Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Recerca de producció de gravitons en escenaris amb dimensions extres al Tevatron amb el detector CDF

Les dimensions extres plantegen una solució al problema de la jerarquia de les forces i proposen una explicació a l’aparent feblesa de la força de la gravetat en front de les altres forces. Utilitzant dades simulades i dades proporcionades pel detector CDF situat en l’accelerador Tevatron a Fermilab (Chicago, EEUU), s’ha realitzat una recerca de dimensions extres i de producció de gravitons.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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

Reduction of periodic difference systems to linear or autonomous ones

We extend Floquet theory for reducing nonlinear periodic difference systems to autonomous ones (actually linear) by using normal form theory.

Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions

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

A public-key cryptosystem based on second order linear sequences

Based on Lucas functions, an improved version of the Diffie-Hellman distribution key scheme and to the ElGamal public key cryptosystem scheme are proposed, together with an implementation and computational cost. The security relies on the difficulty of factoring an RSA integer and on the difficulty of computing the discrete logarithm.

Appropriateness criteria for surgery improve clinical outcomes in patients with low back pain and/or sciatica.

STUDY DESIGN: Prospective, controlled, observational outcome study using clinical, radiographic, and patient/physician-based questionnaire data, with patient outcomes at 12 months follow-up. OBJECTIVE: To validate appropriateness criteria for low back surgery. SUMMARY OF BACKGROUND DATA: Most surgical treatment failures are attributed to poor patient selection, but no widely accepted consensus exists on detailed indications for appropriate surgery. METHODS: Appropriateness criteria for low back surgery have been developed by a multispecialty panel using the RAND appropriateness method. Based on panel criteria, a prospective study compared outcomes of patients appropriately and inappropriately treated at a single institution with 12 months follow-up assessment. Included were patients with low back pain and/or sciatica referred to the neurosurgical department. Information about symptoms, neurologic signs, the health-related quality of life (SF-36), disability status (Roland-Morris), and pain intensity (VAS) was assessed at baseline, at 6 months, and at 12 months follow-up. The appropriateness criteria were administered prospectively to each clinical situation and outside of the clinical setting, with the surgeon and patients blinded to the results of the panel decision. The patients were further stratified into 2 groups: appropriate treatment group (ATG) and inappropriate treatment group (ITG). RESULTS: Overall, 398 patients completed all forms at 12 months. Treatment was considered appropriate for 365 participants and inappropriate for 33 participants. The mean improvement in the SF-36 physical component score at 12 months was significantly higher in the ATG (mean: 12.3 points) than in the ITG (mean: 6.8 points) (P = 0.01), as well as the mean improvement in the SF-36 mental component score (ATG mean: 5.0 points; ITG mean: -0.5 points) (P = 0.02). Improvement was also significantly higher in the ATG for the mean VAS back pain (ATG mean: 2.3 points; ITG mean: 0.8 points; P = 0.02) and Roland-Morris disability score (ATG mean: 7.7 points; ITG mean: 4.2 points; P = 0.004). The ATG also had a higher improvement in mean VAS for sciatica (4.0 points) than the ITG (2.8 points), but the difference was not significant (P = 0.08). The SF-36 General Health score declined in both groups after 12 months, however, the decline was worse in the ITG (mean decline: 8.2 points) than in the ATG (mean decline: 1.2 points) (P = 0.04). Overall, in comparison to ITG patients, ATG patients had significantly higher improvement at 12 months, both statistically and clinically. CONCLUSION: In comparison to previously reported literature, our study is the first to assess the utility of appropriateness criteria for low back surgery at 1-year follow-up with multiple outcome dimensions. Our results confirm the hypothesis that application of appropriateness criteria can significantly improve patient outcomes.

Predicting trabecular bone microdamage initiation and accumulation using a non-linear perfect damage model

Studies evaluating the mechanical behavior of the trabecular microstructure play an important role in our understanding of pathologies such as osteoporosis, and in increasing our understanding of bone fracture and bone adaptation. Understanding of such behavior in bone is important for predicting and providing early treatment of fractures. The objective of this study is to present a numerical model for studying the initiation and accumulation of trabecular bone microdamage in both the pre- and post-yield regions. A sub-region of human vertebral trabecular bone was analyzed using a uniformly loaded anatomically accurate microstructural three-dimensional finite element model. The evolution of trabecular bone microdamage was governed using a non-linear, modulus reduction, perfect damage approach derived from a generalized plasticity stress-strain law. The model introduced in this paper establishes a history of microdamage evolution in both the pre- and post-yield regions

Politics and the Olympics: some new dimensions

Paper given at the Institut de Ciències Polítiques i Socials, Barcelona in 1995 analysing the relationship between politics, the Olympic Games and the Olympic Movement and their influences.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

Art en tres dimensions: construcció de renders 3D amb renders 3D studio max

Treball de recerca realitzat per un alumne d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. Existeixen diversos programes informàtics per a la generació d’imatges en format 3D. S’analitza breument l’oferta del mercat actual de la tecnologia de programari més emprada en la producció de gràfics 3D amb ordinador, identificant les vessants positives i negatives de cadascun. Posteriorment s’examina en profunditat el programa 3D Studio Max, per tal de conèixer-ne les eines de creació d’escenes virtuals i les seves funcionalitats. Finalment s’han desenvolupat projectes d’escenaris 3D en els quals es puguin aplicar els coneixements tècnics obtinguts en la recerca, sempre conceptualitzant aquestes propostes amb un cert criteri artístic.

Comparació de la cobertura de bàlec després de diferents pertorbacions amb foc, tenint en compte l'autocorrelació espacial en transectes de dos dimensions

Projecte de recerca elaborat a partir d’una estada a la University of Alberta entre juliol i octubre del 2007. Es pot comparar la cobertura d'arbustos després d'incendis i de cremes controlades en transectes amb 2 dimensions, tenint en compte l'autocorrelació espacial? Canvia el patró espacial dels arbustos després d'aquestes pertorbacions?

A theoretical and practical study on linear reforms of dual taxes

We extend the linear reforms introduced by Pf¨ahler (1984) to the case of dual taxes. We study the relative effect that linear dual tax cuts have on the inequality of income distribution -a symmetrical study can be made for dual linear tax hikes-. We also introduce measures of the degree of progressivity for dual taxes and show that they can be connected to the Lorenz dominance criterion. Additionally, we study the tax liability elasticity of each of the reforms proposed. Finally, by means of a microsimulation model and a considerably large data set of taxpayers drawn from 2004 Spanish Income Tax Return population, 1) we compare different yield-equivalent tax cuts applied to the Spanish dual income tax and 2) we investigate how much income redistribution the dual tax reform (Act ‘35/2006’) introduced with respect to the previous tax.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.