A research effort spearheaded by CAMS and its former director (currently with the Division of Applied Mathematics at Brown University), Boris Rozovsky, has won a Multidisciplinary University Research Initiative (MURI) grant from the Department of Defense. Worth up to $5 million over five years, the grant will fund the collaborative work of researchers at several universities to develop automated tracking systems suitable for large groups of moving targets.

Among other applications, non-linear filtering can be used to track targets moving erratically in high background noise, such as cruise missiles in the sky or terrorists hiking through rugged terrain.

"It's the problem of finding a needle in a haystack, but the problem is the needle is moving", Rozovsky said. "Or it might not be a (single) needle, but many with different characteristics".

So far, the number of targets trackable at one time has been limited to a few dozen. The MURI project aims to achieve real-time tracking of thousands of mobile agents. Rozovsky called this a “quantum leap” over previous systems made possible by advances in computing power and basic mathematical seach.ch

"Now you could think about tracking a large number of agents", he said.

The same system could be used to detect computer hackers, Rozovsky said, or to track drugs, blood clots or other substances as they move through the body.

Rozovsky, co-developed the first complete non-linear filter in the early 1980s.

His collaborators on the MURI project include Paul Cohen, deputy division director of the Information Sciences Institute; Gerard G. Medioni, Chairman Department of Computer Science, USC; Christos Papadopoulos, Department of Computer Science, Colorado State University; and Alexander Tartakovsky, research scientist in mathematics – all members of CAMS – along with Andrea Bertozzi, Jeffrey Brantingham and Tony Chan of UCLA, and Venugopal Veeravalli of the University of Illinois at Urbana-Champaign.

"Every person is the best in the world in his or her particular area", Rozovsky said. "My main achievement is that I was able to collect a brilliant team".

The MURI program, administered by the Department of Defense, sponsors multidisciplinary projects at U.S. universities with both military and commercial potential.

The Center for Applied Mathematical Sciences is an organized research unit based in the Department of Mathematics at USC. The purpose of CAMS is to foster research and graduate education in Applied Mathematics in a broad sense and in an interdisciplinary mode. One goal of the center’s participants is to facilitate and encourage the development of applicable mathematics and its utilization in problems in engineering and the sciences.

Since July of 1992 till August of 2006, CAMS has been headed by its Director, Dr. B. L. Rozovsky, Professor of Mathematics.  Since August 2006 the director of CAMS became Professor Chunming Wang. The Director is advised by the Board of Directors

The mission of the Center as seen by the Director and the Executive Committee is threefold.

1. To maintain USC’s position as an internationally-recognized center in several important and well defined areas of applied mathematics and statistics.
2. To be a much-needed interface between the Department of Mathematics and other USC departments and schools, industries (in particular, local industries), businesses, and federal funding agencies (Department of Defense, National Science Foundation, National Institutes of Health, etc.)
3. To serve as a catalyst in the development of a state-of-the-art educational program in applied mathematics and statistics at USC.

Research

CAMS is a multidisciplinary research center which encompasses many research projects, groups, and programs. Activities include fundamental applied mathematical research related to stochastic systems, statistics, and computation. The CAMS research program is focused primarily in the following areas:

1. Computational Biology (Tavare, Waterman)
2. Mathematical and Computational Finance
3. Mathematical Methods in Pharmacokinetics (Jelliffe, Schumitzky, Tartakovsky)
4. Mathematical Modeling and Control (Rosen, Wang)
5. Stochastic and Chaotic Systems (Lototsky, Mikulevicius, Piterbarg, Rozovsky)
6. Target Detection and Tracking (Rozovsky, Tartakovsky)
7. Information Assurance and Intrusion Detection in Computer Networks (Jonckheere, Rozovsky, Tartakovsky)
8. Spatial-Temporal Image Processing and Enhancement (Tartakovsky)
9. Decision-making and Optimal Information Fusion in Distributed Sensor Systems (Tartakovsky)

In these areas, CAMS scientists are internationally recognized and are among the leaders in their corresponding fields. Virtually all CAMS research projects are of a multidisciplinary nature and cut across departmental and school boundaries. Some of these projects are described below.

