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We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank $n$ generates the pseudovariety $\boldsymbol{\mathcal{J}}_n$, which corresponds to the class of all piecewise testable languages of height $n$, in the framework of Eilenberg's correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if $n \leq 3$, and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution., Comment: 22 pages. Added results on the finite basis problem for the stylic monoid with involution and updated references

Publisher Copyright: © 2022 Taylor & Francis Group, LLC. In this paper we consider the monoid (Formula presented.) of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of (Formula presented.). We also describe Green’s relations of (Formula presented.) and calculate its cardinal. authorsversion published

Funding Information: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia , I.P., under the scope of the project DSAIPA/DS/0088/2019 and research and development units UNIDEMI (project UIDB/00667/2020 ) and NOVAMath (projects UIDB/00297/2020 and UIDP/00297/2020 ). Publisher Copyright: © 2023 The Author(s) Fires in urban areas typically carry severe consequences. High population density together with the complexity of urban network potentially imply significant impacts in property loss, physical damage and life losses. However, despite the impact that fires may have in urban areas, research in urban fire prediction remains limited. In this study, we modelled urban fire occurrences while making a comparative analysis of different strategies to account for spatial autocorrelation. Considering space dependence in addition to a range of social-economic explanatory variables has proven to strengthen the validity of the fitted models. The spatial Durbin error model, including population density, degraded buildings density and buying power, was selected as having the best fit. This model allowed to map the estimated probability of fire occurrence across Portugal, revealing a spatial pattern with clusters centred on the two main Portuguese city districts (Lisboa and Porto). Ultimately, the analysis of the relation between the observed urban fire incidence and the actual number of fire stations in each municipality allowed to underline the need for planning the spatial configuration of fire stations, both in number and location, at a regional scale. publishersversion published

Funding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações), and PTDC/CCI-BIO/4180/2020 . The second author was financially supported by the Forest Research Center, a research unit funded by Fundação para a Ciência e a Tecnologia (FCT), Portugal , through the project ( UIDB/00239/2020 ). Publisher Copyright: © 2023 The Author(s) Consider a graph with vertex set V and non-negative weights on the edges. For every subset of vertices S, define ϕ(S) to be the sum of the weights of edges with one vertex in S and the other in V∖S, minus the sum of the weights of the edges with both vertices in S. We consider the problem of finding S⊆V for which ϕ(S) is maximized. We call this combinatorial optimization problem the max-out min-in problem (MOMIP). In this paper we (i) present a linear 0/1 formulation and a quadratic unconstrained binary optimization formulation for MOMIP; (ii) prove that the problem is NP-hard; (iii) report results of computational experiments on simulated data to compare the performances of the two models; (iv) illustrate the applicability of MOMIP for two different topics in the context of data analysis, namely in the selection of variables in exploratory data analysis and in the identification of clusters in the context of cluster analysis; and (v) introduce a generalization of MOMIP that includes, as particular cases, the well-known weighted maximum cut problem and a novel problem related to independent dominant sets in graphs. publishersversion published

Let X X be a rearrangement-invariant Banach function space on the unit circle T \mathbb {T} and let H [ X ] H[X] be the abstract Hardy space built upon X X . We prove that if the Cauchy singular integral operator ( H f ) ( t ) = 1 π i ∫ T f ( τ ) τ − t d τ (Hf)(t)=\frac {1}{\pi i}\int _{\mathbb {T}}\frac {f(\tau )}{\tau -t}\,d\tau is bounded on the space X X , then the norm, the essential norm, and the Hausdorff measure of non-compactness of the operator a I + b H aI+bH with a , b ∈ C a,b\in \mathbb {C} , acting on the space X X , coincide. We also show that similar equalities hold for the backward shift operator ( S f ) ( t ) = ( f ( t ) − f ^ ( 0 ) ) / t (Sf)(t)=(f(t)-\widehat {f}(0))/t on the abstract Hardy space H [ X ] H[X] . Our results extend those by Krupnik and Polonskiĭ [Funkcional. Anal. i Priloz̆en. 9 (1975), pp. 73-74] for the operator a I + b H aI+bH and by the second author [J. Funct. Anal. 280 (2021), p. 11] for the operator S S .

This work is funded by national funds through the FCT-Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided. publishersversion published

Funding Information: The presented research was funded by national funds through the FCT—Fundação para a Ciência e a Tecnologia, I.P., under the scope of the research units UIDB/04035/2020 (GeoBioTec Research Centre), UIDB/00297/2020 and UIDP/00297/2020 (Centre for Mathematics and Applications). Publisher Copyright: © 2023 by the authors. In recent years, cocoa and dark chocolate have attracted the interest of consumers not only for their sensory characteristics but also for their nutritional properties and positive impact on health. The baobab is a fruit of African origin with a sour and slightly sweet flavour, widely consumed by local communities due to its unique nutritional features. The aim of this work was to evaluate the impact of the concentration of baobab flour in the development of functional dark chocolate, including physical, chemical, nutritional and sensory evaluations. The results presented a positive correlation between the incorporation of baobab flour and the antioxidant activity (up to 2297 mmol TE/100 g), vitamin C content (up to 49.7 mg/100 g), calcium (up to 1052 mg/kg), potassium (up to 10,175 mg/kg), phosphorus (up to 795.9 mg/kg), chlorine (up to 235.4 mg/kg) and sulphur (up to 1158 mg/kg). The sensory evaluation of dark chocolate with 3% baobab presented the highest evaluation on the parameters “texture” and “overall flavour”, while the parameter “overall flavour” presented the lowest evaluation on chocolate with 9% baobab. No influence was observed on fatty acid profile, protein, fat and hardness. publishersversion published

