arXiv subjects

A. Macedo-Filho

Publications and source records attributed to A. Macedo-Filho.

15 recordsLinked to original sources

arXiv2025

Deep Learning of the Biswas-Chatterjee-Sen Model

We investigate the critical properties of kinetic continuous opinion dynamics using deep learning techniques. The system consists of $N$ continuous spin variables in the interval $[-1,1]$. Dense neural networks are trained on spin configuration data generated via kinetic Monte Carlo simulations, accurately identifying the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and allows estimation of critical exponents. Additionally, variational autoencoders are implemented to study the phase transition through the loss function, which behaves as an order parameter. A correlation function between real and reconstructed data is defined and found to be universal at the critical point.

cond-mat.stat-mech↗

arXiv2025

Supervised and Unsupervised Deep Learning Applied to the Majority Vote Model

We employ deep learning techniques to investigate the critical properties of the continuous phase transition in the majority vote model. In addition to deep learning, principal component analysis is utilized to analyze the transition. For supervised learning, dense neural networks are trained on spin configuration data generated via the kinetic Monte Carlo method. Using independently simulated configuration data, the neural network accurately identifies the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and enables estimation of critical exponents, typically obtained via Monte Carlo importance sampling. Furthermore, deep unsupervised learning is performed using variational autoencoders, which reconstruct input spin configurations and generate artificial outputs. The autoencoders detect the phase transition through the loss function, quantifying the preservation of essential data features. We define a correlation function between the real and reconstructed data, and find that this correlation function is universal at the critical point. Variational autoencoders also serve as generative models, producing artificial spin configurations.

cond-mat.stat-mech↗

arXiv2025

Kinetic Flat-Histogram Simulations of Non-Equilibrium Stochastic Processes with Continuous and Discontinuous Phase Transitions

As far as we know, there is no flat-histogram algorithm to sample the stationary distribution of non-equilibrium stochastic processes. The present work addresses this gap by introducing a generalization of the Wang-Landau algorithm, applied to non-equilibrium stochastic processes with local transitions. The main idea is to sample macroscopic states using a kinetic Monte Carlo algorithm to generate trial moves, which are accepted or rejected with a probability that depends inversely on the stationary distribution. The stationary distribution is refined through the simulation by a modification factor, leading to convergence toward the true stationary distribution. A visitation histogram is also accumulated, and the modification factor is updated when the histogram satisfies a flatness condition. The stationary distribution is obtained in the limit where the modification factor reaches a threshold value close to unity. To test the algorithm, we compare simulation results for several stochastic processes with theoretically known behavior. In addition, results from the kinetic flat-histogram algorithm are compared with standard exact stochastic simulations. We show that the kinetic flat-histogram algorithm can be applied to phase transitions in stochastic processes with bistability, which describe a wide range of phenomena such as epidemic spreading, population growth, chemical reactions, and consensus formation. With some adaptations, the kinetic flat-histogram algorithm can also be applied to stochastic models on lattices and complex networks.

cond-mat.stat-mech↗

arXiv2024

Social dilemmas, network reciprocity and the small-world property

We revisit two evolutionary game theory models, namely the Prisoner and the Snowdrift dilemmas, on top of small-world networks. These dynamics on networked populations (individuals occupying nodes of a graph) are mainly concerning on the competition between to cooperate or to defect, by allowing some process of revision of strategies. Cooperators avoid defectors by forming clusters in a process known as network reciprocity. This defense strategy is based on the fact that any individual interact only with its nearest neighbors. The minimum cluster, in turn, is formed by a set of three completely connected nodes and the bulk of these triplets is associated with the transitivity property of a network. Particularly, we show that the transitivity increases eventually assuming a constant behavior when observed as a function of the number of contacts of an individual. We investigate the influence of the network reciprocity on that transitivity increasing regime on the promotion of a cooperative behavior. The dynamics on small-world networks are compared with those random regular, and annealed networks, the later typically studied as the well-mixed approach. We observe that the Snowdrift Game converge to an annealed scenario as randonness and coordination number increase, whereas the Prisoner's Dilemma becomes more severe against the cooperative behavior under the regime of an increasing network reciprocity.

