100 research outputs found

    Dunkl harmonic oscillator and Witten's perturbation on strata

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    The main goal of this work is to use Witten's perturbation method to prove a version of Morse inequalities for the minimum and maximum ideal boundary conditions of the de Rham complex on strata, endowed with adapted metrics, where compact Thom-Mather strati cations are considered. For that purpose, we study rst eigenfunction estimates and embedding results for the Dunkl harmonic oscillator on the line, which are generalized to other related operators on R+. The study of these operators is the key ingredient in our local analysis of the Witten's perturbation. Thus this thesis has two main parts. The rst part is devoted to the study of eigenfunction estimates and embedding results for the Dunkl harmonic oscillator and related operators. The second part deals with the Witten's perturbation on strata, where the rst part is used. This work is published in the preprints [1, 2]. Let us introduce those chapters separately and state their main results

    El modelo de Passinetti: prsentación analítica

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    De formal general, los modelos de crecimiento que incorporan el progreso técnico postulan un crecimiento uniforme y proporcional de la demanda. El rasgo fundamental del análisis de Pasinetti es la relación entre el progreso técnico y la desestructuración del sistema productivo en el largo plazo. En concreto, como los coeficientes de demanda aumentan de forma discontínua, el modelo muestra la tendencia persistente de las economías industriales hacia el paro tecnológico. Este esquema (que corresponde a un sistema económico "natural") es independiente de la organización institucional (economía de mercado o planificada).Passinetti's Model: an Analytical View. All the models of economic growth with technical progress have postulated either uniform and homothetic expansion of demand. The essential feature of Pasinetti's analysis is the link between technical progress and the change of whole production structure over time. In particular, since production coefficients are decreasing over time while demand coefficients increase in a discontinous way the model give rise to the result of a persistent tendency towards technological unemployment. This scheme (the theoretical scheme of a "natural" economic system) is the most relevant to explain the long-term evolution of industrial systems, independent of the institutional organisation

    A Perturbation of the Dunkl Harmonic Oscillator on the Line

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    Let Jσ be the Dunkl harmonic oscillator on R (σ>−1/2. For 00, it is proved that, if σ>u−1/2, then the operator U=Jσ+ξ|x|−2u, with appropriate domain, is essentially self-adjoint in L2(R,|x|2σdx), the Schwartz space S is a core of U¯¯¯¯1/2, and U¯¯¯¯ has a discrete spectrum, which is estimated in terms of the spectrum of Jσ¯¯¯¯¯. A generalization Jσ,τ of Jσ is also considered by taking different parameters σ and τ on even and odd functions. Then extensions of the above result are proved for Jσ,τ, where the perturbation has an additional term involving, either the factor x−1 on odd functions, or the factor x on even functions. Versions of these results on R+ are derivedThe first author was partially supported by MICINN, Grants MTM2011-25656 and MTM2014-56950-P, and by Xunta de Galicia, Grant Consolidación e estructuración 2015 GPC GI-1574. The third author has received financial support from the Xunta de Galicia and the European Union (European Social Fund - ESF)S

    Genetic distance as an alternative to physical distance for definition of gene units in association studies

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    Background: Some association studies, as the implemented in VEGAS, ALIGATOR, i-GSEA4GWAS, GSA-SNP and other software tools, use genes as the unit of analysis. These genes include the coding sequence plus flanking sequences. Polymorphisms in the flanking sequences are of interest because they involve cis-regulatory elements or they inform on untyped genetic variants trough linkage disequilibrium. Gene extensions have customarily been defined as ±50 Kb. This approach is not fully satisfactory because genetic relationships between neighbouring sequences are a function of genetic distances, which are only poorly replaced by physical distances. Results: Standardized recombination rates (SRR) from the deCODE recombination map were used as units of genetic distances. We searched for a SRR producing flanking sequences near the ±50 Kb offset that has been common in previous studies. A SRR≥2 was selected because it led to gene extensions with median length=45.3 Kb and the simplicity of an integer value. As expected, boundaries of the genes defined with the ±50 Kb and with the SRR≥2 rules were rarely concordant. The impact of these differences was illustrated with the interpretation of top association signals from two large studies including many hits and their detailed analysis based in different criteria. The definition based in genetic distance was more concordant with the results of these studies than the based in physical distance. In the analysis of 18 top disease associated loci form the first study, the SRR≥2 genes led to a fully concordant interpretation in 17 loci; the ±50 Kb genes only in 6. Interpretation of the 43 putative functional genes of the second study based in the SRR≥2 definition only missed 4 of the genes, whereas the based in the ±50 Kb definition missed 10 genes. Conclusions: A gene definition based on genetic distance led to results more concordant with expert detailed analyses than the commonly used based in physical distance. The genome coordinates for each gene are provided to maintain a simple use of the new definitions

    Novel Gene-Based Analysis of ASD GWAS: Insight Into the Biological Role of Associated Genes

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    Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by its significant social impact and high heritability. The latest meta-analysis of ASD GWAS (genome-wide association studies) has revealed the association of several SNPs that were replicated in additional sets of independent samples. However, summary statistics from GWAS can be used to perform a gene-based analysis (GBA). GBA allows to combine all genetic information across the gene to create a single statistic (p-value for each gene). Thus, PASCAL (Pathway scoring algorithm), a novel GBA tool, has been applied to the summary statistics from the latest meta-analysis of ASD. GBA approach (testing the gene as a unit) provides an advantage to perform an accurate insight into the biological ASD mechanisms. Therefore, a gene-network analysis and an enrichment analysis for KEGG and GO terms were carried out. GENE2FUNC was used to create gene expression heatmaps and to carry out differential expression analysis (DEA) across GTEx v7 tissues and Brainspan data. dbMDEGA was employed to perform a DEG analysis between ASD and brain control samples for the associated genes and interactors.AA-G was supported by Fundación María José Jove. CR-F was supported by a contract from the ISCIII and FEDERS