Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- 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.
- Anesthesia and postoperative analgesia for cesarean section: a retrospective observational studyPublication . Pombo, André; Guimarães, Henrique; Araújo, Ana M.; Nunes, Catarina S.; Cabido, Hermínia; Lemos, PauloObjectives: The current state of the art for c‑section anesthesia includes the use of regional anesthesia techniques because of their effectiveness, safety, and extended postoperative analgesia. This study aimed to analyze the anesthetic techniques employed for c‑section and postoperative analgesic regimens and to identify predictive factors for postoperative pain, postoperative complications, and hospitalization time. Study Design: A retrospective, observational study was conducted on pregnant women who underwent c‑section between January and December 2021. Demographic data, medical comorbidities, indications for c‑section, anesthetic techniques, and postoperative outcomes (pain, complications, and hospitalization time) were registered. Linear and logistic regression were applied for data analysis. Results: Data from 925 women who underwent c‑sections were analyzed. Combined spinal–epidural anesthesia was the most used technique for elective c‑sections (423 out of 430 women), while general anesthesia was commonly used in emergent procedures (29 out of 39 women). Epidural analgesia was the most commonly used technique for postoperative pain management (83%), and pruritus (8.9%) and headaches (4.1%) were the most frequently registered complications. Risk factors for moderate/severe pain included lower body mass index, conversion to general anesthesia, and the use of systemic analgesia. Preeclampsia and intrathecal morphine increased postoperative complications. General anesthesia and some postoperative complications were predictors for longer hospitalization times. Conclusions: This study suggests that a multimodal analgesic approach with neuraxial morphine and/or local anesthetics, nonsteroidal anti‑inflammatory drugs, and acetaminophen is central to achieve an effective postoperative analgesia after a c‑section. However, further studies should investigate the optimal neuraxial analgesic combination to minimize side effects.
- Clinical prediction and spatial statistical analysis of ascending thoracic aortic aneurysm structurePublication . Rodriguez, Katalina; Carvalho, Alda; Valente, Rodrigo; Xavier, José; Tomás, AntónioThis study presents an analysis of data from patients with ascending thoracic aortic aneurysms (ATAAs). Two databases of 87 patients were available: one containing clinical variables and the other consisting of measurements of the maximum diameter taken along the ascending aorta. For the clinical database, both a supervised and an unsupervised learning method were applied to explore patterns within the data. On the other hand, for the ascending aorta dataset, experimental variograms were calculated, from which key parameters of interest were extracted. These parameters were then analyzed over time to assess temporal patterns. This analysis aimed to assess the emergence of similar patterns or behaviour in patients with aneurysms of comparable sizes. Based on the analyses conducted, the clinical variables with the greatest importance in surgical decision-making were identified, while the spatial statistical analysis revealed patterns that may be related to elasticity, stiffness, or deformations of the aorta
- Clustering of wind speed time series as a tool for wind farm diagnosisPublication . Martins, Ana; Vaz, Daniel; Silva, Tiago; Cardoso, Margarida; Carvalho, AldaIn several industrial fields, environmental and operational data are acquired with numerous purposes, potentially generating a huge quantity of data containing valuable information for management actions. This work proposes a methodology for clustering time series based on the K-medoids algorithm using a convex combination of different time series correlation metrics, the COMB distance. The multidimensional scaling procedure is used to enhance the visualization of the clustering results, and a matrix plot display is proposed as an efficient visualization tool to interpret the COMB distance components. This is a general-purpose methodology that is intended to ease time series interpretation; however, due to the relevance of the field, this study explores the clustering of time series judiciously collected from data of a wind farm located on a complex terrain. Using the COMB distance for wind speed time bands, clustering exposes operational similarities and dissimilarities among neighboring turbines which are influenced by the turbines’ relative positions and terrain features and regarding the direction of oncoming wind. In a significant number of cases, clustering does not coincide with the natural geographic grouping of the turbines. A novel representation of the contributing distances—the COMB distance matrix plot—provides a quick way to compare pairs of time bands (turbines) regarding various features.
- 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.
- 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.
- 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.
- The MFS-SVD method for the laplace equation in three dimensionsPublication . Antunes, Pedro; Santos, Vinicius; Serranho, PedroThe method of fundamental solutions (MFS) has been widely used to numerically solve boundary value problems involving linear partial differential equations. This method is easy to implement computationally and can be very effective for smooth domains and boundary conditions. The main drawback of the MFS is the ill-conditioning of the associated matrices, which may deteriorate the method’s accuracy. We present three methods to reduce the ill-conditioning of the classical MFS for the Laplace equation defined in bounded star-shaped domains in 3D. The idea is to expand the MFS basis functions in terms of spherical harmonics, in order to use the reduced QR factorization and singular value decomposition to deal with the ill-conditioning, leading to a better function basis that spans the same approximation space as the classical MFS. The numerical results illustrate that these approaches significantly decrease the ill-conditioning, allowing higher accuracy when compared to the classical MFS.
- Some notes on disjunctive short sum: polychromatic nimPublication . Carvalho, Alda; Santos, Carlos Pereira dospolychromatic nim is a version of the classic game nim, played with colored stones, in which each pile has stones of a single color, and the player who successfully extinguishes a color wins the game. This game is closely related to the concept of short rule, the ending condition that states that a disjunctive sum ends as soon as any one of the components ends. Here, we discuss that rule, namely when applied to impartial games, and prove that the Grundy-values of polychromatic nim present an arithmetic-periodic behavior.
- A statistical assessment of drilling effects on glass fiber-reinforced polymeric compositesPublication . Martins, Ana; Carvalho, Alda; Bragança, Ivo; Barbosa, Inês; Barbosa, Joaquim; Loja, AméliaFiber-reinforced composites are extensively used in many components and structures in various industry sectors, and the need to connect and assemble such types of components may require drilling operations. Although drilling is a common machining process; when dealing with fiber-reinforced composite materials, additional and specific problems may arise that can com-promise mechanical integrity. So, the main goal of this work is to assess how various input variables impact two main outcomes in the drilling process: the exit-adjusted delamination factor and the maximum temperature on the bottom surface where the drilling tool exits. The input variables include the type of drilling tools used, the operating speeds, and the thickness of the plates being drilled. By using Analysis of Variance (ANOVA), the analysis aims to identify which factors significantly influence damage and exit temperature. The results demonstrate that the influence of tools and drilling parameters is critical, and those selections impact the quality of the hole and the extent of the induced damage to the surrounding area. In concrete, considering the initially selected set of tools, the BZT03 tool does not lead to high-quality holes when drilling medium- and high-thickness plates. In contrast, the Dagger tool shows potential to reduce exit hole damage while also lowering temperature.