Abelian kernels of monoids of order-preserving maps and of some of its extensions

Semigroup Forum vol. 68 (2004), p. 335–356

A mathematical model for supermarket order picking

Order picking consists in retrieving products from storage locations to satisfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best international practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.

On the monoids of transformations that preserve the order and a uniform partition

Communications in Algebra

Fisioterapia : influência na qualidade de vida da mulher com cancro da mama : contributo para a qualidade do serviço em oncologia

RESUMO - O cancro da mama é uma preocupação da saúde pública a nível mundial, pela sua incidência, mortalidade e custos económicos associados. As terapias utilizadas no seu tratamento, embora eficazes, conduzem a alterações de todas as dimensões da Qualidade de Vida (QdV) da mulher com cancro da mama. A garantia de uma qualidade de serviço prestado deve ser uma prioridade das organizações de saúde, sendo a QdV uma medida de resultado. Partindo do pressuposto que em Portugal existe uma diferença potencial na forma como as mulheres com cancro da mama recebem o apoio por parte da fisioterapia, importa saber se a fisioterapia tem ou não influência na QdV da mulher com cancro da mama, o que, no caso de ser afirmativo, poderá constituir uma mais-valia para a qualidade do serviço prestado em oncologia. O Objectivo deste trabalho é construir um modelo de análise no sentido de responder à questão inicial de investigação: “Será que a fisioterapia contribui para a melhoria da Qualidade de Vida das mulheres com cancro da mama submetidas a cirurgia e outras terapias oncológicas?”. Neste sentido o trabalho de projecto dividiu-se por etapas. Inicialmente foi realizado um enquadramento teórico, através de uma revisão de literatura e da realização de entrevistas exploratórias, permitindo desta forma ter um conhecimento actual das temáticas que definem as variáveis e o objecto de estudo. Na etapa seguinte, foi feita uma análise crítica sobre o conhecimento actual do tema em estudo, que permitiu definir as variáveis a estudar, escolher o instrumento de medida a utilizar, ter conhecimento dos procedimentos a seguir. Após a definição do objectivo geral (avaliar se a fisioterapia tem influência na QdV das mulheres submetidas a cirurgia e outras terapias oncológicas) e dos objectivos específicos, iniciou-se o delineamento da metodologia tida como adequada para responder às questões de investigação levantadas (tipo de estudo, as variáveis, a unidade de análise, os métodos e técnicas de recolha de dados, os procedimentos e a metodologia de tratamento de dados). No âmbito do trabalho de projecto está definida a colocação em campo de um caso de estudo efectivo que permita dar um contributo real no delineamento da metodologia. Neste trabalho optou-se pela realização de um estudo piloto, que se enquadra nos procedimentos da metodologia e que teve por objectivo retirar algumas conclusões sobre: a aplicabilidade do instrumento de medida; os tempos definidos para a recolha de dados; as características sociodemográficas e clínicas da amostra; as questões de investigação levantadas. O estudo piloto consistiu num estudo pré-experimental, com uma amostra de 35 indivíduos, submetidos a cirurgia a cancro da mama e a outras terapias oncológicas. Foram avaliadas as dimensões do bem-estar físico e actividades quotidianas, bem-estar psicológico, relações sociais, sintomas e características sociodemográficas/clínicas, no início do tratamento individual de fisioterapia e no momento de alta. Utilizou-se como instrumento de medida o questionário EORTC QLQ–30 e o seu questionário complementar EORTC QLQ–23. Tendo sido construída uma ficha para recolha de dados sociodemográficos e clínicos. A significância estatística foi aceite para valores de p<0,05. Para comparação entre grupos e evolução dentro de cada grupo aplicou-se o teste t-student e o teste de Mann-Whitney. A análise dos resultados do estudo piloto permitiu verificar que: - O instrumento de medida proposto (questionário EORTC QLQ30 e BR23) mostrou ser de fácil aplicação, não tendo existido dificuldade por parte das doentes no seu preenchimento. Não houve problemas no cálculo dos scores e na sua interpretação; - Parte considerável das mulheres com cancro da mama será submetida