Books
56.
Programação matemática
Torres, Delfim Fernando Marado
UA Editora
O termo "programação matemática" referese ao estudo de problemas de otimização, em que se procura minimizar ou maximizar uma função através da escolha dos valores de variáveis dentro de um determinado conjunto admissível. Em problemas de engenharia, administração, logística, transporte, economia, biologia, medicina ou outras ciências, quando se consegue construir modelos matemáticos representativos dos respetivos sistemas dinâmicos em estudo, é possível aplicar as técnicas matemáticas de otimização para maximizar ou minimizar uma função previamente definida como índice de desempenho ou performance, visando encontrar uma "solução" do problema, isto é, os valores das variáveis que resultem no melhor desempenho possível do sistema, segundo o tal critério previamente definido. O livro "Programação Matemática" é uma obra introdutória, de natureza pedagógica, e que está escrito de uma forma sucinta, clara e rigorosa. Serve de suporte à unidade curricular com o mesmo nome do Departamento de Matemática da Universidade de Aveiro, que tem sido lecionada a alunos provenientes de várias licenciaturas (de Matemática, Física, Economia e Engenharia), oriundos de diversas universidades portuguesas, dos PALOP, Brasil e TimorLeste, assim como de vários países europeus por intermédio do programa Erasmus. Pretende fornecer uma formação básica, mas sólida, em otimização não linear e, em simultâneo, estimular a utilização de tais modelos e resultados na resolução de problemas práticos. Estão incluídos os conceitos essenciais de programação matemática, que alguém que deseje prosseguir estudos na área de otimização deve conhecer e dominar. Os conteúdos são acompanhados de exemplos e exercícios, com o intuito de se desenvolver a capacidade de aplicação dos conceitos matemáticos envolvidos. As demonstrações dos resultados apresentados são dadas com todo o rigor, procurandose estimular o desenvolvimento do raciocínio, essencial numa qualquer atividade profissional.
ria.ua.pt
55.
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
Book Chapters
54.
Statespace estimation using the behavioral approach: a simple particular case
Ntogramatzidis, Lorenzo and Pereira, Ricardo and Rocha, Paula
CONTROLO 2020. Lecture Notes in Electrical Engineering
Springer
In this paper we apply the behavioral estimation theory developed in Ntogramatzidis et al. (2020) to the particular case of statespace systems. We derive new necessary and sufficient conditions for the solvability of the estimation problem in the presence of disturbances, and provide a method to construct an estimator in case the problem is solvable. This is a first step to investigate how our previous results, derived within the more general behavioral context, compare with the results from classical state space theory.
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53.
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.
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52.
Sustainable development in education: a nonparametric analysis
Murillo, Kelly and Rocha, Eugénio
INTED2021 Proceedings
IATED
The SDGs (Sustainable Development Goals) are a universal call to action to end poverty, protect the planet and improve the lives and prospects of everyone, everywhere. In 2015 all UN Member States, adopted the 2030 Agenda for the SDG, which comprises an action plan for people, the planet and prosperity with 17 objectives covering the economic, social and environmental dimensions, [1]. SDG 4 is the goal of quality education with made up of 10 targets to ensure an inclusive and equitable quality education and to promote lifelong learning opportunities for all. In this sense, it is expected that all countries increasing the number of young people and adults with relevant professional skills, decent jobs, entrepreneurship, eliminating gender and income disparities in access to education.
This article examines the quality of education in 17 European countries using a model nonparametric deterministic for measuring efficiency based on MEA (Multidirectional Efficiency Analysis) [2], in combination with other mathematical techniques (such as accumulated effort and group indicator), during seven years (every three years from 20002018). To this end, we analyze the countries evolution at three distinct efficiency stages: levels, patterns and determinants. The study is based on the EU's set of indicators to monitor progress towards the UN SDGs: basic education (early leavers from education and training, participation in early childhood education and achievement in reading, mathematic or science), tertiary education (tertiary education attainment and employment rates of recent graduates) and adult learning (adult participation in learning).
This study allows us to address questions such as: To what extent are European countries improving education quality? Which European countries have significant advances / setbacks over time? What factors are intervening in the process of the countries that are most efficient and least efficient? In other words, our results clarify which are the profiles of the countries that are most efficient, giving some insight about the improvements which could be applied in the less efficient to raise their efficiency, in view of reaching the proposed objectives for the year 2030.
References:
[1] Report of the InterAgency and Expert Group on Sustainable Development Goal Indicators (E/CN.3/2016/2/Rev.1), Economic and Social Council, United Nations, 139, 2016.
[2] P. Bogetoft and J. L. Hougaard, Efficiency evaluations based on potential
(Nonproportional) improvements, J. Productivity Analysis, 12(3), 233247, 1999.
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51.
Análise de regressão linear com autocorrelação nos erros para dados censurados
Sousa, Rodney and Pereira, Isabel and Silva, Maria Eduarda
Estatística: desafios transversais às ciências com dados: atas do XXIV Congresso da Sociedade Portuguesa de Estatística
Sociedade Portuguesa de Estatística
Este trabalho aborda, numa perspetiva bayesiana, a análise
de modelos de regressão linear com erros autocorrelacionados
para dados censurados, recorrendo a métodos Computacionais Bayesianos
Aproximados (ABC) e ao amostrador de Gibbs com a Ampliação
de Dados (GDA). Considerase que o termo dos erros segue
um processo autorregressivo, AR, e investigase o desempenho dos
métodos através de dois estudos de simulação com diferentes cenários
de censura (5%, 20% e 40%) e dimensão de amostras (50, 100 e
500). Os resultados indicam que o método GDA é consistente Bayesiano,
mesmo em cenários em que a proporção de valores censurados
é elevada, enquanto que no método ABC, as estimativas dependem
fortemente das distribuições a priori.