Publisher Copyright: © 2023 Wiley-VCH GmbH. For (Formula presented.) and variable exponents (Formula presented.) and (Formula presented.) with values in [1, ∞], let the variable exponents (Formula presented.) be defined by (Formula presented.) The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space (Formula presented.) to the variable Lebesgue space (Formula presented.) for (Formula presented.), then (Formula presented.) where C is an interpolation constant independent of T. We consider two different modulars (Formula presented.) and (Formula presented.) generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that (Formula presented.) and (Formula presented.), as well as, lead to sufficient conditions for (Formula presented.) and (Formula presented.). We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that (Formula presented.), (Formula presented.) are Lipschitz continuous and bounded away from one and infinity (in this case, (Formula presented.)). authorsversion published

Funding Information: For the second and third authors, this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020, financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported by Fidelidade-Companhia de Seguras, S.A. Funding Information: This work was published with financial support from Fidelidade-Companhia de Seguras, S.A. to which the authors express their warmest acknowledgment. The authors express gratitude to the three referees for their comments, corrections and questions that led to a revised and better version of this work. Publisher Copyright: © 2023 by the authors. We present an analysis on variability Bitcoin characteristics that help to quantitatively differentiate Bitcoin from the state-owned traditional currencies and the asset Gold. We provide a detailed study on returns of exchange rates—against the Swiss Franc—of several traditional currencies together with Bitcoin and Gold; for that purpose, we define a distance between currencies by means of the spectral densities of the ARMA models of the returns of the exchange rates, and we present the computed matrix of the distances between the chosen currencies. A statistical analysis of these matrix distances is further proposed, which shows that the distance between Bitcoin and any other currency or Gold is not comparable to any of the distances between currencies or between currencies and Gold and not involving Bitcoin. This result shows that Bitcoin is essentially different from the traditional currencies and from Gold, at least in what concerns the structure of its variance and auto-covariances. publishersversion published

Let X be a Banach function space on the unit circle $${\mathbb {T}}$$ T , let $$X'$$ X ′ be its associate space, and let H[X] and $$H[X']$$ H [ X ′ ] be the abstract Hardy spaces built upon X and $$X'$$ X ′ , respectively. Suppose that the Riesz projection P is bounded on X and $$a\in L^\infty {\setminus }\{0\}$$ a ∈ L ∞ \ { 0 } . We show that P is bounded on $$X'$$ X ′ . So, we can consider the Toeplitz operators $$T(a)f=P(af)$$ T ( a ) f = P ( a f ) and $$T({\overline{a}})g=P({\overline{a}}g)$$ T ( a ¯ ) g = P ( a ¯ g ) on H[X] and $$H[X']$$ H [ X ′ ] , respectively. In our previous paper, we have shown that if X is not separable, then one cannot rephrase Coburn’s lemma as in the case of classical Hardy spaces $$H^p$$ H p , $$1 1 < p < ∞ , and guarantee that T(a) has a trivial kernel or a dense range on H[X]. The first main result of the present paper is the following extension of Coburn’s lemma: the kernel of T(a) or the kernel of $$T({\overline{a}})$$ T ( a ¯ ) is trivial. The second main result is a generalisation of the Hartman–Wintner–Simonenko theorem saying that if T(a) is normally solvable on the space H[X], then $$1/a\in L^\infty $$ 1 / a ∈ L ∞ .

Funding Information: This work was supported in part by Centro de Matematica e Aplicaçoes, UID (MAT/00297/2020), Portuguese Foundation of Science and Technology. Acknowledgments Publisher Copyright: Copyright © 2023 Torrente, Sousa, Guerreiro, Franco, Hernández, Parejo, Sousa, Campo-Cañaveral, Pimentão and Provencio. Background: Current prognosis in oncology is reduced to the tumour stage and performance status, leaving out many other factors that may impact the patient´s management. Prognostic stratification of early stage non-small-cell lung cancer (NSCLC) patients with poor prognosis after surgery is of considerable clinical relevance. The objective of this study was to identify clinical factors associated with long-term overall survival in a real-life cohort of patients with stage I-II NSCLC and develop a prognostic model that identifies features associated with poor prognosis and stratifies patients by risk. Methods: This is a cohort study including 505 patients, diagnosed with stage I-II NSCLC, who underwent curative surgical procedures at a tertiary hospital in Madrid, Spain. Results: Median OS (in months) was 63.7 (95% CI, 58.7-68.7) for the whole cohort, 62.4 in patients submitted to surgery and 65 in patients submitted to surgery and adjuvant treatment. The univariate analysis estimated that a female diagnosed with NSCLC has a 0.967 (95% CI 0.936 - 0.999) probability of survival one year after diagnosis and a 0.784 (95% CI 0.712 - 0.863) five years after diagnosis. For males, these probabilities drop to 0.904 (95% CI 0.875 - 0.934) and 0.613 (95% CI 0.566 - 0.665), respectively. Multivariable analysis shows that sex, age at diagnosis, type of treatment, ECOG-PS, and stage are statistically significant variables (p1) while adjuvant chemotherapy is a good prognostic variable (HR

