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.

Hexanuclear and undecanuclear iron(III) carboxylates as catalyst precursors for cyclohexane oxidation

Two multinuclear complexes [Fe-6(mu(3)-O)(2)(mu(4)-O-2)L-10(OAc)(2)(H2O)(2)]center dot 2.625Et(2)O center dot 2.375H(2)O (1) and [(Fe11Cl)-Cl-III-(mu(4)-O)(3)(mu(3)-O)(5)L-16(dmf)(2.5)(H2O)(0.5)]center dot Et2O center dot 1.25dmf center dot 3.8H(2)O (2), where HL = 3,4,5-trimethoxybenzoic acid and dmf = dimethylformamide, have been prepared from trinuclear iron(III) carboxylates via their structural rearrangement in dimethylformamide or diethyl ether-dimethylformamide 9:1, respectively, and slow vapor diffusion of diethyl ether into the reaction mixture. Both compounds have been characterized by X-ray diffraction, optical, Mossbauer spectroscopy, and magnetic measurements. Complex 1 possesses a hexanuclear ferric peroxido-dioxido {Fe-6(O-2)(O)(2)}(12+) core unit, which adopts a recliner conformation, while complex 2 contains an unprecedented {Fe11O8Cl}(16+) core, in which 9 ferric ions are six-coordinate and the remaining two are five-coordinate. Another structural feature of note of the undecanuclear core is the presence of a deformed cubane entity {Fe-4(mu(3)-O)(mu(4)-O)(3)}(4+). Both complexes act as catalyst precursors for the oxidation of cyclohexane to cyclohexanol and cyclohexanone with aqueous H2O2, in the presence of pyrazinecarboxylic acid. Remarkable TONs and TOFs (the latter mainly for 1) with concomitant quite good yields have been achieved under mild conditions. Moreover, 1 exhibits remarkably high activity in an exceptionally short reaction time (45 min), being unprecedented for any metal catalyzed alkane oxidation by H2O2. The catalytic reactions proceed via Fenton type chemistry.

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.

PPO Reaction Scale-up

O óxido de polifenileno com a marca comercial PPO® é uma das resinas principais produzidas na SABIC IP e o ingrediente principal do plástico de engenharia com a marca registada, Noryl®. A equipa de tecnologia de processo de PPO® desenvolve uma série de novos produtos em reactores de pequena escala, tanto em Selkirk como em Bergen op Zoom. Para se efectuar uma transição rápida da escala laboratorial para a fábrica, é necessário um conhecimento completo do reactor. O objectivo deste projecto consiste em esboçar linhas gerais para o scale-up de novos produtos de PPO1, do laboratório para a escala industrial, baseado no estudo de um tipo de PPO, PPO 803. Este estudo pode ser dividido em duas fases. Numa primeira fase, as receitas e os perfis da reacção são comparados, de onde se retiram as primeiras conclusões. Posteriormente, com base nestas conclusões, é realizado um planeamento experimental. O estudo inicial sugeriu que a receita, a temperatura inicial do reactor e a velocidade do agitador poderiam influenciar o tempo da reacção bem como a queda da velocidade intrínseca do polímero (IV drop). As reacções experimentais mostraram que a receita é o principal factor que influencia, tanto o tempo de reacção, como a queda de viscosidade intrínseca. O tempo de reacção será tanto maior quanto menor a agitação devido à má dispersão do oxigénio na mistura. O uso de temperaturas iniciais elevadas conduz a uma queda maior da viscosidade intrínseca devido à desactivação do catalisador. O método experimental utilizado no laboratório de Bergen op Zoom é um bom exemplo, simulador, do procedimento utilizado na fábrica.

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 Brasília, 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.

Determination of polyphenols in wines by reaction with 4-aminoantipyrine and photometric flow-injection analysis

A new flow-injection analytical procedure is proposed for the determination of the total amount of polyphenols in wines; the method is based on the formation of a colored complex between 4-aminoantipyrine and phenols, in the presence of an oxidizing reagent. The oxidizing agents hexacyanoferrate(III), peroxodisulfate, and tetroxoiodate(VII) were tested. Batch trials were first performed to select appropriate oxidizing agents, pH, and concentration ratios of reagents, on the basis of their effect on the stability of the colored complex. Conditions selected as a result of these trials were implemented in a flow-injection analytical system in which the influence of injection volume, flow rate, and reaction- coil length, was evaluated. Under the optimum conditions the total amount of polyphenols, expressed as gallic acid, could be determined within a concentration range of 36 to 544 mg L–1, and with a sensitivity of 344 L mol–1 cm–1 and an RSD <1.1%. The reproducibility of analytical readings was indicative of standard deviations <2%. Interference from sugars, tartaric acid, ascorbic acid, methanol, ammonium sulfate, and potassium chloride was negligible. The proposed system was applied to the determination of total polyphenols in red wines, and enabled analysis of approximately 55 samples h–1. Results were usually precise and accurate; the RSD was <3.9% and relative errors, by the Folin–Ciocalteu method, <5.1%.

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

A maioria dos órgãos históricos portugueses data dos finais do século XVIII ou do princípio do século XIX. Durante este período foi construído um invulgar número de instrumentos em Lisboa e nas áreas circundantes por António Xavier Machado e Cerveira (1756-1828) e outros organeiros menos prolíficos. O estudo desses órgãos, muitos dos quais (restaurados ou não) se encontram próximos das condições originais, permite a identificação de um tipo de instrumento com uma morfologia específica, claramente emancipada do chamado «órgão ibérico». No entanto, até muito recentemente, não era conhecida música que se adaptasse às idiossincrasisas daqueles instrumentos. O recente estudo das obras para órgão de José Marques e Silva (1782-1837) permitiu clarificar esta situação. Bem conhecido durante a sua vida como organista e compositor, José Marques e Silva foi um dos ultimos mestres do Seminário Patriarcal. A importância da sua produção musical reside não só num substancial número de obras com autoria firmemente estabelecida – escritas, na maior parte, para coro misto com acompanhamento de órgão obbligato – mas também na íntima relação entre a sua escrita e a morfologia dos órgãos construídos em Portugal durante a sua vida. Este artigo enfatiza a importância de José Marques e Silva (indubitavelmente, o mais significativo compositor português para órgão do seu tempo) sublinhando a relevância das suas obras para órgão solo, cujo uso extensivo de escrita idiomática e indicações de registação fazem delas um dos mais importantes documentos só início do século XIX sobre a prática organística 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.

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

Doutoramento em Gestão

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.

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.

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.

Ground reaction forces and plantar pressure distribution during occasional loaded gait

This study compared the ground reaction forces (GRF) and plantar pressures between unloaded and occasional loaded gait. The GRF and plantar pressures of 60 participants were recorded during unloaded gait and occasional loaded gait (wearing a backpack that raised their body mass index to 30); this load criterion was adopted because is considered potentially harmful in permanent loaded gait (obese people). The results indicate an overall increase (absolute values) of GRF and plantar pressures during occasional loaded gait (p < 0.05); also, higher normalized (by total weight) values in the medial midfoot and toes, and lower values in the lateral rearfoot region were observed. During loaded gait the magnitude of the vertical GRF (impact and thrust maximum) decreased and the shear forces increased more than did the proportion of the load (normalized values). These data suggest a different pattern of GRF and plantar pressure distribution during occasional loaded compared to unloaded gait.

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.

Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system’s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author’s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.