SAMS (available here) is the main culmination of my PhD thesis: a Matlab package to automatically process, register, and analyze collections of anatomical surfaces at the resolution higher than was ever possible before it was published. Read more
The geometric and topological properties of spaces of shapes are not well understood, let alone those of anatomical surfaces. However, those of other spaces (e.g. Hilbert spaces) are. If we were able to embed shapes into a nicer, lower dimensional space, we could use pullbacks of tools on the nicer spaces to learn more about shape spaces. Sparse dictionaries provide a natural, interpretable way to do this. Read more
Fully automated methods for statistical shape analysis are needed in order to do high-resolution analysis of large amounts of data. Existing methods primarily focus on the case when shapes are topological spheres and have little variation. SAMS is a package that will work on all simply-connected shapes and can robustly handle higher variability of data. Read more
Fully automated registration of shapes can prove to be extremely challenging if the shapes have clearly corresponding parts but wildly different features. Read more
Maryland’s congressional redistricting is another commonly cited example of gerrymandering given the complicated shapes behind its districts. But is this a case of partisan gerrymandering, or is it something else? Read more
North Carolina has a storied history with gerrymandering. The 2016 congressional redistricting was accused of being a partisan gerrymander, in part due to the discrepancy between the statewide popular vote (close to a 50/50 split between Republicans and Democrats) to the actual outcome (9 Republicans and 4 Democrats) in 2016. Given the geographical nature of the problem, this is not clear: can we quantify the extent of the gerrymandering in an interpretable way? Read more
Pennsylvania is my home state, and has been panned in the past for the shapes of its districts, including the famous “Goofy Kicking Donald Duck” in the 2010 congressional redistricting. In the process of doing an analysis using different techniques separate than those involved in League of Women Voters v. Commonwealth of PA, we uncovered new information concerning different assumptions made in the sampling process: the role of preserving as many townships as possible. Read more
The word “firewall” is indicative of a structure that prevents something from crossing, as is commonly used when it comes to malware in computers. An analysis of redistricting at the state level in Wisconsin reveals a similar structure. Read more
For centralized algorithms, where there is only one agent optimizing, it is known that strong convexity of objective functions improves convergence rates of optimization methods, and thus improves performance guarantees in online scenarios in the centralized setting, even in the adversarial case. Distributed methods have multiple agents optimizing a function simultaneously. Can we get similar performance guarantees of online methods in the distributed setting, or will requiring communication of agents destroy any hope? Read more
Online convex optimization (OCO) problems typically focus on adversarial scenarios. Many, however, aren’t. If you know this, and have some reasonable model of your future, what improvements can you get? Furthermore, how well can you do if you’re starting from scratch? Read more
How much can we learn about biology by looking at anatomical surfaces? Potentially a lot, but there are many preprocessing issues to deal with before we can. Read more
Partisan gerrymandering is a phenomenon in American politics that, unlike racial gerrymandering, is poorly understood. Read more
Research in optimization has exploded due to increases in computational ability. Online optimization, where objective functions can change in time, is a field with vast potential for both interesting theoretical investigations as well as practical applications well outside areas traditionally considered in, e.g. control and learning communities. Read more
This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown! Read more
This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field. Read more
Students can be much more capable than many instructors/mentors give them credit for, but instructors/mentors must be cognisant of the fact that they might care much more about what they teach and work on than students ever will. That’s not a bad thing. Read more
Students can be much more capable than many instructors/mentors give them credit for, but instructors/mentors must be cognisant of the fact that they might care much more about what they teach and work on than students ever will. That’s not a bad thing. Read more