Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- A hybrid method for the time-harmonic inverse acoustic transmission problemPublication . Paixão, João; Serranho, PedroThe inverse transmission problem of scattering an acoustic wave by a penetrable object has several applications in various fields such as radar, sonar, geophysical exploration, medical imaging and non destructive testing. Here we propose a numerical hybrid method to inverse acoustic scattering by penetrable obstacles from far-field data in two-dimensions, that extends an iterative decomposition method to the transmission problem. The proposed method starts by reconstructing the scattered and interior field by imposing the far-field equation and one of the transmission conditions and, in the second step it uses the second transmission condition to update the position of the approximated boundary, by linearization. Also, we compared two approaches for the linearization step: a Newtontype method; and a gradient-type method with a penalty term for high oscillations of the solution. We also support the methods by a convergence result for a related optimization problem. Numerical results from eight incident directions show the method is feasible, though sensitive to noise.
- Tail-adaptive generation of random numbers from a gamma-order normal distribution using the Ziggurat algorithm with a multivariate extensionPublication . Kitsos, Christos P.; Oliveira, Amilcar; Ulrich, Eschcol Nyamsi; Leiva, Victor; Castro, CecíliaThe Ziggurat algorithm is a well-established rejection-sampling method designed for the efficient generation of pseudo-random numbers from unimodal distributions, particularly the standard normal. In this work, we extend and adapt the Ziggurat algorithm to enable the tail-adaptive generation of random numbers from the gamma-order generalized normal distribution |a flexible family characterized by a tail-shaping parameter that governs transitions between light, Gaussian, and heavy-tailed regimes. The resulting algorithm retains the computational speed of the original Ziggurat algorithm while supporting both univariate and multivariate implementations. This extension is especially relevant in simulation-intensive contexts, such as Bayesian modeling, quantitative nance, and machine learning. We provide the mathematical foundation, reproducible implementation details, and extensive benchmarking results that validate the method's efficiency and accuracy. A multivariate extension based on radial decomposition is also introduced, demonstrating the feasibility of generating random variables from symmetric multivariate distributions in practice. To illustrate the practical utility of the proposed algorithm, we present a comprehensive Monte Carlo simulation study evaluating performance across various shape and scale con gurations. Additionally, we apply the method to real-world data from biomedical signal processing, highlighting its robustness and adaptability to empirical settings where tail behavior plays a crucial role.
- The discrete generalized exchange-driven systemPublication . Barik, Prasanta Kumar; Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael; F.P. DA COSTAWe study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions, we prove that, in the class of models, we call isolated both the total number of particles and the total mass are conserved, whereas in those models, we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations, we obtain uniqueness of solutions to the initial value problems.
- Positive topological entropy for semi-Riemannian geodesic flowsPublication . Bessa, Mário; Dias, João Lopes; Matias, Pedro; Torres, Maria Joana; Wenxian , ShenWe consider a semi-Riemannian metric whose associated geodesic flow either contains a non-hyperbolic periodic orbit or has infinitely many hyperbolic periodic orbits. Under some conditions, we show that the metric can be perturbed such that the geodesic flow exhibits positive topological entropy, there are infinitely many non-lightlike closed geodesics, and their number grows exponentially with respect to the length.
- Finite difference calculus in the continuumPublication . Finkelshtein, Dmitri; Kondratiev, Yuri; Lytvynov, Eugene; Oliveira, Maria JoãoWe describe known and new results on the finite-difference calculus on configuration spaces. We also describe the finite-difference geometry on configuration spaces, relate finite-difference operators to the canonical commutation relations, find explicit form of certain finite-difference Markov generators on configuration spaces, and describe spaces of Newton series defined over the configuration spaces.
- Analysis on the cone of discrete Radon measuresPublication . Finkelshtein, Dmitri; Kondratiev, Yuri; Kuchling, Peter; Lytvynov, Eugene; Oliveira, Maria JoãoWe study analysis on the cone of discrete Radon measures over a locally compact Polish space X. We discuss probability measures on the cone and the corresponding correlation measures and correlation functions on the sub-cone of finite discrete Radon measures over X. For this, we consider on the cone an analogue of the harmonic analysis on the configuration space developed in [Y. G. Kondratiev, T. Kuna, Harmonic analysis on configuration space. I. General theory, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 5 (2002), 201–233.]. We also study elements of finite-difference calculus on the cone: we introduce discrete birth-and-death gradients and study the corresponding Dirichlet forms; finally, we discuss a system of polynomial functions on the cone which satisfy the binomial identity.
- 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.