Rayleigh-Ritz majorization error bounds with applications to FEM

The Rayleigh-Ritz (RR) method finds the stationary values, called Ritz values, of the Rayleigh quotient on a given trial subspace as approximations to eigenvalues of a Hermitian operator $A$. If the trial subspace is $A$-invariant, the Ritz values are exactly some of the eigenvalues of $A$. Given two subspaces \X and \Y of the same finite dimension, such that \X is $A$-invariant, the absolute changes in the Ritz values of $A$ with respect to \X compared to the Ritz values with respect to \Y represent the RR absolute eigenvalue approximation error. Our first main result is a sharp majorization-type RR error bound in terms of the principal angles between \X and \Y for an arbitrary $A$-invariant \X, which was a conjecture in [SIAM J. Matrix Anal. Appl., 30 (2008), pp. 548-559]. Second, we prove a novel type of RR error bound that deals with the products of the errors, rather than the sums. Third, we establish majorization bounds for the relative errors. We extend our bounds to the case \dim\X\leq\dim\Y<\infty in Hilbert spaces and apply them in the context of the finite element method.Comment: 17 pages. Accepted to SIMA

Notas sobre la historia de la enseñanza del derecho en Estados Unidos.

En estas notas, la autora describe, concisamente, la historia de la enseñanza del derecho en Estados Unidos desde sus orígenes hasta los tiempos modernos. La autora relata los obstáculos que hubo que superar para establecer una cátedra de derecho dentro de la universidad, la influencia que los colegios de abogado y la asociación de facultades de derecho tuvieron en este desarrollo, el establecimiento de la metodología del caso como vehículo pedagógico principal, y la función que tienen los abogados dentro de la sociedad. Estas notas concluyen con una breve descripción de los requerimientos actuales para cursar una carrera de derecho en una universidad acreditada americana.In this brief essay, the author describes the origins of American legal education and situates it within the role that lawyers play within American society. The essay explains the development of the profession from the apprenticeship system to the modem day requirement of a gradúate degree and a bar exam. The essay also covers the creation of the fírst full-time teaching positions, the teaching innovations introduced by C. C. Langdell, the influence of the American Bar Association and the Association of American Law Schools in the movement toward the institutionalization of legal studies. It concludes with a brief account of the modem requirements to enter a program of legal studies at an accredited law school.Publicad

The NOBOX protein becomes undetectable in developmentally competent antral and ovulated oocytes

The oocyte-specific NOBOX protein is an important player during oocyte growth. Its absence in Nobox-/- mice arrests the transition from primordial to growing follicles and down-regulates the expression of a number of genes, including Oct4, a transcription factor crucial in the acquisition of oocyte developmental competence. Despite its role during folliculogenesis, a clear description of the expression of NOBOX throughout oocyte growth is lacking. Here, we have analysed the pattern of expression of both the Nobox gene (qRT-PCR) and its protein (immunofluorescence) during folliculogenesis, classifying the oocytes based on their size (six classes: 10-30, 31-40, 41-50, 51-60, 61-70, 71-80 mm) and chromatin organisation (NSN, Non Surrounded Nucleolus or SN, Surrounded Nucleolus). Significant differences were observed in Nobox transcription in the group of 41-50 mm (NSN > SN), 71-80 mm (NSN > SN) and in developmentally incompetent metaphase II-derived NSN (MIINSN) or competent metaphase II-derived SN (MIISN) oocytes (MIINSN > MIISN). The NOBOX protein is expressed throughout oocyte growth in the nucleus of ovarian NSN and in MIINSN oocytes; in contrast, beginning with SN oocytes of 61-70 mm, it becomes almost undetectable. Our data, while being in line with the hypothesis of a regulative role of NOBOX on Oct4 gene expression at the primordial/primary stage, when both transcription factors are coincidentally expressed, also indicate that this role might not be maintained in the subsequent growing stages. Furthermore, the sharp difference of NOBOX expression in developmentally incompetent or competent oocytes makes this protein a putative marker of their quality

Convergence of genes and cellular pathways dysregulated in autism spectrum disorders

Rare copy-number variation (CNV) is an important source of risk for autism spectrum disorders (ASDs). We analyzed 2,446 ASD-affected families and confirmed an excess of genic deletions and duplications in affected versus control groups (1.41-fold, p = 1.0 × 10(-5)) and an increase in affected subjects carrying exonic pathogenic CNVs overlapping known loci associated with dominant or X-linked ASD and intellectual disability (odds ratio = 12.62, p = 2.7 × 10(-15), ∼3% of ASD subjects). Pathogenic CNVs, often showing variable expressivity, included rare de novo and inherited events at 36 loci, implicating ASD-associated genes (CHD2, HDAC4, and GDI1) previously linked to other neurodevelopmental disorders, as well as other genes such as SETD5, MIR137, and HDAC9. Consistent with hypothesized gender-specific modulators, females with ASD were more likely to have highly penetrant CNVs (p = 0.017) and were also overrepresented among subjects with fragile X syndrome protein targets (p = 0.02). Genes affected by de novo CNVs and/or loss-of-function single-nucleotide variants converged on networks related to neuronal signaling and development, synapse function, and chromatin regulation

Ongoing transients in carbonate compensation

Uptake of anthropogenic CO2 is acidifying the oceans. Over the next 2000 years, this will modify the dissolution and preservation of sedimentary carbonate. By coupling new formulas for the positions of the calcite saturation horizon, zsat, the compensation depth, zcc, and the snowline, zsnow, to a biogeochemical model of the oceanic carbonate system, we evaluate how these horizons will change with ongoing ocean acidification. Our model is an extended Havardton-Bear-type box model, which includes novel kinetic descriptions for carbonate dissolution above, between, and below these critical depths. In the preindustrial ocean, zsat and zcc are at 3939 and 4750 m, respectively. When forced with the IS92a CO2 emission scenario, the model forecasts (1) that zsat will rise rapidly (“runaway” conditions) so that all deep water becomes undersaturated, (2) that zcc will also rise and over 1000 years will pass before it will be stabilized by the dissolution of previously deposited CaCO3, and (3) that zsnow will respond slowly to acidification, rising by ∼1150 m during a 2000 year timeframe. A further simplified model that equates the compensation and saturation depths produces quantitatively different results. Finally, additional feedbacks due to acidification on calcification and increased atmospheric CO2 on organic matter productivity strongly affect the positions of the compensation horizons and their dynamics.

