Browsing by Author "Mertz, Rostik"

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Bike Networking
(Montana State University, 2017-04) Mertz, Rostik
I used networking techniques to represent the data that citi Bikes has collected and made public from New York, New York in 2013. By applying my knowledge of networks to this data I was able to graphically represent the data in such a way that it can be easily interpreted. With this I will determine if there is a need for new bike paths in New York based on common routes and destinations through the city. I will also be able to determine where it would be beneficial to place more bike rental locations.
Reconstructing embedded graphs from persistence diagrams
(2020-10) Belton, Robin Lynne; Fasy, Brittany T.; Mertz, Rostik; Micka, Samuel; Millman, David L.; Salinas, Daniel; Schenfisch, Anna; Schupbach, Jordan; Williams, Lucia
The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in Rd (plane graphs in R2) with n vertices from n2 −n+d+1 directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in R2 on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.