Schedule for: 25w5326 - Collective Social Phenomena: Dynamics and Data

Recovering from substance use disorder is challenging, and a majority of former addicts return to drug use within one year of abstinence. Experiencing stressful events and being exposed to sensory stimuli associated with past drug-taking are among the main factors leading to relapse. Stressors and cues elicit memories of drug-induced euphoria and the expectation of relief from current anxiety, igniting an intense craving to use again. Positive experiences and supportive environments may instead act as protective factors. We present a probabilistic model of relapse in drug addiction that draws on known psychiatric paradigms such as `positive affect, negative affect’, ‘negativity bias’, the ‘peak-end’ rule and ‘chasing the first high.’ In our model, relapsing depends on external factors (intensity and timing of random life events) as well as individual traits (mental responses to these events). We study which combinations and ordering of life events lead to the largest probability of relapse and evaluate the first time to relapse from an Ornstein-Uhlenbeck process. Finally, we suggest possible methods to mitigate the likelihood of relapse.

Well into the 21st century, women remain underrepresented in academic mathematics. In this project, we study the dynamics of female gender representation among the faculty of doctorate-granting mathematics departments. We abstract academic genealogies as a multitype branching process in which advisors generate graduated PhD students, and estimate the parameters of this process by fitting a mechanistic model of academic careers to a data set derived from the Mathematics Genealogy Project. Upon fitting our model, we find that male academics enjoy an advantage in production of new PhD students relative to their female colleagues, and that this influences the “next generation” due to homophily effects. Our formalism suggests that, without substantial structural shifts, gender representation in most subfields of mathematics will increase slightly before leveling out well short of parity. We close with some reflections on our model’s limitations and what it suggests about interventions to the representation of women in academic mathematics.

This talk will introduce and connect three approaches to modelling of opinion formation. Beginning with an agent-based model (ABM) with random pairwise interactions, we obtain a system of coupled ordinary or stochastic differential equations (SDEs) by simultaneously rescaling time and the extent to which an agent updates their opinion after an interaction. We show how the precise form of these limiting equations connects to choices made in the ABM. In particular, we focus on how introducing noise at various points in the ABM motivates different diffusion terms in the resulting SDE. Building on this system of SDEs, we then introduce age structure. Each individual ages continuously in time until a maximum age, at which point they die and re-enter the population at age zero with a new, randomly selected opinion. We study the corresponding mean-field limit, a non-linear non-local partial differential equation, showing the existence of steady states and new complex dynamics made possible by the continuous introduction of new individuals to the population.

Firearm violence is a significant public health crisis in the United States, leading to over 200 nonfatal injuries and more than 100 deaths every day. Despite these alarming figures, there are substantial gaps in our understanding of firearm-related harm due to limited federal research funding and the lack of reliable data on firearm ownership and injury. Firearm violence rates likely differ between rural and urban areas, where access to firearms as well as social support systems vary. Urban scaling theory offers a robust framework for quantifying the variation of firearm violence across the rural-urban continuum. Drawing parallels to scaling laws in biological and physical systems, urban scaling posits that the characteristics of a city relate to its population size. Typically, more populous cities exhibit higher per capita rates of patents, wages, and crime, but lower per capita rates of infrastructure such as roads, gas stations, and schools. Using restricted-use data from the CDC Wonder database, we apply urban scaling to firearm-mediated homicides and suicides across cities in the United States. We compare and contrast different time periods and stratify the data by demographics to evaluate the moderating role of critical events such as the COVID-19 pandemic and the implementation of state firearm laws. This work highlights the social resilience offered by urban cities and informs where policy and violence prevention programs need to be focused within states.

This talk splits into three parts. The first part will survey social media interactions and inferences about social events between 2015 and 2019 in several countries. These studies developed a methodology for analysing inauthentic Twitter accounts (bots or sock puppets), gauging how they derailed or impeded discourse between humans. The second part will overview of unpublished work about the Me Too movement in 2017. Using Crimson Hexagon (an extinct Twitter tool), I produced several meta-analyses that showed how the online component of this social movement allowed allied expressions from different countries (outside the US) to piggyback on the attention and bring focus to their local issues. This part is an invitation to critique the available data and potentially help turn it into a publishable piece. The final part is an informal exploration of several million Tweets personally collected (while their APIs still allowed it). They involve many different topics, which could lead to novel collaborations with those interested.

Collective behaviour occurs at all levels of the natural world, from cells joining together to form complex structures, to locusts interacting to form large and destructive plagues. These complex behaviours arise from simple individual and environmental interactions, and thus lend themselves well to mathematical modelling. One simplifying assumption, that of relative homogeneity of organisms, is often applied to keep the mathematics tractable. However, heterogeneity arising due to the internal state of individuals has an impact on these interactions and thus plays a role in group structure and dynamics.        Through the lens of locust foraging, I introduce a continuum model that accounts for this heterogeneity in the form of a state space that maps this internal state to movement characteristics. Then using the model we explore the effect of food, hunger, and gregarisation on locust group formation and structure. Finding that the most gregarious and satiated locusts tend to be located towards the centre of locust groups (Conversely, hunger drives locusts towards the edges of the group). Finally, we find that locust group dispersal may be driven in part by hunger.

