Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- High Positive End-Expiratory Pressure (PEEP) with Recruitment Maneuvers versus Low PEEP during General Anesthesia for Surgery: A Bayesian Individual Patient Data Meta-analysis of Three Randomized Clinical TrialsPublication . Mazzinari, Guido; Zampieri, Fernando G.; Ball, Lorenzo; Campos, Niklas S.; Bluth, Thomas; Hemmes, Sabrine N. T.; Ferrando, Carlos; Librero, Julian; Soro, Marina; Pelosi, Paolo; Abreu, Marcelo Gama de; Schultz, Marcus J.; Neto, Ary Serpa; Nunes, Catarina S.Background: The influence of high positive end-expiratory pressure (PEEP) with recruitment maneuvers on the occurrence of postoperative pulmonary complications after surgery is still not definitively established. Bayesian anal ysis can help to gain further insights from the available data and provide a probabilistic framework that is easier to interpret. The objective was to estimate the posterior probability that the use of high PEEP with recruitment maneuvers is associated with reduced postoperative pulmonary complications in patients with intermediate-to-high risk under neutral, pessimistic, and opti mistic expectations regarding the treatment effect. Methods: Multilevel Bayesian logistic regression analysis was performed on individual patient data from three randomized clinical trials carried out on sur gical patients at intermediate to high risk for postoperative pulmonary com plications. The main outcome was the occurrence of postoperative pulmonary complications in the early postoperative period. This study examined the effect of high PEEP with recruitment maneuvers versus low PEEP ventilation. Priors were chosen to reflect neutral, pessimistic, and optimistic expectations of the treatment effect. Results: Using a neutral, pessimistic, or optimistic prior, the posterior mean odds ratio for high PEEP with recruitment maneuvers compared to low PEEP was 0.85 (95% credible interval, 0.71 to 1.02), 0.87 (0.72 to 1.04), and 0.86 (0.71 to 1.02), respectively. Regardless of prior beliefs, the posterior proba bility of experiencing a beneficial effect exceeded 90%. Subgroup analysis indicated a more pronounced effect in patients who underwent laparoscopy (odds ratio, 0.67 [0.50 to 0.87]) and those at high risk for postoperative pul monary complications (odds ratio, 0.80 [0.53 to 1.13]). Sensitivity analysis, considering severe postoperative pulmonary complications only or applying a different heterogeneity prior, yielded consistent results. Conclusions: High PEEP with recruitment maneuvers demonstrated a moderate reduction in the probability of postoperative pulmonary complica tion occurrence, with a high posterior probability of benefit observed consis tently across various prior beliefs, particularly among patients who underwent laparoscopy.
- Knowledge and perceptions of regional anesthesia and block room usage among orthopaedic surgeons and nursesPublication . Mendes, Ângela Barbosa; Silva, Carlota Carvalho da; Dias, Raquel; Nunes, Catarina S.; Machado, Humberto; Lages, NeusaBackground: The performance of regional anesthesia (RA) in a block room (BR) may have an impact on the efficiency of the orthopaedics operating room (OR). The aim of this study was to understand the knowledge of healthcare professionals regarding RA and BR. Methods: Two types of pilot surveys were developed and applied in three independent hospitals. Statistical validation of the survey was performed (Cronbach alpha coefficient and factor analysis), followed by its restructuring. Validated surveys were randomly delivered to orthopaedists and OR nurses from our institution, and a descriptive analysis was performed. Results: The pilot surveys presented a Cronbach alpha of 0.533 and 0.417 in the orthopaedic and OR nurse groups, respectively. Two questions in each survey were removed, increasing the internal consistency of the final restructured surveys. There was a total of 126 validated surveys completed (46 by orthopaedists and 76 by OR nurses). Both groups consider that, compared with general anesthesia, RA is associated with better pain control (95.7%/93.4%), fewer side effects (63%/73.7%), and improved patient satisfaction (84.7%/69.7%). Both groups would choose RA for themselves (89.1%/89.5%) and recommend it to a family member (89.1%/92.1%). Regarding BR, 80.4% of orthopaedists agreed that it is associated with less time wasted in anesthetic preparation, higher productivity (65.2%), and greater efficacy (65.2%). Conclusions: Most orthopaedists and OR nurses recognized the various benefits of RA. Orthopaedists agreed that BR improves outcomes and provides efficiency gains in the OR. Genuine support from the entire OR team can play a critical role in the change.
- 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, Teresa A.This 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.