Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- Theoretical analysis of a discrete population balance model with sum kernelPublication . Kaushik, Sonali; Kumar, Rajesh; Costa, Fernando Pestana daThe Oort–Hulst–Safronov equation is a relevant population balance model. Its discrete form, developed by Pavel Dubovski, is the main focus of our analysis. The existence and density conservation are established for nonnegative symmetric coagulation rates satisfying V_{i;j} \leq i + j , \forall i, j \in N. Differentiability of the solutions is investigated for kernels with V_{i;j} \leq i^\apha + j^\alpha˛ where 0 \leq \alpha \leq 1 with initial conditions with bounded (1+\alpha)-th moments. The article ends with a uniqueness result under an additional assumption on the coagulation kernel and the boundedness of the second moment.
- A new R-function to estimate the PDF of the product of two uncorrelated normal variablesPublication . Seijas-Macias, J. Antonio; Oliveira, Amilcar; Oliveira, TeresaThis paper analyses the implementation of a procedure using the software R to calculate the Probability Density Function (PDF) of the product of two uncorrelated Normally Distributed Random Variables. The problem of estimating the distribution of the product of two random variables has been solved for some particular cases, but there is no unique expression for all possible situations. In our study, we chose Rohatgi’s theorem as a basis for approximating the product of two uncorrelated Normally Distributed Random Variables. The numerical approximation of the product PDF was calculated using a function that we implemented in R. Several numerical examples show that the approximations obtained in R fit the theoretical values of the product distributions. The results obtained with our R function are very positive when we compare them with the Monte Carlo Simulation of the product of the two variables.
- Simple Lyapunov spectrum for linear homogeneous differential equations with Lp parametersPublication . Amaro, Dinis; Bessa, Mário; Vilarinho, HelderIn the present paper we prove that densely, with respect to an Lp-like topology, the Lyapunov exponents associated to linear continuous-time cocycles induced by second order linear homogeneous differential equations are almost everywhere distinct. The coefficients evolve along the orbit for an ergodic flow defined on a probability space. We also obtain the corresponding version for the frictionless equation and for a Schrödinger equation.
- Genericity of trivial Lyapunov spectrum for L-cocycles derived from second order linear homogeneous differential equationsPublication . Amaro, Dinis; Bessa, Mário; Vilarinho, HelderWe consider a probability space M on which an ergodic flow is defined. We study a family of continuous-time linear cocycles, referred to as kinetic, that are associated with solutions of the second-order linear homogeneous differential equation . Our main result states that for a generic subset of kinetic continuous-time linear cocycles, where generic means a Baire second category with respect to an -like topology on the infinitesimal generator, the Lyapunov spectrum is trivial.
- Billiards in generic convex bodies have positive topological entropyPublication . Bessa, Mário; Del Magno, Gianluigi; Dias, João Lopes; Gaivão, José Pedro; Torres, Maria JoanaWe show that there exists a C2-open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits.
- Improving the conditioning of the method of fundamental solutions for the Helmholtz equation on domains in polar or elliptic coordinatesPublication . Antunes, Pedro R. S.; Calunga, Hernani; Serranho, PedroA new approach to overcome the ill-conditioning of the Method of Fundamental Solutions (MFS) combining Singular Value Decomposition (SVD) and an adequate change of basis was introduced in [1] as MFS-SVD. The original formulation considered polar coordinates and harmonic polynomials as basis functions and is restricted to the Laplace equation in 2D. In this work, we start by adapting the approach to the Helmholtz equation in 2D and later extending it to elliptic coordinates. As in the Laplace case, the approach in polar coordinates has very good numerical results both in terms of conditioning and accuracy for domains close to a disk but does not perform so well for other domains, such as an eccentric ellipse. We therefore consider the MFS-SVD approach in elliptic coordinates with Mathieu functions as basis functions for the latter. We illustrate the feasibility of the approach by numerical examples in both cases.
- Herbrandized modified realizabilityPublication . Ferreira, Gilda; Firmino, PauloRealizability notions in mathematical logic have a long history, which can be tracedback to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations ofintuitionistic logic. Kleene’s initial realizability laid the ground for more sophisticatednotions such as Kreisel’s modified realizability and various modern approaches. Inthis context, our work aligns with the lineage of realizability strategies that emphasizethe accumulation, rather than the propagation of precise witnesses. In this paper, weintroduce a new notion of realizability, namely herbrandized modified realizability.This novel form of (cumulative) realizability, presented within the framework of semi-intuitionistic logic is based on a recently developed star combinatory calculus, whichenables the gathering of witnesses into nonempty finite sets. We also show that theprevious analysis can be extended from logic to (Heyting) arithmetic.
