arXiv subjects

Nancy Rodríguez

Publications and source records attributed to Nancy Rodríguez.

6 recordsLinked to original sources

arXiv2026

Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy

Social systems consist of networks of individuals who influence one another through social interactions. Studying how processes evolve on these networks can help us better understand patterns of social behavior. We study a system that couples online and offline social activity and investigate how to learn effective models directly from data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy), a method for discovering governing equations. We assess learning performance using data generated by a mean-field approximation model of a stochastic interaction process on networks and test how accurately the system can be recovered under different noise levels. Our results show that using more trajectories improves accuracy when noise is high, but only a small number of additional trajectories is needed to gain most of the benefit, with little improvement beyond that. We also learn effective ODE models from averaged stochastic data on networks. When traditional mean-field approximations fail, identifying continuum ODEs directly from stochastic processes yields efficient models that better match the data and provide deeper insight into the underlying dynamics.

math.DS↗

arXiv2026

Learning dynamics from online-offline systems of LLM agents

Online information is increasingly linked to real-world instability, especially as automated accounts and LLM-based agents help spread and amplify news. In this work, we study how information spreads on networks of Large Language Models (LLMs) using mathematical models. We investigate how different types of offline events, along with the "personalities" assigned to the LLMs, affect the network dynamics of online information spread of the events among the LLMs. We introduce two models: 1) a stochastic agent-based network model and 2) a system of differential equations arising from a mean-field approximation to the agent-based model. We fit these models to simulations of the spread of armed-conflict news on social media, using LLM agents each with one of 32 personality trait profiles on k-regular random networks. Our results indicate that, despite the complexity of the news events, personalities, and LLM behaviors, the overall dynamics of the system are well described by a Susceptible-Infected (SI) type model with two transmission rates.

cs.SI↗

arXiv2025

Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks

Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges in activity are likely to occur. A key factor is the transmission rate between the online and offline domains; for offline outbursts to emerge, this rate must fall within a critical range, neither too low nor too high. Additionally, using synthetic networks, we examine how network structure influences the accuracy of these approximations. Our findings indicate that low-density networks need more complex approximations, whereas simpler models can effectively represent higher-density networks. When tested on two real-world networks, however, increased complexity did not enhance accuracy.

physics.soc-ph↗

arXiv2024

The effect of protest management strategies on protesting activity and social tension: a mathematical perspective

Protest activity, a constitutionally protected right in the United States under the First Amendment, serves as a key tool for individuals with limited individual influence to unite collectively and amplify their impact. Despite its legal recognition, the historical interaction between the government and protesters has been complex. In this study, we extend a model proposed in arXiv:1502.04725 [math.AP] to incorporate the influence of protest management strategies. Our research establishes the existence and stability of traveling wave solutions, supported by both theoretical analyses and numerical simulations. We delve into the impact of two distinct protest management approaches on the qualitative and semi-quantitative characteristics of these traveling waves. These metrics can aid in categorizing different types of protests.

math.AP↗

arXiv2024

A dynamical system model of gentrification: Exploring a simple rent control strategy

Motivated by the need to understand the factors driving gentrification, we introduce and analyze two simple dynamical systems that model the interplay between three potential drivers of the phenomenon. The constructed systems are based on the assumption that three canonical drivers exist: a subpopulation that increases the desirability of a neighborhood, the desirability of a neighborhood, and the average price of real estate in a neighborhood. The second model modifies the first and implements a simple rent control scheme. For both models, we investigate the linear stability of equilibria and numerically determine the characteristics of oscillatory solutions as a function of system parameters. Introducing a rent control scheme stabilizes the system, in the sense that the parameter regime under which solutions approach equilibrium is expanded. However, oscillatory time series generated by the rent control model are generally more disorganized than those generated by the non-rent control model; in fact, long-term transient chaos was observed under certain conditions in the rent control case. Our results illustrate that even simple models of urban gentrification can lead to complex temporal behavior.

nlin.AO↗

arXiv2011

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.

math.AP↗