On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.Comment: 36 pages, 12 figures; minor changes in the text, matches published versio

Harsanyi Power Solutions for Games on Union Stable Systems

This paper analyzes Harsanyi power solutions for cooperative games in which partial cooperation is based on union stable systems. These structures contain as particular cases the widely studied communication graph games and permission structures, among others. In this context, we provide axiomatic characterizations of the Harsanyi power solutions which distribute the Harsanyi dividends proportional to weights determined by a power measure for union stable systems. Moreover, the well-known Myerson value is exactly the Harsanyi power solution for the equal power measure, and on a special subclass of union stable systems the position value coincides with the Harsanyi power solution obtained for the influence power measure

An Axiomatization of the Banzhaf Value for Cooperative Games on Antimatroids

Cooperative games on antimatroids are cooperative games restricted by a combinatorial structure which generalize the permission structure. So, cooperative games on antimatroids group several well-known families of games which have important applications in economics and politics. Therefore, the study of the restricted games by antimatroids allows to unify criteria of various lines of research. The current paper establishes axioms that determine the restricted Banzhaf value on antimatroids by conditions on the cooperative game and the structure determined by the antimatroid. The set of given axioms generalize the axiomatizations given for the Banzhaf permission values. We also give an axomatization of the restricted Banzhaf value for the smaller class of poset antimatroids. Finally, we apply the above results to auction situations

High pressure oxidation of dimethoxymethane

The oxidation of dimethoxymethane (DMM) has been studied under a wide range of temperatures (373-1073 K), pressures (20-60 bar) and air excess ratios (¿ = 0.7, 1 and 20), from both experimental and modeling points of view. Experimental results have been interpreted and analyzed in terms of a detailed gas-phase chemical kinetic mechanism for describing the DMM oxidation. The results show that the DMM oxidation regime for 20, 40 and 60 bar is very similar for both reducing and stoichiometric conditions. For oxidizing conditions, a plateau in the DMM, CO and CO2 concentration profiles as a function of the temperature can be observed. This zone seems to be associated with the peroxy intermediate, CH3OCH2O2, whose formation and consumption reactions appear to be important for the description of DMM conversion under high pressure and high oxygen concentration conditions

Intelligent SPARQL Endpoints: Optimizing Execution Performance by Automatic Query Relaxation and Queue Scheduling

The Web of Data is widely considered as one of the major global repositories populated with countless interconnected and struc- tured data prompting these linked datasets to be continuously and sharply increasing. In this context the so-called SPARQL Protocol and RDF Query Language is commonly used to retrieve and manage stored data by means of SPARQL endpoints, a query processing service especially designed to get access to these databases. Nevertheless, due to the large amount of data tackled by such endpoints and their structural complex- ity, these services usually suffer from severe performance issues, including inadmissible processing times. This work aims at overcoming this noted inefficiency by designing a distributed parallel system architecture that improves the performance of SPARQL endpoints by incorporating two functionalities: 1) a queuing system to avoid bottlenecks during the exe- cution of SPARQL queries; and 2) an intelligent relaxation of the queries submitted to the endpoint at hand whenever the relaxation itself and the consequently lowered complexity of the query are beneficial for the over- all performance of the system. To this end the system relies on a two-fold optimization criterion: the minimization of the query running time, as predicted by a supervised learning model; and the maximization of the quality of the results of the query as quantified by a measure of similar- ity. These two conflicting optimization criteria are efficiently balanced by two bi-objective heuristic algorithms sequentially executed over groups of SPARQL queries. The approach is validated on a prototype and several experiments that evince the applicability of the proposed scheme