Tavares, Ana Helena, Brito, Paula, Afreixo, Vera
Neste trabalho abordamos o problema de agrupamento de distribuições discretas no contexto das distâncias entre palavras genómicas. Assumindo que as distribuições de distâncias são resultado da soma de duas componentes, uma que define a tendência de base e outra que define os seus picos, é proposto um procedimento de agrupamento que conjuga elementos das duas componentes. O procedimento é validado através de um estudo de simulação e é aplicado a dados do genoma humano. published
Tavares, Ana Helena, Raymaekers, Jakob, Rousseeuew, Peter, Silva, Raquel M., Bastos, Carlos A. C., Pinho, Armando, Brito, Paula, Afreixo, Vera
Springer
In this work we explore the dissimilarity between symmetric word pairs, by comparing the inter-word distance distribution of a word to that of its reversed complement. We propose a new measure of dissimilarity between such distributions. Since symmetric pairs with different patterns could point to evolutionary features, we search for the pairs with the most dissimilar behaviour. We focus our study on the complete human genome and its repeat-masked version.
Figueiredo, Daniel, Martins, Manuel A.
Reactive frames are those whose structure is not fi xed but can vary according to the path chosen. This kind of frame has been study and both a logic and an axiomatization for it were already developed. In this paper we take this study further and de fine a notion of bisimulation for reactive models. We show that the logic introduced by Marcelino for these frames is invariant under our notion of bisimulation. Finally, we proof the Hennessy-Milner theorem for a class of reactive models.
Hall, Andreia
Cassini
In a way, mathematics can be generally described as a science that studies structure, relations, order or patterns through its own language, in order to help us better understand the world we live in. Structure, relations, order and patterns are also fundamental in art and therefore it is not surprising that mathematics and art share a long historical relationship. Mathematics has inspired several artists and art works are sometimes a good motivation for mathematical reasoning or learning. Combining artistic creativity and mathematical reasoning turns out to be a very appealing way to explore several mathematical topics, in particular symmetry. Learning the mathematical principles of symmetry by first looking at art works and exploring one's own creativity has proven to be a very powerful and attractive strategy. During the last years I have explored symmetry with mathematics teachers of all grades through several professional development courses. In these courses teachers had the opportunity to create their own art works using different materials. The topics explored in these courses covered all types of symmetry in the plane: rosettes, friezes and wallpaper patterns. In this paper we shall present some results of three of these courses, involving about 50 primary and secondary school teachers (grades 1 to 12). In all courses we studied symmetry and the groups of symmetry of plane figures. We produced applications using two specific crafts techniques: patchwork/quilting and ceramics. published
Santos, Cláudia, Pereira, Isabel, Scotto, M. G.
Godel Impresiones Digitales S.L.
A multivariate integer-valued autoregressive model of order one with periodic time-varying parameters, and driven by a periodic inno- vations sequence of independent random vectors is established. The bino- mial thinning operator replaces the scalar multiplication in the common time series models. The matricial form of the multivariate model and its basic statistical properties are de ned. Emphasis is placed upon models with periodic multivariate negative binomial innovations. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method a composite likelihood-based approach is adopted and compared with other traditional competitors. published
Tavares, Ana Helena, Afreixo, Vera, Brito, Paula, Filzmoser, Peter
APRP - Associação Portuguesa de Reconhecimento de Padrões
The detection of outlier curves/images is crucial in many areas, such as environmental, meteorological, medical, or economic contexts. In the functional framework, outlying observations are not only those that contain atypically high or low values, but also curves that present a different shape or pattern from the rest of the curves in the sample. In this short paper, we mention some recent methods for outlier detection in functional data and apply a recently proposed measure, the directional outlyingness, and the functional outlier map to detect words with outlying distance distribution in the human genome. published
Tavares, Ana Helena, Afreixo, Vera, Brito, Paula
Sociedade Portuguesa de Estatística
Este trabalho aborda o problema da deteção de grupos de observações que se afastam da maioria. O objetivo é a deteção de grupos de palavras genómicas cujo padrão de distribuição, ao longo do genoma, se distinga da maioria dos padrões. O método proposto aplica técnicas de classificação hierárquica para identificar classes de pequena dimensão, pois é nesses grupos que se espera encontrar as observações que se demarcam das restantes. Assim, a dimensão das classes serve de ponto de partida para a identificação de potenciais observações atípicas. Num segundo passo, as observações são comparadas com as restantes observações do seu grupo, por forma a avaliar a similaridade entre as distribuições. Para esse efeito é utilizada uma medida de atipicidade funcional que privilegia a forma das distribuições e não apenas a magnitude dos seus valores. published
Melo-Dias, Sara, Tavares, Ana Helena, Valente, Carla, Andrade, Lília, Marques, Alda, Sousa, Ana
Universidade do Algarve
Background: Evidence of the clinical implications of microbiota dysbiosis in chronic obstructive pulmonary disease (COPD) is still lacking, needs validation and is fundamental as microbiota might be a promising biomarker of this disease. We aimed at exploring saliva’s microbiota of patients with COPD to query its relationship with disease-specific clinical parameters and evaluate its potential to be used as a COPD biomarker. Methods: Thirty-eight outpatients with COPD (33 male, 66±8y, BMI 25.0±4.9, FEV1pp 33±7, GOLD III-26, IV-12) and 38 matched healthy controls (33 male, 66±9y, BMI 27.5±3.7, FEV1pp 103±18) were characterised based on sociodemographic, anthropometric, clinical parameters and 16S rRNA profiling of their salivary microbiota. An unsupervised clustering analysis based exclusively on microbiota beta diversity was performed. Moreover, a classification model was developed to assess the microbiota predictive ability of COPD. Results: Proteobacteria (~30% of patients’ salivary microbiota), particularly Neisseria, Haemophilus and Helicobacter, was significantly more abundant in patients with COPD, whereas Firmicutes was significantly enriched in healthy individuals. Furthermore, patients’ microbiota was less diverse than in healthy. The unsupervised clustering analysis distinguished 25% of the most severe and symptomatic patients and 20% of the healthy population. These groups were even more disparate in Proteobacteria abundance (~40% and 10%, respectively). 80% of accuracy was achieved in classifying individuals as sick or healthy based on a small group of salivary bacteria. In sum, saliva’s microbiota shows a strong association with COPD, particularly in more severe cases of the disease, and a remarkable predictive power for disease classification. Not Published
Pereira, Isabel, Silva, Isabel, Silva, Maria Eduarda, McCabe, Brendan
Censored time series arisedwhen explicit limits are placed on observed data and occur in several fields including environmental monitoring, economics, medical and social sciences. The censoring may be due to measuring device limitation, such as detection limits in air pollution or mineral concentration in water. Censoring may also occur when constraints or regulations are imposed, such as in international trade studies where exports and imports are subject to trade barriers or hours worked, often treated as censored variables. The time series of counts under censoring are considered, focusing on the Poisson first-order integer-valued autoregressive (PoINAR) models. This class, while being simple and flexible, is useful for modelling positive-valued and integer-valued time series possessing an autoregressive structure with a non-negative serial correlation. Two natural approaches are investigated to analyze Censored PoINAR(1) time series under the Bayesian framework: the Approximate bayesian Computation (ABC) methodology and the Gibbs sampler with Daata Augmentation (GDA) approach. The parameter estimation performance of both approaches is made through a simulation study. published
Oliveira, Maria Paula
Sociedade Portuguesa de Matemática
O Projecto Matemática Ensino (PmatE) é um projeto de investigação e desenvolvimento, fundado em 1989 na Universidade de Aveiro (UA) que pretende aliar as tecnologias digitais ao desenvolvimento de conteúdos e eventos para a promoção do sucesso escolar e da cultura científica. submitted
Almeida, Ricardo, Girejko, Ewa, Machado, Luís, Malinowska, Agnieszka B., Martins, Natália
IEEE
The paper is devoted to multi-agent systems with memories under denial-of-service (DoS) attacks. The memory is represented by the fractional derivative that appears in the dynamics of the considered systems. The problem that we aim to address is, under which conditions the system continues to be stable or is in consensus mode, despite DoS attacks. Solutions to these problems are proposed in the presented theorems. We strengthen the theoretical considerations with numerical simulations. published
Otani, Mitsuharu, Staicu, Vasile
AIMS
No abstract available. in publication
Hall, A., Pais, S.
IATED
Mathematics is one of the school subjects where demotivation, dislike and failure are frequent concerns. It is necessary to engage students in the classroom and look for resources that make classes attractive and engaging, thus leading to meaningful learning experiences in mathematics. Active learning methodologies provide alternative options to traditional lecturing, actively engaging students in the learning process. The use of a single methodology may not be the best option to address this problem. A diversified approach that incorporates various methodologies and their combinations appears to be a preferable solution, as diversity not only leads to a more dynamic teaching style but also attends to the variety of preferences and needs of the students. In this work, we present a case study where we implemented and combined a range of active learning strategies to enhance student engagement and success in mathematics. Across one semester of undergraduate coursework, we emphasized collaborative group work and discussion groups, integrated peer teaching, flipped classroom, and role-play methodologies, used game-based learning through Kahoot! and Quizizz, and regularly incorporated mathematical magic tricks. The participants in the study are pre-service teachers from a Portuguese higher education institution enrolled in a first year mathematics course. In order to understand how these methodologies were perceived by the students, a survey was conducted. Our findings suggest that this multi-faceted approach effectively increased student interest and improved learning outcomes in mathematics. published
Barbosa, Luís Soares, Madeira, Alexandre
ACM
This position paper builds on the authors’ previous work on paraconsistent transition systems to propose a modelling framework for quantum circuits with explicit representation of decoherence. published
Alonso, Hugo, Candeias, Teresa
SciTePress
The wine industry has becoming increasingly important worldwide and is one of the most significant industries in Portugal. In a previous paper, the problem of predicting how much a Portuguese consumer is willing to pay for a bottle of wine was considered for the first time ever. The problem was treated as a multi-class ordinal classification task. Although we achieved good prediction results, globally speaking, it was difficult to identify rare cases of consumers who are interested in paying for more expensive wines. We found that this was a direct consequence of data imbalance. Therefore, here, we present a first attempt to deal with this issue, based on the use of re-sampling strategies to balance the training data, namely random under-sampling, random over- sampling with replacement and the synthetic minority over-sampling technique. We consider several learning methods and develop various predictive models. A comparative study is carried out and its results highlight the importance of a careful choice of the re-sampling strategy and the learning method in order to get the best possible prediction results. published
Rocha, Anabela, Miranda, Manuela Souto, Branco, João
The Simultaneous Equation Model (SEM) is used for modelling real problems aris ing from Econometrics, Finance and other fields (see, for example, Greene [2003], Chen et al. [2007] or Lee et al. [2017]). The model is caracterized by a system of dependent equations whose coefficients can be estimated by methods like the Three Stages Least Squares (3SLS) or the Generalized Method of Moments (GMM). The corresponding estimators have nice properties but, unfortunately, they are not ro bust. Besides, outlier observations are particularly difficult to detect and interpret in the SEM and the use of non-robust estimators in the process reduces the confi dence on potential outlier detection analysis. We present a study that illustrates the use of a robust outlier detection method. The estimation of the coefficients of the model is performed with a robust version of the GMM. Outliers are interpreted and considered as outliers in the residuals, for the response variables, or as outliers in the explanatory variables. Identification of outlying points is based on the distribution of the robust Mahalanobis distances, computed with Minimum Covariance Determinant estimates and using a generalized inverse. The method is compared with outlier detection based on traditional non robust procedures, namely using Mahalanobis distances with the 3SLS, since the latter is a very popular estimator for the SEM parameters. A real data example with Econometric Portuguese data and a simulation study show the advantages of the robust proposal. published
Oliveira, Ana, Afreixo, Vera, Marques, Alda
Journal of Statistics on Health Decision
Sem resumo disponível. published
Cabral, Jorge, Afreixo, Vera, Marques, Alda
Chronic obstructive pulmonary disease (COPD) is common and progressive. One of its major impacts on daily life is decreased functional status which can be assessed by the one-minute sit-to-stand test (1minSTS). The 2020 imposed lockdown due to the recent pandemic (COVID 19) is likely to have influenced the functional status of this population but this is still unknown. Few feature selection algorithms are available for longitudinal data. We aimed to compare different feature selection methods and describe the effect of the COVID-19 lockdown on the 1minSTS behaviour in people with COPD. Data from 59 people with COPD were collected at baseline (B), 34 of whom belonging to the no-lockdown group. 1minSTS was repeated after one (A1) and five months (A5), which corresponded to the assessments prior and after the lockdown in the lockdown group. Fixed-effects were included in different linear mixed-effects models (LMMs) according to the importance given by Random Forests, Boruta, Extreme Gradient Boosting, automatic backward elimination and L1-penalized estimation algorithms. The LMM with the lowest Akaike’s information criterion (AIC) was chosen. The LMM obtained by automatic backward elimination achieved the lowest AIC (919.7) and was followed by the one using L1-penalized estimation algorithm (923.5) although this one produced a higher conditional R-squared. Boruta algorithm returned the highest AIC (964.2). Difference between B and A1 number of repetitions in 1minSTS was statistically significant in both COVID-19 groups. No difference was found between A1 and A5 in either group suggesting that the lockdown had no effect in the 1minSTS behaviour. published
Machado, Ana, Silva, Pedro Matos, Afreixo, Vera, Caneiras, Cátia, Burtin, Chris, Marques, Alda
Introdução e Objetivos: A reabilitação respiratória (RR) é uma das intervenções mais eficazes na gestão da doença pulmonar obstrutiva crónica (DPOC) estável. No entanto, o seu papel durante as exacerbações agudas da DPOC (EADPOC) é ainda controverso, nomeadamente devido à grande variedade de desenhos de intervenção utilizados. Esta revisão sistemática sintetizou os diferentes desenhos usados para implementar RR durante as EADPOC e explorou quais os mais eficazes. Material e Métodos: Realizou-se uma pesquisa na PubMed, Scopus, Web of Science, EBSCO e Cochrane. Incluíram-se estudos randomizados controlados que compararam RR ou pelo menos uma das suas componentes com o tratamento habitual (farmacológico), ou diferentes componentes da RR. Conduziu-se uma meta-análise em rede no MetaXL 5.3 utilizando uma estrutura de modelação de pares generalizados. Os efeitos combinados gerados (diferença de média ponderada [DMP] ou tamanho do efeito [TE]) e respetivos intervalos de confiança (IC) comparam cada intervenção com o tratamento habitual. Resultados: Incluíram-se 42 estudos. A maioria dos estudos foram conduzidos no internamento (57%) e iniciaram a intervenção 24-48h após a admissão hospitalar (24%). Exercício (71%), educação e apoio psicossocial (57%) e técnicas respiratórias (55%) foram as componentes mais utilizadas. Os estudos que combinaram exercício com técnicas respiratórias foram os mais eficazes na melhoria da tolerância ao esforço (DMP=-41.06, IC95% [-131.70; 49.58]) e qualidade de vida relacionada com a saúde (DMP=16.07, IC95% [10.29; 21.84]). Os estudos que utilizaram apenas técnicas respiratórias apresentaram resultados superiores na redução da dispneia (DMP=16.07, IC95% [10.29; 21.84]) e duração da hospitalização (TE=0.15, IC95% [- 0.28; 0.57]). Encontraram-se poucos e reduzidos efeitos adversos. Conclusões: A RR é uma intervenção segura durante as EADPOC. Exercício, técnicas respiratórias e educação e apoio psicossocial parecem ser as componentes essenciais para implementar programas de RR durante as EADPOC. Estudos futuros deverão explorar o melhor momento para iniciar a intervenção, duração e frequência da mesma, e intensidade para a prescrição de exercício. in publication
Rodrigues, Mónica, Costa, Maria C., Bandeira, Jorge M.
