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.

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.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

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.

Reproductive dynamics of Sterna hirundinacea Lesson, 1831 in Ilha dos Cardos, Santa Catarina, Brazil

In this work, we intend to describe the reproductive dynamics of Sterna hirundinacea in an island fromSouth Brazil.We studied the reproductive biology of this species in its natural environment and provide data on their growth, survival, and reproductive success in Ilha dosCardos, SantaCatarina, South Brazil. Samplingswere carried out daily on the island throughout the reproductive seasons of 2003, 2005, and 2006 and the different stages of development of the chicks were characterized according to age, length of the beak, and plumage characteristics.We provide a basic equation Lm = 167.91 (1 ��� e ���0.062t���(���0.23)) to determine the approximate age of individuals using their body mass. The main cause of chick mortality on the island was natural (63.17% in 2003, 81.41% in 2005, and 79.96% in 2006), whereas predation contributed to mortality in a proportion of 38.83% in 2003, 18.59% in 2005, and 20.04% in 2006.The absence in the area of the chicks��� main predator, Kelp gull (Larus dominicanus), the large number of chicks that reached the final stages of development, and their reproductive success demonstrate that Ilha dos Cardos is an important breeding site for the species in southern Brazil.

Working in and on groups: an illustration of the principles of exploratory practice in an esp classroom

Neste artigo, descrevo e analiso uma actividade de trabalho em grupo desenvolvida para uma aula da disciplina de L��ngua Inglesa VI das turmas do 3�� ano do Curso de L��nguas e Secretariado do Instituto Superior de Contabilidade e Administra����o do Porto (ISCAP). No enquadramento te��rico, abordam-se quest��es relacionadas com o trabalho em grupo numa aula de l��ngua estrangeira, nomeadamente a dimens��o social da sala de aula em geral e da interac����o aluno-aluno em particular. Apresentam-se ent��o os princ��pios da Exploratory Practice, com ��nfase na possibilidade preconizada por esta abordagem de se poder transformar uma actividade de reflex��o e discuss��o sobre o processo de ensino/aprendizagem numa unidade pedag��gica. Segue-se a apresenta����o da proposta did��ctica, respectivo plano de aula e alguns exemplos dos textos produzidos pelos alunos. O artigo termina com a apresenta����o de alguns coment��rios cr��ticos, real��ando-se a contribui����o da Exploratory Practice para o desenvolvimento de uma maior consciencializa����o por parte dos alunos do seu processo de aprendizagem.

Facebook vs moodle : Surveying university students on the use of learning management systems to support learning activities outside the classroom

CISTI'2015 - 10�� Confer��ncia Ib��rica de Sistemas e Tecnologias de Informa����o, 17 a 20 de junho de 2015, ��gueda, Aveiro, Portugal.

Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil

OBJECTIVE: To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS: The study was conducted based on epidemiological data of the 2003 dengue epidemic in Bras��lia, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R0 of imported versus autochthonous cases was used as an estimator of real R0. RESULTS: The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R0 above one, although the real R0 was below one. The same results were seen when the method was applied on simulated epidemics with fixed R0. This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R0 values. CONCLUSIONS: It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease.

Correc����o autom��tica de respostas de texto livre para a aplica����o UNI_NET-Classroom

Ao longo dos tempos foi poss��vel constatar que uma grande parte do tempo dos professores �� gasta na componente de avalia����o. Por esse facto, h�� j�� algumas d��cadas que a correc����o autom��tica de texto livre �� alvo de investiga����o. Sendo a correc����o de exerc��cios efectuada pelo computador permite que o professor dedique o seu tempo em tarefas que melhorem a aprendizagem dos alunos. Para al��m disso, cada vez mais as novas tecnologias permitem o uso de ferramentas com bastante utilidade no ensino, pois para al��m de facilitarem a exposi����o do conhecimento tamb��m permitem uma maior reten����o da informa����o. Logo, associar ferramentas de gest��o de sala de aula �� correc����o autom��tica de respostas de texto livre �� um desafio bastante interessante. O objectivo desta disserta����o foi a realiza����o de um estudo relativamente �� ��rea de avalia����o assistida por computador em que este trabalho se insere. Inicialmente, foram analisados alguns correctores ortogr��ficos para seleccionar aquele que seria integrado no m��dulo proposto. De seguida, foram estudadas as t��cnicas mais relevantes e as ferramentas que mais se enquadram no ��mbito deste trabalho. Neste contexto, a ideia foi partir da exist��ncia de uma ferramenta de gest��o de sala de aula e desenvolver um m��dulo para a correc����o de exerc��cios. A aplica����o UNI_NET-Classroom, que foi a ferramenta para a qual o m��dulo foi desenvolvido, j�� continha um componente de gest��o de exerc��cios que apenas efectuava a correc����o para as respostas de escolha m��ltipla. Com este trabalho pretendeu-se acrescentar mais uma funcionalidade a esse componente, cujo intuito �� dar apoio ao professor atrav��s da correc����o de exerc��cios e sugest��o da cota����o a atribuir. Por ��ltimo, foram realizadas v��rias experi��ncias sobre o m��dulo desenvolvido, de forma a ser poss��vel retirar algumas conclus��es para o presente trabalho. A conclus��o mais importante foi que as ferramentas de correc����o autom��tica s��o uma mais-valia para os professores e escolas.