a protocolos que se poderão prolongar por vários meses após a cirurgia (ex: QT+RT+HT). Esta realidade leva-nos a propor que sejam realizados vários momentos de avaliação, para que possam ser avaliadas as dimensões da QdV ao longo dos diferentes protocolos de tratamentos. Pensamos que o ideal seria a realização de 4 momentos de avaliação (3 a 4 semanas após a cirurgia, 3 meses, 6 meses e 9 meses após cirurgia). Sugerimos também que o estudo proposto seja realizado com uma amostra de maior dimensão; - O estudo piloto como recorreu a uma metodologia pré-experimental (ausência de grupo de controlo e apenas dois momentos de avaliação), não permite a consistência dos resultados; no entanto os resultados obtidos podem constituir um indicador de que a fisioterapia tem influência nas diferentes dimensões da QdV da mulher com cancro da mama submetida a cirurgia e a outras terapias oncológicas, podendo constituir uma mais-valia para a qualidade do serviço prestado em oncologia. Os resultados do estudo piloto permitiram redefinir a metodologia tida como adequada para responder à questão de investigação inicial. Apresentamos de seguida a mesma: Estudo quase-experimental, sendo a amostra constituída por dois grupos de 60 mulheres cada, submetidas a cirurgia a cancro da mama e a outras terapias oncológicas. O grupo experimental será submetido a tratamentos individuais de fisioterapia. Serão avaliadas as dimensões do bem-estar físico e actividades quotidianas, bem-estar psicológico, relações sociais e sintomas. A recolha de dados será realizada 3 semanas, 3 meses, 6 meses e 9 meses após a cirurgia. Como instrumento de medida será utilizado o questionário EORTC QLQ–30 e o seu questionário complementar EORTC QLQ–23, serão também recolhidos dados sociodemográficos e clínicos. A significância estatística será aceite para valores de p<0,05. Para comparação entre grupos e evolução dentro de cada grupo serão utilizados testes paramétricos e não paramétricos. A realização de um estudo que seguisse a metodologia acima referida permitiria uma maior consistência dos resultados, podendo eventualmente existir a confirmação de que a fisioterapia pode ter influência na QdV da mulher submetida a cirurgia a cancro da mama e a outras terapias oncológicas. A evidência de que a fisioterapia tem influência na QdV da mulher com cancro da mama, e o facto de a QdV ser um indicador da qualidade do serviço prestado em oncologia, poderão constituir um agente facilitador para a mudança na gestão de recursos humanos em organizações de saúde com a valência de oncologia, levando a uma alteração dos padrões de prática na área da fisioterapia em oncologia em Portugal, que poderá conduzir a uma melhor qualidade de serviço prestado ao doente oncológico. ----- ABSTRACT - Breast Cancer is a worldwide public health concern due to the incidence, mortality and economic costs associated. Although effective, therapies used in its treatment lead to changes in all Quality of Life (QoL) dimensions of a woman suffering from Breast Cancer. QoL is an outcome measure, and the insurance of quality of care provided should be a priority to health organizations. Taking into consideration that in Portugal there is a potential difference in the way women with Breast Cancer are provided with physical therapy, it is important to know whether physical therapy does or does not influence the QoL of women with breast cancer. If it does, it will lead to a health care quality improvement to cancer patients. The goal of the following study is to build an analysis model in order to answer the initial investigation question: “Does Physical Therapy contribute to enhance the Quality of Life of women with breast cancer who underwent surgery and other oncology treatments?” The project was divided in different stages. Initially, a literature revision was elaborated and exploratory interviews were held, which allowed an actual knowledge of the themes that define the variables and the object of study. The next stage included a critical analysis of the theme, which allowed the definition of variables of study, the choice of instrument of measure and the acquisition of some knowledge on how to proceed. After the definition of the general goal (to evaluate the influence of physical therapy on the QoL of women with breast cancer who underwent surgery and other oncology treatments) and specific goals, the