- with Jacquelyn Fetrow, COMPUTER SCIENCE and PHYSICS, and David J. John, COMPUTER SCIENCE
Algebraic and Statistical Models of Redox Signaling
Awarded $123,379 for the period 4/1/08 to 3/31/09
Source: National Institutes of Health (NIH)
An interdisciplinary research group spanning the Reynolda and Health Sciences campuses aims to develop theory, algorithms, computational tools, and research methodologies for network modeling of redox-regulated events in human cells. Recent research indicates that redox-regulated networks are central to cellular communication under a variety of normal and diseased conditions, including cancer, neurodegenerative diseases, and aging. This project will (1) identify a comprehensive set of cellular proteins modified at cysteine residues as a result of redox-dependent signaling; (2) correlate the concentration of a given cellular perturbant and its associated redox signal; 3) associate networks with particular perturbants; and 4) produce both topological and dynamic models of the cellular network associated with these pathways. These models will then be compared to other data on protein/protein interactions and kinase cascades to produce a more comprehensive model of cellular regulation and its biological outcomes.
- with Errin Fulp, COMPUTER SCIENCE
Modeling Mobile Agent Populations and Movement for CEDS
Awarded $196,473 for the period 12/13/10 to 10/31/13
Source: Pacific Northwest National Laboratory (PNNL)/Battelle Memorial Institute
Mathematical models will be used to clarify the basic performance trade-offs associated with agent populations, pheromone strength, and nonregular geographies. As more advanced features are added to the system, simulation will be used to find appropriate settings. Modeling will also be used to characterize and assure the operational security of the Digital Ants system.
- Optimization Methods for Solving the Einstein Constraint Equations
Awarded $5,000 for the period 6/1/09 to 5/31/10
Source: Oak Ridge Associated Universities (ORAU)
The prestigious and highly competitive Ralph E. Powe Junior Faculty Enhancement Award aims to enrich the research and professional growth of young faculty in a wide variety of fields from over 120 member universities across the USA. This research program aims to develop and implement large-scale optimization methods for solving the Einstein constraint equations. Up to now, attempts at a solution have relied on ad hoc approaches and Newton methods with restarts. This project will tailor unconstrained minimization work to solve the inequality-constrained optimization problem implicit in these equations using state-of-the-art nonlinear optimization techniques. It will also develop a class of preconditioners to help solve the linear system arising from each discretization.
- Second-order Methods for Large-scale Optimization in Compressed Sensing
Awarded $49,659 for the period 4/5/10 to 6/30/11, Year 3
Source: National Science Foundation (NSF)
This 3-year research program aims to develop and implement large-scale optimization methods for recovering sparse signals from a limited number of indirect observations in the context of compressed sensing. Compressed sensing theory states that sparse signals can be recovered very accurately with high probability from indirect measurements by solving an appropriate minimization problem. This emerging area allows data acquisition with fewer measurements and sampling rates in such fields as medical imaging, astrophysics, biosensing, and geophysics.
Building on second-order methods for large-scale unconstrained optimization, the project will develop significantly more efficient methods for solving compressed sensing minimization problems. The algorithms are designed to be matrix-free; they do not require storage of potentially very large second-derivative matrices but use matrices only as operators for matrix-vector products. The research advances state-of-the-art methods for compressed sensing and second-order line-search and trust-region methods for bound-constrained optimization improving large-scale applications, such as image processing, as well as theoretical proofs of convergence and numerical stability of the algorithms.
Invariant Theory of Artin-Schelter Regular Algebras
Awarded $7,000 for the period 9/1/12 to 8/31/13
Source: Simons Foundation
This project will extend results from the classical setting of invariant theory—a finite group acting on a commutative polynomial ring—to a new setting—a finite group acting on an Artin-Schelter regular algebra—to increase our understanding of noncommutative rings with nice properties. Past work has been in collaboration with James Kuzmanovich (WFU) and James Zhang (University of Washington, Seattle), and the grant supports travel.
- Intensive Workshop in 2012 for Macaulay 2 Development
Awarded $17,126 for the period 7/1/12 to 6/30/13
The workshop teaches participants how to implement algorithms in rapidly growing areas of algebraic geometry, such as numerical algebraic geometry, algebraic statistics, enumerative algebraic geometry, and differential graded algebras, with applications in fields as diverse as computational biology, robotics, coding theory, and string theory. Parallelization of new and existing algorithms in Macaulay2 is emphasized. The intensive workshop provides a great opportunity for graduate students and postdoctoral fellows to enhance their package-writing skills, taking advantage of the experience and expertise of more senior researchers.
