Maximal operators and differentiation theorems for sparse sets

"Vegeu el resum a l'inici del document del fitxer adjunt."

Spectral analysis of random sparse matrices

"Vegeu el resum a l'inici del document del fitxer adjunt."

Implementation of zonal control algorithms in adaptive optical systems with sparse control matrices

Miralls deformables més i més grans, amb cada cop més actuadors estan sent utilitzats actualment en aplicacions d'òptica adaptativa. El control dels miralls amb centenars d'actuadors és un tema de gran interès, ja que les tècniques de control clàssiques basades en la seudoinversa de la matriu de control del sistema es tornen massa lentes quan es tracta de matrius de dimensions tan grans. En aquesta tesi doctoral es proposa un mètode per l'acceleració i la paral.lelitzacó dels algoritmes de control d'aquests miralls, a través de l'aplicació d'una tècnica de control basada en la reducció a zero del components més petits de la matriu de control (sparsification), seguida de l'optimització de l'ordenació dels accionadors de comandament atenent d'acord a la forma de la matriu, i finalment de la seva posterior divisió en petits blocs tridiagonals. Aquests blocs són molt més petits i més fàcils de fer servir en els càlculs, el que permet velocitats de càlcul molt superiors per l'eliminació dels components nuls en la matriu de control. A més, aquest enfocament permet la paral.lelització del càlcul, donant una com0onent de velocitat addicional al sistema. Fins i tot sense paral. lelització, s'ha obtingut un augment de gairebé un 40% de la velocitat de convergència dels miralls amb només 37 actuadors, mitjançant la tècnica proposada. Per validar això, s'ha implementat un muntatge experimental nou complet , que inclou un modulador de fase programable per a la generació de turbulència mitjançant pantalles de fase, i s'ha desenvolupat un model complert del bucle de control per investigar el rendiment de l'algorisme proposat. Els resultats, tant en la simulació com experimentalment, mostren l'equivalència total en els valors de desviació després de la compensació dels diferents tipus d'aberracions per als diferents algoritmes utilitzats, encara que el mètode proposat aquí permet una càrrega computacional molt menor. El procediment s'espera que sigui molt exitós quan s'aplica a miralls molt grans.

Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

A Sparse Bayesian Approach for Joint Feature Selection and Classifier Learning

Peer-reviewed

Extracció del mapa de profunditat a partir d'una seqüència d'imatges

Aquest projecte resol les fases inicials d'un altre projecte més gran que té com a objectiu la conversió automàtica de seqüències d'imatges a 3D. El projecte s'ha centrat en la reconstrucció calibrada de col·leccions d'imatges mitjançant la tècnica anomenada structure from motion. Aquesta tècnica forma part de l'àmbit de la visió per computador i s'utilitza per obtenir la posició i l'orientació de les diferents càmeres juntament amb una reconstrucció 3D de l'escena en forma de núvol de punts.

Desarrollo de software para el procesado numérico en tarjetas gráficas

Debido al gran número de transistores por mm2 que hoy en día podemos encontrar en las GPU convencionales, en los últimos años éstas se vienen utilizando para propósitos generales gracias a que ofrecen un mayor rendimiento para computación paralela. Este proyecto implementa el producto sparse matrix-vector sobre OpenCL. En los primeros capítulos hacemos una revisión de la base teórica necesaria para comprender el problema. Después veremos los fundamentos de OpenCL y del hardware sobre el que se ejecutarán las librerías desarrolladas. En el siguiente capítulo seguiremos con una descripción del código de los kernels y de su flujo de datos. Finalmente, el software es evaluado basándose en comparativas con la CPU.

Sound Texture Modelling

In the PhD thesis “Sound Texture Modeling” we deal with statistical modelling or textural sounds like water, wind, rain, etc. For synthesis and classification. Our initial model is based on a wavelet tree signal decomposition and the modeling of the resulting sequence by means of a parametric probabilistic model, that can be situated within the family of models trainable via expectation maximization (hidden Markov tree model ). Our model is able to capture key characteristics of the source textures (water, rain, fire, applause, crowd chatter ), and faithfully reproduces some of the sound classes. In terms of a more general taxonomy of natural events proposed by Graver, we worked on models for natural event classification and segmentation. While the event labels comprise physical interactions between materials that do not have textural propierties in their enterity, those segmentation models can help in identifying textural portions of an audio recording useful for analysis and resynthesis. Following our work on concatenative synthesis of musical instruments, we have developed a pattern-based synthesis system, that allows to sonically explore a database of units by means of their representation in a perceptual feature space. Concatenative syntyhesis with “molecules” built from sparse atomic representations also allows capture low-level correlations in perceptual audio features, while facilitating the manipulation of textural sounds based on their physical and perceptual properties. We have approached the problem of sound texture modelling for synthesis from different directions, namely a low-level signal-theoretic point of view through a wavelet transform, and a more high-level point of view driven by perceptual audio features in the concatenative synthesis setting. The developed framework provides unified approach to the high-quality resynthesis of natural texture sounds. Our research is embedded within the Metaverse 1 European project (2008-2011), where our models are contributting as low level building blocks within a semi-automated soundscape generation system.

On iterative performance of LDPC and Root-LDPC codes over block-fading channels

This paper presents our investigation on iterativedecoding performances of some sparse-graph codes on block-fading Rayleigh channels. The considered code ensembles are standard LDPC codes and Root-LDPC codes, first proposed in and shown to be able to attain the full transmission diversity. We study the iterative threshold performance of those codes as a function of fading gains of the transmission channel and propose a numerical approximation of the iterative threshold versus fading gains, both both LDPC and Root-LDPC codes.Also, we show analytically that, in the case of 2 fading blocks,the iterative threshold root of Root-LDPC codes is proportional to (α1 α2)1, where α1 and α2 are corresponding fading gains.From this result, the full diversity property of Root-LDPC codes immediately follows.

