University of California Los Angeles

We revisit the tears of wine problem for thin films in
water-ethanol mixtures and present a new model for the climbing
dynamics. The new formulation includes a Marangoni stress balanced by
both the normal and tangential components of gravity as well as surface
tension which lead to distinctly different behavior. The combined
physics can be modeled mathematically by a scalar conservation law with
a nonconvex flux and a fourth order regularization due to the bulk
surface tension. Without the fourth order term, shock solutions must
satisfy an entropy condition - in which characteristics impinge on the
shock from both sides. However, in the case of a nonconvex flux, the
fourth order term is a singular perturbation that allows for the
possibility of undercompressive shocks in which characteristics travel
through the shock. We present computational and experimental evidence
that such shocks can happen in the tears of wine problem, with a
protocol for how to observe this in a real life setting.

We investigate a nonlinear version of coevolving voter models, in which both node states and network structure update as a coupled stochastic dynamical process. Most prior work on coevolving voter models has focused on linear update rules with fixed rewiring and adopting probabilities. By contrast, in our nonlinear version, the probability that a node rewires or adopts is a function of how well it "fits in" within its neighborhood. To explore this idea, we incorporate a parameter σ that represents the fraction of neighbors of an updating node that share its opinion state. In an update, with probability σq (for some nonlinearity parameter q), the updating node rewires; with complementary probability 1−σq, the updating node adopts a new opinion state. We study this mechanism using three rewiring schemes: after an updating node deletes a discordant edge, it then either (1) "rewires-to-random" by choosing a new neighbor in a random process; (2) "rewires-to-same" by choosing a new neighbor in a random process from nodes that share its state; or (3) "rewires-to-none" by not rewiring at all (akin to "unfriending" on social media). We compare our nonlinear coevolving model to several existing linear models, and we find in our model that initial network topology can play a larger role in the dynamics, whereas the choice of rewiring mechanism plays a smaller role. A particularly interesting feature of our model is that, under certain conditions, the opinion state that is initially held by a minority of nodes can effectively spread to almost every node in a network if the minority nodes views themselves as the majority. In light of this observation, we relate our results to recent work on the majority illusion in social networks.

Reference: 

Kureh, Yacoub H., and Mason A. Porter. "Fitting In and Breaking Up: A Nonlinear Version of Coevolving Voter Models." arXiv preprint arXiv:1907.11608 (2019).

The vulnerability of a host population to a specific disease measures how likely pathogen introduction will lead to an epidemic outbreak, and how hard it is to contain or eliminate an ongoing one. Predicting vulnerability is thus key to designing risk-reduction strategies that limit disease burden on public health and economic development. To do that, highly-resolved data tracking contacts and mobility of the host population need to integrate into detailed models of disease dynamics. This represents a twofold challenge. Firstly, we need theoretical frameworks that turn data feeds into predictors of epidemic risk, and can identify which of the structural features of the host population drive its vulnerability. Secondly, we need new ways to access, analyze, and share the relevant contact and mobility data: a necessary step to make our predictions realistic and reliable. In my talk, I will address both issues. I will show how to analytically derive the conditions that discriminate between epidemic regime and quick pathogen extinction, by representing empirically measured contacts as time-evolving complex networks. The analytical core of this theory leads to a broad range of applications. At the same time, its data-driven nature prompts context-specific predictions that can inform policymaking, as I will show in two case studies: reorganizing nurse scheduling to reduce the risk of spread of healthcare-associated infections; linking the features of livestock trade movements to the spatial spread of cattle diseases. The latter application is also an example of how limited access and incomplete data collection represent a big hurdle to predictive vulnerability analysis. To overcome this, I will present a collaborative platform for analyzing and comparing trade networks coming from several European countries. Using a bring code to the data approach, our platform surmounts the strict regulations preventing data sharing, and builds an algorithm that predicts vulnerability even in situations when limited data on cattle trade are available. The ultimate goal of all these theoretical and numerical developments is to inform strategies that reduce the vulnerability of the host population by restructuring its contacts. However, such restructuring may entail a feedback effect, acting as selective pressure on the pathogen itself. In the last part of my talk, I will extend the developed formalism to modeling evolutionary pathways that maximize the invasion potential of the pathogen, given the observed host population structure. Specifically, I will link the emergence of exotic replication behaviors in plant-infecting viruses to historical changes in plant distribution patterns.