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Peer Reviewed
Articles
50.
Matrix biorthogonal polynomials: eigenvalue problems and nonAbelian discrete Painlevé equations: a Riemann–Hilbert problem perspective
Branquinho, Amílcar and Moreno, Ana Foulquié and Mañas, Manuel
Journal of Mathematical Analysis and Applications
Elsevier
In this paper we use the Riemann–Hilbert problem, with jumps supported on appropriate curves in the complex plane, for matrix biorthogonal polynomials and apply it to find Sylvester systems of differential equations for the orthogonal polynomials and its second kind functions as well. For this aim, Sylvester type differential Pearson equations for the matrix of weights are shown to be instrumental. Several applications are given, in order of increasing complexity. First, a general discussion of nonAbelian Hermite biorthogonal polynomials on the real line, understood as those whose matrix of weights is a solution of a Sylvester type Pearson equation with coefficients first degree matrix polynomials, is given. All of these are applied to the discussion of possible scenarios leading to eigenvalue problems for second order linear differential operators with matrix eigenvalues. Nonlinear matrix difference equations are discussed next. Firstly, for the general Hermite situation a general non linear relation (non trivial because of the non commutativity features of the setting) for the recursion coefficients is gotten. In the next case of higher difficulty, degree two polynomials are allowed in the Pearson equation, but the discussion is simplified by considering only a left Pearson equation. In the case, the support of the measure is on an appropriate branch of a hyperbola. The recursion coefficients are shown to fulfill a nonAbelian extension of the alternate discrete Painlevé I equation. Finally, a discussion is given for the case of degree three polynomials as coefficients in the left Pearson equation characterizing the matrix of weights. However, for simplicity only odd polynomials are allowed. In this case, a new and more general matrix extension of the discrete Painlevé I equation is found.
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49.
A matrix based list decoding algorithm for linear codes over integer residue rings
Napp, Diego and Pinto, Raquel and Saçıkara, Elif and Toste, Marisa
Linear Algebra and its Applications
Elsevier
In this paper we address the problem of list decoding of linear codes over an integer residue ring Zq, where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Zpr , called the standard form, and the padic expansion of the tobedecoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Zpr . From the paritycheck matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p^{r−1}Zpr .
This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal.
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48.
Robust formulations for economic lotsizing problem with remanufacturing
Attila, Öykü Naz and Agra, Agostinho and Akartunalı, Kerem and Arulselvan, Ashwin
European Journal of Operational Research
Elsevier
In this paper, we consider a lotsizing problem with the remanufacturing option under parameter uncertainties imposed on demands and returns. Remanufacturing has recently been a fast growing area of interest for many researchers due to increasing awareness on reducing waste in production environments, and in particular studies involving remanufacturing and parameter uncertainties simultaneously are very scarce in the literature. We first present a minmax decomposition approach for this problem, where decision maker’s problem and adversarial problem are treated iteratively. Then, we propose two novel extended reformulations for the decision maker’s problem, addressing some of the computational challenges. An original aspect of the reformulations is that they are applied only to the latest scenario added to the decision maker’s problem. Then, we present an extensive computational analysis, which provides a detailed comparison of the three formulations and evaluates the impact of key problem parameters. We conclude that the proposed extended reformulations outperform the standard formulation for a majority of the instances. We also provide insights on the impact of the problem parameters on the computational performance.
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47.
Discrete Hardy spaces for bounded domains in Rn
Cerejeiras, Paula and Kähler, Uwe and Legatiuk, Anastasiia and Legatiuk, Dmitrii
Complex Analysis and Operator Theory
Springer; Birkhäuser
Discrete function theory in higherdimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as halfspace, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higherdimensional function theory to the case of arbitrary bounded domains in R^n. On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.
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46.
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.
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45.
Fractional model of COVID19 applied to Galicia, Spain and Portugal
Ndaïrou, Faïçal and Area, Iván and Nieto, Juan J. and Silva, Cristiana J. and Torres, Delfim F. M.
Chaos, Solitons & Fractals
Elsevier
A fractional compartmental mathematical model for the spread of the COVID19
disease is proposed. Special focus has been done on the transmissibility of
superspreaders individuals. Numerical simulations are shown for data of
Galicia, Spain, and Portugal. For each region, the order of the Caputo
derivative takes a different value, that is not close to one, showing the
relevance of considering fractional models.
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44.
Spininduced scalarized black holes
Herdeiro, Carlos A. R. and Radu, Eugen and Silva, Hector O. and Sotiriou, Thomas P. and Yunes, Nicolás
Physical Review Letters
American Physical Society
It was recently shown that a scalar field suitably coupled to the
GaussBonnet invariant $mathcal{G}$ can undergo a spininduced linear
tachyonic instability near a Kerr black hole. This instability appears only
once the dimensionless spin $j$ is sufficiently large, that is, $j gtrsim
0.5$. A tachyonic instability is the hallmark of spontaneous scalarization.