A framework for deriving semantic web services

Web service-based development represents an emerging approach for the development of distributed information systems. Web services have been mainly applied by software practitioners as a means to modularize system functionality that can be offered across a network (e.g., intranet and/or the Internet). Although web services have been predominantly developed as a technical solution for integrating software systems, there is a more business-oriented aspect that developers and enterprises need to deal with in order to benefit from the full potential of web services in an electronic market. This ‘ignored’ aspect is the representation of the semantics underlying the services themselves as well as the ‘things’ that the services manage. Currently languages like the Web Services Description Language (WSDL) provide the syntactic means to describe web services, but lack in providing a semantic underpinning. In order to harvest all the benefits of web services technology, a framework has been developed for deriving business semantics from syntactic descriptions of web services. The benefits of such a framework are two-fold. Firstly, the framework provides a way to gradually construct domain ontologies from previously defined technical services. Secondly, the framework enables the migration of syntactically defined web services toward semantic web services. The study follows a design research approach which (1) identifies the problem area and its relevance from an industrial case study and previous research, (2) develops the framework as a design artifact and (3) evaluates the application of the framework through a relevant scenario

Performance of case-control rare copy number variation annotation in classification of autism

BACKGROUND: A substantial proportion of Autism Spectrum Disorder (ASD) risk resides in de novo germline and rare inherited genetic variation. In particular, rare copy number variation (CNV) contributes to ASD risk in up to 10% of ASD subjects. Despite the striking degree of genetic heterogeneity, case-control studies have detected specific burden of rare disruptive CNV for neuronal and neurodevelopmental pathways. Here, we used machine learning methods to classify ASD subjects and controls, based on rare CNV data and comprehensive gene annotations. We investigated performance of different methods and estimated the percentage of ASD subjects that could be reliably classified based on presumed etiologic CNV they carry. RESULTS: We analyzed 1,892 Caucasian ASD subjects and 2,342 matched controls. Rare CNVs (frequency 1% or less) were detected using Illumina 1M and 1M-Duo BeadChips. Conditional Inference Forest (CF) typically performed as well as or better than other classification methods. We found a maximum AUC (area under the ROC curve) of 0.533 when considering all ASD subjects with rare genic CNVs, corresponding to 7.9% correctly classified ASD subjects and less than 3% incorrectly classified controls; performance was significantly higher when considering only subjects harboring de novo or pathogenic CNVs. We also found rare losses to be more predictive than gains and that curated neurally-relevant annotations (brain expression, synaptic components and neurodevelopmental phenotypes) outperform Gene Ontology and pathway-based annotations. CONCLUSIONS: CF is an optimal classification approach for case-control rare CNV data and it can be used to prioritize subjects with variants potentially contributing to ASD risk not yet recognized. The neurally-relevant annotations used in this study could be successfully applied to rare CNV case-control data-sets for other neuropsychiatric disorders

The evolutionary rewiring of ubiquitination targets has reprogrammed the regulation of carbon assimilation in the pathogenic yeast Candida albicans

Date of Acceptance: 13/11/2012 This is an open-access article distributed under the terms of the Creative Commons Attribution-Noncommercial-ShareAlike 3.0 Unported license, which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original author and source are credited. Correction for Sandai et al., The Evolutionary Rewiring of Ubiquitination Targets Has Reprogrammed the Regulation of Carbon Assimilation in the Pathogenic Yeast Candida albicans published 20-01-2015 DOI: 10.1128/mBio.02489-14Peer reviewedPublisher PD

Analysis of the gene expression profile of mouse male meiotic germ cells

Wide genome analysis of difference in gene expression between spermatogonial populations from 7-day-old mice and pachytene spermatocytes from 18-day-old mice was performed using Affymetrix gene chips representing approximately 12,500 mouse known genes or EST sequences, spanning approximately 1/3rd of the mouse genome. To delineate differences in the profile of gene expression between mitotic and meiotic stages of male germ cell differentiation, expressed genes were grouped in functional clusters. The analysis confirmed the previously described pre-meiotic or meiotic expression for several genes, in particular for those involved in the regulation of the mitotic and meiotic cell cycle, and for those whose transcripts are accumulated during the meiotic stages to be translated later in post-meiotic stages. Differential expression of several additional genes was discovered. In few cases (pro-apoptotic factors Bak, Bad and Bax), data were in conflict with the previously published stage-dependent expression of genes already known to be expressed in male germ cells. Northern blot analysis of selected genes confirmed the results obtained with the microarray chips. Six of these were novel genes specifically expressed in pachytene spermatocytes: a chromatin remodeling factor (chrac1/YCL1), a homeobox gene (hmx1), a novel G-coupled receptor for an unknown ligand (Gpr19), a glycoprotein of the intestinal epithelium (mucin 3), a novel RAS activator (Ranbp9), and the A630056B21Rik gene (predicted to encode a novel zinc finger protein). These studies will help to delineate the global patterns of gene expression characterizing male germ cell differentiation for a better understanding of regulation of spermatogenesis in mammals