Books
103.
Programação matemática
Torres, Delfim Fernando Marado
UA Editora
O termo "programação matemática" referese ao estudo de problemas de otimização, em que se procura minimizar ou maximizar uma função através da escolha dos valores de variáveis dentro de um determinado conjunto admissível. Em problemas de engenharia, administração, logística, transporte, economia, biologia, medicina ou outras ciências, quando se consegue construir modelos matemáticos representativos dos respetivos sistemas dinâmicos em estudo, é possível aplicar as técnicas matemáticas de otimização para maximizar ou minimizar uma função previamente definida como índice de desempenho ou performance, visando encontrar uma "solução" do problema, isto é, os valores das variáveis que resultem no melhor desempenho possível do sistema, segundo o tal critério previamente definido. O livro "Programação Matemática" é uma obra introdutória, de natureza pedagógica, e que está escrito de uma forma sucinta, clara e rigorosa. Serve de suporte à unidade curricular com o mesmo nome do Departamento de Matemática da Universidade de Aveiro, que tem sido lecionada a alunos provenientes de várias licenciaturas (de Matemática, Física, Economia e Engenharia), oriundos de diversas universidades portuguesas, dos PALOP, Brasil e TimorLeste, assim como de vários países europeus por intermédio do programa Erasmus. Pretende fornecer uma formação básica, mas sólida, em otimização não linear e, em simultâneo, estimular a utilização de tais modelos e resultados na resolução de problemas práticos. Estão incluídos os conceitos essenciais de programação matemática, que alguém que deseje prosseguir estudos na área de otimização deve conhecer e dominar. Os conteúdos são acompanhados de exemplos e exercícios, com o intuito de se desenvolver a capacidade de aplicação dos conceitos matemáticos envolvidos. As demonstrações dos resultados apresentados são dadas com todo o rigor, procurandose estimular o desenvolvimento do raciocínio, essencial numa qualquer atividade profissional.
ria.ua.pt
102.
Estatística: desafios transversais às ciências com dados: atas do XXIV Congresso da Sociedade Portuguesa de Estatística
Milheiro, Paula and Pacheco, António and Sousa, Bruno de and Alves, Isabel Fraga and Pereira, Isabel and Polidoro, Maria João and Ramos, Sandra
Sociedade Portuguesa de Estatística
Sem resumo disponível.
ria.ua.pt
101.
Analysis of infectious disease problems (Covid19) and their global impact
Agarwal, Praveen and Nieto, Juan J. and Ruzhansky, Michael and Torres, Delfim F. M.
Springer
This book is a collection of selected research articles discussing the analysis of infectious diseases by using mathematical modelling in recent times. Divided into two parts, the book gives a general and countrywise analysis of Covid19. Analytical and numerical techniques for virus models are presented along with the application of mathematical modelling in the analysis of their spreading rates and treatments. The book also includes applications of fractional differential equations as well as ordinary, partial and integrodifferential equations with optimization methods. Probability distribution and their biomathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.
ria.ua.pt

doi
Book Chapters
100.
Statespace estimation using the behavioral approach: a simple particular case
Ntogramatzidis, Lorenzo and Pereira, Ricardo and Rocha, Paula
CONTROLO 2020. Lecture Notes in Electrical Engineering
Springer
In this paper we apply the behavioral estimation theory developed in Ntogramatzidis et al. (2020) to the particular case of statespace systems. We derive new necessary and sufficient conditions for the solvability of the estimation problem in the presence of disturbances, and provide a method to construct an estimator in case the problem is solvable. This is a first step to investigate how our previous results, derived within the more general behavioral context, compare with the results from classical state space theory.
ria.ua.pt

doi

Peer Reviewed
99.
Temperature time series forecasting in The Optimal Challenges in Irrigation (TO
CHAIR)
Gonçalves, A. Manuela and Costa, Cláudia and Costa, Marco and Lopes, Sofia O. and Pereira, Rui
Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences. Computational Methods in Applied Sciences
Springer
Predicting and forecasting weather time series has always been a difficult field of research analysis with a very slow progress rate over the years. The main challenge in this project—The Optimal Challenges in Irrigation (TO CHAIR)—is to study how to manage irrigation problems as an optimal control problem: the daily irrigation problem of minimizing water consumption. For that it is necessary to estimate and forecast weather variables in real time in each monitoring area of irrigation. These time series present strong trends and highfrequency seasonality. How to best model and forecast these patterns has been a longstanding issue in time series analysis. This study presents a comparison of the forecasting performance of TBATS (Trigonometric Seasonal, BoxCox Transformation, ARMA errors, Trend and Seasonal Components) and regression with correlated errors models. These methods are chosen due to their ability to model trend and seasonal fluctuations present in weather data, particularly in dealing with time series with complex seasonal patterns (multiple seasonal patterns). The forecasting performance is demonstrated through a case study of weather time series: minimum air temperature.
ria.ua.pt

doi

Peer Reviewed
98.
Torus and quadrics intersection using GeoGebra
Breda, Ana Maria Reis D'Azevedo and Trocado, Alexandre Emanuel Batista da Silva and Santos, José Manuel dos Santos dos
ICGG 2020: proceedings of the 19th International Conference on Geometry and Graphics
Springer
This paper presents the implementation in GeoGebra of algorithms for computing the intersection curve of a quadric surface with a torus surface. We present three approaches to get and visualise the intersection curve in GeoGebra. One of the approaches makes use of the geometric capabilities of GeoGebra. The second described approach makes use of CAS to obtain a parametrization and the corresponding visualisation of the intersection curve. Finally, the third one is based on computing the projection of the intersection curve, determining its singularities and structure, and its lifting to the 3D embedding space. The research carried out reveals some of the difficulties arising from the implementation in GeoGebra of a geometric algorithm based on the algebraic equations characterising the objects in consideration.
ria.ua.pt

doi

Peer Reviewed
97.
Sustainable development in education: a nonparametric analysis
Murillo, Kelly and Rocha, Eugénio
INTED2021 Proceedings
IATED
The SDGs (Sustainable Development Goals) are a universal call to action to end poverty, protect the planet and improve the lives and prospects of everyone, everywhere. In 2015 all UN Member States, adopted the 2030 Agenda for the SDG, which comprises an action plan for people, the planet and prosperity with 17 objectives covering the economic, social and environmental dimensions, [1]. SDG 4 is the goal of quality education with made up of 10 targets to ensure an inclusive and equitable quality education and to promote lifelong learning opportunities for all. In this sense, it is expected that all countries increasing the number of young people and adults with relevant professional skills, decent jobs, entrepreneurship, eliminating gender and income disparities in access to education.
This article examines the quality of education in 17 European countries using a model nonparametric deterministic for measuring efficiency based on MEA (Multidirectional Efficiency Analysis) [2], in combination with other mathematical techniques (such as accumulated effort and group indicator), during seven years (every three years from 20002018). To this end, we analyze the countries evolution at three distinct efficiency stages: levels, patterns and determinants. The study is based on the EU's set of indicators to monitor progress towards the UN SDGs: basic education (early leavers from education and training, participation in early childhood education and achievement in reading, mathematic or science), tertiary education (tertiary education attainment and employment rates of recent graduates) and adult learning (adult participation in learning).
This study allows us to address questions such as: To what extent are European countries improving education quality? Which European countries have significant advances / setbacks over time? What factors are intervening in the process of the countries that are most efficient and least efficient? In other words, our results clarify which are the profiles of the countries that are most efficient, giving some insight about the improvements which could be applied in the less efficient to raise their efficiency, in view of reaching the proposed objectives for the year 2030.
References:
[1] Report of the InterAgency and Expert Group on Sustainable Development Goal Indicators (E/CN.3/2016/2/Rev.1), Economic and Social Council, United Nations, 139, 2016.
[2] P. Bogetoft and J. L. Hougaard, Efficiency evaluations based on potential
(Nonproportional) improvements, J. Productivity Analysis, 12(3), 233247, 1999.
ria.ua.pt

doi

Peer Reviewed
96.
Análise de regressão linear com autocorrelação nos erros para dados censurados
Sousa, Rodney and Pereira, Isabel and Silva, Maria Eduarda
Estatística: desafios transversais às ciências com dados: atas do XXIV Congresso da Sociedade Portuguesa de Estatística
Sociedade Portuguesa de Estatística
Este trabalho aborda, numa perspetiva bayesiana, a análise
de modelos de regressão linear com erros autocorrelacionados
para dados censurados, recorrendo a métodos Computacionais Bayesianos
Aproximados (ABC) e ao amostrador de Gibbs com a Ampliação
de Dados (GDA). Considerase que o termo dos erros segue
um processo autorregressivo, AR, e investigase o desempenho dos
métodos através de dois estudos de simulação com diferentes cenários
de censura (5%, 20% e 40%) e dimensão de amostras (50, 100 e
500). Os resultados indicam que o método GDA é consistente Bayesiano,
mesmo em cenários em que a proporção de valores censurados
é elevada, enquanto que no método ABC, as estimativas dependem
fortemente das distribuições a priori.
ria.ua.pt

Peer Reviewed
95.
Graphic and multimedia design of a narrativebased math game
Afonso, R. and Breda, A. and Rocha, E.
EDULEARN21 Proceedings
IATED
In this paper, we will describe the process of creating the graphic and multimedia design of the math serious game CNME. This game designed to facilitate and “gamify” mathematical learning processes is based on the narrative of MagellanElcano’s epic circumnavigation journey around the world. CNME game was developed by an interdisciplinary team of the research and development thematic line GEOMETRIX.
In graphic and multimedia terms the main function is to illustrate and retell events around this trip in an interactive and dynamic way, captivating and maintaining the user's interest and attention, making mathematical challenges emerge as natural / plausible events within the narrative context that unfolds.
The stimuli, used to anchor the narrative, differ according to the situation/episode that is unfolding. They are employed either to capture the player's attention or to make the experience more engaging and enjoyable.
The game is simple and logical presenting the events methodically. It follows, chronologically, the historical and remarkable events of this famous odyssey, presenting each scene as a different chapter. The exploration of these "chapters" position the user in front of different mathematical, historical, playful or general knowledge challenges and problems, which he / she must solve in order to progress to more advanced levels. These problems / challenges, of such a diverse nature, aim at learning and assessing mathematical, historical and everyday knowledge.
This game can be seen as an interactive learning environment with challenges inserted and contextualized in the game's narrative, involving several game mechanics, among which: collecting items / objects / species and building and dismantling objects.
The design phase is crucial for the development of the game as it encompasses essential factors for the success of the proposed objectives, namely, capturing attention, maintaining motivation, giving reasons for wanting to learn mathematics.
The design process includes: interaction design, graphic design and sound design.
During the interaction with the game the player is visual and aurally stimulated with vibrant landscapes and surrounding sounds, while being, psychologically, challenged to solve problems contextualized in a historical, interesting and real story line, triggering the desire to learn more and more.
ria.ua.pt

doi

Peer Reviewed
94.
CNME a math narrativebased serious game
Martins, Micaela and Breda, Ana and Rocha, Eugénio and Domingues, Ricardo
EDULEARN21 Proceedings
IATED
The teaching method has varied and evolved over the years. The year 2020 is a milestone in this variability. The COVID19 pandemic unleashed the strict need for a radical adaptation of teaching processes that, worldwide, become exclusively or almost exclusively at a distance. The impact of the digital world on our lives has been and is being felt like never before. Nonformal teaching processes gain crucial importance in this scenario.
Serious games are engaging and provide a stimulating environment in which students can explore and discover in a fun and interactive way, improving student’s motivation and performance in mathematics and making them active learners. The adoption in the educational process of serious games, promoting the development of critical thinking, and its interest, as a research topic, by scientists from various areas, namely, mathematics, have gained increasing prominence.
With regard to mathematics, despite its recognized importance in the intellectual human development, children and adolescents usually believe that it is a difficult subject, both at a conceptual and procedural level, leading to a lack of motivation and high failure rates.
In this paper, based on a solid and recent literature review, we look at the role that serious games play in the learning and motivation of children and adolescents, especially the narrative educational games focused on mathematics.
A narrative interactive serious game is defined as a serious game, in which the story exists to improve the gameplay. Within this context, the Thematic Line Geometrix of the Center for Research and Development of Mathematics and Applications (CIDMA) of the University of Aveiro developed the narrative serious game CNME based on the historical event “The Magellan  Elcano circumnavigation around the world”. This game runs on every platform that has a recent browser and it also has an application for Android and iOS. In the CNME digital and interactive game there are two game modes, the generic and the academic mode, depending on the player's profile. The generic modality was designed to promote mathematical literacy and is aimed at any citizen. The academic modality was designed to promote critical and creative thinking and is aimed at young people with mathematical knowledge at the level of the 3rd Cycle of the Portuguese Basic Education. In short, CNME is an interactive mathematical narrative game, aiming at mathematical learning in an interactive, playful and motivating way, anchored in a notable and true historical event conceived under a set of scrutinized scientific evidence.
ria.ua.pt

