1,122 research outputs found
Tool for SPARQL Querying over Compact RDF Representations
Presented at the 4th XoveTIC Conference, A Coruña, Spain, 7–8 October 2021.[Abstract] We present an architecture for the efficient storing and querying of large RDF datasets. Our approach seeks to store RDF datasets in very little space while offering complete SPARQL functionality. To achieve this, our proposal was built over HDT, an RDF serialization framework, and its interaction with the Jena query engine. We propose a set of modifications to this framework in order to incorporate a range of space-efficient compact data structures for data storage and access, while using high-level capabilities to answer more complicated SPARQL queries. As a result, our approach provides a standard mechanism for using low-level data structures in complicated query situations requiring SPARQL searches, which are typically not supported by current solutions.This research was funded by Xunta de Galicia/FEDER grant ED431G 2019/01, Xunta de Galicia/FEDER-UE grant IN852A 2018/14; Ministerio de Ciencia, Innovación y Universidades grants [TIN2016-78011-C4-1-R; PID2019-105221RB-C41]; Consellería de Cultura, Educación e Universidade/Consellería de Economía, Empresa e Innovación/GAIN/Xunta de Galicia grant ED431C 2021/53; and by MICINN (PGE/ERDF) grant PID2020-114635RB-I00.Xunta de Galicia; ED431G 2019/01Xunta de Galicia; IN852A 2018/14Xunta de Galicia; ED431C 2021/5
New data structures and algorithms for the efficient management of large spatial datasets
[Resumen] En esta tesis estudiamos la representación eficiente de matrices multidimensionales,
presentando nuevas estructuras de datos compactas para almacenar y procesar
grids en distintos ámbitos de aplicación. Proponemos varias estructuras de datos
estáticas y dinámicas para la representación de matrices binarias o de enteros
y estudiamos aplicaciones a la representación de datos raster en Sistemas de
Información Geográfica, bases de datos RDF, etc.
En primer lugar proponemos una colección de estructuras de datos estáticas para
la representación de matrices binarias y de enteros: 1) una nueva representación
de matrices binarias con grandes grupos de valores uniformes, con aplicaciones
a la representación de datos raster binarios; 2) una nueva estructura de datos
para representar matrices multidimensionales; 3) una nueva estructura de datos
para representar matrices de enteros con soporte para consultas top-k de rango.
También proponemos una nueva representación dinámica de matrices binarias, una
nueva estructura de datos que proporciona las mismas funcionalidades que nuestras
propuestas estáticas pero también soporta cambios en la matriz.
Nuestras estructuras de datos pueden utilizarse en distintos dominios. Proponemos
variantes específicas y combinaciones de nuestras propuestas para representar
grafos temporales, bases de datos RDF, datos raster binarios o generales y
datos raster temporales. También proponemos un nuevo algoritmo para consultar
conjuntamente un conjuto de datos raster (almacenado usando nuestras propuestas)
y un conjunto de datos vectorial almacenado en una estructura de datos clásica,
mostrando que nuestra propuesta puede ser más rápida y usar menos espacio que
otras alternativas. Nuestras representaciones proporcionan interesantes trade-offs y
son competitivas en espacio y tiempos de consulta con representaciones habituales
en los diferentes dominios.[Resumo] Nesta tese estudiamos a representación eficiente de matrices multidimensionais,
presentando novas estruturas de datos compactas para almacenar e procesar grids
en distintos ámbitos de aplicación. Propoñemos varias estruturas de datos estáticas
e dinámicas para a representación de matrices binarias ou de enteiros e estudiamos
aplicacións á representación de datos raster en Sistemas de Información Xeográfica,
bases de datos RDF, etc.
En primeiro lugar propoñemos unha colección de estruturas de datos estáticas
para a representación de matrices binarias e de enteiros: 1) unha nova representación
de matrices binarias con grandes grupos de valores uniformes, con aplicacións
á representación de datos raster binarios; 2) unha nova estrutura de datos
para representar matrices multidimensionais; 3) unha nova estrutura de datos
para representar matrices de enteiros con soporte para consultas top-k. Tamén
propoñemos unha nova representación dinámica de matrices binarias, unha nova
estrutura de datos que proporciona as mesmas funcionalidades que as nosas
propostas estáticas pero tamén soporta cambios na matriz.
As nosas estruturas de datos poden utilizarse en distintos dominios. Propoñemos
variantes específicas e combinacións das nosas propostas para representar grafos temporais,
bases de datos RDF, datos raster binarios ou xerais e datos raster temporais.
Tamén propoñemos un novo algoritmo para consultar conxuntamente datos raster
(almacenados usando as nosas propostas) con datos vectoriais almacenados nunha
estrutura de datos clásica, amosando que a nosa proposta pode ser máis rápida e
usar menos espazo que outras alternativas. As nosas representacións proporcionan
interesantes trade-offs e son competitivas en espazo e tempos de consulta con
representacións habituais nos diferentes dominios.[Abstract] In this thesis we study the efficient representation of multidimensional grids,
presenting new compact data structures to store and query grids in different
application domains. We propose several static and dynamic data structures for the
representation of binary grids and grids of integers, and study applications to the
representation of raster data in Geographic Information Systems, RDF databases,
etc.
We first propose a collection of static data structures for the representation of
binary grids and grids of integers: 1) a new representation of bi-dimensional binary
grids with large clusters of uniform values, with applications to the representation
of binary raster data; 2) a new data structure to represent multidimensional binary
grids; 3) a new data structure to represent grids of integers with support for top-k
range queries. We also propose a new dynamic representation of binary grids, a new
data structure that provides the same functionalities that our static representations
of binary grids but also supports changes in the grid.
Our data structures can be used in several application domains. We propose
specific variants and combinations of our generic proposals to represent temporal
graphs, RDF databases, OLAP databases, binary or general raster data, and
temporal raster data. We also propose a new algorithm to jointly query a raster
dataset (stored using our representations) and a vectorial dataset stored in a classic
data structure, showing that our proposal can be faster and require less space than
the usual alternatives. Our representations provide interesting trade-offs and are
competitive in terms of space and query times with usual representations in the
different domains
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
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
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\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
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 , , be a sequence of polynomials, , 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 . 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
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