TEMA – Centro de Tecnologia Mecânica e Automação
A predicted increase of connected autonomous vehicles (CAVs) in our roads paved the way for new opportunities and challenges towards the promotion of sustainable mobility. However, the impacts of CAVs on the road environment and its implications are widely dependent on technological choices and public policy [1,2]. Therefore, this research (PhD Workplan) intends to assess whether CAVs could be effective mobility solutions for improving social, economic and environmental efficiency [4]. This question will be addressed by developing a decision support tool driven by comprehensive data analysis and modelling processes. The outputs achieved will integrate a tool that will support transport system’s planning and the implementation of urban strategies to introduce CAVs [3,5]. Thus, the research’s main focus encompasses the development of a model-driven decision support system (DSS) that allows assessing the costs and risks of implementing CAVs in urban context [3,4]. Three specific research objectives are assumed: I) Predicting impacts of CAVs operation in urban contexts, by analyzing cost-efficiency, transportation demand and mobility patterns considering market penetration scenarios of CAVs in Portugal; II) Conceiving a hybrid transport planning tool to assess possible restrictions to CAVs on different types of links through field data testing and simulating scenarios using a microscopic traffic model. Data will support the development of a macroscopic model for a full network assessment performance; III) Developing a multidimensional decision tool directed to a wide range of stakeholders, both from public or private sectors, to compute the benefits, costs, constraints and risks of implementing CAVs on urban mobility systems. Preliminary results from different urban arterials indicate that CAVs can have negative or negligible impacts in some urban contexts. However, if the impact on the traffic flow’s energy performance is considered into the internal car following algorithm, global energy savings of up to 12% can be achieved. published
Sá, Marta, Lousada, Marisa, Sá Couto, Pedro
CLAD
This work addresses the problem of detecting groups of observations (distributions) and flagging those that differ abnormally from the majority of the groups, termed as atypical groups. The proposed method combines a hierarchical classification technique, to identify groups of similar distributions, with a functional outlier detection method, to identify those groups that contain outliers. Groups with outlying observations are forwarded for sub clustering. Once the final partition is obtained, each cluster is represented by a class prototype, whose outlyingness is evaluated according to a functional approach. Clusters with atypical class labels are flagged as atypical groups. The method is applied for the detection of groups of atypical genomic words, based on their distances distributions. published
Marques, João, Tavares, Ana Helena
The tax inspection procedure depends on a set of interactions between the tax inspector and the taxpayer. Tax inspectors are responsible for conducting this relationship and they have a large set of legal prerogatives to use - power actions. The way those power actions are used may define the taxpayers propensity to regularize their tax situation or, on the contrary, adopt a position of resistance or confrontation. From a questionnaire carried out with 85 Portuguese Tax Inspectors (PTIs), 40 power actions were analyzed. We identify five different levels of power actions according to their harshness. We have also analyzed the correlations between frequency of use and perceived efficiency. We conclude that PTIs do not use more invasive power actions very often, even though these are perceived as more efficient. published
Tavares, Ana Helena, Vera Afreixo, Brito, Paula
CLAD, FEUP
In this work, we introduce the concept of atypical group of observations and propose a procedure for its identification. By atypical group, we mean a cluster of observations whose ‘mean’ pattern stands out from the majority of the ‘mean’ patterns of the remaining clusters. Challenges that arise in atypical group detection are firstly to identify a meaningful segmentation of the data, and secondly to flag the atypical segments. Our work focus on data whose elements are discrete distributions. If heterogeneous datasets, where distinct patterns coexist, can validly be clustered, then the class prototypes provide a simplified description of data. Thus, the key idea of our proposal is to combine a clustering method with a functional outlyingness criterion to capture atypical class prototypes. To identify a segmentation of the distributional data we iteratively combine two steps. The first creates a hierarchy of clusters, while the second flags atypical curves within each cluster, based on a measure of functional outlyingness which accounts for the shape of the distributions [1]. Segments with atypical curves, are forwarded for (sub)clustering, and the procedure is repeated until no outlying curves are identified in clusters. Once the final partition is obtained, each cluster is represented by a class prototype, whose outlyingness is evaluated according to the same functional approach. Clusters with an atypical class prototype are pointed as atypical. We apply our procedure to investigate clusters of genomic words in human DNA by studying their inter-word lag distributions. These experiments demonstrate the potential of the new method for identifying clusters of words with outlying patterns. published
Elsevier
The wine industry is an important business sector, generating billions in annual revenue. In the last year, there were several lockdowns due to the COVID-19 pandemic and wine consumption at home has increased. This paper considers the problem of predicting how much a consumer is willing to pay for a bottle of wine to drink at home, in a regular occasion. As far as we know, this is the first study on the subject. The problem is treated as a classification task and several prediction models, based on artificial neural networks, support vector machines and decisions trees, are proposed and compared. published
Faustino, Nelson, Marques, Jorge
Polytechnic of Porto. School of Engineering
We obtain Strichartz estimates for a wide class of space-time fractional evolution equations arising in applications towards the theory of structural damping plate equations. We focus on the case where the damping term is described in terms of the time fractional derivative of order alpha taken in the Caputo-Djrbashian sense and of the fractional Laplacian of order sigma in the space variable. Our results heavily rely on the study of the pseudo-differential representation for the resolvent in terms of the Mittag-Leffler functions. published
Hall, A, Pais, S
Mathematics and art have a long historical relationship stretching back to the ancient Greeks, Romans and Egyptians. Mathematics is all about patterns and rhythms, so it is natural that we can find many mathematical concepts in art. Geometry related topics make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of solid geometry which is addressed along the whole mathematics curriculum in Portugal [1]. This paper presents some results of a professional development course for mathematics teachers where the participants studied solid geometry and developed applied projects in an artistic context. The course took place in a Portuguese university and involved 23 teachers of grades 7 to 12. The authors have developed a mixed case study to evaluate how an artistic approach to the teaching of solid geometry is perceived, by the mathematics teachers, as a contribution to the learning process. Above all, the activities developed have proved to be successful examples of interdisciplinary methodologies that bring into the teaching of mathematics usual procedures in the teaching of the arts. Furthermore, the artistic approach followed during the course helped the teachers develop their geometric competences concerning solid geometry, made the learning process more interesting and promoted a more positive attitude toward mathematics. published
Pais, S., Hall, A., Sousa, A. E.
Mathematics is one of the school subjects where demotivation is a frequent concern. Relating mathematics with other areas usually draws students’ attention and increases their involvement in the classes. It is necessary to go beyond the traditional; the teacher must look for resources that make his classes flow, so that the students acquire or increase their interest in mathematics. After the generalized lockdown imposed by the Covid19 pandemic, millions of students and teachers faced new challenges as they progressively come back to their face-to-face school activities. Despite all the constraints caused by the pandemic, this is an opportunity to move towards an innovative and transformative educational model for the future, which must avoid sending us back to the negative aspects of past educational practices. During the lockdown, with face-to-face teaching activities in schools having been suspended and emergency remote teaching (ERT) being put into practice, the teachers involved in this study were faced with the need to adapt activities and didactic materials to be used exclusively at distance with the aid of technology. This included the promotion of asynchronous tasks/activities, which could be developed autonomously by students. Technologies have multiple benefits in the field of Education, such as improving student performance and motivation. Information and Communication Technologies (ICTs) are tools that may be used to innovate the way mathematics is taught and they may facilitate students' learning. Being aware of these benefits, one of the authors of this work decided to adapt and introduce part of the activities and teaching materials prepared for the ERT, in the face-to-face teaching of her classes after lockdown. In order to understand how these changes were perceived by the students, a quantitative survey was conducted. The participants in the study are undergraduate students from a Portuguese higher education institution enrolled in the curricular unit of Statistical Analysis. published
Breda, A., Carvalho, P., Hall, A.
The use of art in teaching mathematics, as referred to in the literature, enhances the understanding, retention and connection of mathematical concepts to many other areas of knowledge. There is, in fact, a broad consensus on the recognition of mathematics as a universal language for describing the world around us. However, it is in art that the maximum expression is found to represent and recreate it. By combining maths and arts with the use of dynamic geometry environments, promising paths are opened for the development of geometric, critical and creative thinking. It is not by chance that, Portuguese official guidance documents, along with many from other countries, recommend that students are exposed to problems that are interesting, otivating and challenging, making them feel and see the beauty and importance of mathematics. Since problem solving is one of the essential competences for learning in mathematics, teachers must take responsibility for selecting problems and tasks for the classroom or asynchronous activity that meet official recommendations. It was within this context that we came up with the idea of dynamizing a professional development course, for mathematics teachers, where geometry and art were, explicitly, interconnected, using a STEAM approach. The book Beautiful Geometry by Eli Maor and Eugen Jost, was one of the key elements for its planning and implementation. In this paper, we present some results of the proposed professional development course for mathematics teachers. The course took place in a Portuguese university, from April 24th to May 26th 2021, and involved 22 teachers of grades 5 to 12. The supervisors started the course by introducing some geometry topics from the selected book and showed several artworks created by renown artists, based on them. Afterwards, the participants explored other topics from the book, presenting them to the group, showing the relationship between the geometric/mathematical concepts and the artworks that accompany the book. In the final phase of the course, participants chose geometry or mathematics topics and took the role of an artist, creating one or more artworks based on them. The artistic pieces made use of several arts techniques: acrylic, watercolour, textile arts, and mixed media. The authors have developed a mixed case study to evaluate how a STEAM approach to the teaching of mathematics, is perceived and apprehended by mathematics teachers, considering the following aspects: deepening of scientific knowledge and possible repercussions on the teaching practice. Overall, the activities developed have proved to be successful examples of STEAM experiences that bring into the teaching of mathematics, technology and usual procedures in arts teaching. published
Santos, V., Hall, A., Bastos, N. R. O., Caridade, C. M. R.
In recent times, the debate on active methodologies has been intensified with the emergence of strategies that can favor students' autonomy. The active, dynamic and constructive environment can positively influence the perception of teachers and students. One of the ways to achieve this is through the use of technologies that enhance learning. Due to the pandemic situation, the use of technologies was imperative and essential. Three higher education institutions were involved in an active learning project, involving diversified technologies and methodologies to enhance the learning of mathematics. In the University of Aveiro, the experiment involved all the 1st-year students enrolled in the course “Complementary Mathematics II” during the second semester of the academic year 2020-21. These are students of a master’s program for pre-service teachers, preparing to become primary school teachers and mathematics and science teachers, grades 5 and 6. At the Institute of Engineering in Coimbra, the students who attended this experiment were students of Mathematical Analysis I, from the undergraduate degree in Electrical Engineering. In the Polytechnic Institute of Viseu, the students involved in this experiment were students from the Preparation Course in Mathematics (which aims to prepare candidates over 23 who wish to apply to an undergraduate degree in Business). The methodologies used were applied during three distinct phases and according to the students’ profile, related to each course. The methodologies used were very diverse: team-based learning; flipped classroom; peer teaching; think-pair-share and exposition followed by exercise practice; problem-based learning and inquiry-based learning. The technologies were also very diversified: Desmos, Kahoot!, Quizizz, GeoGebra, Excel, OneNote, Google Docs, Zoom, Miro, Wolfram alpha, PowerPoint, calculators and videos. The use of a wide range of methodologies and technologies made it possible to teach during the lockdown imposed by the pandemic situation, and simultaneously motivated the students. In addition, they provided opportunities to adapt the learning process to the diverse knowledge and learning styles of students and increased their involvement. published
Hall, Andreia, Nunes, João, Vettori, Paolo
International Society for the Interdisciplinary Study of Symmetry
Symmetry and antisymmetry are resources used by humans since pre-historic times in their artistic creations. In this work we start by introducing antisymmetry and the 17 possible associated groups. We then present some counts of friezes, built with a particular module, the Truchet tile, which is itself antisymmetric. These counts take into consideration the frieze antisymmetry group and the number of tiles composing the unitary cell which originates the frieze by translation. These Truchet friezes led to the creation of a set of 5 paintings, named Crossings, which illustrate all the possible groups, in an artistic context. published
Nunes, João, Hall, Andreia, Vettori, Paolo
In this work we explore the presence of antisymmetry in Portuguese ceramic tile facades, showing examples from different styles and different antisymmetry groups. We further present some experi-ments with school children who explored symmetry and antisymmetry in a creative way. Children used a particular tile design, the Truchet tile, to create specific types of symmetry and antisymmetry. Truchet tiles can be found in several Portuguese facades from north to south. published
Breda, Ana, Carvalho, Paula, Hall, Andreia
Tessellations Publishing
Mathematics and art have a connection that goes far beyond proximity. In fact, they are two symbiotic areas shaping a beautiful, logical, systematic, and breathtaking world. One of the works that exposes their intrinsic connection, in a clear, rigorous and simple way, is the book Beautiful Geometry by Eli Maor and Eugen Jost. To a greater or lesser degree, we all feel the power that art exerts on our minds, both at a sensory and at a cognitive level. In fact, art is one of the privileged areas for the emergence of creativity. Combining beauty with rigor and reason, and based on the book mentioned above, we designed a professional development course for mathematics teachers, following a STEAM approach. The description of this course, illustrated with part of the graphic/artistic material produced by the participants, is the main object of this paper. published
Rita, Paula, Bastos, Nuno, Hall, Andreia
Portugal has a rich and long cultural heritage which can be used to promote the teaching of Mathematics in schools. Geometry can be explored through the analysis of decorative art found in Portuguese historical buildings, in particular through the analysis of ceramic tile panels and facades used extensively throughout several centuries. Through the analysis of decorative art found using ceramic tiles in two Portuguese monuments, we propose several teaching activities to explore the topics of isometry and symmetry in schools. We give some examples of rosettes, friezes and wallpapers found in the monuments, classified according to their symmetry groups. We also give an example of an applied activity using GeoGebra and exploring Islamic patterns. published
Rocha, Anabela, Miranda, M. Cristina
Sociedade Portuguesa e Estatística
Panel or longitudinal data sets are frequent in financial and economic studies. This type of data combines cross-sectional with time series data, providing extra information and allowing to evaluate and measure statistical effects that would otherwise keep unknown. Different degree of restrictions upon the structure of the data leads to different ap proaches with least squares methodology. This results in estimators that can be highly affected by a violation of those assumptions. The Feasible Generalized Least Squares estimator (FGLS) is an estimator that pre serves good properties without requiring strong distribution requisites. In spite of this, it is highly affected with the presence of observations too much different from all the rest. These are known as atypical ob servations or outliers. Economical and financial real data often present this type of data and the FGLS estimator may be seriously affected by those observations. This might be avoided if a robust option is chosen. Although robustness is a main concern in recent econometric modelling, there is still much to do in this field. Recent studies in those fields point to the advantage of using robust estimators. With this work we want to contribute to the use of robust methodologies in the estimation of panel data models and present a robust version of FGLS, the RFGLS (Robust Feasible Generalized Least Squares). In this paper, the performance of the proposed estimator is compared with the FGLS using a real data previously analysed by some authors. published
Rocha, Anabela, Miranda, M. Cristina, Vieira, Elisabete
O modelo de equações simultâneas (SEM, do inglês simultaneous equations model) (ver, p.ex., [1]) é formalmente semelhante ao modelo de regressão multivariada, mas assume que algumas variáveis resposta são também variáveis explicativas, implicando a dependência entre diferentes equações. Os SEM podem também especi car dependência temporal das observações, mas esta formulação não é recomendada na literatura, pois aumenta consideravelmente a complexidade do modelo e da estimação dos coe cientes, e poderá não compensar nos resultados da modelação. Aparentemente, a informação que os dados podem conter sobre a dependência temporal ca incorporada na endogeneidade de algumas variáveis e os SEM são tipicamente aplicados a variáveis económicas e nanceiras que, geralmente, estão disponíveis em séries temporais (em [2] são nomeadas diversas aplicações). No presente trabalho usa-se o SEM para modelar um conjunto de dados nanceiros em painel, que descreve a relação da propriedade de gestão, estrutura de capital e política de dividendos (variáveis resposta) com outras variáveis nanceiras (variáveis explicativas), consideradas pertinentes na literatura nanceira, e assume a existência de interdependência entre as variáveis resposta. As estimativas dos coe - cientes são obtidas com uma versão robusta do estimador do método dos momentos generalizado (GMM, do inglês generalized method of moments) [3]. Os resultados são comparados com os obtidos considerando a metodologia usual para dados em painel, onde a dependência temporal é explicitada através da decomposição de termo aleatório do modelo de regressão. published
Springer, Cham
Panel or longitudinal data sets are frequent in financial and economic studies. This type of data combines cross-sectional with time-series data, providing extra information and allowing to evaluate and measure the statistical effects that would otherwise keep unknown. Different degree of restrictions upon the structure of the data leads to different approaches with least squares methodology. This results in estimators that can be highly affected by a violation of those assumptions. The Feasible Generalized Least Squares estimator (FGLS) is an estimator that preserves good properties without requiring strong distribution requisites. In spite of this, it is highly affected by the presence of observations too much different from all the rest. These are known as atypical observations or outliers. Economical and financial real data often present this type of data and the FGLS estimator may be seriously affected by those observations. This might be avoided if a robust option is chosen. Although robustness is the main concern in recent econometric modelling, there is still much to do in this field. Recent studies in those fields point to the advantage of using robust estimators. With this work, we want to contribute to the use of robust methodologies in the estimation of panel data models and present a robust version of FGLS, the RFGLS (Robust Feasible Generalized Least Squares). In this paper, the performance of the proposed estimator is compared with the FGLS using real data previously analysed by some authors. published
Monteiro, Magda, Costa, Marco
AIP Publishing
This work presents a comparative study between two approaches to calibrate radar rainfall in real time. The weather radar provides continuous measurements in real-time which have errors of either meteorological or instrumental nature. Locally, gauge measurements have a greater performance than radar measurements that can be used to improve radar estimates. One way of doing that is via a state space representation associated to the Kalman filter algorithm. In the single- site modeling approach we use the linear calibration model applied in [1] and [3] while the multivariate state-space model proposed in [6] is used in the multiple site approach. This work aims to discuss and compare these two different state space formulations based on the same data set.
Cruz, João Pedro, Oliveira, Paula, Seabra, Dina
The authoring of parameterized exercises has been a useful activity both for teachers, who could take advantage of databases of parameterized exercises for preparing study materials, but also for students that learn by producing new problems. This has been verified during the realization of MSc dissertations written by High School teachers that, as students again, have written about the positive aspects of their experience in the production of parameterized exercises. Parameterized exercises can also be used in online systems as a secondary study tool for STEM students (such as SIACUA system [2]). With these goals in mind, we have been developing a package named MEGUA to handle databases of parameterized exercises in the SageMath platform for mathematics. During the use of this system we gathered several requests from users claiming a better system. In this paper we present a redefined tool as well as some first opinions on the new facilities. Originally, this package had the old SageMath Notebook [4] as a front-end which has been presented in ICERI 2013 [3]. A new version of this package has been developed for the new platform named “Sage Math Cloud” (SMC) running in a secure and centralized web platform creating, for each new project, a virtual Linux machine with shell command access. In online systems (or cloud), a supervisor could follow student work and help to solve their problems (at distance) since it can see the student work in progress (no need to send emails with attachments).
Costa, Marco, Monteiro, Magda
Nas últimas décadas, o mundo tem sido confrontado com as consequências do aquecimento global. No entanto, esse fenómeno global não se reflete igualmente em todas as partes do globo. Este trabalho analisa a série temporal de longo-prazo das temperaturas médias mensais do ar na cidade do Porto, Portugal. Neste trabalho propomos um modelo de espaço de estados com estado periódico cujos resultados indicam que existem diferentes taxas de aumento da temperatura estimando-se um aumento médio anual da temperatura de 2,17ºC, por século.
Ferreira, M., Kraußhar, R. S., Rodrigues, M. M., Vieira, N.
We present a generalization of several results of the classical continuous Clifford function theory to the context of fractional Clifford analysis. The aim of this paper is to show how the fractional integro-differential hypercomplex operator calculus can be applied to a concrete fractional Stokes problem in arbitrary dimensions which has been attracting recent interest (cf. \cite{CNP,LAX}). The work of M. Ferreira, M.M. Rodrigues and N. Vieira was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT–Fundação para a Ciência e a Tecnologia”), within project UID/MAT/0416/2013. The work of the authors was supported by the project New Function Theoretical Methods in Computational Electrodynamics / Neue funktionentheoretische Methoden für instationäre PDE, funded by Programme for Cooperation in Science between Portugal and Germany (“Programa de Ações Integradas Luso-Alemãs/2017” - Acção No. A-15/17 - DAAD-PPP Deutschland-Portugal, Ref: 57340281). N. Vieira was also supported by FCT via the FCT Researcher Program 2014 (Ref: IF/00271/2014). published
Cruz, J. P.
