Nonlinear Stability of Riemann Ellipsoids with Symmetric Configurations

We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Riemann ellipsoids having at least two equal axes

Bose-Einstein condensates in deformed traps

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2015, Tutor: Bruno Juliá-DíazIn this degree thesis we study the properties of a Bose-Einstein condensate confined in both isotropic and anisotropic traps using a mean-field description in terms of the Gross-Pitaevskii equation and modified Gross-Pitaevskii equation. We also study the many particle limit and compare it with the Thomas-Fermi limits. Finally we study the aspect ratio of the system and see how it changes for the noninteracting limit and the strong repulsive limit

A Framework for Fast Image Deconvolution with Incomplete Observations

In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard deconvolution techniques normally involve non-diagonalizable operators, resulting in rather slow methods, or, otherwise, use inexact convolution models, resulting in the occurrence of artifacts in the enhanced images. In this paper, we propose a new deconvolution framework for images with incomplete observations that allows us to work with diagonalized convolution operators, and therefore is very fast. We iteratively alternate the estimation of the unknown pixels and of the deconvolved image, using, e.g., an FFT-based deconvolution method. This framework is an efficient, high-quality alternative to existing methods of dealing with the image boundaries, such as edge tapering. It can be used with any fast deconvolution method. We give an example in which a state-of-the-art method that assumes periodic boundary conditions is extended, through the use of this framework, to unknown boundary conditions. Furthermore, we propose a specific implementation of this framework, based on the alternating direction method of multipliers (ADMM). We provide a proof of convergence for the resulting algorithm, which can be seen as a "partial" ADMM, in which not all variables are dualized. We report experimental comparisons with other primal-dual methods, where the proposed one performed at the level of the state of the art. Four different kinds of applications were tested in the experiments: deconvolution, deconvolution with inpainting, superresolution, and demosaicing, all with unknown boundaries.Comment: IEEE Trans. Image Process., to be published. 15 pages, 11 figures. MATLAB code available at https://github.com/alfaiate/DeconvolutionIncompleteOb

A convex formulation for hyperspectral image superresolution via subspace-based regularization

Hyperspectral remote sensing images (HSIs) usually have high spectral resolution and low spatial resolution. Conversely, multispectral images (MSIs) usually have low spectral and high spatial resolutions. The problem of inferring images which combine the high spectral and high spatial resolutions of HSIs and MSIs, respectively, is a data fusion problem that has been the focus of recent active research due to the increasing availability of HSIs and MSIs retrieved from the same geographical area. We formulate this problem as the minimization of a convex objective function containing two quadratic data-fitting terms and an edge-preserving regularizer. The data-fitting terms account for blur, different resolutions, and additive noise. The regularizer, a form of vector Total Variation, promotes piecewise-smooth solutions with discontinuities aligned across the hyperspectral bands. The downsampling operator accounting for the different spatial resolutions, the non-quadratic and non-smooth nature of the regularizer, and the very large size of the HSI to be estimated lead to a hard optimization problem. We deal with these difficulties by exploiting the fact that HSIs generally "live" in a low-dimensional subspace and by tailoring the Split Augmented Lagrangian Shrinkage Algorithm (SALSA), which is an instance of the Alternating Direction Method of Multipliers (ADMM), to this optimization problem, by means of a convenient variable splitting. The spatial blur and the spectral linear operators linked, respectively, with the HSI and MSI acquisition processes are also estimated, and we obtain an effective algorithm that outperforms the state-of-the-art, as illustrated in a series of experiments with simulated and real-life data.Comment: IEEE Trans. Geosci. Remote Sens., to be publishe

The basis determinants : the european case

With subprime mortgage crisis, Lehman Brothers Holdings Inc. bankruptcy and European government credit crisis, the CDS market assisted to a generalized turmoil, contributing for a decrease of CDS market in more than 50% in less than 3 years. This dissertation focuses on testing possible determinants of the basis spread for several European companies, analysing data between June 18 2008 and December 31 2012. All financial information and data used in this thesis was gathered from Bloomberg. Literature on single-name credit modelling and valuing credit derivatives is revised and applied to calculate the basis, with special focus on estimating hazard rates, where we used the optimization method instead of the generally used bootstrap method. We than, followed Zhu work and analysed the proposed determinants for the basis, updating his work by introducing two new variables as potential determinants of the basis: the CDS Big Bang and the Lehman Brothers bailout. Finally, we have found some evidence that efforts to standardize and regulate the credit derivative contracts, the CDS Big Bang has contributed to mitigate part of the counterpart risk, and that have also been reflected on the CDS-ASW basis