IME - Artigos publicados em periódicos

URI Permanente para esta coleçãohttp://200.137.215.59//handle/ri/1341

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Approximate proximal methods for variational inequalities on Hadamard manifolds
(2025) Bento, Glaydston de Carvalho; Ferreira, Orizon Pereira; Papa Quiroz, Erik Alex
In this paper, we present an approximate proximal point method for addressing the variational inequality problem on Hadamard manifolds, and we analyse its convergence properties. The proposed algorithm exhibits inexactness in two aspects. Firstly, each proximal subproblem is approximated by utilizing the enlargement of the vector field under consideration, and subsequently, the next iteration is obtained by solving this subproblem while allowing for a suitable error tolerance. As an illustrative application, we develop an approximate proximal point method for nonlinear optimization problems on Hadamard manifolds.
Subsampled cubic regularization method for finite-sum minimization
(2025) Gonçalves, Max Leandro Nobre
This paper proposes and analyses a subsampled Cubic Regularization Method (CRM) for solving finite-sum optimization problems. The new method uses random subsampling techniques to approximate the functions, gradients and Hessians in order to reduce the overall computational cost of the CRM. Under suitable hypotheses, first- and second-order iteration-complexity bounds and global convergence analyses are presented. We also discuss the local convergence properties of the method. Numerical experiments are presented to illustrate the performance of the proposed scheme.
An inexact proximal point method with quasi-distance for quasiconvex multiobjective optimization problems on Riemannian manifolds
(2025) Upadhyay, Balendu Bhooshan; Poddar, Subham; Ferreira, Orizon Pereira; Jen-Chih, Yao
In this paper, we investigate a class of unconstrained multiobjective optimization problems in the framework of Riemannian manifolds (abbreviated as, MOP-RM), where the components of the objective function are assumed to be locally Lipschitz and quasiconvex. By employing the powerful tool of Mordukhovich limiting subdifferential, we introduce an inexact proximal point algorithm with quasi-distance (abbreviated as, IPPMQ-RM), to solve MOP-RM. Moreover, we establish the well-definedness of the sequence generated by the IPPMQ-RM algorithm. Based on two different versions of error criteria, we introduce two variants of IPPMQ-RM, namely, IPPMQ-RM1 and IPPMQ-RM2. We deduce that the cluster points of the sequences generated by the IPPMQ-RM1 and IPPMQ-RM2 algorithms are Pareto-Mordukhovich critical points of MOP-RM. Further, we derive that if the components of the objective function of MOP-RM are geodesic convex, then these cluster points become Pareto efficient solutions of MOP-RM. We establish the finite termination of the IPPMQ-RM1 and IPPMQ-RM2 algorithms. By employing MATLAB R2023b, a non-trivial numerical example has been furnished to illustrate the effectiveness of the proposed algorithms, namely, IPPMQ-RM1 and IPPMQ-RM2. Moreover, to demonstrate that the sequence generated by the IPPMQ-RM algorithm converges faster than the algorithms existing in the literature, we furnish several non-trivial numerical examples in the framework of well-known Riemannian manifolds.
Quasilinear elliptic problems via nonlinear rayleigh quotient
(2025) Carvalho, Marcos Leandro Mendes; Gasiński, Leszek; Santos Júnior, João Rodrigues dos; Silva, Edcarlos Domingos da
It is established existence and multiplicity of solution for the following class of quasilinear elliptic problems:{−ΔΦu = 𝜆a(x)|u|q−2u + |u|p−2u, x ∈ Ω,u = 0, x ∈ 𝜕Ω,where Ω ⊂ ℝN, N ≥ 2, is a smooth bounded domain, 1 < q < 𝓁 ≤ m < p < 𝓁∗ and Φ : ℝ → ℝ is suitable N-function.The main feature here is to show whether the Nehari method can be applied to ﬁnd the largest positive number 𝜆∗ > 0in such a way that our main problem admits at least two distinct solutions for each 𝜆 ∈ (0, 𝜆∗ ). Furthermore, using someﬁne estimates and some extra assumptions on Φ, we prove the existence of at least two positive solutions for 𝜆 = 𝜆∗and 𝜆 ∈ (𝜆∗, 𝜆) where 𝜆 > 𝜆∗
Conformally invariant skew curves for the total skew curvature on surfaces of R3
(2025) Narvaez Plaza, Luis Felipe; Garcia, Ronaldo Alves
In differential geometry, curvature-based functionals, such as the total Gaussian curvature, the Willmore energy, and the total geodesic torsion, play a central role in both theoretical investigations and practical applications. In this paper, we study geometric properties of the extremal curves for the next functional where ds is the arc element on S and are the principal curvatures. First, we establish that a necessary and sufficient condition for a surface to be a Dupin cyclide is that its lines of curvature and the extremal curves of functional intersect at a constant angle. Secondly, we demonstrate that the extremal curves of the functional are invariant under inversion. Finally, we show that the determination of functional extremal curves of for any cone, general cylinder, and surfaces of revolution can be reduced to quadratures.
