The Kenneth Cooke Summer Research Fellowship is offered each year. Any Pomona College student is eligible to apply for ten weeks of summer research in applied mathematics or statistics. The Fellowship was enabled by The Kenneth Cooke Memorial Endowment Fund which was established in Prof. Cooke's honor by former students, colleagues, family, friends and members of the larger mathematics community. To apply, submit your application to the Mathematics Department.

Your application should include:

- A description, written by the student, of the proposed research project.
- A letter of support from persons directly supervising the research.
- If the research supervisor is not a Pomona faculty member, a letter of recommendation from a Pomona mathematics faculty member serving as mentor on the project.

## Eligibility and Guidelines

Areas of applied mathematics supported by this fellowship are: applications of differential equations, delay-differential equations and functional equations, applied probability, mathematical modeling in biology and epidemiology, applied statistics.

The fellowship may be awarded to a graduating senior if they are continuing a project that started during their career at Pomona. The fellowship may also be repeated for multiple years.

Supervisors can be from other departments and/or institutions (public or private).

The research proposal should be written by the student, and should clearly articulate the specific aims of the research.

*The application deadline is March 31 of the year in which it is granted. More information can be obtained from the Chair of the Pomona College Mathematics Department at (909) 621-8409.*

## Awardees

### Summer 2019

#### Ethan Ashby ’21, Analysis of Time Course RNA-Sequencing Data in *T. brucei *and *E. coli *with J. Hardin

Time course RNA-Seq experiments permit study of dynamic transcriptomic responses to stimuli. However, temporal correlations inherent in time course experiments limit the application of conventional differential expression (DE) algorithms. Two time course RNA-Seq datasets were run through a thoughtfully-constructed differential expression pipeline combining two-sample and serial tools, and visualization and downstream analyses were conducted to address biological questions. The first dataset was a 150 minute time course RNA-Seq experiment of Escherichia coli (E. coli) undergoing cell starvation. Analysis of the onset time parameters of sigmoid functions fit to differentially-expressed gene (DEG) profiles demonstrated that graded sensitivity to the stress-responsive transcription factor, RpoS, did not describe the global transcriptomic trend in response to cell starvation. The second dataset was a 14 day time course RNA-Seq experiment of the insect-form of the protozoal parasite, Trypanosoma brucei, upon chemical knockout of an important class of chromatin-reader proteins. Gene ontology analysis of DEG clusters suggest these chromatin-readers play roles in parasite motility, glycosomal metabolism, and the maintenance of cytosolic stress granules in the insect-form of the parasite. These findings are suggestive of a potential developmental change in the parasite’s life cycle. This work was done in collaboration with Lian Morales and Annie Cohen.

### Summer 2018

#### Erin Angelini ’18, Reduced Models for Spindle Rotation with B. Shtylla

The primary goal of this proposed research is to finish up work initiated in my senior thesis this year, "An Energy-Based Model of Mitotic Spindle Alignment in *C. elegans.*" This work will be conducted in collaboration with the Dawes lab at Ohio State University.

#### Harry Bendekgey ’19, Predicting Elections with G. Chandler

In 1997 Andrew Gelman, a fervent Bayesian, said "Elections are predictable." Despite the surprise of the 2016 election to the general public, forecasting models had considered a Trump victory a real possibility. Looking at the data available to pundits at the time, we can now see that there were plenty of markers that pointed towards a Trump victory. That doesn't mean that forecasters should have said Trump was in the lead, though. It's okay for a forecaster to give a candidate a small (25% let's say) chance of winning and then for them to win; given that prediction, we should see that result one in four times. It's far easier to analyze data in hindsight, which brings us to an important conclusion: elections are predictable when the model is good. The difficulty is in building that model.

### Summer 2017

#### Benji Lu ’17, Constructing Prediction Intervals for Random Forests with J. Hardin

Although random forests are commonly used for regression, our understanding of the prediction error associated with random forest predictions of individual responses is relatively limited. We introduce a novel measure of this error and evaluate its properties, comparing it with the out-of-bag mean of squared residuals estimator that, to our knowledge, is the only measure of random forest prediction error that has been introduced in the literature thus far. We show that our proposed estimator provides an individualized estimate of the error associated with a particular random forest prediction, while the out-of-bag mean of squared residuals estimator provides a more general estimate of the random forest's prediction error as a whole. Through simulations on benchmark and simulated datasets, we also demonstrate that both estimators of prediction error may form the bases for valid random forest prediction intervals. Empirically, these prediction intervals performed as well as quantile regression forest prediction intervals.

#### John Sangyeob Kim ’17, Mathematical Model of Antimicrobial Resistance (AMR): Stability Analysis and Empirical Data Application with A. Rumbos

I regard mathematics as a crucial component of health research. Mathematical modeling allows modelers to devise a framework of hypotheses to describe complex interactions among variables and different aspects of the real world. Modelers then explore the dynamics of the framework to see if the model adequately explains phenomena of interest. If the interpretations are not sufficient, then the original assumptions are further loosened or tweaked to better reflect the reality.

J. S. Kim. Analysis of an Antimicrobial Resistance Transmission Model, SIAM Undergraduate Research Online Journal, Volume 12, 2019, DOI: 10.1137/19S1254805.

### Summer 2014

#### David Morgens ’14, Stochastic Analysis of a Mammalian Circadian Clock Model: Small Protein Number Effects with B. Shtylla

Cells contain complicated biochemical networks that permit adaptability of the cell function in the face of changing signals and environment. Thanks to advances in experimental methods we are learning a lot about the various components that make up these networks, however, how they are combined together remains a mystery that cannot be easily be detangled by experiment alone. This is where mathematical modeling is appropriate and powerful. Accordingly, a new technique called network analysis is becoming popular in the field of systems biology, where it is used to mathematically model responses of various modules of complex biochemical networks.

### Summer 2013

#### Maximilian Hoffman ’16, Evolutionary Dynamics of Chemical Reaction Mechanisms with D. Fryer and C. Galvin

Reaction mechanisms have always been an important facet of chemical and biological studies. Without a fundamental understanding of how reactions proceed, we lack much of our ability to study, improve, and control the science we encounter daily. Accordingly, many attempts have been made to predict reaction paths and products. Kinetic and energetic studies are traditionally employed, however these often lead to unsatisfactory conclusions. Kinetics can only rule out false mechanisms, while computer generated potential energy surfaces have failed to offer reliable pathways. Exciting recent studies have successfully visualized reactions by cooling the reagents to near zero Kelvin temperatures, but to this date chemists are left without predictable guidelines for understanding the principles guiding a reaction mechanism.