Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

PLSR Models for Mechanical Strengths of Concrete Composite Materials Reinforced with Pultrusion Wastes

In this paper, we present two Partial Least Squares Regression (PLSR) models for compressive and flexural strength responses of a concrete composite material reinforced with pultrusion wastes. The main objective is to characterize this cost-effective waste management solution for glass fiber reinforced polymer (GFRP) pultrusion wastes and end-of-life products that will lead, thereby, to a more sustainable composite materials industry. The experiments took into account formulations with the incorporation of three different weight contents of GFRP waste materials into polyester based mortars, as sand aggregate and filler replacements, two waste particle size grades and the incorporation of silane adhesion promoter into the polyester resin matrix in order to improve binder aggregates interfaces. The regression models were achieved for these data and two latent variables were identified as suitable, with a 95% confidence level. This technological option, for improving the quality of GFRP filled polymer mortars, is viable thus opening a door to selective recycling of GFRP waste and its use in the production of concrete-polymer based products. However, further and complementary studies will be necessary to confirm the technical and economic viability of the process.

Supporting leadership development by exposure to role models: two case studies

The idiomatic expression “In Rome be a Roman” can be applied to leadership training and development as well. Leaders who can act as role models inspire other future leaders in their behaviour, attitudes and ways of thinking. Based on two examples of current leaders in the fields of Politics and Public Administration, I support the idea that exposure to role models during their training was decisive for their career paths and current activities as prominent characters in their profession. Issues such as how students should be prepared for community or national leadership as well as cross-cultural engagement are raised here. The hypothesis of transculturalism and cross-cultural commitment as a factor of leadership is presented. Based on current literature on Leadership as well as the presented case studies, I expect to raise a debate focusing on strategies for improving leaders’ training in their cross-cultural awareness.

Long-term price range forecast applied to risk management using regression models

Long-term contractual decisions are the basis of an efficient risk management. However those types of decisions have to be supported with a robust price forecast methodology. This paper reports a different approach for long-term price forecast which tries to give answers to that need. Making use of regression models, the proposed methodology has as main objective to find the maximum and a minimum Market Clearing Price (MCP) for a specific programming period, and with a desired confidence level α. Due to the problem complexity, the meta-heuristic Particle Swarm Optimization (PSO) was used to find the best regression parameters and the results compared with the obtained by using a Genetic Algorithm (GA). To validate these models, results from realistic data are presented and discussed in detail.

Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Derivative-free nonlinear optimization filter simplex

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to use optimization methods where the calculation of the derivatives or the verification of their existence is not necessary: direct search methods or derivative-free methods are examples of such techniques. In this work we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of simplex and filter methods. This method neither computes nor approximates derivatives, penalty constants or Lagrange multipliers.

Sustentabilidade em escolas - um caso de estudo

Devido à actual conjuntura sócio económica e às crescentes preocupações ambientais e sociais houve a necessidade de construir e desenvolver indicadores de sustentabilidade que registassem e avaliassem o desempenho, ano após ano, da comunidade escolar, de modo a melhorá-lo, pois as escolas devem ser elas próprias, modelos de sustentabilidade. Os indicadores formulados e desenvolvidos são ferramentas de gestão pois facultam a identificação de prioridades, o estabelecimento de metas e a tomada de decisões além de possibilitarem a elaboração de um historial que pode ajudar a melhorar o desempenho económico, ambiental e social das escolas, de acordo com os três pilares do desenvolvimento sustentável. Foram aplicados, ao caso de estudo, os indicadores considerados mais relevantes, tendo em conta a globalidade da sua aplicação, a sua clareza, mensurabilidade, compreensibilidade e reprodutibilidade. Obtiveram-se 185 indicadores de eficiência distribuídos pelas áreas ambiental (46), social (85), económica (18) e ensino / aprendizagem (36) e 63 indicadores descritivos distribuídos pelas áreas social (39), económica (9) e ensino / aprendizagem (15). Através de um inquérito realizado para avaliar as expectativas globais da comunidade escolar e dos dados disponibilizados pelo gabinete de qualidade e pela administração da escola, que serviu de caso de estudo, conseguiram-se calcular 71% dos indicadores de eficiência e 70% dos indicadores descritivos propostos.

