Pseudofermion dynamical theory for the spin dynamical correlation functions of the half-filled 1D Hubbard model

A modified version of the metallic-phase pseudofermion dynamical theory (PDT) of the 1D Hubbard model is introduced for the spin dynamical correlation functions of the half-filled 1D Hubbard model Mott– Hubbard phase. The Mott–Hubbard insulator phase PDT is applied to the study of the model longitudinal and transverse spin dynamical structure factors at finite magnetic field h, focusing in particular on the sin- gularities at excitation energies in the vicinity of the lower thresholds. The relation of our theoretical results to both condensed-matter and ultra-cold atom systems is discussed.

L'anoditzat d'alumini com a eina per a la fabricació de nanomaterials 1D

El projecte se centra en la fabricació de nanomaterials 1D mitjançant una estratègia sintètica, basada en la combinació de metodologies top-down i bottom-up: la deposició de materials diversos a l’interior de l’estructura porosa de l’alúmina anòdica. En una primera etapa del treball, es desenvolupa el procés de fabricació de les membranes poroses, conegut com anoditzat de l’alumini. S’analitzen diversos aspectes del procés per tal d’optimitzar-lo i aconseguir la fabricació de capes poroses d’elevada qualitat de manera controlada, reproduïble i utilitzant un alumini de baixa puresa. Posteriorment, s’avalua la versatilitat de les membranes com a plantilla per a l’obtenció de nanomaterials amb geometria 1D (nanofils i nanotubs) mitjançant tècniques diverses. D’una banda es fabriquen nanofils de níquel magnètics mitjançant tècniques electroquímiques de deposició, amb la novetat que la formació del dipòsit té lloc directament a través del sistema alumini – alúmina. D’altra banda, s’obtenen nanotubs d’òxid de ferro magnètic (Fe3O4) mitjançant la tècnica de deposició per capes atòmiques. Les dues tècniques permeten un alt control de tots els paràmetres estructurals. Finalment, s’inclou un estudi sobre la preparació de membranes poroses d’alúmina anòdica avançades. La principal característica d’aquestes membranes és la modulació a voluntat del diàmetre de porus, resultant en pseudo-nanoestructures 1D.

Posada a punt i validació de l'anàlisi d'urea en llet crua mitjançant IR per transformada de Fourier

L’objectiu principal d’aquest projecte és posar a punt el mètode d’anàlisi d’urea en llet crua de vaca mitjançant la tècnica d’Infraroig per Transformada de Fourier (Fourier Transform Infrared Spectroscopy, FTIR). S’haurà de portar a terme la validació del mètode per FTIR (seguint els criteris de la ISO 17025) mitjançant la comparació amb el mètode de referència utilitzat actualment al laboratori.

Credit risk contributions under the Vasicek one-factor model: a fast wavelet expansion approximation

To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

El Calila e Dimna al Llibre de les bèsties : Breu estudi comparatiu dels contes La serp que atemoreix, La pedra preciosa i La rata transformada en dona, en les versions àrab, catalana i castellana

Breu estudi comparatiu dels contes La serp que atemoreix, La pedra preciosa i La rata transformada en dona, de la versió àrab d'Ibn al-Muqaffa', la verió catalana de Ramon Llull a Llibre de meravelles i Llibre de les bèsties i la versió castellana de Calila e Dimna del 1252.

Desenvolupament de programari per a la compressió d'imatges utilitzant els wavelets com a alternativa a la transformada del cosinus

L'objectiu que es persegueix en aquest treball és el d'aprofundir en el món de les tecnologies emprades en la compressió d'imatges. S'introdueixen els conceptes més elementals per així donar un repàs als diferents mètodes tecnològics que s'utilitzen per a la compressió, mirant en detall un dels estàndards més utilitzats en l'actualitat, el JPEG.

Wavelet analysis residual kriging vs. neural network residual kriging

This paper deals with the problem of spatial data mapping. A new method based on wavelet interpolation and geostatistical prediction (kriging) is proposed. The method - wavelet analysis residual kriging (WARK) - is developed in order to assess the problems rising for highly variable data in presence of spatial trends. In these cases stationary prediction models have very limited application. Wavelet analysis is used to model large-scale structures and kriging of the remaining residuals focuses on small-scale peculiarities. WARK is able to model spatial pattern which features multiscale structure. In the present work WARK is applied to the rainfall data and the results of validation are compared with the ones obtained from neural network residual kriging (NNRK). NNRK is also a residual-based method, which uses artificial neural network to model large-scale non-linear trends. The comparison of the results demonstrates the high quality performance of WARK in predicting hot spots, reproducing global statistical characteristics of the distribution and spatial correlation structure.

Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

High-resolution 3D whole-heart coronary MRA: a study on the combination of data acquisition in multiple breath-holds and 1D residual respiratory motion compensation.