We have introduced statistical problems, to be solved using the R software, into a Biostatistics course, in order to increase motivation for the field that requires a certain level of mathematical knowledge when most students are not always inspired for it. Our traditional class style used to be based only on slide presentations followed by pen and paper exercises with a calculator. Our aim was to complement this method with the use of software as a professional tool creating a active learning environment. Students came from Biology degree, Teaching of Geology and Biology degree and Marine Sciences degree. Each of the 200 students were presented with a total of four problems, during the semester, in the topics of Descriptive Statistics, Inference in One Variable, ANOVA and Simple Linear Regression. Students were requested to solve them at home and answer them in a form available in the “Moodle Inquiry” tool. Each student has his own different sample and also, questions were parameterized. For example, questions about Confidence Intervals were posed with different confidence levels (90%, 95% or 99%). Each students sees a different problem. Each of these has more than ten parameterized questions related to the same dataset exposed in the beginning of the text. Moodle doesn’t do this type of deliver different composed problems to each student so a small Python library was used to generate different problems and evaluate each individual student answer (numerical, textual or multiple choice types). To evaluate our methodology, we request students to “Share ideas, thoughts and constructive judgments about the Problems and also about the course” while students were working in the third Problem and also after the First Written Evaluation. The last and fourth Problem has been answered in class and students were requested to grade sentences in a five item Likert scale. Questions were about effort, time, help from other students and help from teacher. The analysis of answers suggest that the methodology of Problem Solving should be used again, with improvements, given the motivation and enthusiasm it promotes. published
Lima, Susana, Gonçalves, A. Manuela, Costa, Marco
This study deals with forecasting economic time series that have strong trends and seasonal patterns. How to bestmodel and forecast these patterns has been a long-standing issue of time series analysis. In this work, we propose a Holt-WintersExponential Smoothing approach to time series forecasting in order to increase the chance of capturing different patterns in the dataand thus improve forecasting performance. Therefore, the main propose of this study is to compare the accuracy of Holt-Wintersmodels (additive and multiplicative) for forecasting and to bring new insights about the methods used via this approach. Thesemethods are chosen because of their ability to model trend and seasonal fluctuations present in economic data. The models arefitted to time series of e-commerce retail sales in Portugal. Finally, a comparison is made and discussed published
Sociedade Galega para a Promoción da Estatística e a Investigación de Operacións (SGAPEIO)
In this work, we present time series of monthly average temperatures in several Euro- pean locations which were statistically analyzed using a state space approach, where it is considered a model with a deterministic seasonal component and a stochastic trend. The analysis of smoother prediction of the stochastic trend and its comparison in a tem- poral viewpoint can reveal patterns about warming in Europe. The temperature rise rates in Europe seem to have increased in the last decades when compared with longer periods, hence a change point detection method is applied to the trend component in order to identify these possible changes in the monthly temperature rise rates. The adopted methodology pointed out, for most series a change point in the late eighties. published
Tavares, A. H., Afreixo, V., Brito, P.
IST Press
Functional data appear in several domains of science, for example, in biomedical, meteorologic or engineering studies. A functional observation can exhibit an atypical behaviour during a short or a large part of the domain and this may be due to magnitude or to shape features. Over the last ten years many outlier detection methods have been proposed. In this work we use the functional data framework to investigate the existence of DNA words with outlying distance distribution, which may be related with biological motifs. A DNA word is a sequence defined in the genome alphabet {ACGT}. Distances between successive occurrences of the same word allow defining the inter-word distance distribution, interpretable as a discrete function. Each word length 𝑘 is associated with a functional dataset formed by 4 𝑘 distance distributions. As the word length increases, greater is the diversity of observed patterns in the functional dataset and larger is the number of distributions displaying strong peaks of frequency. We propose a two-step procedure to detect words with an outlying pattern of distances: first, the functions are clustered according to their global trend; then, an outlier detection method is applied within each cluster. Each distribution trend is obtained by data smoothing, which avoids some distributions’ peaks, and similarities between smoothed data are explored through hierarchical complete linkage clustering. The dissimilarity between functions is evaluated using the Euclidean distance or the Generalized Minimum distance [1], which considers the dependence between domain points. The resulting dendograms are then cut leading to a partition of the distance distributions. For the second step we use the Directional Outlyingness measure which assigns a robust measure of outlyingness to each domain point and is the building block of a graphical tool for visualization of the centrality of the curves [2]. We focus on the human genome and words of length 𝑘 ≤ 7. Results are compared with those obtained by applying only the second step of the procedure [3]. published
Associação Portuguesa de Classificação e Análise de Dados
Neste trabalho abordamos o problema de deteção de distribuições atípicas no contexto das distâncias entre palavras genómicas, seguindo uma abordagem funcional, tendo em conta não apenas a existência de outliers de magnitude, mas também a possível existência de outliers de forma. Aplica-se um procedimento baseado na medida directional outlyingness, que permite detetar outliers de magnitude e outliers de forma. published
Sousa, Virgínia, Alonso, Hugo
Varazdin Development and Entrepreneurship Agency; University North
Having the ability to predict the price of a particular stock share is undoubtedly a major challenge, because of the complexity and implied volatility of the financial markets. This is a topic of great interest to researchers and market players, as the effectiveness of the forecast might translate into huge monetary gains. This work aims to demonstrate the use of neural networks for stock price forecasting. Two financial titles are considered: Microsoft and Apple. The initial choice of the predictor variables comprises the most used and referenced in the scientific papers published on this subject. This work demonstrates the importance of a careful selection of some of those variables for a good neural network performance. published
Candeias, Teresa, Alonso, Hugo
Wine companies are usually operating in larger and diverse markets and consumers show different needs. Given resource constraints, companies must segment the market, because they cannot cover the entire market or, if they do, they need to adopt and implement an appropriate marketing strategy. Market segmentation enables to treat consumers differently through a marketing strategy geared to this purpose. There are several segmentation criteria and one of them is the wine consumption occasion. Here, like other authors do, we consider the following five situations where the consumer pays for a bottle of wine: to drink at home, to drink at home with friends, to drink at a restaurant, to give as a gift and in businesses. We asked to 133 consumers, randomly selected, how much they were willing to pay in each situation: < 1 Euro; 1 – 2 Euros; 2 – 5 Euros; 5 – 10 Euros; 10 – 20 Euros; > 20 Euros. We concluded that the price decision depends on the wine consumption occasion (Friedman test, p-value=0,000). This is in accordance with the literature. Furthermore, we found something that, to our knowledge, is new: at a 5% level of significance, there is no difference between the situations “to drink at home” and “to drink at home with friends” and also between “to drink at a restaurant”, “to give as a gift” and “in businesses”; the difference lies between the former two situations and the latter three. This means that, for market segmentation, we can consider two instead of five wine consumption occasions. We further investigate how this conclusion depends on consumer gender. published
Marques, A., Machado, A., Miranda, S., Jácome, C., Cruz, J., Oliveira, A., Enes, V., Afreixo, V., Martins, V., Andrade, L., Valente, C., Ferreira, D., Simão, P., Brooks, D., Tavares, A.
Portuguese Society of Pulmonology
No abstract available. published
Castro, Daniel, Enes, Vera, Moura, Gabriela, Marques, Alda
University of Aveiro (UA). Hospital Center of Baixo Vouga (CHBV)
No abstract available published
Cabral, Jorge, Afreixo, Vera, Rocha, Vânia, Souto-Miranda, Sara, Marques, Alda
Universidade de Aveiro; Centro Hospitalar do Baixo Vouga
Pais, Sónia, Hall, Andreia
Academic Conferences International Limited Reading
Nowadays we live in an ever-changing society. The educational context is no exception and requires a renewal of paradigms. Profound changes to the role and function of the professor and the students are particularly vital. Active, cooperative and participative methodologies of learning must be privileged, breaking with magisterial education and the mere transmission of knowledge. Mathematics is one of the school subjects where demotivation is a frequent concern. Relating mathematics with other areas usually draws students’ attention and increases their involvement in the classes. It is necessary to go beyond the traditional; the teacher must look for resources that make his classes flow, so that the students acquire or increase their interest in mathematics. In the last few decades, technology has advanced in multiple fields, including education. Some of its benefits include improving student performance and motivation, fostering active learning, and tracking student progress. Kahoot! is an example of a platform that can be used for reviewing content and motivating students for learning. The main reasons for choosing this tool are related to the fact that the application is accessible online free of charge, allows an intuitive use, both by the teacher/author and by the student/player and allows the participation of the whole class in an interactive, stimulating, and playful way. The teachers involved in this study began using Kahoot! in their classes as an alternative teaching methodology. The participants in the study are undergraduate students from a Portuguese higher education institution and encompassed the curricular unit of Statistics. The aim of the study is to investigate students’ perceptions of how Kahoot! can be used as a tool for reviewing class content or designing warm-up activities. A survey was conducted to gather information about students’ insights on the use of Kahoot!. Similar studies have shown that higher education students are usually receptive to the use of this tool, finding it useful to increase their motivation and consider technology can positively impact learning. published
Cruz, J. P., Freitas, A.
ICERI2021
In the last three years, the first author has been producing an online documentation to be applied on a Biostatistics course in a public university, in order to make the study of this subject more dynamic. The target students come from Biology, Geology and Biology, and Marine Sciences degrees. The main goal is to increase the study motivation outside classes offering better study support and providing a means to easily and quickly share new explanations online about subjects when certain frequently asked questions arise. This online material comes to complement traditional paper material such as powerpoint prints and book of exercises. Several sections of this online documentation have been improved and continuously updated with particular focus on online exercises, and more explanations in conceptual parts. For instance, during the last semester of classes (February-June/2021), several parts of a section titled "How to use..." and related to instructions to execute simple exploratory statistical analysis using graphical calculators and R language (also used as a calculator), were incorporated and improved. In the last class semester, and right at the beginning and for a total of 180 students, the online documentation was made available in a website (http://sweet.ua.pt/pedrocruz/bioestatistica/). In order to evaluate the success of this initiative among students, an anonymous inquiry was carried out after final grades have been released. Due to the reduced number of responses (28 students), a semi-structure interview were also carried out a few students which were selected for claiming that they collected the document online. A important conclusion is that the online documentation should continue but also be improved. Another goal was to keep a low time cost and effort for the production of the online documentation. We have used Sphinx markup system that has proved its value in the community of Python programming language. In fact, an huge documentation of scientific computer libraries has been written online in this way. As for other markup systems, there is the possibility of producing documentation for printing with little extra effort. published
Portinha, Susana, Sá Couto, Pedro, Matos, Maria Assunção
University of Aveiro (UA); Hospital Center of Baixo Vouga (CHBV)
Oropharyngeal Dysphagia (OD) and sarcopenia have been recognized as geriatric syndromes and have shown a higher prevalence in institutionalized elderly, being associated with increased socioeconomic burdens. The objectives were to investigate the presence of sarcopenia and risk of OD in a geriatric population and to analyse the relationship between the factors associated with Sarcopenic Dysphagia (SOD). We have observed that female gender, low educational level and score ≥4 on the SARC-F screening test are associated with higher odds of being at risk for OD, sarcopenia, and even probable SOD. Based on the results, we suggested including a Speech and Language Therapist in the multidisciplinary geriatric teams in order to improve the prevention of OD, sarcopenia and SOD, avoiding its consequences. published
Gouveia, Carla, Sá Couto, Pedro, Matos, Assunção
Oropharyngeal dysphagia (OD) is common after stroke. Its presence submits the patient to clinical instability, which can cause complications such as aspiration pneumonia, dehydration, malnutrition and death. The objective was to compare effectiveness of traditional therapy (TT) with associated NMES versus traditional therapy in the rehabilitation of patients with OD after stroke and the effects on their quality of life (QOL). We have observed that in the EG, there is a trend towards a faster recovery of OD, reaching the level 7 of the FOIS scale about a week before the CG. Regarding QOL, it was possible to observe that the patients of both groups, when recovering from DO improved their QOL and that the EG tends to present better results. published
Rocha, Eugénio, Breda, Ana
In this work, we show the first results of a project where a combinatorial mobile application is used as a tool to gather users’ data, allowing some understanding about the learning behaviour of users solving combinatorial tasks, in particular, related with the NIM game. To obtain the results, 6.514 games and 29.667 moves where analysed and players where considered as production units, that transform input resources, i.e. attempts, moves of game pieces, number of games played; into output results, e.g. number of victories. This approach may give some insights to the use of digital games as research tools in Education.
Descalço, L., Canto Filho, A. do, Lima, J. Valdeni de
As a complementary tool for learning Calculus, we have been using SIACUA, a computer system designed to help autonomous learning, which is based on the use of parameterized questions with detailed solutions, also parameterized, with a Bayesian user model for feedback. This system has proven to be effective in keeping the students working during the classes’ period, as the recent data usage we present in this article shows. A difficulty in flipped learning is to guarantee that students study before the classes. We address this issue by trying to provide the best possible conditions for this autonomous work to occur. Hence, we propose an expansion of SIACUA, by combining it with the model MOTRAC, a model for creating learning objects and learning trajectories for meaningful learning, based on Meaningful Learning Theory and Cognitive Load Theory, to achieve good guidance, together with the already existing Bayesian feedback, in a flipped learning set, with active learning occurring in the classes. In the proposed learning set we also use an assessment computer system: PmatE. System PmatE is being used from 1989, mainly in the yearly science competitions, that nowadays join in our University, in the three days of the competitions, about ten thousand students, from all ages, from basic to secondary schools. To achieve some extrinsic motivation, and to further guarantee the students study before the classes, we use system PmatE, which imports contents from SIACUA, for assessment in the end of each class. Past experiences show two main advantages of using two completely different computer systems, one for learning and another one for assessment are: (i) students are more motivated to use the learning system because they know its contents or similar are going to be used for assessment; (ii) students are not afraid of answering questions in the learning system because they know that the diagnosis on this system is not going to be used for assessment and so it is a useful and safe feedback.
Vilaça, Mariana, Silva, Nélia, Coelho, Margarida C.
Cities have been often organized in terms of planning with special attention to motor vehicles and not well prepared for pedestrians and cyclists. In order to privilege active modes, there is the need to ensure the safety of these vulnerable road users. The main objective of this paper is to implement a statistical analysis to assess the occurrence and severity of road crashes involving vulnerable road users. This research is focused on analyzing the trends and causes of road crashes involving cyclists and pedestrians and what are the main difficulties that people using active modes do face in their journeys. In order to reach this objective, a database of crashes registrations involving motor vehicles and vulnerable road users from Aveiro, Portugal, between 2012 and 2015 was created. This analysis intends to evaluate the evolution of the number of crashes and to create patterns of risk factors such as weather conditions, specific locations and singularities that might represent additional risk, profile of pedestrian or cyclist involved. Regarding the analyzed variables that characterize crashes participations, the dependent variables considered were: meteorological conditions, location, proximity to a pedestrians’ crosswalk and gender of the VRU. The probability of the vulnerable road user being a pedestrian increases by 2.7 times if the crash occurs on a urban street segment, 10.6 times if the crash occurs at a pedestrians’ crosswalk, and 3.5 times if the VRU is a female.
Napp, Diego, Pereira, Ricardo, Pinto, Raquel, Rocha, Paula, Aleixo, José Carlos
In this paper we study the realization of periodically time-varying behavioral systems by means of periodic state-space models. In particular, we focus on the case of period two and investigate under which conditions a given behavior with periodic representation obtained by alternating two time-invariant image representations can be realized by a periodic state-space system. We first show that, in general, one cannot expect to obtain a periodic state-space realization by means of the individual realizations of each associated time-invariant behaviors. However, we give conditions for such procedure to hold. The presented results are illustrated by examples. published
Machado, Inês, Sá-Couto, Pedro, Tavares, João
BMC
published
Costa, Lénia, Sá-Couto, Pedro, Tavares, João
Background: The nursing assistant (NA) plays an important role in maintaining the health and independency of institutionalized older adults (OA) [1]. These professionals are required to help OA to achieve and maintain their highest level of function. The Function-Focused Care (FFC) is a philosophy of care that promotes the restoration and/or maintenance of physical function. In the institutional context it is relevant empowering NA to adopted this philosophy [2]. Objective: This study intends to analyse the perception of NA in relation to the FFC, through scales of self-efficacy, outcomes expectations and knowledge, as well as, the validity and reliability related properties. Methods: Quantitative approach of a descriptive/correlational cross-sectional type. A self-report questionnaire consisting of sociodemographic and professional variables and the scales of self-efficacy, expectations and knowledge were applied. Further details about the scales used can be found in Costa [3]. The validation/reliability procedures for each scale consisted in the calculation of exploratory factor analysis, Cronbach's alpha, and in the intra-class correlation coefficient (ICC) for test/retest purposes. Correlation between the scales themselves, with feelings related to the care of elderly, and sociodemographic and professional variables were tested using the Spearman Rank test. Results: The sample consisted of 73 NA (100% women) with a mean age of 46.4 (± 9.9) years from 5 different institutions. The scale of the self-efficacy showed a three-factor model with the total variance of 73.4%, Cronbach's alpha = 85.2% and ICC = 0.80. The scale of outcomes expectations presented one factor, Cronbach's alpha=95.2% and ICC = 0.97. The scale of Knowledge obtained a percentage of correct answers only of 44.7%. It was not possible to develop predictive models to relate these scales in a pre-intervention situation. Also, the low correlation between the scales and feelings related to the care of OA (difficulty, gratification, physical overload and emotional overload) or sociodemographic and professional variables (age, years of experience, and self-knowledge), indicated a weak dependence between them. Finally, the institution variable showed not to be a confounding variable (that is, does not influence these results). Conclusions: The Portuguese version of the scales analysed showed satisfactory data validity and reliability. These results suggest that the Portuguese version of these scales can be used to evaluate the FFC performed by the NA. These results point to the importance of implementing a FFC program in the institutions and analyse its impact on AO care and on NA. This work was supported in part by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. published
Abreu, Liliana, Sá-Couto, Pedro, Mestra, Susana
Background: In practice, a Speech Therapist works with several neurological diseases that present changes in swallowing, especially after acute stroke. These changes, called dysphagia, can lead the patient to death by leading to malnutrition, dehydration, tracheal aspiration and recurrent pneumonia [1]. Since most of these cases are diagnosed in a hospital setting, it becomes increasingly important to create working tools that help health professionals to perform more rigorous therapeutic evaluations and interventions. Objective: The present study aims to contribute to the cultural and linguistic validation and adaptation of the Protocol of Security of a Nasolaryngoscopy Evaluation of Swallowing (PSAND). Methods: The study comprises two parts: a qualitative part, that corresponds to the translation and adaptation of the protocol to European Portuguese Language, and a quantitative part, where the psychometric characteristics of the protocol were studied. Further details about translation and adaptation of the protocol can be found in [2], specially the content validity procedures and its application in a pilot study. A severity assessment scale [3] was used for the functional evaluation of the swallowing safety by classifying the swallow of the subjects as normal, penetration or aspiration. For data collection, it was used the Portuguese adaptation of the PSAND and the nasolaryngoscope as evaluation tools. The content validity index (CVI) was calculated for the qualitative part, and t-student or qui-squared tests were used for comparison between severity groups. Results: The sample consisted of twenty subjects, where all of them have an acute stroke as clinical diagnosis whether or not having dysphagia. The age of the inquired ranged from 31 to 85 years old, being 16 males. The results obtained by the panel of experts allowed us to conclude that all the parameters are relevant to the evaluation of swallowing and important to determinate a safe feeding for each case (CVI>0.80). Thus, by applying the PSAND, it was possible to study two groups: “Penetration” (13 patients) and “Aspiration” (5 patients). There were statistically significant differences (p < 0.05) between the two groups for the variables: dependent or independent feeding; poor oral control; lot of residues; reduction of laryngeal sensitivity; leaking of the bolus and difficulty in cleaning pharyngeal residues. Conclusions: In summary, we can say that the application of this protocol is an asset to diagnose the presence of dysphagia in any clinical diagnosis, evaluate the swallowing function, verifying the risk of penetration and aspiration and classifying the Dysphagia Severity. This work was supported in part by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through Center for Research and Development in Mathematics and Applications (CIDMA), within project UID/MAT/04106/2013. published
Alves, Ana, Simões, João, Rodrigues, Alexandre, Couto, Pedro
Background: The increase on life expectancy, and the raise of chronic condition, represents new challenges to the family nurse practitioner. Cardio-vascular diseases are the main cause of death among the population, however the numbers have been declining in past years [1]. There is an important economic impact that is a result of the incapacity cause by such diseases, as well as the treatment-related costs. Arterial hypertension has been gaining some relevance, due to its prevalence, and because its epidemiological base studies reveal a lack of control sample. Considering this problematic, a study was conducted, that analyses the mental adjustment of patients with arterial hypertension and the impact of the family nurse practitioner during appointments for hypertension monitoring. Objective: The objective was to evaluate the impact of the family nurse practitioner on the mental adjustment of patients that suffer from arterial hypertension, registered at the “HTA” program of the Personalised Healthcare Unit of Healthcare Centre of Sever do Vouga. Methods: A quantitative study was conducted, meeting one of the cycles of the research-action method, since an initial analysis was conducted, followed by the implementation of the intervention, and then carried by a new evaluation. Thus, using the Mental Adjustment to Disease Scale, as an evaluation instrument, regarding mental adjustment, along with a sociodemographic and clinical characterization questionnaire, addressed to the participants. The ethical principles were followed during the entire course of the investigation. Results: The participants in this study had and average age of 70.8 years, and being mostly females, diagnosed with for 8.4 years. To evaluate the internal consistency of MADS, it was calculated the Cronbach Alpha in moments 1 and 2, obtaining acceptable results, except for the subscale regarding fighting spirit. At moment 1 of the data collection, in the subscale regarding fighting spirit, all participants were classified as “fitted”, however for the remaining subscales, the participants were classified as “fitted” and “Not fitted”. The results obtained at moment 2, have revealed the impact from the conducted intervention, since the participants initially classified as “not fitted”, shifted to “fitted” at the 2nd moment. Conclusions: Performing a balance of the internship, it can be claimed that the expected competences and objectives were achieved. Ultimately, we can withdraw the conclusion that the intervention developed for the mental adjustment obtained the expected results, since the participants classified as “not fitted” on the 1st moment, were classified as “fitted” during the 2nd assessment moments. published
Tavares, João Paulo, Sá-Couto, Pedro, Machado, Inês
Hall, Andreia, Almeida, Paulo, Vettori, Paolo, País, Sónia
Associação Ludus
The Mathematical Circus project was created in 2011 by the Ludus Association with the main goal of promoting the interest and motivation for learning mathematics. The Mathematical Circus team performs mathematical magic shows where complementary skills are merged to produce a high intervention capacity within a wide geographical range in Portugal. Some tricks are performed by a mathematical clown, a unique character in the circus world, who brings together the usual foolish characteristics of a clown and the rigorous mathematical knowledge. In this paper we will describe and explain some of the tricks of the Mathematical Circus repertoire involving the clown. published
Abreu, C., Miranda, F., Felgueiras, P.