Satisfação de agentes afectivos no processo de tomada de decisão em grupo

Um dos factores mais determinantes para o sucesso de uma organização é a qualidade das decisões tomadas. Para que as decisões tomadas sejam melhores e potenciem a competitividade das organizações, sistemas como os Sistemas de Apoio à Tomada de Decisão em Grupo (SADG) têm sido fortemente desenvolvidos e estudados nas últimas décadas. Cada vez mais, estes sistemas são populados com um maior número de dados, com o objectivo de serem mais assertivos. Considera-se que com determinados dados seja possível que o sistema possa aferir a satisfação dos participantes com as decisões tomadas, tendencialmente de forma automática. Hoje em dia, as análises de satisfação com as decisões não contemplam na sua maioria factores imprescindíveis, como os emocionais e de personalidade, sendo que os modelos existentes tendem a ser incompletos. Nesta dissertação propõe-se uma metodologia que permite a um SADG aferir a satisfação do participante com a decisão, considerando aspectos como a personalidade, as emoções e as expectativas. A metodologia desenvolvida foi implementada num SADG (ArgEmotionsAgents) com uma arquitectura multiagente, composto por agentes que reflectem participantes reais e que estão modelados com a sua personalidade. De acordo com a sua personalidade, esses agentes trocam argumentos persuasivos de forma a obterem uma decisão consensual. No processo de troca de argumentos os agentes geram emoções que afectam o seu humor. A implementação da metodologia no ArgEmotionsAgents permite que, no final de uma reunião, seja possível aferir a satisfação dos agentes participantes com a decisão final e com o processo que levou à tomada de decisão. De forma a validar a metodologia proposta bem como a implementação que foi desenvolvida, foram realizadas quatro experiências em diferentes cenários. Numa primeira experiência, foi aferida a satisfação dos quatro agentes participantes. Nas experiências seguintes, um dos agentes participantes foi usado como referência e foram alteradas configurações (expectativas, personalidade e reavaliação das alternativas) para perceber de que forma os vários factores afectam a satisfação. Com o estudo concluiu-se que todos os factores considerados no modelo afectam a satisfação. A forma como a satisfação é afectada por cada um dos factores vai ao encontro da lógica apresentada no estado da arte. Os resultados de satisfação aferidos pelo modelo são congruentes.

Modelling and segmentation of the vocal tract during speech production by using deformable models in magnetic resonance images

The first and second authors would like to thank the support of the PhD grants with references SFRH/BD/28817/2006 and SFRH/PROTEC/49517/2009, respectively, from Fundação para a Ciência e Tecnol ogia (FCT). This work was partially done in the scope of the project “Methodologies to Analyze Organs from Complex Medical Images – Applications to Fema le Pelvic Cavity”, wi th reference PTDC/EEA- CRO/103320/2008, financially supported by FCT.

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer

Adhesively-bonded joints are extensively used in several fields of engineering. Cohesive Zone Models (CZM) have been used for the strength prediction of adhesive joints, as an add-in to Finite Element (FE) analyses that allows simulation of damage growth, by consideration of energetic principles. A useful feature of CZM is that different shapes can be developed for the cohesive laws, depending on the nature of the material or interface to be simulated, allowing an accurate strength prediction. This work studies the influence of the CZM shape (triangular, exponential or trapezoidal) used to model a thin adhesive layer in single-lap adhesive joints, for an estimation of its influence on the strength prediction under different material conditions. By performing this study, guidelines are provided on the possibility to use a CZM shape that may not be the most suited for a particular adhesive, but that may be more straightforward to use/implement and have less convergence problems (e.g. triangular shaped CZM), thus attaining the solution faster. The overall results showed that joints bonded with ductile adhesives are highly influenced by the CZM shape, and that the trapezoidal shape fits best the experimental data. Moreover, the smaller is the overlap length (LO), the greater is the influence of the CZM shape. On the other hand, the influence of the CZM shape can be neglected when using brittle adhesives, without compromising too much the accuracy of the strength predictions.

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.

Combined mutation differential evolution to solve systems of nonlinear equations

This paper presents a differential evolution heuristic to compute a solution of a system of nonlinear equations through the global optimization of an appropriate merit function. Three different mutation strategies are combined to generate mutant points. Preliminary numerical results show the effectiveness of the presented heuristic.

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.