The expectation that scientific productivity follows regular patterns over a career underpins many scholarly evaluations, including hiring, promotion and tenure, awards, and grant funding. However, recent studies of individual productivity patterns reveal a puzzle: on the one hand, the average number of papers published per year robustly follows the "canonical trajectory" of a rapid rise to an early peak followed by a gradual decline, but on the other hand, only about 20% of individual productivity trajectories follow this pattern. We resolve this puzzle by modeling scientific productivity as a parameterized random walk, showing that the canonical pattern can be explained as a decrease in the variance in changes to productivity in the early-to-mid career. By empirically characterizing the variable structure of 2,085 productivity trajectories of computer science faculty at 205 PhD-granting institutions, spanning 29,119 publications over 1980--2016, we (i) discover remarkably simple patterns in both early-career and year-to-year changes to productivity, and (ii) show that a random walk model of productivity both reproduces the canonical trajectory in the average productivity and captures much of the diversity of individual-level trajectories. These results highlight the fundamental role of a panoply of contingent factors in shaping individual scientific productivity, opening up new avenues for characterizing how systemic incentives and opportunities can be directed for aggregate effect.

For over six years, the Mexican federal government has maintained that poverty is the primary cause of the violence experienced in the country. This hypothesis has led policymakers to implement public policies centered around providing small individual economic subsidies to people in various sectors of the population. However, a detailed analysis of data reported by the federal government itself reveals no correlation between levels of violence and poverty. In fact, no correlation is found between crime rates and any indicator of social welfare. Therefore, it is necessary to reframe the question regarding the true root causes of violence. In this work, we present a mathematical/computational model that allows us to study the impact of police corruption on the increase in criminal activity. Our data suggest that the degree of respect citizens have for law enforcement agencies and institutions of justice plays a far more critical role in influencing violence than poverty. This respect is strongly influenced by the level of corruption—either real or perceived—within these institutions. These findings help explain why the public policies implemented by the federal government to reduce violence have so far proven ineffective, and they point toward new strategic directions for combating violence and crime.

Despite climate change being a polarizing issue in the United States, many climate mitigation policies enjoy support from large public majorities. Yet most Americans underestimate this support—often by 20 percentage points or more. Such widespread misperception can suppress individual advocacy and influence legislative outcomes. In this work, we combine theory and empirics to investigate two potential drivers of this gap: homophily, or the tendency of like-minded individuals to selectively associate; and false balance in media, where critical viewpoints are overrepresented relative to actual public opinion. Using an agent-based model of social networks and opinion perception, we estimate the severity of homophily and false balance required to produce the observed misperception. We then analyze 2,072 U.S. TV news transcripts to assess how climate policy is framed. The model suggests that homophily alone is insufficient, but that its combination with false balance could explain the misperception. However, our empirical analysis finds no systematic evidence of false balance. Instead, climate policy is often omitted from climate coverage, and when it is mentioned, it is discussed in polarized ways across outlets. To extend our analysis beyond traditional media, we examine climate discourse on Reddit. By mapping how topics like renewable energy, sustainable diets, and public transit are discussed across politically distinct communities, we reveal which policy issues become entangled in partisan identity. These findings point to the limitations of common explanations and suggest alternative hypotheses for future research on perceived public opinion.

Scaling laws are ubiquitous in mechanics, from material strength to turbulence. A scaling law describes the behavior of a system through a power-law, connecting certain properties of the system with its size. Recent studies have identified surprising scaling relationships in living social systems, of which we presently lack a rigorous understanding. To make a first step towards a systematic methodology to unveil the mechanistic underpinnings of scaling laws in these complex systems, we tackle two seemingly different problems: scaling of metabolic rate of insect colonies with colony size and scaling of firearm ownership prevalence with city size. The first problem exemplifies a typical setup in laboratory research, where the researcher designs an experiment and formulates a mathematical model with a hypothesis to test in mind. Grounded in the hypothesis of reverse social contagion, we put forward an experimentally validated compartmental model for energy savings in insect colonies. The second problem exemplifies the less structured scenario in which only ecological data, with all their shortcomings, are available to the researcher. Working with multidimensional data collected on United States cities, we demonstrate the possibility of informing plausible modeling hypotheses through causal discovery and, consequently, formulating network-theoretic models.

Thomas Schelling introduced his agent-based model of segregation in 1971 and concluded that even when there is a low amount of intolerance within society that segregation will develop if people follow their individual preferences. A large body of literature building of this framework has been built and has bolstered this claim. This paper aims to take the same framework but instead look for ways to get to an integrated state. We focus on Allport's contact hypothesis that states that if there is equal status among groups, common goals among groups, and an institutional mechanism supporting intergroup contact then intergroup contact can reduce prejudice. We incorporate the contact hypothesis by having individuals adjust their intolerance based on their current neighborhood composition and the ease of conforming to their surroundings. Furthermore, we add in positive and negative media effects, as individuals are likely to get information about an outgroup from the media (e.g., news, TV, movies, etc.) that they consume. We find that having a society composed of individuals who do not easily conform to their surroundings and displaying positive examples of both groups in media promote integration within society.

Drift-diffusion models are widely used to model how humans and other animals make decisions. Such models describe how the accumulation of uncertain evidence results in a choice. I will show how extending these models to social groups can give some interesting insights into collective decisions of rational agents: For instance, early decisions can signal important information in heterogeneous groups. Moreover, in large groups the first agents to decide almost always hold the strongest initial bias and decide accordingly. Slow agents, conversely, decide as if they held no initial bias. When agents receive correlated evidence, decision accuracy depends on decision order in the absence of initial bias. Interestingly, these are rational agents who use the same decision criterion, and are thus all equally confident in their decisions. Yet, their accuracy differs dramatically. I will make several such observations which follow from our analysis, but for which we do not yet have intuitive explanations.