Matemática e Estatística / Mathematics and Statistics
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Percorrer Matemática e Estatística / Mathematics and Statistics por Domínios Científicos e Tecnológicos (FOS) "Ciências Naturais::Matemáticas"
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- Analysis of thoracic aortic aneurysm CTA scans using spatial statisticsPublication . Rodriguez, Katalina; Carvalho, Alda; Valente, Rodrigo; Xavier, José; Tomás, AntónioThis study leverages spatial statistics to analyze the spatial distribution of the aorta, aiming to better understand the biomechanical behavior of Ascending Thoracic Aortic Aneurysms (ATAA) and its impact on clinical outcomes. CTA angiography was performed on 87 ATAA patients. Experimental variograms were computed for various variables, such as maximum diameter, from which key parameters of interest were extracted. These parameters were then analyzed over time to assess temporal patterns. The goal of this analysis was to identify whether similar patterns or behaviors emerge in features from CTA scans of patients with aneurysms of similar sizes, ultimately aiming to statistically validate the quality of the CTA scans.
- 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.
- An application of time series clustering using a combined distancePublication . Martins, Ana; Vaz, Daniel; Silva, Tiago; Cardoso, Margarida; Carvalho, Alda; Loja, AméliaClustering time series aims at uncovering diverse longitudinal patterns. In this study we analyse time series of various parameters collected atop wind turbines in a wind farm in Portugal. Considering wind data in clustering may reveal differences in operation between neighbouring turbines, due to their position relative to one another and to terrain features. In this work, we use an approach to wind speed time series clustering based on a convex combination of distance measures between time series. For visualizing the resulting groups, we propose a graphical representation, Distance Matrix, which is quite more informative than the classical Multidimensional Scaling (MDS) map. This representation allows for quick comparisons between pairs of turbines for (dis)similarities. Our approach provides distinct insights regarding the differences between time series, emphasizing differences in values (Euclidean distance), trends (Pearson-based distance), and cyclical behaviours (Euclidean distance between periodograms and/or autocorrelation structures). In most cases, we found two groups, which were not always coincident with the geographical groups, but the proposed approach could also find the rationale behind the clusters that were formed. The results obtained may help identifying undesirable aerodynamic loads that the blades of a particular wind turbine may be subjected to, thereby shortening its time in-service.
- 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.
- Geometrical and optimizations aspects for approximating the response surface in industryPublication . Kitsos, Christos P.; Oliveira, Teresa A. ; Oliveira, Amilcar; Pardalos, Panos and Rassias, ThemistoclesThe target of this paper is to discuss an approximation when the experimentalist tries to explore the response surface of his industrial experimentation. Different methods under different designs, have been proposed for Response Surface Methods (RSM). We discuss such designs under a geometrical point of view when the optimal response surface is tried to be estimated. A number of applications in RSM are included.
- 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.