doi

Peer Reviewed
93.
O jogo educacional Multipli enquanto atividade lúdica e de aprendizagem matemática
Sebastião, Fernando and Tavares, Dina and Menino, Hugo and Oliveira, Eunice and la Féria, Ana and Teixeira, Rita
Livro de atas: 8.ª Conferência de Mediação Intercultural e Intervenção Social – Ócio, Jogo e Brincadeira: aprendizagens e mediação intercultural
CICS.NOVA.IPLeiria; ESECS.Politécnico de Leiria
Jogar é uma atividade lúdica que proporciona situações de prazer e de descontração, motivando o envolvimento e a atenção das crianças, o que pode ser um fator decisivo para aprender matemática, de forma significativa (Grando, 2000). Para Ponte (2005), o jogo é um tipo de tarefa que deve integrar a experiência matemática das crianças, cabendo ao professor selecionar os jogos a explorar, de acordo com objetivos curriculares a atingir. Do ponto de vista da investigação afigurase importante proceder à avaliação de jogos educacionais, contribuindo para a melhoria da qualidade desses recursos (Savi et al., 2010). Em relação à dinamização dos jogos, diversos estudos evidenciam que a participação dos alunos em competições matemáticas, de natureza inclusiva, promove a autoconfiança, o autoconceito e a motivação do aluno para aprender matemática (Amado, Carreira & Ferreira, 2016; Tavares & Pinto, 2019). Este estudo pretende avaliar o jogo educacional Multipli, enquanto recurso educativo, e descrever a perceção de crianças relativamente à sua experiência de jogo, no contexto de um campeonato nacional online. Adotase o modelo ARCS (Dempsey & Johnson, 1998) para analisar a motivação dos alunos na aprendizagem, com base em quatro categorias: atenção, relevância, confiança e satisfação. Consideramse também categorias relacionadas com a experiência do utilizador, amplamente utilizadas noutros modelos de avaliação de jogos: imersão, habilidade, divertimento, desafio, interação social e aprendizagem (Savi et al. 2010). O estudo desenvolvido é observacional, de natureza descritiva (Bogdan & Biklen, 1994; McMillan & Schumacher, 2005). O instrumento de recolha de dados é o inquérito por questionário, aplicado a crianças do 3.º, 4.º, 5.º e 6.º anos de escolaridade, que permite recolher a informação avaliada sob a forma de afirmações, segundo uma escala de concordância. É espectável que este estudo contribua para a compreensão e utilização dos jogos ao nível pedagógico enquanto tarefa para a aprendizagem da matemática.
ria.ua.pt

Peer Reviewed
92.
Improving Shortterm Forecasts of Daily Maximum Temperature with the Kalman Filter with GMM Estimation
Costa, Marco and Pereira, Fernanda Catarina and Gonçalves, A. Manuela
The 21st International Conference on Computational Science and Applications (ICCSA 2021)
Springer, Cham
Within the scope of the TO CHAIR project, a state space modeling approach is proposed in order to improve accuracy obtained from the weatherstack.com website with a dataset of real observations. The proposed model establishes a stochastic linear relationship between the maximum temperature observed and the hstepahead forecast pro duced from the website. This relation is modeled in a state space frame work associated to the Kalman filter predictors. Since normality of dis turbances was not a good assumption for this dataset, alternative Gen eralized Method of Moments (GMM) estimators were considered in the models parameters estimation. The results show that this approach al lows reducing the RMSE of the uncorrected forecasts in 16.90% consider ing the 6stepahead forecasts and in 60.45% considering the 1stepahead forecasts, compared with the initial RMSE. Additionally, empirical con fidence intervals at the 95% level have a coverage rate similar to this confidence level. So, this approach has proven suitable for this type of forecasts correction since it considers a stochastic calibration factor in order to model time correlation of this type of variable.
ria.ua.pt

doi

Peer Reviewed
91.
Change point detection in a state space framework applied to climate change in Europe
Monteiro, Magda and Costa, Marco
Computational Science and Its Applications: ICCSA 2021
Springer
This work presents the statistical analysis of time series of monthly average temperatures in several European locations using a state space approach, where it is considered a model with a deterministic seasonal component and a stochastic trend. Temperature rise rates in Europe seem to have increased in the last decades when compared with longer periods, hence change point detection methods were applied to residuals state space models in order to identify these possible changes in the monthly temperature rise rates. In Northern Europe the change points were, almost all, identified in the late 1980s while in Central and Southeastern Europe was, for the majority of cities, in the 1990s and later.
ria.ua.pt

doi

Peer Reviewed
90.
Optimal control of vaccination and plasma transfusion with potential usefulness for Covid19
Couras, Juliana and Area, Iván and Nieto, Juan J. and Silva, Cristiana J. and Torres, Delfim F. M.
Analysis of infectious disease problems (Covid19) and their global impact
Springer
The SEIR model is a compartmental model used to simulate the dynamics of an epidemic. In this chapter, we introduce two control functions in the compartmental SEIR model representing vaccination and plasma transfusion. Optimal control problems are proposed to study the effects of these two control measures, on the reduction of infected individuals and increase of recovered ones, with minimal costs. Up to our knowledge, the plasma transfusion treatment has never been considered as a control strategy for epidemics mitigation. The proposed vaccination and treatment strategies may have a real application in the challenging and hard problem of controlling the Covid19 pandemic.
ria.ua.pt

doi

Peer Reviewed
89.
Modeling the spread of Covid19 pandemic in Morocco
Zine, Houssine and Lotfi, El Mehdi and Mahrouf, Marouane and Boukhouima, Adnane and Aqachmar, Yassine and Hattaf, Khalid and Torres, Delfim F. M. and Yousfi, Noura
Analysis of infectious disease problems (Covid19) and their global impact
Springer
Nowadays, coronavirus disease 2019 (Covid19) poses a great threat to public health and economy worldwide. Unfortunately, there is yet no effective drug for this disease. For this, several countries have adopted multiple preventive interventions to avoid the spread of Covid19. Here, we propose a delayed mathematical model to predict the epidemiological trend of Covid19 in Morocco. Parameter estimation and sensitivity analysis of the proposed model are rigorously studied. Moreover, numerical simulations are presented in order to test the effectiveness of the preventive measures and strategies that were imposed by the Moroccan authorities and also help policy makers and public health administration to develop such strategies.
ria.ua.pt

doi

Peer Reviewed
88.
Towards a specification theory for fuzzy modal logic
Jain, Manisha and Gomes, Leandro and Madeira, Alexandre and Barbosa, Luis S.
2021 International Symposium on Theoretical Aspects of Software Engineering (TASE)
IEEE
Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often noncoincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems.
ria.ua.pt

doi

Peer Reviewed
87.
CDPCA: 10 years after
Freitas, Adelaide
Estatística: desafios transversais às ciências com dados: atas do XXIV Congresso da Sociedade Portuguesa de Estatística
Sociedade Portuguesa de Estatística
Clustering and Disjoint Principal Component Analysis (CDPCA) is a constrained principal component analysis for multivariate
numerical data. The main goal is to detect clusters of objects and, simultaneously, to fi nd a partitioning of variables such that the
between cluster deviance in the reduced space of such partition is maximized. The partition formed by a disjoint set of the original
variables identifi es the groups of variables belonging to the CDPCA components. Recently, this methodology has been implemented in
a Rfunction called CDpca. In this work, we review some theoretical issues of the CDPCA model and present two applications on real
data sets using the Rfunction CDpca.
ria.ua.pt

Peer Reviewed
86.
Multivariate sustainability profile of Global Fortune 500 companies using GRIG4 database
JiménezHernández, Mónica and VicenteGalindo, Purificación and TejedorFlores, Nathalia and Freitas, Adelaide and Galindo, Purificación
Handbook of Research on Applied Data Science and Artificial Intelligence in Business and Industry
IGI Global
The main objective of this research is to find the sustainability gradients of Global Fortune 500 companies and sort them as a function of economic, environmental, and social components using multivariate statistical methods to establish the foundations for better knowledge of the trends and sustainability reporting habits. A combined approach, comprising principal coordinates analysis (PCoA) and logistic regression model (LRM), is proposed to build an external logistics biplot (ELB). Moreover, HJBiplot and parallel coordinates are applied. This chapter helps to understand why many companies view their corporate social responsibility (CSR) reports as a way to guarantee the credibility of the published
information. In particular, based on the Global Reporting Initiative, the sustainability gradients of the Global Fortune 500 companies are obtained and statistically exploited to analyze how the companies can make improvements in terms of sustainability.
ria.ua.pt

doi

Peer Reviewed
Articles
85.
Decompositions with atoms and molecules for variable exponent TriebelLizorkinMorrey spaces
Caetano, António and Kempka, Henning
Constructive Approximation
Springer Verlag
We continue the study of the variable exponent Morreyﬁed TriebelLizorkin spaces introduced in a previous paper. Here we give characterizations by means of atoms and molecules. We also show that in some cases the number of zero moments needed for molecules, in order that an inﬁnite linear combination of them (with coeﬃcients in a natural sequence space) converges in the space of tempered distributions, is much smaller than what is usually required.
We also establish a Sobolev type theorem for related sequence spaces, which might have independent interest.
ria.ua.pt

doi

Peer Reviewed
84.
Matrix biorthogonal polynomials: eigenvalue problems and nonAbelian discrete Painlevé equations: a Riemann–Hilbert problem perspective
Branquinho, Amílcar and Moreno, Ana Foulquié and Mañas, Manuel
Journal of Mathematical Analysis and Applications
Elsevier
In this paper we use the Riemann–Hilbert problem, with jumps supported on appropriate curves in the complex plane, for matrix biorthogonal polynomials and apply it to find Sylvester systems of differential equations for the orthogonal polynomials and its second kind functions as well. For this aim, Sylvester type differential Pearson equations for the matrix of weights are shown to be instrumental. Several applications are given, in order of increasing complexity. First, a general discussion of nonAbelian Hermite biorthogonal polynomials on the real line, understood as those whose matrix of weights is a solution of a Sylvester type Pearson equation with coefficients first degree matrix polynomials, is given. All of these are applied to the discussion of possible scenarios leading to eigenvalue problems for second order linear differential operators with matrix eigenvalues. Nonlinear matrix difference equations are discussed next. Firstly, for the general Hermite situation a general non linear relation (non trivial because of the non commutativity features of the setting) for the recursion coefficients is gotten. In the next case of higher difficulty, degree two polynomials are allowed in the Pearson equation, but the discussion is simplified by considering only a left Pearson equation. In the case, the support of the measure is on an appropriate branch of a hyperbola. The recursion coefficients are shown to fulfill a nonAbelian extension of the alternate discrete Painlevé I equation. Finally, a discussion is given for the case of degree three polynomials as coefficients in the left Pearson equation characterizing the matrix of weights. However, for simplicity only odd polynomials are allowed. In this case, a new and more general matrix extension of the discrete Painlevé I equation is found.
ria.ua.pt

doi

Peer Reviewed
83.
A matrix based list decoding algorithm for linear codes over integer residue rings
Napp, Diego and Pinto, Raquel and Saçıkara, Elif and Toste, Marisa
Linear Algebra and its Applications
Elsevier
In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the padic expansion of the tobedecoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the paritycheck matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr .
This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal.
ria.ua.pt

