Publications 2021


Books


122.  Programação matemática

Torres, Delfim Fernando Marado

UA Editora

O termo "programação matemática" refere-se 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 Timor-Leste, 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, procurando-se estimular o desenvolvimento do raciocínio, essencial numa qualquer atividade profissional.

ria.ua.pt

121.  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

120.  Analysis of infectious disease problems (Covid-19) 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 country-wise analysis of Covid-19. 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 integro-differential equations with optimization methods. Probability distribution and their bio-mathematical applications have also been studied. This book is a valuable resource for researchers, scholars, biomathematicians and medical experts.

ria.ua.pt | doi

Book Chapters


119.  State-space 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 state-space 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

118.  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 high-frequency seasonality. How to best model and forecast these patterns has been a long-standing issue in time series analysis. This study presents a comparison of the forecasting performance of TBATS (Trigonometric Seasonal, Box-Cox 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

117.  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

116.  Sustainable development in education: a non-parametric 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 2000-2018). 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 Inter-Agency and Expert Group on Sustainable Development Goal Indicators (E/CN.3/2016/2/Rev.1), Economic and Social Council, United Nations, 1-39, 2016. [2] P. Bogetoft and J. L. Hougaard, Efficiency evaluations based on potential (Non-proportional) improvements, J. Productivity Analysis, 12(3), 233-247, 1999.

ria.ua.pt | doi | Peer Reviewed

115.  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). Considera-se que o termo dos erros segue um processo autorregressivo, AR, e investiga-se 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

114.  Graphic and multimedia design of a narrative-based 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 Magellan-Elcano’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

113.  CNME a math narrative-based 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 COVID-19 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. Non-formal 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

112.  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 afigura-se 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. Adota-se o modelo ARCS (Dempsey & Johnson, 1998) para analisar a motivação dos alunos na aprendizagem, com base em quatro categorias: atenção, relevância, confiança e satisfação. Consideram-se 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

111.  Improving Short-term 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 h-step-ahead 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 6-step-ahead forecasts and in 60.45% considering the 1-step-ahead 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

110.  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

109.  Optimal control of vaccination and plasma transfusion with potential usefulness for Covid-19

Couras, Juliana and Area, Iván and Nieto, Juan J. and Silva, Cristiana J. and Torres, Delfim F. M.

Analysis of infectious disease problems (Covid-19) 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 Covid-19 pandemic.

ria.ua.pt | doi | Peer Reviewed

108.  Modeling the spread of Covid-19 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 (Covid-19) and their global impact

Springer

Nowadays, coronavirus disease 2019 (Covid-19) 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 Covid-19. Here, we propose a delayed mathematical model to predict the epidemiological trend of Covid-19 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

107.  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 non-coincident 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

106.  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 R-function called CDpca. In this work, we review some theoretical issues of the CDPCA model and present two applications on real data sets using the R-function CDpca.

ria.ua.pt | Peer Reviewed

105.  Multivariate sustainability profile of Global Fortune 500 companies using GRI-G4 database

Jiménez-Hernández, Mónica and Vicente-Galindo, Purificación and Tejedor-Flores, 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, HJ-Biplot 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

104.  Math requirements for admission in elementary school teacher education programs: does it matter?

Hall, A. and Alvelos, H. and Xambre, A. R. and Hall, F. and Costa, A. T. and Silva, P.

