Research Grants

NSF Grant 2008-2011: Nonlinear Signal Processing and Wireless Communications using Frames and Operator Theory
PI: Radu Balan (CSCAMM/Mathematics, University of Maryland)

This proposal develops a new mathematical framework for nonlinear signal processing and wireless communication channels. The nonlinear signal processing problem addressed here is signal reconstruction from the magnitude of a redundant linear representation. When the linear redundant representation is associated to a group representation (such as the Weyl-Heisenberg grgoup), the relevant Hilbert-Schmidt operators inherit this invariance property. Thus a fast (nonlinear) reconstruction algorithm seems possible. A wireless communication channel is modeled as a linear operator that describes how transmit signals propagate to a receiver. For ultrawide band (UWB) signals, the Doppler effect no longer can be modeled as a frequency shift. Instead it is captured as a time dilation operator. A continuous superposition of time-scale shifts is used to model a UWB communication channel, and consequences to pseudo-differential operator theory are analyzed.

The solutions to these problems have a strong impact in the strategic area of information technology. Important applications such as signal processing, X-ray crystallography, and quantum computing are impacted by solutions to the first problem. High-impact applications related to the second problem include UWB through-wall imaging systems, higher throughput 802.15 Wireless Personal Area Networks, and wireless sensor networks.


NIH R01, 2008-2012: Interplay Between Cancer and Immune Cells on Targeted Therapy
PI: Peter Lee, MD (Hematology, Stanford University)
Co-PI: Doron Levy, PhD (CSCAMM/Mathematics, University of Maryland)

The role of the host immune response in relation to current therapies in controlling cancer remains unclear.  We hypothesize that novel molecular targeted therapies, such as imatinib for chronic myelogenous leukemia (CML), may render leukemic cells immunogenic as patients enter remission.  This relates to the relative selectivity of imatinib over standard chemotherapy for leukmic cells, thus sparing normal immune cells.  In addition, cancer has potent immunsuppressive activity.  As leukemic cell population decreases with imatinib, immune function may be restored while cancer antigens are still present at significant levels, thus leading to maintain disease control (remission), and may be further expanded to eliminate residual leukemic cells for a durable cure.  In preliminary studies, we used a novel combined experimental and modeling approach to address the immune response to leukemia.  We showed that the majority of CML patients develop robust anti-leukemia T cell responses upon remission on imatinib.  Intriguingly, CD4+ T cells producing TNF-represent the dominant response, with levels reaching 40% in one patient.  Analysis of IFN-production by CD8+ T cells alone, as commonly done today, would not reveal the entire anti-leukemia T cell response.  We studied the dynamics of these responses and showed that they peak around the time patients enter cytogenetic remission, but wane to undetectable levels shortly thereafter.  We utilized mathematical modeling to gain insights into the dynamics of leukemia and the immune response, and the complex interplay between these populations.  Our results suggest that anti-leukemia T cell responses may contribute to the maintenance of remission under imatinib therapy.  The goal of this proposal is to expand on these findings by conducting and integrating additional experiments and mathematical modeling.  We will analyze in detail 10 patients per year over 5 years, for a total of 50 patients using an array of novel immunological techniques (Aim 1).  We will develop new mathematical models of the interplay between leukemia and immune cells.  These models will extend our preliminary findings to independently consider CD4 T cells, CD8 T cells, NK cells, B cell response (antibodies), and different cytokine patterns (Aim 2).  We will use the new experimental data for evaluating patient-dependent model parameters, and study whether the magnitude, timing, and dynamics of the immune response can be correlated with the clinical outcome.  Lastly, we will develop novel therapeutic strategies in silico (Aim 3).  Using our mathematical models and real patient parameters, we will study cancer vaccines, structured treatment interruptions, and mini-transplants.  If successful, this work will provide important insights into the role of the host immune response in CML under targeted therapy, and may lead to novel treatment strategies combining therapy with immunotherapy.


NSF Focus Research Group Grant 2008-2011: Collaborative Research on Kinetic Description of Multiscale Phenomena: Modeling, Theory and Computation
PI: Eitan Tadmor (CSCAMM/Mathematics/IPST, University of Maryland)
Co-PI: Thanos Tzavaras (Mathematics, University of Maryland)

Kinetic equations play a central role in many areas of mathematical physics, from micro- and nano-physics to continuum mechanics. They are an indispensable tool in the mathematical description of applications in physical and social sciences, from semi-conductors, polymers and plasma to traffic networking and swarming. The ultimate goal of this proposal is to develop novel analytical and numerical methods based on kinetic descriptions of complex phenomena with multiple scales and with a wide range of applications. The objective is to achieve a better understanding of problems which are in the forefront of current research and to contribute to the solution of long standing problems by synergetic collaboration of theory, modeling and numerics.

