Proceedings in RIA


A family of graded epistemic logics

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).

ria.ua.pt

ModelMaker, a Multidisciplinary Web Application to Build Question Generator Models From Basic to Higher Education

Camejo, Jorge, Silva, Alexandre, Descalço, Luís, Oliveira, Paula

IATED

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.

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Bisimulation for reactive frames

Figueiredo, Daniel, Martins, Manuel António

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.

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Matrices related to orthogonal hypercomplex polynomial systems

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.

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Arte modular com azulejos de Truchet

Hall, Andreia

Sociedade Portuguesa de Matemática

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.

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Simetria e antissimetria de rosáceas e frisos

Hall, Andreia

Sociedade Portuguesa de Matemática

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.

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Permutations of functional magnetic resonance imaging classification may not be normally distributed

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.

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A Tool for Visually Exploring Multi-objective Mixed-Integer Optimization Models

Lopes, Rui Borges, Sousa Santos, Beatriz, Ferreira, Carlos

IEEE

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.

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Region-based approximation of probability distributions (for visibility between imprecise points among obstacles)

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.

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A faster algorithm to compute the visibility map of a 1.5D terrain

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.

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Colored Ray Configurations

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.

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Statistical analysis of the occurrence and severity of crashes involving vulnerable road users

Vilaça, Mariana, Silva, Nélia, Coelho, Margarida C.

Elsevier

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.

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Input-state-output representations of concatenated 2D convolutional codes

Simões, Rita, Napp, Diego, Pinto, Raquel

Springer

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.

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An interpolation problem arising in a coupling of the finite element method with holomorphic basis functions

Gürlebeck, K., Kähler, U., Legatiuk, D.

AIP Publishing

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.

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Noether's theorem for higher-order variational problems of Herglotz type

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.

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Predicting student performance with data from an interactive learning system

Gonçalves, Ana, Tomé, Ana, Descalço, Luís

Universidade de Aveiro

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.

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Deteção de outliers no modelo de equações simultâneas usando o estimador GMM robusto

Rocha, Anabela, Souto de Miranda, Manuela, Branco, João

Sociedade Portuguesa de Estatística

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.

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Series concatenation of 2D convolutional codes

Climent, Joan-Josep, Napp, Diego, Pinto, Raquel, Simões, Rita

IEEE

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.

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Integração de sistemas informáticos no apoio ao estudo autónomo e avaliação

Descalço, Luís, Carvalho, Paula, Oliveira, Paula

Universidade de Aveiro

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.

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Learning environment for autism spectrum disorders: a universal approach to the promotion of mathematical reasoning

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.

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Redesigning LEMA: a web based classroom application to promote mathematical reasoning in autistic children

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.

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MRD Rank Metric Convolutional Codes

Napp, Diego, Pinto, Raquel, Rosenthal, Joachim, Vettori, Paolo

IEEE

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.

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Hyers-Ulam and Hyers-Ulam-Rassias stability of a class of integral equations on finite intervals

Castro, L. P., Simões, A. M.

CMMSE

The purpose of this work is to study different kinds of stability for a class of integral equations defined on a finite interval. Sufficient conditions are derived in view to obtain Hyers-Ulam stability and Hyers-Ulam-Rassias stability by using fixed point techniques and the Bielecki metric.

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Generalized column distances for convolutional codes

Cardel, Sara D., Firer, Marcelo, Napp, Diego

IEEE

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.

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Sobre vértices do esqueleto do politopo de emparelhamentos de um grafo

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.

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Conditioned invariance and detectability subspaces in the behavioral approach

Pereira, Ricardo, Rocha, Paula

Elsevier

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.

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A State Space Approach to Periodic Convolutional Codes

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.

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Some properties of generalized fractional integral with Lengendre functions kernels

Rodrigues, M. M.

AIP Publishing

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. 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

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Previsão das dormidas mensais na região Norte de Portugal em anos recentes: um estudo preliminar

Silva, Joaquim, Alonso, Hugo, Silva, Isabel

Instituto Nacional de Estatística

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.

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Preface of the "3rd Symposium on Modelling and Simulation in Computer Sciences and Engineering"

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.

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Thermal analysis of lithium-ion batteries with square frame geometries by theoretical simulations

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.

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Learning Trajectories with Bayesian student model for autonomous study in flipped learning

Descalço, L., Canto Filho, A. do, Lima, J. Valdeni de

IATED

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.