The emergence of a curriculum model for online learning in a context of late investment in distance education

ECER 2015 "Education and Transition - Contributions from Educational Research", Corvinus University of Budapest from 7 to 11 September 2015.

Efic��cia da escola e efic��cia do professor no ��mbito do ensino-aprendizagem da Hist��ria e Geografia

Mestrado, Ensino de Hist��ria e de Geografia no 3.�� Ciclo do Ensino B��sico e no Ensino Secund��rio, 9 de Mar��o de 2016, Universidade dos A��ores (Relat��rio de Est��gio).

Indisciplina na sala de aula: a perspetiva de professores do 3�� Ciclo do Ensino B��sico e do Ensino Secund��rio

Disserta����o apresentada �� Escola Superior de Educa����o de Lisboa para obten����o de grau de mestre em Ci��ncias da Educa����o

Dynamics and orchestral effects in late Eighteenth-Century portuguese organ music: the works of Jos�� Marques e Silva (1782-1837) and the organs of Ant��nio Xavier Machado e Cerveira (1756-1828)

A maioria dos ��rg��os hist��ricos portugueses data dos finais do s��culo XVIII ou do princ��pio do s��culo XIX. Durante este per��odo foi constru��do um invulgar n��mero de instrumentos em Lisboa e nas ��reas circundantes por Ant��nio Xavier Machado e Cerveira (1756-1828) e outros organeiros menos prol��ficos. O estudo desses ��rg��os, muitos dos quais (restaurados ou n��o) se encontram pr��ximos das condi����es originais, permite a identifica����o de um tipo de instrumento com uma morfologia espec��fica, claramente emancipada do chamado ����rg��o ib��rico��. No entanto, at�� muito recentemente, n��o era conhecida m��sica que se adaptasse ��s idiossincrasisas daqueles instrumentos. O recente estudo das obras para ��rg��o de Jos�� Marques e Silva (1782-1837) permitiu clarificar esta situa����o. Bem conhecido durante a sua vida como organista e compositor, Jos�� Marques e Silva foi um dos ultimos mestres do Semin��rio Patriarcal. A import��ncia da sua produ����o musical reside n��o s�� num substancial n��mero de obras com autoria firmemente estabelecida ��� escritas, na maior parte, para coro misto com acompanhamento de ��rg��o obbligato ��� mas tamb��m na ��ntima rela����o entre a sua escrita e a morfologia dos ��rg��os constru��dos em Portugal durante a sua vida. Este artigo enfatiza a import��ncia de Jos�� Marques e Silva (indubitavelmente, o mais significativo compositor portugu��s para ��rg��o do seu tempo) sublinhando a relev��ncia das suas obras para ��rg��o solo, cujo uso extensivo de escrita idiom��tica e indica����es de regista����o fazem delas um dos mais importantes documentos s�� in��cio do s��culo XIX sobre a pr��tica organ��stica em Portugal.

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn���Engdahl (F���E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

Multidimensional scaling analysis of the dynamics of a country economy

This paper analyzes the Portuguese short-run business cycles over the last 150 years and presents the multidimensional scaling (MDS) for visualizing the results. The analytical and numerical assessment of this long-run perspective reveals periods with close connections between the macroeconomic variables related to government accounts equilibrium, balance of payments equilibrium, and economic growth. The MDS method is adopted for a quantitative statistical analysis. In this way, similarity clusters of several historical periods emerge in the MDS maps, namely, in identifying similarities and dissimilarities that identify periods of prosperity and crises, growth, and stagnation. Such features are major aspects of collective national achievement, to which can be associated the impact of international problems such as the World Wars, the Great Depression, or the current global financial crisis, as well as national events in the context of broad political blueprints for the Portuguese society in the rising globalization process.