This is an exciting time in engineering and mathematics. The complexity of the world requires the ability to think quantitatively and handle large amounts of data.
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The Diagnostic Gait
The Smart and Frugal Home
Can the Smart home also be frugal?
Topology of Traffic Congestion
Roads and traffic make complex networks. Can we find robust patterns of congestion in a city?
Time for Accidents
How much time would you have to give up to avoid accidents? We combined some datasets from New York City to understand this tradeoff
The Smart Strawberry Field
While many crops already are or are becoming mechanized, many valuable crops still are hand-picked. These crops sometimes need new ways to collect precise geospatial harvest data which can then be used to monitor, measure, and optimize what is happening in the field.
Optimal Transport in Hand-Picked Crops
A number of hIgh-value hand-picked specialty crops are very susceptible to spoilage after they have been picked and while they are waiting to be refrigerated. We would like to model and minimize this spoilage.
Press release: https://news.illinois.edu/view/6367/469804
Uncertainty is a crucial factor in financial stability, but it is notoriously difficult to measure. This working paper extends techniques from engineering to quantify fundamental economic uncertainty, and applies the method to an example of portfolio stress testing. By this measure, uncertainty peaked in late 2008. Preprint.
Dynamics of Bankrupt Stocks
Bankrupt stocks are still traded while the court winds the company down. This creates some interesting dynamics as traders short a finite number of shares of the stock. Preprint.
Stochastic Moving Boundary Problem
The dynamics of many multiphase systems are described by moving boundary problems. What happens if we add noise to these PDE’s? Preprint.
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