doi

Peer Reviewed
82.
Robust formulations for economic lotsizing problem with remanufacturing
Attila, Öykü Naz and Agra, Agostinho and Akartunalı, Kerem and Arulselvan, Ashwin
European Journal of Operational Research
Elsevier
In this paper, we consider a lotsizing problem with the remanufacturing option under parameter uncertainties imposed on demands and returns. Remanufacturing has recently been a fast growing area of interest for many researchers due to increasing awareness on reducing waste in production environments, and in particular studies involving remanufacturing and parameter uncertainties simultaneously are very scarce in the literature. We first present a minmax decomposition approach for this problem, where decision maker’s problem and adversarial problem are treated iteratively. Then, we propose two novel extended reformulations for the decision maker’s problem, addressing some of the computational challenges. An original aspect of the reformulations is that they are applied only to the latest scenario added to the decision maker’s problem. Then, we present an extensive computational analysis, which provides a detailed comparison of the three formulations and evaluates the impact of key problem parameters. We conclude that the proposed extended reformulations outperform the standard formulation for a majority of the instances. We also provide insights on the impact of the problem parameters on the computational performance.
ria.ua.pt

doi

Peer Reviewed
81.
Discrete Hardy spaces for bounded domains in Rn
Cerejeiras, Paula and Kähler, Uwe and Legatiuk, Anastasiia and Legatiuk, Dmitrii
Complex Analysis and Operator Theory
Springer; Birkhäuser
Discrete function theory in higherdimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as halfspace, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higherdimensional function theory to the case of arbitrary bounded domains in R^n. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.
ria.ua.pt

doi

Peer Reviewed
80.
Eigenfunctions of the time‐fractional diffusion‐wave operator
Ferreira, Milton and Luchko, Yury and Rodrigues, M. Manuela and Vieira, Nelson
Mathematical Methods in the Applied Sciences
Wiley
In this paper, we present some new integral and series representations for the eigenfunctions of the multidimensional time‐fractional diffusion‐wave operator with the time‐fractional derivative of order β ∈]1, 2[ defined in the Caputo sense. The integral representations are obtained in form of the inverse Fourier–Bessel transform and as a double contour integrals of the Mellin–Barnes type. Concerning series expansions, the eigenfunctions are expressed as the double generalized hypergeometric series for any β ∈]1, 2[ and as Kampé de Fériet and Lauricella series in two variables for the rational values of β. The limit cases β=1 (diffusion operator) and β=2 (wave operator) as well as an intermediate case β=32 are studied in detail. Finally, we provide several plots of the eigenfunctions to some selected eigenvalues for different particular values of the fractional derivative order β and the spatial dimension n.
ria.ua.pt

doi

Peer Reviewed
79.
Bivariate models for time series of counts: a comparison study between PBINAR models and dynamic factor models
Monteiro, Magda and Pereira, Isabel and Scotto, Manuel G.
Communications in Statistics  Simulation and Computation
Taylor and Francis
The aim of this work is to assess the modeling performance of two bivariate models for time series of counts, within the context of a forest fires analysis in two counties of Portugal. The first model is a periodic bivariate integervalued autoregressive (PBINAR), easily interpreted due to the PINAR description of each component. The alternative model is a bivariate dynamic factor (BDF) that has a flexible structure, with the dynamics described through the mean value of each component that is a function of latent factors. The results reveal that BDF model exhibits a better ability to capture the dependence structure.
ria.ua.pt

doi

Peer Reviewed
78.
Fractional model of COVID19 applied to Galicia, Spain and Portugal
Ndaïrou, Faïçal and Area, Iván and Nieto, Juan J. and Silva, Cristiana J. and Torres, Delfim F. M.
Chaos, Solitons & Fractals
Elsevier
A fractional compartmental mathematical model for the spread of the COVID19
disease is proposed. Special focus has been done on the transmissibility of
superspreaders individuals. Numerical simulations are shown for data of
Galicia, Spain, and Portugal. For each region, the order of the Caputo
derivative takes a different value, that is not close to one, showing the
relevance of considering fractional models.
ria.ua.pt

doi

Peer Reviewed
77.
Spininduced scalarized black holes
Herdeiro, Carlos A. R. and Radu, Eugen and Silva, Hector O. and Sotiriou, Thomas P. and Yunes, Nicolás
Physical Review Letters
American Physical Society
It was recently shown that a scalar field suitably coupled to the
GaussBonnet invariant $mathcal{G}$ can undergo a spininduced linear
tachyonic instability near a Kerr black hole. This instability appears only
once the dimensionless spin $j$ is sufficiently large, that is, $j gtrsim
0.5$. A tachyonic instability is the hallmark of spontaneous scalarization.
Focusing, for illustrative purposes, on a class of theories that do exhibit
this instability, we show that stationary, rotating black hole solutions do
indeed have scalar hair once the spininduced instability threshold is
exceeded, while black holes that lie below the threshold are described by the
Kerr solution. Our results provide strong support for spininduced black hole
scalarization.
ria.ua.pt

doi

Peer Reviewed
76.
Multipolar boson stars: macroscopic BoseEinstein condensates akin to hydrogen orbitals
Herdeiro, C. A. R. and Kunz, J. and Perapechka, I. and Radu, E. and Shnir, Ya.
Physics Letters B
Elsevier
Boson stars are often described as macroscopic BoseEinstein condensates. By
accommodating large numbers of bosons in the same quantum state, they
materialize macroscopically the intangible probability density cloud of a
single particle in the quantum world. We take this interpretation of boson
stars one step further. We show, by explicitly constructing the fully
nonlinear solutions, that static (in terms of their spacetime metric,
$g_{munu}$) boson stars, composed of a single complex scalar field, $Phi$,
can have a nontrivial multipolar structure, yielding the same morphologies for
their energy density as those that elementary hydrogen atomic orbitals have for
their probability density. This provides a close analogy between the elementary
solutions of the nonlinear EinsteinKleinGordon theory, denoted
$Phi_{(N,ell,m)}$, which could be realized in the macrocosmos, and those of
the linear Schr"odinger equation in a Coulomb potential, denoted
$Psi_{(N,ell,m)}$, that describe the microcosmos. In both cases, the
solutions are classified by a triplet of quantum numbers $(N,ell,m)$. In the
gravitational theory, multipolar boson stars can be interpreted as individual
bosonic lumps in equilibrium; remarkably, the (generic) solutions with $mneq
0$ describe gravitating solitons $[g_{munu},Phi_{(N,ell,m)}]$ without any
continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are
also constructed.
ria.ua.pt

doi

Peer Reviewed
75.
Stability analysis and optimal control of a fractional HIVAIDS epidemic model with memory and general incidence rate
Boukhouima, Adnane and Lotfi, El Mehdi and Mahrouf, Marouane and Rosa, Silvério and Torres, Delfim F. M. and Yousfi, Noura
The European Physical Journal Plus
Springer Verlag; EDP Sciences; Società Italiana di Fisica
We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIVAIDS infection. The infection process is modelled by a general functional response, and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.
ria.ua.pt

doi

Peer Reviewed
74.
Phenomenology of vectorlike leptons with Deep Learning at the Large Hadron Collider
Freitas, Felipe F. and Gonçalves, João and Morais, António P. and Pasechnik, Roman
Journal of High Energy Physics
Springer Verlag
In this paper, a model inspired by Grand Unification principles featuring three generations of vectorlike fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the stateoftheart Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vectorlike leptons (VLLs) and their possible signatures at CERN’s Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vectorboson fusion and VLL pair production topologies, both involving a final state containing a pair of charged leptons of different flavor and two sterile neutrinos that provide a missing energy. We also consider the case of VLL single production where, in addition to a pair of sterile neutrinos, the final state contains only one charged lepton. We propose a novel method to identify missing transverse energy vectors by comparing the detector response with MonteCarlo simulated data. All calculated observables are provided as data sets for Deep Learning analysis, where a neural network is constructed, based on results obtained via an evolutive algorithm, whose objective is to maximise either the accuracy metric or the Asimov significance for different masses of the VLL. Taking into account the effect of the three analysed topologies, we have found that the combined significance for the observation of new VLLs at the highluminosity LHC can range from 5.7σ, for a mass of 1.25 TeV, all the way up to 28σ if the VLL mass is 200 GeV. We have also shown that by the end of the LHC RunIII a 200 GeV VLL can be excluded with a confidence of 8.8 standard deviations. The results obtained show that our model can be probed well before the end of the LHC operations and, in particular, providing important phenomenological information to constrain the energy scale at which new gauge symmetries emergent from the considered Grand Unification picture can be manifest.
ria.ua.pt

doi

Peer Reviewed
73.
Numerical solution of a class of thirdkind Volterra integral equations using Jacobi wavelets
Nemati, S. and Lima, Pedro M. and Torres, Delfim F. M.
Numerical Algorithms
Springer
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss–Jacobi quadrature formula, for solving a class of thirdkind Volterra integral equations. To do this, the interval of integration is first transformed into the interval [− 1, 1], by considering a suitable change of variable. Then, by introducing special Jacobi parameters, the integral part is approximated using the Gauss–Jacobi quadrature rule. An approximation of the unknown function is considered in terms of Jacobi wavelets functions with unknown coefficients, which must be determined. By substituting this approximation into the equation, and collocating the resulting equation at a set of collocation points, a system of linear algebraic equations is obtained. Then, we suggest a method to determine the number of basis functions necessary to attain a certain precision. Finally, some examples are included to illustrate the applicability, efficiency, and accuracy of the new scheme.
ria.ua.pt

doi

Peer Reviewed
72.
A new rank metric for convolutional codes
Almeida, P. and Napp, D.
Designs, Codes and Cryptography
Springer
Let F[D] be the polynomial ring with entries in a finite field F. Convolutional codes are submodules of F[D]n that can be described by left prime polynomial matrices. In the last decade there has been a great interest in convolutional codes equipped with a rank metric, called sum rank metric, due to their wide range of applications in reliable linear network coding. However, this metric suits only for delay free networks. In this work we continue this thread of research and introduce a new metric that overcomes this restriction and therefore is suitable to handle more general networks. We study this metric and provide characterizations of the distance properties in terms of the polynomial matrix representations of the convolutional code. Convolutional codes that are optimal with respect to this new metric are investigated and concrete constructions are presented. These codes are the analogs of Maximum Distance Profile convolutional codes in the context of network coding. Moreover, we show that they can be built upon a class of superregular matrices, with entries in an extension field, that preserve their superregularity properties even after multiplication with some matrices with entries in the ground field.
ria.ua.pt

doi

Peer Reviewed
71.
The degrees of toroidal regular proper hypermaps
Fernandes, Maria Elisa and Piedade, Claudio Alexandre
The Art of Discrete and Applied Mathematics
Slovenian Discrete and Applied Mathematics Society; University of Primorska, FAMNI
Recently the classification of all possible faithful transitive permutation representations of the group of symmetries of a regular toroidal map was accomplished.
In this paper we complete this investigation on a surface of genus 1 considering the group of a regular toroidal hypermap of type (3,3,3).
ria.ua.pt

doi

Peer Reviewed
70.
The Hjoin of arbitrary families of graphs
Cardoso, Domingos M. and Gomes, Helena and Pinheiro, Sofia J
arXiv
The Hjoin of a family of graphs G = {G1, . . . , Gp}, also called the generalized
composition, H[G1, . . . , Gp], where all graphs are undirected, simple and finite, is
the graph obtained from the graph H replacing each vertex i of H by Gi and adding
to the edges of all graphs in G the edges of the join Gi ∨ Gj , for every edge ij of H.
Some well known graph operations are particular cases of the Hjoin of a family of
graphs G as it is the case of the lexicographic product (also called composition) of
two graphs H and G, H[G], which coincides with the Hjoin of family of graphs G
where all the graphs in G are isomorphic to a fixed graph G.
So far, the known expressions for the determination of the entire spectrum of the
Hjoin in terms of the spectra of its components and an associated matrix are
limited to families of regular graphs. In this paper, we extend such a determination
to families of arbitrary graphs.
ria.ua.pt
69.
Spontaneous vectorization of electrically charged black holes
Oliveira, João M. S. and Pombo, Alexandre M.
Physical Review D
In this work, we generalise the spontaneous scalarization phenomena in EinsteinMaxwellScalar
models to a higher spin field. The result is an EinsteinMaxwellVector model wherein a vector field
is nonminimally coupled to the Maxwell invariant by an exponential coupling function. We show that
the latter guarantees the circumvention of an associated nohair theorem when the vector field has the
form of an electric field. Different than its scalar counterpart, the new spontaneously vectorized ReissnerNordstr¨om (RN) black holes are, always, undercharged while being entropically preferable. The solution
profile and domain of existence are presented and analysed.
ria.ua.pt