EDULEARN21 Proceedings

IATED

In Portugal, the initial training of teachers for the first three levels of education (children from 3 to 12 years old) is carried out through a single 3-years undergraduate degree, called Basic Education. This training is completed with a professional master's degree where future teachers choose which levels they will teach. Most master's degrees cover two levels of education: pre-school and 1st cycle or 1st and 2nd cycles. This means that most teachers become qualified to teach the 1st cycle, usually known as elementary school. First cycle teachers teach all educational areas, including mathematics. It is, therefore, essential that they finish their degree in Basic Education with a solid background in Mathematics. Until the academic year 2017-18 there was no mandatory entry requirement in Mathematics to the Basic Education Degree and many students were admitted without having had any Mathematics in secondary education. To ensure a better pre-university training in Mathematics, the Portuguese government imposed an admission exam, as from the academic year 2018-19. This work aims to assess the impact of the government measure on the training of future teachers in the area of mathematics, through the analysis of the performance of students in the 1st year of the Basic Education Degree, from a Portuguese university, in a mathematics course of the 1st semester, over the academic years 2017-18 to 2019-20. The statistical study carried out reveals that there were significant improvements in the results of the students. An analysis of the gender tendency in the choice of the teaching profession was also done and showed that there is a disproportion between men and women in pre-service teachers, since most young people who want to become teachers are female. This study contributes to a better understanding of the impact certain measures and policies can have on the quality of Higher Education academic training. This type of approach can be applied to other similar situations, for other programs and other courses, helping, in this way, decision making in Higher Education admission policies, as well as researchers in this field.

ria.ua.pt | doi | Peer Reviewed

Articles


103.  Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces

Caetano, António and Kempka, Henning

Constructive Approximation

Springer Verlag

We continue the study of the variable exponent Morreyfied Triebel-Lizorkin 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

102.  Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian 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 non-Abelian 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 non-Abelian 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

101.  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 p-adic expansion of the to-be-decoded 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 parity-check 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

100.  Robust formulations for economic lot-sizing 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 lot-sizing 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 min-max 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

99.  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 higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional 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

98.  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

97.  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 integer-valued 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

96.  Fractional model of COVID-19 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 COVID-19 disease is proposed. Special focus has been done on the transmissibility of super-spreaders 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

95.  Spin-induced 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 Gauss-Bonnet invariant $mathcal{G}$ can undergo a spin-induced 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 spin-induced instability threshold is exceeded, while black holes that lie below the threshold are described by the Kerr solution. Our results provide strong support for spin-induced black hole scalarization.

ria.ua.pt | doi | Peer Reviewed

94.  Multipolar boson stars: macroscopic Bose-Einstein 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 Bose-Einstein 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 non-linear solutions, that static (in terms of their spacetime metric, $g_{munu}$) boson stars, composed of a single complex scalar field, $Phi$, can have a non-trivial 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 non-linear Einstein--Klein-Gordon 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

93.  Stability analysis and optimal control of a fractional HIV-AIDS 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 HIV-AIDS 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

92.  Phenomenology of vector-like 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 vector-like fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the state-of-the-art Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vector-like leptons (VLLs) and their possible signatures at CERN’s Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vector-boson 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 Monte-Carlo 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 high-luminosity 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 Run-III 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

91.  Numerical solution of a class of third-kind 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 third-kind 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

90.  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

89.  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

88.  The H-join of arbitrary families of graphs

Cardoso, Domingos M. and Gomes, Helena and Pinheiro, Sofia J

arXiv

The H-join 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 H-join 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 H-join 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 H-join 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

87.  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 Einstein-Maxwell-Scalar models to a higher spin field. The result is an Einstein-Maxwell-Vector model wherein a vector field is non-minimally coupled to the Maxwell invariant by an exponential coupling function. We show that the latter guarantees the circumvention of an associated no-hair 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

86.  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

85.  Modeling and forecasting of COVID-19 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 (COVID-19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID-19 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 well-known SIR compartmental model to deterministic and stochastic time-delayed models in order to predict the epidemiological trend of COVID-19 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 well-posedness of the models and conditions under which the COVID-19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID-19 spreading as well as verification of theoretical results.

ria.ua.pt | doi | Peer Reviewed

84.  Optimal control of the COVID-19 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 Fonseca-Pinto, Rui and Passadouro, Rui and Santos, Estevão Soares dos and Abreu, Wilson and Mira, Jorge

Scientific Reports

Nature Research

The COVID-19 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 COVID-19 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

