Dr. Emerenini's project this summer is on modeling and analysis of competition and antagonism in biofilms in plant roots induced by the Type VI secretion system (T6SS), which is a potent mechanism of bacterial aggression. T6SS is a molecular machine used by a wide range of gram-negative bacterial species to transport proteins from the interior (cytoplasm or cystosol) of bacterial cells across the cellular envelop into an adjacent target cell. T6SS can negatively contribute to microbial interactions and mediate virulence and bifiolm detachment and chemotaxis by cellular disruption.

Dr. Petsche proposes an exploration of topics in algebraic dynamical systems in several variables over p-adic and other non-Archimedean fields. Possible projects include:

- Find a new, dynamical proof of the non-Archimedean Perron-Frobenius theorem established in the 2015 OSU REU, based on fixed-point theory. Does such an approach have further non-Archimedean applications in parallel with the real setting? Is there a generalization to nonlinear maps?

- Classify the dynamics of non-Archimedean Henon maps in residue characteristic 2, the excluded case in the 2016 OSU REU.

- Perform new and interesting calculations of dynamical invariants, such as entropy, Hausdorff dimension, and the growth rate of periodic points, in the context of p-adic plane automorphisms.

Dr. Restrepo's project this summer will use probability, dynamics, and machine learning tools to study whether a health policy is effective in curbing the likelihood of an epidemic. Anti vaxxers have become a recent cause of public health concern. They will actively discourage their children from receiving vaccines that would protect them from several communicable health threats. The anti vaxxers presume that their actions will protecting young children from health effects attributed to the vaccines themselves. These children become highly mobile vectors of diseases caused by these pathogens. But more critically, they become the living resources that these disease-causing viruses require for mutation and eventual immunity to existing vaccines. Public health officials develop policies for vaccination that respond to increases in reported infection rates. The question we are going to pursue is whether a health policy is effective enough, capable of curbing the likelihood of an epidemic. Using probabilistic techniques, dynamics, and machine learning tools we will establish whether a specific public health strategy will be capable of controlling the spread of a disease to levels well below those of an epidemic. The tools we will develop would be useful to public health officials that are interested in determining whether a significant outbreak could develop into an epidemic or not, given an active public health policy aimed at combating the disease.

In general, the proceedings from the past few years will give an idea of the variety and general levels of the projects.