arXiv subjects

Juan Pablo Pinasco

Publications and source records attributed to Juan Pablo Pinasco.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic SIS opinion-driven models with asymmetric awareness feedback: macroscopic limit and polarization

We study a kinetic multi-agent framework coupling opinion dynamics with epidemic spreading, where individual social behaviour both affects and is affected by disease transmission. Each agent is characterised by an epidemiological state and a continuous opinion variable measuring compliance with non-pharmaceutical interventions. The key mechanism of the model is an asymmetric opinion update driven by epidemic encounters: infection events induce more cautious attitudes, while failed transmissions push individuals toward more extreme opinions. We focus on a prototypical SIS setting, for which we derive a macroscopic kinetic description and, in a fast social-interaction regime, a reduced system of differential equations capturing the feedback between epidemic prevalence and opinion evolution. Convergence of the reduced model is rigorously quantified through a modified Wasserstein distance. Numerical simulations highlight how infection-induced awareness and non-infection-driven extremization jointly shape collective epidemic-opinion dynamics.

physics.soc-ph↗

arXiv2024

Analytical insights from a model of opinion formation based on Persuasive Argument Theory

In recent years, numerous mathematical models of opinion formation have been developed, incorporating diverse interaction mechanisms such as imitation and majority rule. However, limited attention has been given to models grounded in persuasive arguments theory (PAT), which describes how individuals may alter their opinions through the exchange of arguments during discussions. Moreover, analytical investigations of PAT-based models remain sparse. In this study, we propose an analytical model rooted in PAT, demonstrating that a group of agents can exhibit two distinct collective dynamics: quasi-consensus and bipolarization. Specifically, we explore various scenarios characterized by the number of arguments and the degree of homophily, revealing that bipolarization arises within this framework only in the presence of homophily.

physics.soc-ph↗

arXiv2022

Mesoscopic analytical approach in a three state opinion model with continuous internal variable

Analytical approaches in models of opinion formation have been extensively studied either for an opinion represented as a discrete or a continuous variable. In this paper, we analyze a model which combines both approaches. The state of an agent is represented with an internal continuous variable (the leaning or propensity), that leads to a discrete public opinion: pro, against or neutral. This model can be described by a set of master equations which are a nonlinear coupled system of first order differential equations of hyperbolic type including non-local terms and non-local boundary conditions, which can't be solved analytically. We developed an approximation to tackle this difficulty by deriving a set of master equations for the dynamics of the average leaning of agents with the same opinion, under the hypothesis of a time scale separation in the dynamics of the variables. We show that this simplified model accurately predicts the expected transition between a neutral consensus and a bi-polarized state, and also gives an excellent approximation for the dynamics of the average leaning of agents with the same opinion, even when the time separation scale hypothesis is not completely fulfilled.

physics.soc-ph↗

arXiv2021

Random multi-player games

The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case can not be reduced to pairwise interactions. In this work we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability $p$, and by three players with the complementary probability $1-p$. We show the existence of equilibria in pure and mixed strategies depending on the probability $p$, on a concrete example of the duel-truel game. We find a range of $p$ values for which the game has a mixed equilibrium and the proportion of players in each strategy depends on the particular value of $p$. We prove that each of these mixed equilibrium points are ESS. A more realistic way to study this dynamics with high-order interactions is to look at how it evolves in complex networks. We introduce and study an agent-based model on a network with a fixed number of nodes, which evolves as the replicator equation predicts. By studying the dynamics of this model on random networks we find that the phase transitions between the pure and mixed equilibria depend on the probability $p$ and also on the mean degree of the network.

physics.soc-ph↗

arXiv2021

Optimal control for a SIR epidemic model with limited quarantine

We study first order necessary conditions for an optimal control problem of a Susceptible-Infected-Recovered (SIR) model with limitations on the duration of the quarantine. The control is done by means of the reproduction number, i.e., the number of secondary infections produced by a primary infection, which represents an external intervention that we assume time-dependent. Moreover, the control function can only be applied over a finite time interval, and the duration of the most strict quarantine (smallest possible reproduction number) is also bounded. We consider a maximization problem where the cost functional has two terms: one is the number of susceptible individuals in the long-term and the other depends on the cost of interventions. When the intervention term is linear with respect to the control, we obtain that the optimal solution is bang-bang, and we characterize the times to begin and end the strict quarantine. In the general case, when the cost functional includes the term that measures the intervention cost, we analyze the optimality of controls through numerical computations.

math.OC↗

arXiv2021

Analytical formulation for multidimensional continuous opinion models

Usually, opinion formation models assume that individuals have an opinion about a given topic which can change due to interactions with others. However, individuals can have different opinions in different topics and therefore n-dimensional models are best suited to deal with these cases. While there have been many efforts to develop analytical models for one dimensional opinion models, less attention has been paid to multidimensional ones. In this work, we develop an analytical approach for multidimensional models of continuous opinions where dimensions can be correlated or uncorrelated. We show that for any generic reciprocal interactions between agents, the mean value of initial opinion distribution is conserved. Moreover, for positive social influence interaction mechanisms, the variance of opinion distributions decreases with time and the system converges to a delta distributed function. In particular, we calculate the convergence time when agents get closer in a discrete quantity after interacting, showing a clear difference between correlated and uncorrelated cases.