83.  Spontaneous scalarization of a conducting sphere in Maxwell-scalar 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 Maxwell-scalar 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 Einstein-Maxwell-scalar (generalized scalar-tensor) models. In the Maxwell-scalar case, unlike the black hole cases, closed-form 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 extended-scalar-Gauss-Bonnet 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 scalar-free conducting sphere; but radiative boundary conditions always yield an unstable scalar-free solution and preference for scalarization. Finally, we perform numerical evolution of the full Maxwell-scalar 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

82.  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

81.  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 half-line, 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 half-line. 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

80.  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 long-lived. 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 Reissner-Nordstr"{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

79.  Quasinormal modes of hot, cold and bald Einstein–Maxwell-scalar black holes

Blázquez-Salcedo, 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–Maxwell-scalar models allow for different classes of black hole solutions, depending on the non-minimal 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 (Blázquez-Salcedo 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 scalar-led modes, polar and axial electromagnetic-led modes, and polar and axial gravitational-led modes. We demonstrate that the only unstable mode present is the radial scalar-led mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both mode-stable. The non-trivial 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

78.  Control of COVID-19 dynamics through a fractional-order 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 SARS-CoV-2 virus transmission. Two controls are considered in our model for eradication of the spread of COVID-19: 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

77.  Analysis of Hilfer fractional integro-differential 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 integro-differential 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

76.  On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers

Andrade, Enide and Carrasco-Olivera, Dante and Manzaneda, Cristina

Linear Algebra and its Applications

Elsevier

In this work a new type of matrix called circulant-like matrix is introduced. This type of matrix includes the classical k-circulant 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

75.  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 multi-agent model. The Caputo fractional derivative, in the equations describing the dynamics of a consensus parameter, makes it possible to take into account in the self-organization 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

74.  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 time-varying 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

73.  Optimal leader-following 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 fractional-order derivative determines the impact of the memory during the opinion evolution. The problem of leader-following 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

72.  Optimality conditions for variational problems involving distributed-order 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: distributed-order 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

71.  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 non-linear 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

70.  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 right-sided 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

69.  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

68.  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 self-aware 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 self-aware 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 Hopf-bifurcation when time delays cross critical values. Optimal control theory has been applied for the cost-effectiveness of the delayed system. Numerical simulations illustrate the obtained analytical results.

ria.ua.pt | doi | Peer Reviewed

67.  Two families of locally toroidal regular 4-hypertopes 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 star-shaped 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

66.  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 well-known 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

65.  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

64.  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

63.  Non-dual modal operators as a basis for 4-valued 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 four-valued. 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

62.  A fractional analysis in higher dimensions for the Sturm-Liouville problem

Ferreira, M. and Rodrigues, M. M. and Vieira, N.

Fractional Calculus and Applied Analysis

De Gruyter

In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville 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

61.  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

60.  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

59.  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 integer-valued autoregressive model of order one with periodic time-varying 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 likelihood-based 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

58.  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 low-grade 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 post-surgery, 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 (DuLIP-EP) 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

57.  A dynamically-consistent 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

56.  Pak-Stanley labeling of the m-Catalan hyperplane arrangement

Duarte, Rui and Guedes de Oliveira, António

Advances in Mathematics

Elsevier

We characterize in simple terms the Pak-Stanley labels λ(R) of the regions R of the m-Catalan 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

55.  Generalizações da etiquetagem de Pak-Stanley

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 Pak-Stanley''), 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 afastar-se 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 Pak-Stanley 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

54.  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

53.  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 non-homogeneous time-space-fractional telegraph equation in $n$-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and non-homogeneous 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 Mittag-Leffler function. In the end of the paper some illustrative examples are presented.

ria.ua.pt | doi | Peer Reviewed

52.  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 pest-free 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 pest-free and coexistence equilibria is shown using the Routh–Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pest-free 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

51.  Investigating carbon emissions from electricity generation and GDP nexus using maximum entropy bootstrap: evidence from oil-producing 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 oil-producing 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

50.  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 behaviour-abstractor framework to the case of dynamic logic with binders and silent transitions. As a particular outcome we provide an invariance theorem and show the Hennessy-Milner 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

49.  Mathematical analysis of a fractional COVID-19 model applied to Wuhan, Spain and Portugal

Ndaïrou, Faïçal and Torres, Delfim F. M.

