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Please submit abstracts to adamiano@gmu.edu by May 10th
Please submit abstracts to adamiano@gmu.edu by May 10th
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the speaker's name
| SPEAKER |
TITLE |
| Baras |
Network Tomography: From Resistors to the Internet |
| Berenstein |
Internet Tomography |
| Casadio Tarabusi |
|
| Chang | Geometric Analysis on a Family of Pseudoconvex Hypersurfaces |
| Damiano | Computational Algorithms for the Computation of Noetherian Operators |
| Ehrenpreis | Special Functions |
| Grinberg | Spectral Synthesis and Spectral
Analysis on the Space of Convex Bodies |
| Kaiser | Pulsed-Beam Wavelets and the Wave Equation |
| Kiselman |
Subharmonic functions on discrete structures |
| Krishnaprasad | Geometry of Blind Signal Processing |
| Li | Entire solutions of certain non-linear partial differential equations |
| Marmolejo-Olea |
The Monogenic Radon-Nikodym Property for Clifford Modules |
| Napoletani | Embedding Threshold Estimators |
| Poovendran |
Performance Metrics and Related
Complexities in Energy-Efficient Wireless Networking for Routing and Security |
| Ryan | Analysis and applications of solutions to the Dirac- Hodge and Laplace equations with respect to the hyperbolic metric |
| Sabadini | Different approaches to the study of resolutions of several Cauchy-Fueter and Dirac operators |
| Sadosky | The BMO Extended Family in Product Spaces |
| Suslov | Completeness of q-trigonometric system in Lp |
| Taylor | Algebraic Varieties on which the Phragmen-Lindelof Inequalities hold |
| Walnut |
Local reconstruction from averages over parallelograms |
| Yger | Analytic and Algebraic ideas : how to profit from their complementarity |
College of Arts and Sciences
George Mason University
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4400 University Drive, MSN 3A3
Fairfax, Virginia 22030-4444
Phone: 703-9931002
email: artsandsciences@gmu.edu
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Please send any comments on this website to A. Damiano at
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Geometry of Blind Signal Processing
P. S. Krishnaprasad (with B. Afsari)
Department of Electrical and Computer Engineering and
Institute for Systems Research
University of Maryland
College Park, MD 20742
email: krishna@isr.umd.edu
http://www.isr.umd.edu/~krishna
The problem of extracting
information from sensor data in the absence of detailed knowledge of
physical models of the transduction process appears in a variety of
domains. Solutions to this problem have playedan increasingly central
role, either as tools for fundamenatal scientific investigations (e.g.
experimental neuroscience), or as key elements of technology (e.g.
modern communication systems). This talk will be devoted to exploring
interesting geometric aspects of such blind signal processing
algorithms. Flows on classical groups and their homogeneous spaces arise
naturally in this context and we argue that elucidating the ``phase
portraits'' of such flows is of interest in devising better algorithms.
The most commonly studied
special functions are hypergeometric. They interrelate group
representations, Fourier transforms, and differential equations, and
they have special types of integral representations and power
series. Some such functions, such as Laguerre functiions, which
were studied by Carlos Berenstein, appear in several contexts, such as
the Heisenberg group and SL(2,R). We shall explain the interrelations of
these appearences. "Beyond" hypergeometric functions lie Mathiew
functions and Lame functions. We shall show how such funtctions
share some of the properties ofhypergeometric functions using the
concept of "Fourier transform on varieties".
^back^
Pulsed-Beam Wavelets and the Wave Equation
G. Kaiser
email: kaiser@wavelets.com
DOWNLOAD THE ABSTRACT IN PDF FORMAT
G. Kaiser
email: kaiser@wavelets.com
DOWNLOAD THE ABSTRACT IN PDF FORMAT
^back^
Analysis
and applications of solutions to the Dirac-Hodge and Laplace equations
with respect to the hyperbolic metric
J. Ryan (with Y. Qiao)
email: jryan@uark.edu
J. Ryan (with Y. Qiao)
email: jryan@uark.edu
Using a Cauchy integral formula
and Green's formulas for solutions to Dirac-Hodge and Laplace equations
we investigate basic properties of the solutions. The analysis takes
place in upper half space endowed with the hyperbolic metric. Our study
includes an introduction to Hardy spaces, Bergman spaces and boundary
value problems.