Mary Ann Liebert
Preprandial insulin bolus is adjusted taking into account the carbohydrate content of each meal, the patient’s glycemic targets (GHyper, GT and GHypo), the insulin sensitivity factor (ISF), and the insulin-to-carb ratio (ICR) throughout the day. Evidence suggests that accurate carbohydrate counting may have positive effects not only on reducing glycosylated hemoglobin concentration but also on decreasing the incidence of hypoglycemic episodes. Therefore, the efficacy of carbohydrate counting depends not only on the ability of each patient accurately estimate the carbohydrate content of each meal but also on each patient glycemic targets. published
Machado, Ana, Afreixo, Vera, Marques, Alda
Journal Statistics on Health Decision
Tavares, Ana Helena, Enes, Vera, Afreixo, Vera, Machado, Ana Filipa, Marques, Alda
Universidade de Aveiro
Enes, Vera, Tavares, Ana Helena, Afreixo, Vera, Machado, Ana Filipa, Marques, Alda
Barbosa, Fábio, Sousa, Amaro de, Agra, Agostinho, Walkowiak, Krzysztof, Goscien, Roza
Institute of Electrical and Electronics Engineers (IEEE)
An Elastic Optical Network (EON) provides a lot of flexibility on the way an optical network supports the demands of multiple services. This flexibility is given by the Routing, Modulation and Spectrum Assignment (RMSA) algorithm whose primary goal is to use the spectrum resources of the network in an efficient way. Recently, large-scale failures are becoming a concern and one source of such failures is malicious human activities. In terrorist attacks, although node shutdowns are harder to realize than link cuts, they are the most rewarding in the attackers’ perspective since the shutdown of one node also shuts down all its connected links. In order to obtain a RMSA algorithm resilient to multiple node failures, we propose the use of a path disaster availability metric which measures the probability of each path not being affected by a multiple node failure. We present computational results considering a mix of unicast and anycast services in 3 well-known topologies. We assess the trade-off between spectrum usage efficiency and resilience to multiple node failures of our proposal against other previous known algorithms. The results show that the RMSA decision is always better when the disaster path availability metric is used. Moreover, the best way to use the path disaster availability metric in the RMSA decision depends on the traffic load of the EON. published
Rebelo, Patrícia Filipa Sobral, Oliveira, Ana Luísa, Paixão, Cátia Filipa, Sara Souto Miranda, Machado, Ana Filipa, Alves, Ana Queiroz, Cruz, Joana, Jácome, Cristina, Almeida, Sara Lebre, Tavares, Ana Helena, Marques, Alda Sofia
European Respiratory Society
Fatigue is a prevalent, multi-dimensional and burdensome symptom in chronic obstructive pulmonary disease (COPD), yet it is still underdiagnosed, undertreated and little understood. This study explored associations between fatigue and key outcomes in COPD and which of them could explain fatigue. A cross-sectional study with people with COPD was conducted. Assessments included the modified functional assessment of chronic illness therapy-fatigue subscale (mod-FACIT-FS; lower scores mean worst fatigue), modified Medical Research Council dyspnea scale (mMRC), six-minute walk test (6MWT), COPD assessment test (CAT) and St. George’s Respiratory Questionnaire (SGRQ). Correlations were explored with the Pearson’s (r)/Spearman’s (rs) coefficients. Multiple linear regressions were performed with the stepwise model and the variance inflation factor (VIF) was confirmed. 89 people with COPD (68±9years; 76%male; 50±18FEV1pp) were enrolled. Significant moderate correlations were found between the mod-FACIT-FS and all outcomes (mMRC:rs=-0.53; 6MWT:r=0.50; CAT:r=-0.56; SGRQ:r=-0.63; p<0.01). The linear regression model showed that SGRQ, 6MWT and CAT explained 51% of the variability in the mod-FACIT-FS (p<0.01; VIF<2)(Figure 1). This study suggests that health-related quality of life, exercise tolerance and impact of the disease are correlated with fatigue in COPD. Comprehensive assessments including fatigue are needed to optimise COPD management. published
Tribuna, L., Clemente, A., Teixeira, T., Couto, P. Sá, Oliveira, P., Agostinho, P.
Oxford University Press
Araújo, Ana, Sá-Couto, Pedro, Valente, Paula, Matos, Maria
Sociedade Portuguesa do AVC
Pereira, Ricardo, Malonek, Paula Rocha, Napp, Diego
In this paper we use some classical ideas from linear systems theory to analyse convolutional codes. In particular, we exploit input-state-output representations of periodic linear systems to study periodically time-varying convolutional codes. In this preliminary work we focus on the column distance of these codes and derive explicit necessary and sufficient conditions for an (n, 2, 1) periodically time-varying convolutional code to have Maximum Distance Profile (MDP).
Miranda, Francisco, Abreu, Carlos, Miranda, Daniel
American Institute of Physics
The 3rdSymposium on Modelling and Simulation in Computer Sciences and Engineering was held in the14th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2016), Rhodes, Greece, 19-25 September 2016.
Miranda, D., Miranda, F., Costa, C. M., Almeida, A. M., Lanceros-Méndez, S.
AIP - American Institute of Physics (Theodore Simos and Charalambos Tsitouras)
Thermal analysis of battery geometries is essential for applications, as the thermal behavior of a battery influences its cycling life. Two geometries, square frame and conventional, have been studied for a scan rate of 290C. The square frame shows a capacity value of 290,15 Ahm−2 which is 446 times higher than the one for the conventional geometry, when the area is maintained constant for all components. In the adiabatic model, the square frame geometry has higher capacity value in comparison to the conventional geometry.
Al-Rawi, M. S., Freitas, A., Duarte, J. V., Cunha, J. P., Castelo-Branco, M.
Sage
A fundamental question that often occurs in statistical tests is the normality of distributions. Countless distributions exist in science and life, but one distribution that is obtained via permutations, usually referred to as permutation distribution, is interesting. Although a permutation distribution should behave in accord with the central limit theorem, if both the independence condition and the identical distribution condition are fulfilled, no studies have corroborated this concurrence in functional magnetic resonance imaging data. In this work, we used Anderson–Darling test to evaluate the accordance level of permutation distributions of classification accuracies to normality expected under central limit theorem. A simulation study has been carried out using functional magnetic resonance imaging data collected, while human subjects responded to visual stimulation paradigms. Two scrambling schemes are evaluated: the first based on permuting both the training and the testing sets and the second on permuting only the testing set. The results showed that, while a normal distribution does not adequately fit to permutation distributions most of the times, it tends to be quite well acceptable when mean classification accuracies averaged over a set of different classifiers is considered. The results also showed that permutation distributions can be probabilistically affected by performing motion correction to functional magnetic resonance imaging data, and thus may weaken the approximation of permutation distributions to a normal law. Such findings, however, have no relation to univariate/univoxel analysis of functional magnetic resonance imaging data. Overall, the results revealed a strong dependence across the folds of cross-validation and across functional magnetic resonance imaging runs and that may hinder the reliability of using cross-validation. The obtained p-values and the drawn confidence level intervals exhibited beyond doubt that different permutation schemes may beget different permutation distributions as well as different levels of accord with central limit theorem. We also found that different permutation schemes can lead to different permutation distributions and that may lead to different assessment of the statistical significance of classification accuracy. © 2015, © The Author(s) 2015.
Neste estudo pretende-se avaliar o desempenho de modelos competitivos para descrever os valores mensais do oxigénio dissolvido em estações de monitorização da qualidade da ́água no rio Vouga. O confronto ́é realizado entre um modelo de regressão com erros correlacionados e dois modelos de espaço de estados.
Gonçalves, A. Manuela, Amorim, M. Teresa, Costa, Marco
A deterioração progressiva dos recursos hídricos e a grande quantidade de água poluída gerada pelas sociedades modernas faz com que as estações de tratamento de águas residuais (ETAR) tenham uma extrema importância na prevenção e controlo da qualidade da água. Numa ETAR, o processo de lamas activadas é a tecnologia mais comumente usada para remover poluentes orgânicos das águas residuais (por meio de suspensão de biomassa bacteriana). Esta é a tecnologia com melhor custo- benefício, é muito flexível e pode ser adaptada a diferentes tipos de águas residuais. Por conseguinte, é muito importante compreender e modelar os processos biológicos utilizados numa ETAR, por forma a estimar os custos de tratamento com maior precisão e estabelecer uma melhor relação custo-eficácia. Neste trabalho a discussão centra-se no estabelecimento de análises e modelos estatísticos a fim de quantificar e caracterizar padrões de interacção entre as águas residuais dos afluentes que são tributários para as ETAR, as variáveis hidro-meteorológicas, as variáveis físico- químicas e as variáveis de custos associados aos tratamentos. O procedimento de modelação estatística foi aplicado a um conjunto de ETAR localizadas na região Noroeste de Portugal, em que os dados foram observados num período de dois anos (de Janeiro de 2015 até Dezembro de 2016). As metodologias desenvolvidas contribuíram para o aumento da eficiência de gestão, em particular da eficiência energética e da sustentabilidade dos sistemas de tratamento e exploração de águas residuais.
Hall, Andreia, Pais,Sonia
Magic and mathematics appear hand in hand when it comes to promoting the interest and motivation for learning mathematics. Portugal, like other countries, has a high failure rate in school mathematics, which of course causes a negative attitude towards this subject in society. Mathematics is generally thought of as a difficult subject with little practical importance. Motivated by the need to fight this stigma, the Mathematical Circus Project emerged in 2012. Linking mathematics with the performing arts (theater and circus) is not as common as other connections such as with the visual arts. The Mathematical Circus team performs mathematical magic shows with a circus atmosphere in schools, science centers and other public spaces. In a traditional magic show, one often realizes that what causes the fantastic effects is the magician’s ability to manipulate objects combined with the art of controlling the perception of the spectators. The tricks performed in the Mathematical Circus are exclusively based on mathematical principles. In this paper we describe the Mathematical Circus project: its context, goals, contents and achievements. published
Murillo, Kelly, Rocha, Eugénio
Education is of vital importance for the competitiveness and growth of a country, but it is affected by the amount of public and private investment, in particular, by governments and the economic leverage of citizens to pay tuitions. The financial crisis, originated in 2008, had some degree of impact in the European education system, which has not been completely understood. Spain is one of the countries that has suffered most from its impact, as reflected in the report of the Organization for Economic Cooperation and Development (OECD) of 2016, see [1]. While in most European countries public spending on education has remained stable at 11%, in Spain public spending on education has fallen from 9% to 8% from 2008 to 2013. The expenditure per student was below the OECD average in all stages, from primary to university. Nevertheless, such data are usually known for the public sector whereas the impact of the private sector is neglected. Here we want to focus on precisely the Spanish private educational sector, since a considerable percentage of students in Spain received education in private institutions, turning it a good case-study for understanding the impact of economy in education. Our work examines the financial efficiency of more than 4.000 Spanish private institutions divided into four educational levels: pre-primary, primary, secondary and higher education, in the period 2013- 2016. Their evolution is evaluated at three distinct stages: efficiency levels; efficiency patterns; and efficiency determinants. Our results clarify which are the profile of institutions that are most efficient, and which are not, giving some insight about the improvements which could be applied to raise their effectiveness. To this end, we take as a starting point the financial statements of each institution, considering variables that allow us to interpret measures of leverage, liquidity, profitability, management and evaluation of the institution. The main mathematical tool used is a nonparametric deterministic method for measuring efficiency, the Multidirectional Efficiency Analysis (MEA) of Bogetoft and Hougaard [2], in combination with other techniques. In contrast with the standard DEA, MEA also allows to investigate changes in efficiency patterns. Since the selection of relevant variables is of major importance, a combination of techniques to choose the most meaningful ones is used, namely, through Principal Component Analysis and to avoid loss of information (under-fitting) or the adding random noise (over-fitting), the RV coefficient is computed, see [3]. Comparisons between groups with different levels of efficiency are made by calculating an index that measures the effort to obtain input resources in a sequence of years. published
Barros, Pedro, Breda, Ana, Rocha, Eugénio, Gomes, Maria Isabel
World Academy of Science, Engineering and Technology
As visual and spatial awareness develop, children apprehension of the concept of direction, (relative) distance and (relative) location materializes. Here we present the educational inclusive digital game ORIESPA, under development by the Thematic Line Geometrix, for children, aged between 6 and10 years old, aiming the improvement of their visual and spatial awareness.Visual-spatial abilities are of crucial importance to succeed in many everyday life tasks. Unavoidable in the technological age we are living in, these abilities are very important, for instance, in mathematics.The game, set on a 2D/3D environment, focuses in tasks/challenges categorized on the following categories: (1) static orientation of the subject and object, requiring an understanding of the notions of up–down, left–right, front–back, higher-lower or nearer-farther; (2) interpretation of perspectives of three-dimensional objects, requiring the understanding of 2D and 3D representations of three-dimensional objects; and (3) orientation of the subject in real space, requiring the reading and interpreting of itineraries. In ORIESPA, simpler tasks are based on a quadrangular grid, where the front-back and left-right directions and the rotations of ±90º, ±180º and ±270º play the main requirements.The more complex ones are produced on a cubic grid adding the up and down movements. In the first levels, the game's mechanics regarding the reading and interpreting maps (from point A to point B) is based on map routes, following a given set of instructions. In higher levels, the playermust produce a list of instructions taking the game character to the desired destination, avoiding obstacles. Being an inclusive game,the user has the possibility to interact through the mouse (point and click with a single button), the keyboard (small set of well-recognized keys) or a Kinect device (using simple gesture moves). The character control requires the action on buttons corresponding to movements in 2D and 3D environments. Buttons and instructions are complemented with text, sound and, soon, with sign language. published
Carvalho, Paula, Oliveira, Paula
Institute of Electrical and Electronics Engineers
It is undeniable that mathematics is indispensable in education and practice of Engineering in all areas. In this paper we discuss the use of some active learning strategies on calculus applied in the first and second years of Engineering degrees. Among other experiences we report a flipped classroom experience, autonomous study and self evaluation using dedicated technological platforms and also active learning by solving proposed challenges outside the classroom where group and team work is encouraged in order to improve writing skills and the ability to communicate in mathematics. published
Hall, Andreia, Brás, Isabel, Pais, Sónia
Elliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning [1]. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of non-Euclidean geometry which is now briefly addressed in the middle school mathematics curriculum in Portugal [2]. We believe that the learning and teaching of non-Euclidean geometry can be facilitated by taking the role of an artist and creating works of art, eventually inspired by renowned artists such as M.C. Escher. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied basic non-Euclidean geometry concepts and created ceramic pieces using the Poincaré disk. The course took place in a Portuguese university, from January to March 2018, and involved 20 teachers of grades 1 to 12. The authors have developed a qualitative case study to evaluate how an artistic approach to the teaching of non-Euclidean geometry is perceived, by the mathematics teachers, as a contribution to the learning process. Overall, the activities developed have proved to be successful examples of interdisciplinary methodologies that bring into the teaching of mathematics usual procedures in the teaching of the arts. Moreover, the artistic approach followed during the course helped the teachers develop their geometric competences concerning non-Euclidean geometry in a more solid appropriation and application of the geometric concepts involved. published
Hall, Andreia, Pais, Sónia
Nowadays we live in an ever-changing society. The educational context is no exception, and requires a renewal of paradigms. Profound changes to the role and function of the teacher and the students are particularly vital [1], [2], [3]. The current University students have different motivations, different attitudes towards the teaching and learning process, and different responses to specific classroom environments and instructional practices [4]. The challenge that teachers face today is to motivate students to learn, get them to commit to and have an active role in their learning [5]. Considering that it is imperative to make the teaching and learning process of mathematics more stimulating, taking into account modern society and student’s interests [6], the authors have developed several strategies to increase the interest and improve the success of students in mathematics. Thus, they decided to use mathematical magic tricks in their classes to raise the motivation of the students, captivating them and stimulating their interest in mathematics. In this work, a case study to evaluate how mathematical magic can contribute to increase students' motivation for learning mathematics is presented. The paper describes how it is conceived as well as the main results. published
Breda, Ana, Santos, José Santos dos
In previous works we have ilustrate a procedure to obtain spherical tiling with GeoGebra. We have found new classes of monohedral spherical tiling by four spherical pentagons, and new class of dihedral spherical tiling by twelve spherical pentagons. One again, we would make use of GeoGebra to show how we can do generate new classes of monohedral non-convex hexagonal spherical tilings, H(C,τ), changing the side gluing rules of the regular spherical octahedral tiling, by local action of particular subgroups of spherical isometries. In relation to one of the new classes, by hexagonal tiles, we describe some of its properties. We also show the existence of a a new family of monohedral pentagonal tiling which arises as a degenarated case associated to the family H(C ,0) . All these classes of spherical tilings have emerged as a result of an interactive construction process, only possible by the use of newly produced GeoGebra tools and the dynamic interaction capabilities of this software. published
Carvalho, Maria José, Fernandes, José António, Freitas, Adelaide
Universidad de Granada, Facultad de Ciencias de la Educacion
Neste estudo são analisadas as resoluções de 23 alunos portugueses, do 8.º ano, de tarefas sobre o tema diagramas de extremos e quartis (DEQ) quando os dados são fornecidos de duas formas distintas: dados não organizados e dados representados num... This study analyses 23 Portuguese 8th grade students’ resolutions of tasks about boxplots where the data are provided by two different ways: collection of unorganized data and bar chart. Applying a qualitative methodology of case study and an... published
Murillo, K., Rocha, E.
