Variational Principles for multisymplectic second-order classical field theories

We state a unified geometrical version of the variational principles for second-order classical field theories. The standard Lagrangian and Hamiltonian variational principles and the corresponding field equations are recovered from this unified framework.Comment: 6 pp. Minor corrections. Clarifications and comments have been added. Two new sections ("Introduction" and "The higher-order case") have been added. Bibliography enlarge

A new multisymplectic unified formalism for second-order classical field theories

We present a new multisymplectic framework for second-order classical field theories which is based on an extension of the unified Lagrangian-Hamiltonian formalism to these kinds of systems. This model provides a straightforward and simple way to define the Poincar\'e-Cartan form and clarifies the construction of the Legendre map (univocally obtained as a consequence of the constraint algorithm). Likewise, it removes the undesirable arbitrariness in the solutions to the field equations, which are analyzed in-depth, and written in terms of holonomic sections and multivector fields. Our treatment therefore completes previous attempt to achieve this aim. The formulation is applied to describing some physical examples; in particular, to giving another alternative multisymplectic description of the Korteweg-de Vries equation.Comment: 52 pp. Revision of our previous paper. Minor corrections on the statement of some results. A new example is added (Section 6.1). Conclusions and bibliography have been enlarged, and some comments on the higher-order case have been adde

Universal Indexes for Highly Repetitive Document Collections

Indexing highly repetitive collections has become a relevant problem with the emergence of large repositories of versioned documents, among other applications. These collections may reach huge sizes, but are formed mostly of documents that are near-copies of others. Traditional techniques for indexing these collections fail to properly exploit their regularities in order to reduce space. We introduce new techniques for compressing inverted indexes that exploit this near-copy regularity. They are based on run-length, Lempel-Ziv, or grammar compression of the differential inverted lists, instead of the usual practice of gap-encoding them. We show that, in this highly repetitive setting, our compression methods significantly reduce the space obtained with classical techniques, at the price of moderate slowdowns. Moreover, our best methods are universal, that is, they do not need to know the versioning structure of the collection, nor that a clear versioning structure even exists. We also introduce compressed self-indexes in the comparison. These are designed for general strings (not only natural language texts) and represent the text collection plus the index structure (not an inverted index) in integrated form. We show that these techniques can compress much further, using a small fraction of the space required by our new inverted indexes. Yet, they are orders of magnitude slower.Comment: This research has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie Actions H2020-MSCA-RISE-2015 BIRDS GA No. 69094

RDF-TR: Exploiting structural redundancies to boost RDF compression

The number and volume of semantic data have grown impressively over the last decade, promoting compression as an essential tool for RDF preservation, sharing and management. In contrast to universal compressors, RDF compression techniques are able to detect and exploit specific forms of redundancy in RDF data. Thus, state-of-the-art RDF compressors excel at exploiting syntactic and semantic redundancies, i.e., repetitions in the serialization format and information that can be inferred implicitly. However, little attention has been paid to the existence of structural patterns within the RDF dataset; i.e. structural redundancy. In this paper, we analyze structural regularities in real-world datasets, and show three schema-based sources of redundancies that underpin the schema-relaxed nature of RDF. Then, we propose RDF-Tr (RDF Triples Reorganizer), a preprocessing technique that discovers and removes this kind of redundancy before the RDF dataset is effectively compressed. In particular, RDF-Tr groups subjects that are described by the same predicates, and locally re-codes the objects related to these predicates. Finally, we integrate RDF-Tr with two RDF compressors, HDT and k2-triples. Our experiments show that using RDF-Tr with these compressors improves by up to 2.3 times their original effectiveness, outperforming the most prominent state-of-the-art techniques

Proposta metodològica per a l'estudi de la ceràmica prehistòrica

Títol original: Propuesta metodológica para el estudio de la cerámica prehistóric

¿Cuántos clusters hay en una población?

Sea una población cerrada formada por un número desconocido K y finito de clusters. El método bootstrap es utilizado para estimar el número de clusters que constituyen una población. Se propone un estimador para K, el cual es ajustado y corregido por su sesgo estimado mediante el método bootstrap de Efron (1979). La varianza del "estimador bootstrap" se calcula por el método jackknife agrupado. Mediante simulación, el estimador es comparado con el de Bickel y Yavah (1985)