arXiv subjects

Sebastian Gonçalves

Publications and source records attributed to Sebastian Gonçalves.

15 recordsLinked to original sources

arXiv2026

Phase Transitions in Economic Inequality:Taxation and Extremal Replacement Dynamics

We present a minimal agent-based model of interacting agents characterized by their wealth to study taxation and inequality in a non-conservative economy. Wealth evolves through an extremal stochastic replacement process in which the poorest agent has its wealth replaced by a new random value, financed through a collective taxation mechanism. We explore taxation regimes ranging from regressive to progressive schemes and tune the overall redistribution strength. Under regressive taxation, the system self-organizes into two distinct stationary phases when changing the total tax collected: a non-ergodic, high-inequality regime characterized by wealth condensation in a subset of agents that permanently escape replacement, and a more homogeneous ergodic phase in which all agents participate in the dynamics. Increasing taxes drives an abrupt transition between these phases. The transition is discontinuous and exhibits hysteresis and bistability, consistently detected through the Gini index, the Top $1\%$ wealth share, the entropy, and the Binder cumulant. In contrast, neutral and progressive taxation suppress persistent wealth concentration, preventing the emergence of strongly unequal states and eliminating hysteretic behavior. We complement the simulations with a parameter-free mean-field theory of the wealth dynamics that reproduces the stationary distributions and explains the transition by locating the two spinodals that bound the bistable region. These results show that minimal stochastic redistribution mechanisms alone can produce discontinuous transitions, metastability, and non-ergodicity, demonstrating that taxation structure can determine the emergence and stability of macroscopic inequality.

physics.soc-ph↗

arXiv2026

Does a rising tide lift all boats? A wealth exchange model on a dynamic network with economic growth

Wealth inequality, although an age-old problem, has seen a substantial rise since the early XXI century. The distributions of wealth and income across countries follow a universal pattern, typically manifesting as a two-class division, which suggests that fundamental mechanisms underpin the emergence of these economic disparities. Agent-based models, which allow the rules of interaction between economic agents to be explicitly defined, are particularly well-suited for studying economic systems and analyzing their emergent properties. In this work, we examine a recently proposed dynamic complex network agent-based model within the context of a growing economy. The model evolves via three alternating processes: independent stochastic wealth growth of each agent, wealth exchanges between connected agents, and the rewiring of connections within the complex network. The wealth growth of each agent is governed by a stochastic process characterized by two parameters: a drift term $μ$, representing economic growth, and volatility $σ$, reflecting heterogeneity in productivity. We analyze the outcomes for various values of a social protection factor $f$, which favors the poorer agent in each transaction. Higher values of $f$ amplify the effect of economic growth: while increasing $μ$ reduces inequality, increasing $σ$ has the opposite effect. In this context, economic growth benefits the poorest agents only when strong social protection is in place.

physics.soc-ph↗

arXiv2026

A Shared IPTC Topic Space for Cross-Source Topic Modelling

Comparing topic attention across different media is hindered by a fundamental modelling problem: topic models fitted separately to each corpus produce corpus-specific topic spaces that cannot be aligned directly. This paper presents a reproducible framework that places corpora in a single shared topic space defined by a taxonomy. Discovered topics are obtained with guided BERTopic, scored against the ninety-four IPTC Media Topics' taxonomy topics (level-1) through weighted keyword and target centroids, and then collapsed upward to seventeen IPTC parent topics by a maximum-similarity rule. The framework was developed and selected on a controlled New York Times 2011 corpus through a narrowing sequence: a broad model screen, a focused mapping refinement, a strict finalist comparison, a target-construction ablation, and a threshold calibration. In this corpus, the guided family retained substantially stronger mapped coverage than a zero-shot benchmark under stricter assignment thresholds, a parent-enriched target construction improved both coverage and parent consistency, and coverage declined gradually rather than collapsing as the assignment threshold was tightened. The contribution is an externally anchored method for constructing a shared topic space that enables reproducible cross-source topic comparison.

cs.IR↗

arXiv2026

Can Rising Consumption Deepen Inequality?