doi

Peer Reviewed
68.
Focus point: cancer and HIV/AIDS dynamics: from optimality to modelling
Debbouche, Amar and Nieto, Juan J. and Torres, Delfim F. M.
The European Physical Journal Plus
Springer
Human cancer is a multistep process involving acquired genetic mutations, each of which imparts a particular type of growth advantage to the cell and ultimately leads to the development of a malignant phenotype. It is also a generic term for a group of diseases and figures as a leading cause of death globally; it lays a significant burden on healthcare systems and continues to be among the major health problems worldwide. The consequences of mutations in tumor cells include alterations in cell signaling pathways that result in uncontrolled cellular proliferation, insensitivity to growth inhibitory signals, resistance to apoptosis, development of cellular immortality, angiogenesis, tissue invasion and metastasis.
ria.ua.pt

doi

Peer Reviewed
67.
Modeling and forecasting of COVID19 spreading by delayed stochastic differential equations
Mahrouf, Marouane and Boukhouima, Adnane and Zine, Houssine and Lotfi, El Mehdi and Torres, Delfim F. M. and Yousfi, Noura
Axioms
MDPI
The novel coronavirus disease (COVID19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the wellknown SIR compartmental model to deterministic and stochastic timedelayed models in order to predict the epidemiological trend of COVID19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the wellposedness of the models and conditions under which the COVID19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID19 spreading as well as verification of theoretical results.
ria.ua.pt

doi

Peer Reviewed
66.
Optimal control of the COVID19 pandemic: controlled sanitary deconfinement in Portugal
Silva, Cristiana J. and Cruz, Carla and Torres, Delfim F. M. and Muñuzuri, Alberto P. and Carballosa, Alejandro and Area, Iván and Nieto, Juan J. and FonsecaPinto, Rui and Passadouro, Rui and Santos, Estevão Soares dos and Abreu, Wilson and Mira, Jorge
Scientific Reports
Nature Research
The COVID19 pandemic has forced policy makers to decree urgent confinements
to stop a rapid and massive contagion. However, after that stage, societies are
being forced to find an equilibrium between the need to reduce contagion rates
and the need to reopen their economies. The experience hitherto lived has
provided data on the evolution of the pandemic, in particular the population
dynamics as a result of the public health measures enacted. This allows the
formulation of forecasting mathematical models to anticipate the consequences
of political decisions. Here we propose a model to do so and apply it to the
case of Portugal. With a mathematical deterministic model, described by a
system of ordinary differential equations, we fit the real evolution of
COVID19 in this country. After identification of the population readiness to
follow social restrictions, by analyzing the social media, we incorporate this
effect in a version of the model that allow us to check different scenarios.
This is realized by considering a Monte Carlo discrete version of the previous
model coupled via a complex network. Then, we apply optimal control theory to
maximize the number of people returning to "normal life" and minimizing the
number of active infected individuals with minimal economical costs while
warranting a low level of hospitalizations. This work allows testing various
scenarios of pandemic management (closure of sectors of the economy,
partial/total compliance with protection measures by citizens, number of beds
in intensive care units, etc.), ensuring the responsiveness of the health
system, thus being a public health decision support tool.
ria.ua.pt

doi

Peer Reviewed
65.
Spontaneous scalarization of a conducting sphere in Maxwellscalar models
Herdeiro, Carlos A. R. and Ikeda, Taishi and Minamitsuji, Masato and Nakamura, Tomohiro and Radu, Eugen
Physical Review D
American Physical Society
We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwellscalar models in flat spacetime, wherein the scalar field
ϕ
is nonminimally coupled to the Maxwell electrodynamics. This setup serves as a toy model for the spontaneous scalarization of charged (vacuum) black holes in EinsteinMaxwellscalar (generalized scalartensor) models. In the Maxwellscalar case, unlike the black hole cases, closedform solutions exist for the scalarized configurations. We compute these configurations for three illustrations of nonminimal couplings: one that exactly linearizes the scalar field equation, and the remaining two that produce nonlinear continuations of the first one. We show that the former model leads to a runaway behavior in regions of the parameter space and neither the Coulomb nor the scalarized solutions are stable in the model; but the latter models can heal this behavior producing stable scalarized solutions that are dynamically preferred over the Coulomb one. This parallels reports on black hole scalarization in the extendedscalarGaussBonnet models. Moreover, we analyze the impact of the choice of the boundary conditions on the scalarization phenomenon. Dirichlet and Neumann boundary conditions accommodate both (linearly) stable and unstable parameter space regions, for the scalarfree conducting sphere; but radiative boundary conditions always yield an unstable scalarfree solution and preference for scalarization. Finally, we perform numerical evolution of the full Maxwellscalar system, following dynamically the scalarization process. They confirm the linear stability analysis and reveal that the scalarization phenomenon can occur in qualitatively distinct ways.
ria.ua.pt

doi

Peer Reviewed
64.
A new convolution operator for the linear canonical transform with applications
Castro, Luís P. and Goel, Navdeep and Silva, Anabela S.
Computational and Applied Mathematics
Springer
The linear canonical transform plays an important role in engineering and many
applied fields, as it is the case of optics and signal processing. In this paper, a new
convolution for the linear canonical transform is proposed and a corresponding product
theorem is deduced. It is also proved a generalized Young's inequality for the introduced
convolution operator. Moreover, necessary and sufficient conditions are obtained for the
solvability of a class of convolution type integral equations associated with the linear
canonical transform. Finally, the obtained results are implemented in multiplicative
filters design, through the product in both the linear canonical transform domain and
the time domain, where specific computations and comparisons are exposed.
ria.ua.pt

doi

Peer Reviewed
63.
New convolutions with Hermite weight functions
Castro, Luís Pinheiro and Silva, Anabela Sousa and Tuan, Nguyen Minh
Bulletin of the Iranian Mathematical Society
Springer
In this paper, we are working with convolutions on the positive halfline, for Lebesgue
integrable functions. Six new convolutions are introduced. Factorization identities for
these convolutions are derived, upon the use of Fourier sine and cosine transforms and
Hermite functions. Such convolutions allowus to consider systems of convolution type
equations on the halfline. Using two different methods, such systems of convolution
integral equations will be analyzed. Conditions for their solvability will be considered
and, under such conditions, their solutions are obtained.
ria.ua.pt

doi

Peer Reviewed
62.
Black holes, stationary clouds and magnetic fields
Santos, Nuno M. and Herdeiro, Carlos A. R.
Physics Letters B
Elsevier
As the electron in the hydrogen atom, a bosonic field can bind itself to a
black hole occupying a discrete infinite set of states. When (i) the spacetime
is prone to superradiance and (ii) a confinement mechanism is present, some of
such states are infinitely longlived. These equilibrium configurations, known
as stationary clouds, are states "synchronized" with a rotating black hole's
event horizon. For most, if not all, stationary clouds studied in the
literature so far, the requirements (i)(ii) are independent of each other.
However, this is not always the case. This paper shows that massless neutral
scalar fields can form stationary clouds around a ReissnerNordstr"{o}m black
hole when both are subject to a uniform magnetic field. The latter
simultaneously enacts both requirements by creating an ergoregion (thereby
opening up the possibility of superradiance) and trapping the scalar field in
the black hole's vicinity. This leads to some novel features, in particular,
that only black holes with a subset of the possible charge to mass ratios can
support stationary clouds.
ria.ua.pt

doi

Peer Reviewed
61.
Quasinormal modes of hot, cold and bald Einstein–Maxwellscalar black holes
BlázquezSalcedo, Jose Luis and Herdeiro, Carlos A. R. and Kahlen, Sarah and Kunz, Jutta and Pombo, Alexandre M. and Radu, Eugen
The European Physical Journal C
SpringerOpen
Einstein–Maxwellscalar models allow for different classes of black hole solutions, depending on the nonminimal coupling function f(ϕ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, f(ϕ)=1+αϕ4 (BlázquezSalcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalarled modes, polar and axial electromagneticled modes, and polar and axial gravitationalled modes. We demonstrate that the only unstable mode present is the radial scalarled mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both modestable. The nontrivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.
ria.ua.pt

doi

Peer Reviewed
60.
Control of COVID19 dynamics through a fractionalorder model
Bushnaq, Samia and Saeed, Tareq and Torres, Delfim F. M. and Zeb, Anwar
Alexandria Engineering Journal
Elsevier
We investigate, through a fractional mathematical model, the effects of
physical distance on the SARSCoV2 virus transmission. Two controls are
considered in our model for eradication of the spread of COVID19: media
education, through campaigns explaining the importance of social distancing,
use of face masks, etc., towards all population, while the second one is
quarantine social isolation of the exposed individuals. A general fractional
order optimal control problem, and associated optimality conditions of
Pontryagin type, are discussed, with the goal to minimize the number of
susceptible and infected while maximizing the number of recovered. The
extremals are then numerically obtained.
ria.ua.pt

doi

Peer Reviewed
59.
Analysis of Hilfer fractional integrodifferential equations with almost sectorial operators
Karthikeyan, Kulandhaivel and Debbouche, Amar and Torres, Delfim F. M.
Fractal and Fractional
MDPI
In this work, we investigate a class of nonlocal integrodifferential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.
ria.ua.pt

doi

Peer Reviewed
58.
On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers
Andrade, Enide and CarrascoOlivera, Dante and Manzaneda, Cristina
Linear Algebra and its Applications
Elsevier
In this work a new type of matrix called circulantlike matrix is introduced. This type of matrix includes the classical kcirculant matrix, introduced in [4], in a natural sense. Its eigenvalues and its inverse and some other properties are studied, namely, it is shown that the inverse of a matrix of this type is also a matrix of this type and that its first row is the unique solution of a certain system of linear equations. Additionally, for some of these matrices whose entries are written as function of Horadam, Fibonacci, Jacobsthal and Pell numbers we study its eigenvalues and write it as function of those numbers. Moreover, the same study is done if the entries are arithmetic sequences.
ria.ua.pt

doi

Peer Reviewed
57.
On the necessary optimality conditions for the fractional Cucker–Smale optimal control problem
Almeida, Ricardo and Kamocki, Rafał and Malinowska, Agnieszka B. and Odzijewicz, Tatiana
Communications in Nonlinear Science and Numerical Simulation
Elsevier
This paper develops a sparse flocking control for the fractional Cucker–Smale multiagent
model. The Caputo fractional derivative, in the equations describing the dynamics of a consensus parameter, makes it possible to take into account in the selforganization of group
its history and memory dependency. External control is designed based on necessary conditions for a local solution to the appropriate optimal control problem. Numerical simulations demonstrate the effectiveness of the control scheme.
ria.ua.pt

doi

Peer Reviewed
56.
Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input
Almeida, R. and Hristova, S. and Dashkovskiy, S.
International Journal of Robust and Nonlinear Control
Wiley
The bounded input bounded output (BIBO) stability for a nonlinear Caputo
fractional system with timevarying bounded delay and nonlinear output is
studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input
bounded output stability criteria are derived. Also, explicit and independent on
the initial time bounds of the output are provided. Uniform BIBO stability and
uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system’s dynamic response, and demonstrate the
effectiveness of our theoretical results.
ria.ua.pt

doi

Peer Reviewed
55.
Optimal leaderfollowing consensus of fractional opinion formation models
Almeida, Ricardo and Kamocki, Rafał and Malinowska, Agnieszka B. and Odzijewicz, Tatiana
Journal of Computational and Applied Mathematics
Elsevier
This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractionalorder derivative determines the impact of the memory during the opinion evolution. The problem of leaderfollowing consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.
ria.ua.pt

