Juniper Lovato, Director of Outreach for Complex Systems, University of Vermont

Limits of individual consent and models of distributed consent in online social networks

Personal data is not discrete in socially-networked digital environments. A user who consents to allow access to their profile can expose the personal data of their network connections to non-consented access. Therefore, the traditional consent model (informed and individual) is not appropriate in social networks where informed consent may not be possible for all users affected by data processing and where information is distributed across users. In this talk we will outline the adequacy of consent for data transactions. Informed by the shortcomings of individual consent, we introduce both a platform-specific model of ``distributed consent’' and a cross-platform model of a ``consent passport.‘’ In both models, individuals and groups can coordinate by giving consent conditional on that of their network connections. We simulate the impact of these distributed consent models on the observability of social networks and find that low adoption would allow macroscopic subsets of networks to preserve their connectivity and privacy.

Off

Elizabeth Cherry, School of Computational Science and Engineering, Georgia Tech

Off

Taxation, Redistribution, and Wealth in Simple Economic Models

The distribution of wealth has been a topic of much interest over the last several years. In this presentation, I will discuss the effects of various tax and redistribution strategies on the distribution of wealth in two economic models. In the first part of the presentation, I will discuss the effects of taxation and redistribution on a modified Bennati-Dragulescu-Yakovenko (BDY) game, an agent-based simple exchange game. Several different taxes are applied to the BDY game, some of which are modeled after past and current US tax policy. I will present the effects of various taxation and redistribution models on the BDY game's Gini coefficient, a quantitative measure of income or wealth inequality.  In the second part of the presentation, I will discuss the effects of taxation and redistribution on a simple model of inheritance. In the inheritance model, estate taxes are collected, and we'll examine how the redistribution of collected estate taxes affects the Gini coefficient and two social welfare functions of the population. Like the taxes in the BDY game, some of the estate taxes collected in the inheritance model will be modeled after US tax policy.

Off

Buckling, wrinkling and folding

Buckling, wrinkling and folding of elastic structures will be discussed and illustrated. Two cases will be examined in detail: the case of a floating elastic sheet subjected to horizontal compression, and the case of a laterally compressed circular tube or ring. The results will be described in terms of bifurcation diagrams with a particular emphasis on the wrinkle-to-fold transition. In each case the lowest energy state will be determined as a function of compression.  The results will be related to existing experiments.

This is joint work with Ben Foster, Nicolas Verschueren and Leonardo Gordillo.

Off

Laurent Hebert-Dufresne, Department of Computer Science, University of Vermont

Approximate master equations for contagions on higher-order networks

Simple models of contagions tend to assume random mixing of elements (e.g. people), but real interactions are not random pairwise encounters: they occur within clearly defined higher-order structures (e.g. communities) which can be heterogeneous in size and nature. Likewise, not all groups are equivalent and important dynamical correlations can be missed by averaging over groups. To accurately describe spreading processes on these higher-order networks and correctly account for the heterogeneity of the underlying structure, we leverage an approximate master equations framework. This mathematical model allows us to unveil and characterize important properties of these systems. Here we focus on three of them: The localization of contagions within certain substructures, the bistability of the stationary state and optimal seeding strategies through influential groups. Altogether, these results highlight the complex behavior of contagions on higher-order networks, and the power of approximate master equations in capturing this complexity in a whole range of applications.

Off

Javier Buldu; Applied Mathematics, Materials Science and Engineering and Electronic Technology; University of King Juan Carlos; Madrid, Spain

How to use Network Science to unveil football's complexity

The recent ability to record, tag, and evaluate the outcome of all events occurring during a football match, including the Euclidean position of the players and the ball, has opened the door to a new kind of studies where it is possible to analyze and quantify the behavior of a team as a whole, together with the role of its players. Under this framework, the organization of a team can be considered as the result of the complex interactions between teammates and rivals, making Complexity Sciences the perfect framework for its analysis. In this presentation, I will show new methodologies, based on Network Science, that can help to extract new (and useful) information from the event and tracking datasets recorded during a football match.