Axioms

MDPI

We propose a qualitative analysis of a recent fractional-order COVID-19 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

48.  GW190521 as a Merger of Proca Stars: A Potential New Vector Boson of 8.7×10^{-13}  eV

Bustillo, Juan Calderón and Sanchis-Gual, Nicolas and Torres-Forné, 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 LIGO-Virgo have reported a short gravitational-wave signal (GW190521) interpreted as a quasicircular merger of black holes, one at least populating the pair-instability 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 pre-merger emission, however, GW190521 merits further investigation of the pre-merger dynamics and even of the very nature of the colliding objects. We show that GW190521 is consistent with numerically simulated signals from head-on 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 gravitational-wave 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

47.  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 multi-soliton 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

46.  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 Sanchis-Gual, 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 self-interacting fields. The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact — i.e., possess LRs — but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions 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 self-interactions, 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

45.  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 shadow-degenerate 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 shadow-degenerate geometries are classified into two classes. The first shadow-equivalent 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 shadow-degenerate class contains spacetimes with different redshift profiles and an explicit family of metrics within this class is presented. In the stationary, axi-symmetric case, we determine a sufficient condition for the metric to be shadow degenerate with Kerr for far-away observers. Again we provide two classes of examples. The first class contains metrics whose constant (Boyer-Lindquist-like) 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 Newman-Janis algorithm. The second class of examples pertains BHs that fail to have the standard north-south $mathbb{Z}_2$ 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

44.  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 non-minimal 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 non-minimal 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 non-Abelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions in a particular Einstein-GB-scalar 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 non-minimally coupled to the GB invariant.

ria.ua.pt | doi | Peer Reviewed

43.  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 Einstein-Klein-Gordon theory with a QCD axion-like potential. They are regular everywhere on and outside the event horizon. The potential is characterised by two parameters: the mass of the axion-like 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 non-linearities 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 non-negligible impact of the self-interactions.

ria.ua.pt | doi | Peer Reviewed

42.  De-singularizing the extremal GMGHS black hole via higher derivatives corrections

Herdeiro, Carlos and Radu, Eugen and Uzawa, Kunihito

Physics Letters B

Elsevier

The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (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 non-linear equations of motion. The de-singularization is supported by the $mathcal{O}(alpha')$-terms. The regularised extremal GMGHS BHs are asymptotically flat, possess a regular (non-zero 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

41.  Multifield, multifrequency bosonic stars and a stabilization mechanism

Sanchis-Gual, 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, ℓ-BSs. As the simplest illustration, we construct the ℓ=1 BSs family, that includes several single-frequency 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 hybrid-ℓ 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) Klein-Gordon 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

40.  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 p-adic expansion of w and particular representations of the parity-check 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 parity-check 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

39.  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 p-median problem, the set covering problem, and the stochastic lot-sizing 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

38.  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 min-max 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 lot-sizing 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 lot-sizing 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 lot-sizing 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

37.  Minimal state-space representation of convolutional product codes

Climent, Joan-Josep and Napp, Diego and Pinto, Raquel and Requena, Verónica

Mathematics

MDPI

In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space 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

36.  GW190521 formation scenarios via relativistic accretion

Cruz-Osorio, Alejandro and Lora-Clavijo, Fabio D. and Herdeiro, Carlos

Journal of Cosmology and Astroparticle Physics

IOP Publishing

The recent gravitational wave transient GW190521 has been interpreted by the LIGO-Virgo 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 so-called pair-instability supernova mass gap. This raises the important question of how and when these progenitors formed. In this paper we use an accretion model with super-Eddington 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 red-shifts z = 100, 50, and 20. We found three distinct possible types of OPs: (i) 10-4 M☉ - 3 M☉ almost non-rotating (with Kerr spin parameter a☆ < 10-2) primordial BHs; (ii) 3M☉ - 40M☉ slowly rotating (10-2 < 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 red-shifts, 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