physics.soc-ph↗

arXiv2021

SIR dynamics with Vaccination in a large Configuration Model

We consider a SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of optimal controls for the limiting equations formulated in the framework of game theory, both in the centralized and decentralized setting. We show how the characteristics of the graph (degree distribution) influence the vaccination efficiency for optimal strategies, and we compute the limiting final size of the epidemic depending on the degree distribution of the graph and the parameters of infection, recovery and vaccination. We also present several simulations for two types of vaccination, showing how the optimal controls allow to decrease the number of infections and underlining the crucial role of the network characteristics in the propagation of the disease and the vaccination program.

math.PR↗

arXiv2020

A novel analytical formulation of the Axelrod model

The Axelrod model of cultural dissemination has been widely studied in the field of statistical mechanics. The traditional version of this agent-based model is to assign a cultural vector of $F$ components to each agent, where each component can take one of $Q$ cultural trait. In this work, we introduce a novel set of mean field master equations to describe the model for $F=2$ and $F=3$ in complete graphs where all indirect interactions are explicitly calculated. We find that the transition between different macroscopic states is driven by initial conditions (set by parameter $Q$) and the size of the system $N$, who measures the balance between linear and cubic terms in master equations. We also find that this analytical approach fully agrees with simulations where the system does not break up during the dynamics and a scaling relation related to missing links reestablishes the agreement when this happens.

physics.soc-ph↗

arXiv2020

Interacting particles systems with delay and random delay differential equations

In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial conditions. We analyze two different dynamics, one based on the full knowledge of the individual trajectories of each particle, and another one based only on the trace of the particle cloud, loosing track of the individual trajectories. Notice that in the first dynamic the state of a particles is its path, whereas it is simply a point in $\R^d$ in the second case. We analyse in both cases the corresponding mean-field dynamic obtaining an equation for the time evolution of the distribution of the particles states. Well-posedness of the equation is proved by a fixed-point argument. We conclude the paper with some possible future research directions and modelling applications.

math.AP↗

arXiv2020

Evolutionary game theory in mixed strategies: from microscopic interactions to kinetic equations

In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play the successful pure strategy used in the match. We derive the Boltzmann equation which describes the macroscopic effects of this microscopical rule, and we obtain a first order, nonlocal, partial differential equation as the limit when the probability change goes to zero. We study the relationship between this equation and the well known replicator equations, showing the equivalence between the concepts of Nash equilibria, stationary solutions of the partial differential equation, and the equilibria of the replicator equations. Finally, we relate the long time behavior of solutions to the partial differential equation and the stability of the replicator equations.

math.AP↗

arXiv2020

A model for the competition between political mono-polarization and bi-polarization

We investigate the phenomena of political bi-polarization in a population of interacting agents by means of a generalized version of the model introduced in PRE E 101, 012101 (2020) for the dynamics of voting intention. Each agent has a propensity $p$ in $[0,1]$ to vote for one of two political candidates. In an iteration step, two agents $i$ and $j$ with respective propensities $p_i$ and $p_j$ interact, and then $p_i$ either increases by an amount $h>0$ with a probability that is a nonlinear function of $p_i$ and $p_j$ or decreases by $h$ with the complementary probability. We study the behavior of the system under variations of a parameter $q \ge 0$ that measures the nonlinearity of the propensity update rule. We focus on the stability properties of the two distinct stationary states: mono-polarization in which all agents share the same extreme propensity ($0$ or $1$), and bi-polarization where the population is divided into two groups with opposite and extreme propensities. We find that the bi-polarized state is stable for $q q_c$, where $q_c$ is a transition value that decreases as $h$ decreases. We develop a rate equation approach whose stability analysis reveals that $q_c$ vanishes when $h$ becomes infinitesimally small. This result is supported by the analysis of a transport equation derived in the continuum $h \to 0$ limit. We also show by Monte Carlo simulations that the mean time $τ$ to reach mono-polarization in a system of size $N$ scales as $τ\sim N^α$ at $q_c$ , where $α(h)$ is a non-universal exponent.