- Intensive Workshop in 2012 for Macaulay2 Package Development
Awarded $12,050 for the period 8/11/11 to 8/10/12
Source: National Security Agency
The workshop will implement algorithms in such rapidly growing areas as numerical algebraic geometry, algebraic statistics, enumerative algebraic geometry, and differential graded algebras with applications in fields as diverse as computational biology, robotics, coding theory, and string theory. Special attention will be paid to parallelization of new and existing algorithms in Macaulay2, a new parallel computing engine.
Conference on Applications of Geometry to Topology and Physics, November 2008, Newark, NJ
Awarded $19,900 for the period 9/1/08 to 8/31/09
The 3-day conference at Rutgers University-Newark focuses on applying geometry to problems in physics and topology. It will also celebrate the achievements of Herman Gluck, a distinguished University of Pennsylvania geometer and topologist, whose 70th birthday falls during the dates of the conference.
Robert J. Plemmons (see also Computer Science)
- Comprehensive space-object characterization using spectrally compressive polarimetric imaging
Awarded $70,000 for the period 7/15/12 to 7/14/13
Source: Air Force Office of Scientific Research (AFOSR)/University of New Mexico
In collaboration with the University of New Mexico and Duke University, advanced imaging methods are used to identify and track objects in space. Space surveillance allows US space system operators to determine the capabilities of potential adversaries, to warn of an attack on a US space system, and to predict potential collisions and re-entry impact points.
- Supplement to Novel Imaging Tools for Improved Space Objective Identification
Awarded $20,000 for the period 5/3/11 to 7/31/11
Source: AFOSR/University of New Mexico
- Novel Imaging Tools for Improved Space Objective Identification
Awarded $10,084 for the period 7/1/10 to 11/30/10
Source: AFOSR/University of New Mexico
With increased deployment of ever-smaller satellites at various altitudes, present-day imaging and nonimaging capabilities are often inadequate. Compressive sampling of spectral-spatial imaging data can rapidly identify space objects by cross-constraining object information and exploiting fundamental trade-offs implicit in such data. This system performance analysis will improve compressive sensor design and information transmission and formulate computationally efficient data postprocessing algorithms for identifying space objects. An experimental program will complement and validate the project’s theory, simulation, and processing.
Combining Imaging and Nonimaging Observations for Improved Space Object Identification
Awarded $29,994 for the period 12/1/09 to11/30/10
Source: Air Force Office of Scientific Research (AFOSR)/University of New Mexico
Current imaging and nonimaging capabilities are often inadequate to robustly and reliably determine the properties of ever-smaller satellites deployed at varying altitudes in space. This project’s low-dimensional parametric approach jointly models the essential literal and nonliteral characteristics of space objects in terms of a relatively small set of physically motivated parameters, whose values are estimated by digital postprocessing. Polarimetric and spectral data will be used to cross-constrain the radiometric information and to reconstruct space objects by exploring fundamental trade-offs, yielding data based on a priori constraints. This approach will overcome the resolution limits of even the largest existing and foreseeable AF/DoD assets.
- Integrated Optical-Digital Imaging Camera System: Phase III: Computation Team Research and Development
Awarded $69,784 for the period 11/9/07 to 9/30/09
Source: Defense Microelectronics Activity; Catholic University of America
Prior notice needed for publicity.
- Integrated Optical-Digital Imaging Camera System
Awarded $52,975 for the period 1/22/07 to 10/15/07
Source: US Department of Defense / University of New Mexico
No publicity allowed.
- Phase II: Practical Enhanced-Resolution Integrated Optical-Digital
Awarded $103,464 for the period 1/22/07 to 6/30/07
Source: University of New Mexico
- DTO Advanced Imaging Seedling Project, A Practical Enhanced-Resolution
Integrated Optical Imaging Camera (PERIODIC) System, Supplementary
Awarded $62,026 for the period 9/15/00 to 02/28/07
Source: Army Research Office (ARO)
This project aims to analyze,
optimize, simulate, design, and fabricate a beta prototype,
integrated, optical-digital, low-profile, low-cost, array-based
imaging system. Considerable progress has been made in the
theoretical, computational, and design/fabrication aspects,
leading to the development of very promising workable prototype
systems. Successful completion of this seedling effort is
expected by the end of 2006, with the help of the supplemental
funds, which will support two graduate and one undergraduate
student, working with Professors Pauca, Plemmons, and Torgersen.
