Lipschitz harmonic capacity and Bilipschitz images of cantor sets

For bilipschitz images of Cantor sets in Rd we estimate the Lipschitz harmonic capacity and show this capacity is invariant under bilipschitz homeomorphisms.

The distributional consequences of tax reforms under market distortions

In this paper we examine the importance of imperfect competition in product and labour markets in determining the long-run welfare e¤ects of tax reforms assuming agent heterogeneneity in capital hold- ings. Each of these market failures, independently, results in welfare losses for at least a segment of the population, after a capital tax cut and a concurrent labour tax increase. However, when combined in a realistic calibration to the UK economy, they imply that a capital tax cut will be Pareto improving in the long run. Consistent with the the- ory of second-best, the two distortions in this context work to correct the negative distributional e¤ects of a capital tax cut that each one, on its own, creates.

A type of perturbation of the harmonic oscillator

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

Hyperglycemia-induced abnormalities in rat and human corneas: the potential of second harmonic generation microscopy.

BACKGROUND: Second Harmonic Generation (SHG) microscopy recently appeared as an efficient optical imaging technique to probe unstained collagen-rich tissues like cornea. Moreover, corneal remodeling occurs in many diseases and precise characterization requires overcoming the limitations of conventional techniques. In this work, we focus on diabetes, which affects hundreds of million people worldwide and most often leads to diabetic retinopathy, with no early diagnostic tool. This study then aims to establish the potential of SHG microscopy for in situ detection and characterization of hyperglycemia-induced abnormalities in the Descemet's membrane, in the posterior cornea. METHODOLOGY/PRINCIPAL FINDINGS: We studied corneas from age-matched control and Goto-Kakizaki rats, a spontaneous model of type 2 diabetes, and corneas from human donors with type 2 diabetes and without any diabetes. SHG imaging was compared to confocal microscopy, to histology characterization using conventional staining and transmitted light microscopy and to transmission electron microscopy. SHG imaging revealed collagen deposits in the Descemet's membrane of unstained corneas in a unique way compared to these gold standard techniques in ophthalmology. It provided background-free images of the three-dimensional interwoven distribution of the collagen deposits, with improved contrast compared to confocal microscopy. It also provided structural capability in intact corneas because of its high specificity to fibrillar collagen, with substantially larger field of view than transmission electron microscopy. Moreover, in vivo SHG imaging was demonstrated in Goto-Kakizaki rats. CONCLUSIONS/SIGNIFICANCE: Our study shows unambiguously the high potential of SHG microscopy for three-dimensional characterization of structural abnormalities in unstained corneas. Furthermore, our demonstration of in vivo SHG imaging opens the way to long-term dynamical studies. This method should be easily generalized to other structural remodeling of the cornea and SHG microscopy should prove to be invaluable for in vivo corneal pathological studies.

Perspectives of auto-correcting lens distortions in mosaic-based underwater navigation

When unmanned underwater vehicles (UUVs) perform missions near the ocean floor, optical sensors can be used to improve local navigation. Video mosaics allow to efficiently process the images acquired by the vehicle, and also to obtain position estimates. We discuss in this paper the role of lens distortions in this context, proving that degenerate mosaics have their origin not only in the selected motion model or in registration errors, but also in the cumulative effect of radial distortion residuals. Additionally, we present results on the accuracy of different feature-based approaches for self-correction of lens distortions that may guide the choice of appropriate techniques for correcting distortions

Harmonic active contours.

We propose a segmentation method based on the geometric representation of images as 2-D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.

Harmonic Nanocrystals for Biolabeling: A Survey of Optical Properties and Biocompatibility.

Nonlinear optical nanocrystals have been recently introduced as a promising alternative to fluorescent probes for multiphoton microscopy. We present for the first time a complete survey of the properties of five nanomaterials (KNbO(3), LiNbO(3), BaTiO(3), KTP, and ZnO), describing their preparation and stabilization and providing quantitative estimations of their nonlinear optical response. In the light of their prospective use as biological and clinical markers, we assess their biocompatibility on human healthy and cancerous cell lines. Finally, we demonstrate the great potential for cell imaging of these inherently nonlinear probes in terms of optical contrast, wavelength flexibility, and signal photostability.

Counterpoise-corrected geometries and harmonic frequencies of N-body clusters: application to (HF)n (n=3,4)

A study was conducted on the methods of basis set superposition error (BSSE)-free geometry optimization and frequency calculations in clusters larger than a dimer. In particular, three different counterpoise schemes were critically examined. It was shown that the counterpoise-corrected supermolecule energy can be easily obtained in all the cases by using the many-body partitioning of energy

Production and Abatement Distortions under Noisy Green Taxes, October 2005

Pigouvian taxes are typically imposed in situations where there is imperfect knowledge on the extent of damage caused by a producing firm. A regulator imposing imperfectly informed Pigouvian taxes may cause the firms that should (should not) produce to shut down (produce). In this paper we use a Bayesian information framework to identify optimal signal-conditioned taxes in the presence of such losses. The tax system involves reducing (increasing) taxes on firms identified as causing high (low) damage. Unfortunately, when an abatement decision has to be made, the tax system that minimizes production distortions also dampens the incentive to abate. In the absence of wrong-firm concerns, a regulator can solve the problem by not adjusting taxes for signal noise. When wrong-firm losses are a concern, the regulator has to trade off losses from distorted production incentives with losses from distorted abatement incentives. The most appropriate policy may involve a combination of instruments.

Temperature-induced sex reversal is not responsible for sex-ratio distortions in grayling Thymallus thymallus or brown trout Salmo trutta.

On the basis of the experiments carried out over various years, it was concluded that (1) grayling Thymallus thymallus and brown trout Salmo trutta are resistant to temperature-induced sex reversal at ecologically relevant temperatures, (2) environmental sex reversal is unlikely to cause the persistent sex ratio distortion observed in at least one of the study populations and (3) sex-specific tolerance of temperature-related stress may be the cause of distorted sex ratios in populations of T. thymallus or S. trutta.

Spin-Peierls vs Peierls distortions in a family of conjugated polymers

Distortions in a family of conjugated polymers are studied using two complementary approaches: within a many-body valence bond approach using a transfer-matrix technique to treat the Heisenberg model of the systems, and also in terms of the tight-binding band-theoretic model with interactions limited to nearest neighbors. The computations indicate that both methods predict the presence or absence of the same distortions in most of the polymers studied.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Valence-bond treatment of distortions in polyacene polymers

Distortions of polyacene polymers are studied within a many-body valence-bond framework using a powerful transfer-matrix technique for the valence-bond (or Heisenberg) model of the system. The computations suggest that the ground-state geometry is either totally symmetric or possibly exhibits a slight (A2 or B2 symmetry) bond-alternation distortion. The lowest-energy (nonsymmetric, in-plane) distortions are the A2 and B2 modes, which, within our approximations, are degenerate.