Off

Dan Larremore, Department of Computer Science, Â鶹ӰԺ

Model-informed COVID-19 vaccine prioritization strategies by age and serostatus

Limited initial supply of SARS-CoV-2 vaccine raises the question of how to prioritize available doses. One might reason, intuitively, that doses should be prioritized to directly protect those who are most vulnerable. Yet one might also intuitively argue that we should use vaccination as a means to break chains of transmission by prioritizing early doses to those most responsible for transmission, thereby indirectly protecting the vulnerable by reducing prevalence. Unfortunately, these two intuitive solutions make orthogonal recommendations. Here, we introduce a family of mixed discrete and differential equation models to resolve the tension between these recommendations, and compare five age-stratified vaccine prioritization strategies. By considering the demographics and contact patterns in the country of interest, transmission rates, vaccine properties, and the accumulated immunity in the population due to prior infection with SARS-CoV-2, we show how one can use differential equation models to quantify the tradeoffs between vaccine rollout strategies in a context-specific ways. We also highlight ways in which these models can help ameliorate existing pandemic-related inequities in access to healthcare and protection. In this talk, we will cover both the high-level results and recommendations, as well as vaccine-related modeling choices that complicate the more typical and standard "SIR" type disease model.  This work is a collaboration with Kate M. Bubar (CU APPM) and Kyle Reinholt (CU CSCI), among others.

Off

Heather Zinn Brooks, Department of Mathematics, Harvey Mudd College

Bounded-confidence models for media impact on online social networks  

Online social media networks have become extremely influential sources of news and information. Given the large audience and the ease of sharing content online, the content that spreads on online social networks can have important consequences on public opinion, policy, and voting. To better understand the online content spread, mathematical modeling of opinion dynamics is becoming an increasingly popular field of study. In this talk, I will introduce you to a special class of models of opinion dynamics on networks called bounded-confidence models. I will then discuss some of the applications and theory that my collaborators and I have been developing with these models, including the impact of media, opinion dissemination, mean-field dynamics, and extensions to hypergraphs and multilayer networks. This talk will also include some unsolved questions for future work.  

Off

John Parker, Integrated Applied Mathematics, University of New Hampshire

Chaotic Stabilization in Neural Systems

Recent work in dynamical systems theory has shown how chaotic systems are able to be controlled. One control scheme, adapted from Hayes, Grebogi, and Ott, was applied to a chaotic double scroll oscillator and produced stabilized periodic orbits called cupolets (chaotic, unstable, periodic orbit-lets). It was then demonstrated by Morena and Short that interacting cupolets can produce mutual stabilization. Mutual stabilization occurs when two interacting systems maintain a persistent, periodic trajectory that would not exist without the interaction. One interaction function used was based on integrate-and-fire dynamics often seen in neural systems. Here, work is shown that provides evidence of mutual stabilization within interacting neural systems. First, published work is presented that shows how a bidirectional, two-cell FitzHugh-Nagumo neural model can transition from chaotic to periodic behavior through synaptic learning activated by a particular external signal. Then, preliminary work is discussed concerning the existence of cupolets in a Hindmarsh-Rose neuron. Periodic pulses are then generated using these cupolets and coupled into the Hindmarsh-Rose system to recreate the corresponding stabilized periodic orbit.  

Off

jimi adams, Health and Behavioral Sciences, University of Colorado Denver

Peer Network Processes in Adolescents' Health Lifestyles

Combining theories of health lifestyles—interrelated health behaviors arising from group-based identities—with network and behavior change, we examined influence and selection processes between friendship networks and health lifestyles. We propose that friendship networks shape lifestyles, while simultaneously being a product of lifestyles. We examine these questions using data from two high schools with longitudinal, complete friendship network data from the National Longitudinal Study of Adolescent to Adult Health. Latent class analyses characterized each school’s predominant health lifestyles based on several health behavior domains. School-specific stochastic actor-based models evaluated the bidirectional relationship between friendship networks and health lifestyles. Predominant lifestyles remained stable within schools over time, even as individuals transitioned between lifestyles. In both schools, friends displayed more similarity in health lifestyles than other peers, and this similarity resulted primarily from selection, but also from influence processes.  

Off