^back^
Analytic and Algebraic ideas: how to profit from their complementarity
A. Yger, Bordeaux University
email: alain.yger@math.u-bordeaux.fr
Analytic and Algebraic ideas: how to profit from their complementarity
A. Yger, Bordeaux University
email: alain.yger@math.u-bordeaux.fr
Facing algebraic questions with
some analytic vision (also some analytic motivation as for questions
related to exponential polynomials) has been the guide line of the joint
work which we pursue for almost 20 years with Carlos. I will try to
present the state of the art about such questions, indicate a list of
prospective developments where the ideas that analysis suggest play a
major role: intersection theory in the non-complete intersection
case, analysis of the dependence of residual objects such as
Bochner-Martinelli currents in terms of parameters, ... I will also
focuse on the crucial following fact, namely that in the ''dictionary''
between the analytic and algebraic points of view in multidimensional
residue theory, integral symbols happen to be the analytic substitutes
for power series developments in terms of parameters. Recent advances
about ''algebraic tomography'' (Abel's theorem and its inverse, together
with their translation in terms of the ''rigidity'' of some particular
differential non linear systems) will also be presented.
^back^
Different approaches to the study of resolutions
of several Cauchy-Fueter and Dirac operators
I. Sabadini (with D.C. Struppa)
mailto: sabadini@mate.polimi.it dstruppa@gmu.edu
I. Sabadini (with D.C. Struppa)
mailto: sabadini@mate.polimi.it dstruppa@gmu.edu
In the recent years, a lot of
attention has been devoted to problems related to generalization of the
theory of several complex variables to higher dimensions. Back in 1995,
in a joint work with Carlos Berenstein and Daniele Struppa, we started
the study of resolutions of several Cauchy-Fueter operators with the
purpose to construct a theory of hyperfunctions of several quaternionic
variables. Since then, several progresses have been done in different
directions and using different techniques. The theory of Grobner bases,
which underlies the computational results we have obtained, has been a
major tool in studying the algebraic properties of the Cauchy-Fueter
complex from which several analytical properties can be derived.
Recently, it has been proved that the Cauchy-Fueter complex can be
obtained also using the methods of representation theory,since
quaternionic geometry is a special case of so called parabolic
geometries.
As a further generalization, we discuss complex of several Dirac operatorsacting on functions with values in a Clifford algebra and the so called Dirac complex. Despite the complexity, due to the fact that the dimension of the algebra is not fixed a priori so it is hard to use Grobner bases techniques or invariant operator theory, we show that under suitable assumptions on the number of operators considered the complex can be treated within the so called radial algebra.
Therefore, we can easly describe all the maps in the complex and we can still derive some analytical properties. We conclude by describing an alternative way to obtain the maps in the Dirac complex, using the analogue of the Dolbeault complex, based on a suitable theory of generalized differential forms.
As a further generalization, we discuss complex of several Dirac operatorsacting on functions with values in a Clifford algebra and the so called Dirac complex. Despite the complexity, due to the fact that the dimension of the algebra is not fixed a priori so it is hard to use Grobner bases techniques or invariant operator theory, we show that under suitable assumptions on the number of operators considered the complex can be treated within the so called radial algebra.
Therefore, we can easly describe all the maps in the complex and we can still derive some analytical properties. We conclude by describing an alternative way to obtain the maps in the Dirac complex, using the analogue of the Dolbeault complex, based on a suitable theory of generalized differential forms.