The impact of rising consumption on wealth inequality remains an open question. Here we revisit and extend the Social Architecture of Capitalism agent-based model proposed by Ian Wright, which reproduces stylized facts of wealth and income distributions. In a previous study, we demonstrated that the macroscopic behavior of the model is predominantly governed by a single dimensionless parameter, the ratio between average wealth per capita and mean salary, denoted by R. The shape of the wealth distribution, the emergence of a two-class structure, and the level of inequality - summarized by the Gini index - were found to depend mainly on R, with inequality increasing as R increases. In the present work, we examine the robustness of this result by relaxing some simplifying assumptions of the model. We first allow transactions such as purchases, salary payments, and revenue collections to occur with different frequencies, reflecting the heterogeneous temporal dynamics of real economies. We then impose limits on the maximum fractions of wealth that agents can spend or collect at each step, constraining the amplitude of individual transactions. We find that the dependence of the inequality on R remains qualitatively robust, although the detailed distribution patterns are affected by relative frequencies and transaction limits. Finally, we analyze a further variant of the model with adaptive wages emerging endogenously from the dynamics, showing that self-organized labor-market feedback can either stabilize or amplify inequality depending on macroeconomic conditions.

physics.soc-ph↗

arXiv2026

Epidemic Extinction in a Continuous SIRS Model with Vaccination

Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to epidemic extinction stand out as a central-if not the fundamental-question in epidemic modeling. In this work, we study epidemic extinction in a continuous SIRS (Susceptible-Infected-Recovered-Susceptible) model governed by a system of ordinary differential equations (ODEs). The model includes vaccination as a time-dependent process and considers the reinfection of recovered individuals through waning immunity. We analyze how different parameter regimes -- particularly infection, recovery, and immunity loss rates -- affect the persistence or extinction of the epidemic. Special attention is given to the limitations of continuous population models, in which the infected fraction can fall below the equivalent of a single individual, leading to nonphysical outcomes such as unrealistically long persistence or artificial secondary peaks. By comparing the continuous SIRS dynamics with expected real-world thresholds for extinction, we highlight the importance of incorporating stochasticity or discrete effects to accurately describe epidemic fade-out.

q-bio.PE↗

arXiv2025

The number of spanning trees as an indicator of critical phenomena: When Kirchhoff meets Ising

Visibility graphs are spatial interpretations of time series. When derived from the time evolution of physical systems, the graphs associated with such series may exhibit properties that can reflect aspects such as ergodicity, criticality, or other dynamical behaviors. It is important to describe how the criticality of a system is manifested in the structure of the corresponding graphs or, in a particular way, in the spectra of certain matrices constructed from them. In this paper, we show how the critical behavior of an Ising spin system manifests in the spectra of the adjacency and Laplacian matrices constructed from an ensemble of time evolutions simulated via Monte Carlo (MC) Markov Chains, even for small systems and short MC steps. In particular, we show that the number of spanning trees -- or its logarithm -- , which represents a kind of \emph{structural entropy} or \emph{topological complexity} here obtained from Kirchhoff's theorem, can, in an alternative way, describe the criticality of the spin system. These findings parallel those obtained from the spectra of correlation matrices, which similarly encode signatures of critical and chaotic behavior.

cond-mat.stat-mech↗

arXiv2025

Limiting risk to reduce inequality: insights from the Yard-Sale model

Wealth inequality remains a critical socioeconomic challenge, driven by systemic dynamics and self-reinforcing mechanisms that amplify the economic imbalances. Simplified models from statistical physics provide valuable insights into the fundamental mechanisms governing wealth distribution. In this study, we extend the Yard-Sale model -- a minimal kinetic exchange framework -- to investigate how limiting risk in economic transactions affects inequality. While previous research demonstrates that such models naturally lead to wealth concentration, we introduce a mechanism that restricts the maximum risk agents can assume during exchanges. Numerical simulations reveal that this modification fosters more equitable wealth distributions and significantly reduces extreme disparities. These findings highlight the importance of individual-level constraints in shaping systemic outcomes, offering new perspectives on promoting economic balance.

