Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Hábitos de utilização da internet nos alunos do ensino superior: caso de estudo

Coletânea de artigos no âmbito da Conferência Investigação e Intervenção em Recursos Humanos: Gestão para a Cidadania, Vila do Conde, 2009

Comparison of internet usage habits in two generations of higher education students: a case study

Posters

A Lei de ZIPF ou Regra 80/20 da Internet

As Leis de Potência, LP, (Power Laws, em inglês), Leis de Pareto ou Leis de Zipf são distribuições estatísticas, com inúmeras aplicações práticas, em sistemas naturais e artificiais. Alguns exemplos são a variação dos rendimentos pessoais ou de empresas, a ocorrência de palavras em textos, as repetições de sons ou conjuntos de sons em composições musicais, o número de vítimas em guerras ou outros cataclismos, a magnitude de tremores de terra, o número de vendas de livros ou CD’s na internet, o número de sítios mais acedidos na Internet, entre muitos outros. Vilfredo Pareto (1897-1906) afirma, no manual de economia política “Cours d’Economie Politique”, que grande parte da economia mundial segue uma determinada distribuição, em que 20% da população reúne 80% da riqueza total do país, estando, assim uma pequena fração da sociedade a controlar a maior fatia do dinheiro. Isto resume o comportamento de uma variável que segue uma distribuição de Pareto (ou Lei de Potência). Neste trabalho pretende-se estudar em pormenor a aplicação das leis de potência a fenómenos da internet, como sendo o número de sítios mais visitados, o número de links existentes em determinado sítio, a distribuição de nós numa rede da internet, o número livros vendidos e as vendas em leilões online. Os resultados obtidos permitem-nos concluir que todos os dados estudados são bem aproximados, numa escala logarítmica, por uma reta com declive negativo, seguindo, assim, uma distribuição de Pareto. O desenvolvimento e crescimento da Web, tem proporcionado um aumento do número dos utilizadores, conteúdos e dos sítios. Grande parte dos exemplos presentes neste trabalho serão alvo de novos estudos e de novas conclusões. O fato da internet ter um papel preponderante nas sociedades modernas, faz com que esteja em constante evolução e cada vez mais seja possível apresentar fenómenos na internet associados Lei de Potência.

The Port as a “Non Consensual” Organisation: An IC Management Perspective

This paper addresses a gap in the literature concerning the management of Intellectual Capital (IC) in a port, which is a network of independent organizations that act together in the provision of a set of services. As far as the authors are aware, this type of empirical context has been unexplored when regarding knowledge management or IC creation/destruction. Indeed, most research in IC still focus on individual firms, despite the more recent interest placed on the analysis of macro-level units such as regions or nations. In this study, we conceptualise the port as meta-organisation, which has the generic goal of economic development, both for itself and for the region where it is located. It provides us with a unique environment due to its complexity as an “organisation” composed by several organisations, connected by interdependency relationships and, typically, with no formal hierarchy. Accordingly, actors’ interests are not always aligned and in some situations their individual interests can be misaligned with the collective goals of the port. Moreover, besides having their own interests, port actors also have different sources of influence and different levels of power, which can impact on the port’s Collective Intellectual Capital (CIC). Consequently, the management of the port’s CIC can be crucial in order for its goals to be met. With this paper we intend to discuss how the network coordinator (the port authority) manages those complex relations of interest and power in order to develop collaboration and mitigate conflict, thus creating collective intellectual assets or avoiding intellectual liabilities that may emerge for the whole port. The fact that we are studying complex and dynamic processes, about which there is a lack of understanding, in a complex and atypical organisation, leads us to consider the case study as an appropriate method of research. Evidence presented in this study results from preliminary interviews and also from document analysis. Findings suggest that alignment of interests and actions, at both dyadic and networking levels, is critical to develop a context of collaboration/cooperation within the port community and, accordingly, the port coordinator should make use of different types of power in order to ensure that port’s goals are achieved.

