Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Interpolation and sampling in small Bergman spaces

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

Classification of sags according to their origin based on the waveform similarity

A statistical method for classification of sags their origin downstream or upstream from the recording point is proposed in this work. The goal is to obtain a statistical model using the sag waveforms useful to characterise one type of sags and to discriminate them from the other type. This model is built on the basis of multi-way principal component analysis an later used to project the available registers in a new space with lower dimension. Thus, a case base of diagnosed sags is built in the projection space. Finally classification is done by comparing new sags against the existing in the case base. Similarity is defined in the projection space using a combination of distances to recover the nearest neighbours to the new sag. Finally the method assigns the origin of the new sag according to the origin of their neighbours

Interpolation-free Coregistration and Phase-Correction of Airborne SAR Interferograms

This letter discusses the detection and correction ofresidual motion errors that appear in airborne synthetic apertureradar (SAR) interferograms due to the lack of precision in the navigationsystem. As it is shown, the effect of this lack of precision istwofold: azimuth registration errors and phase azimuth undulations.Up to now, the correction of the former was carried out byestimating the registration error and interpolating, while the latterwas based on the estimation of the phase azimuth undulations tocompensate the phase of the computed interferogram. In this letter,a new correction method is proposed, which avoids the interpolationstep and corrects at the same time the azimuth phase undulations.Additionally, the spectral diversity technique, used to estimateregistration errors, is critically analyzed. Airborne L-bandrepeat-pass interferometric data of the German Aerospace Center(DLR) experimental airborne SAR is used to validate the method

Real interpolation for families of Banach spaces (II)

In this paper, we study the dual space and reiteration theorems for the real method of interpolation for infinite families of Banach spaces introduced in [2]. We also give examples of interpolation spaces constructed with this method.

Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega

A Geometric Characterization of Interpolation in $\hat{\E}^\prime(\R)$

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

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.

A(-infinity)-interpolation in the ball

We give a necessary and sufficient condition for a sequence [ak}k in the unit ball of C° to be interpolating for the class A~°° of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H°° functions in the ball, is given in terms of the derivatives of m > n functions F Fm e A~°° vanishing on {ak)k.

Waveform-independent frame-timing acquisition for UWB signals

In this paper, the problem of frame-level symboltiming acquisition for UWB signals is addressed. The main goalis the derivation of a frame-level timing estimator which does notrequire any prior knowledge of neither the transmitted symbolsnor the received template waveform. The independence withrespect to the received waveform is of special interest in UWBcommunication systems, where a fast and accurate estimation ofthe end-to-end channel response is a challenging and computationallydemanding task. The proposed estimator is derived under theunconditional maximum likelihood criterion, and because of thelow power of UWB signals, the low-SNR assumption is adopted. Asa result, an optimal frame-level timing estimator is derived whichoutperforms existing acquisition methods in low-SNR scenarios.

NDA waveform estimation in the low-SNR regime

This correspondence addresses the problem of nondata-aidedwaveform estimation for digital communications. Based on the unconditionalmaximum likelihood criterion, the main contribution of this correspondenceis the derivation of a closed-form solution to the waveform estimationproblem in the low signal-to-noise ratio regime. The proposed estimationmethod is based on the second-order statistics of the received signaland a clear link is established between maximum likelihood estimation andcorrelation matching techniques. Compression with the signal-subspace isalso proposed to improve the robustness against the noise and to mitigatethe impact of abnormals or outliers.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Investigació integrada amb EPs i RMf de la interacció entre la memòria de treball i la distracció

Estudi elaborat a partir d’una estada a la University of Wales, Bangor, Regne Unit entre setembre i desembre del 2006. Els sons distractors augmenten el temps de reacció i el nombre de respostes incorrectes en una tasca de classificació visual, demostrant que hi ha distracció conductual durant la realització de la tasca visual. L’enregistrament concomitant de potencials evocats durant la distracció mostra un patró neuroelèctric característic, el potencial de distracció, que es caracteritza per una ona trifàsica. Darrerament, s’ha demostrat que factors “des de dalt” associats al muntatge experimental tindrien una gran influència en els efectes que els estímuls distractors tindrien en la tasca. Estudis recents mostrarien que aquesta resposta d’atenció exògena es pot modular per la càrrega en memòria de treball, reduint-ne la distracció amb la càrrega, fet que contradiu altres dades que mostraven l’efecte oposat. L’objectiu d’aquest estudi ha estat investigar en quines condicions la càrrega en memòria de treball pot exercir un efecte modulador en les respostes conductuals i cerebrals als sons novedosos distractors, i establir la dinàmica espacio-temporal d’aquesta modulació.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.