^back^
C. Sadosky
mailto: cs@scs.howard.edu
The Monogenic Radon-Nikodym Property for Clifford Modules
E.Marmolejo-Olea (with S. Perez-Esteva)
mailto: emilio@matcuer.unam.mx
Computational Algorithms for the Computation of
Noetherian Operators
A.Damiano (with I. Sabadini and D.C. Struppa)
mailto: adamiano@gmu.edu
Completeness of q-trigonometric
system in Lp
S. Suslov
mailto: sks@adu.edu
S. Suslov
mailto: sks@adu.edu
We discuss several
results on completeness of q-trigonometric systems in Lp spaces in the
framework of a general approach to basic Fourier series.
^back^
Embedding
Threshold Estimators
D. Napoletani
mailto: dnapolet@gmu.edu
D. Napoletani
mailto: dnapolet@gmu.edu
Wavelet related thresholding
estimators have been very successful in a variety of denoising problems.
As much as they represent a fundamental achievement in the field of
optimal estimation, their weakness is that they do not preserve fine,
low intensity, non-noisy features and that they are specifically adapted
to deal with constant variance white noise. In this talk we propose a
method of denoising that tries to overcome these shortcomings. The
method, which we call embedding threshold estimator, is based on the
analysis of delay-coordinates embeddings of sets of coefficients of the
measured signal in some chosen frame. We apply the embedding threshold
to heavily corrupted speech signals choosing, as frame, the window
Fourier frame. A regularized pointwise mean SNR is introduced to
estimate the perceptual quality of the reconstructions.
Algebraic Varieties on which the Phragmen-Lindelof
Inequalities hold
B. A. Taylor
University of Michigan
Ann Arbor, MI 48109
mailto: taylor@umich.edu
B. A. Taylor
University of Michigan
Ann Arbor, MI 48109
mailto: taylor@umich.edu
The Phragmen-Lindelof theorem
implies that a subharmonic function u(z)
on the complex plane that satisfies the asymptotic bound u(z) < |z| + o(|z|) and is
bounded above by 0 on the real
axis must in fact be bounded above by |Im
z| for all complex z.
We will give a geometric characterization of the algebraic varieties in Cn on which the
plurisubharmonic functions satisfy an analogous estimate. One
reason for the interest in this question results from a theorem of L.
Hormander, who showed that the validity of such an estimate on the
homogeneous variety that is the zero set of the principal symbol of a
constant coefficient partial differential operator is equivalent to the
surjectivity of the operator on the space of real analytic functions on Rn.
C. Sadosky
mailto: cs@scs.howard.edu
The space BMO, of functions of bounded mean
oscillation, plays an important role in harmonic analysis and PDE
theory. In product spaces, a BMO
scale appears naturally, corresponding to the different, yet equivalent,
characterizations of BMO in one
variable, solving outstanding problems in multiparametric harmonic
analysis and operator theory. The characterization of the endspaces in
the BMO scale gave the clue to
finally grasp ''product'' BMO,
the dual of the Hardy space H1Re(Td), in terms of nested
commutators.
^back^
Geometric Analysis on a Family of
Pseudoconvex Hypersurfaces
D.C. Chang
mailto: chang@georgetown.edu
DOWNLOAD THE ABSTRACT IN PDF FORMAT
D.C. Chang
mailto: chang@georgetown.edu
DOWNLOAD THE ABSTRACT IN PDF FORMAT
^back^
Entire solutions of certain
non-linear partial differential equations
We will consider the following
two problems: (a) characterize entire solutions of non-linear partial
differential equations such as Fermat type pdes; and (b) characterize
common factors of certain meromorphic functions under functional
composition. We will show that while these problems are of independent
interests in partial differential equations and complex variables, they
are closely related; and characterizations will be given using their
relations.
^back^
Subharmonic functions on discrete
structures
K. Kiselman
Uppsala University
mailto: kiselman@math.uu.se
www.math.uu.se/~kiselman
K. Kiselman
Uppsala University
mailto: kiselman@math.uu.se
www.math.uu.se/~kiselman
The problem of describing the
shape of a three-dimensional object is important in many applications.
Images in medicine and industry are often three-dimensional nowadays.
