Short Description: A brain cell outputs sequences of electrical spikes. The rate of spiking often varies substantially during the course of an experimental trial and it varies substantially depending on the type of experiment. An important problem in neuroscience is to identify regions of time during which the spiking rate differs from one experiment to another. There are two main statistical challenges: (1) dealing with multiple hypothesis tests corresponding to different time periods, and (2) selecting the appropriate time scale for comparison. The goal of this project is to explore some techniques for simultaneously testing all time periods and time scales. Although we will test the methods on real data, the primary task is to implement and test the techniques on simulated data where the truth is known.  

Number of Students: 1 or 2

Prerequisites: Programming experience and interest in learning Matlab. Enjoyment of mathematics. Familiarity with conditional probability and hypothesis testing.

 Faculty Advisor: Chris Genovese

Short Description: Cosmologists have long sought to estimate the distribution of mass through the universe because that distribution tells us a great deal about fundamental physics. What is dark matter? Does dark energy exist? How will the unverse end? How did it begin? A challenging approach to this problem is to infer the distribution of mass by detecting subtle distortions in the light from background galaxies. This is called weak lensing.

Number of Students: 1

Prerequisites: Curiosity, willingness to learn, some basic stats and calculus experience would help.