Publisher Copyright: © 2023 International Academic Press In a system of regression models, finding a feasible shrinkage is demanding since the covariance structure is unknown and cannot be ignored. On the other hand, specifying sub-space restrictions for adequate shrinkage is vital. This study proposes feasible shrinkage estimation strategies where the sub-space restriction is obtained from LASSO. Therefore, some feasible LASSO-based Stein-type estimators are introduced, and their asymptotic performance is studied. publishersversion published

Funding Information: This study was supported by national funds through FCT–Foundation for Science and Technology, I.P., within the scope of the project 2022.03892.PTDC. Declaration of interest: The author declares no competing interest. Data availability: Data generated or analyzed during this study are available from the author on request. Publisher Copyright: © 2023 by authors; license EJSME by Bastas. Teachers’ knowledge plays a central role in technology integration. In this study we analyze situations, where there is some divergence between the mathematical results and the information offered by the graphing calculator (lack of mathematical fidelity), putting the focus in the teachers and in their approaches. The goal of this study is to analyze, in the light of knowledge for teaching mathematics with technology (KTMT) model, the teachers’ professional knowledge, assuming the situations of lack of mathematical fidelity as having the potential to reveal some characteristics of their knowledge. Specifically, considering the teaching of functions at 10th grade (age 16), we intend to analyze: (1) What knowledge do the teachers have of technology and of its mathematical fidelity? (2) What can the teachers’ options related to situations of lack of mathematical fidelity tell us about their knowledge in other KTMT domains? The study adopts a qualitative and interpretative approach based on the case studies of two teachers. Data were collected by interviews and class observation, being the analysis guided by the KTMT model. The main result points to the relevance of the mathematics and technology knowledge. However, there is evidence of some difficulties to integrate the information provided by the technology with the mathematics, and also of some interference of the teaching and learning and technology knowledge, and specifically of the knowledge related to the students. This suggests that the analysis of the teachers’ actions in relation to situations of lack of mathematical fidelity, can be useful to characterize their KTMT. publishersversion published

UIDB/04647/2020 UIDP/04647/2020 Pretende-se averiguar a importância que o ensino do desenho assume na educação técnico-profissional. Em primeiro lugar, buscaremos a evolução das intenções legislativas sobre o ensino dessa disciplina e o modo como seu âmbito foi sendo alterado. Em segundo lugar, analisa-se um manual prestigiado do princípio do século XX, que condensa o saber escolar sobre desenho, tal como era entendido nessa época. The article intends to ascertain the importance of teaching drawing in technical and professional education. First, we will look for the evolution of the legislative intentions on teaching this discipline and the way its scope has been changed. Second, we analyse a prestigious manual from the beginning of the 20th century, that which condenses school knowledge about drawing, as it was understood at that time. publishersversion published

Funding Information: Funding information : This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal. Publisher Copyright: © 2023 João Lita da Silva, published by De Gruyter. In this article, we express the eigenvalues of real antitridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues. publishersversion published

UIDB/04647/2020 UIDP/04647/2020 PTDC/CED-EDG/32422/2017 A Coleção História e Memória do Ensino da Matemática, apoiada pelo Grupo de Trabalho sobre História e Memória do Ensino da Matemática da Associação de Professores de Matemática, pretende divulgar trabalhos científicos sobre história do ensino da Matemática, difundindo perspetivas, metodologias e temas entre investigadores da área e divulgando junto de professores e do público em geral produções nesta área. Esse livro em específico contém a transcrição de artigos sobre matemática publicados em Portugal entre 1857 e 1872. Nele consta a proposta de cada um dos quatro volumes da série e um índice. Os artigos transcritos estão separados por seus anos, entre 1857 – 1872. publishersversion published

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01100526). Publisher Copyright: © 2022 by the authors. The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test. publishersversion published

Funding Information: For the first author this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020 financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported by Fidelidade-Companhia de Seguros, S.A. to which the authors express their warmest acknowledgment. Funding Information: This work was published with financial support from by the New University of Lisbon. The authors express gratitude to the comments, corrections, and questions of the referees that led to a revised and better version of this work. Publisher Copyright: © 2023 by the authors. The structure of the random matrices introduced in this work is given by deterministic matrices—the skeletons of the random matrices—built with an algorithm of matrix substitutions with entries in a finite field of integers modulo some prime number, akin to the algorithm of one dimensional automatic sequences. A random matrix has the structure of a given skeleton if to the same number of an entry of the skeleton, in the finite field, it corresponds a random variable having, at least, as its expected value the correspondent value of the number in the finite field. Affine matrix substitutions are introduced and fixed point theorems are proven that allow the consideration of steady states of the structure which are essential for an efficient observation. For some more restricted classes of structured random matrices the parameter estimation of the entries is addressed, as well as the convergence in law and also some aspects of the spectral analysis of the random operators associated with the random matrix. Finally, aiming at possible applications, it is shown that there is a procedure to associate a canonical random surface to every random structured matrix of a certain class. publishersversion published