physics.soc-ph↗

arXiv2024

Generalized Diffusive Epidemic Process with Permanent Immunity in Two Dimensions

We introduce the generalized diffusive epidemic process, which is a metapopulation model for an epidemic outbreak where a non-sedentary population of walkers can jump along lattice edges with diffusion rates $D_S$ or $D_I$ if they are susceptible or infected, respectively, and recovered individuals possess permanent immunity. Individuals can be contaminated with rate $\mu_c$ if they share the same lattice node with an infected individual and recover with rate $\mu_r$, being removed from the dynamics. Therefore, the model does not have the conservation of the active particles composed of susceptible and infected individuals. The reaction-diffusion dynamics are separated into two stages: (i) Brownian diffusion, where the particles can jump to neighboring nodes, and (ii) contamination and recovery reactions. The dynamics are mapped into a growing process by activating lattice nodes with successful contaminations where activated nodes are interpreted as infection sources. In all simulations, the epidemic starts with one infected individual in a lattice filled with susceptibles. Our results indicate a phase transition in the dynamic percolation universality class controlled by the population size, irrespective of diffusion rates $D_S$ and $D_I$ and a subexponential growth of the epidemics in the percolation threshold.

cond-mat.stat-mech↗

arXiv2024

Critical Short-Time Behavior of Majority-Vote Model on Scale-Free Networks

We discuss the short-time behavior of the majority vote dynamics on scale-free networks at the critical threshold. We introduce a heterogeneous mean-field theory on the critical short-time behavior of the majority-vote model on scale-free networks. In addition, we also compare the heterogeneous mean-field predictions with extensive Monte Carlo simulations of the short-time dependencies of the order parameter and the susceptibility. We obtained a closed expression for the dynamical exponent $z$ and the time correlation exponent $ν_\parallel$. Short-time scaling is compatible with a non-universal critical behavior for $5/2 < γ< 7/2$, and for $γ\geq 7/2$, we have the mean-field Ising criticality with additional logarithmic corrections for $γ=7/2$, in the same way as the stationary scaling.

cond-mat.stat-mech↗

arXiv2024

Estimating thresholds for asynchronous susceptible-infected-removed model on complex networks

We use the pair heterogeneous mean-field (PHMF) approximation for an asynchronous version of the susceptible-infected-removed (SIR) model to estimate the epidemic thresholds on complex quenched networks. Our results indicate an improvement compared to the heuristic heterogeneous mean-field theory developed for one vertex (HMF) when the dynamic evolves on top random regular and power-law networks. However, there is a slight overestimation of the transition point for the later network type. We also analyze scaling for random regular networks near the thresholds. For this region, collapses were shown at the subcritical and supercritical phases.

physics.soc-ph↗

arXiv2023

Droplet Finite-Size Scaling of the Majority Vote Model on Quenched Scale-Free Networks

We consider the Majority Vote model coupled with scale-free networks. Recent works point to a non-universal behavior of the Majority Vote model, where the critical exponents depend on the connectivity while the network's effective dimension $D_\mathrm{eff}$ is unity for a degree distribution exponent $5/2<γ<7/2$. We present a finite-size theory of the Majority Vote Model for uncorrelated networks and present generalized scaling relations with good agreement with Monte-Carlo simulation results. The presented finite-size theory has two main sources of size dependence. The first source is an external field describing a mass media influence on the consensus formation and the second source is the scale-free network cutoff. The model indeed presents non-universal critical behavior where the critical exponents depend on the degree distribution exponent $5/2<γ<7/2$. For $γ\geq 7/2$, the model is on the same universality class of the Majority Vote model on Erdös-Renyi random graphs, while for $γ=7/2$, the critical behavior presents additional logarithmic corrections.

cond-mat.stat-mech↗

arXiv2022

Epidemic Outbreaks on Quenched Scale-Free Networks

We present a finite-size scaling theory of a contact process with permanent immunity on uncorrelated scale-free networks. We model an epidemic outbreak by an analog of the susceptible-infected-removed model where an infected individual attacks only one susceptible in a time unit in a way we can expect a non-vanishing critical threshold at scale-free networks. As we already know, the susceptible-infected-removed model can be mapped in a bond percolation process, allowing us to compare the critical behavior of site and bond universality classes on networks. We used the external field finite-scale theory, where the dependence on the finite size enters the external field defined as the initial number of infected individuals. We can impose the scale of the external field as $N^{-1}$. The system presents an epidemic-endemic phase transition where the critical behavior obeys the mean-field universality class, as we show theoretically and by simulations.

cond-mat.stat-mech↗

arXiv2022

Phase Diagram of the Contact Process on Barabasi-Albert Networks

We show results for the contact process on Barabasi networks. The contact process is a model for an epidemic spreading without permanent immunity that has an absorbing state. For finite lattices, the absorbing state is the true stationary state, which leads to the need for simulation of quasi-stationary states, which we did in two ways: reactivation by inserting spontaneous infected individuals, or by the quasi-stationary method, where we store a list of active states to continue the simulation when the system visits the absorbing state. The system presents an absorbing phase transition where the critical behavior obeys the Mean Field exponents $β=1$, $γ'=0$, and $ν=2$. However, the different quasi-stationary states present distinct finite-size logarithmic corrections. We also report the critical thresholds of the model as a linear function of the network connectivity inverse $1/z$, and the extrapolation of the critical threshold function for $z \to \infty$ yields the basic reproduction number $R_0=1$ of the complete graph, as expected. Decreasing the network connectivity leads to the increase of the critical basic reproduction number $R_0$ for this model.