Contribuição do setor segurador para a internacionalização das empresas portuguesas: estudo de caso da Somelos Tecidos, S.A.

Dissertação apresentada ao Instituto Politécnico do Porto – Instituto Superior de Contabilidade e Administração do Porto - para obtenção do Grau de Mestre em Empreendedorismo e Internacionalização Orientador: Doutor Orlando Manuel Martins Marques de Lima Rua

Persistent organic pollutant levels in human visceral and subcutaneous adipose tissue in obese individuals - Depot differences and dysmetabolism implications

Background: The role of persistent organic pollutants (POPs) with endocrine disrupting activity in the aetiology of obesity and other metabolic dysfunctions has been recently highlighted. Adipose tissue (AT) is a common site of POPs accumulation where they can induce adverse effects on human health. Objectives: To evaluate the presence of POPs in human visceral (vAT) and subcutaneous (scAT) adipose tissue in a sample of Portuguese obese patients that underwent bariatric surgery, and assess their putative association with metabolic disruption preoperatively, as well as with subsequent body mass index (BMI) reduction. Methods: AT samples (n=189) from obese patients (BMI ≥35) were collected and the levels of 13 POPs were determined by gas chromatography with electron-capture detection (GC-ECD). Anthropometric and biochemical data were collected at the time of surgery. BMI variation was evaluated after 12 months and adipocyte size was measured in AT samples. Results: Our data confirm that POPs are pervasive in this obese population (96.3% of detection on both tissues), their abundance increasing with age (RS=0.310, p<0.01) and duration of obesity (RS=0.170, p<0.05). We observed a difference in AT depot POPs storage capability, with higher levels of ΣPOPs in vAT (213.9±204.2 compared to 155.1±147.4 ng/g of fat, p<0.001), extremely relevant when evaluating their metabolic impact. Furthermore, there was a positive correlation between POP levels and the presence of metabolic syndrome components, namely dysglycaemia and hypertension, and more importantly with cardiovascular risk (RS=0.277, p<0.01), with relevance for vAT (RS=0.315, p<0.01). Finally, we observed an interesting relation of higher POP levels with lower weight loss in older patients. Conclusion: Our sample of obese subjects allowed us to highlight the importance of POPs stored in AT on the development of metabolic dysfunction in a context of obesity, shifting the focus to their metabolic effects and not only for their recognition as environmental obesogens.

Proof of Concept of the Electrochemical Sensing of 3-Iodothyronamine (T1AM) and Thyronamine (T0AM)

Recent studies have shown that, besides the well-recognized T3 and T4 hormones, there are other relevant thyroid hormones circulating in the human body. In particular, this is the case for 3-iodothyronamine (T1AM) and thyronamine (T0AM). One of the reasons for the lack of studies showing their precise importance is the absence of analytical methodologies available. Herein, for the first time, T1AM and T0AM are electrochemically characterized. T0AM was sensed by means of a glassy carbon electrode; furthermore, T1AM was sensed both with a graphitic surface (oxidatively) as well as with mercury (reductively). For both compounds, after oxidation, it was possible to observe the reversible redox reaction concerning the benzoquinone/hydroquinone couple, thus increasing the specificity of the electroanalysis. Therefore, this work provides the basis for an ‘at-point-of-use’ electrochemical strip test for T1AM and T0AM.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.

Multidimensional scaling visualization of earthquake phenomena

Earthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the Flinn–Engdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Space-time and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the non-uniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. 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 behavior of earthquakes.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.

Double power laws, fractals and self-similarity

Power law (PL) distributions have been largely reported in the modeling of distinct real phenomena and have been associated with fractal structures and self-similar systems. In this paper, we analyze real data that follows a PL and a double PL behavior and verify the relation between the PL coefficient and the capacity dimension of known fractals. It is to be proved a method that translates PLs coefficients into capacity dimension of fractals of any real data.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.