On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that the global behavior of a smooth positive definite function is, to a large extent, determined solely by the sequence of even-order derivatives at the origin: if a single one of these vanishes then the function is constant; if they are all non-zero and satisfy a natural growth condition, the function is real-analytic and consequently extends holomorphically to a maximal horizontal strip of the complex plane.

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.

Synthesis of optimization of [11C] Pittsburgh compound B by the captive solvent method

Mestrado em Medicina Nuclear.

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.

Complex variable positive definite functions

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Multiobjective design of viscoelastic laminated composite sandwich panels

The optimal design of laminated sandwich panels with viscoelastic core is addressed in this paper, with the objective of simultaneously minimizing weight and material cost and maximizing modal damping. The design variables are the number of layers in the laminated sandwich panel, the layer constituent materials and orientation angles and the viscoelastic layer thickness. The problem is solved using the Direct MultiSearch (DMS) solver for multiobjective optimization problems which does not use any derivatives of the objective functions. A finite element model for sandwich plates with transversely compressible viscoelastic core and anisotropic laminated face layers is used. Trade-off Pareto optimal fronts are obtained and the results are analyzed and discussed.

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.

Direct multisearch for multiobjective optimization

In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. Our framework is inspired by the search/poll paradigm of direct-search methods of directional type and uses the concept of Pareto dominance to maintain a list of nondominated points (from which the new iterates or poll centers are chosen). The aim of our method is to generate as many points in the Pareto front as possible from the polling procedure itself, while keeping the whole framework general enough to accommodate other disseminating strategies, in particular, when using the (here also) optional search step. DMS generalizes to multiobjective optimization (MOO) all direct-search methods of directional type. We prove under the common assumptions used in direct search for single objective optimization that at least one limit point of the sequence of iterates generated by DMS lies in (a stationary form of) the Pareto front. However, extensive computational experience has shown that our methodology has an impressive capability of generating the whole Pareto front, even without using a search step. Two by-products of this paper are (i) the development of a collection of test problems for MOO and (ii) the extension of performance and data profiles to MOO, allowing a comparison of several solvers on a large set of test problems, in terms of their efficiency and robustness to determine Pareto fronts.

Meios de comunicação como instrumentos de inserção da comunidade cabo-verdiana na sociedade de acolhimento: o caso da área metropolitana de Lisboa

Dissertação apresentada à Escola Superior de Comunicação Social como parte dos requisitos para obtenção de grau de mestre em Jornalismo.

José Saramago e os jornais: os anos de 1968 a 1975

Dissertação apresentada à Escola Superior de Comunicação Social como parte dos requisitos para obtenção de grau de mestre em Jornalismo.

Periodic paths on nonautonomous graphs

We define nonautonomous graphs as a class of dynamic graphs in discrete time whose time-dependence consists in connecting or disconnecting edges. We study periodic paths in these graphs, and the associated zeta functions. Based on the analytic properties of these zeta functions we obtain explicit formulae for the number of n-periodic paths, as the sum of the nth powers of some specific algebraic numbers.

Sobrevivência das redes de transporte da nova geração

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Quanto tempo dura um instante?: da dualidade do efémero e da permanência do serviço educativo

Relatório de Estágio submetido à Escola Superior de Teatro e Cinema para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Teatro – Especialização em Produção

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.