Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

Additive adaptive thinking in 1st and 2nd grades pupils

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. It discusses what is meant by adaptive thinking and presents the results of individual interviews with four pupils. The main goal of the study is to understand pupils’ reasoning when solving numerical tasks involving additive situations, and identify features associated with adaptive thinking. The results show that, in the case of first grade pupils, the semantic aspects of the problem are involved in its resolution and the pupils’ performance appears to be related to the development of number sense. The 2nd grade pupils seem to see the quantitative difference as an invariant numerical relationship.

'Day number': a promoter routine of flexibility and conceptual understanding

This paper is part of the Project “Adaptive thinking and flexible computation: Critical issues”. In this paper we discuss different perspectives of flexibility and adaptive thinking in literature. We also discuss the idea of proceptual thinking and how this idea is important in our perspective of adaptive thinking. The paper analyses a situation developed with a first grade classroom and its teacher named the day number. It is a daily activity at the beginning of the school day. It consists on to look for the date number and to think about different ways of writing it using the four arithmetic operations. The analyzed activity was developed on March 19, so the challenge was to write 19 in several ways. The data show the pupils’ enthusiasm and their efforts to find different ways of writing the number. Some used large numbers and division, which they were just starting to learn. The pupils presented symbolic expressions of 19, decomposing and recomposing it in a flexible manner.

Genotoxicity biomarkers: application in histopathology laboratories

Most cancers results from man-made and natural environmental exposures (such as tobacco smoke; chemical pollutants in air, water, food, drugs; radon; and infectious agents) acting in concert with both genetic and acquired characteristics. It has been estimated that without these environmental factors, cancer incidence would be dramatically reduced, by as much as 80%-90%. The modulation of environmental factors by host susceptibility was rarely evaluated. However, within the past few years, the interaction between environmental factors and host susceptibility factors has become a very active area of research. Molecular biology as a tool for use in epidemiological studies has significant potential in strengthening the identification of cancers associated with environmental exposures related to lifestyle, occupation, or ambient pollution. In molecular epidemiology, laboratory methods are employed to document the molecular basis and preclinical effects of environmental carcinogenesis. Molecular epidemiology has become a major field of research and considerable progress has been made in validation and application of biomarkers and its greatest contribution has been the insights provided into interindividual variation in human cancer risk and the complex interactions between environmental factors and host susceptibility factors, both inherited and acquired, in the multistage process of carcinogenesis.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Práticas curriculares em jardim de infância com crianças com perturbações do espetro do autismo

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção do grau de Mestre em Educação - Especialização em Educação Especial

Perceção da contemporaneidade pelos pré-adolescentes: o que se aprende com a obra de arte

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Artística, na Especialização de Artes Plásticas na Educação

Transitional justice in the judiciary: lessons from the portuguese democratisation

The nature of the Portuguese transition to democracy and the following state crises (1974-1975) created a ‘window of opportunity’ in which the ‘reaction to the past’ was much stronger than in the other Southern or even of Central and Eastern European transitions. In Portugal, initiatives of symbolic rupture with the past began soon after the April 25, 1974, coup d’état and transitional justice policies assumed mainly three formulas. First, the institutional reforms directed primarily to abusive state institutions such as the political police (PIDE-DGS) and political courts (Plenary courts) in order to dismantle the repressive apparatus and prevent further human rights abuses and impunity. Secondly, the criminal prosecutions addressed to perpetrators considered as being the most responsible for repression and abuses. Finally, lustration or political purges (saneamentos, the term used in Portugal to designate political purges) which were, in fact, the most common form of political justice in Portuguese transition to democracy. This paper deals with the peculiarities of transitional justice in Portugal devoting a particular attention to the judicial, a key sector to understand the way the Portuguese dealt with their authoritarian past.