Stability and bifurcation analysis of a Holling-Tanner model with discontinuous harvesting action
(2025) Cristiano, Rony
This work addresses the study of dynamics and bifurcations in a prey–predator model, known in the literature as the Holling–Tanner model, subject to a harvesting action of predators that is activated when the prey population is less than a certain threshold, and stopped otherwise. Such a model is represented by a piecewise smooth system with a switching boundary given by a straight line that is defined by the threshold established for the prey population. Under certain conditions on the system parameters, a pseudo-focus point appears at the switching boundary. Based on the Poincaré map defined in a neighborhood of the pseudo-focus, explicit conditions are given on the system parameters that determine its local stability, the occurrence of Hopf-like bifurcations and the emergence of crossing limit cycles. In addition to Hopf-like bifurcations, other local and global bifurcations such as the classical Hopf bifurcation, the Boundary Equilibrium bifurcations, the Saddle–Node bifurcation of periodic orbits and the Grazing bifurcation are also identified. A complete description of the existence and stability of equilibria and periodic orbits is provided based on the obtained two-parameter bifurcation set, from which the coexistence of four periodic orbits in the phase portrait of the system under study is proved.
On projection mappings and the gradient projection method on hyperbolic space forms
(2025) Bergmann, Ronny; Ferreira, Orizon Pereira; Németh, Sándor Zoltán; Jian-Kang, Zhu
This paper presents several new properties of the intrinsic -projection into -hyperbolically convex sets of -hyperbolic space forms, along with closed-form formulas for the intrinsic -projection into specific -hyperbolically convex sets. It also discusses the relationship between the intrinsic -projection, the Euclidean orthogonal projection and the Lorentz projection. These properties lay the groundwork for analyzing the gradient projection method and hold importance in their own right. Additionally, new properties of the gradient projection method to solve constrained optimization problems in -hyperbolic space forms are established, considering both constant and backtracking step sizes in the analysis. It is shown that every accumulation point of the sequence generated by the method for both step sizes is a stationary point for the given problem. Additionally, an iteration complexity bound is provided that upper bounds the number of iterations needed to achieve a suitable measure of stationarity for both step sizes. Finally, the properties of the constrained Fermat–Weber problem are explored, demonstrating that the sequence generated by the gradient projection method converges to its unique solution. Numerical experiments on solving the Fermat–Weber problem are presented, illustrating the theoretical findings and demonstrating the effectiveness of the proposed methods.