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Dissimilar Symmetric Word Pairs in the Human Genome

Tavares, Ana Helena, Raymaekers, Jakob, Rousseeuew, Peter, Silva, Raquel M., Bastos, Carlos A. C., Pinho, Armando, Brito, Paula, Afreixo, Vera

Springer International Publishing

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.

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Contributions to a decision support system based on depth of anesthesia signals

Sebastião, Raquel, Silva, Margarida Martins da, Gama, João, Mendonça, Teresa

IEEE

In the clinical practice the concerns about the administration of hypnotics and analgesics for minimally invasive diagnostics and therapeutic procedures have enormously increased in the past years. The automatic detection of changes in the signals used to evaluate the depth of anesthesia is hence of foremost importance in order to decide how to adapt the doses of hypnotics and analgesics that should be administered to patients. The aim of this work is to online detect drifts in the referred depth of anesthesia signals of patients undergoing general anesthesia. The performance of the proposed method is illustrated using BIS records previously collected from patients subject to abdominal surgery. The results show that the drifts detected by the proposed method are in accordance with the actions of the clinicians in terms of times where a change in the hypnotic or analgesic rates had occurred. This detection was performed under the presence of noise and sensor faults. The presented algorithm was also online validated. The results encourage the inclusion of the proposed algorithm in a decision support system based on depth of anesthesia signals.

ria.ua.pt

Integer-valued APARCH processes in the analysis of time series of counts

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.

ria.ua.pt

An optimization method for the best fractional order to estimate real 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.

ria.ua.pt

Monogenic polynomials of four variables with binomial expansion

Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth Robert

Springer International Publishing

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.

ria.ua.pt | doi

On numerical aspects of pseudo-complex powers in R^3

Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth Robert

Springer International Publishing

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.

ria.ua.pt | doi

Matrix approach to Frobenius-Euler polynomials

Tomaz, Graça, Malonek, Helmuth Robert

Springer International Publishing

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.

ria.ua.pt | doi

A note on totally regular variables and Appell sequences in hypercomplex function theory

Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth Robert

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.

ria.ua.pt | doi

3D mappings by generalized Joukowski transformations

Cruz, Carla, Falcão, Maria Irene, Malonek, Helmuth Robert

Springer Berlin Heidelberg

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.

ria.ua.pt | doi

On generalized hypercomplex Laguerre-type exponentials and applications

Cação, Isabel, Falcão, Maria Irene, Malonek, Helmuth Robert

Springer Berlin Heidelberg

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.

ria.ua.pt | doi

On an hypercomplex generalization of Gould-Hopper and related Chebyshev polynomials

Cação, Isabel, Malonek, Helmuth Robert

Springer Berlin Heidelberg

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.

ria.ua.pt | doi

Laguerre polynomials in several hypercomplex variables and their matrix representation

Malonek, Helmuth Robert, Tomaz, Graça

Springer Berlin Heidelberg

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.

ria.ua.pt | doi

Les règles d’un quart et un vingtième et des comptes de Flandre comme modélisation du réel

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.

ria.ua.pt

Dynamic fator Models for bivariate Count Data: an application to fire activity

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.

ria.ua.pt

An alternative benchmarking approach for electricity utility regulation using maximum entropy

Silva, Elvira, Macedo, Pedro, Soares, Isabel

IEEE

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.

ria.ua.pt | doi

MDP periodically time-varying convolutional codes

Pereira, Ricardo, Malonek, Paula Rocha, Napp, Diego

Springer

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).

ria.ua.pt | doi

Rank metric convolutional codes

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.

ria.ua.pt

Classificação hierárquica com distribuições a posteriori: um estudo de simulação em padrões temporais de VIH

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.

ria.ua.pt

Ambiente digital de aprendizagem promotor do desenvolvimento do raciocínio matemático em alunos com perturbações do espetro do Autismo

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.

ria.ua.pt

Pavimentar a esfera com o GeoGebra

Breda, Ana, Santos, José Manuel Santos dos

ria.ua.pt

Complex functions with Geogebra

Breda, Ana, Santos, José Manuel dos Santos dos

Universidade do Algarve

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.

ria.ua.pt

GeoGebra, Complex Maps and Riemann Sphere

Breda, Ana, Santos, José Manuel Santos dos

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.

ria.ua.pt

Using GeoGebra to study complex functions

Breda, Ana, Santos, José Manuel dos Santos dos

Universidade do Algarve

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.

