outer envelopes of early-type galaxies are a formidable frontier for observers, but promise to put constraints on the ratio of accreted stellar mass versus that formed 'in situ' - a key feature of recent galaxy formation models. Galaxy environment appears to play a key role in controlling the stellar population properties of low mass galaxies. Simulations remind us, however, that current day galaxies are the product of a complex assembly and environment history, which gives rise to the trends we see. This has strong implications for our interpretation of environmental trends.Comment: 10 pages, 4 figures, LaTeX. Invited talk for the IAU Symposium 295 "The Intriguing Life of Massive Galaxies". To appear in Proc. of the XXVIII IAU General Assembly, Beijing, China, August 2012, eds. D. Thomas, A. Pasquali; I. Ferreras. Cambridge University Pres