**2018 REU (Research Experience for Undergraduates) program in Computational and Applied Mathematics**

In the summer of 2018, we offered several research projects, including the following:

**Organization of multinucleated cells**

With plentiful nutrients, free living cells continuously grow and divide. Recent mathematical modeling has revealed the mechanisms by which cells monitor their size and use this information to decide when they should divide. However, many organisms, including fungi (and even cell types in our own bodies, such as muscle cells) are multinucleated, that is a single cell contains many nuclei sharing a single bag of fluid. As these cells grow, individual nuclei must choose when to divide. But if all nuclei were to divide at once then there would be chaos within the cell. Accordingly the nuclei must decide collectively which nuclei will divide. Ideally, nuclei would take it in turns to divide (so that a single nucleus does not get to populate the entire cell with its offspring, at the cost of the others). How does the nuclear college make this decision? We will use modeling and experiments to study nuclear replication in the model fungus *Neurospora crassa*, studying how division rates are affected by the lineage that a nucleus is in, as well as the cues it receives from the surrounding cell (e.g. the amount of surrounding space). Our goal is to develop mechanistic models for how nuclei use information to make decisions both individually and collectively.

**Patterns of Lyme disease**

We are interested in discovering hidden patterns in recently acquired large-scale Lyme disease data. We would like to detect relationships between patient symptoms, diagnosis, and treatment that could lead to understanding the mechanisms of the disease as well as better diagnostic tools and treatment protocols. The project will include topic modeling, deep learning, classification, and compressed techniques and develop skills in numerical linear algebra, machine learning, and probability.

**Probing financial transaction networks**

Analyzing connections and flows within complex financial transaction networks can reveal organized criminal or terrorist activity. We will examine synthetic graphs that model financial transaction networks. We are interested in developing scalable algorithms to identify patterns of activity in these systems.

**Classifying body worn video data**

The Los Angeles Police Department has collected massive amounts of data from cameras worn by officers while on active duty. It is impossible to curate these videos manually, and new algorithms are needed to analyze the videos to classify officer activity, and the people that officers interact with. This project would build on prior work by earlier REU teams.

**Microfluidic device design**

The equations of fluid flow are among the best studied of all equations in mathematics. But it is surprisingly difficult to use all of this mathematical knowledge to control fluid flows. We will study recent experiments in which fluid threads flow around ordered arrays of posts. Flowing around the posts change the cross-section shape of the thread. Initially rectangular threads turn into bat-wings or spirals. Can we design our post arrays to create jets with desired cross-section shapes? We will work with a library of the simulated flows around 10000 different posts to try to systematically understand what kinds of thread shape changes each type of post produces, and use machine learning and clustering tools to dissect what classes of shape change are possible, as well as to solve the inverse problem of designing an array to create a desired change in shape. This project will suit either students with interests in physics or in machine learning methods.

**Studying topic dynamics in Twitter**

Twitter has created a global platform for conversation. But can these data be used to detect and understand social change? We plan to build a real-time machine learning platform to classify topics and locations of tweets in Los Angeles as they change over time. We would like to develop an active website showing the latest threads and their spatial locations from geotagged twitter. This project will involve topic modeling (including numerical linear algebra and statistics) and web design.