choice of a right methodology took place, in order to answer the investigation questions (type of study, variables, unit analysis, methods and techniques on data collection, procedures and data treatment). In the scope of the project, it is decided to put out on the field an effective case-study which assures a real contribution on the choice of te methodology. In this particular work, there was a pilot study, included in the methodology procedures, with the goal of obtaining conclusions on the applicability of the instrument of measure; the length of time to collect data, the socio-demographic and clinical characteristics of the sample; the investigation questions. The pilot study consisted on a one group pretest-postest design, with a sample of 35 individuals who underwent surgery and other oncology treatments. Dimensions such as physical well-being and everyday life activities, psychological well-being, social relationships, symptoms and socio-demographical/clinical characteristics were assessed at the beginning of physical therapy individual treatment and at the moment of release. The instrument of measure used was the EORTC QLQ–30 questionnaire and its complementary questionnaire EORTC QLQ–23. A chart was made in order to collect socio-demographic and clinical data. Statistic significance was accepted for values of p<0,05. To compare between groups and to detect the evolution within each group, the t-student test and the Mann-Whitney test were applied. The outcome analysis of the pilot study allowed to verify that: - The instrument of measure proposed (EORTC QLQ30 and BR23) was easy to apply, and the subjects did not show any difficulty in filling it up. There was also no problem on calculating the scores or interpreting them; - A considerable part of the women with breast cancer will be submitted to protocols that may occur throughout several months after surgery (e.g., QT+RT+HT). This reality leads us to suggest several moments of assessment of the QoL dimensions in various moments of the different protocol treatments. We consider that the ideal number of evaluations would be 4 (3/4 weeks, 3 months, 6 months and 9 months after surgery). We also suggest the use of a larger sample; - Since the pilot study resorted to a one group pretest-postest design (there is an absence of control group and only two moments of assessment), there is no consistency of outcome. However, the results obtained indicate that physical therapy influences the dimensions of QoL on women with breast cancer who underwent surgery and other oncology treatments, which may be an asset to the quality of care provided to cancer patients. The outcome of the pilot study allowed to redefine the methodology given as adequate to answer the initial investigation question. Our suggestion is as follows: quasi-experimental design, with a sample of 120 subjects (2 groups of 60 women) with breast cancer who underwent surgery and other oncology treatments. The experimental group will be submitted to individual treatments of physical therapy. Dimensions such as physical well-being and everyday life activities, psychological well-being, social relationships and symptoms will be assessed. The collection of data will occur at 3 weeks, 3 months, 6 months and 9 months after surgery. The instrument of measure is the EORTC QLQ–30 questionnaire and its complementary questionnaire EORTC QLQ–23, and social-demographic and clinical information will also be collected. The statistic significance will be accepted for values of p<0,05. Parametric and non-parametric tests will be used to compare between groups and to detect the evolution within each group. Carrying out a study that followed the methodology discussed above would allow a better consistency of results, possibly enabling the confirmation that physical therapy influences the QoL of women with breast cancer who underwent surgery and other oncology treatments. The evidence that physical therapy influences the QoL of women with breast cancer, and the fact that QoL is an indicator of quality of care provided to cancer patients, may work as a facilitating agent in the change of human resources management in health organizations associated to oncology, which will lead to a change in oncology physical therapy practice patterns in Portugal, guiding to a health care quality improvement to cancer patients.