Focusing, for illustrative purposes, on a class of theories that do exhibit
this instability, we show that stationary, rotating black hole solutions do
indeed have scalar hair once the spininduced instability threshold is
exceeded, while black holes that lie below the threshold are described by the
Kerr solution. Our results provide strong support for spininduced black hole
scalarization.
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43.
Multipolar boson stars: macroscopic BoseEinstein condensates akin to hydrogen orbitals
Herdeiro, C. A. R. and Kunz, J. and Perapechka, I. and Radu, E. and Shnir, Ya.
Physics Letters B
Elsevier
Boson stars are often described as macroscopic BoseEinstein condensates. By
accommodating large numbers of bosons in the same quantum state, they
materialize macroscopically the intangible probability density cloud of a
single particle in the quantum world. We take this interpretation of boson
stars one step further. We show, by explicitly constructing the fully
nonlinear solutions, that static (in terms of their spacetime metric,
$g_{munu}$) boson stars, composed of a single complex scalar field, $Phi$,
can have a nontrivial multipolar structure, yielding the same morphologies for
their energy density as those that elementary hydrogen atomic orbitals have for
their probability density. This provides a close analogy between the elementary
solutions of the nonlinear EinsteinKleinGordon theory, denoted
$Phi_{(N,ell,m)}$, which could be realized in the macrocosmos, and those of
the linear Schr"odinger equation in a Coulomb potential, denoted
$Psi_{(N,ell,m)}$, that describe the microcosmos. In both cases, the
solutions are classified by a triplet of quantum numbers $(N,ell,m)$. In the
gravitational theory, multipolar boson stars can be interpreted as individual
bosonic lumps in equilibrium; remarkably, the (generic) solutions with $mneq
0$ describe gravitating solitons $[g_{munu},Phi_{(N,ell,m)}]$ without any
continuous symmetries. Multipolar boson stars analogue to hybrid orbitals are
also constructed.
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42.
Stability analysis and optimal control of a fractional HIVAIDS epidemic model with memory and general incidence rate
Boukhouima, Adnane and Lotfi, El Mehdi and Mahrouf, Marouane and Rosa, Silvério and Torres, Delfim F. M. and Yousfi, Noura
The European Physical Journal Plus
Springer Verlag; EDP Sciences; Società Italiana di Fisica
We investigate the celebrated mathematical SICA model but using fractional differential equations in order to better describe the dynamics of HIVAIDS infection. The infection process is modelled by a general functional response, and the memory effect is described by the Caputo fractional derivative. Stability and instability of equilibrium points are determined in terms of the basic reproduction number. Furthermore, a fractional optimal control system is formulated and the best strategy for minimizing the spread of the disease into the population is determined through numerical simulations based on the derived necessary optimality conditions.
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41.
Phenomenology of vectorlike leptons with Deep Learning at the Large Hadron Collider
Freitas, Felipe F. and Gonçalves, João and Morais, António P. and Pasechnik, Roman
Journal of High Energy Physics
Springer Verlag
In this paper, a model inspired by Grand Unification principles featuring three generations of vectorlike fermions, new Higgs doublets and a rich neutrino sector at the low scale is presented. Using the stateoftheart Deep Learning techniques we perform the first phenomenological analysis of this model focusing on the study of new charged vectorlike leptons (VLLs) and their possible signatures at CERN’s Large Hadron Collider (LHC). In our numerical analysis we consider signal events for vectorboson fusion and VLL pair production topologies, both involving a final state containing a pair of charged leptons of different flavor and two sterile neutrinos that provide a missing energy. We also consider the case of VLL single production where, in addition to a pair of sterile neutrinos, the final state contains only one charged lepton. We propose a novel method to identify missing transverse energy vectors by comparing the detector response with MonteCarlo simulated data. All calculated observables are provided as data sets for Deep Learning analysis, where a neural network is constructed, based on results obtained via an evolutive algorithm, whose objective is to maximise either the accuracy metric or the Asimov significance for different masses of the VLL. Taking into account the effect of the three analysed topologies, we have found that the combined significance for the observation of new VLLs at the highluminosity LHC can range from 5.7σ, for a mass of 1.25 TeV, all the way up to 28σ if the VLL mass is 200 GeV. We have also shown that by the end of the LHC RunIII a 200 GeV VLL can be excluded with a confidence of 8.8 standard deviations. The results obtained show that our model can be probed well before the end of the LHC operations and, in particular, providing important phenomenological information to constrain the energy scale at which new gauge symmetries emergent from the considered Grand Unification picture can be manifest.
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40.
Numerical solution of a class of thirdkind Volterra integral equations using Jacobi wavelets
Nemati, S. and Lima, Pedro M. and Torres, Delfim F. M.
Numerical Algorithms
Springer
We propose a spectral collocation method, based on the generalized Jacobi wavelets along with the Gauss–Jacobi quadrature formula, for solving a class of thirdkind Volterra integral equations. To do this, the interval of integration is first transformed into the interval [− 1, 1], by considering a suitable change of variable. Then, by introducing special Jacobi parameters, the integral part is approximated using the Gauss–Jacobi quadrature rule. An approximation of the unknown function is considered in terms of Jacobi wavelets functions with unknown coefficients, which must be determined. By substituting this approximation into the equation, and collocating the resulting equation at a set of collocation points, a system of linear algebraic equations is obtained. Then, we suggest a method to determine the number of basis functions necessary to attain a certain precision. Finally, some examples are included to illustrate the applicability, efficiency, and accuracy of the new scheme.