35.  Variational problems with time delay and higher-order distributed-order 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 higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order 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 well-known results can be obtained as particular cases.

ria.ua.pt | doi | Peer Reviewed

34.  State realizations of 2-periodic convolutional codes: a switching system approach

Fornasini, Ettore and Napp, Diego and Pereira, Ricardo and Pinto, Raquel and Rocha, Paula

IFAC-PapersOnLine

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 state-space realizations of 2-periodic convolutional codes. Although one cannot expect, in general, to obtain a periodic state-space realization of a periodic convolutional code by means of the individual realizations of each of the associated time-invariant 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

33.  Time-fractional 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 time-fractional 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 H-function 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 second-order moment (variance) in the time domain.

ria.ua.pt | doi | Peer Reviewed

32.  On a non-Newtonian 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 non-Newtonian 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 (non-Newtonian) 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 non-Newtonian calculus of variations we introduce here provides a natural framework for problems involving functions with positive images. Our main result is a first-order 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

31.  Hybrid dynamic logic institutions for event/data-based systems

Hennicker, Rolf and Knapp, Alexander and Madeira, Alexandre

Formal Aspects of Computing

Springer

We propose ED-logic as a formal foundation for the specification and development of event-based 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. ED-logic 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 ED-logic is powerful enough to characterise the semantics of an operational specification by a single ED-sentence. Thus the whole (formal) development process for event/data-based systems relies on ED-logic 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

30.  Pontryagin maximum principle for distributed-order fractional systems

Ndaïrou, Faïçal and Torres, Delfim F. M.

Mathematics

MDPI

We consider distributed-order non-local 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 needle-like 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 distributed-order fractional optimal control problems, illustrating its applicability with an example.

ria.ua.pt | doi | Peer Reviewed

29.  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 Schwarzschilld-Melvin 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

28.  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 X-ray 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

27.  Local existence and uniqueness for a fractional SIRS model with Mittag-Leffler 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 Atangana-Baleanu-Caputo (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 Adams-Bashforth-Moulton method.

ria.ua.pt | doi | Peer Reviewed

26.  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 immobile-index-based 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

25.  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 Triebel--Lizorkin 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

24.  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

23.  Analysis of a COVID-19 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 COVID-19. By using the free and open-source 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

22.  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 posicionarem-se 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

21.  An empirical comparison of two approaches for CDPCA in high-dimensional 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 high-dimensional 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 step-SDP 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 two-step-SDP algorithm: it provides faster results than ALS and, since it employs a clustering procedure (k-means) 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 two-step-SDP 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 two-step-SDP approach yields higher variance. Moreover, experimental tests suggest that the two-step-SDP 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

20.  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

19.  Hybrid method for simulation of a fractional COVID-19 model with real case application

Din, Anwarud and Khan, Amir and Zeb, Anwar and Ammi, Moulay Rchid Sidi and Tilioua, Mouhcine and Torres, Delfim F. M.

Axioms

MDPI

In this research, we provide a mathematical analysis for the novel coronavirus responsible for COVID-19, which continues to be a big source of threat for humanity. Our fractional-order analysis is carried out using a non-singular kernel type operator known as the Atangana-Baleanu-Caputo (ABC) derivative. We parametrize the model adopting available information of the disease from Pakistan in the period 9 April to 2 June 2020. We obtain the required solution with the help of a hybrid method, which is a combination of the decomposition method and the Laplace transform. Furthermore, a sensitivity analysis is carried out to evaluate the parameters that are more sensitive to the basic reproduction number of the model. Our results are compared with the real data of Pakistan and numerical plots are presented at various fractional orders.

