Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

An application of structural equation modeling of test dispositional optimism as mediator or moderator in quality of life in patients with chronic disease

The aim of the present study was to test a hypothetical model to examine if dispositional optimism exerts a moderating or a mediating effect between personality traits and quality of life, in Portuguese patients with chronic diseases. A sample of 540 patients was recruited from central hospitals in various districts of Portugal. All patients completed self-reported questionnaires assessing socio-demographic and clinical variables, personality, dispositional optimism, and quality of life. Structural equation modeling (SEM) was used to analyze the moderating and mediating effects. Results suggest that dispositional optimism exerts a mediator rather than a moderator role between personality traits and quality of life, suggesting that “the expectation that good things will happen” contributes to a better general well-being and better mental functioning.

Removal of Cd(II), Zn(II) and Pb(II) from aqueous solutions by brown marine macro algae: kinetic modelling

Specific marine macro algae species abundant at the Portuguese coast (Laminaria hyperborea, Bifurcaria bifurcata, Sargassum muticum and Fucus spiralis) were shown to be effective for removing toxic metals (Cd(II), Zn(II) and Pb(II)) from aqueous solutions. The initial metal concentrations in solution were about 75–100 mg L−1. The observed biosorption capacities for cadmium, zinc and lead ions were in the ranges of 23.9–39.5, 18.6–32.0 and 32.3–50.4 mg g−1, respectively. Kinetic studies revealed that the metal uptake rate was rather fast, with 75% of the total amount occurring in the first 10 min for all algal species. Experimental data were well fitted by a pseudo-second order rate equation. The contribution of internal diffusion mechanism was significant only to the initial biosorption stage. Results indicate that all the studied macro algae species can provide an efficient and cost-effective technology for eliminating heavy metals from industrial effluents.

On local fractional continuous wavelet transform

We introduce a new wavelet transform within the framework of the local fractional calculus. An illustrative example of local fractional wavelet transform is also presented.

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.

Influence of network effects on the diffusion of information systems: the case of open source

Doutoramento em Gestão

Fractional model for malaria transmission under control strategies

We study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

Effects of international diffusion of a general purpose technology on wage inequality

This paper studies the effects of the diffusion of a General Purpose Technology (GPT) that spreads first within the developed North country of its origin, and then to a developing South country. In the developed general equilibrium growth model, each final good can be produced by one of two technologies. Each technology is characterized by a specific labor complemented by a specific set of intermediate goods, which are enhanced periodically by Schumpeterian R&D activities. When quality reaches a threshold level, a GPT arises in one of the technologies and spreads first to the other technology within the North. Then, it propagates to the South, following a similar sequence. Since diffusion is not even, neither intra- nor inter-country, the GPT produces successive changes in the direction of technological knowledge and in inter- and intra-country wage inequality. Through this mechanism the different observed paths of wage inequality can be accommodated.

Fractional dynamics of genetic algorithms using hexagonal space tessellation

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Fractional coins and fractional derivatives

This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.