NSF REU Site: Mathematical Modeling at UCLA/ California Research Training Program in Computational and Applied Mathematics

Marcus Roper, NSF REU Site Principal Investigator; Andrea L. Bertozzi, co-PI and Director of Applied Math

This Computational and Applied Mathematics program engages students starting and finishing the critical transition point from undergraduate to PhD student in high quality university level research. Students experience both the development of independent research projects and the milestones needed to get admitted to and succeed in a top PhD program. They participate in summer research modules on topics such as crime modeling, fluid dynamics experiments and modeling, robotics and control, medical imaging, video processing, and algorithm design for microscopy. The program involves faculty from Mathematics in collaboration with faculty in Medicine, Anthropology, Engineering, Chemistry, and other disciplines. The project includes a training program for postdocs and junior faculty to learn how to involve pre-PhD students in publication-level research. The training program is based at UCLA and includes undergraduate and masters student participation from nearby colleges and universities. The program goal is to directly address diversity and access to top level PhD programs in computational and applied mathematics.

Part of this training program includes three projects specifically funded by a three-year NSF-funded REU site (NSF DMS grant 1659676) to support a total of twelve undergraduate students. Student participants will learn to build mathematical models for problems from across the sciences. Research projects will focus on three areas: (1) Biology: how fungal spores cooperate to create networks; (2) Social sciences: mathematical patterns underlying urban crime; and (3) Physics: predicting the catastrophes that occur when industrial or geophysical slurries start to flow. A link to the NSF award can be found here .

The full program provides:

  • (a) summer fellowships for undergraduates to participate in research in computational and applied mathematics;
  • (b) first year PhD fellowships to recruit and train a more diverse group of PhD students
  • (c) postdoctoral traineeships for recent PhDs with an interesting in mentoring undergraduates on research problems;
  • (d) summer research mentorships for postdocs to work with younger students on research modules.

    To see a list of REU participants post graduation placement, click on the list of mentors, participants and projects for each year.

    Mentors, Participants, and Projects Summer 2017

    Schedule Summer 2017

    Final Presentation Schedule 2017

    Mentors, Participants, and Projects Summer 2018

    Schedule Summer 2018

    Final Presentation Schedule 2018

    Mentors, Participants, and Projects Summer 2019

    Schedule Summer 2019

    Publications and Preprints from this Program

    From Summer 2017

  • Yonatan Dukler, Yurun Ge, Yizhou Qian, Shintaro Yamamoto, Baichuan Yuan, Long Zhao, Andrea L. Bertozzi, Blake Hunter, Rafael Llerena, and Jesse T. Yen, Automatic decomposition and mitral valve segmentation of cardiac ultrasound time series data, Proc. SPIE conference on medical imaging, 2018.
  • D. J. Arnold, D. Fernandez, R. Jia, C. Parkinson, D. Tonne, Y. Yaniv, A. L. Bertozzi, and S. J. Osher, Modeling environmental crime in protected areas using the level set method, accepted SIAM J. Appl. Math, 2019.
  • Brendon Anderson, Eva Loeser, Marissa Gee, Felix Ren, Swagata Biswas, Olga Turanova, Matt Haberland, and Andrea L. Bertozzi, Quantitative Assessment of Robotic Swarm Coverage, Proc. 15th Int. Conf. on Informatics in Control, Automation, and Robotics (ICINCO 2018), vol. 2, pp. 91-101, 2018.

    From Summer 2018

  • Y. Qiao, C. Shi, C. Wang, H. Li, M. Haberland, X. Luo, A. M. Stuart, and A. L. Bertozzi, Uncertainty Quantification for Semi-supervised Multi-class Classification in Image Processing and Ego-Motion Analysis of Body-Worn Videos, IS&T International Symposium on Electronic Imaging 2019: Image Processing: Algorithms and Systems XVII proceedings, Burlingame, CA.
  • Jacob D. Moorman, Qinyi Chen, Thomas K. Tu, Zachary M. Boyd, Andrea L. Bertozzi, Filtering Methods for Subgraph Matching on Multiplex Networks, Proc. GTA3 workshop, IEEE Conference on BIG DATA, Seattle Dec. 2018, pp. 3979-3984.