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39.
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.
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38.
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).
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37.
The Hjoin of arbitrary families of graphs
Cardoso, Domingos M. and Gomes, Helena and Pinheiro, Sofia J
arXiv
The Hjoin of a family of graphs G = {G1, . . . , Gp}, also called the generalized
composition, H[G1, . . . , Gp], where all graphs are undirected, simple and finite, is
the graph obtained from the graph H replacing each vertex i of H by Gi and adding
to the edges of all graphs in G the edges of the join Gi ∨ Gj , for every edge ij of H.
Some well known graph operations are particular cases of the Hjoin of a family of
graphs G as it is the case of the lexicographic product (also called composition) of
two graphs H and G, H[G], which coincides with the Hjoin of family of graphs G
where all the graphs in G are isomorphic to a fixed graph G.
So far, the known expressions for the determination of the entire spectrum of the
Hjoin in terms of the spectra of its components and an associated matrix are
limited to families of regular graphs. In this paper, we extend such a determination
to families of arbitrary graphs.
ria.ua.pt
36.
Spontaneous vectorization of electrically charged black holes
Oliveira, João M. S. and Pombo, Alexandre M.
Physical Review D
In this work, we generalise the spontaneous scalarization phenomena in EinsteinMaxwellScalar
models to a higher spin field. The result is an EinsteinMaxwellVector model wherein a vector field
is nonminimally coupled to the Maxwell invariant by an exponential coupling function. We show that
the latter guarantees the circumvention of an associated nohair theorem when the vector field has the
form of an electric field. Different than its scalar counterpart, the new spontaneously vectorized ReissnerNordstr¨om (RN) black holes are, always, undercharged while being entropically preferable. The solution
profile and domain of existence are presented and analysed.
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35.
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.
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34.
Modeling and forecasting of COVID19 spreading by delayed stochastic differential equations
Mahrouf, Marouane and Boukhouima, Adnane and Zine, Houssine and Lotfi, El Mehdi and Torres, Delfim F. M. and Yousfi, Noura
Axioms
MDPI
The novel coronavirus disease (COVID19) pneumonia has posed a great threat to the world recent months by causing many deaths and enormous economic damage worldwide. The first case of COVID19 in Morocco was reported on 2 March 2020, and the number of reported cases has increased day by day. In this work, we extend the wellknown SIR compartmental model to deterministic and stochastic timedelayed models in order to predict the epidemiological trend of COVID19 in Morocco and to assess the potential role of multiple preventive measures and strategies imposed by Moroccan authorities. The main features of the work include the wellposedness of the models and conditions under which the COVID19 may become extinct or persist in the population. Parameter values have been estimated from real data and numerical simulations are presented for forecasting the COVID19 spreading as well as verification of theoretical results.
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33.
Optimal control of the COVID19 pandemic: controlled sanitary deconfinement in Portugal
Silva, Cristiana J. and Cruz, Carla and Torres, Delfim F. M. and Muñuzuri, Alberto P. and Carballosa, Alejandro and Area, Iván and Nieto, Juan J. and FonsecaPinto, Rui and Passadouro, Rui and Santos, Estevão Soares dos and Abreu, Wilson and Mira, Jorge
Scientific Reports
Nature Research
The COVID19 pandemic has forced policy makers to decree urgent confinements
to stop a rapid and massive contagion. However, after that stage, societies are
being forced to find an equilibrium between the need to reduce contagion rates
and the need to reopen their economies. The experience hitherto lived has
provided data on the evolution of the pandemic, in particular the population
dynamics as a result of the public health measures enacted. This allows the
formulation of forecasting mathematical models to anticipate the consequences
of political decisions. Here we propose a model to do so and apply it to the
case of Portugal. With a mathematical deterministic model, described by a
system of ordinary differential equations, we fit the real evolution of
COVID19 in this country. After identification of the population readiness to
follow social restrictions, by analyzing the social media, we incorporate this
effect in a version of the model that allow us to check different scenarios.
This is realized by considering a Monte Carlo discrete version of the previous
model coupled via a complex network. Then, we apply optimal control theory to
maximize the number of people returning to "normal life" and minimizing the
number of active infected individuals with minimal economical costs while
warranting a low level of hospitalizations. This work allows testing various
scenarios of pandemic management (closure of sectors of the economy,
partial/total compliance with protection measures by citizens, number of beds
in intensive care units, etc.), ensuring the responsiveness of the health
system, thus being a public health decision support tool.
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32.