ria.ua.pt | doi | Peer Reviewed

18.  Traversable wormholes in Einstein-Dirac-Maxwell theory

Blázquez-Salcedo, Jose Luis and Knoll, Christian and Radu, Eugen

Physical Review Letters

American Physical Society

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordström black holes. They also possess a finite mass M and electric charge Q_{e}, with Q_{e}/M>1. An exact wormhole solution with ungauged, massless fermions is also reported.

ria.ua.pt | doi | Peer Reviewed

17.  An exact robust approach for the integrated berth allocation and quay crane scheduling problem under uncertain arrival times

Rodrigues, Filipe and Agra, Agostinho

European Journal of Operational Research

Elsevier

We consider an integrated berth allocation and quay crane assignment and scheduling problem where the arrival times of the vessels may be affected by uncertainty. The problem is modelled as a two-stage robust mixed integer program where the berth allocation decisions are taken before the exact arrival times are known, and the crane assignment and scheduling operations are adjusted to the arrival times. To solve the robust two-stage model, we follow a decomposition algorithm that decomposes the problem into a master problem and a separation problem. A new scenario reduction procedure for solving the separation problem is proposed as well as a warm start technique for reducing the number of iterations performed by the decomposition algorithm. To scale the proposed decomposition algorithm for large size instances, it is combined with a rolling horizon heuristic.The efficiency and effectiveness of the proposed algorithms are demonstrated through extensive computational experiments carried out on randomly generated instances with both homogeneous and heterogeneous cranes as well as on instances from the literature.

ria.ua.pt | doi | Peer Reviewed

16.  Method of nose stretching in Newton's problem of minimal resistance

Plakhov, Alexander

Nonlinearity

IOP Publishing

We consider the problem $infbig{ int!!int_Omega (1 + |nabla u(x_1,x_2)|^2)^{-1} dx_1 dx_2 : text{ the function } u : Omega to mathbb{R} text{ is concave and } 0 le u(x) le M text{ for all } x = (x_1, x_2) in Omega ={ |x| le 1 } , big}$ (Newton's problem) and its generalizations. In the paper by Brock, Ferone, and Kawohl (1996) it is proved that if a solution $u$ is $C^2$ in an open set $mathcal{U} subset Omega$ then $det D^2u = 0$ in $mathcal{U}$. It follows that graph$(u)rfloor_mathcal{U}$ does not contain extreme points of the subgraph of $u$. In this paper we prove a somewhat stronger result. Namely, there exists a solution $u$ possessing the following property. If $u$ is $C^1$ in an open set $mathcal{U} subset Omega$ then graph$(urfloor_mathcal{U})$ does not contain extreme points of the convex body $C_u = { (x,z) :, x in Omega, 0 le z le u(x) }$. As a consequence, we have $C_u = text{rm Conv} (overline{text{rm Sing$C_u$}})$, where Sing$C_u$ denotes the set of singular points of $partial C_u$. We prove a similar result for a generalization of Newton's problem.

ria.ua.pt | doi | Peer Reviewed

15.  Approximate iterative method for initial value problem of impulsive fractional differential equations with generalized proportional fractional derivatives

Agarwal, Ravi P. and Hristova, Snezhana and O’Regan, Donal and Almeida, Ricardo

Mathematics

MDPI

The main aim of the paper is to present an algorithm to solve approximately initial value problems for a scalar non-linear fractional differential equation with generalized proportional fractional derivative on a finite interval. The main condition is connected with the one sided Lipschitz condition of the right hand side part of the given equation. An iterative scheme, based on appropriately defined mild lower and mild upper solutions, is provided. Two monotone sequences, increasing and decreasing ones, are constructed and their convergence to mild solutions of the given problem is established. In the case of uniqueness, both limits coincide with the unique solution of the given problem. The approximate method is based on the application of the method of lower and upper solutions combined with the monotone-iterative technique.

