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.

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.

China's space program : a new tool for PRC "soft power" in international relations?

When China launched an anti-satellite (ASAT) weapon in January 2007 to destroy one of its inactive weather satellites, most reactions from academics and U.S. space experts focused on a potential military “space race” between the United States and China. Overlooked, however, is China’s growing role as global competitor on the non-military side of space. China’s space program goes far beyond military counterspace applications and manifests manned space aspirations, including lunar exploration. Its pursuit of both commercial and scientific international space ventures constitutes a small, yet growing, percentage of the global space launch and related satellite service industry. It also highlights China’s willingness to cooperate with nations far away from Asia for political and strategic purposes. These partnerships may constitute a challenge to the United States and enhance China’s “soft power” among key American allies and even in some regions traditionally dominated by U.S. influence (e.g., Latin America and Africa). Thus, an appropriate U.S. response may not lie in a “hard power” counterspace effort but instead in a revival of U.S. space outreach of the past, as well as implementation of more business-friendly export control policies.

Famílias de pessoas com síndromes psicóticas : análise dimensional e avaliação da efectividade de uma intervenção em grupos para familiares

RESUMO:Enquadramento teórico Nas famílias das pessoas com síndromas psicóticas, a história natural da prestação de cuidados informais é ainda pouco conhecida. Independentemente disso, o impacto sobre os cuidadores tem sido alvo de intervenções familiares (IF) psicoeducativas. Não esquecendo que contextos clínicos diferentes, como é o caso das demências, exibem, nas famílias, especificidades a explorar, torna-se crucial aperfeiçoar métodos para avaliação de grupos de risco e estudo da efectividade das IF. As intervenções em grupos para familiares (IGF) são exequíveis e cobrem parte das necessidades das famílias. Ao invés de outras IF, falta evidência inequívoca de que as IGF influenciem o prognóstico da esquizofrenia (diminuindo as taxas de recaída ou melhorando o funcionamento dos doentes). Em Portugal, são praticamente inexistentes dados sobre avaliação de IGF. O estudo FAPS (FAmílias de Pessoas com PSicose) teve como objectivos: estudar a adesão a uma IGF, avaliar a efectividade desta e estudar prospectivamente uma coorte de familiares que não tivessem aderido (considerando dimensões da experiência de cuidar e preditores putativos: suporte social, coping, sentido de coerência-SOC, covariáveis clínico-funcionais do doente). Adicionalmente, intentou a validação do Involvement Evaluation Questionnaire, versão europeia (IEQ-EU), numa população portuguesa.

FROM NON-PLACE TO PLACE: A STUDY OF EUROPEAN PUBLIC SPACE AS A SPACE OF IDENTITY

Master Erasmus Mundus Crossways in European Humanities

Design of New Materials for Passive Vibration Control

The aim of this contribution is to extend the techniques of composite materials design to non-linear material behaviour and apply it for design of new materials for passive vibration control. As a first step a computational tool allowing determination of macroscopic optimized one-dimensional isolator behaviour was developed. Voigt, Maxwell, standard and more complex material models can be implemented. Objective function considers minimization of the initial reaction and/or displacement peak as well as minimization of the steady-state amplitude of reaction and/or displacement. The complex stiffness approach is used to formulate the governing equations in an efficient way. Material stiffness parameters are assumed as non-linear functions of the displacement. The numerical solution is performed in the complex space. The steady-state solution in the complex space is obtained by an iterative process based on the shooting method which imposes the conditions of periodicity with respect to the known value of the period. Extension of the shooting method to the complex space is presented and verified. Non-linear behaviour of material parameters is then optimized by generic probabilistic meta-algorithm, simulated annealing. Dependence of the global optimum on several combinations of leading parameters of the simulated annealing procedure, like neighbourhood definition and annealing schedule, is also studied and analyzed. Procedure is programmed in MATLAB environment.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

State Space Analysis of Forest Fires

This paper studies forest fires from the perspective of dynamical systems. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated by means of different mathematical tools. First, we use mutual information to reveal potential relationships in the data. Second, we adopt the state space portrait to characterize the system’s behavior. Third, we compare the annual state space curves and we apply clustering and visualization tools to unveil long-range patterns. We use forest fire data for Portugal, covering the years 1980–2003. The territory is divided into two regions (North and South), characterized by different climates and vegetation. The adopted methodology represents a new viewpoint in the context of forest fires, shedding light on a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels.

An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Three-Dimensional Contrast-Enhanced Magnetic Resonance Pulmonary Angiography in the Study of Pulmonary Vascular Pathology

OBJECTIVES: To assess the feasibility of performing pulmonary angiography using MRI with contrast enhancement in patients with pulmonary vascular disease. METHODS: We present our experience in ten individuals, two controls and eight patients who underwent the exam after injection of a gadolinium-based contrast agent on a 1 Tesla MR scanner using a time-of-flight sequence and breath-holding during injection of contrast. RESULTS: Pathology in the main pulmonary artery and its major branches was detected easily while resolution at the segmental and subsegmental levels was inadequate. CONCLUSION: Contrast-enhanced magnetic resonance pulmonary angiography is feasible on a 1 Tesla MR scanner for the study of pathology of the main pulmonary artery and its major branches, like massive pulmonary embolism. However its ability to detect and define distal vessel pathology as found in chronic thromboembolic pulmonary hypertension and small pulmonary emboli is limited.