Spontaneous scalarization of a conducting sphere in Maxwellscalar models
Herdeiro, Carlos A. R. and Ikeda, Taishi and Minamitsuji, Masato and Nakamura, Tomohiro and Radu, Eugen
Physical Review D
American Physical Society
We study the spontaneous scalarization of a standard conducting charged sphere embedded in Maxwellscalar models in flat spacetime, wherein the scalar field
ϕ
is nonminimally coupled to the Maxwell electrodynamics. This setup serves as a toy model for the spontaneous scalarization of charged (vacuum) black holes in EinsteinMaxwellscalar (generalized scalartensor) models. In the Maxwellscalar case, unlike the black hole cases, closedform solutions exist for the scalarized configurations. We compute these configurations for three illustrations of nonminimal couplings: one that exactly linearizes the scalar field equation, and the remaining two that produce nonlinear continuations of the first one. We show that the former model leads to a runaway behavior in regions of the parameter space and neither the Coulomb nor the scalarized solutions are stable in the model; but the latter models can heal this behavior producing stable scalarized solutions that are dynamically preferred over the Coulomb one. This parallels reports on black hole scalarization in the extendedscalarGaussBonnet models. Moreover, we analyze the impact of the choice of the boundary conditions on the scalarization phenomenon. Dirichlet and Neumann boundary conditions accommodate both (linearly) stable and unstable parameter space regions, for the scalarfree conducting sphere; but radiative boundary conditions always yield an unstable scalarfree solution and preference for scalarization. Finally, we perform numerical evolution of the full Maxwellscalar system, following dynamically the scalarization process. They confirm the linear stability analysis and reveal that the scalarization phenomenon can occur in qualitatively distinct ways.
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31.
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.
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30.
New convolutions with Hermite weight functions
Castro, Luís Pinheiro and Silva, Anabela Sousa and Tuan, Nguyen Minh
Bulletin of the Iranian Mathematical Society
Springer
In this paper, we are working with convolutions on the positive halfline, for Lebesgue
integrable functions. Six new convolutions are introduced. Factorization identities for
these convolutions are derived, upon the use of Fourier sine and cosine transforms and
Hermite functions. Such convolutions allowus to consider systems of convolution type
equations on the halfline. Using two different methods, such systems of convolution
integral equations will be analyzed. Conditions for their solvability will be considered
and, under such conditions, their solutions are obtained.
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29.
Black holes, stationary clouds and magnetic fields
Santos, Nuno M. and Herdeiro, Carlos A. R.
Physics Letters B
Elsevier
As the electron in the hydrogen atom, a bosonic field can bind itself to a
black hole occupying a discrete infinite set of states. When (i) the spacetime
is prone to superradiance and (ii) a confinement mechanism is present, some of
such states are infinitely longlived. These equilibrium configurations, known
as stationary clouds, are states "synchronized" with a rotating black hole's
event horizon. For most, if not all, stationary clouds studied in the
literature so far, the requirements (i)(ii) are independent of each other.
However, this is not always the case. This paper shows that massless neutral
scalar fields can form stationary clouds around a ReissnerNordstr"{o}m black
hole when both are subject to a uniform magnetic field. The latter
simultaneously enacts both requirements by creating an ergoregion (thereby
opening up the possibility of superradiance) and trapping the scalar field in
the black hole's vicinity. This leads to some novel features, in particular,
that only black holes with a subset of the possible charge to mass ratios can
support stationary clouds.
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28.
Quasinormal modes of hot, cold and bald Einstein–Maxwellscalar black holes
BlázquezSalcedo, Jose Luis and Herdeiro, Carlos A. R. and Kahlen, Sarah and Kunz, Jutta and Pombo, Alexandre M. and Radu, Eugen
The European Physical Journal C
SpringerOpen
Einstein–Maxwellscalar models allow for different classes of black hole solutions, depending on the nonminimal coupling function f(ϕ) employed, between the scalar field and the Maxwell invariant. Here, we address the linear mode stability of the black hole solutions obtained recently for a quartic coupling function, f(ϕ)=1+αϕ4 (BlázquezSalcedo et al. in Phys. Lett. B 806:135493, 2020). Besides the bald Reissner–Nordström solutions, this coupling allows for two branches of scalarized black holes, termed cold and hot, respectively. For these three branches of black holes we calculate the spectrum of quasinormal modes. It consists of polar scalarled modes, polar and axial electromagneticled modes, and polar and axial gravitationalled modes. We demonstrate that the only unstable mode present is the radial scalarled mode of the cold branch. Consequently, the bald Reissner–Nordström branch and the hot scalarized branch are both modestable. The nontrivial scalar field in the scalarized background solutions leads to the breaking of the degeneracy between axial and polar modes present for Reissner–Nordström solutions. This isospectrality is only slightly broken on the cold branch, but it is strongly broken on the hot branch.
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27.
Control of COVID19 dynamics through a fractionalorder model
Bushnaq, Samia and Saeed, Tareq and Torres, Delfim F. M. and Zeb, Anwar
Alexandria Engineering Journal
Elsevier
We investigate, through a fractional mathematical model, the effects of
physical distance on the SARSCoV2 virus transmission. Two controls are
considered in our model for eradication of the spread of COVID19: media
education, through campaigns explaining the importance of social distancing,
use of face masks, etc., towards all population, while the second one is
quarantine social isolation of the exposed individuals. A general fractional
order optimal control problem, and associated optimality conditions of
Pontryagin type, are discussed, with the goal to minimize the number of
susceptible and infected while maximizing the number of recovered. The
extremals are then numerically obtained.
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26.
Analysis of Hilfer fractional integrodifferential equations with almost sectorial operators
Karthikeyan, Kulandhaivel and Debbouche, Amar and Torres, Delfim F. M.
Fractal and Fractional
MDPI
In this work, we investigate a class of nonlocal integrodifferential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder’s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.
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25.