OBJECT: To study a scan protocol for coronary magnetic resonance angiography based on multiple breath-holds featuring 1D motion compensation and to compare the resulting image quality to a navigator-gated free-breathing acquisition. Image reconstruction was performed using L1 regularized iterative SENSE. MATERIALS AND METHODS: The effects of respiratory motion on the Cartesian sampling scheme were minimized by performing data acquisition in multiple breath-holds. During the scan, repetitive readouts through a k-space center were used to detect and correct the respiratory displacement of the heart by exploiting the self-navigation principle in image reconstruction. In vivo experiments were performed in nine healthy volunteers and the resulting image quality was compared to a navigator-gated reference in terms of vessel length and sharpness. RESULTS: Acquisition in breath-hold is an effective method to reduce the scan time by more than 30 % compared to the navigator-gated reference. Although an equivalent mean image quality with respect to the reference was achieved with the proposed method, the 1D motion compensation did not work equally well in all cases. CONCLUSION: In general, the image quality scaled with the robustness of the motion compensation. Nevertheless, the featured setup provides a positive basis for future extension with more advanced motion compensation methods.

Waveform inversion of crosshole georadar data: influence of source wavelet variability and the suitability of a single wavelet assumption

Waveform-based tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of electrical properties in near-surface environments with unprecedented spatial resolution. A critical issue with waveform inversion is the a priori unknown source signal. Indeed, the estimation of the source pulse is notoriously difficult but essential for the effective application of this method. Here, we explore the viability and robustness of a recently proposed deconvolution-based procedure to estimate the source pulse during waveform inversion of crosshole georadar data, where changes in wavelet shape with location as a result of varying near-field conditions and differences in antenna coupling may be significant. Specifically, we examine whether a single, average estimated source current function can adequately represent the pulses radiated at all transmitter locations during a crosshole georadar survey, or whether a separate source wavelet estimation should be performed for each transmitter gather. Tests with synthetic and field data indicate that remarkably good tomographic reconstructions can be obtained using a single estimated source pulse when moderate to strong variability exists in the true source signal with antenna location. Only in the case of very strong variability in the true source pulse are tomographic reconstructions clearly improved by estimating a different source wavelet for each transmitter location.

Multiresolution-based image fusion with additive wavelet decomposition

The standard data fusion methods may not be satisfactory to merge a high-resolution panchromatic image and a low-resolution multispectral image because they can distort the spectral characteristics of the multispectral data. The authors developed a technique, based on multiresolution wavelet decomposition, for the merging and data fusion of such images. The method presented consists of adding the wavelet coefficients of the high-resolution image to the multispectral (low-resolution) data. They have studied several possibilities concluding that the method which produces the best results consists in adding the high order coefficients of the wavelet transform of the panchromatic image to the intensity component (defined as L=(R+G+B)/3) of the multispectral image. The method is, thus, an improvement on standard intensity-hue-saturation (IHS or LHS) mergers. They used the ¿a trous¿ algorithm which allows the use of a dyadic wavelet to merge nondyadic data in a simple and efficient scheme. They used the method to merge SPOT and LANDSATTM images. The technique presented is clearly better than the IHS and LHS mergers in preserving both spectral and spatial information.

A wavelet-based method for the determination of the relative resolution between remotely sensed images

Spatial resolution is a key parameter of all remote sensing satellites and platforms. The nominal spatial resolution of satellites is a well-known characteristic because it is directly related to the area in ground that represents a pixel in the detector. Nevertheless, in practice, the actual resolution of a specific image obtained from a satellite is difficult to know precisely because it depends on many other factors such as atmospheric conditions. However, if one has two or more images of the same region, it is possible to compare their relative resolutions. In this paper, a wavelet-decomposition-based method for the determination of the relative resolution between two remotely sensed images of the same area is proposed. The method can be applied to panchromatic, multispectral, and mixed (one panchromatic and one multispectral) images. As an example, the method was applied to compute the relative resolution between SPOT-3, Landsat-5, and Landsat-7 panchromatic and multispectral images taken under similar as well as under very different conditions. On the other hand, if the true absolute resolution of one of the images of the pair is known, the resolution of the other can be computed. Thus, in the last part of this paper, a spatial calibrator that is designed and constructed to help compute the absolute resolution of a single remotely sensed image is described, and an example of its use is presented.

Introduction of sensor spectral response into image fusion methods. Application to wavelet-based methods

Usual image fusion methods inject features from a high spatial resolution panchromatic sensor into every low spatial resolution multispectral band trying to preserve spectral signatures and improve spatial resolution to that of the panchromatic sensor. The objective is to obtain the image that would be observed by a sensor with the same spectral response (i.e., spectral sensitivity and quantum efficiency) as the multispectral sensors and the spatial resolution of the panchromatic sensor. But in these methods, features from electromagnetic spectrum regions not covered by multispectral sensors are injected into them, and physical spectral responses of the sensors are not considered during this process. This produces some undesirable effects, such as resolution overinjection images and slightly modified spectral signatures in some features. The authors present a technique which takes into account the physical electromagnetic spectrum responses of sensors during the fusion process, which produces images closer to the image obtained by the ideal sensor than those obtained by usual wavelet-based image fusion methods. This technique is used to define a new wavelet-based image fusion method.

Multifractal wavelet filter of natural images

Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this Letter we show that those properties uniquely define an intrinsic wavelet and present a suitable technique to obtain it from an ensemble of images. Once this wavelet is known, images can be represented as expansions in the associated wavelet basis. The resulting code has the remarkable properties that it separates independent features at different resolution level, reducing the redundancy, and remains essentially unchanged under changes in the power spectrum. The possible generalization of this representation to other systems is discussed.

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.