Let $R$ and $S$ be two sequences of positive integers in nonincreasing order having the same sum. We denote by ${\cal A}(R,S)$ the class of all $(0,1)$-matrices having row sum vector $R$ and column sum vector $S$. Brualdi and Deaett (More on the Bruhat order for $(0,1)$-matrices, Linear Algebra Appl., 421:219--232, 2007) suggested the study of the secondary Bruhat order on ${\cal A}(R,S)$ but with some constraints. In this paper, we study the cover relation and the minimal elements for this partial order relation, which we call the little secondary Bruhat order, on certain classes ${\cal A}(R,S)$. Moreover, we show that this order is different from the Bruhat order and the secondary Bruhat order. We also study a variant of this order on certain classes of symmetric matrices of ${\cal A}(R,S)$.

Using the recent geometric Parter-Wiener, etc. theorem and related results, it is shown that much of the multiplicity theory developed for real symmetric matrices associated with paths and generalized stars remains valid for combinatorially symmetric matrices over a field. A characterization of generalized stars in the case of combinatorially symmetric matrices is given.

We present a methodology to connect an ordinary differential equation (ODE) model of interacting entities at the individual level, to an open Markov chain (OMC) model of a population of such individuals, via a stochastic differential equation (SDE) intermediate model. The ODE model here presented is formulated as a dynamic change between two regimes; one regime is of mean reverting type and the other is of inverse logistic type. For the general purpose of defining an OMC model for a population of individuals, we associate an Ito processes, in the form of SDE to ODE system of equations, by means of the addition of Gaussian noise terms which may be thought to model non essential characteristics of the phenomena with small and undifferentiated influences. The next step consists on discretizing the SDE and using the discretized trajectories computed by simulation to define transitions of a finite valued Markov chain; for that, the state space of the Ito processes is partitioned according to some rule. For the example proposed for illustration, the state space of the ODE system referred – corresponding to a model of a viral infection – is partitioned into six infection classes determined by some of the critical points of the ODE system; we detail the evolution of some infected population in these infection classes.

UIBD/MAT/00297/2020 In a previous paper, the authors introduced and studied the Bruhat order in the class of Latin squares of order n. In this paper, we investigate the restriction of the Bruhat order in a class of isotopic Latin squares. We present equivalent conditions for two Latin squares be related by the Bruhat order when one of them is obtained from the other by interchanging rows or columns or symbols. The cover relation is also addressed, and we present orthogonal isotopic Latin squares related by the Bruhat order. authorsversion published

UID/MAT/00297/2019 UID/MAT/04721/2019 We consider the class (Formula presented.) of symmetric (Formula presented.) -matrices with zero trace and constant row sums k which can be identified with the class of the adjacency matrices of k-regular undirected graphs. In a previous paper, two partial orders, the Bruhat and the Bruhat-graph order, have been introduced in this class. In fact, when k = 1 or k = 2, it was shown that the two orders coincide, while for (Formula presented.) the two orders are distinct. In this paper we give general properties of minimal and maximal matrices for these orders on (Formula presented.) and study the minimal and maximal matrices when k = 1, 2 or 3. publishersversion published

Funding Information: This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UIDB/00297/2020 (Centro de Matemática e Aplicações) and UIDB/00006/2020 (Centro de Estatística e Aplicações/UL). Publisher Copyright: © 2022 American Institute of Physics Inc.. All rights reserved. When extending the analysis of the limiting behaviour of the extreme values from independent and identically distributed sequences to stationary sequences a key parameter appears, the extremal index θ, whose accurate estimation is not easy and is not completely solved. Here we focus on the estimation of θ using blocks estimators, that can be constructed by using disjoint or sliding blocks. Both blocks construction require the choice of a threshold and a block length. The main objective of this work is to revisit another block estimation procedure that only depends on the block length, although some conditions on the underlying process need to be verified. An application will be presented for illustrating the proposed procedure. publishersversion published

This paper presents new results on the identities satisfied by the hypoplactic monoid. We show how to embed the hypoplactic monoid of any rank strictly greater than 2 (including infinite rank) into a direct product of copies of the hypoplactic monoid of rank 2. This confirms that all hypoplactic monoids of rank greater than or equal to 2 satisfy exactly the same identities. We then give a complete characterization of those identities, and prove that the variety generated by the hypoplactic monoid has finite axiomatic rank, by giving a finite basis for it., Comment: 19 pages

UIDB/04647/2020 UIDP/04647/2020 A aplicação das ideias da matemática moderna nas escolas portuguesas decorreu entre os anos 1960 e o final dos anos 1980. Este texto pretende contribuir para a compreensão dos diversos modos como essa aplicação de desenvolveu em livros de texto. Para isso efetuaremos uma comparação entre três coleções de livros de texto dedicados ao curso unificado dos 7.º, 8.º e 9.º anos de escolaridade iniciado a partir de 1976. Compararemos estas inovações curriculares a partir da forma como os autores apresentam o seu trabalho. Estudaremos, em particular, a introdução de um tema do programa procurando as diferenças e semelhanças entre as obras analisadas. La aplicación de las ideas de las matemáticas modernas en las escuelas portuguesas tuvo lugar entre los años 60 y finales de los 80. Este texto tiene como objetivo contribuir a la comprensión de las diferentes formas en que esta aplicación se desarrolló en libros de texto. Para eso efectuaremos una comparación entre tres colecciones de libros de texto dedicados al curso unificado dos 7.º, 8.º e 9.º anos de escolaridad iniciado a partir de 1976. Compararemos estas innovaciones curriculares a partir da forma como os autores presentan o tu trabajo. Estudiaremos, en particular, la introducción de un tema del programa buscando las diferencias y similitudes entre las obras analizada. publishersversion published