On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers
Andrade, Enide and CarrascoOlivera, Dante and Manzaneda, Cristina
Linear Algebra and its Applications
Elsevier
In this work a new type of matrix called circulantlike matrix is introduced. This type of matrix includes the classical kcirculant matrix, introduced in [4], in a natural sense. Its eigenvalues and its inverse and some other properties are studied, namely, it is shown that the inverse of a matrix of this type is also a matrix of this type and that its first row is the unique solution of a certain system of linear equations. Additionally, for some of these matrices whose entries are written as function of Horadam, Fibonacci, Jacobsthal and Pell numbers we study its eigenvalues and write it as function of those numbers. Moreover, the same study is done if the entries are arithmetic sequences.
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24.
On the necessary optimality conditions for the fractional Cucker–Smale optimal control problem
Almeida, Ricardo and Kamocki, Rafał and Malinowska, Agnieszka B. and Odzijewicz, Tatiana
Communications in Nonlinear Science and Numerical Simulation
Elsevier
This paper develops a sparse flocking control for the fractional Cucker–Smale multiagent
model. The Caputo fractional derivative, in the equations describing the dynamics of a consensus parameter, makes it possible to take into account in the selforganization of group
its history and memory dependency. External control is designed based on necessary conditions for a local solution to the appropriate optimal control problem. Numerical simulations demonstrate the effectiveness of the control scheme.
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Peer Reviewed
23.
Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input
Almeida, R. and Hristova, S. and Dashkovskiy, S.
International Journal of Robust and Nonlinear Control
Wiley
The bounded input bounded output (BIBO) stability for a nonlinear Caputo
fractional system with timevarying bounded delay and nonlinear output is
studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input
bounded output stability criteria are derived. Also, explicit and independent on
the initial time bounds of the output are provided. Uniform BIBO stability and
uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system’s dynamic response, and demonstrate the
effectiveness of our theoretical results.
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Peer Reviewed
22.
Optimal leaderfollowing consensus of fractional opinion formation models
Almeida, Ricardo and Kamocki, Rafał and Malinowska, Agnieszka B. and Odzijewicz, Tatiana
Journal of Computational and Applied Mathematics
Elsevier
This paper deals with a control strategy enforcing consensus in a fractional opinion formation model with leadership, where the interaction rates between followers and the influence rate of the leader are functions of deviations of opinions between agents. The fractionalorder derivative determines the impact of the memory during the opinion evolution. The problem of leaderfollowing consensus control is cast in the framework of nonlinear optimal control theory. We study a finite horizon optimal control problem, in which deviations of opinions between agents and with respect to the leader are penalized along with the control that is applied only to the leader. The existence conditions for optimal consensus control are proved and necessary optimality conditions for the considered problem are derived. The results of the paper are illustrated by some examples.
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Peer Reviewed
21.
Optimality conditions for variational problems involving distributedorder fractional derivatives with arbitrary kernels
Cruz, Fátima and Almeida, Ricardo and Martins, Natália
AIMS Mathematics
AIMS Press
In this work we study necessary and sufficient optimality conditions for variational
problems dealing with a new fractional derivative. This fractional derivative combines two known
operators: distributedorder derivatives and derivatives with arbitrary kernels. After proving a
fractional integration by parts formula, we obtain the Euler–Lagrange equation and natural boundary
conditions for the fundamental variational problem. Also, fractional variational problems with integral
and holonomic constraints are considered. We end with some examples to exemplify our results.
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Peer Reviewed
20.
Global stability of a Caputo fractional SIRS model with general incidence rate
Ammi, Moulay Rchid Sidi and Tahiri, Mostafa and Torres, Delfim F. M.
Mathematics in Computer Science
Springer
We introduce a fractional order SIRS model with nonlinear incidence rate. Existence of a unique positive solution to the model is proved. Stability analysis of the disease free equilibrium and positive fixed points are investigated. Finally, a numerical example is presented.
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Peer Reviewed
19.
A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
Almeida, Ricardo and Martins, Natália
Fractal and Fractional
MDPI
In this paper, we present a new fractional variational problem where the Lagrangian
depends not only on the independent variable, an unknown function and its left and rightsided
Caputo fractional derivatives with respect to another function, but also on the endpoint conditions
and a free parameter. The main results of this paper are necessary and sufficient optimality conditions
for variational problems with or without isoperimetric and holonomic restrictions. Our results not
only provide a generalization to previous results but also give new contributions in fractional
variational calculus. Finally, we present some examples to illustrate our results.
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18.
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.
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17.
Pest control using farming awareness: impact of time delays and optimal use of biopesticides
Abraha, Teklebirhan and Al Basir, Fahad and Obsu, Legesse Lemecha and Torres, Delfim F. M.
Chaos, Solitons & Fractals
Elsevier
We investigate a mathematical model in crop pest management, considering
plant biomass, pest, and the effect of farming awareness. The pest population
is divided into two compartments: susceptible pest and infected pest. We assume
that the growth rate of selfaware people is proportional to the density of
healthy pests present in the crop field. Impacts of awareness is modeled via a
saturated term. It is further assumed that selfaware people will adopt
biological control methods, namely integrated pest management. Susceptible
pests are detrimental to crops and, moreover, there may be some time delay in
measuring the healthy pests in the crop field. A time delay may also take place
while becoming aware of the control strategies or taking necessary steps to
control the pest attack. In agreement, we develop our model incorporating two
time delays into the system. The existence and the stability criteria of the
equilibria are obtained in terms of the basic reproduction number and time
delays. Stability switches occur through Hopfbifurcation when time delays
cross critical values. Optimal control theory has been applied for the
costeffectiveness of the delayed system. Numerical simulations illustrate the
obtained analytical results.