To this end, this Focus Research Group (FRG) will provide a platform, led by leading researchers from Universities of Maryland, Brown, Iowa State, Wisconsin-Madison, Arizona State, Austin-Texas and Toulouse, France, who will merge their expertise in the construction, analysis and implementation of kinetic descriptions for a selected suite of problems with crossing scales from quantum and micro scales to the macro scales. Topics to be discussed include:

● Kinetic descriptions of microscopic and quantum phenomena

● Kinetic descriptions of macroscopic phenomena

and finally, as a recent novel example for the kinetic methodology we will use kinetic descriptions to study

● hyperbolic flows for complex supply chains.

The theoretical and modeling aspects of this research program, on both microscopic and macroscopic scales, will be integrated with kinetic based numerical methods for capturing “smaller scales phenomena". The rationale behind this proposal is a timely effort to address several important issues in modern applied mathematics. Kinetic theories are not new. Yet, there has been many major developments in kinetic modeling, kinetic theories and related numerical methods, with the potential for a considerable impact on emerging new fields in physical and social sciences.

The proposed effort will significantly strengthen the leading role that the US researchers can play in pursuing cutting-edge research and training a new generation of applied mathematicians in this important field.

We expect this project to contribute to the development of scientific workforce by advanced training for doctoral and postdoctoral researchers and by providing a platform for interdisciplinary interactions with researchers from related disciplines. Interactions - internal and external, should be maintained through synergetic cooperations which will come to fruition during the three annual workshops planned to be held in Maryland (YEAR 1), France and Brown (YEAR 2) and Wisconsin (YEAR 3). In this context, we plan to hold (inter-)national meetings, as part of the series of interdisciplinary focused workshops organized by the Center for Scientific Computation and Mathematical Modeling (CSCAMM) in the University of Maryland. We also expect to gain from collaboration with the DOE Center for Multiscale Plasma Dynamics housed in CSCAMM, the DOE Ames Laboratory in Iowa State University and the Institute for Computational Engineering and Sciences (ICES) in UT Austin.


NSF Grant 2007-2010: Regularity and Critical Thresholds in Nonlinear Transport-Diffusion Equations
PI: Eitan Tadmor (CSCAMM/Mathematics/IPST, University of Maryland)

The ultimate goal of this proposal is to study the persistence of global features in nonlinear transport-diffusion equations which arise in a wide variety of applications. Examples include nonlinear conservation laws with degenerate diffusion which model sedimentation, traffic flows and data driven applications in image processing, the ubiquitous Eulerian dynamics governing a range of phenomena from the small scale of semi-conductors through the largest scale of stars formation, or chemotaxis models found in biological applications. We focus our attention on the unifying mathematical content of the underlying transport-diffusion equations. Of primary interest are problems with critical regularity properties which hinge on a borderline balance between the nonlinear convection mechanisms, the nonlinear diffusion processes and the possibly nonlinear forcing driving such problems.

We plan to use modern mathematical tools complemented by novel computational simulations to examine the phenomena of regularizing effects, critical thresholds, time decay, entropy stability, scaling and more, where the following questions will be addressed in the context of (i) Transport-diffusion equations: how do diffusion and entropy dissipation dictate the regularizing effect in such equations? (ii) Eulerian dynamics: how does the competition between rotation and pressure forcing determine the overall stability? (iii) Chemotaxis and related bio-related transport-diffusion models: how should we interpret the solutions beyond their critical time? (iv) Hierarchical decompositions of images: how does the inverse scale space can be adapted to the data for effective image processing?

The principle investigator together with his collaborators plan to pursue the development of new analytical and computational tools to explore transport-diffusion models, which are expected to impact our overall understanding of the dynamics of such realistic models in a variety of applications.


DOE Grant 2004-2009: Center for Multiscale Plasma Dynamics
PI: William Dorland (CSCAMM/Physics, University of Maryland)

The Center for Multiscale Plasma dynamics is a joint UCLA/Maryland fusion science center focused on the interaction of microscale and macroscale dynamics in key plasma physics problems. Foremost among these problems are the sawtooth crash, the growth of neoclassical magnetic islands, and the formation and collapse of transport barriers -- all of central importance to the fusion program. Each involves large scale flows and magnetic fields tightly coupled to the small scale, kinetic dynamics of turbulence, particle acceleration, and energy cascade. The interaction between these vastly disparate scales controls the evolution of the system. The enormous range of temporal and spatial scales associated with these problems renders direct simulation intractable, even in computations that use the largest existing parallel computers. Powerful new multiscale algorithms are emerging from the applied mathematics and engineering communities. A central mission of the center is to adapt, modify and extend these ideas to model multiscale plasma dynamics. This mission puts the center in one of the most active and rapidly advancing areas of computational research.