doi

Peer Reviewed
54.
Optimality conditions for variational problems involving distributedorder fractional derivatives with arbitrary kernels
Cruz, Fátima and Almeida, Ricardo and Martins, Natália
AIMS Mathematics
AIMS Press
In this work we study necessary and sufficient optimality conditions for variational
problems dealing with a new fractional derivative. This fractional derivative combines two known
operators: distributedorder derivatives and derivatives with arbitrary kernels. After proving a
fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary
conditions for the fundamental variational problem. Also, fractional variational problems with integral
and holonomic constraints are considered. We end with some examples to exemplify our results.
ria.ua.pt

doi

Peer Reviewed
53.
Global stability of a Caputo fractional SIRS model with general incidence rate
Ammi, Moulay Rchid Sidi and Tahiri, Mostafa and Torres, Delfim F. M.
Mathematics in Computer Science
Springer
We introduce a fractional order SIRS model with nonlinear incidence rate. Existence of a unique positive solution to the model is proved. Stability analysis of the disease free equilibrium and positive fixed points are investigated. Finally, a numerical example is presented.
ria.ua.pt

doi

Peer Reviewed
52.
A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
Almeida, Ricardo and Martins, Natália
Fractal and Fractional
MDPI
In this paper, we present a new fractional variational problem where the Lagrangian
depends not only on the independent variable, an unknown function and its left and rightsided
Caputo fractional derivatives with respect to another function, but also on the endpoint conditions
and a free parameter. The main results of this paper are necessary and sufficient optimality conditions
for variational problems with or without isoperimetric and holonomic restrictions. Our results not
only provide a generalization to previous results but also give new contributions in fractional
variational calculus. Finally, we present some examples to illustrate our results.
ria.ua.pt

doi

Peer Reviewed
51.
A semantics and a logic for Fuzzy Arden Syntax
Gomes, Leandro and Madeira, Alexandre and Barbosa, Luís Soares
Soft Computing
Springer
Fuzzy programming languages, such as the Fuzzy Arden Syntax (FAS), are used to describe behaviours which evolve in a fuzzy way and thus cannot be characterized neither by a Boolean outcome nor by a probability distribution. This paper introduces a semantics for FAS, focusing on the weighted parallel interpretation of its conditional statement. The proposed construction is based on the notion of a fuzzy multirelation which associates with each state in a program a fuzzy set of weighted possible evolutions. The latter is parametric on a residuated lattice which models the underlying semantic ‘truth space’. Finally, a family of dynamic logics, equally parametric on the residuated lattice, is introduced to reason about FAS programs.
ria.ua.pt

doi

Peer Reviewed
50.
Pest control using farming awareness: impact of time delays and optimal use of biopesticides
Abraha, Teklebirhan and Al Basir, Fahad and Obsu, Legesse Lemecha and Torres, Delfim F. M.
Chaos, Solitons & Fractals
Elsevier
We investigate a mathematical model in crop pest management, considering
plant biomass, pest, and the effect of farming awareness. The pest population
is divided into two compartments: susceptible pest and infected pest. We assume
that the growth rate of selfaware people is proportional to the density of
healthy pests present in the crop field. Impacts of awareness is modeled via a
saturated term. It is further assumed that selfaware people will adopt
biological control methods, namely integrated pest management. Susceptible
pests are detrimental to crops and, moreover, there may be some time delay in
measuring the healthy pests in the crop field. A time delay may also take place
while becoming aware of the control strategies or taking necessary steps to
control the pest attack. In agreement, we develop our model incorporating two
time delays into the system. The existence and the stability criteria of the
equilibria are obtained in terms of the basic reproduction number and time
delays. Stability switches occur through Hopfbifurcation when time delays
cross critical values. Optimal control theory has been applied for the
costeffectiveness of the delayed system. Numerical simulations illustrate the
obtained analytical results.
ria.ua.pt

doi

Peer Reviewed
49.
Two families of locally toroidal regular 4hypertopes arising from toroids
Fernandes, Maria Elisa and Leemans, Dimitri and Piedade, Claudio Alexandre and Weiss, Asia Ivić
Contemporary Mathematics
American Mathematical Society
In this paper we present two inﬁnite families of locally toroidal hypertopes of rank 4 that are constructed from regular toroids of types {4, 3, 4}_(s,s,0) and {3, 3, 4, 3}_(s,0,0,0). The Coxeter diagram of the ﬁrst of the two families is starshaped and the diagram of the other is a square. In both cases the toroidal residues are regular toroidal maps of type {3, 6}.
ria.ua.pt

doi

Peer Reviewed
48.
New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
Almeida, Ricardo and Martins, Natália
Symmetry
MDPI
This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize wellknown results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.
ria.ua.pt

doi

Peer Reviewed
47.
A new spectral method based on two classes of hat functions for solving systems of fractional differential equations and an application to respiratory syncytial virus infection
Nemati, Somayeh and Torres, Delfim F. M.
Soft Computing
Springer
We propose a new spectral method, based on two classes of hat functions, for solving systems of fractional differential equations. The fractional derivative is considered in the Caputo sense. Properties of the basis functions, Caputo derivatives and Riemann–Liouville fractional integrals, are used to reduce the main problem to a system of nonlinear algebraic equations. By analyzing in detail the resulting system, we show that the method needs few computational efforts. Two test problems are considered to illustrate the efficiency and accuracy of the proposed method. Finally, an application to a recent mathematical model in epidemiology is given, precisely to a system of fractional differential equations modeling the respiratory syncytial virus infection.
ria.ua.pt

doi

Peer Reviewed
46.
Introducing fuzzy reactive graphs: a simple application on biology
Santiago, Regivan and Martins, Manuel A. and Figueiredo, Daniel
Soft Computing
Springer
In this paper, we propose a generalization for fuzzy graphs in order to model reactive systems with fuzziness. As we will show, the resulting fuzzy structure, called fuzzy reactive graphs (FRG), is able to model dynamical aspects of some entities which generally appear in: biology, computer science and some other fields. The dynamical aspect is captured by a transition function which updates the values of the graph after an edge has been crossed. The update process takes into account aggregation functions. The paper proposes a notion for bisimulation for such graphs and briefly shows how modal logic can be used to verify properties of systems modeled with FSGs. The paper closes with a toy example in the field of Biology.
ria.ua.pt

doi

Peer Reviewed
45.
Nondual modal operators as a basis for 4valued accessibility relations in Hybrid logic
Costa, Diana and Martins, Manuel A.
Journal of Logical and Algebraic Methods in Programming
Elsevier
The modal operators usually associated with the notions of possibility and necessity are classically duals. This paper aims to defy that duality in a paraconsistent environment, namely in a Belnapian Hybrid logic where both propositional variables and accessibility relations are fourvalued. Hybrid logic, which is an extension of Modal logic, incorporates extra machinery such as nominals – for uniquely naming states – and a satisfaction operator – so that the formula under its scope is evaluated in the state whose name the satisfaction operator indicates.
In classical Hybrid logic the semantics of negation, when it appears before compound formulas, is carried towards subformulas, meaning that eventual inconsistencies can be found at the level of nominals or propositional variables but appear unrelated to the accessibility relations. In this paper we allow inconsistencies in propositional variables and, by breaking the duality between modal operators, inconsistencies at the level of accessibility relations arise. We introduce a sound and complete tableau system and a decision procedure to check if a formula is a consequence of a set of formulas. Tableaux will be used to extract syntactic models for databases, which will then be compared using different inconsistency measures. We conclude with a discussion about bisimulation.
ria.ua.pt

doi

Peer Reviewed
44.
A fractional analysis in higher dimensions for the SturmLiouville problem
Ferreira, M. and Rodrigues, M. M. and Vieira, N.
Fractional Calculus and Applied Analysis
De Gruyter
In this work, we consider the ndimensional fractional SturmLiouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right RiemannLiouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.
ria.ua.pt

doi

Peer Reviewed
43.
Cauchy’s formula on nonempty closed sets and a new notion of Riemann–Liouville fractional integral on time scales
Torres, Delfim F. M.
Applied Mathematics Letters
Elsevier
We prove Cauchy’s formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.
ria.ua.pt

doi

Peer Reviewed
42.
On strong duality in linear copositive programming
Kostyukova, O. I. and Tchemisova, T. V.
Journal of Global Optimization
Springer
The paper is dedicated to the study of strong duality for a problem of linear copositive
programming. Based on the recently introduced concept of the set of normalized immobile
indices, an extended dual problem is deduced. The dual problem satisfies the strong dual ity relations and does not require any additional regularity assumptions such as constraint
qualifications. The main difference with the previously obtained results consists in the fact
that now the extended dual problem uses neither the immobile indices themselves nor the
explicit information about the convex hull of these indices. The strong duality formulations
presented in the paper for linear copositive problems have similar structure and properties as
that proposed in the works by M. Ramana, L. Tuncel, and H. Wolkowicz, for semidefinite
programming.
ria.ua.pt

doi

Peer Reviewed
41.
On the theory of periodic multivariate INAR processes
Santos, Cláudia and Pereira, Isabel and Scotto, Manuel G.
Statistical Papers
Springer
In this paper a multivariate integervalued autoregressive model of order one with
periodic timevarying parameters, and driven by a periodic innovations sequence of
independent random vectors is introduced and studied in detail. Emphasis is placed on
models with periodic multivariate negative binomial innovations. Basic probabilistic
and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihoodbased approach is adopted. The performance of such method is
compared with that of some traditional competitors, namely moment estimators and
conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.
ria.ua.pt

doi

Peer Reviewed
40.
Language assessment in awake brain surgery: the Portuguese adaptation of the Dutch linguistic intraoperative protocol (DuLIP)
Alves, Joana and Cardoso, Mafalda and Morgado, Mariana and De Witte, Elke and Satoer, Djaina and Hall, Andreia and Jesus, Luis M. T.
Clinical Linguistics & Phonetics
Taylor & Francis
Awake brain surgery, combined with neurophysiological evaluation and intraoperative mapping, is one of the preferential lines of treatment when approaching lowgrade gliomas. Speech and language assessment is used while applying Direct Electrical Stimulation (DES) and during the resection of a lesion/tumour, as it allows to establish related eloquent areas and optimise the extent of the resection and avoid impairments. Patients need to be assessed pre, intra and postsurgery, but in under resourced countries such as Portugal, there are still no standardised and validated tools to conduct this type of evaluation. To address this need, the tasks of the Dutch Linguistic Intraoperative Protocol (DuLIP) were adapted to European Portuguese, and the resulting materials were standardised for a group of 144 Portuguese participants. For each task, the impact of age, gender and schooling were measured. The resulting Portuguese version of the DuLIP (DuLIPEP) consists of 17 tasks, including phonological, syntactic, semantic, naming and articulatory tests. No significant differences were found between male and female participants. However, schooling influenced phonological and syntactic fluency, object naming and verb generation. Schooling and age had a significant impact on semantic fluency and reading with semantic odd word out tasks. This is the first contribution to the standardisation of a tool that can be used during an awake brain surgery in Portugal, which includes a new phonological odd word out task that is not currently available in the Dutch version.
ria.ua.pt

doi

Peer Reviewed
39.
A dynamicallyconsistent nonstandard finite difference scheme for the SICA model
Vaz, Sandra and Torres, Delfim F. M.
Mathematical Biosciences and Engineering
AIMS Press
In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible–Infected–Chronic–AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and their local and global stability.
ria.ua.pt

doi

Peer Reviewed
38.
PakStanley labeling of the mCatalan hyperplane arrangement
Duarte, Rui and Guedes de Oliveira, António
Advances in Mathematics
Elsevier
We characterize in simple terms the PakStanley labels λ(R) of the regions
R of the mCatalan arrangement. We also propose a simple algorithm that returns R
from λ(R). Finally, we characterize in close terms the labels of the relatively bounded
regions.
ria.ua.pt

doi

Peer Reviewed
37.
Generalizações da etiquetagem de PakStanley
Duarte, Rui and Guedes de Oliveira, António
Boletim da Sociedade Portuguesa de Matemática
Sociedade Portuguesa de Matemática
Neste artigo pretendemos dar a conhecer ao leitor uma área que consideramos particularmente atraente, onde temos obtido alguns resultados que tentaremos também relatar.
O ponto de partida é uma construção (a "etiquetagem de PakStanley''), que associa um vetor a cada uma das regiões em que determinado conjunto de hiperplanos divide o espaço euclideano $R^n$. Regiões vizinhas diferem (em $1$) numa coordenada, crescendo ao afastarse de uma determinada região, etiquetada com $(1,1,dotsc,1)$.
Há cerca de vinte anos, Pak e Stanley mostraram que, no caso de os hiperplanos formarem o "arranjo de Shi'', as etiquetas de PakStanley formam um conjunto previamente estudado, o conjunto das "parking functions'', e
que a etiquetagem é bijetiva, muito embora seja difícil definir a função inversa, isto é, obter a região a partir da etiqueta.
Esta construção tem uma extensão natural a outros arranjos. Recentemente, Mazin obteve uma caracterização muito geral dos conjuntos de etiquetas assim obtidos, que implica, em particular, o resultado de Pak e Stanley. Com base neste trabalho de Mazin, estudamos as etiquetagens de outro arranjos, o arranjo de Ish recentemente definido e um conjunto de arranjos por nós introduzido, que constitui uma classe naturalmente balizada, por um lado, pelo arranjo de Shi, e por outro, pelo arranjo de Ish.
O nosso trabalho, em traços gerais, consistiu em descrever o conjunto das etiquetas respetivas e em mostrar que as etiquetagens são bijetivas, recorrendo a diferentes técnicas e resultados que aqui são explicitamente referidos. A exposição dessas técnicas e o relato desses resultados, alguns já "clássicos'' da área e outros muito recentes, foram talvez a nossa razão mais forte para a escrita deste pequeno texto.
ria.ua.pt