- Online group consultation on labor analgesia for pregnant women: is it feasible?Publication . Tomás, Ana Sofia; Dias, Raquel M.; Cabido, Hermínia; Nunes, Catarina S.; Lemos, PauloIntroduction: Our department of anesthesiology has been conducting weekly, for several years, a group consultation to educate childbearing people about labor analgesia. The emergence of the COVID-19 pandemic forced an adaptation to a virtual consultation format. Since there are no studies about online group consultation on labor analgesia in order to understand its role, an anonymous questionnaire was created and applied. The objective was to evaluate this new consultation format, namely the ease of access, usefulness of the content provided, and its impact on the satisfaction and experience of childbirth. Materials and methods: An observational prospective study was conducted. A questionnaire was sent by email after childbirth to all childbearing people participating in the online consultation from January 20, 2021, to March 2, 2022. SPSS Statistics version 28.0 (IBM Corp. Released 2021. IBM SPSS Statistics for Windows, Version 28.0. Armonk, NY: IBM Corp) was used for statistical analysis. Internal consistency was analyzed using Cronbach’s alpha. Results: A total of 563 participants were eligible, and 404 (71.8%) completed questionnaires were analyzed. A few technical problems were reported. The participants considered their privacy respected, and more than 90% were satisfied with the content of the online consultation, the opportunity to pose questions, and the help managing expectations. Considering face-to-face consultation, 89.6% of patients considered the online format an effective alternative, 63.2% believed it could replace the old model, and 96.3% would recommend it. Conclusions: Our study demonstrates that online consultation on labor analgesia was a good strategy during the COVID-19 pandemic and has the potential to be used in this format in the future.
- Incidence of postoperative residual neuromuscular blockade: a multicenter, observational study in Portugal (INSPIRE 2)Publication . Esteves, Simão; Barros, Filinto Correia de; Nunes, Catarina S.; Puga, Andreia; Gomes, Blandina; Abelha, Fernando; Machado, Humberto; Ferreira, Milene; Fernandes, Nuno; Vítor, Paula; Pereira, Sandra; Lapa, Teresa A.; Oliveira, Vítor PinhoBackground: Although the use of neuromuscular blocking agents (NMBAs) optimizes surgical conditions and facilitates tracheal intubation, it can lead to residual neuromuscular blockade (RNMB), with postoperative complications. This study aimed to assess RNMB incidence and management in Portugal. Methods: Prospective observational study of patients admitted for elective surgery requiring general anesthesia with nondepolarizing NMBAs between July 2018 and July 2019 at 10 Portuguese hospitals. The primary endpoint was the proportion of patients arriving at postanesthesia care unit (PACU) with a TOF ratio ,0.9. Results: A total of 366 patients were included, with a median age of 59 years, and 89.1% classified as ASA II or III. Rocuronium was the most used NMBA (99.5%). A total of 96.2% of patients received a reversal agent, 96.6% of which sugammadex and 3.4% neostigmine. Twenty patients displayed a TOF ratio ,0.9 at PACU arrival, representing an RNMB incidence of 5.5% (95% CI, 3.1%–7.8%). Only two patients displayed a TOF ratio ,0.7. RNMB incidence was 16.7% with neostigmine and 5.3% with sugammadex (P 5 .114). In patients with intraoperative neuromuscular blockade (NMB) monitoring, RNMB incidence was 5% (95% CI, 2%–8%), which varied significantly according to the type of monitoring (P 5 .018). Incidence of adverse events was 3.3% (2 severe and 10 moderate). Conclusions: The reported overall incidence of 5.5% is numerically lower than results from similar observational studies. An appropriate pharmacological neuromuscular reversal strategy, guided by quantitative neuromuscular monitoring, has the potential to achieve even better results, converting RNMB from an unusual to a very rare or even inexistent event.
- Acid phosphatase, some genetic polymorphism and obesity risk factors in adult womenPublication . Carolino, E.; Oliveira, T.; Silva, A. P.; Carvalho, R; Bicho, M.Recent works point out to a relation between some genetic factors and the predisposition for obesity. We believe, therefore, to be relevant to conduct this kind of study in the Portuguese population. In the present work the following genetic factors are considered: Haptoglobin phenotype, the Acid Phosphatasehenotype and two blood group systems, the MN System and the Lewis System. In addition, it was also considered one demographic factor, age, and one enzymatic activity, the Acid Phosphatase Activity. Haptoglobin (Hp) is a hemoglobin-binding protein of the immune system expressed by a genetic polymorphism with three major phenotypes. This protein is associated in some works with susceptibility for common pathological situations, such as some disorders related with obesity. The Acid phosphatase, more precisely the Acid phosphatase locus 1 (ACP1), is a highly polymorphic enzyme that has an important role in flavoenzyme activity and in the control of insulin receptor activity. High ACP1 activity was positively associated with high glycemic levels and with high body mass index (BMI) values. The MN blood system is a blood group system with three phenotypes each one showing different associations with some diseases, including some related with obesity. Finally, the Lewis System was focused on a single locus with two antigens, Le a and Le b. Confirming this characteristic as a genetic marker of obesity may contribute to the explanation of individual differences in the prevalence of obesity. The group under study involves 85 Portuguese adult women with complete data for all variables, taken from a data base with 714 subjects from the Genetic Laboratory, Centre of Endocrinology and Metabolism of University of Lisbon. The aim of the study is to explore and examine the relationship between the weight categories and the explanatory variables, with emphasis on risk for obesity. Therefore, an ordinal regression model was tried, considering as the regressor variables the Haptoglobin phenotype, Acid phosphatase (ACP1) phenotype, MN blood group system, Lewis system, the enzymatic activity of ACP1, age and some association effects between these factors. Some significant main effects were found at a 5% significance level: the phenotypeLe(a-b+) of Lewis System (p-value=0,021) and age (p-value=0,002). The phenotype Le(a-b+) of Lewis System is associated with a decreased risk for obesity (odds ratio 0,139; CI95%(0,016; 0,754)); age (as expected) is associated with an increased risk for obesity (odds ratio 1,11; CI95%(1,038; 1,190))