The 1531 Lisbon Earthquake: A Tsunami In the Tagus Estuary?

On 26 January 1531, a strong-magnitude earthquake heavily impacted Lisbon downtown. Immediately after the earthquake, the eyewitnesses reported large waves in the Tagus estuary, mainly north of the city and along the northern bank of the river. Descriptions include large impacts on ships anchored in the estuary and even morphological changes in the riverbed. We present a synthesis of the available information concerning both the earthquake and the water disturbance as a basis for the discussion of the probable tectonic source and the magnitude of the associated river oscillations. We hypothesize that the initial disturbance of the water can be attributed to the coseismic deformation of the estuary riverbed, and we use a nonlinear shallow water model to simulate the tsunami propagation and inundation. We show that the Vila Franca de Xira fault is the most probable source of the 1531 event. The largest inundation effects of the model correlate well with the historical descriptions: the impact is relevant in the inner Tagus estuary, but inundation in downtown Lisbon is small.

Intermittent claudication and physical exercise: effectiveness of a home-based program

Peripheral arterial disease (PAD) as a high incidence in general population and 12% to 20% of population with more than 60 years has already clinical symptoms, such as intermittent claudication (IC), pain, loss of strength and functional incapacity. There are already some studies that refer the possible positive effects of physical exercise in functional consequences of PAD. The purpose of this study was to verify the results of a home-based (HB) weekly supervised physical exercise program in patients with IC in consequence of PAD in lower limbs, and observe the medium number of diary steps walked by the subjects of our study.

Programa de intervenção segundo o modelo de auto-regulação na esclerose múltipla

A auto-regulação é um processo sistemático do comportamento que envolve a definição de metas pessoais e comportamentos, bem como a orientação para a realização de metas estabelecidas. Este processo envolve: orientação de estratégias eficazes para alcançar objectivos, feedback e auto-avaliação da parte dos indivíduos. Objectivo deste estudo: melhorar a actividade física e participação dos indivíduos com esclerose múltipla.

Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.