A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Value and depreciation of mineral resources over the very long run: An empirical contrast of different methods

The paper contrasts empirically the results of alternative methods for estimating thevalue and the depreciation of mineral resources. The historical data of Mexico andVenezuela, covering the period 1920s-1980s, is used to contrast the results of severalmethods. These are the present value, the net price method, the user cost method andthe imputed income method. The paper establishes that the net price and the user costare not competing methods as such, but alternative adjustments to different scenariosof closed and open economies. The results prove that the biases of the methods, ascommonly described in the theoretical literature, only hold under the most restrictedscenario of constant rents over time. It is argued that the difference between what isexpected to happen and what actually did happen is for the most part due to a missingvariable, namely technological change. This is an important caveat to therecommendations made based on these models.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Comparison of different methods for thin section EM analysis of Mycobacterium smegmatis.

Bacteria are generally difficult specimens to prepare for conventional resin section electron microscopy and mycobacteria, with their thick and complex cell envelope layers being especially prone to artefacts. Here we made a systematic comparison of different methods for preparing Mycobacterium smegmatis for thin section electron microscopy analysis. These methods were: (1) conventional preparation by fixatives and epoxy resins at ambient temperature. (2) Tokuyasu cryo-section of chemically fixed bacteria. (3) rapid freezing followed by freeze substitution and embedding in epoxy resin at room temperature or (4) combined with Lowicryl HM20 embedding and ultraviolet (UV) polymerization at low temperature and (5) CEMOVIS, or cryo electron microscopy of vitreous sections. The best preservation of bacteria was obtained with the cryo electron microscopy of vitreous sections method, as expected, especially with respect to the preservation of the cell envelope and lipid bodies. By comparison with cryo electron microscopy of vitreous sections both the conventional and Tokuyasu methods produced different, undesirable artefacts. The two different types of freeze-substitution protocols showed variable preservation of the cell envelope but gave acceptable preservation of the cytoplasm, but not lipid bodies, and bacterial DNA. In conclusion although cryo electron microscopy of vitreous sections must be considered the 'gold standard' among sectioning methods for electron microscopy, because it avoids solvents and stains, the use of optimally prepared freeze substitution also offers some advantages for ultrastructural analysis of bacteria.

Computation of multiple correspondence analysis, with code in R

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational steps involved in performing a multiple correspondence analysis, including the special aspects of adjusting the principal inertias to correct the percentages of inertia, supplementary points and subset analysis. Furthermore, we give the algorithm for joint correspondence analysis where the cross-tabulations of all unique pairs of variables are analysed jointly. The code in the R language for every step of the computations is given, as well as the results of each computation.

Methods for integration site distribution analyses in animal cell genomes.

The question of where retroviral DNA becomes integrated in chromosomes is important for understanding (i) the mechanisms of viral growth, (ii) devising new anti-retroviral therapy, (iii) understanding how genomes evolve, and (iv) developing safer methods for gene therapy. With the completion of genome sequences for many organisms, it has become possible to study integration targeting by cloning and sequencing large numbers of host-virus DNA junctions, then mapping the host DNA segments back onto the genomic sequence. This allows statistical analysis of the distribution of integration sites relative to the myriad types of genomic features that are also being mapped onto the sequence scaffold. Here we present methods for recovering and analyzing integration site sequences.

Isolating DNA from sexual assault cases: a comparison of standard methods with a nuclease-based approach.

AbstractText BACKGROUND: Profiling sperm DNA present on vaginal swabs taken from rape victims often contributes to identifying and incarcerating rapists. Large amounts of the victim's epithelial cells contaminate the sperm present on swabs, however, and complicate this process. The standard method for obtaining relatively pure sperm DNA from a vaginal swab is to digest the epithelial cells with Proteinase K in order to solubilize the victim's DNA, and to then physically separate the soluble DNA from the intact sperm by pelleting the sperm, removing the victim's fraction, and repeatedly washing the sperm pellet. An alternative approach that does not require washing steps is to digest with Proteinase K, pellet the sperm, remove the victim's fraction, and then digest the residual victim's DNA with a nuclease. METHODS: The nuclease approach has been commercialized in a product, the Erase Sperm Isolation Kit (PTC Labs, Columbia, MO, USA), and five crime laboratories have tested it on semen-spiked female buccal swabs in a direct comparison with their standard methods. Comparisons have also been performed on timed post-coital vaginal swabs and evidence collected from sexual assault cases. RESULTS: For the semen-spiked buccal swabs, Erase outperformed the standard methods in all five laboratories and in most cases was able to provide a clean male profile from buccal swabs spiked with only 1,500 sperm. The vaginal swabs taken after consensual sex and the evidence collected from rape victims showed a similar pattern of Erase providing superior profiles. CONCLUSIONS: In all samples tested, STR profiles of the male DNA fractions obtained with Erase were as good as or better than those obtained using the standard methods.

