## Emilie Purvine

## Emilie Purvine

## Biography

Emilie Purvine joined Pacific Northwest National Laboratory (PNNL) in 2011 as a post-doctorate research assistant in the Computational Mathematics group, then transitioned to a staff scientist in November of 2012. In 2015, Purvine moved over to the National Security Directorate’s Data Science group and transferred to the PNNL-Seattle campus in January 2016. There, she focuses on applications of combinatorics and computational topology, together with theoretical advances needed to support the applications.

Over her time at PNNL, she has served as both a primary investigator and technical staff member on several projects in applications ranging from computational chemistry and biology to cybersecurity and power grid modeling. Purvine also coordinated PNNL’s Postgraduate Organization from 2012 to 2022, which plans career development seminars, an annual research symposium, and promotes networking and mentorship for PNNL’s post-bachelors, post-masters, and post-doctorate research associates.

## Research Interest

- Combinatorics
- Computational Topology
- Discrete Mathematics
- Graph Theory
- Hypergraph Theory
- Mentoring
- Python

## Education

- PhD in mathematics, Rutgers, State University of New Jersey
- BS in mathematics, University of Wisconsin – Madison

## Affiliations and Professional Service

- Associate Editor, American Mathematical Society, 2019–present
- Member, Mathematical Association of America Committee on Membership, 2018–2020 term
- Chair, Mathematical Association of America Committee on Membership, 2020–2023 term
- Post Graduate Organization Manager, Pacific Northwest National Laboratory, 2014–2022

## Awards and Recognitions

- Mathematical Association of America, Association for Women in Mathematics - Section Lecturer
- Collaborative projects chosen for Collaborate@ICERM and American Institute of Mathematics Structured Quartet Research Ensembles research groups

## Publications

## 2023

- A.D. Myers, C.A. Joslyn, W.W. Kay, E. Purvine, G. Henselman-Petrusek, and M.R. Shapiro. “Topological Analysis of Temporal Hypergraphs.” In Workshop on Algorithms and Models for the Web Graph (WAW), 2023.
- E. Purvine, D.R. Brown, B.A. Jefferson, C.A. Joslyn, B.L. Praggastis, A. Rathore, and M.R. Shapiro, B. Wang, Y. Zhou. “Experimental Observations of the Topology of Convolutional Neural Network Activations.” In AAAI Conference on Artificial Intelligence, 2023.

## 2022

- B. Kay, S.G. Aksoy, M. Baird, D.M. Best, H. Jenne, C. Joslyn, C. Potvin, G. Henselman- Petrusek, G. Seppala, S.J. Young, E. Purvine. “Hypergraph Topological Features for Autoencoder- Based Intrusion Detection for Cybersecurity Data.” In ICML workshop on Machine Learning for Cybersecurity. 2022.
- Y. Zhou, A. Rathore, E. Purvine, and B. Wang, “Topological Simplifications of Hypergraphs” in IEEE Transactions on Visualization & Computer Graphics, 2022.
- Gasparovic E., M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier. “Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules.” In Research in Computational Topology 2. Association for Women in Mathematics Series, edited by E. Gasparovic, V. Robins and K Turner. 63–76. Springer, Cham. 2022.

## 2021

- Feng, S., Heath, E., Jefferson, B., Joslyn, C., Kvinge, H., Mitchell, H.D., Praggastis, B., et al., and Purvine, E., 2021. Hypergraph models of biological networks to identify genes critical to pathogenic viral response. BMC Bioinformatics, 22(1), pp.1-21.

## 2020

- S.G. Aksoy, C.A. Joslyn, C.M. Ortiz Marrero, B.L. Praggastis, and E. Purvine. “Hypernet- work science via high-order hypergraph walks.”
*EPJ Data Science*9.1 (2020): 16. - C.A. Joslyn, S.G. Aksoy, T. Callahan, L. Hunter, B.A. Jefferson, B.L. Praggastis, E. Purvine, Tripodi, I.J. ”Hypernetwork Science: From Multidimensional Networks to Computational Topology.” In International Conference on Complex Systems, 2020.
- M. Adamasek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, and B. Wang, et al. “On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings.”
*Journal of Applied and Computational Topology*, May 2020.

## 2019

- E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier. “The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs.”
*Journal of Applied and Computational Topology*, 10(1), 477–499, 2019.

## 2018

- M. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, L. Ziegelmeier. Vietoris-Rips and Čech Complexes of Metric Gluings, 34th Symposium on Computational Geometry (2018), 3:1-3:15. https://arxiv.org/abs/1712.06224
- E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, L. Ziegelmeier. A Complete Characterization of the One-Dimensional Intrinsic Čech Persistence Diagrams for Metric Graphs. In: Chambers E., Fasy B., Ziegelmeier L. (eds) Research in Computational Topology. Association for Women in Mathematics Series, vol 13. Springer, Cham. 2018.
- P. Bruillard, K. Nowak and E. Purvine, “Anomaly Detection Using Persistent Homology,”
*2016 Cybersecurity Symposium (CYBERSEC)*, Coeur d’Alene, ID, 2016, pp. 7-12.