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16.
Two families of locally toroidal regular 4hypertopes arising from toroids
Fernandes, Maria Elisa and Leemans, Dimitri and Piedade, Claudio Alexandre and Weiss, Asia Ivić
Contemporary Mathematics
American Mathematical Society
In this paper we present two inﬁnite families of locally toroidal hypertopes of rank 4 that are constructed from regular toroids of types {4, 3, 4}_(s,s,0) and {3, 3, 4, 3}_(s,0,0,0). The Coxeter diagram of the ﬁrst of the two families is starshaped and the diagram of the other is a square. In both cases the toroidal residues are regular toroidal maps of type {3, 6}.
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15.
New variational problems with an action depending on generalized fractional derivatives, the free endpoint conditions, and a real parameter
Almeida, Ricardo and Martins, Natália
Symmetry
MDPI
This work presents optimality conditions for several fractional variational problems where the Lagrange function depends on fractional order operators, the initial and final state values, and a free parameter. The fractional derivatives considered in this paper are the Riemann–Liouville and the Caputo derivatives with respect to an arbitrary kernel. The new variational problems studied here are generalizations of several types of variational problems, and therefore, our results generalize wellknown results from the fractional calculus of variations. Namely, we prove conditions useful to determine the optimal orders of the fractional derivatives and necessary optimality conditions involving time delays and arbitrary real positive fractional orders. Sufficient conditions for such problems are also studied. Illustrative examples are provided.
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14.
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.
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13.
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.
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12.
Nondual modal operators as a basis for 4valued accessibility relations in Hybrid logic
Costa, Diana and Martins, Manuel A.
Journal of Logical and Algebraic Methods in Programming
Elsevier
The modal operators usually associated with the notions of possibility and necessity are classically duals. This paper aims to defy that duality in a paraconsistent environment, namely in a Belnapian Hybrid logic where both propositional variables and accessibility relations are fourvalued. Hybrid logic, which is an extension of Modal logic, incorporates extra machinery such as nominals – for uniquely naming states – and a satisfaction operator – so that the formula under its scope is evaluated in the state whose name the satisfaction operator indicates.
In classical Hybrid logic the semantics of negation, when it appears before compound formulas, is carried towards subformulas, meaning that eventual inconsistencies can be found at the level of nominals or propositional variables but appear unrelated to the accessibility relations. In this paper we allow inconsistencies in propositional variables and, by breaking the duality between modal operators, inconsistencies at the level of accessibility relations arise. We introduce a sound and complete tableau system and a decision procedure to check if a formula is a consequence of a set of formulas. Tableaux will be used to extract syntactic models for databases, which will then be compared using different inconsistency measures. We conclude with a discussion about bisimulation.
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11.
A fractional analysis in higher dimensions for the SturmLiouville problem
Ferreira, M. and Rodrigues, M. M. and Vieira, N.
Fractional Calculus and Applied Analysis
De Gruyter
In this work, we consider the ndimensional fractional SturmLiouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right RiemannLiouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.
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10.
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.
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Peer Reviewed
9.
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.
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8.
On the theory of periodic multivariate INAR processes
Santos, Cláudia and Pereira, Isabel and Scotto, Manuel G.
Statistical Papers
Springer
In this paper a multivariate integervalued autoregressive model of order one with
periodic timevarying parameters, and driven by a periodic innovations sequence of
independent random vectors is introduced and studied in detail. Emphasis is placed on
models with periodic multivariate negative binomial innovations. Basic probabilistic
and statistical properties of the novel model are discussed. Aiming to reduce computational burden arising from the use of the conditional maximum likelihood method, a composite likelihoodbased approach is adopted. The performance of such method is
compared with that of some traditional competitors, namely moment estimators and
conditional maximum likelihood estimators. Forecasting is also addressed. Furthermore, an application to a real data set concerning the monthly number of fires in three counties in Portugal is presented.
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7.
Language assessment in awake brain surgery: the Portuguese adaptation of the Dutch linguistic intraoperative protocol (DuLIP)
Alves, Joana and Cardoso, Mafalda and Morgado, Mariana and De Witte, Elke and Satoer, Djaina and Hall, Andreia and Jesus, Luis M. T.
Clinical Linguistics & Phonetics
Taylor & Francis
Awake brain surgery, combined with neurophysiological evaluation and intraoperative mapping, is one of the preferential lines of treatment when approaching lowgrade gliomas. Speech and language assessment is used while applying Direct Electrical Stimulation (DES) and during the resection of a lesion/tumour, as it allows to establish related eloquent areas and optimise the extent of the resection and avoid impairments. Patients need to be assessed pre, intra and postsurgery, but in under resourced countries such as Portugal, there are still no standardised and validated tools to conduct this type of evaluation. To address this need, the tasks of the Dutch Linguistic Intraoperative Protocol (DuLIP) were adapted to European Portuguese, and the resulting materials were standardised for a group of 144 Portuguese participants. For each task, the impact of age, gender and schooling were measured. The resulting Portuguese version of the DuLIP (DuLIPEP) consists of 17 tasks, including phonological, syntactic, semantic, naming and articulatory tests. No significant differences were found between male and female participants. However, schooling influenced phonological and syntactic fluency, object naming and verb generation. Schooling and age had a significant impact on semantic fluency and reading with semantic odd word out tasks. This is the first contribution to the standardisation of a tool that can be used during an awake brain surgery in Portugal, which includes a new phonological odd word out task that is not currently available in the Dutch version.
