Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

What is a fractional derivative?

This paper discusses the concepts underlying the formulation of operators capable of being interpreted as fractional derivatives or fractional integrals. Two criteria for required by a fractional operator are formulated. The Grünwald–Letnikov, Riemann–Liouville and Caputo fractional derivatives and the Riesz potential are accessed in the light of the proposed criteria. A Leibniz rule is also obtained for the Riesz potential.

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.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Learning in higher education: strategies to overcome challenges faced by adult students - lessons drawn from two studies in portugal

Int’l J. of Information and Communication Technology Education, 3(2), 1-14, April-June 2007

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.

Online versus postal questionnaires: a comparison between two data collection methods

Objectives : The purpose of this article is to find out differences between surveys using paper and online questionnaires. The author has deep knowledge in the case of questions concerning opinions in the development of survey based research, e.g. the limits of postal and online questionnaires. Methods : In the physician studies carried out in 1995 (doctors graduated in 1982-1991), 2000 (doctors graduated in 1982-1996), 2005 (doctors graduated in 1982-2001), 2011 (doctors graduated in 1977-2006) and 457 family doctors in 2000, were used paper and online questionnaires. The response rates were 64%, 68%, 64%, 49% and 73%, respectively. Results : The results of the physician studies showed that there were differences between methods. These differences were connected with using paper-based questionnaire and online questionnaire and response rate. The online-based survey gave a lower response rate than the postal survey. The major advantages of online survey were short response time; very low financial resource needs and data were directly loaded in the data analysis software, thus saved time and resources associated with the data entry process. Conclusions : The current article helps researchers with planning the study design and choosing of the right data collection method.

Post-surgical wound infections involving Enterobacteriaceae with reduced susceptibility to ß-lactams in two Portuguese hospitals

The post-surgical period is often critical for infection acquisition. The combination of patient injury and environmental exposure through breached skin add risk to pre-existing conditions such as drug or depressed immunity. Several factors such as the period of hospital staying after surgery, base disease, age, immune system condition, hygiene policies, careless prophylactic drug administration and physical conditions of the healthcare centre may contribute to the acquisition of a nosocomial infection. A purulent wound can become complicated whenever antimicrobial therapy becomes compromised. In this pilot study, we analysed Enterobacteriaceae strains, the most significant gram-negative rods that may occur in post-surgical skin and soft tissue infections (SSTI) presenting reduced β-lactam susceptibility and those presenting extended-spectrum β-lactamases (ESBL). There is little information in our country regarding the relationship between β-lactam susceptibility, ESBL and development of resistant strains of microorganisms in SSTI. Our main results indicate Escherichia coli and Klebsiella spp. are among the most frequent enterobacteria (46% and 30% respectively) with ESBL production in 72% of Enterobacteriaceae isolates from SSTI. Moreover, coinfection occurred extensively, mainly with Pseudomonas aeruginosa and Methicillin-resistant Staphylococcus aureus (18% and 13%, respectively). These results suggest future research to explore if and how these associations are involved in the development of antibiotic resistance.

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.

Image upsampling algorithms applied on Nuclear Medicine: comparision of hqnx and nxSaI algorithms families with two interpolation algorithms - nearest neighbour and bicubic interpolation

Introduction: Image resizing is a normal feature incorporated into the Nuclear Medicine digital imaging. Upsampling is done by manufacturers to adequately fit more the acquired images on the display screen and it is applied when there is a need to increase - or decrease - the total number of pixels. This paper pretends to compare the “hqnx” and the “nxSaI” magnification algorithms with two interpolation algorithms – “nearest neighbor” and “bicubic interpolation” – in the image upsampling operations. Material and Methods: Three distinct Nuclear Medicine images were enlarged 2 and 4 times with the different digital image resizing algorithms (nearest neighbor, bicubic interpolation nxSaI and hqnx). To evaluate the pixel’s changes between the different output images, 3D whole image plot profiles and surface plots were used as an addition to the visual approach in the 4x upsampled images. Results: In the 2x enlarged images the visual differences were not so noteworthy. Although, it was clearly noticed that bicubic interpolation presented the best results. In the 4x enlarged images the differences were significant, with the bicubic interpolated images presenting the best results. Hqnx resized images presented better quality than 4xSaI and nearest neighbor interpolated images, however, its intense “halo effect” affects greatly the definition and boundaries of the image contents. Conclusion: The hqnx and the nxSaI algorithms were designed for images with clear edges and so its use in Nuclear Medicine images is obviously inadequate. Bicubic interpolation seems, from the algorithms studied, the most suitable and its each day wider applications seem to show it, being assumed as a multi-image type efficient algorithm.