This work examines the financial efficiency of private institutions of secondary and higher education in the Iberian Peninsula, during the period 2013-2016. In particular, we study the evolution of 117 Portuguese institutions and 1885 Spanish institutions. To this end, we analyze the evolution of financial statements of each institution regarding its efficiency at three distinct stages: efficiency levels; efficiency patterns; and efficiency determinants. We use a nonparametric method that allows us to investigate changes in the institutions' efficiency standards, namely a model based on the Multidirectional Efficiency Analysis (MEA) in combination with other mathematical techniques, such that principal component analysis, clustering analysis and accumulated effort. The study allows a parallel between Spain and Portugal, characterizing the behavior of the educational levels after the financial crisis that Europe suffered in mid-2008. Our results indicate which are the levels of education that are more efficient and those that are less efficient, and which improvements could be applied to propose more effective measures according to other European experiences. The results show that Spanish higher education is more efficient than Portuguese one and the same conclusion can be inferred, with a lower degree, for the secondary education, except in 2016. Looking to higher versus secondary education, secondary education presents the biggest resource management inefficiency. Cluster analysis was applied to avoid the disparity of data in Spain. In 2015, Spain cluster 1 presents the greatest difference between the accumulated efforts of the two education levels. In contrast, Spain cluster 2 attains the smallest difference. published
Barbosa, Fábio, de Sousa, Amaro, Agra, Agostinho
Consider the resilience of a network defined by the average 2-terminal reliability (A2TR) against a set of critical node failures. Consider an existing transparent optical network with a total fibre length L. The first goal of this paper is to assess the resiliency gap between the existing topology and a new network topology designed to maximize its resilience with the same fibre budget L. The resiliency gap gives us a measure of how good the resilience of existing network topologies are. Consider now that an existing network is upgraded with new links aiming to maximize its resiliency improvement with a fibre budget L'. The second goal of this paper is to assess how much the resiliency gap can be reduced between a good upgraded solution and a network topology designed to maximize its resiliency with the same fibre budget L + L'. The gap reduction gives us a measure of how close to the best resilience the upgraded solutions can get for different values of L'. To reach these goals, we first describe how the Critical Node Detection problem is defined and solved in the context of transparent optical networks. Then, we propose a multi-start greedy randomized method to generate network topologies, with a given fibre length budget, that are resilient to critical node failures. This method is also adapted to the upgrade of an existing network topology. At the end, we run the proposed methods on network topologies with public available information. The computational results show that the resiliency gap of existing topologies is significantly large but network upgrades with L' = 10%L can significantly reduce the resiliency gaps provided that such upgrades are aimed at maximizing the network resilience to multiple node failures. published
Barbosa, Fábio, Agra, Agostinho, de Sousa, Amaro
Springer International Publishing
For a given graph representing a transparent optical network, a given weight associated to each node pair and a given positive integer c, the Critical Node Detection problem variant addressed here is the determination of the set of c nodes that, if removed from the graph, minimizes the total weight of the node pairs that remain connected. In the context of transparent optical networks, a node pair is considered connected only if the surviving network provides it with a shortest path not higher than a given positive value T representing the optical transparent reach of the network. Moreover, the length of a path depends both on the length of its links and on its number of intermediate nodes. A path-based Integer Linear Programming model is presented together with a row generation approach to solve it. We present computational results for a real-world network topology with 50 nodes and 88 links and for c=2 up to 6. The optimal results are compared with node centrality based heuristics showing that such approaches provide solutions which are far from optimal. published
Consider an existing Elastic Optical Network (EON) with a given topology composed by nodes and connecting fibers, each fiber with a given spectrum capacity. Consider an estimated set of demands to be supported and a routing, modulation and spectrum assignment (RMSA) policy adopted by the operator both for the regular state and for the failure states. First, we address the resilience evaluation of the EON to multiple node failures. We adopt a worst-case approach by identifying the nodes (named critical nodes) whose simultaneous failure maximally reduce the demand percentage that is supported by the network and we use this percentage as the resilience metric. Then, for the same estimated demands, the same RMSA policy and a fiber budget equal to the total fiber length of the existing network, we address the design problem aiming to determine a new EON maximizing the resilience metric imposed by its critical nodes. We use a multi-start greedy randomized method that generates multiple EONs and returns the best one, i.e., the EON with the highest resilience metric. We run the evaluation and design methods on known network topologies. The computational results let us (i) analyze the efficiency of the methods and (ii) assess how far the resilience of existing networks are from the best ones. This paper is based upon work from COST Action CA15127 (”Resilient communication services protecting end-user appli- cations from disaster-based failures – RECODIS”) supported by COST (European Cooperation in Science and Technology). The work was also supported by FCT, Portugal, through project ResNeD CENTRO-01-0145-FEDER-029312 and PhD grant SFRH/BD/132650/2017. Second and third authors were supported by FCT through projects UID/EEA/50008/2019 and UID/MAT/04106/2019, respectively. published
Descalço, Luís, Carvalho, Paula
We have been using a combination of computer systems in Calculus for some years. The system MEGUA on Sagemath for authoring parameterized contents, system SIACUA for helping autonomous learning with the parameterized contents created, with Bayesian feedback and finally PmatE, a computer system used in Portuguese national competitions, for doing the assessment. Although this combined use of the systems accomplishes one of our goals, to motivate study during the whole semester instead of only before the main tests, it does not seem to be enough to convince students to work before the classes in an inverted learning environment. Students tend to use the systems only before the assessment tests. In the academic year 2018/2019, we have confirmed this thesis. Although our effort to provide to students the best possible conditions for working before the classes, they correspond to this motivation only it this work is assessed in the beginning of the class. Hence, giving the materials and assuming they work is, at least in our context, an ineffective approach. We compare two topics in flipped learning in a course with 99 students of Industrial Management Engineering (IME): a topic where assessment took place in the beginning of the class with another one for which, there was no assessment in the beginning of the class. Moreover, we compare the performance of these students in IME with others of a similar sample, from other engineering courses, on the same topic in flipped learning. The first ones knew they would be evaluated by a mini-test and the later knew that they would not be subject to evaluation. Our main conclusion is that, at least in our context, it is not safe to assume students work seriously before classes in flipped learning. In the absence of intrinsic motivation, using assessment in the beginning of the class is the best approach to convince students to do the previous work. Also, in some simple topics, providing appropriate learning materials, including short videos, this approach can improve learning outcomes. The data we use include, computer systems usage data, student’s marks and interviews of IME students with the best final marks in the Calculus course. published
Costa, Cláudia, Gonçalves, A. Manuela, Costa, Marco, Lopes, Sofia O.
IWSM2019
Climate change is a reality and efficient use of scarce resources is vital. The challenge of this project is to study the behaviour of humidity in the soil by mathematical/statistical modeling in order to find optimal solutions to improve the efficiency of daily water use in irrigation systems. For that, it is necessary to estimate and forecast weather variables, in this particular case daily maximum and minimum air temperature. These time series present strong trend and high- frequency seasonality. This way, we perform a state space modeling framework using exponential smoothing by incorporating Box-Cox transformations, ARMA residuals, Trend and Seasonality. This research was partially financed by Portuguese funds by the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (”Fundação para a Ciência e a Tecnologia” - FCT), within project UID/MAT/04106 2019. This research was partially financed by Portuguese funds through Portuguese Foundation for Science and Technology (”Fundação para a Ciência e a Tecnologia” - FCT), within project UID/MAT/00013/2013. FEDER/ COMPETE/- NORTE2020/ POCI/FCT funds through grants PTDC-EEI-AUT-2933-2014116858-TOCCATA and To CHAIR - POCI-01-0145-FEDER-028247 Financial support from the Portuguese Foundation for Science and Technology (FCT) within the framework of Strategic Financing UIDIFIS/04650/2013 is also acknowledged. published
Macedo, Pedro
APDR
Stochastic frontier analysis with maximum entropy estimation has received considerable attention in the literature in the recent years. In this work, the estimation of stochastic and deterministic production frontiers with maximum entropy methods, the advantages and disadvantages relatively to maximum likelihood, and some proposals to improve maximum entropy estimation in this context are presented and discussed. The author was supported by Fundação para a Ciência e a Tecnologia (FCT), within project UID/MAT/04106/2019 (CIDMA). published
Sério, Filipe, Costa, Marco, Ribeiro, Humberto
Varazdin Development and Entrepreneurship Agency (VADEA)
The food retail sector in Portugal is mostly concentrated in five main players holding 69.6% of its market share, with two groups leading the Portuguese preference, Continente with 21.9% market share, Pingo Doce with 20.8% market share, followed by Jumbo, Lidl and Intermarché with 9.5%, 8.8% and 8.6%, respectively. These operators up to the year 2012 have guided their performance and price strategy by applying the strategy Every-day-Low-Price that privileges the application of low and stable prices. In this paper we aim to characterize the food retail market in Portugal after the year 2012, identifying the main factors and contextualizing the economic climate. This analysis takes into account that most retailers opted to follow a strategy of high low pricing, which determined that 47% of sales of the year 2018 correspond to promotional sales; in this way, we will devote the analysis of the promotion and the impacts that it has for forecasting sales and supply chain management. Thus, to evaluate the influence of promotions on global sales, we will use weekly data referring to sales in the hypermarkets & "Superstores" channel that includes hypermarkets> 2,500 m2; Supermarkets 400-2,500 m2; Proximity <400 m2, in the period between the first week of 2012 and the last week of 2018, and also data on the number of promotions printed on promotional leaflets on the same the period in question. Applying multiple linear regression models and a previous exploratory analysis of the data we can conclude that the promotions carried out via leaflets actions have a weak capacity to explain the sales obtained in the Hypermarkets & Superstores channel and that are explained in large scale by other variables and the impact of these variables should be object of study in future works. published
Espadilha, Stephanie, Costa, Marco, Magueta, Daniel
The oil and energy sector is a very traditional, controversial and competitive sector. This study is based on a Portuguese fuel company and its main objective is to identify and characterize potential variables with predictive capacity for sales of new fuel stations. The database consists of a set of context variables with predictive potential for sales of fuel stations and monthly sales in terms of fuel volume. The research methodology focused on statistical methods of exploratory data analysis, clusters analysis and regression models. The fuel station context variables tend to characterize the socio-economic conditions of the area of influence of each station, such as population density variable, others related to the similar existing supply of both the company itself and the competing companies, and others related to geographical location and accessibility. The exploratory data analysis allowed to identify several patterns in the time series of sales indicating that the investigation of factors must be segmented. Homogeneous groups of fuel stations were identified through a hierarchical agglomerative clustering procedure considering the Ward's minimum variance method and the square Euclidian distance as distance measure. For each of the groups identified, multiple linear regression models were adjusted considering the annual fuel sales in the 1st, 2nd and 3rd years of operation of the stations as dependent variables. The results show that not all the exogenous variables are statistically significant. However, it is possible to conclude that the average daily traffic is the variable with predicted capacity for the most of the groups of fuel stations analyzed. published
Elliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education. One such topic is the study of non-Euclidean geometry. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied non-Euclidean geometry concepts. The participants created ceramic pieces using the Poincaré disk and styrofoam balls covered with fabrics using spherical geometry. published
Simões, Rita, Napp, Diego, Pinto, Raquel
In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-state-output (ISO) model to represent these codes. More concretely, we interconnect in series two ISO representations of two 2D convolutional codes and derive the ISO representation of the ob- tained 2D convolutional code. We provide necessary condition for this representation to be minimal. Moreover, structural properties of modal reachability and modal observability of the resulting 2D convolutional codes are investigated.
Kostyukova, Olga, Tchemisova, Tatiana, Kurdina, Maryia
Belarusian State University
We consider properties of one class of Nonlinear Programming problems arising in study of parametric problems of Semi-Infinite Programming
Pereira, Ricardo, Rocha, Paula, Napp, Diego
Springer - Lecture Notes in Computer Science
In this paper we study periodically time-varying convolutional codes by means of input-state-output representations. Using these representations we investigate under which conditions a given time-invariant convolutional code can be transformed into an equivalent periodic time-varying one. The relation between these two classes of convolutional codes is studied for period 2. We illustrate the ideas presented in this paper by constructing a periodic time-varying convolutional code from a time-invariant one. The resulting periodic code has larger free distance than any time-invariant convolutional code with equivalent parameters.
Breda, Ana, Rocha, Eugénio, Santos, Maria Isabel Gomes dos
The Learning Environment on Mathematics for Autistic Children (LEMA) is a digital mathematical learning environment with modalities of dynamic adaptations of the proposed activities having in consideration the user’s profile. Training Sessions with special teachers highlighted the need to add new technologies to LEMA. Following this line of thought it would be of great educational value the incorporation of a tabletop technology in LEMA. Among several major tabletop hardware, we have opted by the use of Kinects with a multi-touch tabletop system which can detect all the movements of the user making the human body as a remote control to assist the human computer interaction allowing the manipulation of simple objects connected with the scope of the embodied learning activities. In this paper, we will explain the several phases to the integration of this new technology in LEMA, giving special emphasis to the pedagogical framework underlying the adaptations of the incorporated math activities.
Benevides, Mário, Madeira, Alexandre, Martins, Manuel A.
Multi-Agent Epistemic Logic has been investigated in Computer Science [5] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [4] and also with a fuzzy semantics have been proposed [6,13]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [11,12]. The parameter in both methods is the same: an action lattice [9]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).
Camejo, Jorge, Silva, Alexandre, Descalço, Luís, Oliveira, Paula
PmatE (Mathematics and Education Project) is a Research and Development project started in 1989 at the University of Aveiro, Portugal. For 27 years, PmatE has maintained the mission of applying technologies and developing content and events to foster school success and scientific culture. PmatE provides a large repository of learning objects, with particular emphasis in Question Generator Models (QGM) or simply Models. A QGM is an object for generating questions targeting specific scientific and pedagogical-didactic objectives. Each QGM generates thousands of different questions, thus enabling the exposure of students to the same core problems, but with different instantiations, preventing cheating in exams. The QGM’s are the basis of Portugal National Science Competitions (NSC), a three-day yearly event with about ten thousand participants, and are widely used by schools nationwide, at various levels of education (from basic to higher education), for test and diagnostic exams in several areas (e.g., Mathematics, Physics, Biology, Portuguese, Financial Education, Geosciences and Chemistry). Until September 2015, each QGM created was written in a LaTeX template, as an intermediate specification of the Model, and later implemented by dedicated programmers from PmatE, thus making the Model development and later corrections a tedious, lengthy and time-consuming task. This work presents PmatE ModelMaker solution, which enables professors with neither a coding background nor latex knowledge, from basic school to higher education from all areas mentioned above, to create and share QGMs through a Web application. ModelMaker, keeps the core concepts of QGM such as “boxes” and “variables”, in order to guarantee the random screens concretization, and incorporates new functionalities and advantages (e.g., autonomy, model versioning, storage of instantiated models, and a management optimization of PmatE Subject Classification). Application ModelMaker, developed in ASP.NET, with SQL databases and Javascript frameworks, has proven to be a successful tool for saving time and giving total autonomy to QGM authors in the creation of the last 134 models in several areas of knowledge, as evidenced by the usage statistics extracted during the last eight months since the application has been available. This improvement in the QGMs development methodology is an important mark in the history of PmatE.
Cação, I., Malonek, H. R., Tomaz, G.
Universidade de Cadiz
We show how special well known matrices, namely, the creation and shift matrices play an important role on a matrix representation of orthogonal systems of polynomials with a hypercomplex variable and values in a Cli ord algebra.
A construção de obras de arte baseadas num módulo - arte modular - está presente ao longo de toda a história da humanidade. A recombinação do módulo pode ser mais ou menos flexível dando origem a resultados com diferentes graus de regularidade. Naturalmente, a modularidade é um campo fértil para a ocorrência de simetrias e também de antissimetrias. Neste apresentação consideramos a utilização de um módulo particular que consiste num quadrado dividido por uma das suas diagonais em dois triângulos de cores diferentes, que designamos por \textit{azulejo de Truchet}. A partir deste módulo considerámos rosáceas e frisos de diferentes dimensões e estudámos as suas propriedades quanto às possíveis simetrias e antissimetrias. Fizemos também contagens das configurações distintas que se podem obter para diferentes dimensões das rosáceas e dos frisos. Para terminar apresentam-se alguns trabalhos realizados por professores do ensino básico/secundário no contexto de uma ação de formação de professores realizada na Universidade de Aveiro nos meses de fevereiro a abril de 2017.
Pretende-se com este curso aprender (ou recordar) a classificar rosáceas e frisos quanto ao seu grupo de simetria. Pretende-se também abordar o conceito de antissimetria e com ele identificar e criar figuras de diversos tipos. O conceito de antissimetria é um conceito simples e apelativo que pode ajudar os alunos a assimilar e consolidar o conceito de simetria. Estes conceitos são explorados durante o curso através de diversos exemplos com especial incidência em figuras construídas a partir dum módulo simples, um quadrado dividido por uma das suas diagonais em dois triângulos de cores diferentes.
