Extreme values for Benedicks-Carleson quadratic maps

We consider the quadratic family of maps given by $f_{a}(x)=1-a x^2$ with $x\in [-1,1]$, where $a$ is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes $X_0,X_1,...$, given by $X_{n}=f_a^n$, for every integer $n\geq0$, where each random variable $X_n$ is distributed according to the unique absolutely continuous, invariant probability of $f_a$. Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of $M_n=\max\{X_0,...,X_{n-1}\}$ is the same as that which would apply if the sequence $X_0,X_1,...$ was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of $M_n$ is of Type III (Weibull).Comment: 18 page

Exploring RNA-targeted gene therapy approaches for hypertrophic cardiomyopathy

Relatório de projeto no âmbito do Programa de Bolsas Universidade de Lisboa/Fundação Amadeu Dias (2011/2012). Universidade de Lisboa. Faculdade de Medicin

Two-loop fermionic electroweak corrections to the Z-boson width and production rate

Improved predictions for the Z-boson decay width and the hadronic Z-peak cross-section within the Standard Model are presented, based on a complete calculation of electroweak two-loop corrections with closed fermion loops. Compared to previous partial results, the predictions for the Z width and hadronic cross-section shift by about 0.6 MeV and 0.004 nb, respectively. Compact parametrization formulae are provided, which approximate the full results to better than 4 ppm.Comment: 7 pages; v2: few typos fixed and minor corrections of numbers in table

On minimal eigenvalues of Schrodinger operators on manifolds

We consider the problem of minimizing the eigenvalues of the Schr\"{o}dinger operator H=-\Delta+\alpha F(\ka) ($\alpha>0$) on a compact $n-$manifold subject to the restriction that \ka has a given fixed average \ka_{0}. In the one-dimensional case our results imply in particular that for F(\ka)=\ka^{2} the constant potential fails to minimize the principal eigenvalue for \alpha>\alpha_{c}=\mu_{1}/(4\ka_{0}^{2}), where $\mu_{1}$ is the first nonzero eigenvalue of $-\Delta$. This complements a result by Exner, Harrell and Loss (math-ph/9901022), showing that the critical value where the circle stops being a minimizer for a class of Schr\"{o}dinger operators penalized by curvature is given by $\alpha_{c}$. Furthermore, we show that the value of $\mu_{1}/4$ remains the infimum for all $\alpha>\alpha_{c}$. Using these results, we obtain a sharp lower bound for the principal eigenvalue for a general potential. In higher dimensions we prove a (weak) local version of these results for a general class of potentials F(\ka), and then show that globally the infimum for the first and also for higher eigenvalues is actually given by the corresponding eigenvalues of the Laplace-Beltrami operator and is never attained.Comment: 7 page

Distinguishing Majorana and Dirac Gluinos and Neutralinos

While gluinos and neutralinos are Majorana fermions in the MSSM, they can be Dirac fermion fields in extended supersymmetry models. The difference between the two cases manifests itself in production and decay processes at colliders. In this contribution, results are presented for how the Majorana or Dirac nature of gluinos and neutralinos can be extracted from di-lepton signals at the LHC.Comment: 4 pages; to appear in the proceedings of the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY09), Boston, USA, 5-10 Jun 200