Comparative study between two distinct methods for attenuation correction and the use of no-attenuation correction for the assessment of relative uptake of 99mTc-DMSA on pediatric patients

Introduction: Although relative uptake values aren’t the most important objective of a 99mTc-DMSA scan, they are important quantitative information. In most of the dynamic renal scintigraphies attenuation correction is essential if one wants to obtain a reliable result of the quantification process. Although in DMSA scans the absent of significant background and the lesser attenuation in pediatric patients, makes that this attenuation correction techniques are actually not applied. The geometric mean is the most common method, but that includes the acquisition of an anterior (extra) projection, which it is not acquired by a large number of NM departments. This method and the attenuation factors proposed by Tonnesen will be correlated with the absence of attenuation correction procedures. Material and Methods: Images from 20 individuals (aged 3 years +/- 2) were used and the two attenuation correction methods applied. The mean time of acquisition (time post DMSA administration) was 3.5 hours +/- 0.8h. Results: The absence of attenuation correction showed a good correlation with both attenuation methods (r=0.73 +/- 0.11) and the mean difference verified on the uptake values between the different methods were 4 +/- 3. The correlation was higher when the age was lower. The attenuation correction methods correlation was higher between them two than with the “no attenuation correction” method (r=0.82 +/- 0.8), and the mean differences of the uptake values were 2 +/- 2. Conclusion: The decision of not doing any kind of attenuation correction method can be justified by the minor differences verified on the relative kidney uptake values. Nevertheless, if it is recognized that there is a need for an accurate value of the relative kidney uptake, then an attenuation correction method should be used. Attenuation correction factors proposed by Tonnesen can be easily implemented and so become a practical and easy to implement alternative, namely when the anterior projection - needed for the geometric mean methodology – is not acquired.

Sintonia de controladores baseada em Sistemas de Inferência Difusa

Este trabalho de pesquisa e desenvolvimento tem como fundamento principal o Conceito de Controlo por Lógica Difusa. Utilizando as ferramentas do software Matlab, foi possível desenvolver um controlador com base na inferência difusa que permitisse controlar qualquer tipo de sistema físico real, independentemente das suas características. O Controlo Lógico Difuso, do inglês “Fuzzy Control”, é um tipo de controlo muito particular, pois permite o uso simultâneo de dados numéricos com variáveis linguísticas que tem por base o conhecimento heurístico dos sistemas a controlar. Desta forma, consegue-se quantificar, por exemplo, se um copo está “meio cheio” ou “meio vazio”, se uma pessoa é “alta” ou “baixa”, se está “frio” ou “muito frio”. O controlo PID é, sem dúvida alguma, o controlador mais amplamente utilizado no controlo de sistemas. Devido à sua simplicidade de construção, aos reduzidos custos de aplicação e manutenção e aos resultados que se obtêm, este controlador torna-se a primeira opção quando se pretende implementar uma malha de controlo num determinado sistema. Caracterizado por três parâmetros de ajuste, a saber componente proporcional, integral e derivativa, as três em conjunto permitem uma sintonia eficaz de qualquer tipo de sistema. De forma a automatizar o processo de sintonia de controladores e, aproveitando o que melhor oferece o Controlo Difuso e o Controlo PID, agrupou-se os dois controladores, onde em conjunto, como poderemos constatar mais adiante, foram obtidos resultados que vão de encontro com os objectivos traçados. Com o auxílio do simulink do Matlab, foi desenvolvido o diagrama de blocos do sistema de controlo, onde o controlador difuso tem a tarefa de supervisionar a resposta do controlador PID, corrigindo-a ao longo do tempo de simulação. O controlador desenvolvido é denominado por Controlador FuzzyPID. Durante o desenvolvimento prático do trabalho, foi simulada a resposta de diversos sistemas à entrada em degrau unitário. Os sistemas estudados são na sua maioria sistemas físicos reais, que representam sistemas mecânicos, térmicos, pneumáticos, eléctricos, etc., e que podem ser facilmente descritos por funções de transferência de primeira, segunda e de ordem superior, com e sem atraso.

Evaluation of ochratoxin A exposure degree in two Portuguese cities through wheat and maize bread consumption during the winter 2007

The occurrence of OTA in fresh and packed wheat and in maize bread and the evaluation of the exposure degree through their consumption in two Portuguese populations from Porto and Coimbra, during the winter of 2007, were studied. One hundred and sixty eight bread samples, 61 maize and 107 wheat, were analysed by liquid chromatography–fluorescence detection (LC–FD). The results showed that 84% of samples were contaminated, with a maximum level of 3.85 ng/g (above the EU maximum limit, 3 ng/g). Fresh wheat bread presented higher levels than packed wheat bread. Moreover, the traditional maize bread, in either city, was consistently more contaminated than wheat bread, 0.25 vs 0.19 ng/g, and 0.48 vs 0.34 ng/ g for Porto and Coimbra, respectively. Avintes maize bread showed the highest mean contamination and maximum levels. The higher estimated daily intake of OTA from both types of bread in the population of Coimbra compared to Porto reflects the higher average contamination of bread in the first city.

Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.