Contributos do associativismo na (re)construção da identidade profissional dos professores de matemática do 2º ciclo

Dissertação apresentada na Escola Superior de Educação de Lisboa para obtenção do grau de Mestre em Educação Matemática na Educação Pré-escolar e no 1º e 2º ciclos do Ensino Básico

ECG-based biometrics: A real time classification approach

Behavioral biometrics is one of the areas with growing interest within the biosignal research community. A recent trend in the field is ECG-based biometrics, where electrocardiographic (ECG) signals are used as input to the biometric system. Previous work has shown this to be a promising trait, with the potential to serve as a good complement to other existing, and already more established modalities, due to its intrinsic characteristics. In this paper, we propose a system for ECG biometrics centered on signals acquired at the subject's hand. Our work is based on a previously developed custom, non-intrusive sensing apparatus for data acquisition at the hands, and involved the pre-processing of the ECG signals, and evaluation of two classification approaches targeted at real-time or near real-time applications. Preliminary results show that this system leads to competitive results both for authentication and identification, and further validate the potential of ECG signals as a complementary modality in the toolbox of the biometric system designer.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Juggling time concepts: complex metanarrative in Alejandro González Iñárritu’s 21 Grams

ABSTRACT - Starting with the explanation of metanarrative as a sort of self-reflexive storytelling (as defended by Kenneth Weaver Hope in his unpublished PhD. thesis), I propose to talk about enunciative practices that stress the telling more than the told. In line with some metaficcional practices applied to cinema, such as the ‘mindfuck’ film (Jonathan Eig, 2003), the ‘psychological puzzle film’ (Elliot Panek, 2003) and the ‘mind-game film’ (Thomas Elsaesser, 2009), I will address the manipulations that a narrative film endures in order to produce a more fruitful and complex experience for the viewer. I will particularly concentrate on the misrepresentation of time as a way to produce a labyrinthine work of fiction where the linear description of events is replaced by a game of time disclosure. The viewer is thus called upon to reconstruct the order of the various situations portrayed in a process that I call ‘temporal mapping’. However, as the viewer attempts to do this, the film, ironically, because of the intricate nature of the plot and the uncertain status of the characters, resists the attempt. There is a sort of teasing taking place between the film and its spectator: an invitation of decoding that is half-denied until the end, where the puzzle is finally solved. I will use three of Alejandro Iñárritu’s films to better convey my point: Amores perros (2000), 21 Grams (2003) and Babel (2006). I will consider Iñárritu’s methods to produce a non-linear storytelling as a way to stress the importance of time and its validity as one of the elements that make up for a metanarrative experience in films. I will focus especially on 21 Grams, which I consider to be a paragon of the labyrinth.