Peer Reviewed
36.
A behavioral approach to estimation in the presence of disturbances
Pereira, Ricardo and Rocha, Paula and Ntogramatzidis, Lorenzo
IEEE Transactions on Automatic Control
IEEE
In this article, we study the problem of estimation in the presence of disturbances within the context of the behavioral approach developed by J.C. Willems. For this purpose, we use the behavioral theory of observers introduced by Valcher, Willems, Trentelman, and Trumpf, combined with the notions of behavioral invariance, conditioned invariance, and behavioral detectability subspaces. With these tools, we provide necessary and sufficient conditions for the solvability of the aforementioned problem together with the construction of an estimator.
ria.ua.pt

doi

Peer Reviewed
35.
Application of the fractional Sturm–Liouville theory to a fractional Sturm–Liouville telegraph equation
Ferreira, M. and Rodrigues, M. M. and Vieira, N.
Complex Analysis and Operator Theory
Springer
In this paper, we consider a nonhomogeneous timespacefractional telegraph equation in $n$dimensions, which is obtained from the standard telegraph equation by replacing the first and secondorder time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional SturmLiouville operator defined in terms of right and left fractional RiemannLiouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and nonhomogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate MittagLeffler function. In the end of the paper some illustrative examples are presented.
ria.ua.pt

doi

Peer Reviewed
34.
Farming awareness based optimum interventions for crop pest control
Abraha, Teklebirhan and Al Basir, Fahad and Obsu, Legesse Lemecha and Torres, Delfim F. M.
Mathematical Biosciences and Engineering
AIMS Press
We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pestfree and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pestfree and coexistence equilibria is shown using the Routh–Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pestfree equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.
ria.ua.pt

doi

Peer Reviewed
33.
Investigating carbon emissions from electricity generation and GDP nexus using maximum entropy bootstrap: evidence from oilproducing countries in the Middle East
Zanjani, Zeinab and Macedo, Pedro and Soares, Isabel
Energies
MDPI
The maximum entropy bootstrap for time series is applied in this study to investigate the nexus between carbon emissions from electricity generation and the gross domestic product, using a bivariate framework for eight Middle Eastern countries between 1995 and 2017. The sample under study includes oilproducing countries such as Bahrain, Iran, Iraq, Kuwait, Oman, Qatar, Saudi Arabia, and United Arab Emirates. As the electricity generation in these economies relies mainly on oil and gas, finding out the existence and direction of the relationship between the two considered variables has remarkable implications for policymakers and governments in these countries to achieve both higher economic growth and environmental protection. As expected, this nexus is validated for all countries in the sample but not in all models, time periods, and lags. Therefore, policymakers can set appropriate electricity conservation policies based on these varied empirical findings to boost economic growth with minimum environmental degradation.
ria.ua.pt

doi

Peer Reviewed
32.
Observational interpretations of hybrid dynamic logic with binders and silent transitions
Hennicker, Rolf and Knapp, Alexander and Madeira, Alexandre
Journal of Logical and Algebraic Methods in Programming
We extend hybrid dynamic logic with binders (for state variables) by distinguishing between observable and silent transitions. This differentiation gives rise to two kinds of observational interpretations: The first one relies on observational abstraction from the ordinary model class of a specification Sp by considering its closure under weak bisimulation. The second one uses an observational satisfaction relation for the axioms of the specification Sp, which relaxes the interpretation of state variables and the satisfaction of modal formulæ by abstracting from silent transitions. We establish a formal relationship between both approaches and show that they are equivalent under mild conditions. For the proof we instantiate the previously introduced concept of a behaviourabstractor framework to the case of dynamic logic with binders and silent transitions. As a particular outcome we provide an invariance theorem and show the HennessyMilner property for weakly bisimilar labelled transition systems and observational satisfaction. In the second part of the paper we integrate our results in a development methodology for reactive systems leading to two versions of observational refinement. We provide conditions under which both kinds of refinement are semantically equivalent, involving implementation constructors for relabelling, hiding, and parallel composition.
ria.ua.pt

doi

Peer Reviewed
31.
Mathematical analysis of a fractional COVID19 model applied to Wuhan, Spain and Portugal
Ndaïrou, Faïçal and Torres, Delfim F. M.
Axioms
MDPI
We propose a qualitative analysis of a recent fractionalorder COVID19 model. We start by showing that the model is mathematically and biologically well posed. Then, we give a proof on the global stability of the disease free equilibrium point. Finally, some numerical simulations are performed to ensure stability and convergence of the disease free equilibrium point.
ria.ua.pt

doi

Peer Reviewed
30.
GW190521 as a Merger of Proca Stars: A Potential New Vector Boson of 8.7×10^{13} eV
Bustillo, Juan Calderón and SanchisGual, Nicolas and TorresForné, Alejandro and Font, José A and Vajpeyi, Avi and Smith, Rory and Herdeiro, Carlos and Radu, Eugen and Leong, Samson H W
Physical review letters
American Physical Society
Advanced LIGOVirgo have reported a short gravitationalwave signal (GW190521) interpreted as a quasicircular merger of black holes, one at least populating the pairinstability supernova gap, that formed a remnant black hole of M_{f}∼142 M_{⊙} at a luminosity distance of d_{L}∼5.3 Gpc. With barely visible premerger emission, however, GW190521 merits further investigation of the premerger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from headon collisions of two (equal mass and spin) horizonless vector boson stars (aka Proca stars), forming a final black hole with M_{f}=231_{17}^{+13} M_{⊙}, located at a distance of d_{L}=571_{181}^{+348} Mpc. This provides the first demonstration of close degeneracy between these two theoretical models, for a real gravitationalwave event. The favored mass for the ultralight vector boson constituent of the Proca stars is μ_{V}=8.72_{0.82}^{+0.73}×10^{13} eV. Confirmation of the Proca star interpretation, which we find statistically slightly preferred, would provide the first evidence for a long sought dark matter particle.
ria.ua.pt

doi

Peer Reviewed
29.
Chains of boson stars
Herdeiro, C. A. R. and Kunz, J. and Perapechka, I. and Radu, E. and Shnir, Y.
Physical Review D
American Physical Society
We study axially symmetric multisoliton solutions of a complex scalar field
theory with a sextic potential, minimally coupled to Einstein's gravity. These
solutions carry no angular momentum and can be classified by the number of
nodes of the scalar field, $k_z$, along the symmetry axis; they are interpreted
as chains with $k_z+1$ boson stars, bound by gravity, but kept apart by
repulsive scalar interactions. Chains with an odd number of constituents show a
spiraling behavior for their ADM mass (and Noether charge) in terms of their
angular frequency, similarly to a single fundamental boson star, as long as the
gravitational coupling is small; for larger coupling, however, the inner part
of the spiral is replaced by a merging with the fundamental branch of radially
excited spherical boson stars. Chains with an even number of constituents
exhibit a truncated spiral pattern, with only two or three branches, ending at
a limiting solution with finite values of ADM mass and Noether charge.
ria.ua.pt

doi

Peer Reviewed
28.
The imitation game: proca stars that can mimic the Schwarzschild shadow
Herdeiro, Carlos A. R. and Pombo, Alexandre M. and Radu, Eugen and Cunha, Pedro V. P. and SanchisGual, Nicolas
Journal of Cosmology and Astroparticle Physics
IOP Publishing
Can a dynamically robust bosonic star (BS) produce an (effective) shadow that
mimics that of a black hole (BH)? We focus on models of spherical BSs with free scalar or
vector fields, as well as with polynomial or axionic selfinteracting fields. The BH shadow
is linked to the existence of light rings (LRs). For free bosonic fields, yielding miniBSs,
it is known that these stars can become ultracompact — i.e., possess LRs — but only
for perturbatively unstable solutions. We show this remains the case even when different
selfinteractions are considered. However, an effective shadow can arise in a different way:
if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike
geodesics (located at rISCO = 6M for a Schwarzschild BH of mass M), the accretion flow
morphology around BHs is mimicked and an effective shadow arises in an astrophysical
environment. Even though spherical BSs may accommodate stable timelike circular orbits
all the way down to their centre, we show the angular velocity Ω along such orbits may have
a maximum away from the origin, at RΩ; this scale was recently observed to mimic the BH’s
ISCO in some scenarios of accretion flow. Then: (i) for free scalar fields or with quartic
selfinteractions, RΩ 6= 0 only for perturbatively unstable BSs; (ii) for higher scalar selfinteractions, e.g. axionic, RΩ 6= 0 is possible for perturbatively stable BSs, but no solution
with RΩ = 6M was found in the parameter space explored; (iii) but for free vector fields,
yielding Proca stars, perturbatively stable solutions with RΩ 6= 0 exist, and indeed RΩ = 6M
for a particular solution. Thus, dynamically robust spherical Proca stars succeed in the
imitation game: they can mimic the shadow of a (near)equilibrium Schwarzschild BH with
the same M, in an astrophysical environment, despite the absence of a LR, at least under
some observation conditions, as we confirm by explicitly comparing the lensing of such Proca
stars and Schwarzschild BHs.
ria.ua.pt

doi

Peer Reviewed
27.
Can different black holes cast the same shadow?
Junior, Haroldo C. D. Lima and Crispino, Luís C. B. and Cunha, Pedro V. P. and Herdeiro, Carlos A. R.
Physical Review D
American Physical Society
We consider the following question: may two different black holes (BHs) cast
exactly the same shadow? In spherical symmetry, we show the necessary and
sufficient condition for a static BH to be shadowdegenerate with Schwarzschild
is that the dominant photonsphere of both has the same impact parameter, when
corrected for the (potentially) different redshift of comparable observers in
the different spacetimes. Such shadowdegenerate geometries are classified into
two classes. The first shadowequivalent class contains metrics whose constant
(areal) radius hypersurfaces are isometric to those of the Schwarzschild
geometry, which is illustrated by the Simpson and Visser (SV) metric. The
second shadowdegenerate class contains spacetimes with different redshift
profiles and an explicit family of metrics within this class is presented. In
the stationary, axisymmetric case, we determine a sufficient condition for the
metric to be shadow degenerate with Kerr for faraway observers. Again we
provide two classes of examples. The first class contains metrics whose
constant (BoyerLindquistlike) radius hypersurfaces are isometric to those of
the Kerr geometry, which is illustrated by a rotating generalization of the SV
metric, obtained by a modified NewmanJanis algorithm. The second class of
examples pertains BHs that fail to have the standard northsouth $mathbb{Z}_2$
symmetry, but nonetheless remain shadow degenerate with Kerr. The latter
provides a sharp illustration that the shadow is not a probe of the horizon
geometry. These examples illustrate that nonisometric BH spacetimes can cast
the same shadow, albeit the lensing is generically different.
ria.ua.pt

