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.

    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 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

    Mentor, Participants, and Projects Summer 2015

    Schedule Summer 2015

    Mentors, Participants, and Projects Summer 2016

    Schedule Summer 2016

    Mentors, Participants, and Projects Summer 2017

    Schedule Summer 2017

    Publications and Preprints from this Program

    From Summer 2016

  • Victoria Chayes, Kevin Miller, Rasika Bhalerao, Jiajie Luo, Wei Zhu, Andrea L. Bertozzi, Wenzhi Liao, Stanley Osher, Pre-processing and classification of hyperspectral imagery via selective inpainting, ICASSP 2017.
  • Baichuan Yuan, Sathya R Chitturi, Geoffrey Iyer, Nuoyu Li, Xiaochuan Xu, Ruohan Zhan, Rafael Llerena, Jesse T Yen, Andrea L Bertozzi, Machine Learning for Cardiac Ultrasound Time Series Data, Proc. SPIE 10137, Medical Imaging 2017: Biomedical Applications in Molecular, Structural, and Functional Imaging, 101372D.
  • Hanjun Li, Chunhan Feng, Henry Ehrhard, Yijun Shen, Bernardo Cobos, Fangbo Zhang, Karthik Elamvazhuthi, Spring Berman, Matt Haberland, Andrea L. Bertozzi, Decentralized Stochastic Control of Robotic Swarm Density: Theory, Simulation, and Experiment, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) September 24-28, 2017, Vancouver, BC, Canada, pp. 4341-4347, 2017.

    From Summer 2015

  • Wei Zhu, Victoria Chayes, Alexandre Tiard, Stephanie Sanchez, Devin Dahlberg, Da Kuang, Andrea L. Bertozzi, Stanley Osher, Dominique Zosso, Unsupervised Classification in Hyperspectral Imagery with Nonlocal Total Variation and Primal-Dual Hybrid Gradient Algorithm, IEEE Trans. Geo. Remote Sensing, 55(5), pp. 2786-2798, 2017.
  • M. Cucuringu, C. Marshak, D. Montag, P. Rombach, Rank Aggregation for Course Sequence Discovery, Proc. International Conference on Complex Networks and their Applications (Springer), pp. 139-150, 2017.
  • Hao-Jun Michael Shi, Mindy Case, Xiaoyi Gu, Shenyinying Tu, Deanna Needell, "Methods for Quantized Compressed Sensing", Proc. Information Theory and Applications, La Jolla CA, Jan. 2016.
  • Sean Wilson, Ruben Gameros, Michael Sheely, Matthew Lin, Kathryn Dover, Robert Gevorkyan, Matt Haberland, Andrea Bertozzi, and Spring Berman, Pheeno, A Versatile Swarm Robotic Research and Education Platform, Robotics and Automation Letters (RA-L), 1(2), pp. 884-891, 2016.
  • Bohyun Kim, Samuel Birns, Stephanie Ku, Kevin Stangl, and Deanna Needell, A Practical Study of Longitudinal Reference Based Compressed Sensing MRI, Rose-Hulman Undergraduate Mathematics Journal, 17(2), 2016.
  • Kevin Bui, Jacob Fauman, David Kes, Leticia Torres Mandiola, Adina Ciomaga, Ricardo Salazar, Andrea L. Bertozzi, Jerome Gilles, Andrew I. Guttentag, Paul S. Weiss, Segmentation of Scanning Tunneling Microscopy Images Using Variational Methods and Empirical Wavelets, accepted pattern analysis and applications, 2019.
  • Chaohao Pan, Bo Li, Chuntian Wang, Yuqi Zhang, Nathan Geldner, Li Wang, and Andrea L. Bertozzi, Crime modeling with truncated L\'evy flights for residential burglary models, Mathematical Models and Methods in Applied Sciences, 28(9), pp. 1857-1880, 2018.

