California Research Training Program in Computational and Applied Mathematics

Andrea Bertozzi, Principal Investigator



The thrust of this Computational and Applied Mathematics program is engaging 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, cancer stem cells, bone growth, remote sensing applications, alcohol biosensors, photovoltaic cells, 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. This program is funded by National Science Foundation Grant DMS-1045536. The program provides:

  • (a) summer fellowships for undergraduates to participate in research in computational and applied mathematics;
  • (b) summer research fellowships for masters students from non-PhD granting institutions;
  • (c) a summer traineeships for faculty from non-PhD granting institutions to gain experience supervising undergraduate research and to collaborate with research faculty based at UCLA;
  • (d) first year PhD fellowships to recruit and train a more diverse group of PhD students
  • (e) postdoctoral traineeships for recent PhDs with an interesting in mentoring undergraduates on research problems;
  • (f) summer research mentorships for postdocs to work with younger students on research modules.

    Mentors, Participants, and Projects Summer 2011

    Schedule Summer 2011

    Project Reports and Presentations Summer 2011

    GRE/MATLAB Boot Camp 2011 Schedule for GRE Math Subject Exam Prep and Matlab Tutorials

    Mentors, Participants, and Projects Summer 2012

    Schedule Summer 2012

    GRE/MATLAB Boot Camp 2012 Schedule for GRE Math Subject Exam Prep and Matlab Tutorials

    Project Reports and Presentations Summer 2012

    Mentors, Participants, and Projects Summer 2013

    Schedule Summer 2013

    Project Reports and Presentations Summer 2013

    Mentors, Participants, and Projects Summer 2014

    Schedule Summer 2014

    Publications and Preprints from this Program

    From Summer 2014

  • C. Garnatz, X. Gu, A. Kingman, J. LaManna, D. Needell, S. Tu, Practical approximate projection schemes in greedy signal space methods Proc. 2014 Allerton Conference on Communication, Control, and Computing, Allerton IL, Oct. 2014, ArXiv:1409.1527.

    From Summer 2013

  • J. Sunu, J.-M. Chang, and Andrea L. Bertozzi, Simultaneous spectral analysis of multiple video sequence data for LWIR gas plumes, SPIE Defense and Security Conference, Baltimore, MD, May 2014.
  • L. Wang, A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta, and K. Huang, Rarefaction-singular shock dynamics for conserved volume gravity driven particle-laden thin film, submitted 2014.

    From Summer 2012

  • S. Lee, A. Mavromoustaki, G. Urdaneta, K. Huang, and A. L. Bertozzi, Experimental investigation of bidensity slurries on an incline, Granular Matter, 16(2), pp. 269-274, 2014.
  • T. Gerhart, J. Sunu, L. Lieu, E. Merkurjev, J.-M. Chang, J. Gilles, A. L. Bertozzi, Detection and tracking of gas plumes in LWIR hyperspectral video sequence data, SPIE Conference on Defense Security and Sensing, 2013, Baltmore, MD, April 29-May 3, 2013.
  • Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov and Scott G. McCalla, Crime Modeling with Levy Flights, SIAM J. Appl. Math, 73(4), 1703-1720, 2013, a preprint version.
  • D. Barrow, I. Drayer, P. Elliott, G. Gaut, and B. Osting, Ranking rankings: an empirical comparison of the predictive power of sports ranking methods, Journal of Quantitative Analysis in Sports, 9(2) pp. 187-202, (2013). preprint .