doi

Peer Reviewed
26.
Embedding Gauss–Bonnet scalarization models in higher dimensional topological theories
Herdeiro, Carlos and Radu, Eugen and Tchrakian, D. H.
Symmetry
MDPI
In the presence of appropriate nonminimal couplings between a scalar field and the
curvature squared Gauss–Bonnet (GB) term, compact objects such as neutron stars and black holes
(BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The nonminimal coupling functions that
allow this mechanism are, however, always postulated ad hoc. Here, we point out that families
of such functions naturally emerge in the context of Higgs–Chern–Simons gravity models, which
are found as dimensionally descents of higher dimensional, purely topological, Chern–Pontryagin
nonAbelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions
in a particular EinsteinGBscalar field model, whose coupling is obtained from this construction,
pointing out novel features and caveats thereof. The possibility of vectorization is also discussed,
since this construction also originates vector fields nonminimally coupled to the GB invariant.
ria.ua.pt

doi

Peer Reviewed
25.
Kerr black holes with synchronised axionic hair
Delgado, Jorge F. M. and Herdeiro, Carlos A. R. and Radu, Eugen
Physical Review D
American Physical Society
We construct and analyse Kerr black holes (BHs) with synchronised axionic
hair. These are the BH generalisations of the recently constructed rotating
axion boson stars arXiv:2005.05982. Such BHs are stationary, axially symmetric,
asymptotically flat solutions of the complex EinsteinKleinGordon theory with
a QCD axionlike potential. They are regular everywhere on and outside the
event horizon. The potential is characterised by two parameters: the mass of
the axionlike particle, $m_a$ and the decay constant $f_a$. The limit $f_a
rightarrow infty$ recovers the original example of Kerr BHs with synchronised
scalar hair arXiv:1403.2757. The effects of the nonlinearities in the
potential become important for $f_a lesssim 1$. We present an overview of the
parameter space of the solutions together with a study of their basic geometric
and phenomenological properties, for an illustrative value of the coupling that
yields a nonnegligible impact of the selfinteractions.
ria.ua.pt

doi

Peer Reviewed
24.
Desingularizing the extremal GMGHS black hole via higher derivatives corrections
Herdeiro, Carlos and Radu, Eugen and Uzawa, Kunihito
Physics Letters B
Elsevier
The GibbonsMaedaGarfinkleHorowitzStrominger (GMGHS) black hole is an
influential solution of the low energy heterotic string theory. As it is well
known, it presents a singular extremal limit. We construct a regular extension
of the GMGHS extremal black hole in a model with $mathcal{O}(alpha')$
corrections in the action, by solving the fully nonlinear equations of motion.
The desingularization is supported by the $mathcal{O}(alpha')$terms. The
regularised extremal GMGHS BHs are asymptotically flat, possess a regular
(nonzero size) horizon of spherical topology, with an $AdS_2times S^2$ near
horizon geometry, and their entropy is proportional to the electric charge. The
near horizon solution is obtained analytically and some illustrative bulk
solutions are constructed numerically.
ria.ua.pt

doi

Peer Reviewed
23.
Multifield, multifrequency bosonic stars and a stabilization mechanism
SanchisGual, Nicolas and Di Giovanni, Fabrizio and Herdeiro, Carlos and Radu, Eugen and Font, José A.
Physical Review Letters
American Physical Society
Scalar bosonic stars (BSs) stand out as a multipurpose model of exotic compact objects. We enlarge the landscape of such (asymptotically flat, stationary, everywhere regular) objects by considering multiple fields (possibly) with different frequencies. This allows for new morphologies and a stabilization mechanism for different sorts of unstable BSs. First, any odd number of complex fields, yields a continuous family of BSs departing from the spherical, equal frequency, ℓBSs. As the simplest illustration, we construct the ℓ=1 BSs family, that includes several singlefrequency solutions, including even parity (such as spinning BSs and a toroidal, static BS) and odd parity (a dipole BS) limits. Second, these limiting solutions are dynamically unstable, but can be stabilized by a hybridℓ construction: adding a sufficiently large fundamental ℓ=0 BS of another field, with a different frequency. Evidence for this dynamical robustness is obtained by nonlinear numerical simulations of the corresponding Einstein(complex, massive) KleinGordon system, both in formation and evolution scenarios, and a suggestive correlation between stability and energy distribution is observed. Similarities and differences with vector BSs are anticipated.
ria.ua.pt

doi

Peer Reviewed
22.
List decoding of convolutional codes over integer residue rings
Lieb, Julia and Napp, Diego and Pinto, Raquel
Finite Fields and Their Applications
Elsevier
A convolutional code over is a submodule of where stands for the ring of polynomials with coefficients in . In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword when some of its coefficients have been erased. We do that using the padic expansion of w and particular representations of the paritycheck polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that w must satisfy and have only coefficients in the field . We exploit the natural block Toeplitz structure of the sliding paritycheck matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword w, that is, a list with the closest codewords to w.
ria.ua.pt

doi

Peer Reviewed
21.
Weighted proximity search
Rodrigues, Filipe and Agra, Agostinho and Hvattum, Lars Magnus and Requejo, Cristina
Journal of Heuristics
Springer
Proximity search is an iterative method to solve complex mathematical programming problems. At each iteration, the objective function of the problem at hand is replaced by the Hamming distance function to a given solution, and a cutoff constraint is added to impose that any new obtained solution improves the objective function value. A mixed integer programming solver is used to find a feasible solution to this modified problem, yielding an improved solution to the original problem. This paper introduces the concept of weighted Hamming distance that allows to design a new method called weighted proximity search. In this new distance function, low weights are associated with the variables whose value in the current solution is promising to change in order to find an improved solution, while high weights are assigned to variables that are expected to remain unchanged. The weights help to distinguish between alternative solutions in the neighborhood of the current solution, and provide guidance to the solver when trying to locate an improved solution.
Several strategies to determine weights are presented, including both static and dynamic strategies. The proposed weighted proximity search is compared with the classic proximity search on instances from three optimization problems: the pmedian problem, the set covering problem, and the stochastic lotsizing problem. The obtained results show that a suitable choice of weights allows the weighted proximity search to obtain better solutions, for 75% of the cases, than the ones obtained by using proximity search and for 96% of the cases the solutions are better than the ones obtained by running a commercial solver with a time limit.
ria.ua.pt

doi

Peer Reviewed
20.
Lagrangian duality for robust problems with decomposable functions: the case of a robust inventory problem
Rodrigues, Filipe and Agra, Agostinho and Requejo, Cristina and Delage, Erick
INFORMS Journal on Computing
INFORMS
We consider a class of minmax robust problems in which the functions that need to be “robustified” can be decomposed as the sum of arbitrary functions. This class of problems includes many practical problems, such as the lotsizing problem under demand uncertainty. By considering a Lagrangian relaxation of the uncertainty set, we derive a tractable approximation, called the dual Lagrangian approach, that we relate with both the classical dualization approximation approach and an exact approach. Moreover, we show that the dual Lagrangian approach coincides with the affine decision rule approximation approach. The dual Lagrangian approach is applied to a lotsizing problem, in which demands are assumed to be uncertain and to belong to the uncertainty set with a budget constraint for each time period. Using the insights provided by the interpretation of the Lagrangian multipliers as penalties in the proposed approach, two heuristic strategies, a new guided iterated local search heuristic, and a subgradient optimization method are designed to solve more complex lotsizing problems in which additional practical aspects, such as setup costs, are considered. Computational results show the efficiency of the proposed heuristics that provide a good compromise between the quality of the robust solutions and the running time required in their computation.
ria.ua.pt

doi

Peer Reviewed
19.
Minimal statespace representation of convolutional product codes
Climent, JoanJosep and Napp, Diego and Pinto, Raquel and Requena, Verónica
Mathematics
MDPI
In this paper, we study product convolutional codes described by statespace representations. In particular, we investigate how to derive statespace representations of the product code from the horizontal and vertical convolutional codes. We present a systematic procedure to build such representation with minimal dimension, i.e., reachable and observable.
ria.ua.pt

doi

Peer Reviewed
18.
GW190521 formation scenarios via relativistic accretion
CruzOsorio, Alejandro and LoraClavijo, Fabio D. and Herdeiro, Carlos
Journal of Cosmology and Astroparticle Physics
IOP Publishing
The recent gravitational wave transient GW190521 has been interpreted by the LIGOVirgo collaboration (LVC) as sourced by a binary black hole (BH) merger. According to the LVC parameter estimation, at least one of these progenitors falls into the socalled pairinstability supernova mass gap. This raises the important question of how and when these progenitors formed. In this paper we use an accretion model with superEddington mass accretion rate obtained from General Relativity hydrodynamics simulations to analyse the scenario wherein the GW190521 original progenitors (OPs) formed at lower masses (and spins) and grew to their estimated LVC parameters by relativistic accretion. We consider that the environment wherein the binary is immersed has density gradients as well as a dependence on the Mach number of the gas. Taking the LVC parameter estimation at z = 0.82 as the endpoint of the accretion evolution, we estimate the initial masses and spins of the OPs at three different redshifts z = 100, 50, and 20. We found three distinct possible types of OPs: (i) 104 M☉  3 M☉ almost nonrotating (with Kerr spin parameter a☆ < 102) primordial BHs; (ii) 3M☉  40M☉ slowly rotating (102 < a☆ < 0.5) stellar mass BHs; (iii) 40M☉  70M☉ BHs with a moderate spin parameter a☆ ~ 0.5, which could originate from the collapse of high mass Pop III stars. The mass spread is due to varying the density gradient and the relativistic Mach number of the cosmic plasma; the variation of the masses due to the origin at different redshifts, on the other hand, is negligible, ~ 2%. For high Mach number scenarios, the BHs have low mass and spin accretion rates, leading to OPs with masses and spins close to the GW190521 LVC estimated values. We have also compared our results with previous studies where the Newtonian accretion model was used, finding relativistic corrections of ~ 13% for the OPs masses. In particular, the relativistic model leads to smaller initial masses.
ria.ua.pt

doi

Peer Reviewed
17.
Variational problems with time delay and higherorder distributedorder fractional derivatives with arbitrary kernels
Cruz, Fátima and Almeida, Ricardo and Martins, Natália
Mathematics
MDPI
In this work, we study variational problems with time delay and higherorder distributedorder fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributedorder derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some wellknown results can be obtained as particular cases.
ria.ua.pt

doi

Peer Reviewed
16.
State realizations of 2periodic convolutional codes: a switching system approach
Fornasini, Ettore and Napp, Diego and Pereira, Ricardo and Pinto, Raquel and Rocha, Paula
IFACPapersOnLine
Elsevier; IFAC
In this work we investigate the realization problem of periodic convolutional codes. As convolutional codes are discrete linear systems over a finite field we use systems theory techniques to address our problem. In particular, we aim at deriving and studying statespace realizations of 2periodic convolutional codes. Although one cannot expect, in general, to obtain a periodic statespace realization of a periodic convolutional code by means of the individual realizations of each of the associated timeinvariant codes, we show that one can implement the periodic system switching periodically the output in each state system. Comments on the minimality of this realization are given.
ria.ua.pt

doi

Peer Reviewed
15.
Timefractional telegraph equation of distributed order in higher dimensions
Vieira, N. and Rodrigues, M. M. and Ferreira, M.
Communications in Nonlinear Science and Numerical Simulation
Elsevier
In this work, the Cauchy problem for the timefractional telegraph equation of distributed order in $BR^n times BR^+$ is considered. By employing the technique of the Fourier, Laplace and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox Hfunction is obtained. Some particular choices of the density functions in the form of elementary functions are studied. Fractional moments of the fundamental solution are computed in the Laplace domain. Finally, by application of the Tauberian theorems, we study the asymptotic behaviour of the secondorder moment (variance) in the time domain.
ria.ua.pt

