Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process

A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the problem of discriminating signals produced by different phenomena when the order of the signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and Theoretical (2007

Relationship between rules and technical and tactical contents in minibasket

Las reglas condicionan el desarrollo del juego en cualquier deporte ya que delimita lo que se puede hacer. Se pretende conocer el orden de importancia de las reglas en minibasket, así como los medios técnico-tácticos que se derivan éstas. El método utilizado para la toma de datos ha sido el grupo nominal. Los participantes han sido siete expertos que cumplían unas condiciones mínimas. Con relación a la primera pregunta, el orden de importancia de las reglas ha sido: los pasos, dobles, líneas delimitadoras, faltas, árbitro, reglas de tiempo y puntuación. Con relación a los medios técnico-tácticos que se derivan de las reglas más importantes, a modo de ejemplo, a través de los pasos se aprende el bote, las arrancadas, las paradas, entradas, etc. Estos datos permiten organizar una programación basada en las reglasThe rules determine the development of the game in every sport because they put a limit to what you can do and what not. The aims of the research were to determine the order of importance of the basic basketball rules as well as the technical and tactical contents deriving from these rules. The method used for the data collection was that of the nominal group technique. The nominal group consisted of seven experts who fulfilled the minimum conditions. Regarding the first question, the order of importance of the rules was: steps, double dribble, lines, fouls, referee, rules regarding time limits and score. With regard to the technical and tactical contents deriving from the most important rules, for example, through the steps’ rules, players can learn starts, stops, lay-up, etc. These data allow organizing a program based on the rule

On the Complexity of tt-Closeness Anonymization and Related Problems

An important issue in releasing individual data is to protect the sensitive information from being leaked and maliciously utilized. Famous privacy preserving principles that aim to ensure both data privacy and data integrity, such as $k$-anonymity and $l$-diversity, have been extensively studied both theoretically and empirically. Nonetheless, these widely-adopted principles are still insufficient to prevent attribute disclosure if the attacker has partial knowledge about the overall sensitive data distribution. The $t$-closeness principle has been proposed to fix this, which also has the benefit of supporting numerical sensitive attributes. However, in contrast to $k$-anonymity and $l$-diversity, the theoretical aspect of $t$-closeness has not been well investigated. We initiate the first systematic theoretical study on the $t$-closeness principle under the commonly-used attribute suppression model. We prove that for every constant $t$ such that $0\leq t<1$, it is NP-hard to find an optimal $t$-closeness generalization of a given table. The proof consists of several reductions each of which works for different values of $t$, which together cover the full range. To complement this negative result, we also provide exact and fixed-parameter algorithms. Finally, we answer some open questions regarding the complexity of $k$-anonymity and $l$-diversity left in the literature.Comment: An extended abstract to appear in DASFAA 201

Stabilized Schemes for the Hydrostatic Stokes Equations

Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation ap- proximation for primitive equations requires the well-known Ladyzhenskaya–Babuˇska–Brezzi condi- tion related to the Stokes problem and an extra inf-sup condition relating the pressure and the vertical velocity. The main goal of this paper is to avoid this extra condition by adding a residual stabilizing term to the vertical momentum equation. Then, the stability for Stokes-stable FE combinations is extended to the primitive equations and some error estimates are provided using Taylor–Hood P2 –P1 or miniele- ment (P1 +bubble)–P1 FE approximations, showing the optimal convergence rate in the P2 –P1 case. These results are also extended to the anisotropic (nonhydrostatic) problem. On the other hand, by adding another residual term to the continuity equation, a better approximation of the vertical derivative of pressure is obtained. In this case, stability and error estimates including this better approximation are deduced, where optimal convergence rate is deduced in the (P 1 +bubble)–P1 case. Finally, some numerical experiments are presented supporting previous results

A competitive scheme for storing sparse representation of X-Ray medical images

A competitive scheme for economic storage of the informational content of an X-Ray image, as it can be used for further processing, is presented. It is demonstrated that sparse representation of that type of data can be encapsulated in a small file without affecting the quality of the recovered image. The proposed representation, which is inscribed within the context of data reduction, provides a format for saving the image information in a way that could assist methodologies for analysis and classification. The competitiveness of the resulting file is compared against the compression standards JPEG and JPEG200