Ciência e Natura

On an agent-based SIR model for multi-populations

2024-11-20T12:26:20-03:00

In this paper, we investigate the impact of epidemic spread in a SIR type model with saturation between multiple interacting populations. The model is derived from an average threshold that considers multiple agents. Theoretical analysis confirms the model's well-posedness, indicating that it possesses a unique solution that varies continuously on the basis of the initial conditions and parameters. Additionally, we conduct numerical simulations for a scenario involving two circulating strains, where we also explore the scenario in which the disease mutates upon transmission, leading to increased transmissibility. A comparison between the dynamics of the SIR model with and without saturation reveals that saturation results in a milder disease dynamics.

{ANN-MoC method for the inverse problem of source characterization

2024-11-19T16:01:42-03:00

Inverse problems of neutral particle transport have significant applications in engineering and medicine. In this study, we present a new application of the ANN-MoC method to solve inverse problems of source characterization. It involves estimating the source parameters based on measurements of particle density at the boundaries of a one-dimensional computational domain. In summary, the method employs an artificial neural network (ANN) as a regression model. The neural network is trained using data generated from solutions of the method of characteristics (MoC) for the associated direct transport problem. Results of three test cases are presented. In the first, we highlight the advantage of preprocessing the input data. For all cases, sensibility tests are provided to study the advantages and limitations of the proposed approach in solving inverses problems with noisy data.

Modeling the effect of memory on the propagation of fake news between two populations that share information

2024-11-20T12:42:17-03:00

The dissemination of information can have a huge impact on public opinion, especially if it is false (fake news). In this work, we propose and analyze a reinterpretation of the SIR model that takes into account the effect of memory on the dynamics of fake news diffusion, resulting from use of fractional derivatives, between two distinct population groups. From a theoretical point of view, we will show that the proposed model is well-posed. Furthermore, we will present simulated scenarios showing that the presence of memory reduces the proportion and propagation time of fake news in both populations that interact. Furthermore, we show numerically that the inverse of the rigidity radius cannot be used as a measure of the rate at which fake news disappears.

Circadian rhythm synchronization under the influence of pain: PIM model with memory

2024-11-20T08:01:43-03:00

In this work, we propose and analyze the existence of synchronization/dissynchronization states of in-phase and coupled oscillators that model the influence of external factors such as pain on the biological rhythms of sleep-wakefulness and body temperature under the memory effect. We show the well-posedness of the proposed model and derive analytical solutions for the oscillator system in the synchronized state. The theoretical results are accompanied by some numerical simulations that indicate that the existence of memory contributes to the synchronization of the oscillator system.

Vibratory behavior of Euler-Bernoulli beams on elastic foundation: non-classical boundary conditions, orthogonality and external force

2024-11-22T22:48:02-03:00

In this work we present the Euler-Bernoulli beam theory, also known as classical theory, for a beam on an elastic foundation and with non-classical boundary conditions. Our objective is to expand the class of problems that use fundamental solution theory to obtain the characteristic equation, natural frequencies, modes of vibration and the forced response of problems involving vibrations. As the problem considered is non-classical, due to the boundary conditions considered, it is necessary to obtain an orthogonality condition that involves the mass attached to the end of the beam to decouple the equations and write the forced response.

Burgers' PINNs with transfer learning by θ-scheme

2024-11-29T10:35:16-03:00

The Burgers equation is a well-established test case in the computational modeling of several phenomena, such as fluid dynamics, gas dynamics, shock theory, cosmology and others. In this work, we present the application of physics-informed neural networks (PINNs) with a transfer learning approach using the θ-scheme to solve the Burgers' equation. The proposed approach consists of searching for a discrete solution in time through a sequence of artificial neural networks (ANNs). At each time step, the previous ANN transfers its learning to the next network model, which learns the solution in the current time by minimizing a loss function based on the θ-scheme approximation of the Burgers' equation. To test this approach, we present its application to two benchmark problems with known analytical solutions. Compared to usual PINN models, the proposed approach has the advantage of requiring smaller neural network architectures with similar accurate results and potentially decreasing computational costs.

On a level-set regularization strategy for the identification of a piecewise constant rigidity coefficient in a beam

2024-12-30T11:32:46-03:00

In this work, we analyze a level set regularization strategy to identify the constant piecewise stiffness coefficient in a static Euler-Bernoulli beam, based on indirect deflection measurements. The theoretical results presented are illustrated by some numerical simulations.

Conjugation between tree-subshifts of finite type and Markov tree-subshifts in examples

2024-12-09T09:51:49-03:00

Tree-shifts are a class of discrete dynamical systems, from a certain point of view, intermediate between one-dimensional and multidimensional symbolic dynamics. The concept of conjugation between tree-subshifts has great relevance in this context, since it allows different dynamical systems to be related. It is possible, for example, to obtain several properties of a tree-subshift of finite type from the Markov tree-subshift conjugated to it, for which several results can be found in the literature. However, due to the lack of examples that explore such properties, in this work we present two examples of conjugation between a tree-subshift of finite type and a Markov tree-subshift given by transition matrices and obtain descriptions about the value of entropy, irreducibility, mixing, density of periodic points and chaos in the sense of Devaney of the first from the second.

An Implementation of the Eigenvalue Localization Algorithm for Threshold Graphs in Python

2024-12-15T14:44:58-03:00

A threshold graph of order may be characterized by a binary sequence . We shall present the particulars of the algorithm known as Diagonalize, which provides the location of the eigenvalues of the adjacency matrix of a threshold graph, relying solely on its geometry, without the need for direct manipulations with the matrix itself. We shall observe that the binary characterization is a facilitative tool for a linear implementation of this algorithm in Python.