Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- 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.
- Variability on functionally graded plates’ deflection due to uncertainty on carbon nanotubes’ propertiesPublication . Carvalho, Alda; Martins, Ana; Mota, Ana; Loja, AméliaCarbon nanotubes are widely used as material reinforcement in diverse fields of engineering. Being that their contribution is significant to improving the mean properties of the resulting materials, it is important to assess the influence of the variability on carbon nanotubes’ material and geometrical properties to structures’ responses. This work considers functionally graded plates constituted by an aluminum continuous phase reinforced with single-walled or multi-walled carbon. The nanotubes' weight fraction evolution through the thickness is responsible for the plates’ functional gradient. The plates’ samples are simulated considering that only the nanotubes’ material and geometrical characteristics are affected by uncertainty. The results obtained from the multiple regression models developed allow us to conclude that the length of the nanotubes has no impact on the maximum transverse displacement of the plates in opposition to the carbon nanotubes’ weight fraction evolution, their internal and external diameters, and the Young’s modulus. The multiple regression models developed can be used as alternative prediction tools within the domain of the study.
- 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.
- 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.
- How to avoid the commuting conversions of IPCPublication . Espírito Santo, José; Ferreira, GildaSince the observation in 2006 that it is possible to embed IPC into the atomic polymorphic λ-calculus (a predicative fragment of system F with universal instantiations restricted to atomic formulas) different such embeddings appeared in the literature. All of them comprise the Russell-Prawitz translation of formulas, but have different strategies for the translation of proofs. Although these embeddings preserve proof identity, all fail in delivering preservation of reduction steps. In fact, they translate the commuting conversions of IPC to β-equality, or to other kinds of reduction or equality generated by new principles added to system F. The cause for this is the generation of redexes by the translation itself. In this paper, we present an embedding of IPC into atomic system F, still based on the same translation of formulas, but which maps commuting conversions to syntactic identity, while simulating the other kinds of reduction steps present in IPC by βη-reduction. In this sense the translation achieves a truly commuting-conversion-free image of IPC in atomic system F.
- 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.