Documentación espacial del patrimonio: preservación de la información. Necesidades, posibilidades, estrategias y estándares

[ES] La parte práctica de esta tesis se centra en un proyecto ERASMUS realizado en el Monasterio de San Prudencio de Monte Laturce (Clavijo, La Rioja). Dicho proyecto aparece descrito en varios registros de este mismo repositorio a los que se puede acceder a través del siguiente:

[B_Muskiz_Muñatones] Documentación geométrica y modelado virtual del Castillo de Muñatones (Muskiz, Bizkaia)

[ES] Este proyecto tuvo una continuación en 2008, cuando se documentó la muralla interior del castillo. Este trabajo también está disponible en este repositorio. Asimismo, algunos artículos y proyectos fin de carrera hacen referencia a los datos capturados en este proyecto. En concreto, los registros relacionados son los siguientes:

Uso de la Realidad Aumentada para facilitar la lectura e interpretación de planos

[ES] Este proyecto genera productos adicionales de trabajos también disponibles en el repositori, en concreto:

Problems when generating virtual models representing real objects: Hondarribia walls

[EN] This paper is based in the following project:

Reflexiones sobre la puesta en valor del Monasterio de San Prudencio de Monte Laturce

[ES] Los datos de este registro provienen de la una actividad académica que también aparece descrita en el repositorio y desde donde se puede acceder a otros trabajos relacionados con el Monasterio:

A geometric analysis of convex demixing

Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components; and (iii) identifying a binary codeword with impulsive corruptions. This thesis describes and analyzes a convex optimization framework for solving an array of demixing problems.

Our framework includes a random orientation model for the constituent signals that ensures the structures are incoherent. This work introduces a summary parameter, the statistical dimension, that reflects the intrinsic complexity of a signal. The main result indicates that the difficulty of demixing under this random model depends only on the total complexity of the constituent signals involved: demixing succeeds with high probability when the sum of the complexities is less than the ambient dimension; otherwise, it fails with high probability.

The fact that a phase transition between success and failure occurs in demixing is a consequence of a new inequality in conic integral geometry. Roughly speaking, this inequality asserts that a convex cone behaves like a subspace whose dimension is equal to the statistical dimension of the cone. When combined with a geometric optimality condition for demixing, this inequality provides precise quantitative information about the phase transition, including the location and width of the transition region.

Modelo de representación y difusión de cavidades. Cueva de Praileaitz. Deba, Gipuzkoa

[ES] Este artículo está basado en el siguiente proyecto que también puede ser consultado en este repositorio:

Rank-preserving geometric means of positive semi-definite matrices

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces.© 2012 Elsevier Inc. All rights reserved.

Geometric phase of a bipartite system with Dzyaloshinski-Moriya interaction

The Berry phase of a bipartite system described by a Heisenberg XXZ model driven by a one-site magnetic field is investigated. The effect of the Dzyaloshinski-Moriya (DM) anisotropic interaction on the Berry phase is discussed. It is found that the DM interaction affects the Berry phase monotonously. and can also cause sudden change of the Berry phase for some weak magnetic field cases. (c) 2008 Elsevier B.V. All rights reserved.

Ultrafast geometric manipulation of electron spin and detection of the geometric phase via Faraday rotation spectroscopy

Time-resolved Faraday rotation spectroscopy is currently exploited as a powerful technique to probe spin dynamics in semiconductors. We propose here an all-optical approach to geometrically manipulate electron spin and to detect the geometric phase by this type of extremely sensitive experiment. The global nature of the geometric phase can make the quantum manipulation more stable, which may find interesting applications in quantum devices.