Percepção do estado de saúde da pessoa idosa institucionalizada

RESUMO: O envelhecimento da população portuguesa é um facto. Esta alteração da estrutura demográfica exige o investimento no conhecimento científico para que se conheçam as consequências a nível, económico, social, cultural, biológico, físico e, principalmente, a nível da saúde. Isto porque, é emergente que a sociedade tenha capacidade para responder às necessidades específicas das pessoas neste estádio de vida, tendo sempre por base o conceito de qualidade de vida. Este estudo teve como objectivo avaliar a percepção do estado de saúde da pessoa idosa institucionalizada. Foram nove as instituições participantes, denominadas por lares de idosos de residência permanente, onde se contou com uma amostra de 75 indivíduos entre os 66 e 100 anos, de ambos os sexos. Foram recolhidos dados através de uma caracterização sócio-demográfica, através do Mini Mental State e através do Questionário de auto-avaliação da saúde e do bem-estar físico (de Fonseca e Paúl, 1999). Os dados obtidos foram trabalhados numa perspectiva de estatística descritiva e estatística inferencial, nomeadamente com a análise do coeficiente de Spearman. A partir desta análise determinou-se que: a grande maioria da amostra designa como “aceitável” ou “fraca” a sua percepção da saúde, em geral; os dados sócio-demográficos, e a instituição a que cada indivíduo pertence não têm relação com a percepção do estado de saúde destas pessoas; existe relação significativa entre a percepção do estado de saúde das pessoas idosas institucionalizadas e a saúde dos seus pares, essencialmente quando se abordam itens relacionados com aspectos físicos; no que concerne aos hábitos de vida, não existe relação entre a percepção do estado de saúde das pessoas idosas e os hábitos tabágicos e os hábitos alcoólicos. Os dados obtidos nem sempre são os dados que se esperavam efectivamente, porém fazem sentido ao serem consolidados com a teoria.--------ABSTRACT: The aging of the Portuguese population is a reality. It is imperative that society has the capacity to face the specific necessities of those who are in this phase of their lives. Therefore, this change in the demographics requires investment in scientific knowledge in order to know the consequences at levels such as: the economic, social cultural, biological and physical, mainly related to health. The main purpose of this study has been to evaluate the perceptions of elderly people concerning their health conditions. There were nine institutions involved, which are referred to as nursing homes, and a sample of 75 people between 66 and 100 years-old, from both genders, cooperated. Data has been collected through social-demographic, Mini Mental State and also through the questionnaire of the self-evaluation of health and physical well-being (from Fonseca and Paúl, 1999). The obtained data was worked within a perspective of descriptive/ inference statistic. From this analysis, it was determined that the great majority of the sample describes their perception of health as “acceptable” or “weak”, in general; the social-demographic information and the institution to where each person belongs do not show a connection with their perception of their health condition; however, there seems to be a significant relation between an institutionalized elderly person´s perception of their health condition and their spouse’s health, mainly when related to physical issues. In as far as life styles are concerned, do not show a connection between elderly people’s perception of health and smoking habits and alcohol habits. The obtained data does not always match expectations; nevertheless they make sense when being complemented by the theory.

Hybrid systems biology: application to Escherichia coli

Dissertation presented to obtain a Master degree in Biotechnology

The interrogation of witnesses abroad in execution of a european investigation order: an examination from eyes of the defence

European Master Human Rights and Democratisation

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Fractional order describing functions

This paper addresses limit cycles and signal propagation in dynamical systems with backlash. The study follows the describing function (DF) method for approximate analysis of nonlinearities and generalizes it in the perspective of the fractional calculus. The concept of fractional order describing function (FDF) is illustrated and the results for several numerical experiments are analysed. FDF leads to a novel viewpoint for limit cycle signal propagation as time-space waves within system structure.

Fractional Order Junctions

Gottfried Leibniz generalized the derivation and integration, extending the operators from integer up to real, or even complex, orders. It is presently recognized that the resulting models capture long term memory effects difficult to describe by classical tools. Leon Chua generalized the set of lumped electrical elements that provide the building blocks in mathematical models. His proposal of the memristor and of higher order elements broadened the scope of variables and relationships embedded in the development of models. This paper follows the two directions and proposes a new logical step, by generalizing the concept of junction. Classical junctions interconnect system elements using simple algebraic restrictions. Nevertheless, this simplistic approach may be misleading in the presence of unexpected dynamical phenomena and requires including additional “parasitic” elements. The novel γ-junction includes, as special cases, the standard series and parallel connections and allows a new degree of freedom when building models. The proposal motivates the search for experimental and real world manifestations of the abstract conjectures.

Fractional Order Description of DNA

This study addresses the deoxyribonucleic acid (DNA) and proposes a procedure based on the association of statistics, information theory, signal processing, Fourier analysis and fractional calculus for describing fundamental characteristics of the DNA. In a first phase the 24 chromosomes of the Human are evaluated. In a second phase, 10 chromosomes for different species are also processed and the results compared. The results reveal invariance in the description and close resemblances with fractional Brownian motion.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.