Using qualia information to identify lexical semantic classes in an unsupervised clustering task

Acquiring lexical information is a complex problem, typically approached by relying on a number of contexts to contribute information for classification. One of the first issues to address in this domain is the determination of such contexts. The work presented here proposes the use of automatically obtained FORMAL role descriptors as features used to draw nouns from the same lexical semantic class together in an unsupervised clustering task. We have dealt with three lexical semantic classes (HUMAN, LOCATION and EVENT) in English. The results obtained show that it is possible to discriminate between elements from different lexical semantic classes using only FORMAL role information, hence validating our initial hypothesis. Also, iterating our method accurately accounts for fine-grained distinctions within lexical classes, namely distinctions involving ambiguous expressions. Moreover, a filtering and bootstrapping strategy employed in extracting FORMAL role descriptors proved to minimize effects of sparse data and noise in our task.

Nets: Network estimation for time series

This work proposes novel network analysis techniques for multivariate time series.We define the network of a multivariate time series as a graph where verticesdenote the components of the process and edges denote non zero long run partialcorrelations. We then introduce a two step LASSO procedure, called NETS, toestimate high dimensional sparse Long Run Partial Correlation networks. This approachis based on a VAR approximation of the process and allows to decomposethe long run linkages into the contribution of the dynamic and contemporaneousdependence relations of the system. The large sample properties of the estimatorare analysed and we establish conditions for consistent selection and estimation ofthe non zero long run partial correlations. The methodology is illustrated with anapplication to a panel of U.S. bluechips.

Communication in networks with hierarchical branching

We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.

Exemplar-based interpolation of sparsely sampled images

A nonlocal variational formulation for interpolating a sparsel sampled image is introduced in this paper. The proposed variational formulation, originally motivated by image inpainting problems, encouragesthe transfer of information between similar image patches, following the paradigm of exemplar-based methods. Contrary to the classical inpaintingproblem, no complete patches are available from the sparse imagesamples, and the patch similarity criterion has to be redefined as here proposed. Initial experimental results with the proposed framework, at very low sampling densities, are very encouraging. We also explore somedepartures from the variational setting, showing a remarkable ability to recover textures at low sampling densities.

The 2010 May Flaring Episode of Cygnus X-3 in Radio, X-rays, and γ-rays

In 2009, Cygnus X-3 (Cyg X-3) became the first microquasar to be detected in the GeV γ-ray regime, via the satellites Fermi and AGILE. The addition of this new band to the observational toolbox holds promise for building a more detailed understanding of the relativistic jets of this and other systems. We present a rich data set of radio, hard and soft X-ray, and γ-ray observations of Cyg X-3 made during a flaring episode in 2010 May. We detect a ~3 day softening and recovery of the X-ray emission, followed almost immediately by a ~1 Jy radio flare at 15 GHz, followed by a 4.3σ γ-ray flare (E > 100 MeV) ~1.5 days later. The radio sampling is sparse, but we use archival data to argue that it is unlikely the γ-ray flare was followed by any significant unobserved radio flares. In this case, the sequencing of the observed events is difficult to explain in a model in which the γ-ray emission is due to inverse Compton scattering of the companion star's radiation field. Our observations suggest that other mechanisms may also be responsible for γ-ray emission from Cyg X-3.

Partial correlation : Network analysis

The final year project came to us as an opportunity to get involved in a topic which has appeared to be attractive during the learning process of majoring in economics: statistics and its application to the analysis of economic data, i.e. econometrics.Moreover, the combination of econometrics and computer science is a very hot topic nowadays, given the Information Technologies boom in the last decades and the consequent exponential increase in the amount of data collected and stored day by day. Data analysts able to deal with Big Data and to find useful results from it are verydemanded in these days and, according to our understanding, the work they do, although sometimes controversial in terms of ethics, is a clear source of value added both for private corporations and the public sector. For these reasons, the essence of this project is the study of a statistical instrument valid for the analysis of large datasets which is directly related to computer science: Partial Correlation Networks.The structure of the project has been determined by our objectives through the development of it. At first, the characteristics of the studied instrument are explained, from the basic ideas up to the features of the model behind it, with the final goal of presenting SPACE model as a tool for estimating interconnections in between elements in large data sets. Afterwards, an illustrated simulation is performed in order to show the power and efficiency of the model presented. And at last, the model is put into practice by analyzing a relatively large data set of real world data, with the objective of assessing whether the proposed statistical instrument is valid and useful when applied to a real multivariate time series. In short, our main goals are to present the model and evaluate if Partial Correlation Network Analysis is an effective, useful instrument and allows finding valuable results from Big Data.As a result, the findings all along this project suggest the Partial Correlation Estimation by Joint Sparse Regression Models approach presented by Peng et al. (2009) to work well under the assumption of sparsity of data. Moreover, partial correlation networks are shown to be a very valid tool to represent cross-sectional interconnections in between elements in large data sets.The scope of this project is however limited, as there are some sections in which deeper analysis would have been appropriate. Considering intertemporal connections in between elements, the choice of the tuning parameter lambda, or a deeper analysis of the results in the real data application are examples of aspects in which this project could be completed.To sum up, the analyzed statistical tool has been proved to be a very useful instrument to find relationships that connect the elements present in a large data set. And after all, partial correlation networks allow the owner of this set to observe and analyze the existing linkages that could have been omitted otherwise.