Lopes, Rui Borges, Sousa Santos, Beatriz, Ferreira, Carlos
Multi-objective optimization models have been increasingly used as optimal decisions are searched in settings considering several conflicting objectives. In these cases compromises must be made and often a large number of nondominated optimal solutions exist. From these solutions decisionmakers must find the preferred one. This is a difficult task both from a computational and cognitive point of views, as it requires several solutions to be obtained and compared. An interactive visualization tool for fully understanding the best trade-offs is therefore becoming increasingly important. This paper proposes visualization solutions, implemented in a tool, for aiding decision-makers in finding the preferred solution in multiobjective optimization problems.
Buchin, Kevin, Kostitsyna, Irina, Loffler, Maarten, Silveira, Rodrigo
Let p and q be two imprecise points, given as probability density functions on R 2, and let R be a set of n line segments in R 2 . We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R. To solve this problem, we approximate each density function by a weighted set of polygons; a novel approach to dealing with probability density functions in computational geometry.
Loffler, Maarten, Saumell, M., Silveira, Rodrigo
Given a 1.5D terrain, i.e., an x-monotone polygonal line in R 2 with n vertices, and 1 ≤ m ≤ n viewpoints placed on some of the terrain vertices, we study the problem of computing the parts of the terrain that are visible from at least one of the viewpoints. We present an algorithm that runs in O(n + m log m) time. This improves over a previous algorithm recently proposed.
Fabila, Ruy, Garcia, Alfredo, Hurtado, Ferran, Jaume, Rafel, Perez-Lantero, Pablo, Saumell, Maria, Silveira, Rodrigo, Tejel, Javier, Urrutia, Jorge
We study the cyclic sequences induced at infinity by pairwise-disjoint colored rays with apices on a given balanced bichromatic point set, where the color of a ray is inherited from the color of its apex. We derive a lower bound on the number of color sequences that can be realized from any fixed point set. We also examine sequences that can be realized regardless of the point set and exhibit negative examples as well. In addition, we provide algorithms to decide whether a sequence is realizable from a given point set on a line or in convex position.
Breda, Ana, Santos, José Manuel Santos dos
Federación Española de Sociedades de Profesores de Matemáticas
El objetivo de este mini curso es presentar algunas de las estrategias estudiadas para utilizar GeoGebra en el análisis de funciones complejas. Las tareas propuestas se centran en algunos temas de análisis compleja, uno de los objetivos para los estudiantes de primer año de educación superior, que se pueden adaptar fácilmente a los estudiantes preuniversitarios. En la primera parte de este mini curso vamos a ilustrar cómo usar las dos vistas gráficas de GeoGebra para representar funciones complejas de variables complejas. La segunda parte presentará el uso del color dinámico Geogebra para obtener dominios coloreados que correspondan a la representación gráfica de funciones complejas. Finalmente, usaremos la vista gráfica tridimensional en GeoGebra para estudiar las funciones componentes de una función compleja. Durante el mini curso se proporcionarán guiones de orientación de las diferentes tareas propuestas para ser realizadas en computadoras con Geogebra
Gonçalves, A. Manuela, Baturin, Olexandr, Costa, Marco
Time series analysis by state space models provide a very flexible tool for analysing dynamic phenomena and evolving systems, and have significantly contributed to extending the classical domains of application of statistical time series analysis. In this study, in the context of a surface water quality monitoring problem in a river basin, it is proposed an approach for the structural time series analysis based on the state space models associated to the Kalman filter. The main goals are to analyse and evaluate the temporal evolution of the environmental time series, and to identify trends or possible changes in the water quality on a dynamic monitoring procedure. The data concerns the River Ave’s hydrological basin located in the Northwest of Portugal, where monitoring has become a priority in water quality planning and management because its water has been in a state of obvious environmental degradation for many years. As a result, the watershed is now monitored by seven monitoring sites distributed along the River Ave and its main streams. For the modeling process we consider the monthly dissolved oxygen concentration dataset between January 1999 and January 2014. The framework of the state space models shows versatility to incorporate unobserved components, such as trends, cycles and seasonals, that have a natural interpretation and represent the salient features of the environmental time series under investigation. From the environmental point of view, the proposed approach allows to obtain pertinent findings concerning water surface quality interpretation and change point, thus highlighting the potential value of this type of analysis, and it is also relevant to identify unanticipated changes that are important in the management process and for the assessment of water quality. A. Manuela Gonçalves was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the FCT-Fundação para a Ciência e aTecnologia, through the Project PEstOE/MAT/UI0013/2014. Marco Costa was supported by Portuguese funds through the CIDMA-Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ”FCT-Fundação para a Ciência e a Tecnologia”, within project UID/MAT/04106/2013. published
Silva, Isabel, Alonso, Hugo
Instituto Nacional de Estatística
A previsão do número de dormidas mensais é um problema importante para a gestão dos alojamentos turísticos. Neste trabalho, analisa-se a série temporal do número de dormidas mensais na região Norte de Portugal entre janeiro de 2009 e junho de 2017, e obtêm-se previsões através da aplicação de redes neuronais e da análise espectral singular. published
Alonso, Hugo
Managing an airport is very complex. Decisions are often based on common sense and influence several variables, such as flight delay. In a previous work, we conducted a preliminary study where we were interested in predicting flight departure delay at Porto Airport. The problem was treated as an ordinal classification task and we built classifiers based on the unimodal paradigm. Here, we consider other approaches to ordinal classification and compare the performance of the resulting classifiers. published
Descalço, L., Carvalho, P., Oliveira, P.
For the flipped learning environment to be effective, it is essential that students use the learning materials before the classes, where they are supposed to practice, collaborating with colleagues with the help and guidance of the teacher. Students can easily get lost and unmotivated if the teacher simply gives them the learning material for studying before the classes. There is a need for some level of guidance and orientation in this autonomous learning for many students or they will go to the classes without having done the previous work required. We have developed a computer system with the main goal of motivating and guiding students to do this work before the classes. The computer system implements a Bayesian student model together with a learning trajectories model and makes use of a parameterized question generator, without any limitations on the parameterization we have also helped to develop. In practice, the computer system for learning presents the materials in an appealing and appropriate way, individually according to each student progress, including videos and other materials. Students can answer some of the many existing questions, generated among many parameterized templates, see detailed solutions of questions, also generated, and finally obtain a feedback about their progress in the learning contents required to next class. In the first semester of academic year 2017/2018, we have used our computer system with students in some of the topics of a course about calculus with several variables. The system keeps track of all activity and allows us to investigate student behaviour during the semester. We present an analysis of the system usage data on the topics in the experience comparing to those on traditional teaching, and relate with the results in final assessment, with the main goal of investigating the effectiveness of the use of this kind of computer systems in a flipped learning environment for motivating and guiding autonomous work before the classes. published
Descalço, L., Oliveira, P.
Many studies have shown positive effects of gamification and serious games on teaching and learning. From 1989, we have been organizing National Science Competitions in Portugal, with participants from schools from all over the Country. In this work, we assess the impact of these competitions on student’s motivation and performance in the school. The study is mainly based on surveys done on the years 2015 and 2017. Both, students and their teachers, have participated in the surveys. We also present some data about usage of the computer system used in the competitions during the event and for practicing to the event. Based on teacher’s opinions we conclude the events have some positive influence on student’s motivation. published
Aleixo, José Carlos, Napp, Diego, Pereira, Ricardo, Pinto, Raquel, Rocha, Paula
In this paper we consider 2D behaviors with periodic image representations and provide conditions under which a simple method for obtaining state space realizations by means of 2D periodic (separable) Roesser models can be applied. For the sake of simplicity we restrict our attention to the (2,2)-periodic case. Project POCI-01-0145- FEDER-006933 - SYSTEC - Research Center for Systems and Technologies - funded by FEDER funds through COMPETE20 published
Almeida, Ricardo Miguel
The purpose of this study is to present necessary conditions for calculus of variations problems, where the Lagrange function involves a Caputo fractional derivative with nonconstant order. The fractional operator depends on another function, and for particular choices of that function, we obtain some well-known fractional derivatives. Several necessary conditions of optimality are proven, namely the Euler–Lagrange equation published
Hall, Andreia, Pais, Sonia
Mathematics, considered one of the basic areas of various formations, has been the subject of concern for many authors and researchers due to its enormous academic and educational failure [1]. Its importance in day-to-day life and the formation of individuals is irrefutable [2]. One of the problems identified in the failure of mathematics teaching is the lack of motivation that students feel towards the discipline. According to [3], motivation is an essential factor in any learning since the quality of learning is not only related to the capacity to learn, but also to the level of motivation that we have to carry out this same learning. Considering that it is imperative to make the teaching and learning process of mathematics more stimulating, taking into account modern society and student’s interests [4], the authors have developed a qualitative case study to evaluate how "mathematical magic" can contribute to increase students’ motivation for learning mathematics. In order to develop this experience, the techniques of inquiry, direct observation and analysis of documents were applied and the following instruments were used: questionnaires and respective analysis grids; production of a battery of tasks of a diversified nature; field notes and interviews. Although this project is still ongoing and therefore not yet completed, a previous analysis of the collected data allows us to conclude that the use of mathematical magic tricks in the classroom, with the purpose of motivating the students to learn mathematics, was revealed effective. Students were curious about the new tricks and were positively surprised at the relative simplicity of their explanation, as if saying to themselves, "How can such mathematical concepts bring so much surprise?" The students showed that the topics gained more meaning after performing the tricks because they witnessed real applications of the concepts, with an extremely attractive purpose. They often stated that they were going to play the tricks on their friends / family outside the classroom context, which meant that they were mastering the concepts involved. published
Hall, Andreia, Bento, Sandra, Ferreira, Helena
Research on Voronoi Diagrams evolved a great deal from the original setting where a network of polygons marks the separation of points by regions of influence. Multiple approaches have been taken to solve the elementary geometry problems of bisecting segments and intersecting half-planes.The methods vary according to the type of point, the distance used and the type of bisector. In this work we propose some didactical tasks based on creating Voronoi diagrams. We also present some artistic quilt work, designed with the help of a Wolfram demonstrations project applet, based on a convenient choice of the generating points of a Voronoi Diagram. published
Anic, Filip, Penava, Davorin, Legatiuk, Dmitrii, Abrahamczyk, Lars, Kahler, Uwe
A 3D FE micromodel of a bare RC frame was developed. The model is based on validated 2D micromodel. The 3D model obtained higher response when compared to its 2D counterpart. Consequently, a calibration of the frame was initiated. Calibration involved modifying parameters that govern the plastic behaviour of the computational model, such as fracture energy, plastic displacement and direction of plastic flow. It was shown that the greatest effect in lowering the response had the direction of plastic flow. Plastic flow direction was selected as -0.1 as it has greatest correlation with the experimental data. Negative value denotes that material volume will decrease due to crushing. published
Rodrigues, Alexandre, Simões, João Lindo, Carramate, Lara, Pereira, Rui Miguel, de Francesco, Silvia, Sá-Couto, Pedro
European Society of Radiology
The learning process in a simulation context envisages the students to integrate a realistic situation probable in their professional future, in which they feel the difficulties, try to overcome them and acquires a real perception of the working environment. The greatest advantage of learning in a simulation context relies on the promotion of deep knowledge, since the student effectively participates in the scenario, instead of only being a passive element in the learning process [1]. In this work, a simulation of a pace maker implantation with imaging support requirement took place at the Clinical Simulation Centre of the University of Aveiro, "Simula", with the purpose of training future medical imaging professionals. The main objectives were to enhance and develop technical, problem-solving and interpersonal skills as well as to implant teamwork values [1]. published
Costa, Beatriz, Gouveia, Carla, Sá Couto, Pedro, Matos, Maria Assunção, Jesus, Luís
Objectives: Amyotrophic Lateral Sclerosis (ALS) is a progressive neurological disease whose number of cases in Portugal and in the rest of the world is increasing, being a condition increasingly studied in the scientific world. In Portugal, there are no available validated screening tools for this condition. This study aims to translate and validate the “Self-Administered Amyotrophic Lateral Sclerosis Functional Rating Scale - Revised” (Self-administered ALSFRS-R) to the European Portuguese language (EP). Methods: The English version of the Self-administered ALSFRS-R was translated into EP, by a bilingual translator and a speech and language therapist. A common version was agreed. Back translation was completed by a bilingual teacher. A panel of experts, composed of several health professionals with experience in the area, analyzed this version, and classified all its items in terms of relevance, clarity, ambiguity and conceptual adequacy (phase I). Some modifications were suggested and incorporated. The new version was reanalyzed by the same group (phase II). Data resulting from both phases were statistically analysed using the Content Validity Index (CVI). A pilot test was performed with 12 people with ALS and the internal validity was obtained. Results: Results obtained from phase II show high agreement between all experts regarding the clarity (CVI phase I=92%; phase II=100%), ambiguity (CVI phase I=92%; phase II=100%), relevance (CVI phase I=92%; phase II=100%) and adequacy of the concepts (CVI phase I=92%; phase II=100%), and for the overall score (phase I=83%; phase II=100%). In the pilot study, the internal consistency result was also very high (Cronbach’s α = 0.92). Conclusions: The Self-administered ALSFRS-R Portuguese version presented good values for content validity and internal consistency. It is therefore possible to use this instrument at various stages of the disease and to determine the degree of functionality of the Portuguese patients. Further studies are needed in order to analyze its psychometric characteristics. published
Alcaide, Joana, Matos, Maria, Sá Couto, Pedro, Jesus, Luís, Perdigão, Joana, Farinha, Joana
CPLOL
Objectives: Dysphagia is a swallowing disorder commonly diagnosed after stroke. Due to its serious consequences, an early diagnosis is fundamental. The patients with an early diagnosis should be referred for further clinical assessment. These assessments should include several evaluation techniques, including the use of self-administered Functional Health Status inventories. In Portugal, there is a lack of validated assessment scales and/or questionnaires related to dysphagia. The aim of this project is the translation and cultural adaptation of the Sidney Swallow Questionnaire (SSQ) to European Portuguese (EP). Methods: The English version of the SSQ was translated into EP by two independent bilingual translators, fluent in both languages, with EP as their mother tongue. A common version was agreed. A bilingual translator fluent in both languages, and whose mother tongue is English, completed back translation. A panel of experts composed of several health professionals with experience in the area, analysed this version and classified all its items in terms of their semantic, idiomatic, experiential and conceptual equivalence (phase I). Some modifications were then suggested and incorporated. The new version was re-examined by the same group (phase II). The data resulting from both phases were statistically analysed using the Content Validity Index (CVI). Results: The CVI values obtained for phase I were: 0.97, 0.98, 0.96 and 0.95, showing very good agreement between experts for semantic, idiomatic, experiential and conceptual domains. The CVI values for phase II were identical to the ones presented in phase I. Conclusions: The SSQ-EP version presented very good CVI values for semantic, idiomatic, experiential and conceptual domains. The SSQ is a quick and simple self-filling questionnaire and allows quantifying the symptomatic severity of oropharyngeal dysphagia as experienced by the patient. Further studies are needed in order to analyse its psychometric characteristics. published
Simões, Rita, Pinto, Raquel, Napp, Diego, Perea, Carmen, Iglesias, Jose
In this paper we address the problem of extending the well-known notion of column distance of one-dimensional (1D) convolutional codes to the context of multidimensional (nD) convolutional codes. In particular, we treat the 2D case and propose a new and more general notion than the one previously introduced in this context. We derive upper bounds on the distances that lead to the novel notion of Maximum Separation Set Distance Profile 2D convolutional codes. This notion naturally extends the notion of Maximum Distance Profile 1D convolutional code. Characterizations in terms of the sliding paritycheck matrices are presented. published
Konstantin Preslavsky University Press
The construction of art works based on a module --- \textit{modular art} --- is present throughout all human history. Naturally, modularity is a fertile field for the occurrence of symmetries. In this paper we consider the use of a particular module consisting of a square divided by one of its diagonals into two triangles of different colors, known as a \textit{Truchet tile}. From this module we considered rosettes and friezes of different dimensions and studied their properties regarding possible symmetries and antisymmetries. We have also counted the different configurations that can be obtained for different dimensions of rosettes and friezes. Symmetry and antissymmetry can be useful when creating art works and interlacing mathematics with the arts in the classroom can be a successful way to promote the interest for both subjects. We present some works carried out by primary and secondary school students and teachers. published
Napp, Diego, Pinto, Raquel, Rosenthal, Joachim, Vettori, Paolo
A new construction of maximum rank distance systematic rank metric convolutional codes is presented, which permits to reduce the computational complexity of the decoding procedure, i.e., of the underlying Viterbi algorithm. This result is achieved by lowering the number of branch metrics to be calculated and by setting to the highest value the metric of the remaining edges in the trellis. published
Cruz, Catarina, Breda, Ana
The Golomb-Welch conjecture states that there is no perfect r-error correcting Lee code of word length n over Z for n≥3 and r≥2. This problem has received great attention due to its importance in applications in several areas beyond mathematicsand computer sciences. Here, we give a contribution for the proof of the Golomb-Welch conjecture which reinforces it, proving the non-existence of perfect 2-error correcting Lee codes of word length 7 over Z. published
Santos, M. Isabel, Breda, A., Almeida, A.M.
This paperdescribes the several phases for the design and development of the digital Learning Environment on Mathematics for Autistic children (LEMA). LEMA is a prototype of a digital mathematical learning environment which activities are dynamically adapted to the user’s profile, towards the development of mathematical abilities of children aged 6–12 years diagnosed with autism spectrum disorders (ASD). This prototypehas already been evaluated with end-users (both students and teacher’s experts) and based on the analysis of the collected data readjustments were made, enabling the continuous improvement of the prototype, namely considering the integration of universal design for learning approaches, which are of most importance in ASD, due to its heterogeneity. The learning strategies incorporated in LEMA are also described. published
Gürlebeck, K., Kähler, U., Legatiuk, D.
The purpose of this paper is to prove an interpolation theorem which arises in a method of coupling of a finite element and an analytical solution for boundary value problems with singularities.
Santos, Simão P. S., Martins, Natália, Torres, Delfim F. M.
American Institute of Mathematical Sciences
We approach higher-order variational problems of Herglotz type from an optimal control point of view. Using optimal control theory, we derive a generalized Euler–Lagrange equation, transversality conditions, DuBois–Reymond necessary optimality condition and Noether’s theorem for Herglotz’s type higher-order variational problems, valid for piecewise smooth functions.