UIDB/00297/2020 Asmar et al. [Note on norm convergence in the space of weak type multipliers. J Operator Theory. 1998;39(1):139–149] proved that the space of weak-type Fourier multipliers acting from (Formula presented.) into (Formula presented.) is continuously embedded into (Formula presented.). We obtain a sharper result in the setting of abstract Lorentz spaces (Formula presented.) with (Formula presented.) built upon a Banach function space X on (Formula presented.). We consider a source space (Formula presented.) and a target space (Formula presented.) in the class of admissible spaces (Formula presented.). Let (Formula presented.) denote the space of Fourier multipliers acting from (Formula presented.) to (Formula presented.). We show that if the space X satisfies the weak doubling property, then the space (Formula presented.) is continuously embedded into (Formula presented.) for every (Formula presented.). This implies that (Formula presented.) is a quasi-Banach space for all choices of source and target spaces (Formula presented.). publishersversion published

DOCTORATES 4 COVID-19", number 2020.10172.BD. PP UIDB/00297/2020 UIDB/04621/2020 UIDP/04621/2020 In this work we use simple mathematical models to study the impact of vaccination against COVID-19 in Portugal. First, we fit a SEIR type model without vaccination to the Portuguese data on confirmed cases of COVID-19 by the date of symptom onset, from the beginning of the epidemic until the 23rd January of 2021, to estimate changes in the transmission intensity. Then, by including vaccination in the model we develop different scenarios for the fade-out of the non pharmacological intervention (NPIs) as vaccine coverage increases in the population according to Portuguese vaccination goals. We include a feedback function to mimic the implementation and relaxation of NPIs, according to some disease incidence thresholds defined by the Portuguese health authorities. publishersversion published

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing state that is extensively used in population genetics models. We will consider the Moran process as a paradigm for this class, and will extend our discussion to other models outside this class. We will also discuss the relation between non-extensive entropies in physics and epistasis (i.e., when the effects of different alleles are not independent) and the role of symmetries in population genetic models., Comment: 27 pages, 2 figures

Funding Information: Funding: For the second author, this work was done under partial financial support of RFBR (Grant No. 19-01-00451). For the first, third and fourth authors this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020 financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was funded by the insurance company Future Healthcare. Funding Information: Acknowledgments: This work was published with finantial support from the insurance company Future Healthcare. The authors would like to thank Future Healthcare for this generous support and for their interest in the development of models for disease and health insurance problems in Portugal. The authors wish to express their gratitude to JLS, former publisher at McGraw-Hill Book Company, for his extensive revision of the English language in this work. Funding Information: For the second author, this work was done under partial financial support of RFBR (Grant No. 19-01-00451). For the first, third and fourth authors this work was partially supported through the project of the Centro de Matem?tica e Aplica??es, UID/MAT/00297/2020 financed by the Funda??o para a Ci?ncia e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was funded by the insurance company Future Healthcare. Publisher Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. Made available in DSpace on 2022-02-12T23:27:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-12-15 publishersversion published

Grant n. 19-01-00451 UID/MAT/00297/2020 We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step. publishersversion published

info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00239%2F2020/PT Centrality on graphs aims at ranking vertices in terms of their contribution to facilitate the communication flow in the network. Tukey depth is one of most widely used statistical measures to assess the centrality of a point within a cloud of points in the multidimensional space. In this paper we propose and discuss how to adapt Tukey depth to develop a novel centrality index for vertices of a graph. We present some properties of the indices on several classes of graphs, show that computing the indices is NP-hard, extend the indices to assess the centrality of group of vertices and give 0/1 linear formulations to calculate them. authorsversion published