Examples of Recent and Current Research Projects

• Active Suppression of Noise and Vibration
• Computational Biology
• Mathematical and Computational Finance
• Mathematical Control of Intelligent Manufacture of Semiconductor Devices
• Mathematical Models of Neural Prostheses and Biomechanics
• Mathematical Optimization of Drug Therapy
• Nonlinear Filtering and Target Tracking
• Stochastic Modeling in Oceanography
• Stochastic Modeling in Speech Recognition
• Target Detection and Tracking by IRST
• Virtual Reality System
• Rapid Intrusion Detection in Computer Networks
• Information Assurance Project
• Image Super Stabilization and Super-Resolution for Airborne Surveillance

CAMS Directory

Director

Associate Director

Members

Affiliated Members

Associate Departments

• Department of Aerospace and Mechanical Engineering
• Department of Biological Sciences
• Department of Chemical Engineering
• Department of Computer Science
• Department of Economics
• Department of Electrical Engineering
• Department of Mathematics
• School of Medicine
• Department of Physics
• Laboratory of Applied Pharmacokinetics

Associate Companies

• Raytheon
• Space and Naval Warfare Systems Command
• Lockheed Martin
• Boeing
• Torrey Pines Logic, Inc

Graduate Programs in Applied Mathematics and Statistics

Graduate programs in Applied Mathematics and Statistics at USC are shaped and directed by CAMS members and activities.

Currently, we are adapting the model for graduate education in the laboratory sciences and engineering to applied mathematics by involving students in hands-on interdisciplinary research projects very early on in their doctoral programs. These projects involve industrial partners or research teams in other science or engineering departments either at USC or at other universities. This approach allows us to produce Ph.D.’s in applied mathematics with the skills necessary to immediately embark on careers involving multi-disciplinary research in an academic or industrial setting. In addition, such a program attracts people working in industry who are returning to school to pursue advanced degrees.

The NSF Division of Mathematical Sciences offers support for graduate students through Industry-Based Graduate Research Assistantships or Cooperative Fellowships. These research assistantships permit graduate students to move between university and industrial environments and become the mediating bodies for strong university/industry interaction. The cooperative fellowships permit graduate students to work full-time in an industrial setting for a fixed period of up to one year. CAMS intends to take full advantage of this NSF initiative.

Links to Graduate Programs

• Ph.D. in Applied Math
• Professional MS in Math Finance
• Professional Ph.D in Computational Biology
• MS in Applied Math
• MA in Applied Math
• MS in Statistics 
  

Industrial Liaison Committee

• John Barnett, Ph.D., Science Applications International Corporation, San Diego, CA
• Leo Volfson, Ph.D., President,Torey Pines Logic, Inc., Del Mar, CA
  
• Craig Polling, Ph.D., Chief Scientist, Lockheed Martin Tactical Defense
  Systems, Eagan, MN
• Paul F. Singer, Ph.D., Chief Scientist, Signal Processing Laboratory, Tactical
  Engineering Division, Raytheon Systems Company, El Segundo, CA.

Conferences and Workshops

The organization of conferences and workshops is an important part of CAMS academic activities. Since 1992, CAMS has organized or participated in the organization of more than 60 conferences. The following list provides some illuminating examples of CAMS activities in this area:

2006

• Geophysical Fluid Dynamics Workshop, American Institute of Mathematics, Palo Alto, February 2006
• Programme on "Optimization Problems in Financial Economics", Banff International Research Station, Banff, Canada, 20-25 May 2006
• The 9th International Conference on Information Fusion, 10-13 July 2006, Florence, Italy; Special Invited Session "Distributed Inference and Decision-Making in Multisensor Systems"

2005

• Workshop on Population Pharmacokinetic/Pharmacodynamic Modeling, Computer Laboratory, Faculty of Pharmacy, Universiti Teknologi MARA, Kuala Lumpur, 14-15 December 2005
• Analytical and Stochastic Fluid Dynamics Workshop, MSRI ( Berkeley), October, 2005
• Conference "Random Media and Stochastic Partial Differential Equations", University of Southern California, June 14-18 2005
• Southern California Applied Mathematics Conference, Los Angeles, May, 2005
• Workshop on New advances in Therapeutic Drug Monitoring and Individualized Drug Therapy, a postcongress workshop following the International Congress of Therapeutic Drug Monitoring and Clinical Toxicology, Louisville KY, April 29-30 2005
• Workshop on Analytical and Stochastic Fluid Dynamics, MSRI, Berkeley, 2005