Distributional equivalence and subcompositional coherence in the analysis of contingency tables, ratio-scale measurements and compositional data

We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices to analyse the ratios of the data values. The usual approach to dimension reduction in compositional data analysis is to perform principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence. We show that by introducing weights for the rows and columns, the method achieves this desirable property. This weighted log-ratio analysis is theoretically equivalent to spectral mapping , a multivariate method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship between spectral mapping and correspondence analysis is also explained, as well as their connection with association modelling. The weighted log-ratio methodology is applied here to frequency data in linguistics and to chemical compositional data in archaeology.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Cerebrospinal fluid PCR analysis and biochemistry in bodies with severe decomposition.

The aim of this study was to assess whether Neisseria meningitidis, Listeria monocytogenes, Streptococcus pneumoniae and Haemophilus influenzae can be identified using the polymerase chain reaction technique in the cerebrospinal fluid of severely decomposed bodies with known, noninfectious causes of death or whether postmortem changes can lead to false positive results and thus erroneous diagnostic information. Biochemical investigations, postmortem bacteriology and real-time polymerase chain reaction analysis in cerebrospinal fluid were performed in a series of medico-legal autopsies that included noninfectious causes of death with decomposition, bacterial meningitis without decomposition, bacterial meningitis with decomposition, low respiratory tract infections with decomposition and abdominal infections with decomposition. In noninfectious causes of death with decomposition, postmortem investigations failed to reveal results consistent with generalized inflammation or bacterial infections at the time of death. Real-time polymerase chain reaction analysis in cerebrospinal fluid did not identify the studied bacteria in any of these cases. The results of this study highlight the usefulness of molecular approaches in bacteriology as well as the use of alternative biological samples in postmortem biochemistry in order to obtain suitable information even in corpses with severe decompositional changes.

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.

Analysis of matched matrices

We consider the joint visualization of two matrices which have common rowsand columns, for example multivariate data observed at two time pointsor split accord-ing to a dichotomous variable. Methods of interest includeprincipal components analysis for interval-scaled data, or correspondenceanalysis for frequency data or ratio-scaled variables on commensuratescales. A simple result in matrix algebra shows that by setting up thematrices in a particular block format, matrix sum and difference componentscan be visualized. The case when we have more than two matrices is alsodiscussed and the methodology is applied to data from the InternationalSocial Survey Program.

Genome-Wide Prediction Methods in Highly Diverse and Heterozygous Species: Proof-of-Concept through Simulation in Grapevine.

Nowadays, genome-wide association studies (GWAS) and genomic selection (GS) methods which use genome-wide marker data for phenotype prediction are of much potential interest in plant breeding. However, to our knowledge, no studies have been performed yet on the predictive ability of these methods for structured traits when using training populations with high levels of genetic diversity. Such an example of a highly heterozygous, perennial species is grapevine. The present study compares the accuracy of models based on GWAS or GS alone, or in combination, for predicting simple or complex traits, linked or not with population structure. In order to explore the relevance of these methods in this context, we performed simulations using approx 90,000 SNPs on a population of 3,000 individuals structured into three groups and corresponding to published diversity grapevine data. To estimate the parameters of the prediction models, we defined four training populations of 1,000 individuals, corresponding to these three groups and a core collection. Finally, to estimate the accuracy of the models, we also simulated four breeding populations of 200 individuals. Although prediction accuracy was low when breeding populations were too distant from the training populations, high accuracy levels were obtained using the sole core-collection as training population. The highest prediction accuracy was obtained (up to 0.9) using the combined GWAS-GS model. We thus recommend using the combined prediction model and a core-collection as training population for grapevine breeding or for other important economic crops with the same characteristics.