Resumo: A investigação tem evidenciado o potencial da tecnologia para transformar o ensino da Matemática, mas também a relevância do professor e do seu conhecimento profissional. Neste artigo adota-se uma metodologia qualitativa, com base em estudo de caso, e analisam-se dois episódios da prática de uma professora no âmbito do estudo de funções no 10.º ano de escolaridade, tendo por base o modelo do Conhecimento para Ensinar Matemática com a Tecnologia (KTMT). A intenção é caracterizar o conhecimento da professora a partir da sua prática, compreendendo simultaneamente como esta contribui para promover o desenvolvimento do conhecimento da professora. As conclusões alcançadas evidenciam a importância do modelo KTMT incluir na sua concepção aspetos realçados pela investigação sobre integração da tecnologia, determinantes na caracterização do conhecimento da professora. Mostram ainda a relevância da prática para o desenvolvimento do conhecimento da professora e a perspectiva dinâmica sobre o conhecimento que este modelo pode proporcionar. Abstract: Research has highlighted the potential of technology to transform the teaching of Mathematics, but also the relevance of teachers and their professional knowledge. In this article, a qualitative methodology is adopted and two episodes of the practice of one teacher are analyzed in the scope of the study of functions in the 10th grade, based on the model of Knowledge for Teaching Mathematics with Technology (KTMT). The goal is to characterize the teacher's knowledge from her practice, simultaneously understanding how this contributes to promoting the development of the teacher's knowledge. The conclusions reached show the importance of including in the KTMT conception aspects highlighted by the research on technology integration. These aspects are determinant to characterize the teacher's knowledge. They also show the relevance of the practice for the development of the teacher's knowledge and the dynamic character of the vision of knowledge offered by KTMT. Resumen: La investigación ha puesto de relieve el potencial de la tecnología para transformar la enseñanza de las matemáticas, pero también la relevancia de los docentes y sus conocimientos profesionales. Este artículo adopta una metodología cualitativa y analiza dos episodios de la práctica docente en el contexto del estudio de funciones en el décimo grado, basado en el Modelo de Conocimiento para la Enseñanza de las Matemáticas con Tecnología (KTMT). La intención es caracterizar el conocimiento del docente desde su práctica, entendiendo simultáneamente cómo esto contribuye a promover el desarrollo del conocimiento. Las conclusiones alcanzadas muestran la importancia del modelo KTMT incluir en su concepción aspectos destacados por la investigación sobre la integración de la tecnología, determinantes en la caracterización del conocimiento del docente. También muestran la relevancia de la práctica para el desarrollo del conocimiento del docente y la perspectiva dinámica sobre el conocimiento que este modelo puede proporcionar. publishersversion published

Probabilistic complexity classes, despite capturing the notion of feasibility, have escaped any treatment by the tools of so-called implicit-complexity. Their inherently semantic nature is of course a barrier to the characterization of classes like BPP or ZPP, but not all classes are semantic. In this paper, we introduce a recursion-theoretic characterization of the probabilistic class PP, using recursion schemata with pointers., LIPIcs, Vol. 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), pages 35:1-35:12

Background Genomic prediction (GP) is used in animal and plant breeding to help identify the best genotypes for selection. One of the most important measures of the effectiveness and reliability of GP in plant breeding is predictive accuracy. An accurate estimate of this measure is thus central to GP. Moreover, regression models are the models of choice for analyzing field trial data in plant breeding. However, models that use the classical likelihood typically perform poorly, often resulting in biased parameter estimates, when their underlying assumptions are violated. This typically happens when data are contaminated with outliers. These biases often translate into inaccurate estimates of heritability and predictive accuracy, compromising the performance of GP. Since phenotypic data are susceptible to contamination, improving the methods for estimating heritability and predictive accuracy can enhance the performance of GP. Robust statistical methods provide an intuitively appealing and a theoretically well justified framework for overcoming some of the drawbacks of classical regression, most notably the departure from the normality assumption. We compare the performance of robust and classical approaches to two recently published methods for estimating heritability and predictive accuracy of GP using simulation of several plausible scenarios of random and block data contamination with outliers and commercial maize and rye breeding datasets. Results The robust approach generally performed as good as or better than the classical approach in phenotypic data analysis and in estimating the predictive accuracy of heritability and genomic prediction under both the random and block contamination scenarios. Notably, it consistently outperformed the classical approach under the random contamination scenario. Analyses of the empirical maize and rye datasets further reinforce the stability and reliability of the robust approach in the presence of outliers or missing data. Conclusions The proposed robust approach enhances the predictive accuracy of heritability and genomic prediction by minimizing the deleterious effects of outliers for a broad range of simulation scenarios and empirical breeding datasets. Accordingly, plant breeders should seriously consider regularly using the robust alongside the classical approach and increasing the number of replicates to three or more, to further enhance the accuracy of the robust approach.

The diversity and abundance of cleaner species have been frequently associated with ectoparasite load and ecological wealth of tropical fish communities. Cleaning behaviour in temperate regions has received less attention, with few labrid species being described as cleaners. The context and frequency of cleaning behaviour by juvenile white seabream Diplodus sargus are described. Surface observations from pontoons in yachting marinas were carried out based on a method used in a recent first report of cleaning behaviour by this northeastern Atlantic and Mediterranean sparid. A total of 51 h of observations revealed that these juveniles (

This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacees). The aging population alongside little availability of informal care are two of the several factors leading to an increased need for assisted living support. In this work, we tackle a home social care service problem, motivated by two real case studies where a new loyalty scheme must be considered: within a week, patient-caregiver loyalty should be pursued but, between weeks, the caregivers must rotate among patients (non-loyalty). In addition, a common situation in this kind of service is also addressed: the need of a constant re-planning caused by the leaving of patients and the arrival of new ones. This new plan should be such that minimum disturbance is caused to the visiting hours of current patients, the caregivers’ travelling time between visits is minimized, and the workload is balanced among caregivers. A multi-objective optimization approach based on mixed-integer models is developed. Results on the two real case studies show that both institutions can efficiently re-plan their activities without much disturbance on the visits of their patients, and with a patient-caregiver loyalty scheme suiting their needs. authorsversion published

An abelian antipower of order k (or simply an abelian k-antipower) is a concatenation of k consecutive words of the same length having pairwise distinct Parikh vectors. This definition generalizes to the abelian setting the notion of a k-antipower, as introduced in Fici et al. (2018) [7] , that is a concatenation of k pairwise distinct words of the same length. We aim to study whether a word contains abelian k-antipowers for arbitrarily large k. S. Holub proved that all paperfolding words contain abelian powers of every order (Holub, 2013 [8] ). We show that they also contain abelian antipowers of every order.