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6.
A dynamicallyconsistent nonstandard finite difference scheme for the SICA model
Vaz, Sandra and Torres, Delfim F. M.
Mathematical Biosciences and Engineering
AIMS Press
In this work, we derive a nonstandard finite difference scheme for the SICA (Susceptible–Infected–Chronic–AIDS) model and analyze the dynamical properties of the discretized system. We prove that the discretized model is dynamically consistent with the continuous, maintaining the essential properties of the standard SICA model, namely, the positivity and boundedness of the solutions, equilibrium points, and their local and global stability.
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5.
PakStanley labeling of the mCatalan hyperplane arrangement
Duarte, Rui and Guedes de Oliveira, António
Advances in Mathematics
Elsevier
We characterize in simple terms the PakStanley labels λ(R) of the regions
R of the mCatalan arrangement. We also propose a simple algorithm that returns R
from λ(R). Finally, we characterize in close terms the labels of the relatively bounded
regions.
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4.
Generalizações da etiquetagem de PakStanley
Duarte, Rui and Guedes de Oliveira, António
Boletim da Sociedade Portuguesa de Matemática
Sociedade Portuguesa de Matemática
Neste artigo pretendemos dar a conhecer ao leitor uma área que consideramos particularmente atraente, onde temos obtido alguns resultados que tentaremos também relatar.
O ponto de partida é uma construção (a "etiquetagem de PakStanley''), que associa um vetor a cada uma das regiões em que determinado conjunto de hiperplanos divide o espaço euclideano $R^n$. Regiões vizinhas diferem (em $1$) numa coordenada, crescendo ao afastarse de uma determinada região, etiquetada com $(1,1,dotsc,1)$.
Há cerca de vinte anos, Pak e Stanley mostraram que, no caso de os hiperplanos formarem o "arranjo de Shi'', as etiquetas de PakStanley formam um conjunto previamente estudado, o conjunto das "parking functions'', e
que a etiquetagem é bijetiva, muito embora seja difícil definir a função inversa, isto é, obter a região a partir da etiqueta.
Esta construção tem uma extensão natural a outros arranjos. Recentemente, Mazin obteve uma caracterização muito geral dos conjuntos de etiquetas assim obtidos, que implica, em particular, o resultado de Pak e Stanley. Com base neste trabalho de Mazin, estudamos as etiquetagens de outro arranjos, o arranjo de Ish recentemente definido e um conjunto de arranjos por nós introduzido, que constitui uma classe naturalmente balizada, por um lado, pelo arranjo de Shi, e por outro, pelo arranjo de Ish.
O nosso trabalho, em traços gerais, consistiu em descrever o conjunto das etiquetas respetivas e em mostrar que as etiquetagens são bijetivas, recorrendo a diferentes técnicas e resultados que aqui são explicitamente referidos. A exposição dessas técnicas e o relato desses resultados, alguns já "clássicos'' da área e outros muito recentes, foram talvez a nossa razão mais forte para a escrita deste pequeno texto.
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3.
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.
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2.
Application of the fractional Sturm–Liouville theory to a fractional Sturm–Liouville telegraph equation
Ferreira, M. and Rodrigues, M. M. and Vieira, N.
Complex Analysis and Operator Theory
Springer
In this paper, we consider a nonhomogeneous timespacefractional telegraph equation in $n$dimensions, which is obtained from the standard telegraph equation by replacing the first and secondorder time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional SturmLiouville operator defined in terms of right and left fractional RiemannLiouville derivatives. Using the method of separation of variables, we derive series representations of the solution in terms of Wright functions, for the homogeneous and nonhomogeneous cases. The convergence of the series solutions is studied by using well known properties of the Wright function. We show also that our series can be written using the bivariate MittagLeffler function. In the end of the paper some illustrative examples are presented.
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1.
Farming awareness based optimum interventions for crop pest control
Abraha, Teklebirhan and Al Basir, Fahad and Obsu, Legesse Lemecha and Torres, Delfim F. M.
Mathematical Biosciences and Engineering
AIMS Press
We develop a mathematical model, based on a system of ordinary differential equations, to the upshot of farming alertness in crop pest administration, bearing in mind plant biomass, pest, and level of control. Main qualitative analysis of the proposed mathematical model, akin to both pestfree and coexistence equilibrium points and stability analysis, is investigated. We show that all solutions of the model are positive and bounded with initial conditions in a certain significant set. The local stability of pestfree and coexistence equilibria is shown using the Routh–Hurwitz criterion. Moreover, we prove that when a threshold value is less than one, then the pestfree equilibrium is locally asymptotically stable. To get optimum interventions for crop pests, that is, to decrease the number of pests in the crop field, we apply optimal control theory and find the corresponding optimal controls. We establish existence of optimal controls and characterize them using Pontryagin's minimum principle. Finally, we make use of numerical simulations to illustrate the theoretical analysis of the proposed model, with and without control measures.
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