physics.soc-ph↗

arXiv2025

Mean-field and Monte Carlo Analysis of Multi-Species Dynamics of agents

We propose a mean-field (MF) approximation for the recurrence relation governing the dynamics of $m$ species of particles on a square lattice, and we simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to emulate the intricate motion observed in environments such as subway corridors and scramble crossings in large cities. Each species moves according to transition probabilities influenced by its respective static floor field and the state of neighboring cells. To illustrate the methodology, we analyze statistical fluctuations in the spatial distribution for $m = 1$, $m = 2$, and $m = 4$ and for different regimes of average density and biased movement. A numerical comparison is conducted to determine the best agreement between the MC simulations and the MF approximation considering a renormalization exponent $β$ that optimizes the fit between methods. Finally, we report a phenomenon we term "Gaussian-to-Gaussian" behavior, in which an initially normal distribution of particles becomes distorted due to interactions among same and opposing species, passes through a transient regime, and eventually returns to a Gaussian-like profile in the steady state, after multiple rounds of motion under periodic boundary conditions.

cond-mat.stat-mech↗

arXiv2025

Inequality in a model of capitalist economy

We analyze inequality aspects of the agent-based model of capitalist economy named it Social Architecture of Capitalism that has been introduced by Ian Wright. The model contemplates two main types of agents, workers and capitalists, which can also be unemployed. Starting from a state where all agents are unemployed and possess the same initial wealth, the system, governed by a few simple rules, quickly self-organizes into two classes. After a transient, the model reproduces the statistics of many relevant macroeconomic quantities of real economies worldwide, notably the two regimes of the distributions of wealth and income. We perform extensive simulations testing the role of the model parameters (number of agents, total wealth, and salary range) on the resulting distribution of wealth and income, the social distribution of agents, and other stylized facts of the dynamics. Our main finding is that, according to the model, in an economy where total wealth is conserved and with a fixed average wage, the increase in wealth per capita comes with more inequality.

physics.soc-ph↗

arXiv2025

Homophilic Effects on Economic Inequality: A Dynamic Network Agent-Based Model

Wealth transactions are central to economic activity, and their particularities shape macroeconomic outcomes. We propose an agent-based model to investigate how homophily influences economic inequality. The model simulates wealth exchanges in a dynamic network composed of two groups, $A$ and $B$, differentiated by a homophily parameter $δ$, which increases intragroup connections within $A$. Economic interactions alternate between conservative wealth exchanges and connection rewiring, both influenced by agents' wealth and $δ$. We examine economic and network dynamics under varying levels of social protection $f$, which favor poorer agents in transactions. At low $f$, results reveal high inequality and link concentration, with $δ$ impacting only transient dynamics. At high $f$, homophily becomes an economic advantage, as increasing $δ$ directs wealth flow to group $A$. However, since this flow benefits the wealthiest agents, it simultaneously exacerbates internal inequality within the group. These findings show that homophily is a significant driver of inequality, directing wealth towards the homophilous group and worsening internal disparities.