Gonçalves, Ana, Tomé, Ana, Descalço, Luís
Nowadays Interactive Learning Systems have been developed to provide students with new forms of practicing concepts. In this work we propose to predict if the student fails or succeeds in the introductory mathematics course based on the information collected by an interactive learning platform. The predicting models are based on binary support vector machines (SVM). As some of the collected data sets are unbalanced the study was conducted with suitable strategies to train this binary classifier.SIACUA - Sistema Interativo de Aprendizagem por Computador, Universidade de Aveiro - is a web application designed to support autonomous study. For each subject is defined a concept map with questions associated to each concept. The system is supplied with parametrized questions from PmatE (pmate.ua.pt) and MEGUA (cms.ua.pt/megua) projects. It implements a user model based on Bayesian networks.
Rocha, Anabela, Souto de Miranda, Manuela, Branco, João
O modelo SEM é uma generalização do modelo de regressão multivariado que assume dependência entre equações. Esta característica do SEM cria dificuldades adicionais às que já existem na deteção de outliers em modelos multivariados. Neste trabalho, propõe-se um novo método para detetar outliers em SEM. A proposta baseia-se numa versão robusta do estimador GMM e adapta ao SEM uma metodologia que foi recentemente utilizada para o modelo SUR, uma vez que este modelo também pressupõe dependência entre equações. As técnicas aplicadas mostraram-se adequadas para a deteção de outliers; o desempenho deste método foi comparado com o dos métodos convencionais, com base num estudo de simulação e num conjunto de dados reais. Os resultados mostraram vantagens na utilização da metodologia robusta que aqui se propõe, o que resulta numa mais valia do uso destes modelos na resolução de uma grande variedade de problemas que surgem na prática.
Climent, Joan-Josep, Napp, Diego, Pinto, Raquel, Simões, Rita
In this paper we study two-dimensional (2D) con-volutional codes which are obtained from series concatenation of two 2D convolutional codes. In this preliminary work we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-state-output (ISO) model representations. In particular, we show that the series concatenation of two 2D convolutional codes is again a 2D convolutional code and we explicitly compute an ISO representation of the code. Within these ISO representations we study when the structural properties of reachability and observability of the two given ISO representations carry over to the resulting 2D convolutional code.
Descalço, Luís, Carvalho, Paula, Oliveira, Paula
Dispomos na Universidade de Aveiro de três sistemas informáticos, com origem no Departamento de Matemática, que podem ser utlizados em conjunto no apoio ao estudo autónomo e avaliação também noutras áreas. São eles o MEGUA (Mathematics Exercise Generator, Universidade de Aveiro), que permite a criação de questões de escolha múltipla parametrizadas, o SIACUA (Sistema Interativo de Aprendizagem por Computador, Universidade de Aveiro), que permite mostrar as questões aos estudantes e seu progresso geral no curso com base nas respostas às questões, e ainda a plataforma do PmatE (Projeto Matemática Ensino) que permite a criação de testes para a avaliação. Está a ser usada pela primeira vez este ano, em diversas Unidades Curriculares da UA e também no exterior, uma nova funcionalidade que permite a criação de testes de avaliação na plataforma do PmatE, fazendo uso dos cursos e questões disponíveis no sistema de apoio ao estudo autónomo SIACUA. Estão ainda disponíveis novas funcionalidades no SIACUA que permitem a criação de cursos e questões dentro da própria aplicação. Estes sistemas, em conjunto, constituem um meio de apoio ao estudo autónomo e avaliação facilmente utilizável por docentes de outros departamentos que tenham interesse em criar questões sobre os assuntos que ensinam, disponibilizar essas questões para os estudantes no SIACUA e usar as mesmas, ou semelhantes, na avaliação. Apresentamos brevemente o modo como estas ferramentas podem ser reutilizadas e também alguns dados atuais de utilização das ferramentas pelos estudantes.
Santos, Maria Isabel, Breda, Ana, Almeida, Ana Margarida
ACM Press
The use of digital media is considered an effective way to work academic content with students with Autism Spectrum Disorders (ASD) enabling the creation of creative and constructive environments and the development of differentiated, meaningful and quality activities. Despite this scenario, the proposal of digital applications for children and youth with ASD continues to attract little attention, namely, regarding the promotion of deductive reasoning, an area of great interest for individuals with this disorder. Due to its heterogeneity, ASD are an interesting filed to explore the potential of using universal design for learning (UDL) approaches. This paper describes a learning environment developed under this universal scope, emphasizing the results obtained during evaluation sessions conducted with end users aiming to evaluate a prototype of this environment with dynamic adaptation features and specifically designed to support the development of Mathematical Reasoning in children with ASD. The results obtained during the evaluation sessions reveal that the digital environment is of easy interaction, simple and intuitive, and has a great potential to be an important tool to support the promotion of mathematical reasoning in children with ASD. The data collected allowed the identification of some adjustments that must be performed to improve the digital environment.
Santos, Maria Isabel, Ribeiro, Tânia, Breda, Ana, Almeida, Ana Margarida
IATED Academy
The purpose of this work focused in some design characteristics of Learning Environment on Mathematics for Autistic Children (LEMA), a digital mathematical learning environment with modalities of dynamic adaptations of the proposed activities having in consideration the user’s profile. The activities designed to enable adaptation were also conceived to promote the development of mathematical reasoning in children with Autism Spectrum Disorders, (ASD) aged between 6 and 12, fostering access and equity in the teaching and learning of mathematics. In this paper, the readjustments on LEMA’s interface are presented, namely considering the new dimension of gamification integrating game-design elements and game principles in non-game contexts, as a form of enhancing the user’ motivation.
So far, in the area of Random Linear Network Coding, attention has been given to the so-called one-shot network coding, meaning that the network is used just once to propagate the information. In contrast, one can use the network more than once to spread redundancy over different shots. In this paper, we propose rank metric convolutional codes for this purpose. The framework we present is slightly more general than the one which can be found in the literature. We introduce a rank distance, which is suitable for convolutional codes, and derive a new Singleton-like upper bound. Codes achieving this bound are called Maximum Rank Distance (MRD) convolutional codes. Finally, we prove that this bound is optimal by showing a concrete construction of a family of MRD convolutional codes.
Cardel, Sara D., Firer, Marcelo, Napp, Diego
In this work, we adapt the notion of generalized Hamming weight of block codes to introduce the novel concept of generalized column distances for convolutional codes. This can be considered as an extension of the work done in [18] on the generalized Hamming weights for free distance of convolutional codes. We also introduce the concept of Almost-MDP and NearMDP convolutional code. The problem of constructing convolutional codes with design generalized column distances remains an interesting open problem that requires further research.
Abreu, Nair M. M., Costa, Liliana M. G. C., Nascimento, Carlos H. P., Patuzzi, Laura
Sobrapo
O politopo de emparelhamentos de um grafo G, M(G), e ́ o fecho convexo dos vetores de incidência de emparelhamentos de G. O esqueleto deste politopo, G(M(G)), e ́ o grafo cujos vértices e arestas são, respectivamente, os vértices e arestas de M(G). Neste trabalho calculamos o grau do vértice do esqueleto correspondente ao emparelhamento vazio. Mostramos que, dado qualquer subgrafo próprio H de um grafo G, o grau de um vértice de G(M(H)) e ́ estritamente menor que o grau deste em G(M(G)). Além disso, determinamos o número de vértices e o grau mínimo (e máximo, em alguns casos) do esqueleto do politopo de emparelhamentos de grafos pertencentes a duas classes: a primeira, constituída por grafos unicíclicos obtidos pela adição de uma aresta entre dois vértices não adjacentes de um caminho; a segunda, dada por grafos resultantes da ligação de um dado vértice a todos os vértices de uma estrela.
Pereira, Ricardo, Rocha, Paula
In this paper we extend the state space geometric notions of conditioned invariance and detectability subspaces to the behavioral framework. This is achieved based on the existing notions of behavioral tracking observer and of behavioral asymptotic observer introduced by Valcher, Willems, Trentelman and Trumph, combined with a notion of behavioral invariance introduced here. Moreover, we provide characterizations for the newly de ned behavioral properties.
Rodrigues, M. M.
CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e a Tecnologia”), within project PEst-OE/MAT/UI4106/2014 In this paper we introduce two integral transforms involving the Legendre function in the kernel which generalize the classical Liouville fractional integrals. Then, we study their boundedness as operators mapping the space L_{v,r} into the spaces L_{v−α,r}. Moreover, we calculate the Mellin transform of the fractional integrals presented in this paper.
Silva, Joaquim, Alonso, Hugo, Silva, Isabel
O setor do Turismo é um dos mais importantes para a economia da região Norte de Portugal e tem crescido de ano para ano. Este trabalho considera dados recentes das dormidas mensais nos alojamentos turísticos da região, analisa-os e compara os resultados de previsões obtidas por meio da aplicação de redes neuronais artificiais e da análise espectral singular.
Costa, Maria Conceição, Pereira, Isabel, Scotto, Manuel Gonzalez
Copicentro Granada S.L
The Asymmetric Power Arch representation for the volatility was introduced by Ding et al.(1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brannas and Quoreshi (2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.
Almeida, Ricardo, Bastos, R. O. Nuno, Monteiro, M. Teresa T.
CMMSE
In this paper we consider fractional differential equations, with dependence on a Caputo fractional derivative of real order. Using real experimental data of Blood Alcohol Level we obtain a system of fractional differential equations that model the problem. A numerical optimization approach based on least squares approximation is used to determine the order of the fractional operator that better describes real data as well as other related parameters. We prove that it describes better the dynamics than the classical one.
Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth Robert
In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.
In this paper we consider a particularly important case of 3D monogenic polynomials that are isomorphic to the integer powers of one complex variable (called pseudo-complex powers or pseudo-complex polynomials, PCP). The construction of bases for spaces of monogenic polynomials in the framework of Clifford Analysis has been discussed by several authors and from different points of view. Here our main concern are numerical aspects of the implementation of PCP as bases of monogenic polynomials of homogeneous degree k. The representation of the well known Fueter polynomial basis by a particular PCP-basis is subject to a detailed analysis for showing the numerical efficiency of the use of PCP. In this context a modification of the Eisinberg-Fedele algorithm for inverting a Vandermonde matrix is presented.
Tomaz, Graça, Malonek, Helmuth Robert
In the last two years Frobenius-Euler polynomials have gained renewed interest and were studied by several authors. This paper presents a novel approach to these polynomials by treating them as Appell polynomials. This allows to apply an elementary matrix representation based on a nilpotent creation matrix for proving some of the main properties of Frobenius-Euler polynomials in a straightforward way.
Springer Berlin Heidelberg
The aim of our contribution is to call attention to the relationship between totally regular variables, introduced by R. Delanghe in 1970, and Appell sequences with respect to the hypercomplex derivative. Under some natural normalization condition the set of all paravector valued totally regular variables defined in the three dimensional Euclidean space will be completely characterized. Together with their integer powers they constitute automatically Appell sequences, since they are isomorphic to the complex variables.
The classical Joukowski transformation plays an important role in different applications of conformal mappings, in particular in the study of flows around the so-called Joukowski airfoils. In the 1980s H. Haruki and M. Barran studied generalized Joukowski transformations of higher order in the complex plane from the view point of functional equations. The aim of our contribution is to study the analogue of those generalized Joukowski transformations in Euclidean spaces of arbitrary higher dimension by methods of hypercomplex analysis. They reveal new insights in the use of generalized holomorphic functions as tools for quasi-conformal mappings. The computational experiences focus on 3D-mappings of order 2 and their properties and visualizations for different geometric configurations, but our approach is not restricted neither with respect to the dimension nor to the order.
Cação, Isabel, Falcão, Maria Irene, Malonek, Helmuth Robert
In hypercomplex context, we have recently constructed Appell sequences with respect to a generalized Laguerre derivative operator. This construction is based on the use of a basic set of monogenic polynomials which is particularly easy to handle and can play an important role in applications. Here we consider Laguerre-type exponentials of order m and introduce Laguerre-type circular and hyperbolic functions.
Cação, Isabel, Malonek, Helmuth Robert
An operational approach introduced by Gould and Hopper to the construction of generalized Hermite polynomials is followed in the hypercomplex context to build multidimensional generalized Hermite polynomials by the consideration of an appropriate basic set of monogenic polynomials. Directly related functions, like Chebyshev polynomials of first and second kind are constructed.
Malonek, Helmuth Robert, Tomaz, Graça
Recently the creation matrix, intimately related to the Pascal matrix and its generalizations, has been used to develop matrix representations of special polynomials, in particular Appell polynomials. In this paper we describe a matrix approach to polynomials in several hypercomplex variables based on special block matrices whose structures simulate the creation matrix and the Pascal matrix. We apply the approach to hypercomplex Laguerre polynomials, although it can be used for other Appell sequences, too.
Clain, Teresa de Jesus Costa Pereira Caracol
La Maison de l’Inde et le comptoir de Flandre sont à l’origine de règles spécifiques dont on ne trouve pas d’équivalent dans les traités d’arithmétique des autres pays. La règle d’un quart et un vingtième correspond à un prélèvement d’un quart plus un vingtième des trois quarts restants, c'est-à-dire 1/4+1/20×3/4=23/80 de la quantité initiale. La règle des comptes de Flandre correspond à une formule de conversion. Dans cette session, nous proposons une introduction à ces règles spécifiques du commerce des épices au Portugal à l'époque de la Renaissance, en tenant compte de l'interaction entre les Mathématiques, l'Histoire et l'introduction de la mentalité quantitative pour la modélisation du réel.
Costa, Marco, Baturin, Olexandr, Gonçalves, A. Manuela
A structural time series model is one which is set up in terms of components which have a direct interpretation. In this paper, the discussion focuses on the dynamic modeling procedure based on the state space approach (associated to the Kalman filter), in the context of surface water quality monitoring, in order to analyze and evaluate the temporal evolution of the environmental variables, and thus identify trends or possible changes in water quality (change point detection). The approach is applied to environmental time series: time series of surface water quality variables in a river basin. The statistical modeling procedure is applied to monthly values of physico- chemical variables measured in a network of 8 water monitoring sites over a 15-year period (1999-2014) in the River Ave hydrological basin located in the Northwest region of Portugal.
Monteiro, Magda, Pereira, Isabel, Scotto, Manuel G.
The study of forest re activity, in its several aspects, is essencial to understand the phenomenon and to prevent environmental public catastrophes. In this context the analysis of monthly number of res along several years is one aspect to have into account in order to better comprehend this tematic. The goal of this work is to analyze the monthly number of forest res in the neighboring districts of Aveiro and Coimbra, Portugal, through dynamic factor models for bivariate count series. We use a bayesian approach, through MCMC methods, to estimate the model parameters as well as to estimate the common latent factor to both series.
Silva, Elvira, Macedo, Pedro, Soares, Isabel
The main purpose of this study is to present an alternative benchmarking approach that can be used by national regulators of utilities. It is widely known that the lack of sizeable data sets limits the choice of the benchmarking method and the specification of the model to set price controls within incentive-based regulation. Ill-posed frontier models are the problem that some national regulators have been facing. Maximum entropy estimators are useful in the estimation of such ill-posed models, in particular in models exhibiting small sample sizes, collinearity and non-normal errors, as well as in models where the number of parameters to be estimated exceeds the number of observations available. The empirical study involves a sample data used by the Portuguese regulator of the electricity sector to set the parameters for the electricity distribution companies in the regulatory period of 2012-2014. DEA and maximum entropy methods are applied and the efficiency results are compared.
Pinto, Raquel, Napp, Diego, Vettori, Paolo, Rosenthal, Joachim
In this contribution, we propose a first general definition of rank-metric convolutional codes for multi-shot network coding. To this aim, we introduce a suitable concept of distance and we establish a generalized Singleton bound for this class of codes.
Rocha, Diana, Gouveia, Sónia, Pinto, Carla, Scotto, Manuel Gonzalez, Tavares, João Nuno
O objetivo deste trabalho é avaliar diferentes abordagens para identificação de grupos de pacientes VIH com padrões temporais de evolução da doença similares. Foi considerado um sistema de equações diferenciais ordinárias para caracterizar a comportamento ao longo do tempo de um paciente VIH sob tratamento antiretroviral - TAR de longo prazo, com 5 parâmetros estimados a partir de metodologia Bayesiana. As distribuições a posteriori foram usadas para quantificar distâncias (univariadas) entre pacientes, através do valor médio da distribuição a posteriori, e considerando a distância entre as distribuições a posteriori para cada parâmetro. O resultado do agrupamento hierárquico obtido pelas duas abordagens sugere que o uso de uma distância que considere a distribuição a posteriori é preferível. Trabalho futuro irá considerar distâncias multivariadas em vez de distâncias univariadas.
Santos, M. Isabel, Breda, Ana, Almeida, Ana Margarida
Universidade do Minho, Centro de Competência TIC do Instituto de Educação
A utilização das tecnologias é considerada um meio eficaz para trabalhar conteúdos académicos com alunos com Perturbações do Espetro do Autismo (PEA) possibilitando a criação de ambientes criativos e construtivos onde se podem desenvolver atividades diferenciadas, significativas e de qualidade. Contudo, o desenvolvimento de aplicações tecnológicas para crianças e jovens com PEA continua a merecer pouca atenção, nomeadamente no que respeita à promoção do raciocínio dedutivo, apesar desta ser uma área de grande interesse para indivíduos com esta perturbação. Para os alunos com PEA, o desenvolvimento do raciocínio matemático torna-se crucial, considerando a importância destas competências para o sucesso de uma vida autónoma. Estas evidências revelam o contributo inovador que o ambiente de aprendizagem descrito nesta comunicação poderá dar nesta área. O desenvolvimento deste ambiente começou por uma etapa de criação e validação de um modelo que permitiu especificar e prototipar a solução desenvolvida que oferece modalidades de adaptação dinâmica das atividades propostas ao perfil do utilizador, procurando promover o desenvolvimento do raciocínio matemático (indutivo e dedutivo). Considerando a heterogeneidade das PEA, o ambiente desenvolvido baseia-se em modalidades de adaptação dinâmica e em atividades ajustadas ao perfil dos utilizadores. Nesta comunicação procurámos dar a conhecer o trabalho de investigação já desenvolvido, bem como perspetivar a continuidade do trabalho a desenvolver. The use of technology is considered an effective way to work academic content with students with Autism Spectrum Disorders (ASD) enabling the creation of creative and constructive environments where it can be developped diferentiated, meaningful and quality activities. However, the development of technological applications for children and youth with ASD continues to attract little attention, namely the ones regarding the promotion of deductive reasoning, although this is an area of great interest for individuals with this disorder. For students with ASD, the development of mathematical reasoning becomes crucial, considering the importance of these skills for a successful independent living. These evidences show the innovative contribution that the learning environment described in this communication may give in this area. The development of this environment started by a step of creation and validation of a model that allowed the specifying and the prototyping of a solution providing dynamic adaptation modalities of the proposed activities to the user's profile and seeks to promote the development of mathematical reasoning (inductive and deductive). Given the heterogeneity of ASD, the developed environment is based on modalities of dynamic adaptation and in activities adjusted to the user’s profile. In this communication we present the research work done till now and give a perspective of the continuity of the work to be done.
