2021 Summer REU Program

Title: Long-term consequences of repeated collective decision-making cycles on population stability

Mentors:  Dr. Jason Graham, Scranton University, and Dr. Simon Garnier, NJIT

Recent events have highlighted the destructive role of unmoderated social interactions and false information on the stability of human groups. Indeed, while social influences can improve the outcome of a collective decision-making process, they also have a non-zero chance to trigger cascades of wrong decisions through, for instance, groupthink. Even in stable social groups, the likelihood of such catastrophic cascades can be increased when the population goes through repeated cycles of collective decision-making. Through computer and mathematical modeling, this project will investigate how social interactions and individual decision accuracy affect the long-term fate of populations during repeated episodes of collective decision-making. We will explore how populations grow or shrink after multiple episodes of collective decision-making when the individual decision-making accuracy of its members and their reliance on social information changes. Finally, we will attempt to determine whether there exists an optimal balance between personal and social information that minimizes the risk of catastrophic cascades while maximizing the long-term collective output of the population.

Title: Modeling and simulation of the motion of zebra larval fish

Mentors: Enkeleida Lushi, NJIT and Kristen Severi, NJIT

These millimeter-long swimmers display complex behavior as they move in water. It is influenced by the mechanical and social interactions with other larval fish, the presence of interfaces, and any introduction of light or food. These various mechanisms can result in intricate collective motion, especially in the presence of walls. Inspired by the experimental observations in the laboratory, the students will devise a mathematical model consisting of coupled ordinary differential equations describing the swimmer motion and orientation and any interactions. They will implement the equations into a computer simulation and compare the results to the experimental observations. The students will learn mathematical modeling as well as numerical methods for simulations using softwares like Matlab or Python.

Title: Modeling the effects of behavior in epidemics

Mentor: Dr. Matthew Wascher, OSU and Olivia Cleymaet, OSU

The COVID-19 epidemic in the US has gone through multiple waves, with multiple peaks of high infection as well as periods of lower infection. However, traditional mathematical models of epidemics are often designed to model an epidemic curve that increases to a single peak before decreasing and dying out or reaching a low endemic state. Why is the COVID-19 curve so different? One possible explanation is that it has been affected by behavior, both of individuals and groups, such as self-isolation, government shutdowns, and travel. This project aims to explore how mathematical models that attempt to model these behaviors might be able to model epidemics with features like multiple peaks, oscillations, and plateaus that we have observed with COVID-19. You will work with agent-based models (models that model each individual) and explore how different behaviors by individuals can affect the course of an epidemic. A basic understanding of probability and basic computing skills will be helpful in working on this project.

Title: Analyzing COVID-19 transmission in Ohio

Mentors: Dr. Greg Rempala, OSU and Dr. Eben Kenah, OSU

In their most recent work, Drs. Rempala and Kenah are developing new ways to analyze and predict disease transmission. The summer research project will involve analyzing data from the current Covid 19 outbreak in Ohio using concepts from survival analysis and epidemic modeling. Basic knowledge of statistical concepts and the programming language R are a plus but not strictly necessary as appropriate training will be provided.

Title: Untangling the web of life: phylogenetic networks and their normalization

Mentors: Dr. Kristina Wicke, OSU and Dr. Laura Kubatko, OSU

Traditionally, the evolutionary relationships among species were represented by phylogenetic trees. However, it is now commonly accepted that evolution is not always tree-like, and phylogenetic networks have been introduced as a generalization of phylogenetic trees. They allow for the representation of reticulate evolutionary events such as hybridization and horizontal gene transfer. Reconstructing phylogenetic networks from biological data (e.g., DNA sequences) is one of the most active areas of research in mathematical biology, but the reconstructed networks are often very complex and tangled, making them hard to interpret biologically. It was thus recently suggested to transform a phylogenetic network into a simpler graphical structure that summarizes the network’s most important features and evolutionary information. This is called the “normalization” of a network. In this project, we will explore mathematical and biological properties of the normalization of phylogenetic networks. Specifically, we will consider the following problem: given a normalization , can we characterize the networks that normalize to  (currently an open question in the literature)? We will also study the normalization of phylogenetic networks reconstructed from empirical data and analyze their characteristics.

Reference:

A. Francis, D. H. Huson, and Mike Steel. Normalising phylogenetic networks. arXiv e-prints, art 2008.07797, Aug 2020.