physics.soc-ph↗

arXiv2024

One predator and two prey: Coexistence of pumas, guanacos and sheep in Patagonia

The ecosystem considered in this study is the outcome of a lengthy sequence of historical and ecological events. Patagonia's indigenous fauna comprises survivors of five significant extinction events, with the notable presence of the puma and the guanaco, two of the largest native mammals. In addition to these, European immigrants introduced sheep into the ecosystem. Together, these three species form a straightforward trophic network, featuring one predator and two prey species, all competing within the Patagonian steppe. For ranchers, guanacos and pumas are frequently perceived as threats to their economic interests. In recent decades, the field of biology, particularly ecology, has witnessed a substantial increase in the development of equation-based models. Scientists are interested in the ability to systematize hypotheses and gain insights into the behavior of complex biological systems, such as the one presented in this study. However, the nonlinear nature and the large number of parameters of models, represent a challenge when one wants to explore the parameter space. To overcome this and, at the same time, improve the understanding of the Patagonia ecosystem, we start by building an equation-based model based on previous contributions, and we reduce it to the essential minimum set of parameters. Then, we introduce two tools, a generalization of ternary graphs and a perceptron based ML, to help understand the response of the system equation to the key parameters. The perceptron tool allows us to visualize/interpret the influence of each parameter on the survival or extinction of each species. Through the generalization of the ternary graph, it was possible to conveniently visualize how the system responds to different combinations/variations of the five parameters of the reduced system equation in a single graphical representation.

q-bio.PE↗

arXiv2024

Interplay of Reward and Size of Groups in the Optional Public Goods Game

The Optional Public Goods Game is a three-strategy game in which an individual can play as a cooperator or defector or decide not to participate. Despite its simplicity, this model can effectively represent many human social dilemmas, such as those found in the use of public services, environmental concerns, or other activities related to society. In this contribution, we present a comprehensive analysis of the conditions under which spontaneous, sustained cooperation emerges and the characteristics of these cooperative states. Through simulations, we demonstrate the conditions leading to the coexistence of the three strategies in a steady equilibrium or the alternate dominance of each strategy in a rock-paper-scissors fashion. The results identify each of the possible scenarios in terms of two key parameters: the multiplication rate of the public good game (reward) and the size of the group of potential players. We also discuss other details of the game that may influence the appearance of cycles, along with relevant characteristics of these cycles, such as the prevalence of cooperation.

physics.soc-ph↗

arXiv2017

The web of federal crimes in Brazil: topology, weaknesses, and control

Law enforcement and intelligence agencies worldwide struggle to find effective ways to fight and control organized crime. However, illegal networks operate outside the law and much of the data collected is classified. Therefore, little is known about criminal networks structure, topological weaknesses, and control. In this contribution we present a unique criminal network of federal crimes in Brazil. We study its structure, its response to different attack strategies, and its controllability. Surprisingly, the network composed of multiple crimes of federal jurisdiction has a giant component, enclosing more than a half of all its edges. This component shows some typical social network characteristics, such as small-worldness and high clustering coefficient, however it is much "darker" than common social networks, having low levels of edge density and network efficiency. On the other side, it has a very high modularity value, $Q=0.96$. Comparing multiple attack strategies, we show that it is possible to disrupt the giant component of the network by removing only $2\%$ of its edges or nodes, according to a module-based prescription, precisely due to its high modularity. Finally, we show that the component is controllable, in the sense of the exact network control theory, by getting access to $20\%$ of the driver nodes.

physics.soc-ph↗

arXiv2016

An Algebraic Solution for the Kermack-McKendrick Model

We present an algebraic solution for the Susceptible-Infective-Removed (SIR) model originally presented by Kermack-McKendrick in 1927. Starting from the differential equation for the removed subjects presented by them in the original paper, we re-write it in a slightly different form in order to derive formally the solution, unless one integration. Then, using algebraic techniques and some well justified numerical assumptions we obtain an analytic solution for the integral. Finally, we compare the numerical solution of the differential equations of the SIR model with the analytically solution here proposed, showing an excellent agreement.

physics.soc-ph↗

arXiv2013

Epidemic oscillations: Interaction between delays and seasonality

Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails for almost all infectious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We show a general treatment for an SIRS model in which both the infected and the immune phases admit such a description. The general behavior of the system shows transitions between endemic and oscillating situations that could be relevant in many real scenarios. The interaction with the other main source of oscillations, seasonality, is also discussed.

q-bio.PE↗