FC - DM | Documentos por Auto-Depósito
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- À conversa com o coautor, que o não quis ser, ChatGPTPublication . Moreira, Catarina; França, Pedro; Beites, P. D.; Ersari, EbruNum artigo sobre literatura artificial, Camarneiro (2023) refere a muito atual discussão da aplicação da Inteligência Artificial a tarefas complexas, tais como a produção de literatura e de conhecimento, consideradas humanas. Neste sentido e inspirados ainda por um editorial carregado de humor, no qual o Diretor Figueiredo (2023) do jornal Notícias da Covilhã interage com o ChatGPT para o ajudar a pensar no tema do editorial, decidimos convidar o ChatGPT como coautor do presente manuscrito. Fruto da interação com o ChatGPT, começamos com a apresentação deste modelo de linguagem. Continuando a interação, discutimos a resolução de uma generalização de uma equação matricial proposta numa referência de Álgebra Linear. Atendendo aos erros cometidos pelo ChatGPT nesta interação, tentamos encontrar explicações para os mesmos. Terminamos com direções para investigação futura, nomeadamente no que se refere à possibilidade de utilização do ChatGPT nos processos de ensino e de aprendizagem de Matemática.
- Action of Curcumin on Glioblastoma Growth: A Systematic Review with Meta-Analysis of Animal Model StudiesPublication . Luís, Ângelo; Amaral, Leonor; Domingues, F.C.; Pereira, L.; Cascalheira, JoséGliomas are aggressive brain tumors with poor prognosis even after surgical removal and radio-chemotherapy, stressing the urgency to find alternative therapies. Several preclinical studies evaluating the anticancer effect of curcumin in animal models of glioma are reported, but a systematic review with meta-analysis of these studies, considering the different experimental conditions used, has not been made up to this date. A search in different databases (Pubmed, Web of Science, Scopus, and SciELO) following the PRISMA statement was conducted during November 2023 to systematically identify articles assessing the effect of curcumin in murine xenograft models of glioma and identified 15 articles, which were subdivided into 24 studies. Tumor volume before and after treatment with curcumin or vehicle was extracted and the efficacy of curcumin was evaluated by performing a random effects meta-analysis of the data. Publication bias and the impact of different experimental conditions on curcumin efficacy were assessed. Treatment with curcumin decreased tumor volume. Comparing curcumin with control groups, the overall weighted standardized difference in means was −2.079 (95% CI: −2.816 to −1.341; p-value < 0.001). The curcumin effect was observed for different animal models, types of glioma cells, administration routes, and curcumin formulations. Publication bias was identified but does not invalidate curcumin’s effectiveness. The findings suggest the potential therapeutic efficacy of curcumin against glioma.
- Analysis of grade repetition through multilevel models: A study from PortugalPublication . Bastos, Amélia; Ferrão, Maria EugéniaThis paper investigates grade repetition in Portugal using microdata. Drawing on multilevel models, we analyse the number of times the student repeated a grade in compulsory education – our dependent variable – in association with children’s individual characteristics, household sociodemographic and economic background, and children’s living conditions – our covariates. Furthermore, we also attempt to shed light on the impact of schools on the endogenous variable. Our results confi rm the importance of individual, family, and neighbourhood characteristics on the rate of grade repetition. In terms of schools, the results obtained show that the student’s probability of failure vary across schools, demonstrating the importance of the impact of the school itself on grade repetition.
- Analyzing the Gaver - Lewis Pareto Process under an Extremal PerspectivePublication . Ferreira, Marta; Ferreira, HelenaPareto processes are suitable to model stationary heavy-tailed data. Here, we consider the auto-regressive Gaver–Lewis Pareto Process and address a study of the tail behavior. We characterize its local and long-range dependence. We will see that consecutive observations are asymptotically tail independent, a feature that is often misevaluated by the most common extremal models and with strong relevance to the tail inference. This also reveals clustering at “penultimate” levels. Linear correlation may not exist in a heavy-tailed context and an alternative diagnostic tool will be presented. The derived properties relate to the auto-regressive parameter of the process and will provide estimators. A comparison of the proposals is conducted through simulation and an application to a real dataset illustrates the procedure.
- ANOVA with random sample sizes: An application to a Brazilian database on cancer registriesPublication . Nunes, Célia; Capistrano, Gilberto; Ferreira, Dário; Ferreira, Sandra S.ANOVA is routinely used in many situations, namely in medical research, where the sample sizes may not be previously known. This leads us to consider the samples sizes as realizations of random variables. The aim of this paper is to extend one-way random effects ANOVA to those situations and apply our results to a Brazilian database on cancer registries.
- Application domains for the Delta methodPublication . Nunes, Célia; Oliveira, Manuela M.; Mexia, João T.The Delta method uses truncated Lagrange expansions of statistics to obtain approximations to their distributions. In this paper, we consider statistics Y = g(μ + X), where X is any random vector.We obtain domains D such that, when μ ∈ D, we may apply the distribution derived from the Delta method. Namely, we will consider an application on the normal case to illustrate our approach.
- Approximate Normality of Low Degree Polynomials in Normal Independent VariablesPublication . Ferreira, Dário; Ferreira, Sandra S.; Nunes, Célia; Ramos, Luís; Mexia, João T.In this paper, we emphasize that polynomials are asymptotically linear functions and show, through Monte Carlo methods, that when the variation coefficients are small, low degree polynomials in normal independent variables are approximately normal. An application which illustrates the approach is presented.
- Arithmetic for closed ballsPublication . Beites, P. D.; Nicolás, A. P.; Vitoria, JoseInspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn.
- Asymptotic dependence of bivariate maximaPublication . Ferreira, Helena; Ferreira, MartaThe Ledford and Tawn model for the bivariate tail incorporates a coefficient, η, as a measure of pre-asymptotic dependence between the marginals. However, in the limiting bivariate extreme value model, G, of suitably normalized component-wise maxima, it is just a shape parameter without reflecting any description of the dependency in G. Under some local dependence conditions, we consider an index that describes the pre-asymptotic dependence in this context. We analyze some particular cases considered in the literature and illustrate with examples. A small discussion on inference is presented at the end.
- Balanced prime basis factorial fixed effects model with random number of observationsPublication . Oliveira, Sandra; Nunes, Célia; Moreira, Elsa; Fonseca, Miguel; Mexia, João T.Factorial designs are in general more efficient for experiments that involve the study of the effects of two or more factors. In this paper we consider a p^U factorial model with U factors, each one having a p prime number of levels. We consider a balanced (r replicates per treatment) prime factorial with fixed effects. Our goal is to extend these models to the case where it is not possible to known in advance the number of treatments replicates, r. In these situations is more appropriate to consider r as a realization of a random variable R, which will be assumed to be geometrically distributed. The proposed approach is illustrated through an application considering simulated data.