Strong asymptotics for orthogoal polynomials with varying measures and Hermite-Padé approximants

13 pages, no figures.-- MSC1991 codes: 42C05; 30E10.-- Issue title: "Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Application" (Seville, Spain, Sep. 1997), edited by Antonio J. Durán.MR#: MR1662686 (99i:42035)Zbl#: Zbl 0933.42017The strong asymptotic behaviour of orthogonal polynomials with respect to a general class of varying measures is given for the case of the unit circle and the real line. These results are used to obtain certain asymptotic relations for the polynomials involved in the construction of Hermite-Padé approximants of a Nikishin system of functions.The research of the second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad

Weak convergence of varying measures and Hermite-Padé orthogonal polynomials

23 pages, no figures.-- MSC1991 codes: 42C05, 30E10.MR#: MR1702795 (2000j:42036)Zbl#: Zbl 1058.42503It is known that the common denominator of the Hermite-Padé approximants of a mixed Angelesco-Nikishin system shares orthogonality relations with respect to each function in the system. It is less well known that they also satisfy full orthogonality with respect to a varying measure. This problem motivates our interest in extending the class of varying measures with respect to which weak asymptotics of orthogonal polynomials takes place. In particular, for the case of a Nikishin system, we prove weak asymptotics of the corresponding varying measures.Research by second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad

Convergence of multipoint Padé-type approximants

22 pages, no figures.-- MSC2000 code: 41A21.MR#: MR1820896 (2002a:41014)Zbl#: Zbl 0982.41008Let μ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in \bbfC\setminus I\$ and r(\infty)=0$. We consider multipoint rational interpolants of the function$$f(z)=\int {d\mu(x)\over z-x}+r(z)$$, where some poles are fixed and others are left free. We show that if the interpolation points and the fixed poles are chosen conveniently then the sequence of multipoint rational approximants converges geometrically to f in the chordal metric on compact subsets of$\bbfC\setminus I\$.The second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under Grant PB 96-0120-C03-01 and by INTAS under Grant 93-0219 EXT.Publicad

Convergencia relativa de polinomios ortogonales variantes

12 pages, no figures.-- MSC2000 codes: Primary: 42C05, 30E15; Secondary: 30E10.We consider the relative asymptotic behaviour of orthogonal polynomials with respect to varying measures supported on the real line and the unit circle. The main feature of the results is the generality of the class of measures studied.El trabajo de los dos autores ha sido parcialmente financiado por la Dirección General de Investigación, Ministerio de Ciencia y Tecnología, a través del proyecto BFM2000-0206-C04-01 y además, en el caso de G. López, por el INTAS.Publicad

Modelo basado en técnicas de procesamiento de lenguaje natural para extraer y anotar información de publicaciones científicas

La rápida evolución experimentada en los últimos años por las tecnologías de Internet ha estimulado la proliferación de recursos software en varias disciplinas científicas, especialmente en bioinformática. En la mayoría de los casos, la tendencia actual es publicar dichos recursos como servicios accesibles libremente a través de Internet, utilizando tecnologías y patrones de diseño definidos para la implementación de Arquitecturas Orientadas a Servicios (SOA). La combinación simultánea de múltiples servicios dentro de un mismo flujo de trabajo abre la posibilidad de crear aplicaciones potencialmente más útiles y complejas. La integración de dichos servicios plantea grandes desafíos, tanto desde un punto de vista teórico como práctico, como por ejemplo, la localización y acceso a los recursos disponibles o la coordinación entre ellos. En esta tesis doctoral se aborda el problema de la identificación, localización, clasificación y acceso a los recursos informáticos disponibles en Internet. Con este fin, se ha definido un modelo genérico para la construcción de índices de recursos software con información extraída automáticamente de artículos de la literatura científica especializada en un área. Este modelo consta de seis fases que abarcan desde la selección de las fuentes de datos hasta el acceso a los índices creados, pasando por la identificación, extracción, clasificación y “curación” de la información relativa a los recursos. Para verificar la viabilidad, idoneidad y eficiencia del modelo propuesto, éste ha sido evaluado en dos dominios científicos diferentes—la BioInformática y la Informática Médica—dando lugar a dos índices de recursos denominados BioInformatics Resource Inventory (BIRI) y electronic-Medical Informatics Repository of Resources(e-MIR2) respectivamente. Los resultados obtenidos de estas aplicaciones son presentados a lo largo de la presente tesis doctoral y han dado lugar a varias publicaciones científicas en diferentes revistas JCR y congresos internacionales. El impacto potencial y la utilidad de esta tesis doctoral podrían resultar muy importantes teniendo en cuenta que, gracias a la generalidad del modelo propuesto, éste podría ser aplicado en cualquier disciplina científica. Algunas de las líneas de investigación futuras más relevantes derivadas de este trabajo son esbozadas al final en el último capítulo de este libro. ABSTRACT The rapid evolution experimented in the last years by the Internet technologies has stimulated the proliferation of heterogeneous software resources in most scientific disciplines, especially in the bioinformatics area. In most cases, current trends aim to publish those resources as services freely available over the Internet, using technologies and design patterns defined for the implementation of Service-Oriented Architectures (SOA). Simultaneous combination of various services into the same workflow opens the opportunity of creating more complex and useful applications. Integration of services raises great challenges, both from a theoretical to a practical point of view such as, for instance, the location and access to the available resources or the orchestration among them. This PhD thesis deals with the problem of identification, location, classification and access to informatics resources available over the Internet. On this regard, a general model has been defined for building indexes of software resources, with information extracted automatically from scientific articles from the literature specialized in the area. Such model consists of six phases ranging from the selection of data sources to the access to the indexes created, covering the identification, extraction, classification and curation of the information related to the software resources. To verify the viability, feasibility and efficiency of the proposed model, it has been evaluated in two different scientific domains—Bioinformatics and Medical Informatics—producing two resources indexes named BioInformatics Resources Inventory (BIRI) and electronic-Medical Informatics Repository of Resources (e-MIR2) respectively. The results and evaluation of those systems are presented along this PhD thesis, and they have produced different scientific publications in several JCR journals and international conferences. The potential impact and utility of this PhD thesis could be of great relevance considering that, thanks to the generality of the proposed model, it could be successfully extended to any scientific discipline. Some of the most relevant future research lines derived from this work are outlined at the end of this book

