Andrea Bertozzi Research Group

Current Postdocs   (Former Postdocs)

• Blake Hunter - large data, spectral clustering
• Sungyon Lee - fluid dynamics
• Aliki Mavromoustaki - fluid dynamics
• Scott McCalla - dynamical systems and crime models
• Jesus Rosado - nonlinear PDE
• Yves van Gennip - pattern formation, image and data analysis
• James von Brecht - pattern formation in particle interactions and networks

Current Ph.D. Students   (Former Students)

• Tijana Kostic,
  Density estimation and segmentation
• Huiyi Hu,
  Graphical models for data analysis
• Ekaterina Merkurjev,
  Graphical models for image analysis
• Alexey Stomakhin,
  Gang models and missing data, joint student with Joey Teran
• Hui Sun
  Swarming models and fluid dynamics
• Joseph Zipkin
  spatially embedded crime models

Undergraduate researchers (Former undergraduate researchers)

• See web page of Todd Wittman for current REU projects in Imaging

  Current Projects

• Fluid interfaces and moving contact lines . We work on modeling of microfluidic devices and have some ongoing experiments on thin film slurry flow in the Applied Math Lab. Mathematical models include phase field methods and hyperbolic conservation laws.
• Cooperative motion and swarming We are interested in modeling both biological swarms and artificial swarms. We study the mathematical properties of collective groups and the large scale dynamics that ensues from small scale motion.
• Image processing We are interested in hyperspectral imagery, road inpainting, and imaging through turbulence.
  1. The work on cooperative motion and image processing includes a joint research project with USC, Brown, and Univ. of IL on Nonlinear Tracking click here to access the web page
  2. Los Angeles Multi-Band Data Analysis (LAMBDA) group is a project on hyperspectral imagery that I am involved with.
• Crime Hot Spots is funded by the NSF and the DoD and includes collaborations with Jeff Brantingham in Anthropology and with Lincoln Chayes.

Current Research Grants

1. W. M. Keck Foundation, Leveraging Sparsity in Instrumentation, Machine Learning and Multimodal Data, $1,000,000, Jan 2013-Dec 2014, Paul Weiss PI, Bertozzi, Osher and Cohen, coPIs.
2. UC Lab Fees Research grant 12-LR-236660, Sparse modeling for high dimensional data, joint with Stan Osher and Luinita Vese (UCLA), Rick Chartrand and Brendt Wohlberg (Los Alamos National Lab), July 1, 2012-June 30, 2015, $1.5M total.
3. ONR grant N000141210838, Machine Reasoning and Intelligence for Naval Sensing, July 1, 2012-June 30, 2015, S. Osher PI, joint with Larry Carin at Duke University
4. ONR grant N000141210040, Analysis and Design of Fast Graph Based Algorithms for High Dimensional Data, November 2011-September 2014
5. ARO MURI grant W911NF-11-1-0332, with M. Short and J. Brantingham, Scalable, Stochastic and Spatiotemporal Game Theory for Real-World Human Adversarial Behavior, August 2011-July 2016, subaward from USC, Milind Tambe PI.
6. NSF grant DMS-1118971 Algorithms for Threat Detection in Sensor Systems for Analyzing Chemical and Biological Systems Based on Compressive Sensing and L1 Related Optimization, joint grant with Stanley Osher (PI), 8/15/11-7/31/16
7. NSF grant DMS-1045536 California Research Training Program in Computational and Applied Mathematics, training grant for a summer REU program and graduate/postdoc mentorship program, 6/15/11-6/14/16.
8. AFOSR MURI grant FA9550-10-1-0569 ``Inferring Structure and Forecasting Dynamics on Evolving Networks'' coPI, P. J. Brantingham lead PI, 9/30/10-9/29/15.
9. NSF grant EFRI-1024765 Collaborative Research: Characterization and Control of Emergent Behavior in Complex Systems, joint with Manish Kumar and Subramanian Ramakrishnan, U Cincinatti, 9/15/10-8/31/13.
10. ARO grant W911NF1010472, reporting number 58344-MA, Dynamic Models of Insurgent Activity, Aug 2010-December 2013, joint with Jeff Brantingham and George Mohler
11. NSF grant DMS-0968309 FRG: Collaborative Research: Mathematics of large scale urban crime, PIs: Bertozzi (lead), Tita (UCI), Brantingham, Mohler, Short, Chayes, Schoenberg, 9/2010-8/2013
12. ONR grant N000141010221, Information Fusion of Human Activity, Social Networks, and Geography Using Fast Compressive Sensing, 1/10-12/12, co PIs Stan Osher, Jeff Brantingham, George Tita (UCI), $1.2M total, approx.
13. NSF grant CBET-0940417 CDI Type I: Real-time adaptive imaging algorithms for atomic force microscopy, 1/10-12/12, joint grant with Paul Ashby and Jim DeYoreo, Molecular Foundry, Lawrence Berkeley National Laboratory.
14. NSF grant DMS-0907931 Dynamics of aggregation and collapse in multidimensional swarming models, 9/09-8/13.
15. NSF grant DMS-0914856 Algorithms for Threat Detection (ATD): adaptive sensing and sensor fusion for real time chemical and biological threats, 9/09-8/13.
16. UC Lab Fees Research Grant 09-LR-04-116741-BERA, "Multiscale methods of fracture and multimaterial debris flow", with Stan Osher, Joey Teran, and Lawrence Livermore National Laboratory (David Eder).

Past Research Funding

Other Research Funding

Additional research support comes from the Department of Defense and Industry, through short term contracts directly related to our research projects. Industrial sponsors and collaborators (past and present) include Raytheon Space and Airborne Systems, Los Alamos National Laboratory, Lockheed Martin, and Nekton Research (now part of iRobot Corp.).

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UCLA * Department of Mathematics *