Submitted by Isabel Melo (imelo@sa.isel.pt) on 2020-05-13T18:05:16Z No. of bitstreams: 1 Ranks_TMQuinteiro.pdf: 404654 bytes, checksum: db135bf332f766653a2b0e9c4e96ef20 (MD5) Made available in DSpace on 2020-05-13T18:05:16Z (GMT). No. of bitstreams: 1 Ranks_TMQuinteiro.pdf: 404654 bytes, checksum: db135bf332f766653a2b0e9c4e96ef20 (MD5) Previous issue date: 2019-04-19 info:eu-repo/semantics/publishedVersion

We address a multi-period facility location problem with two customer segments having distinct service requirements. While customers in one segment receive preferred service, customers in the other segment accept delayed deliveries as long as lateness does not exceed a pre-specified threshold. The objective is to define a schedule for facility deployment and capacity scalability that satisfies all customer demands at minimum cost. Facilities can have their capacities adjusted over the planning horizon through incrementally increasing or reducing the number of modular units they hold. These two features, capacity expansion and capacity contraction, can help substantially improve the flexibility in responding to demand changes. Future customer demands are assumed to be unknown. We propose two different frameworks for planning capacity decisions and present a two-stage stochastic model for each one of them. While in the first model decisions related to capacity scalability are modeled as first-stage decisions, in the second model, capacity adjustments are deferred to the second stage. We develop the extensive forms of the associated stochastic programs for the case of demand uncertainty being captured by a finite set of scenarios. Additional inequalities are proposed to enhance the original formulations. An extensive computational study with randomly generated instances shows that the proposed enhancements are very useful. Specifically, 97.5% of the instances can be solved to optimality in much shorter computing times. Important insights are also provided into the impact of the two different frameworks for planning capacity adjustments on the facility network configuration and its total cost.

Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario. publishersversion published

This article belongs to the Special Issue Mathematical Biology: Developments in Epidemic and Endemic Models In this paper, we present an age-structured SEIR model that uses contact patterns to reflect the physical distance measures implemented in Portugal to control the COVID-19 pandemic. By using these matrices and proper estimates for the parameters in the model, we were able to ascertain the impact of mitigation strategies employed in the past. Results show that the March 2020 lockdown had an impact on disease transmission, bringing the effective reproduction number (R(t)) below 1. We estimate that there was an increase in the transmission after the initial lift of the measures on 6 May 2020 that resulted in a second wave that was curbed by the October and November measures. December 2020 saw an increase in the transmission reaching an R(t) = 1.45 in early January 2021. Simulations indicate that the lockdown imposed on the 15 January 2021 might reduce the intensive care unit (ICU) demand to below 200 cases in early April if it lasts at least 2 months. As it stands, the model was capable of projecting the number of individuals in each infection phase for each age group and moment in time. The authors acknowledge financial support from the Fundação para a Ciência e Tecnologia—FCT through project 692 2ª edição Research 4 covid, project name Projeção do Impacte das medidas Não-farmacológicas de Controlo e mitigação da epidemia de COVID-19 em Tempo ReaL (COVID-19 in-CTRL). The first author also acknowledges FCT within the PhD grants “DOCTORATES 4 COVID-19”, number 2020.10172.BD. The second author also acknowledges FCT within projects UIDB/04621/2020 and UIDP/04621/2020. The third author also acknowledges FCT within the Strategic Project UIDB/00297/2020 (Centro de Matemática e Aplicações, FCT NOVA). info:eu-repo/semantics/publishedVersion

Let $$\mathcal {M}_{X(\mathbb {R})}$$ be the Banach algebra of all Fourier multipliers on a Banach function space $$X(\mathbb {R})$$ such that the Hardy–Littlewood maximal operator is bounded on $$X(\mathbb {R})$$ and on its associate space $$X'(\mathbb {R})$$ . For two sets $$\varPsi ,\varOmega \subset \mathcal {M}_{X(\mathbb {R})}$$ , let $$\varPsi _\varOmega$$ be the set of those $$c\in \varPsi$$ for which there exists $$d\in \varOmega$$ such that the multiplier norm of $$\chi _{\mathbb {R}\setminus [-N,N]}(c-d)$$ tends to zero as $$N\rightarrow \infty$$ . In this case, we say that the Fourier multiplier c is equivalent at infinity to the Fourier multiplier d. We show that if $$\varOmega$$ is a unital Banach subalgebra of $$\mathcal {M}_{X(\mathbb {R})}$$ consisting of nice Fourier multipliers (for instance, continuous or slowly oscillating in certain sense) and $$\varPsi$$ is an arbitrary unital Banach subalgebra of $$\mathcal {M}_{X(\mathbb {R})}$$ , then $$\varPsi _\varOmega$$ is a also a unital Banach subalgebra of $$\mathcal {M}_{X(\mathbb {R})}$$ .