physics.soc-ph↗

arXiv2019

The role of voting intention in public opinion polarization

We introduce and study a simple model for the dynamics of voting intention in a population of agents that have to choose between two candidates. The level of indecision of a given agent is modeled by its propensity to vote for one of the two alternatives, represented by a variable $p \in [0,1]$. When an agent $i$ interacts with another agent $j$ with propensity $p_j$, then $i$ either increases its propensity $p_i$ by $h$ with probability $P_{ij}=ωp_i+(1-ω)p_j$, or decreases $p_i$ by $h$ with probability $1-P_{ij}$, where $h$ is a fixed step. We analyze the system by a rate equation approach and contrast the results with Monte Carlo simulations. We found that the dynamics of propensities depends on the weight $ω$ that an agent assigns to its own propensity. When all the weight is assigned to the interacting partner ($ω=0$), agents' propensities are quickly driven to one of the extreme values $p=0$ or $p=1$, until an extremist absorbing consensus is achieved. However, for $ω>0$ the system first reaches a quasi-stationary state of symmetric polarization where the distribution of propensities has the shape of an inverted Gaussian with a minimum at the center $p=1/2$ and two maxima at the extreme values $p=0,1$, until the symmetry is broken and the system is driven to an extremist consensus. A linear stability analysis shows that the lifetime of the polarized state, estimated by the mean consensus time $τ$, diverges as $τ\sim (1-ω)^{-2} \ln N$ when $ω$ approaches $1$, where $N$ is the system size. Finally, a continuous approximation allows to derive a transport equation whose convection term is compatible with a drift of particles from the center towards the extremes.

physics.soc-ph↗

arXiv2018

Opinion formation models with heterogeneous persuasion and zealotry

In this work an opinion formation model with heterogeneous agents is proposed. Each agent is supposed to have different power of persuasion, and besides its own level of zealotry, that is, an individual willingness to being convinced by other agent. In addition, our model includes zealots or stubborn agents, agents that never change opinions. We derive a Bolzmann-like equation for the distribution of agents on the space of opinions, which is approximated by a transport equation with a nonlocal drift term. We study the long-time asymptotic behavior of solutions, characterizing the limit distribution of agents, which consists of the distribution of stubborn agents, plus a delta function at the mean of their opinions, weighted by they power of persuasion. Moreover, explicit bounds on the rate of convergence are given, and the time to convergence is shown to decrease when the number of stubborn agents increases. This is a remarkable fact observed in agent based simulations in different works.

math.AP↗

arXiv2017

A game theoretic model of wealth distribution

In this work we consider an agent based model in order to study the wealth distribution problem where the interchange is determined with a symmetric zero sum game. Simultaneously, the agents update their way of play trying to learn the optimal one. Here, the agents use mixed strategies. We study this model using both simulations and theoretical tools. We derive the equations for the learning mechanism, and we show that the mean strategy of the population satisfies an equation close to the classical replicator equation. Concerning the wealth distribution, there are two interesting situations depending on the equilibrium of the game. If the equilibrium is a pure strategy, the wealth distribution is fixed after some transient time, and those players which are close to optimal strategy are richer. When the game has an equilibrium in mixed strategies, the stationary wealth distribution is close to a Gamma distribution with variance depending on the coefficients of the game matrix. We compute theoretically their second moment in this case.

physics.soc-ph↗

arXiv2016

Asymptotic behavior of the curves in the Fu{č}{\'ı}k spectrum

In this work we study the asymptotic behavior of the curves of the Fu{č}{\'ı}k spectrum for weighted second order linear ordinary differential equations. We prove a Weyl type asymptotic behavior of the hyperbolic type curves in the spectrum in terms of some integrals of the weights. We present an algorithm which computes the intersection of the Fu{č}{\'ı}k spectrum with rays through the origin, and we compare their values with the asymptotic ones.

math.AP↗

arXiv2016

Modeling Opinion Dynamics: Theoretical analysis and continuous approximation

Frequently we revise our first opinions after talking over with other individuals because we get convinced. Argumentation is a verbal and social process aimed at convincing. It includes conversation and persuasion. In this case, the agreement is reached because the new arguments are incorporated. In this paper we deal with a simple model of opinion formation with such persuasion dynamics, and we find the exact analytical solutions for both, long and short range interactions. A novel theoretical approach has been used in order to solve the master equations of the model with non-local kernels. Simulation results demonstrate an excellent agreement with results obtained by the theoretical estimation.

physics.soc-ph↗

arXiv2016

Homogenization of Fučík eigencurves

In this work we study the convergence of an homogenization problem for half-eigenvalues and Fučík eigencurves. We provide quantitative bounds on the rate of convergence of the curves for periodic homogenization problems.

math.AP↗

arXiv2015

The undecided have the key: Interaction-driven opinion dynamics in a three state model

The effects of interpersonal interactions on individual's agreements result in a social aggregation process which is reflected in the formation of collective states, as for instance, groups of individuals with a similar opinion about a given issue. This field, which has been a longstanding concern of sociologists and psychologists, has been extended into an area of experimental social psychology, and even has attracted the attention of physicists and mathematicians. In this article, we present a novel model of opinion formation in which agents may either have a strict preference for a choice, or be undecided. The opinion shift emerges during interpersonal communications, as a consequence of a cumulative process of conviction for one of the two extremes opinions through repeated interactions. There are two main ingredients which play key roles in determining the steady state: the initial fraction of undecided agents and the conviction's sensitivity in each interaction. As a function of these two parameters, the model presents a wide range of possible solutions, as for instance, consensus of each opinion, bi-polarisation or convergence of undecided individuals. We found that a minimum fraction of undecided agents is crucial not only for reaching consensus of a given opinion, but also to determine a dominant opinion in a polarised situation. In order to gain a deeper comprehension of the dynamics, we also present the theoretical master equations of the model.

physics.soc-ph↗