arXiv subjects

Heather Z. Brooks

Publications and source records attributed to Heather Z. Brooks.

8 recordsLinked to original sources

arXiv2025

Modeling Social Systems: Transparency, Reproducibility, and Responsibility

Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect millions of lives. Thus, it is especially important to formulate and present them with transparency, reproducibility, and humility. Modeling in social domains, however, is often uniquely challenging. Unlike in physics or engineering, researchers often lack controlled experiments or abundant, clean data. Observational data is sparse, noisy, partial, and missing in systematic ways. In such an environment, how can we build models that can inform science and decision-making in transparent and responsible ways?

math.HO↗

arXiv2024

An "Opinion Reproduction Number" for Infodemics in a Bounded-Confidence Content-Spreading Process on Networks

We study the spreading dynamics of content on networks. To do this, we use a model in which content spreads through a bounded-confidence mechanism. In a bounded-confidence model (BCM) of opinion dynamics, the agents of a network have continuous-valued opinions, which they adjust when they interact with agents whose opinions are sufficiently close to theirs. The employed content-spreading model introduces a twist into BCMs by using bounded confidence for the content spread itself. We define an analogue of the basic reproduction number from disease dynamics that we call an \emph{opinion reproduction number}. A critical value of the opinion reproduction number indicates whether or not there is an ``infodemic'' (i.e., a large content-spreading cascade) of content that reflects a particular opinion. By determining this critical value, one can determine whether or not an opinion dies off or propagates widely as a cascade in a population of agents. Using configuration-model networks, we quantify the size and shape of content dissemination by calculating a variety of summary statistics, and we illustrate how network structure and spreading-model parameters affect these statistics. We find that content spreads most widely when the agents have a large expected mean degree or a large receptiveness to content. When the spreading process slightly exceeds the infodemic threshold, there can be longer dissemination trees than when the expected mean degree or receptiveness are larger, even though the total number of content shares is smaller.

physics.soc-ph↗

arXiv2023

Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics

We study a nonlinear bounded-confidence model (BCM) of continuous-time opinion dynamics on networks with both persuadable individuals and zealots. The model is parameterized by a scalar $γ$, which controls the steepness of a smooth influence function. This influence function encodes the relative weights that nodes place on the opinions of other nodes. When $γ= 0$, this influence function recovers Taylor's averaging model; when $γ\rightarrow \infty$, the influence function converges to that of a modified Hegselmann--Krause (HK) BCM. Unlike the classical HK model, however, our sigmoidal bounded-confidence model (SBCM) is smooth for any finite $γ$. We show that the set of steady states of our SBCM is qualitatively similar to that of the Taylor model when $γ$ is small and that the set of steady states approaches a subset of the set of steady states of a modified HK model as $γ\rightarrow \infty$. For several special graph topologies, we give analytical descriptions of important features of the space of steady states. A notable result is a closed-form relationship between the stability of a polarized state and the graph topology in a simple model of echo chambers in social networks. Because the influence function of our BCM is smooth, we are able to study it with linear stability analysis, which is difficult to employ with the usual discontinuous influence functions in BCMs.

math.DS↗

arXiv2023

Data science and social justice in the mathematics community

Data science for social justice (DS4SJ) is data-scientific work that supports the liberation of oppressed and marginalized people. By nature, this work lies at the intersection of technical scholarship and activist practice. We discuss this growing efforts in DS4SJ within the broad mathematics community. We begin by defining terms and offering a series of guiding principles for engaging in critical data science work, providing examples of how these principles play out in practice. We then highlight the roles that DS4SJ can play in the scholarship and pedagogy of practicing mathematicians. We focus in particular on the engagement of early-career mathematicians in DS4SJ, which we illustrate through a series of four personal vignettes. While the primary aim of DS4SJ is to achieve impact for marginalized communities, we also argue that engagement with DS4SJ can benefit the entire mathematical ecosystem, including researchers, instructors, students, departments, institutes, and professional societies. We close with reflections on how these various actors can support ongoing efforts in data science for social justice.

math.HO↗

arXiv2023

A tutorial on networks in social systems: A mathematical modeling perspective

This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential terminology. We describe several network properties of interest and techniques for measuring these properties. We also discuss some popular generative models of networks and see how the study of these models provides insight into the mechanisms for the emergence of structural patterns. Throughout, we will highlight the patterns that commonly emerge in social networks. The goal is to provide an accessible, broad, and solid foundation for a reader who is new to the field so that they may confidently engage more deeply with the mathematical study of social networks.

physics.soc-ph↗

arXiv2021

A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

People's opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of opinion dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to an asynchronous BCM on hypergraphs, in which arbitrarily many nodes can be connected by a single hyperedge. We show that our hypergraph BCM converges to consensus under a wide range of initial conditions for the opinions of the nodes, including for non-uniform and asymmetric initial opinion distributions. We also show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We demonstrate that the opinions of individuals can sometimes jump from one opinion cluster to another in a single time step, a phenomenon (which we call ``opinion jumping'') that is not possible in standard dyadic BCMs. Additionally, we observe that there is a phase transition in the convergence time on {a complete hypergraph} when the variance $σ^2$ of the initial opinion distribution equals the confidence bound $c$. We prove that the convergence time grows at least exponentially fast with the number of nodes when $σ^2 > c$ and the initial opinions are normally distributed. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.

cs.SI↗

arXiv2020

Disease Detectives: Using Mathematics to Forecast the Spread of Infectious Diseases

The COVID-19 pandemic has led to significant changes in how people are currently living their lives. To determine how to best reduce the effects of the pandemic and start reopening societies, governments have drawn insights from mathematical models of the spread of infectious diseases. In this article, we give an introduction to a family of mathematical models (called "compartmental models") and discuss how the results of analyzing these models influence government policies and human behavior, such as encouraging mask wearing and physical distancing to help slow the spread of the disease.

q-bio.OT↗

arXiv2020

A Model for the Influence of Media on the Ideology of Content in Online Social Networks

Many people rely on online social networks as sources of news and information, and the spread of media content with ideologies across the political spectrum influences online discussions and impacts actions offline. To examine the impact of media in online social networks, we generalize bounded-confidence models of opinion dynamics by incorporating media accounts as influencers in a network. We quantify partisanship of content with a continuous parameter on an interval, and we formulate higher-dimensional generalizations to incorporate content quality and increasingly nuanced political positions. We simulate our model with one and two ideological dimensions, and we use the results of our simulations to quantify the "entrainment" of content from non-media accounts to the ideologies of media accounts in a network. We maximize media impact in a social network by tuning the number of media accounts that promote the content and the number of followers of the accounts. Using numerical computations, we find that the entrainment of the ideology of content spread by non-media accounts to media ideology depends on a network's structural features, including its size, the mean number of followers of its nodes, and the receptiveness of its nodes to different opinions. We then introduce content quality --- a key novel contribution of our work --- into our model. We incorporate multiple media sources with ideological biases and quality-level estimates that we draw from real media sources and demonstrate that our model can produce distinct communities ("echo chambers") that are polarized in both ideology and quality. Our model provides a step toward understanding content quality and ideology in spreading dynamics, with ramifications for how to mitigate the spread of undesired content and promote the spread of desired content.

physics.soc-ph↗