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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

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

In this work, we derived new asymptotic results for multinomial models. To obtain these results, we started by studying limit distributions in models with a compact parameter space. This restriction holds since the key parameter whose components are the probabilities of the possible outcomes have non-negative components that add up to 1. Based on these results, we obtained confidence ellipsoids and simultaneous confidence intervals for models with normal limit distributions. We then studied the covariance matrices of the limit normal distributions for the multinomial models. This was a transition between the previous general results and on the inference for multinomial models in which we considered the chi-square tests, confidence regions and non-linear statistics—namely log-linear models with two numerical applications to those models. Namely, our approach overcame the hierarchical restrictions assumed to analyse the multidimensional contingency table. publishersversion published

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than the use of a uniform mesh, in the case of nonsmooth solutions., The authors acknowledge the support of the Center for Mathematics and Applications (CMA)—FCT-NOVA, Center for Computational and Stochastic Mathematics, Instituto Superior Técnico, and CMAT—Centre of Mathematics—University of Minho. The first author acknowledges Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) within Projects UIDB/04621/2020 and UIDP/04621/2020. The second author acknowledges the Fundação para a Ciência e a Tecnologia through Project UIDB/00297/2020 (Centro de Matemática e Aplicações). The third author acknowledges the funding by Fundação para a Ciência e Tecnologia through Projects UIDB/00013/2020 and UIDP/00013/2020

Funding Information: Funding: For the second author, this work was done under partial financial support of RFBR (Grant n. 19-01-00451). For the first and third 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 funded by the insurance company Fidelidade. We address the problem of finding a natural continuous time Markov type process—in open populations—that best captures the information provided by an open Markov chain in discrete time which is usually the sole possible observation from data. Given the open discrete time Markov chain, we single out two main approaches: In the first one, we consider a calibration procedure of a continuous time Markov process using a transition matrix of a discrete time Markov chain and we show that, when the discrete time transition matrix is embeddable in a continuous time one, the calibration problem has optimal solutions. In the second approach, we consider semi-Markov processes—and open Markov schemes—and we propose a direct extension from the discrete time theory to the continuous time one by using a known structure representation result for semi-Markov processes that decomposes the process as a sum of terms given by the products of the random variables of a discrete time Markov chain by time functions built from an adequate increasing sequence of stopping times. publishersversion published

This work is financed by national funds through FCT-Foundation for Science and Technology-under the projects UID/MAT/00297/2013 and UID/MAT/00006/2013. The Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health services. This study aims to describe and evaluate the use of LS24. Since for LS24 data, the location attribute is an important source of information to describe its use, this study analyses the number of calls received, at a municipal level, under two different spatial econometric approaches. This analysis is important for future development of decision support indicators in a hospital context, based on the economic impact of the use of this health line. Considering the discrete nature of data, the number of calls to LS24 in each municipality is better modelled by a Poisson model, with some possible covariates: demographic, socio-economic information, characteristics of the Portuguese health system and development indicators. In order to explain model spatial variability, the data autocorrelation can be explained in a Bayesian setting through different hierarchical log-Poisson regression models. A different approach uses an autoregressive methodology, also for count data. A log-Poisson model with a spatial lag autocorrelation component is further considered, better framed under a Bayesian paradigm. With this empirical study we find strong evidence for a spatial structure in the data and obtain similar conclusions with both perspectives of the analysis. This supports the view that the addition of a spatial structure to the model improves estimation, even in the case where some relevant covariates have been included. publishersversion published