Unitary invariants for Hilbert modules of finite rank

We associate a sheaf model to a class of Hilbert modules satisfying a natural finiteness condition. It is obtained as the dual to a linear system of Hermitian vector spaces (in the sense of Grothendieck). A refined notion of curvature is derived from this construction leading to a new unitary invariant for the Hilbert module. A division problem with bounds, originating in Douady's privilege, is related to this framework. A series of concrete computations illustrate the abstract concepts of the paper.

Modified Newton, rank-1 Broyden update and rank-2 BFGS update methods in helicopter trim: A comparative study

Nonlinear equations in mathematical physics and engineering are solved by linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For strongly nonlinear problems, the solution obtained in the iterative process can diverge due to numerical instability. As a result, the application of numerical simulation for strongly nonlinear problems is limited. Helicopter aeroelasticity involves the solution of systems of nonlinear equations in a computationally expensive environment. Reliable solution methods which do not need Jacobian calculation at each iteration are needed for this problem. In this paper, a comparative study is done by incorporating different methods for solving the nonlinear equations in helicopter trim. Three different methods based on calculating the Jacobian at the initial guess are investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Fast acoustic likelihood computation using low-rank matrix approximation

Acoustic modeling using mixtures of multivariate Gaussians is the prevalent approach for many speech processing problems. Computing likelihoods against a large set of Gaussians is required as a part of many speech processing systems and it is the computationally dominant phase for LVCSR systems. We express the likelihood computation as a multiplication of matrices representing augmented feature vectors and Gaussian parameters. The computational gain of this approach over traditional methods is by exploiting the structure of these matrices and efficient implementation of their multiplication.In particular, we explore direct low-rank approximation of the Gaussian parameter matrix and indirect derivation of low-rank factors of the Gaussian parameter matrix by optimum approximation of the likelihood matrix. We show that both the methods lead to similar speedups but the latter leads to far lesser impact on the recognition accuracy. Experiments on a 1138 word vocabulary RM1 task using Sphinx 3.7 system show that, for a typical case the matrix multiplication approach leads to overall speedup of 46%. Both the low-rank approximation methods increase the speedup to around 60%, with the former method increasing the word error rate (WER) from 3.2% to 6.6%, while the latter increases the WER from 3.2% to 3.5%.

Some questions on integral geometry on noncompact symmetric spaces of higher rank

Let be a noncompact symmetric space of higher rank. We consider two types of averages of functions: one, over level sets of the heat kernel on and the other, over geodesic spheres. We prove injectivity results for functions in which extend the results in Pati and Sitaram (Sankya Ser A 62:419-424, 2000).

Fuzzy Approach to Rank Global Climate Models

Eleven coupled model intercomparison project 3 based global climate models are evaluated for the case study of Upper Malaprabha catchment, India for precipitation rate. Correlation coefficient, normalised root mean square deviation, and skill score are considered as performance indicators for evaluation in fuzzy environment and assumed to have equal impact on the global climate models. Fuzzy technique for order preference by similarity to an ideal solution is used to rank global climate models. Top three positions are occupied by MIROC3, GFDL2.1 and GISS with relative closeness of 0.7867, 0.7070, and 0.7068. IPSL-CM4, NCAR-PCMI occupied the tenth and eleventh positions with relative closeness of 0.4959 and 0.4562.

Neighborhoods attributes as determinants of children's academic achievement

Resumen: Los estudios sobre los efectos del vecindario sobre los logros educativos han confirmado la existencia de estos efectos particularmente en la adolescencia. Una deficiencia común de la investigación empírica hasta la fecha, la falta de información en múltiples contextos, se aborda en este trabajo mediante el uso de encuestas escolares de datos para obtener una mayor comprensión sobre el efecto de la pobreza en los niños que cursan el nivel primario de enseñanza en los EE.UU. Este trabajo propone la utilización de un modelo jerárquico lineal de clasificación cruzada para tomar en cuenta en forma apropiada la estructura anidada de la información ya que los niños pertenecen simultáneamente a los dos grupos, el barrio y la escuela. Los resultados que se presentan, basados en la encuesta ECLS-K, una muestra de más de 20000 niños en aproximadamente 1.000 vecindarios y 1200 escuelas 1200, pone de manifiesto la asociación entre la composición socioeconómica del vecindario y los resultados académicos de los estudiantes. Este estudio proporciona evidencia a favor de las teorías de la socialización y epidémica. La presencia de adultos con buen nivel educativo en el vecindario así como la mediana de ingresos tienen impacto positivo en el logro del estudiante. De la misma forma, elevados niveles de pobreza tienen una influencia significativa, pero negativa en los resultados académicos. Sin embargo, el impacto se produce cuando se supera el umbral de 30% de hogares pobres en el vecindario. Los resultados agregados son invariantes a distintas especificaciones en términos de variables, esto no sucede cuando se analizan subgrupos clasificados según su origen étnico, género y estatus socio-económico.

Full Implementation of Rank Dependent Prizes

A manager/mechanism designer must allocate a set of money prizes ($1, $2, .., $n) between n agents working in a team. The agents know the state i.e. who contributed most, second most, etc. The agents' prefer- ences over prizes are state independent. We incorporate the possibility that the manager knows the state with a tiny probability and present a simple mechanism that uniquely implement prizes that respects the true state.

Intensive Program ERASMUS: TOPCART. Geometric Documentation of the Heritage (administrative and academic documentation)

[EN] This academic activity has been the origin of other work that are also located in this repository. The first one is the dataset of information about the geometry of the Monastery recorded during the two years of fieldwork, then some bachelor thesis and papers are listed: