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

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

A Topological Approach to Unifying Compactifications of Symmetric Spaces

In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber

Extreme Value Laws in Dynamical Systems for Non-smooth Observations

We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a counterpart to the result of the authors in the absolutely continuous case. Moreover, we prove an equivalent result for returns to dynamically defined cylinders. This allows us to show that we have Extreme Value Laws for various dynamical systems with equilibrium states with good mixing properties. In order to achieve these goals we tailor our observables to the form of the measure at hand

Galactic exploration by directed Self-Replicating Probes, and its implications for the Fermi paradox

This paper proposes a long term scheme for robotic exploration of the galaxy,and then considers the implications in terms of the `Fermi paradox' and our search for ETI. We discuss the parameter space of the `galactic ecology' of civilizations in terms of the parameters T (time between ET civilizations arising) and L, the lifetime of these civilizations. Six different regions are described.Comment: 1 figur

Speed of convergence for laws of rare events and escape rates

We obtain error terms on the rate of convergence to Extreme Value Laws for a general class of weakly dependent stochastic processes. The dependence of the error terms on the `time' and `length' scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems

Proselytism and the right to freedom from improper irreligious influence: the example of public school education

Jurisprudentially speaking, proselytism is a concept within the larger genus of the protection of religious rights and freedoms. The word lends itself to differing opinions. However, there is a popular school of thought that proselytism has to do only with influencing people to adopt a particular religion. Such an understanding relies on the view that only the religious can be insidious and bear the potential to improperly proselytise, and thus excludes the possibility of improper irreligious forms of influence. In referring to the example of public-school education, it is argued that as much as the religious has the potential for improper proselytising, irreligious teachings or expressions also run the risk of improper proselytising. Not only are irreligious beliefs in many instances diametrically opposed to religious beliefs; they are a belief in themselves and cannot be seen as necessarily harmless or without the potential to proselytise improperly. Consequently, this article introduces an equitable and accommodative understanding of proselytism, which places the potentially harmful effects of both religious and irreligious beliefs on an equal footing with each other (something befitting to plural and democratic paradigms). This article therefore also cultivates further debate on improper irreligious proselytism in religious rights and freedoms jurisprudence, a scant topic in human rights jurisprudence

Waveguides with combined Dirichlet and Robin boundary conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet-Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kriz.Comment: 20 pages, LaTeX with 1 EPS figure; to appear in Mathematical Physics, Analysis and Geometr