    From Summer 2011

  • Jérôme Gilles, Balaji R. Sharma, Will Ferenc, Hannah Kastein, Lauren Lieu, Ryan Wilson, Yuan Rick Huang, Andrea L. Bertozzi, Baisravan HomChaudhuri, Subramanian Ramakrishnan, and Manish Kumar, Robotic Swarming over the Internet, refereed conference proceedings, Proceedings of the 2012 American Control Conference.
  • Timothy Lucas, Garrett Johns, Wancen Jiang, Lucie Yang, A Population Model of Chaparral Vegetation Response to Frequent Wildfires, Bull. Math. Bio., Volume 75, Issue 12, pp 2324-2345, December 2013.
  • Garren R. J. Gaut, Katja Goldring, Francesca Grogan, Cymra Haskell, and Robert J. Sacker, Difference Equations with the Allee Effect and the Periodic Sigmoid Beverton-Holt Equation Revisited, J. Biological Dynamics, 6(2), pp. 1019-1033, 2012. preprint version
  • Yves van Gennip, Blake Hunter, Raymond Ahn, Peter Elliott, Kyle Luh, Megan Halvorson, Shannon Reid, Matt Valasik, James Wo, George E. Tita, Andrea L. Bertozzi, P. Jeffrey Brantingham, Community detection using spectral clustering on sparse geosocial data, SIAP, 73(1), pp. 67-83, 2013.
  • Travis R. Meyer, Dominik Ziegler, Christoph Brune, Alex Chen, Rodrigo Farnham, Nen Huynh, Jen-Mei Chang, Andrea Bertozzi, and Paul D. Ashby, Height Drift Correction in Non-Raster Atomic Force Microscopy, Ultramicroscopy, 137, pp. 48-54, 2014.

    Conference Presentations

  • "Outstanding Presentations" at the Undergraduate Poster Session on January 17, 2014 at Joint Mathematics Meetings in Baltimore, MD: (a)Supervised STM Image Segmentation of Self-Assembled Molecule Layers by Daniel Lander, Rodrigo Rios, Matthew Volmer and Daniel Zhou (b)A Contagion Model of Emergency Airplane Evacuations by Junyuan Lin
  • American Physical Society Division of Fluid Dynamics, 2013, Contributed Presentation, An experimental investigation of the settling and resuspension of gravity-drive, mono- and bi-disperse slurries, Gilberto Urdaneta, Matt Hin, Kaiwen Huang , Shreyas Kumar , Aliki Mavromoustaki , Jeffrey Wong , Sungyon Lee , Andrea Bertozzi
  • American Physical Society Division of Fluid Dynamics, 2013, Poster Presentation, Computationally and experimentally assessed gravity-driven, mono- and bi-disperse, particle-laden flows, Gilberto Urdaneta, Matt Hin, Kaiwen Huang , Shreyas Kumar , Aliki Mavromoustaki , Jeffrey Wong , Sungyon Lee , Andrea Bertozzi
  • "Outstanding Presentations" at the Undergraduate Poster Session on January 11, 2013 at Joint Mathematics San Diego: Ranking Rankings: a Comparison of the Predictive Power of Sports Ranking Methods Peter Elliott, Daniel Barrow, Ian Drayer, Garren Gaut, Advisor: Braxton Osting
  • "Outstanding Presentations" at the Undergraduate Poster Session on January 6, 2012 Boston MA: Chaparral Population Models in Response to Wildfires Garrett Johns, Wancen Jiang, Yuezhao Yang, advisor Tim Lucas Pepperdine.
  • Talk at Southern California Conference on Undergraduate Research, Mt. San Antonio College, November 2011
  • Talk at Pacific Coast Undergraduate Mathematics Conference, Cal Poly Pomona, March 2012
  • Talk at Southern California Conference on Undergraduate Research, Cal State Channel Islands, November 2011
  • American Physical Society Division of Fluid Dynamics, 2012, Contributed Presentation, Bi-disperse particle-laden flows in the Stokes regime, Gilberto Urdaneta, Saro Meguerdijian, Kali Allison, Thomas Crawford, Wylie Rosenthal, Sungyon Lee, Aliki Mavromoustaki, and Andrea Bertozzi
  • American Physical Society Division of Fluid Dynamics, 2011, Contributed Presentation, An experimental study of gravity-driven thin-film flow with buoyant particles, W. Rosenthal, P. Latterman, S. Hill, P. David, M. Mata, A Mavromoustaki, and A. Bertozzi
  • American Physical Society Division of Fluid Dynamics, 2011, Contributed Presentation, Theoretical challenges in modeling gravity-driven thin-film flow with buoyant particles, P. David, S. Hill, P. Latterman, W. Rosenthal, A. Mavromoustaki, M. Mata, and A. Bertozzi
  • Video Presentation, Gallery of Fluid Motion, APS DFD 2011, Aliki Mavromoustaki, Paul David, Spencer Hill, Paul Latterman, Wylie Rosenthal, Matthew Mata, Andrea Bertozzi