2004

• Workshop on Pharmacocinetique clinique chez la personne agee Atelier de prestige, at the 20th Journees Nationales dinformation des Pharmaciens Hospitaliers, Toulon, France, September 17 2004
• A session on "Financial Mathematics", AMS West Meeting, USC, April 2004
• The Third International Seminar on New Developments in Optimal Individualization of Drug Therapy and Pharmacokinetic/Pharmacodynamic Modeling: Basic Concepts and Clinical Applications, and of Concepts and problems in Studies of Bioequivalence, Faculty of Pharmacy, University of Sofia, Bulgaria, October 5-7 2004
• Workshop on Clinical Approaches to Individualizing Therapy with Toxic Drugs: Problem Cases and Methods for Solving them.The National Jewish Hospital, and the University of Colorado School of Pharmacy, Thursday, November 18 2004
• Workshop on Clinical Approaches to Individualizing Therapy with Toxic Drugs: Problem Cases and Methods for Solving them, The Institute for Physical and Chemical Medicine, Moscow, Russia, April 21-22, 2004
• A session on Financial Mathematics, AMS West Meeting, University of Southern California, April 2004
• Preconference workshop on PK/PD Modeling Methods and Clinical Applications (Intermediate - Advanced - Expert Level), September 7-8, 2004, before the World Conference on Magic Bullets (CELEBRATING PAUL EHRLICH'S 150th BIRTHDAY), September 9-11, 2004, Nürnberg, Germany

2003

• Workshop on Parametric and Nonparametric Population Pharmacokinetic and Dynamic Modeling Applications to Therapeutic Drug Monitoring and Optimal Drug Dosage Individualization. Society for Comp$
• Hands-on workshop on Parametric and Nonparametric Population Pharmacokinetic and Dynamic Modeling Applications to Therapeutic Drug Monitoring and Optimal Drug Dosage Individualization. School $
• Workshop on Principles of Pharmacokinetics - Parametric and Nonparametric Population PK and PD Modeling: Applications to Therapeutic Drug Monitoring and to Optimal Individualization of Drug Thera$
• Workshop on Population Pharmacokinetic/Dynamic Modeling: Basic Concepts and Clinical Applications to Optimally Individualized Drug Therapy. School of Pharmacy, University of Bulgaria, Sofia, Bulga$
• The 6^th International Conference on Information Fusion, 8-11 July 2003, Radisson Hotel, Cairns, Queensland, Australia; Special Invited Session
• Satellite workshop on New Advances in Model-Based/Goal-Oriented Optimal Individualized Drug Therapy: Relationship to Population PK/PD Modeling and to Multiple Model Methods for Optimal Tracking o$
• Conference on Numerical Probabilistic Methods for High-Dimensional Problems in Finance, AIM, Palo Alto, December 2003
• 3rd Southern California Applied Mathematics Symposium, UCI, Irvine, CA, 2003

2002

• Second Southern California Applied Mathematics Symposium, IPAM, Los Angeles, CA, 2002
• 8th International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius, Lithuania, 2002
• Workshop on New Directions in Financial Modeling, University of Southern California, April 2002
• The 5^th International Conference on Information Fusion, 8-11 July 2002, Loews Annapolis Hotel, Annapolis, MD, USA; Special Invited Session "Distributed Detection, Classification, and Recognition"
• CAMS Open House, Friday November 15, 2002, DRB 351, USC University Park Campus

2001

• January 03-12, 2001, IPAM Conference on "Financial Mathematics: Risk Management and Numerical Methods, UCLA, Los Angeles
• Conference on Financial Mathematics: Risk Management, Modeling and Numerical Methods, Institute for Pure and Applied Mathematics, Los Angeles, January 2001
• Summer School in Mathematical Finance, Dubrovnik, Croatia, September 2001
• December 15-17, 2001, 4-th Columbia-JAFEE Conference on Mathematics of Finance, Tokyo, Japan
• The National Academy of Engineering, 2001 Frontiers of Engineering Conference
• First Southern California Applied Mathematics Symposium, Caltech, Pasadena, CA, 2001
• Sessions on Wireless Communications at the 2001 and 2002 Allerton Conferences

2000

• Nonlinear Analysis 2000 -->May 28 - June 2, 2000, Courant Institute, New York University
• A new workshop on "Parametric and Non-parametric Population PK/PD Modeling - Optimal Approaches for Drug Development and Patient Care."

All events attracted a substantial number of leading experts from the U.S. and abroad, and the future events will continue to do the same.

Seminars and Visitors to CAMS

CAMS conducts several academic seminars in the fields of Applied Mathematics, Industrial Mathematics, Mathematical Biology and Stochastic Numerics. A constant influx of young and distinguished visitors is extremely important to the vitality of the CAMS research and educational programs. It broadens the scope of CAMS activities and diversifies learning opportunities for the graduate students.

CAMS Seminars and Visitors

2007

2006

2005

2004

2003

2002