In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H 2 , we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain.

In the theory of multiplicities for eigenvalues of symmetric matrices whose graph is a tree, it proved very useful to understand the change in status (Parter, neutral, or downer) of one vertex upon removal of another vertex of given status (both in case the two vertices are adjacent or non-adjacent). As the subject has evolved toward the study of more general matrices, over more general fields, with more general graphs, it is appropriate to resolve the same type of question in the more general settings. “Multiplicity” now means geometric multiplicity. Here, we give a complete resolution in three more general settings and compare these with the classical case (216 “Yes” or “No” results). As a consequence, several unexpected insights are recorded. authorsversion published

Let $G_{k}$ G k be a bouquet of circles, i.e., the quotient space of the interval $[0,k]$ [ 0 , k ] obtained by identifying all points of integer coordinates to a single point, called the branching point of $G_{k}$ G k . Thus, $G_{1}$ G 1 is the circle, $G_{2}$ G 2 is the eight space, and $G_{3}$ G 3 is the trefoil. Let $f: G_{k} \to G_{k}$ f : G k → G k be a continuous map such that, for $k>1$ k > 1 , the branching point is fixed.If $\operatorname{Per}(f)$ Per ( f ) denotes the set of periods of f, the minimal set of periods of f, denoted by $\operatorname{MPer}(f)$ MPer ( f ) , is defined as $\bigcap_{g\simeq f} \operatorname{Per}(g)$ ⋂ g ≃ f Per ( g ) where $g:G_{k}\to G_{k}$ g : G k → G k is homological to f.The sets $\operatorname{MPer}(f)$ MPer ( f ) are well known for circle maps. Here, we classify all the sets $\operatorname{MPer}(f)$ MPer ( f ) for self-maps of the eight space.

Direct Multisearch (DMS) is a Derivative-free Optimization class of algorithms suited for computing approximations to the complete Pareto front of a given Multiobjective Optimization problem. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with the definition of a search step based on the minimization of quadratic polynomial models, corresponding to the algorithm BoostDMS. In this work, we propose and numerically evaluate the performance of parallelization strategies for this solver, applied to the search and to the poll steps. The final parallelized version not only considerably decreases the computational time required for solving a Multiobjective Optimization problem, but also increases the quality of the computed approximation to the Pareto front. Extensive numerical results will be reported in an academic test set and in a chemical engineering application., Comment: 20 pages, 26 figures

UID/MAT/00297/2020 Regime switching diffusion processes with one or two thresholds and regime switching occurring by a change in the diffusion drift and/or volatility functions parameters of a stochastic differential equation, whose solution defines a continuous time diffusion process, were defined in previous works; the change in regime occurring whenever the trajectory of the process crosses a threshold, possibly with some delay. In this paper we generalise the previous results by allowing the underlying diffusion process to change from one family of diffusions in one regime to an entirely different one in the other regime; these families of diffusions are characterised by specific functional forms for drift and volatility coefficients depending on parameters. We propose an estimation procedure for all the parameters, namely the thresholds, the delay and, for both regimes, diffusion’s parameters and we apply the introduced estimation procedure to both simulated and real data. publishersversion published

Funding Information: This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matemática e Aplicações). Publisher Copyright: © 2021, Springer Nature Switzerland AG. The synchronization phenomenon was reported for the first time by Christiaan Huygens, when he noticed the strange tendency of a couple of clocks to synchronise their movements. More recently this phenomena was shown to be ubiquitous in nature and it is broadly studied by its applications, for example in biological cycles. We consider the problem of synchronization of a general network of linearly coupled oscillators, not necessarily identical. In this case the existence of a linear synchronization space is not expected, so we present an approach based on the proof of the existence of a synchronization manifold, the so-called generalised synchronization. Based on some results developed by R. Smith and on Wazewski’s principle, a general theory on the existence of invariant manifolds that attract the solutions of the system that are bounded in the future, is presented. Applications and estimates on parameters for the existence of synchronization are presented for several examples: systems of coupled pendulum type equations, coupled Lorenz systems of equations, and oscillators coupled through a medium, among many others. authorsversion published

SFRH/BD/117845/2016 IF/01053/2015 UIDB/00297/2020 Linear infrastructures, such as power lines and roads, are an important source of bird mortality. However, little is known on the potential effect of these infrastructures on local scavenger guilds, their foraging activity and the resulting bird carcass removal patterns. This is an important source of bias in studies aiming to quantify bird fatalities due to linear infrastructures. We used camera-traps to record scavenger identity and persistence patterns of bird carcasses placed close to linear infrastructure and nearby controls in two Mediterranean agricultural regions. We found that linear infrastructure influence on scavenger identity varied depending on the region. Contrary to expectations, linear infrastructure presence had either none or a positive effect on carcass persistence, meaning that carcasses placed within power line or road rights-of-way were not removed faster than the ones placed in controls. We conclude that linear infrastructure effect on vertebrate scavenging patterns is likely to be region-specific, and that reliable correction factors for carcass removal-bias in bird fatality estimates require site-specific experiments to characterize local scavenging processes. publishersversion published