doi

Peer Reviewed
14.
On a nonNewtonian calculus of variations
Torres, Delfim F. M.
Axioms
MDPI
The calculus of variations is a field of mathematical analysis born in 1687 with Newton’s problem of minimal resistance, which is concerned with the maxima or minima of integral functionals. Finding the solution of such problems leads to solving the associated Euler–Lagrange equations. The subject has found many applications over the centuries, e.g., in physics, economics, engineering and biology. Up to this moment, however, the theory of the calculus of variations has been confined to Newton’s approach to calculus. As in many applications negative values of admissible functions are not physically plausible, we propose here to develop an alternative calculus of variations based on the nonNewtonian approach first introduced by Grossman and Katz in the period between 1967 and 1970, which provides a calculus defined, from the very beginning, for positive real numbers only, and it is based on a (nonNewtonian) derivative that permits one to compare relative changes between a dependent positive variable and an independent variable that is also positive. In this way, the nonNewtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a firstorder optimality condition of Euler–Lagrange type. The new calculus of variations complements the standard one in a nontrivial/multiplicative way, guaranteeing that the solution remains in the physically admissible positive range. An illustrative example is given.
ria.ua.pt

doi

Peer Reviewed
13.
Hybrid dynamic logic institutions for event/databased systems
Hennicker, Rolf and Knapp, Alexander and Madeira, Alexandre
Formal Aspects of Computing
Springer
We propose EDlogic as a formal foundation for the specification and development of eventbased systems with data states. The framework is presented as an institution in the sense of Goguen and Burstall and the logic itself is parametrised by an underlying institution D whose structures are used to model data states. EDlogic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. It uses modal diamond and box operators over complex actions adopted from dynamic logic. Atomic actions are pairs of events and state transition predicates capturing the allowed reactions to the event. To write concrete specifications of recursive process structures we integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that EDlogic is powerful enough to characterise the semantics of an operational specification by a single EDsentence. Thus the whole (formal) development process for event/databased systems relies on EDlogic and its semantics as a common basis. It is supported by a variety of implementation constructors which can express, among others, event refinement and parallel composition. Due to the genericity of the approach, it is also possible to change a data state institution during system development when needed. All steps of our formal treatment are illustrated by a running example.
ria.ua.pt

doi

Peer Reviewed
12.
Pontryagin maximum principle for distributedorder fractional systems
Ndaïrou, Faïçal and Torres, Delfim F. M.
Mathematics
MDPI
We consider distributedorder nonlocal fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needlelike control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributedorder fractional optimal control problems, illustrating its applicability with an example.
ria.ua.pt

doi

Peer Reviewed
11.
Shadows and lensing of black holes immersed in strong magnetic fields
Junior, Haroldo C. D. Lima and Cunha, Pedro V. P. and Herdeiro, Carlos A. R. and Crispino, Luís C. B.
Physical Review D
American Physical Society
We investigate the null geodesic flow and in particular the light rings (LRs), fundamental photon orbits (FPOs) and shadows of a black hole (BH) immersed in a strong, uniform magnetic field, described by the SchwarzschilldMelvin electrovacuum solution. The empty Melvin magnetic Universe contains a tube of planar LRs. Including a BH, for weak magnetic fields, the shadow becomes oblate, whereas the intrinsic horizon geometry becomes prolate. For strong magnetic fields (overcritical solutions), there are no LRs outside the BH horizon, a result explained using topological arguments. This feature, together with the light confining structure of the Melvin universe yields panoramic shadows, seen (almost) all around the equator of the observer’s sky. Despite the lack of LRs, there are FPOs, including polar planar ones, which define the shadow edge. We also observe and discuss chaotic lensing, including in the empty Melvin universe, and multiple disconnected shadows.
ria.ua.pt

doi

Peer Reviewed
10.
Krein reproducing kernel modules in Clifford analysis
Alpay, Daniel and Cerejeiras, Paula and Kähler, Uwe
Journal d'Analyse Mathématique
Springer
Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic Xray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford–Krein modules are
naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products for duality and topology, we are going to demonstrate how one can work with them. Taking into account possible applications and the nature of hypercomplex analysis, special attention will be given to the study of Clifford–Krein modules with reproducing kernels. In the end we will discuss the interpolation problem in Clifford–Krein modules with reproducing kernel.
ria.ua.pt

doi

Peer Reviewed
9.
Local existence and uniqueness for a fractional SIRS model with MittagLeffler law
Sidi Ammi, Moulay Rchid and Tahiri, Mostafa and Torres, Delfim F. M.
General Letters in Mathematics
Refaad
In this paper, we study an epidemic model with AtanganaBaleanuCaputo (ABC) fractional derivative. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of a solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the ABC fractional derivative sense is solved numerically by the AdamsBashforthMoulton method.
ria.ua.pt

doi

Peer Reviewed
8.
Face reduction and the immobile indices approaches to regularization of linear Copositive Programming problems
Kostyukova, O. I. and Tchemisova, T. V.
arXiv
The paper is devoted to the regularization of linear Copositive Programming problems which consists of transforming a problem to an equivalent form, where the Slater condition is satisfied and the strong duality holds. We describe here two regularization algorithms based on the concept of immobile indices and an understanding of the important role these indices play in the feasible sets' characterization. These algorithms are compared to some regularization procedures developed for a more general case of convex problems and based on a facial reduction approach. We show that the immobileindexbased approach combined with the specifics of copositive problems allows us to construct more explicit and detailed regularization algorithms for linear Copositive Programming problems than those already available.
ria.ua.pt
7.
Density results for Sobolev, Besov and Triebel–Lizorkin spaces on rough sets
Caetano, A. M. and Hewett, D. P. and Moiola, A.
Journal of Functional Analysis
Elsevier
We investigate two density questions for Sobolev, Besov and TriebelLizorkin
spaces on rough sets. Our main results, stated in the simplest Sobolev space
setting, are that: (i) for an open set $Omegasubsetmathbb R^n$,
$mathcal{D}(Omega)$ is dense in ${uin H^s(mathbb R^n):{rm supp},
usubset overline{Omega}}$ whenever $partialOmega$ has zero Lebesgue
measure and $Omega$ is "thick" (in the sense of Triebel); and (ii) for a
$d$set $Gammasubsetmathbb R^n$ ($0
ria.ua.pt

doi

Peer Reviewed
6.
Optimal control problems involving combined fractional operators with general analytic kernels
Ndaïrou, Faïçal and Torres, Delfim F. M.
Mathematics
MDPI
Fractional optimal control problems via a wide class
of fractional operators with a general analytic kernel
are introduced. Necessary optimality conditions of
Pontryagin type for the considered problem are obtained
after proving a Gronwall type inequality as well as
results on continuity and differentiability of
perturbed trajectories. Moreover, a Mangasarian type
sufficient global optimality condition for the general
analytic kernel fractional optimal control problem
is proved. An illustrative example is discussed.
ria.ua.pt

doi

Peer Reviewed
5.
Analysis of a COVID19 compartmental model: a mathematical and computational approach
Abreu, Zita and Cantin, Guillaume and Silva, Cristiana J.
Mathematical Biosciences and Engineering
AIMS Press
In this note, we consider a compartmental epidemic mathematical model given by a system of differential equations. We provide a complete toolkit for performing both a symbolic and numerical analysis of the spreading of COVID19. By using the free and opensource programming language Python and the mathematical software SageMath, we contribute for the reproducibility of the mathematical analysis of the stability of the equilibrium points of epidemic models and their fitting to real data. The mathematical tools and codes can be adapted to a wide range of mathematical epidemic models.
ria.ua.pt

doi

Peer Reviewed
4.
Marketing Verde: comparando o consumo de produtos ecológicos nas gerações X e Y
Magalhães, Carla and Paço, Arminda and Alonso, Hugo and Oliveira, Marta
CBR  Consumer Behavior Review
Universidade Federal de Pernambuco
Este estudo analisa a influência de
determinados estímulos de marketing
(propaganda, informação veiculada e preço)
no consumo de produtos ecológicos, comparando o comportamento dos
consumidores portugueses das gerações X e Y.
Através de uma pesquisa quantitativa, crosssectional, com base num questionário online,
cujos resultados foram analisados com recurso
ao software SPSS Statistics 25, concluímos que
existem algumas semelhanças entre ambas as
gerações, como a capacidade de identificação
dos produtos ecológicos e a predisposição para
a sua compra, o impacto positivo das
campanhas de comunicação com apelo
emocional e a perceção da importância dos
rótulos dos produtos ecológicos. A variável que
mais distingue o comportamento de ambas as
gerações é o preço, pois a geração Y está mais
predisposta a pagar um valor superior por um
produto ecológico. Esta investigação contribui
para a literatura sobre o comportamento do
consumidor, especialmente no âmbito da
variável “geração”, aplicado ao contexto do
consumo de produtos ecológicos. Também
ajuda as empresas a posicionaremse melhor
na relação com os consumidores de ambas as
gerações analisadas. A definição de estratégias
de targeting mais acuradas relativamente à
promoção, preço e decisão de compra pode
então tomar como ponto de partida os
resultados deste estudo.
ria.ua.pt

doi

Peer Reviewed
3.
An empirical comparison of two approaches for CDPCA in highdimensional data
Freitas, Adelaide and Macedo, Eloísa and Vichi, Maurizio
Statistical Methods & Applications
Springer
Modifed principal component analysis techniques, specially those yielding sparse solutions, are attractive due to its usefulness for interpretation purposes, in particular, in highdimensional data sets. Clustering and disjoint principal component analysis (CDPCA) is a constrained PCA that promotes sparsity in the loadings matrix. In particular, CDPCA seeks to describe the data in terms of disjoint (and possibly sparse) components and has, simultaneously, the particularity of identifying clusters of objects. Based on simulated and real gene expression data sets where the number of variables is higher than the number of the objects, we empirically compare the performance of two diferent heuristic iterative procedures, namely ALS and two stepSDP algorithms proposed in the specialized literature to perform CDPCA. To avoid possible efect of diferent variance values among the original variables, all the data was standardized. Although both procedures perform well, numerical tests highlight two main features that distinguish their performance, in particular related to the twostepSDP algorithm: it provides faster results than ALS and, since it employs a clustering procedure (kmeans) on the variables, outperforms ALS algo rithm in recovering the true variable partitioning unveiled by the generated data sets.
Overall, both procedures produce satisfactory results in terms of solution precision, where ALS performs better, and in recovering the true object clusters, in which twostepSDP outperforms ALS approach for data sets with lower sample size and more structure complexity (i.e., error level in the CDPCA model). The proportion of explained variance by the components estimated by both algorithms is affected by the data structure complexity (higher error level, the lower variance) and presents similar values for the two algorithms, except for data sets with two object clusters where the twostepSDP approach yields higher variance. Moreover, experimental tests suggest that the twostepSDP approach, in general, presents more ability to recover the true number of object clusters, while the ALS algorithm is better in terms of quality of object clustering with more homogeneous, compact and well separated clusters in the reduced space of the CDPCA components.
ria.ua.pt

doi

Peer Reviewed
2.
Structural properties of faces of the cone of copositive matrices
Kostyukova, Olga and Tchemisova, Tatiana
Mathematics
MDPI
In this paper, we study the properties of faces and exposed faces of the cone of copositive matrices (copositive cone), paying special attention to issues related to their geometric structure. Based on the concepts of zero and minimal zero vectors, we obtain several explicit representations of faces of the copositive cone and compare them. Given a face of the cone of copositive matrices, we describe the subspace generated by that face and the minimal exposed face containing it. Summarizing the results obtained in the paper, we systematically show what information can be extracted about the given copositive face in the case of incomplete data. Several examples for illustrating the main findings of the paper and also for justifying the usefulness of the developed approach to the study of the facial structure of the copositive cone are discussed.
ria.ua.pt

doi

Peer Reviewed
Proceedings
1.
Behaviour of the oneminute sittostand test during six months in people with COPD
Cabral, Jorge and Afreixo, Vera and Rocha, Vânia and SoutoMiranda, Sara and Marques, Alda
Journal of Statistics on Health Decision
Universidade de Aveiro; Centro Hospitalar do Baixo Vouga
No abstract available.
ria.ua.pt

doi

Peer Reviewed