    From Summer 2014

  • Xiaoyi Gu, Deanna Needell, and Shenyingying Tu, On Practical Approximate Projection Schemes in Signal Space Methods, SIURO volume 9, 2016.
  • Jessica Nadalin, Topics in Compressed Sensing for fMRI, Senior Thesis at UC Berkeley, Jeff Calder mentor, 2015.
  • Jing An, ``Beltrami Energy Based Partitioning Model for Image Segmentation'', UCLA 2015 Library Prize for Undergraduate Research, supervised by D. Zosso
  • Y. Lin, M. Tomasek, and M. Roper, Evaporation rates allow filamentous fungi to monitor wind speed, submitted 2015.
  • Jing Qin, Thomas Laurent, Kevin Bui, Ricardo V. Tan, Jasmine Dahilig, Shuyi Wang, Jared Rohe, Justin Sunu, Andrea L. Bertozzi, Detecting Plumes in LWIR Using Robust Nonnegative Matrix Factorization with Graph-based Initialization, in SPIE Defense and Security, Baltimore MD April 2015.
  • D. Zosso, J. An, J. Stevick, N. Takaki, M. Weiss, L. S. Slaughter, H. H. Cao, P. S. Weiss, A. L. Bertozzi, Image Segmentation with Dynamic Artifacts Detection and Bias Correction, AIMS Inverse Problems and Imaging (accepted).
  • Mitchell Horning, Matthew Lin, Srinivasan Siddarth, Simon Zou, Matt Haberland, Ke Yin, Andrea L. Bertozzi, Compressed Sensing Environmental Mapping by an Autonomous Robot, Proceedings of the Second International Workshop on Robotic Sensor Networks, Seattle WA, April 13, 2015.
  • E. Lai, D. Moyer, B. Yuan, E. Fox, B. Hunter, A. L. Bertozzi, and P. J. Brantingham, Topic Time Series Analysis of Microblogs, IMA Journal of Applied Mathematics, 81(3) pp. 409-431, 2016.
  • 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.
  • J. Luo, K. Shapiro, H-J M. Shi, Q. Yang, and K. Zhu, Practical Algorithms for Learning Near-isometric Linear Embeddings, SIURO May 2016, project mentor - Wotao Yin.

    From Summer 2013

  • K. Dong, Y. Cao, B. Siercke, M. Wilber, and S. G. McCalla, Advising caution in studying seasonal oscillations in crime rates, PLOS One, Sept. 2017.
  • L. Ma, B. Song, T. Curran, N. Phong, E. Dressaire, and M. Roper, Defining individual size in the model filamentous fungus Neurospora crassa, Proc. Roy. Soc. B, Biological Sciences, 283(1826), 20152470, 2016 DOI: 10.1098/rspb.2015.2470.
  • Emilie Dressaire, Lisa Yamada, Boya Song, and Marcus Roper, Mushrooms use convectively created airflows to disperse their spores PNAS 113(11) pp. 2833-2838, 2016. preprint version.
  • J. Lin and T. Lucas, A Particle Swarm Optimization Model of Emergency Airplane Evacuations with Emotion, Networks and Heterogeneous Media, 10(3), 2015, pp. 631-646.
  • 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, Physics of Fluids, 27, 033301, 2015. preprint version.

    From Summer 2012

  • Timothy A. Lucas, Reanna A. Doña, Wancen Jiang, Garrett C. Johns, Dayna J. Mann, Cassandra N. Seubert, Noah B.C. Webster, Charlotte H. Willens, Stephen D. Davis, An Individual-Based Model of Chaparral Vegetation Response to Frequent Wildfires to appear in Theoretical Ecology, 2016 [from both the 2012 and 2011 programs]
  • Maria-Grazia Ascenzi, Xia Du, James I. Harding, Emily N. Beylerian, Brian M. de Silva, Ben J. Gross, Hannah K. Kastein, Weiguang Wang, Karen M. Lyons, Hayden Schaeffer, Automated Cell Detection and Morphometry on Growth Plate Images of Mouse Bone, Applied Mathematics, 5, 2866-2880, 2014.
  • 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

  • Victoria Chayes, oral presentation, Preprocessing and classification of hyperspectral imagery via selective inpainting, March 6, ICASSP 2017 (see paper listed above).
  • Nuoyi Li, poster presentation at SPIE Medical imaging conference, Orlando Florida, February 2017 Machine Learning for Cardiac Ultrasound Time Series Data.
  • Juan Carrillo (presenter), Biyi Fang, Tian Ye, Yandi Shen, and Ziqi Xiong, Poster Presentation, "L1-2 Regularized Logistic Regression", Southern California Conference for Undergraduate Research (SCCUR), Harvey Mudd College, CA, Nov 21, 2015.
  • Second International Workshop on Robotic and Sensor Networks, oral presentation by Siddarth Srinivasan and Simon Zou, Seattle April 13, 2015.
  • J. Luo, K. Shapiro, H.M. Shi., Q. Yang, K. Zhu, M. Yan, and W. Yin, "Learning Near-Isometric Linear Embeddings", Poster presentation, Joint Mathematics Meetings 2015, San Antonio, Texas, Jan. 10-13, 2015.
  • NGA NARP Symposium, Washington DC, Sept. 2014, posters presentented by Baichuan Yuan and Eric Lai, on their work from Summer 2014.
  • "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