ria.ua.pt

Some results in fractional Clifford analysis

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.

ria.ua.pt

Discrete hypercomplex function theory and its applications

Kähler, Uwe

AIP Publishing

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.

ria.ua.pt | doi

On numerical testing of the regularity of semidefinite problems

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.

ria.ua.pt

Statistical Methods and Optimization in Data Mining

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.

ria.ua.pt

Interface design for a sensory analysis decision support system

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.

ria.ua.pt

Cell formation problem: a genetic algorithm based on an inter-operation flow matrix

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.

ria.ua.pt

Viral marketing as epidemiological model

Rodrigues, Helena Sofia, Fonseca, Manuel

CMMSE

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.

ria.ua.pt

Parameterized exercises in SMC

Cruz, João Pedro, Oliveira, Paula, Seabra, Dina

IATED

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).

ria.ua.pt

New CQ-free optimality criterion for convex SIP problems with polyhedral index sets

Kostyukova, Olga, Tchemisova, Tatiana

University of Evora; Dorodnicyn Computing Center of Russian Academy of Sciences

No abstract.

ria.ua.pt

Using bayesian networks and parameterized questions in independent study

Descalço, Luís, Carvalho, Paula, Cruz, João Pedro, Oliveira, Paula, Seabra, Dina

IATED

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.

ria.ua.pt

Computer-assisted independent study in multivariate calculus

Descalço, Luís, Carvalho, Maria Paula, Cruz, João Pedro, Oliveira, Maria Paula de Sousa, Seabra, Dina

IATED

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.

ria.ua.pt

Comparative study on efficiency of mirror retroreflectors

Cruz, João Pedro, Plakhov, Alexander

Springer

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.

ria.ua.pt | doi

Modelling and numerical simulation of the recent outbreak of Ebola

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.

ria.ua.pt

Economic and environmental efficiency in Europe: evidence from a new stochastic frontier model

Alves, Margarita, Moutinho, Vítor, Macedo, Pedro

IEEE

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.

ria.ua.pt | doi

Predicting flight departure delay at Porto Airport: a preliminary study

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.

ria.ua.pt

Preface of the "Symposium on modelling and simulation in computer sciences and engineering"

Miranda, Francisco, Abreu, Carlos

AIP - American Institute of Physics

Resumo indisponível.

ria.ua.pt | doi

Estimating the impact of adding sensor nodes to biomedical wireless sensor networks

Abreu, Carlos, Miranda, Francisco, Mendes, Paulo Mateus

AIP - American Institute of Physics

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.

ria.ua.pt | doi

Using parameterized calculus questions for learning and assessment

Descalço, Luís, Carvalho, Paula Reis

IEEE

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.

ria.ua.pt | doi

Multiple choice parameterized exercises in Logic

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.

ria.ua.pt

Quaternionic symmetry of linear dynamical systems

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.

ria.ua.pt | doi

A remark on conditioned invariance in the behavioral approach

Pereira, Ricardo, Rocha, Paula

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.

ria.ua.pt

Free time fractional optimal control problems

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.

ria.ua.pt

A symmetric quantum calculus

Cruz, A. M. C. B. da, Martins, N., Torres, D. F. M.

Springer

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.

ria.ua.pt | doi

A symmetric nörlund sum with application to inequalities

Cruz, A. M. C. Brito da, Martins, N., Torres, D. F. M.

Springer

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.

ria.ua.pt | doi

Kernel behaviors on time scales

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.

ria.ua.pt

Global reachability of 2D structured systems

Pereira, Ricardo, Rocha, Paula, Simões, Rita

IFAC

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.

ria.ua.pt

Linear fractional discrete-time systems

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.

ria.ua.pt

Bibo-stability of quaternionic systems

Pereira, Ricardo, Rocha, Paula, Vettori, Paolo

IFAC

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.

ria.ua.pt

Model reduction of linear dynamical systems with quaternionic symmetry

Pereira, Ricardo, Vettori, Paolo

IFAC

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.

ria.ua.pt

Dynamical properties of quaternionic behavioral systems

Pereira, Ricardo, Vettori, Paolo

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.

ria.ua.pt

Stability of quaternionic systems: a determinantal approach

Pereira, Ricardo, Rocha, Paula

MTNS

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.

ria.ua.pt

On the stability of linear fractional difference systems

Vettori, Paolo, Pereira, Ricardo

IFAC/APCA

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.

ria.ua.pt

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