Stieltjes-type polynomials on the unit circle

29 pages, no figures.-- MSC2000 codes: Primary 65D32, 42A10, 42C05; Secondary 30E20.MR#: MR2476567Stieltjes-type polynomials corresponding to measures supported on the unit circle T are introduced and their asymptotic properties away from T are studied for general classes of measures. As an application, we prove the convergence of an associated sequence of interpolating rational functions to the corresponding Carathéodory function. In turn, this is used to give an estimate of the rate of convergence of certain quadrature formulae that resemble the Gauss-Kronrod rule, provided that the integrand is analytic in a neighborhood of T.The work of B. de la Calle received support from Dirección General de Investigación (DGI), Ministerio de Educación y Ciencia, under grants MTM2006-13000-C03-02 and MTM2006-07186 and from UPM-CAM under grants CCG07-UPM/000-1652 and CCG07-UPM/ESP-1896. The work of G. López was supported by DGI under grant MTM2006-13000-C03-02 and by UC3M-CAM through CCG06-UC3M/ESP-0690. The work of L. Reichel was supported by an OBR Research Challenge Grant.Publicad

Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures

34 pages, no figures.-- MSC1991 codes: 42C05, 41A28.-- Dedicated to Barry Simon on the occasion of his sixtieth birthday.MR#: MR2220040 (2006m:42002)Zbl#: Zbl 1100.42014Let μ be a finite positive Borel measure with compact support consisting of an interval [c,d] ⊂ R plus a set of isolated points in R\[c,d], such that μ′>0 almost everywhere on [c,d]. Let $\{w_{2n}\}$, $n\in\Bbb Z_+$, be a sequence of polynomials, $\deg w_{2n}\leq2n$, with real coefficients whose zeros lie outside the smallest interval containing the support of μ. We prove ratio and relative asymptotics of sequences of orthogonal polynomials with respect to varying measures of the form $\frac{d\mu_n}{w_{2n}}$. In particular, we obtain an analogue for varying measures of Denisov's extension of Rakhmanov's theorem on ratio asymptotics. These results on varying measures are applied to obtain ratio asymptotics for orthogonal polynomials with respect to fixed measures on the unit circle and for multi-orthogonal polynomials in which the measures involved are of the type described above.Research of D.B. Rolanía was partially supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grant BFM 2003-06335-C03-02. Research of de la Calle Ysern was supported by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grants BFM 2002-04315-C02-01 and BFM 2003-06335-C03-02. Research of G.L. Lagomasino was supported by Grants INTAS 03-516637, NATO PST.CLG.979738, and by Dirección General de Investigación, Ministerio de Ciencia y Tecnología, under Grant BFM 2003-06335-C03-02.Publicad

Direct and Inverse Results on Row Sequences of Hermite-Padé Approximation

We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of simultaneous rational interpolants with a bounded number of poles. The conditions are expressed in terms of intrinsic properties of the system of functions used to build the approximants. Exact rates of convergence for these denominators and the simultaneous rational approximants are provided.The work of B. de la Calle Ysern received support from MINCINN under grant MTM2009-14668-C02-02 and from UPM through Research Group “Constructive Approximation Theory and Applications”. The work of J. Cacoq and G. López was supported by Ministerio de Economía y Competitividad under grants MTM2009-12740-C03-01 and MTM2012-36372-C03-01

The dicode workbench: A flexible framework for the integration of information and web services

Aiming to address requirements concerning integration of services in the context of ?big data?, this paper presents an innovative approach that (i) ensures a flexible, adaptable and scalable information and computation infrastructure, and (ii) exploits the competences of stakeholders and information workers to meaningfully confront information management issues such as information characterization, classification and interpretation, thus incorporating the underlying collective intelligence. Our approach pays much attention to the issues of usability and ease-of-use, not requiring any particular programming expertise from the end users. We report on a series of technical issues concerning the desired flexibility of the proposed integration framework and we provide related recommendations to developers of such solutions. Evaluation results are also discussed

A Method for Indexing Biomedical Resources over the Internet

A large number of biomedical resources are publicly available over the Internet. This number grows every day. Biomedical researchers face the problem of locating, identifying and selecting the most appropriate resources according to their interests. Some resource indexes can be found in the Internet, but they only provide information and links related to resources created by the owner institution of each website. In this paper we propose a novel method for extracting information from the literature and create a Resourceome, i.e. an index of biomedical resources (databases, tools and services) in a semi-automatic way. In this approach we consider only the information provided by the abstracts of relevant papers in the area. Building a comprehensive resource index is the first step towards the development of new methodologies for the automatic or semi-automatic construction of complex biomedical workflows which allow combining several resources to obtain higher-level functionalities