Predicting leishmaniasis outbreaks in Brazil using machine learning models based on disease surveillance and meteorological data
(2025) Donizette, André Cintas; Rocco, Cleber Damião; Queiroz, Thiago Alves de
Leishmaniasis poses a significant global health concern due to the absence of vaccines for humans and high infection rates in some countries. It is classified as a neglected tropical disease. In 2022, roughly 85% of global visceral leishmaniasis cases were reported in seven countries: Brazil, Ethiopia, India, Kenya, Somalia, South Sudan, and Sudan. Despite Brazil’s advanced medical capabilities compared to other affected regions, certain areas still witness a significant number of cases, prompting increased attention from researchers and raising concerns within the healthcare system. This study explores the application of artificial intelligence algorithms, particularly machine learning (ML) models to predict leishmaniasis outbreaks in selected Brazilian cities based on accumulated cases from 2007 to 2022, leveraging available meteorological data to enhance model accuracy. Our investigation concentrated on the following cities in Brazil: Fortaleza/CE, Teresina/PI, and São Luís/MA were chosen for the study of visceral leishmaniasis, whereas Manaus/AM, Rio Branco/AC, and Macapá/AP were selected for the study of tegumentary leishmaniasis, encompassing both cutaneous and mucocutaneous forms. Several Artificial Neural Network (ANN) architectures were evaluated, including a Simple Feedforward Neural Network (SFNN), a Deep Feedforward Neural Network (DFNN), and a Long Short-Term Memory (LSTM) recurrent neural network. Additionally, the Support Vector Machine (SVM), specifically the Support Vector Regression (SVR), was tested. Various metrics were used to identify the most effective models, in which the Root Mean Squared Error (RMSE) was the primary one. The results highlight the significance of meteorological data as a crucial factor in ML models for predicting leishmaniasis outbreaks, while also emphasizing the importance of fine-tuning these models to achieve greater accuracy. Finally, data and the pseudo-code of the models are accessible through an open repository to encourage further studies in this area.
On small breathers of nonlinear Klein-Gordon equations via exponentially small homoclinic splitting
(2025) Gomide, Otávio Marçal Leandro; Guardia, Marcel; Martinez-Seara Alonso, Maria Teresa; Chongchun, Zeng
Inexact Newton methods for solving generalized equations on riemannian manifolds
(2025) Louzeiro, Maurício Silva; Silva, Gilson do Nascimento; Jinyun, Yuan; Daoping, Zhang
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically.
An adaptive cubic regularization inexact-Newton method on riemannian manifolds
(2025) Louzeiro, Maurício Silva; Silva, Gilson do Nascimento; Jinyun, Yuan; Daoping, Zhang
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Under appropriate conditions and without any additional geometric assumptions, local convergence results with linear and quadratic rates, as well as a semi-local convergence result, are obtained for the proposed method. Finally, the theory is applied to the problem of finding a singularity for the sum of two vector fields. In particular, the KKT system for the constrained Riemannian center of mass on the sphere is explored numerically.
A proof of a conjecture of W. Hsiang on invariant cmc hypersurfaces with a singularity at the origin
(2025) Silva, Hilário Alencar da; Garcia, Ronaldo Alves; Silva Neto, Gregório Manoel da
In differential geometry, curvature-based functionals, such as the total Gaussian curvature, the Willmore energy, and the total geodesic torsion, play a central role in both theoretical investigations and practical applications. In this paper, we study geometric properties of the extremal curves for the next functional where ds is the arc element on S and are the principal curvatures. First, we establish that a necessary and sufficient condition for a surface to be a Dupin cyclide is that its lines of curvature and the extremal curves of functional intersect at a constant angle. Secondly, we demonstrate that the extremal curves of the functional are invariant under inversion. Finally, we show that the determination of functional extremal curves of for any cone, general cylinder, and surfaces of revolution can be reduced to quadratures.
Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations
(2025) Silva Júnior, Paulo César da; Ferreira, Orizon Pereira; Silva, Gilson do Nascimento
This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are not necessarily differentiable. The proposed method integrates the classical secant approach with techniques inspired by the Conditional Gradient method to handle constraints effectively. We establish local convergence results by applying the contraction mapping principle. Specifically, under assumptions of Lipschitz continuity, a modified Broyden update for derivative approximation, and the metric regularity property, we show that the algorithm generates a well-defined sequence that converges locally at a Q-linear rate.
On generating properties of the weak commutativity of p-groups, p odd
(2025) Bastos Júnior, Raimundo de Araújo; Oliveira, Ricardo Nunes de; Gonçalves, Nathália Nogueira; Monetta, Carmine
In the present paper, we examine the generating properties of Sidki’s weak commutativity group. More precisely, if G and G φ are two isomorphic groups, the weak commutativity group χ(G) is the group generated by G and G φ subject to the relations[g, g φ ] = 1 for all g ∈ G. Here we provide bounds for the number of generators of some subgroups of χ(G) when G is a p-group of odd order and either G is powerful or D(G) is abelian.