Breda, Ana, Santos, José Manuel dos Santos dos
Complex functions, generally feature some interesting peculiarities, seen as extensions real functions, complementing the study of real analysis. However, the visualization of some complex functions properties requires the simultaneous visualization of two-dimensional spaces. The multiple Windows of GeoGebra, combined with its ability of algebraic computation with complex numbers, allow the study of the functions defined from ℂ to ℂ through traditional techniques and by the use of Domain Colouring. Here, we will show how we can use GeoGebra for the study of complex functions, using several representations and creating tools which complement the tools already provided by the software. Our proposals designed for students of the first year of engineering and science courses can and should be used as an educational tool in collaborative learning environments. The main advantage in its use in individual terms is the promotion of the deductive reasoning (conjecture / proof). In performed the literature review few references were found involving this educational topic and by the use of a single software.
This paper gives a vision of the work we have been carried out over the past two years, presented at the meetings “III Dia GeoGebra Portugal”, Aveiro University, May, 2013” and “IV Dia GeoGebra Portugal”, Superior School of Education of Oporto Polytechnic Institute, May 2014, and the improvements done so far having in mind didactical purposes. In the first meeting, we have shown how we could use GeoGebra to create colouring domains enabling the representation of complex function graphics and opening a promising path for the exploration of properties of functions of two real variables. In the second meeting we have unveiled the relation between Mobius transformations and the movements of a Riemann Sphere. Now our focus of attention is in the use of this software as a tool for learn, teach and research complex analysis.
The aim of this workshop to present some of the strategies studied to use GeoGebra in the analysis of complex functions. The proposed tasks focus on complex analysis topics target for students of the 1st year of higher education, which can be easily adapted to pre-university students. In the first part of this workshop we will illustrate how to use the two graphical windows of GeoGebra to represent complex functions of complex variable. The second part will present the use of the dynamic color Geogebra in order to obtain Coloring domains that correspond to the graphic representation of complex functions. Finally, we will use the threedimensional graphics window in GeoGebra to study the component functions of a complex function. During the workshop will be provided scripts orientation of the different tasks proposed to be held on computers with Geogebra version 5.0 or high.
Vieira, Nelson Felipe Loureiro
Bauhaus-University Weimar
What is nowadays called (classic) Clifford analysis consists in the establishment of a function theory for functions belonging to the kernel of the Dirac operator. While such functions can very well describe problems of a particle with internal $SU(2)$-symmetries, higher order symmetries are beyond this theory. Although many modifications (such as Yang-Mills theory) were suggested over the years they could not address the principal problem, the need of a $n$-fold factorization of the d'Alembert operator. In this paper we present the basic tools of a fractional function theory in higher dimensions, for the transport operator $(\alpha =\alfa)$, by means of a fractional correspondence to the Weyl relations via fractional Riemann-Liouville derivatives. A Fischer decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers are constructed.
Kähler, Uwe
Recently, one can observe an increased interest in discrete function theories and their applications. Although we will give a broader overview in our talk we would like to give a closer idea on the topic and its applications. To this end we present the question of boundary values of discrete monogenic functions in this short text. We also show their applicability in the theory of discrete Riemann boundary value problems (Riemann BVP’s). The grid itself was chosen in view of applications to image processing, such as discrete monogenic functions.
Macedo, Eloísa
Instituto Politécnico de Bragança
This paper is devoted to study regularity of Semidefinite Programming (SDP) problems. Current methods for SDP rely on assumptions of regularity such as constraint qualifications and wellposedness. Absence of regularity may compromise characterization of optimality and algorithms may present numerical difficulties. Prior that solving problems, one should evaluate the expected efficiency of algorithms. Therefore, it is important to have simple procedures that verify regularity. Here we use an algorithm to test regularity of linear SDP problems in terms of Slater’s condition. We present numerical tests using problems from SDPLIB and compare our results with those from others available in literature.
Macedo, Eloísa, Freitas, Adelaide
University of Évora, Dorodnicyn Computing Centre of Russian Academy of Sciences
The main objective of this work is to test the ability of the new tech- nique CDPCA - Clustering and Disjoint Principal Component Analysis on biological data sets to make possible visual representation of relevant characteristics for data interpretation. For this purpose, we im- plemented CDPCA in R language and conducted several experiments. Numerical results show its efficiency.
Xambre, Ana Raquel, Ramos, Ana Luísa, Teixeira, Leonor, Filipe, Nelson, Alvelos, Helena
IADIS
Adequate interfaces are an essential part of any Decision Support System (DSS) since they can contribute to a more efficient use of that system. Also, a user-friendly design can facilitate the acceptance and utilization of the software by its end users. This work presents the development process of the interfaces designed for a DSS that is being developed in order to help decision-making in a context of Sensory Analysis. That process began with the construction of mock-ups and, for that purpose, the tool chosen was Lumzy, a web-based wireframing tool for rapid user-interface prototyping.
Xambre, A. R.
Computers & Industrial Engineering
When designing a Cellular Manufacturing System an essential step is to solve the cell formation problem: determining which machines and parts belong to each cell. The main purpose is to obtain autonomous cells capable of completely processing the respective family of parts and thus eliminate, or at least reduce, intercellular flow. Additionally, if there is more than one machine of each type (i.e. if a certain operation can be performed in different machines) the assignment of operations to specific machines becomes part of the cell formation problem. In this paper an algorithm for the cell formation problem with multiple identical machines, which minimises the intercellular flow, is presented. The algorithm uses the information provided by an inter-operation flow matrix so the real flow, associated with each solution, can be adequately determined. Furthermore, due to the combinatorial nature of this problem, the procedure is based on genetic algorithms in order to improve the exploration of the solution space.
Rodrigues, Helena Sofia, Fonseca, Manuel
In epidemiology, an epidemic is defined as the spread of an infectious disease to a large number of people in a given population within a short period of time. In the marketing context, a message is viral when it is broadly sent and received by the target market through person-to-person transmission. This specific marketing communication strategy is commonly referred as viral marketing. Due to this similarity between an epidemic and the viral marketing process and because the understanding of the critical factors to this communications strategy effectiveness remain largely unknown, the mathematical models in epidemiology are presented in this marketing specific field. In this paper, an epidemiological model SIR (Susceptible-Infected-Recovered) to study the effects of a viral marketing strategy is presented. It is made a comparison between the disease parameters and the marketing application, and simulations using the Matlab software are performed. Finally, some conclusions are given and their marketing implications are exposed: interactions across the parameters are found that appear to suggest some recommendations to marketers, as the profitability of the investment or the need to improve the targeting criteria of the communications campaigns.
Kostyukova, Olga, Tchemisova, Tatiana
University of Evora; Dorodnicyn Computing Center of Russian Academy of Sciences
No abstract.
This work presents some common issues in the statistical analysis of time series of environmental area. The discussion and the presentation of solutions is raised by the study of a time series of the oxygen concentration variable in a water quality monitoring site in the river Vouga hydrological basin in Portugal. Issues such as trends, seasonality, temporal correlation and detection of change points are addressed.
Costa, Marco, Gonçalves, A. Manuela, Silva, Joana
Exponential smoothing methods are the most used in time series modeling and forecasting, due to their versatility and the vast model option they integrate. Also, within the computing statistical area, Bootstrap methodology is widely applied in statistical inference concerning time series. Therefore, this study’s main objective is to analyse Holt-Winters exponential smoothing method’s performance associated to Bootstrap methodology, as an alternative procedure for modeling and forecasting in time series. The Bootstrap methodology combined with Holt-Winters methodology is applied to a study case on an environmental time series concerning a surface water quality variable, Dissolved Oxygen (DO). The proposed procedure allows to obtaining better point forecasts and interval forecasts with less amplitude than those obtained by means of the usual methods.
Descalço, Luís, Carvalho, Paula, Cruz, João Pedro, Oliveira, Paula, Seabra, Dina
The teaching paradigm is changing from a traditional model of teachers as suppliers of knowledge and toward a model of teachers as advisers who carefully observe students, identify their learning needs, and help them in their independent study. In this new paradigm, computers and communication technology can be effective, not only as means for knowledge transmission, but also as tools for automatically providing feedback and diagnosis in the learning process. We present an approach integrating parameterized questions from two computer systems (Megua and PmatE), combined with a Web application (Siacua) implementing a Bayesian user model, using already many hundreds of questions from each of the two systems. Our approach allows the students a certain level of independence and provides some orientation in their independent study, by giving feedback about answers to questions and also about the general progress in the study subject. This progress is shown in the form of progress bars computed by Bayesian networks where nodes represent “concepts” and knowledge evidences. Teachers use Megua for creating and organizing their own database of (parameterized) questions, make them available for students, and for seeing the progress of each student or class in every topic being studied.
Descalço, Luís, Carvalho, Maria Paula, Cruz, João Pedro, Oliveira, Maria Paula de Sousa, Seabra, Dina
Learning mathematics requires students to work in an independent way which is particularly challenging for such an abstract subject. Advancements in technology and, taking the student as the focus of his own learning, led to a change of paradigm in the design and development of educational contents. In this paper we describe the first experience with an interactive feedback and assessment tool (Siacua), based on parameterized math exercises, and explain how we use it to motivate student independent study in a multivariate calculus environment. We have defined an index about the subject, trying to make it consensual enough for being used in other courses about multivariate calculus. Then we have created a concept map, selected some existing parameterized true/false questions from PmatE project and classified them using our concept map, for being reused in our system. For complementing the course we have created about one hundred parameterized multiple choice question templates in system Megua and generated about one thousand instances for using in Siacua. Results based on data collected by this tool and also based on an informal survey are presented. This first experience allows us to conclude our approach has an important impact on student motivation and contributes to the success on learning multivariate calculus.
Cruz, João Pedro, Plakhov, Alexander
Here we study retroreflectors based on specular reflections. Two kinds of asymptotically perfect specular retroreflectors in two dimensions, Notched angle and Tube, are known at present. We conduct comparative study of their efficiency, assuming that the reflection coefficient is slightly less than 1. We also compare their efficiency with the one of the retroreflector Square corner (the 2D analogue of the well-known and widely used Cube corner). The study is partly analytic and partly uses numerical simulations. We conclude that the retro-reflectivity of Notched angle is normally much greater than those of Tube and the Square corner. Additionally, simple Notched angle shapes are constructed, whose efficiency is significantly higher than that of the Square corner.
Rachah, Amira, Torres, Delfim F. M.
APMTAC
We present a mathematical model that describes one of the most virulent pathogens for humans - the Ebola virus. The spread of this lethal virus is investigated by the SEIR (Susceptible, Exposed, Infectious, Recovered) model. We discuss and simulate the model and then control the evolution of the Ebola virus with the goal to study the impact of vaccination on its spread.
Alves, Margarita, Moutinho, Vítor, Macedo, Pedro
This study aims to evaluate the resource and environment efficiency problem of European countries. We specify a new stochastic frontier model where Gross Domestic Product (GDP) is considered as the desirable output and Greenhouse Gases (GHG) emissions as the undesirable output. Capital, Labour, Fossil fuels and Renewable Energy consumption are regarded as inputs. The study is divided into two distinct periods, 2000-2004 and 2005-2011, in order to evaluate the difference between efficiency levels before and after the establishment of environmental targets related with the implementation of the Kyoto Protocol in 2005. A maximum entropy approach to assess technical efficiency is discussed.
Alonso, Hugo, Loureiro, António
SCITEPRESS – Science and Technology Publications
Managing an airport is very complex. Decisions are often based on common sense and influence several variables, such as flight delay. This paper considers the problem of predicting flight departure delay at Porto Airport. As far as we know, this the first study on the subject. The problem is treated as an ordinal classification task and a suitable approach, based on the so-called unimodal model, is used to predict the delay. The unimodal model is implemented using neural networks and, for comparison purposes, also using trees.
Miranda, Francisco, Abreu, Carlos
AIP - American Institute of Physics
Resumo indisponível.
Abreu, Carlos, Miranda, Francisco, Mendes, Paulo Mateus
Biomedical wireless sensor networks enable the development of real-time patient monitoring systems, either to monitor chronically ill persons in their homes or to monitor patients in step-down hospital units. However, due to the critical nature of medical data, these networks have to meet demanding quality of service requirements, ensuring high levels of confidence to their users. These goals depend on several factors, such as the characteristics of the network deployment area or the network topology. In such context, this work proposes a method to find the best network physical topology in order to maximise the quality of service provided by the network. The proposed method makes use of “virtual sensor nodes” to estimate the impact of adding real sensor nodes to the network in a specific location. Thus, assessing different locations, it is possible to find the best location to place the new sensor node while maximising the quality of service provided by the network. In particular, this work studies the feasibility of using “virtual sensor nodes” to assess the impact of adding a new sensor node to a biomedical wireless sensor network and presents some results showing the viability of the proposed method.
Descalço, Luís, Carvalho, Paula Reis
We have implemented a Web application reusing questions from two computer systems, true/false questions from Project A and multiple choice questions from Project B. Our application implements a Bayesian user model for diagnosing student knowledge in the topics covered. In this article we propose the use of this system for both learning and assessment in a calculus course, encouraging the students to work during the semester without increasing the work load for teachers.
Poças, Jacinta, Cruz, João Pedro, Descalço, Luís, Carvalho, Paula Reis
IRISA
The first contact of students with logic is not straightforward since they are not familiar with its notation and with logical thinking. For this discipline to become more attractive and in order to avoid this intimidating first contact, interactive didactic tools can be useful. In the University of Aveiro there exists a group of teachers developing an interactive platform that provides students some guidance in their independent study in several courses. We propose and describe the use of this platform as a complement for teaching the logic course of Mathematics Department in this University.
Pereira, Ricardo, Vettori, Paolo
IFAC
In this paper we study a particular kind of symmetry of linear dynamical systems, the quaternionic symmetry. After giving some basic notions about quaternions and behavioral systems, we introduce and characterize linear systems with quaternionic symmetry. Finally we propose a state-space realization algorithm for input/output systems.
Costa, Marco, Monteiro, Magda, Gonçalves, A. Manuela
Komarek, Arnost & Nagy, Stanislav
This work presents a comparative study of some models to estimate radar rainfall in real time using the Kalman filtering approach. This comparison adresses the parameters estimation, the assessment of the accuracy estimates obtained by each model and the impact of the number of rain gauges used in the improvement of radar calibration estimates.
European Control Association (EUCA)
In this paper a definition for the property of behavioral invariance is proposed with the purpose of generalizing the state space geometric approach to the behavioral setting. Based on this notion together with the well-known notion of behavioral observer, a definition of conditioned invariance is also presented. The results obtained for the characterization of the defined properties put into evidence some problems that, in our opinion, should deserve attention. This could serve as a starting point for a discussion on the foundations of an analogue of the geometric theory within the behavioral setting.
Pooseh, S., Almeida, R., Torres, D. F. M.
We present necessary optimality conditions for a class of optimal control problems. The dynamic constraints involve fractional-order and integer-order derivatives and the final time is free. Optimality conditions are obtained using variational principles and some typical problems are solved by approximating the fractional derivatives in terms of integer ones. © 2013 EUCA.
Cruz, A. M. C. B. da, Martins, N., Torres, D. F. M.
We introduce the α,β-symmetric difference derivative and the α,β-symmetric Nörlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward h-calculus. © Springer Science+Business Media New York 2013.
Cruz, A. M. C. Brito da, Martins, N., Torres, D. F. M.
Properties of an α,β-symmetric Nörlund sum are studied. Inspired in the work by Agarwal et al., α,β-symmetric quantum versions of Hölder's, Cauchy-Schwarz's and Minkowski's inequalities are obtained. © Springer Science+Business Media New York 2013.
Brás, Isabel, Pawłuszewicz, Ewa
Associação Portuguesa de Controlo Automático
This paper is a first attempt to introduce the behavioral approach into dynamical systems define on a time scale. The notion of kernel behavior on a time scale as the kernel of a delta differential matrix operator is introduced. Basic properties, as surjectivity and injectivity, of this operator are studied. A characterization of equivalent kernel representations is given. Additionally, the question whether a behavior that admits a representation with auxiliary variables is also a kernel behavior is analyzed.
Pereira, Ricardo, Rocha, Paula, Simões, Rita
In this paper the new concept of 2D structured system is defined and a characterization of global reachability is obtained. This extends a well known result for 1D structured systems, according to which (A ,B ) is (generically) reachable if and only if the matrix [A B] is full generically row rank and irreducible.
Vettori, Paolo
IFAC/APCA
Mathematicians have been discussing about the existence (and the meaning) of derivatives and integrals of fractional order since the beginnings of differential calculus. Various concepts of fractional calculus have been developed and some of them were already applied to dynamical systems. In particular, the author already proposed a way to consider systems defined by linear differential equations of fractional order within the so-called behavioral approach. In this paper, it is shown how to generalize, analogously, discrete-time linear systems by defining a certain type of difference equations of fractional order. Some of the ideas and techniques which will be used belong to the theory of dynamical systems on time scales.
Pooseh, Shakoor, Almeida, Ricardo, Torres, Delfim F. M.
FDA
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional derivative. Using the Gr¨unwald–Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.
Pereira, Ricardo, Rocha, Paula, Vettori, Paolo
The main goal of this paper is to characterize BIBO-stability of input/output quaternionic systems. After defining and investigating properties of quaternionic polynomials and rational functions, the Smith and the Smith-McMillan forms of quaternionic matrices are studied. Finally, the stability of quaternionic behavioral systems is analyzed using these tools.
Model reduction techniques permit to approximate a dynamical system by a simpler one. However, it is desirable that some characteristics of the system are not lost in this process. In this paper we present a model reduction algorithm that preserves the symmetry of linear dynamical systems with quaternionic symmetry.
MTNS
In this paper we study behavioral systems whose trajectories are given as solutions of quaternionic difference equations. As happens in the commutative case, it turns out that quaternionic polynomial matrices play an important role in this context. Therefore we focus our attention on such matrices and derive new results concerning their Smith form. Based on these results, we obtain characterizations of system theoretic properties of quaternionic behaviors.
In this paper we propose a definition of determinant for quaternionic polynomial matrices. This definition is later used in the study of stability of linear quaternionic systems within the behavioral setting.
Vettori, Paolo, Pereira, Ricardo
A fractional linear system is defined by differential or difference equations of non-integer order. A well-known result about the stability of fractional differential systems will be extended to discrete-time systems defined by fractional difference equations. This will be accomplished using time scales, which permit to unify continuous and discrete-time systems.
This paper aims to discuss some problems on state space models with estimated parameters. While existing research focus on the prediction mean squared error, this work presents some results on bias propagation into forecast and filter predictions when the mean vector of the state is taking with an estimation bias, namely, non recursive analytical expression for them. In particular, it is discussed the impact of mean bias in invariant state space models.