Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model.

We show that the order-disorder phase transition in the three-state Potts ferromagnet on a square lattice is driven by a coupled proliferation of domain walls and vortices. Raising the vortex core energy above a threshold value decouples the proliferation and splits the transition into two. The phase between the two transitions exhibits an emergent U(1) symmetry and quasi-long-range order. Lowering the core energy below a threshold value also splits the order-disorder transition but the system forms a vortex lattice in the intermediate phase.

Minimal and adaptive numerical strategy for critical resource planning in a pandemic.

Current epidemiological models can in principle model the temporal evolution of a pandemic. However, any such model will rely on parameters that are unknown, which in practice are estimated using stochastic and poorly measured quantities. As a result, an early prediction of the long-term evolution of a pandemic will quickly lose relevance, while a late model will be too late to be useful for disaster management. Unless a model is designed to be adaptive, it is bound either to lose relevance over time, or lose trust and thus not have a second chance for retraining. We propose a strategy for estimating the number of infections and the number of deaths, that does away with time-series modeling, and instead makes use of a "phase portrait approach." We demonstrate that, with this approach, there is a universality to the evolution of the disease across countries, that can then be used to make reliable predictions. These same models can also be used to plan the requirements for critical resources during the pandemic. The approach is designed for simplicity of interpretation, and adaptivity over time. Using our model, we predict the number of infections and deaths in Italy and New York State, based on an adaptive algorithm which uses early available data, and show that our predictions closely match the actual outcomes. We also carry out a similar exercise for India, where in addition to projecting the number of infections and deaths, we also project the expected range of critical resource requirements for hospitalizations in a location.

Estimating the herd immunity threshold by accounting for the hidden asymptomatics using a COVID-19 specific model.

A quantitative COVID-19 model that incorporates hidden asymptomatic patients is developed, and an analytic solution in parametric form is given. The model incorporates the impact of lock-down and resulting spatial migration of population due to announcement of lock-down. A method is presented for estimating the model parameters from real-world data, and it is shown that the various phases in the observed epidemiological data are captured well. It is shown that increase of infections slows down and herd immunity is achieved when active symptomatic patients are 10-25% of the population for the four countries we studied. Finally, a method for estimating the number of asymptomatic patients, who have been the key hidden link in the spread of the infections, is presented.