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Research Interests for Paul L Bendich

Research Interests:

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involved the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning, as well as building connections between computational topology and diffusion geometry.

Recent Publications
  1. Garagić, D; Peskoe, J; Liu, F; Claffey, MS; Bendich, P; Hineman, J; Borggren, N; Harer, J; Zulch, P; Rhodes, BJ, Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration, Ieee Aerospace Conference Proceedings, vol. 2018-March (June, 2018), pp. 1-8, ISBN 9781538620144 [doi[abs]
  2. Tralie, CJ; Smith, A; Borggren, N; Hineman, J; Bendich, P; Zulch, P; Harer, J, Geometric Cross-Modal Comparison of Heterogeneous Sensor Data, Proceedings of the 39th IEEE Aerospace Conference (March, 2018) [abs]
  3. Bendich, P; Chin, SP; Clark, J; Desena, J; Harer, J; Munch, E; Newman, A; Porter, D; Rouse, D; Strawn, N; Watkins, A, Topological and statistical behavior classifiers for tracking applications, Ieee Transactions on Aerospace and Electronic Systems, vol. 52 no. 6 (December, Accepted, 2016), pp. 2644-2661 [doi[abs]
  4. Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric Models for Musical Audio Data, Proceedings of the 32st International Symposium on Computational Geometry (SOCG) (June, 2016)
  5. Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric models for musical audio data, Leibniz International Proceedings in Informatics, Lipics, vol. 51 (June, 2016), pp. 65.1-65.5, ISBN 9783959770095 [doi[abs]

 

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Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320