Funds will also purchase additional equipment and supplies
by the design and fabrication group at Catholic University
- Postdetection Processing and Inverse Problems in Ground-Based
Awarded $15,000 for the period 12/31/04 to 6/30/07
Source: Air Force Office of Scientific Research (AFOSR), subcontract with
University of New Mexico
High-resolution images are essential to many important defense,
science, engineering, law enforcement, and commercial applications.
Extracting meaningful information from degraded images is
especially vital for such biometric DoD applications as integrated
optical imaging systems for personnel identification using
This project conducts extensive, novel research in pupil
phase engineering (PPE) to help develop, along with industrial
partner CDM Optics Company, a reliable, easy-to-use,
low-cost iris recognition system for personal verification to ensure
computer network security. The primary technical goal
is to make iris recognition easier to use by greatly expanding
the imaging system's iris capture volume; we estimate
that our methods can increase iris capture volume more than 100
times over current systems. The design of overall optical
masks is a nontrivial problem and involves the numerical
solution of highly nonlinear and ill-posed optimization
problems with multiple design parameters.
Dr. Plemmons serves as Senior Scientific Consultant to establish
a major research and development program in ground-based
imaging for the Air Force Research Laboratory, including
the Maui High Performance Computing Center, which houses
one of the world's largest supercomputers.
- A Practical, Enhanced-Resolution, Integrated
Optical-Digital Imaging Camera (PERIODIC) System
Awarded $63,486 for the period 05/23/05 to 8/30/06
Source: United States Department of Energy
This project aims to design an end-to-end optimized,
compact, integrated, digital camera system with a modular
architecture. Novel interferometric enhancements of optical
resolution and use of information theory as an optimization
tool will lead to imaging-system designs that maximize
information throughput. Surveillance imaging systems
will be developed for intelligence agency applications.
- Innovative Computational Methods for Inverse
Problems in Optical Imaging
Awarded $51,255 for the period 6/29/05 to 2/28/06
Source: Army Research Office
Dr. Plemmons and colleagues will investigate and implement
innovative approaches to pupil-mask design to control
the depth-of-focus of imaging systems. The traditional
imaging system suffers from limited depth-of-focus that
can be extended most simply by reducing the pupil size.
This approach is undesirable, because the light flux
and resolution are both decreased. Instead, the investigators
plan to use multiple parameters that can control pupil
phase variation rather finely. They foresee vigorous
technology transfer to the military and industrial arenas
and generalization of the theoretical concepts to other
domains of imaging.
- Asymptotic behavior of solutions to nonlinear dispersive equations
Awarded $35,000 for the period 9/1/12 to 8/31/17
Source: Simons Foundation
Most partial differential equations are far too complex to solve explicitly, except perhaps to find a few special solutions. Given a physical problem expressed as a partial differential equation, Dr. Raynor uses real analysis energy estimates, degree theory, regularity theory, and harmonic analysis to study the qualitative behavior of solutions: Do they exist? Are they unique, or can more than one be guaranteed to exist with the same input? How are they affected by a slight change in the input? Can they collapse? Can they blow up?
- Asymptotic Behavior of Solutions to the Nonlinear
Awarded $5,000 for the period 1/1/06 to 12/31/06
Source: WFU Science Research Fund
This project will investigate the long-term, qualitative behavior of
solutions to the nonlinear Schrodinger equation, which models
important physical systems in quantum mechanics, optics, and
fluid mechanics. It is also the canonical example of a nonlinear
dispersive partial differential equation and provides a testing
ground for a wide range of mathematical techniques and hypotheses.
SEARCDE 2012 Conference
Awarded $24,832 for the period 9/15/12 to 8/31/13
The Southeastern-Atlantic Regional Conference on Differential Equations (SEARCDE) brings together established and new researchers to exchange ideas. It has met annually since 1981 and in 2012, was held at Wake Forest. Funding helped to defer the travel expenses of advanced graduate and undergraduate students and recent PhD recipients and four invited plenary speakers as well as staffing and supplies.
Distribution of the Fourier coefficients of modular forms and arithmetic applications
Awarded $51,530 for the period 7/16/10 to 7/31/12
Source:NSF/University of Illinois
This 3-year research program studies the distribution of the Fourier coefficients of modular forms (both Archimedean and p-adic), arithmetic dynamics, and quadratic forms. It will focus on understanding the number of representations of an integer as a sum of squares and generalizing Bhargava and Hanke's famous 290 theorem.