A model for querying semistructured data through the exploitation of regular sub-structures

Much research has been undertaken in order to speed up the processing of semistructured data in general and XML in particular. Many approaches for storage, compression, indexing and querying exist, e.g. [1, 2]. We do not present yet another such algorithm but a unifying model in which these algorithm can be understood. The key idea behind this research is the assumption, that most practical queries are based on a particular pattern of data that can be deduced from the query and which can then be captured using a regular structure amendable to efficient processing techniques

Generating admissible space-time meshes for moving domains in d+1d+1-dimensions

In this paper we present a discontinuous Galerkin finite element method for the solution of the transient Stokes equations on moving domains. For the discretization we use an interior penalty Galerkin approach in space, and an upwind technique in time. The method is based on a decomposition of the space-time cylinder into finite elements. Our focus lies on three-dimensional moving geometries, thus we need to triangulate four dimensional objects. For this we will present an algorithm to generate $d+1$-dimensional simplex space-time meshes and we show under natural assumptions that the resulting space-time meshes are admissible. Further we will show how one can generate a four-dimensional object resolving the domain movement. First numerical results for the transient Stokes equations on triangulations generated with the newly developed meshing algorithm are presented

Compact in-memory representation of XML data : design and implementation of a compressed DOM for data-centric documents

Over recent years XML has evolved from a document exchange format to a multi-purpose data storage and retrieval solution. To make use of the full potential of XML in the domain of large, data-centric documents it is necessary to have easy and fast access to individual data elements. We describe an implementation of the Document Object Model (DOM) that is designed with these objectives in mind. It uses compression to allow large documents to be stored in the computer's main memory. Query-relevant DOM methods are optimised to work on top of the created data structure. Measurements indicate that compression up to a factor of 5 is possible without losing the ability to directly address individual elements. No prior decompression is needed to query and locate nodes

TypEx : a type based approach to XML stream querying

We consider the topic of query evaluation over semistructured information streams, and XML data streams in particular. Streaming evaluation methods are necessarily eventdriven, which is in tension with high-level query models; in general, the more expressive the query language, the harder it is to translate queries into an event-based implementation with finite resource bounds

A positive lower bound for lim inf⁡N→∞∏r=1N∣2sin⁡πrφ∣\liminf_{N\to\infty} \prod_{r=1}^N \left| 2\sin \pi r \varphi \right|

Nearly 60 years ago, Erd\H{o}s and Szekeres raised the question of whether $$\liminf_{N\to \infty} \prod_{r=1}^N \left| 2\sin \pi r \alpha \right| =0$$ for all irrationals $\alpha$. Despite its simple formulation, the question has remained unanswered. It was shown by Lubinsky in 1999 that the answer is yes if $\alpha$ has unbounded continued fraction coefficients, and it was suggested that the answer is yes in general. However, we show in this paper that for the golden ratio $\varphi=(\sqrt{5}-1)/2$, $$\liminf_{N\to \infty} \prod_{r=1}^N \left| 2\sin \pi r \varphi \right| >0 ,$$ providing a negative answer to this long-standing open problem

The auxiliary space preconditioner for the de Rham complex

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of the preconditioners in 4D. Extensive numerical experiments illustrate their performance, practical scalability, and parameter robustness, all in accordance with the theory

Space-Time Isogeometric Analysis of Parabolic Evolution Equations

We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the IgA space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the IgA spaces yields an a priori discretization error estimate with respect to the discrete norm. The theoretical results are confirmed by several numerical experiments with low- and high-order IgA spaces