physics.soc-ph↗

arXiv2021

Modified Epidemic Diffusive Process on the Apollonian Network

We present an analysis of an epidemic spreading process on the Apollonian network that can describe an epidemic spreading in a non-sedentary population. The modified diffusive epidemic process was employed in this analysis in a computational context by means of the Monte Carlo method. Our model has been useful for modeling systems closer to reality consisting of two classes of individuals: susceptible (A) and infected (B). The individuals can diffuse in a network according to constant diffusion rates $D_{A}$ and $D_{B}$, for the classes A and B, respectively, and obeying three diffusive regimes, i.e., $D_{A} D_{B}$. Into the same site $i$, the reaction occurs according to the dynamical rule based on Gillespie's algorithm. Finite-size scaling analysis has shown that our model exhibit continuous phase transition to an absorbing state with a set of critical exponents given by $β/ν=0.66(1)$, $1/ν=0.46(2)$, and $γ/ν=-0.24(2)$ common to every investigated regime. In summary, the continuous phase transition, characterized by this set of critical exponents, does not have the same exponents of the Mean-Field universality class in both regular lattices and complex networks.

cond-mat.stat-mech↗

arXiv2021

Diffusive Majority Vote Model

We define a stochastic reaction-diffusion process that describes a consensus formation in a non-sedentary population. The process is a diffusive version of the Majority Vote model, where the state update follows two stages: in the first stage, spins are allowed to hop to neighbor nodes with different probabilities for the respective spin orientation, and in the second stage, the spins in the same node can change its values according to the majority vote update rule. The model presents a consensus formation phase when concentration is greater than a threshold value, and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. The threshold vanishes for unequal diffusion probabilities, which means that the system has a consensus state for all values of population densities. The stationary collective opinion is dominated by the individuals that diffuse more.

cond-mat.stat-mech↗

arXiv2019

BCS model on Quasiperiodic Lattices

We study the Biswas-Chatterjee-Sen (BCS) model, also known as the KCOD (Kinetic Continuous Opinion Dynamics) model on quasiperiodic lattices by using Kinetic Monte Carlo simulations and Finite Size Scaling technique. Our results are consistent with a continuous phase transition, controlled by an external noise. We obtained the order parameter $M$, defined as the averaged opinion, the fourth-order Binder cumulant $U$, and susceptibility $χ$ as functions of the noise parameter. We estimated the critical noises for Penrose, and Ammann-Beenker lattices. We also considered 7-fold and 9-fold quasiperiodic lattices and estimated the respective critical noises as well. Irrespective of rotational and translational long-range order of the lattice, the system falls in the same universality class of the two-dimensional Ising model. Quasiperiodic order is irrelevant and it does not change any critical exponents for BCS model.

cond-mat.stat-mech↗

arXiv2019

Epidemic Outbreaks on Random Delaunay Triangulations

We study epidemic outbreaks on random Delaunay triangulations by applying Asynchronous SIR (susceptible-infected-removed) model kinetic Monte Carlo dynamics coupled to lattices extracted from the triangulations. In order to investigate the critical behavior of the model, we obtain the cluster size distribution by using Newman-Ziff algorithm, allowing to simulate random inhomogeneous lattices and measure any desired percolation observable. We numerically calculate the order parameter, defined as the wrapping cluster density, the mean cluster size, and Binder cumulant ratio defined for percolation in order to estimate the epidemic threshold. Our findings suggest that the system falls into two-dimensional dynamic percolation universality class and the quenched random disorder is irrelevant, in agreement with results for classical percolation.

cond-mat.stat-mech↗

arXiv2019

Asynchronous SIR model on Two-Dimensional Quasiperiodic Lattices

We considered the Asynchronous SIR (susceptible-infected-removed) model on Penrose and Ammann-Beenker quasiperiodic lattices, and obtained its critical behavior by using Newman-Ziff algorithm to track cluster propagation by making a tree structure of clusters grown at the dynamics, allowing to simulate SIR model on non-periodic lattices and measure any observable related to percolation. We numerically calculated the order parameter, defined in a geographical fashion by distinguish between an epidemic state, characterized by a spanning cluster formed by the removed nodes and the endemic state, where there is no spanning cluster. We obtained the averaged mean cluster size which plays the role of a susceptibility, and a cumulant ratio defined for percolation to estimate the epidemic threshold. Our numerical results suggest that the system falls into two-dimensional dynamic percolation universality class and the quasiperiodic order is irrelevant, in according to results for classical percolation.

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