Dynamics of an intermittent HIV treatment using piecewise smooth vector fields with two switching manifolds
(2025) Carvalho, Tiago de; Cunha, Jackson Luiz Orione Rafael; Euzébio, Rodrigo Donizete; Florentino, Marco Aurélio do Carmo
In this paper we study the dynamics of a piecewise smooth vector field modeling an intermittent human immunodeficiency virus treatment where the patient is recurrently submitted and removed from drug administration. In fact, the protocol says that the drugs are administered when the level of CD4 T defense cells is smaller than a fixed number . When the level of CD4 T cells is greater than a fixed number (distinct from ) the drugs are not administered to provide a better recovery from side effects. Moreover, the orbits of the piecewise smooth vector fields are trapped within a compact set, which proves that the protocol controls the disease.
Characterization of non-deterministic chaos in two-dimensional non-smooth vector fields
(2025) Euzébio, Rodrigo Donizete; Mattos, Pedro Griguol de; Varão Filho, José Régis Azevedo
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos when the Filippov system has non-empty sliding or escaping regions. A fundamental result for continuous flows is the equivalence of topological transitivity and existence of a dense orbit. We prove in our setting that topological transitivity for Filippov systems is indeed equivalent to the existence of a dense Filippov orbit, although, in contrast to the continuous case, we are not able to guarantee that the dense orbit implies the existence of a residual set of dense orbits. Finally, we prove that, in this context, topological transitivity implies strictly positive topological entropy for the Filippov system. This calculation is made using techniques similar to those from symbolic dynamics.
On the local structure of degenerate Teixeira singularities in 3D Filippov systems
(2025) Ramirez Cespedes, Oscar Alexander; Cristiano, Rony; Gomide, Otávio Marçal Leandro
The main goal of this paper is to emphasize the richness of the dynamics emanating from degeneracies at the so-called T-singularity in Filippov systems. More specifically, we characterize the local sliding and crossing dynamics around an invisible two-fold singularity in Filippov systems which presents a degeneracy arising from the contact between the tangency fold curves of a system with the switching manifold. In particular, we prove that, when the contact between such curves is 2 or 3 at this point, then it presents a nonsmooth diabolo emanating from it which has one branch or two branches, respectively. We also analyze global bifurcations of a family of Filippov systems which presents an invisible two-fold singularity having a cubic contact between the fold curves and we show that there is an invariant surface foliated by crossing heteroclinic orbits between -singularities bifurcating from this degenerate singularity. Finally, we show that such kind of scenario appears naturally in applied models of switched electronic circuits and this singularity is realized in an specific model.
Chapple porism: a visual spell
(2025) Russo, Liliana Gabriela; Garcia, Ronaldo Alves
Pascal and a triangular billiard
(2025) Russo, Liliana Gabriela; Garcia, Ronaldo Alves
Is any triangle fit to be a billiard orbit in some ellipse? Is it unique? Can we draw it as a point-conic? We show that this is always the case and provide a synthetic proof leading to a new construction for both the billiard and its caustic. The link between the billiard, incircle, and Euler circle emerges almost naturally. Neat geometric ties between the caustic and exinscribed circles are also brought to light.
Uniform dispersion in growth models on homogeneous trees
(2025) Vargas Júnior, Valdivino; Machado, Fabio Prates; Roldan Correa, Alejandro
We consider the dynamics of a population spatially structured in colonies that are vulnerable to catastrophic events occurring at random times, which randomly reduce their population size and compel survivors to disperse to neighboring areas. The dispersion behavior of survivors is critically significant for the survival of the entire species. In this paper, we consider an uniform dispersion scheme, where all possible survivor groupings are equally probable. The aim of the survivors is to establish new colonies, with individuals who settle in empty sites potentially initiating a new colony by themselves. However, all other individuals succumb to the catastrophe. We consider the number of dispersal options for surviving individuals in the aftermath of a catastrophe to be a fixed value d within the neighborhood. In this context, we conceptualize the evolution of population dynamics occurring over a homogeneous tree. We investigate the conditions necessary for these populations to survive, presenting pertinent bounds for survival probability, the number of colonized vertices, the extent of dispersion within the population, and the mean time to extinction for the entire population.

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