ria.ua.pt | doi | Peer Reviewed

14.  On generalized Newton's aerodynamic problem

Plakhov, Alexander

Transactions of the Moscow Mathematical Society

American Mathematical Society

We consider the generalized Newton's least resistance problem for convex bodies: minimize the functional $int!!int_Omega (1 + |nabla u(x,y)|^2)^{-1} dx, dy$ in the class of concave functions $u: Omega to [0,M]$, where the domain $Omega subset mathbb{R}^2$ is convex and bounded and $M > 0$. It has been known cite{BFK} that if $u$ solves the problem then $|nabla u(x,y)| ge 1$ at all regular points $(x,y)$ such that $u(x,y) < M$. We prove that if the upper level set $L = { (x,y): u(x,y) = M }$ has nonempty interior, then for almost all points of its boundary $(bar x, bar y) in pl L$ one has $lim_{stackrel{(x,y)to(bar x,bar y)}{u(x,y)

ria.ua.pt | Peer Reviewed

13.  Synchronization of Caputo fractional neural networks with bounded time variable delays

Almeida, Ricardo and Hristova, Snezhana and Tersian, Stepan

Open Mathematics

De Gruyter Open

One of the main problems connected with neural networks is synchronization. We examine a model of a neural network with time-varying delay and also the case when the connection weights (the influential strength of the jth neuron to the ith neuron) are variable in time and unbounded. The rate of change of the dynamics of all neurons is described by the Caputo fractional derivative. We apply Lyapunov functions and the Razumikhin method to obtain some sufficient conditions to ensure synchronization in the model. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. We illustrate our theory with a particular nonlinear neural network.

ria.ua.pt | doi | Peer Reviewed

12.  On systems of fractional differential equations with the ψ‐Caputo derivative and their applications

Almeida, Ricardo and Malinowska, Agnieszka B. and Odzijewicz, Tatiana

Mathematical Methods in the Applied Sciences

Wiley

Systems of fractional differential equations with a general form of fractional derivative are considered. A unique continuous solution is derived using the Banach fixed point theorem. Additionally, the dependence of the solution on the fractional order and on the initial conditions are studied. Then the stability of autonomous linear fractional differential systems with order 0<α<1 of the ψ-Caputo derivative is investigated. Finally, an application of the theoretical results to the problem of the leader-follower consensus for fractional multi-agent systems is presented. Sufficient conditions are given to ensure that the tracking errors asymptotically converge to zero. The results of the paper are illustrated by some examples.

ria.ua.pt | doi | Peer Reviewed

11.  Global stability condition for the disease-free equilibrium point of fractional epidemiological models

Almeida, Ricardo and Martins, Natália and Silva, Cristiana J.

Axioms

MDPI

In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.

ria.ua.pt | doi | Peer Reviewed

10.  Evacuation by leader-follower model with bounded confidence and predictive mechanisms

Almeida, Ricardo and Girejko, Ewa and Machado, Luís and Malinowska, Agnieszka B. and Martins, Natália

Archives of Control Sciences

Polskiej Akademii Nauk

This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.

ria.ua.pt | doi | Peer Reviewed

9.  Non-instantaneous impulsive fractional differential equations with state dependent delay and practical stability

Agarwal, Ravi and Almeida, Ricardo and Hristova, Snezhana and O’Regan, Donal

Acta Mathematica Scientia

Springer

Nonlinear delay Caputo fractional differential equations with non-instantaneous impulses are studied and we consider the general case of delay, depending on both the time and the state variable. The case when the lower limit of the Caputo fractional derivative is fixed at the initial time, and the case when the lower limit of the fractional derivative is changed at the end of each interval of action of the impulse are studied. Practical stability properties, based on the modified Razumikhin method are investigated. Several examples are given in this paper to illustrate the results.

ria.ua.pt | doi | Peer Reviewed

8.  CP violating hW+W− coupling in the standard model and beyond

Huang, Da and Morais, António P. and Santos, Rui

Journal of High Energy Physics

Springer Verlag

Inspired by the recent development in determining the property of the observed Higgs boson, we explore the CP-violating (CPV) −

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