One should be able to store the description of a shape in a computer and
be able to compare it with other shapes, using some measure of likeness.
One approach to shape description is to introduce a triangulation
of the surface of the object and then map this triangulation to a
sphere. The position of a point on the surface is then a function on the
sphere, and can be expanded in terms of spherical harmonics. This
approach, initiated by C. Brechbuhler, G. Gerig, and O.
Kubler, will be the background of my talk, and it leads to the study of
harmonic, or more generally subharmonic, functions on a graph or a
directed graph. It turns out that the values of harmonic functions often
cluster together in an undesirable way, and to get rid of this
clustering is aspecial problem of importance in the shape-description
project of Ola Weistrand. There are various remedies, one being to use
different weights in the definition of harmonicity. In my talk I shall
give an introduction to the study of harmonic and subharmonic functions
on discrete structures. The Dirichlet problem will be studied and
explicit solutions in some simple cases will be given. In other cases,
however, explicit formulas corresponding to well-known solutions in the
classical setting are apparently not known.
The Monogenic Radon-Nikodym Property for Clifford Modules
E.Marmolejo-Olea (with S. Perez-Esteva)
mailto: emilio@matcuer.unam.mx
Abstract: We characterized the
boundary limits of Monogenic functions defined in the unit ball in Rn
with values in a Banach Space X which is also a
Clifford Module as a class of
vector-valued Measures. The case when X is a Banach lattice
is also considered.
vector-valued Measures. The case when X is a Banach lattice
is also considered.
Computational Algorithms for the Computation of
Noetherian Operators
A.Damiano (with I. Sabadini and D.C. Struppa)
mailto: adamiano@gmu.edu
The original definition of
Noetherian Operators is not constructive. Several recent results, due
for example to U. Oberst and Marinari-Moeller-Mora, have begun the
process of explicitly constructing such operators, though not in the
general case. In this talk we present some concrete algorithms that, at
least in theory, allow the computation of the Noetherian operators in
some particular cases, and we discuss their implementation on some
computer algebra packages (CoCoA and Singular) with their
limitations.
Local reconstruction from averages
over parallelograms
D. Walnut (with R. Rom)
mailto: dwalnut@gmu.edu
D. Walnut (with R. Rom)
mailto: dwalnut@gmu.edu
This work provides a
generalization in two dimensions of the Local Three Squares Theorem,
proved by Carlos, R. Gay, and A. Yger which asserts that a function is
uniquely determined locally by its averages over shifts of three squares
with parallel sides if and only if the side lengths of the squares are
pairwise irrationally related. We give a necessary and sufficient
algebraic condition on the side vectors of a triple of parallelograms in
the plane which corresponds to the irrationally related condition in the
three squares case. The proof relies on the generalization of a
recent result of Y. Lyubarskii (NTNU Trondheim) describing sets of
sampling and interpolation for functions bandlimited to symmetric
even-sided polygons in the plane.
^back^
Some topics in integral geometry on
hyperbolic spaces and their discrete counterparts
The talk will focus on some
problems of integral geometry studied jointly with Carlos, namely
several kinds of Radon transform on continuous and on discrete
structures (which show a few analogies), as well as their applications
to some medical imaging techniques that motivated their investigation.
^back^
Abstract: Networks like the
Internet and highways, for instance, the Washington Beltway, suffer from
two types of problems. Either some nodes become disabled or the traffic
load among two nodes is sufficiently big to disable the corresponding
link. In order to keep track of them and try to prevent their occurrence
or create adequate alternatives, one needs to have a monitoring system
that from "boundary" measurements would allow to obtain this "internal"
information. This is akin to medical tomography and to the inverse
conductivity problem. I'll try to explain briefly how we're trying to
profit from this analogy to create such a monitoring system.
^back^
Spectral Synthesis and Spectral
Analysis
on the Space of Convex Bodies
on the Space of Convex Bodies
Harmonic analysis, spectral
synthesis and analysis are usually applied to spaces of functions
(sections of bundles, etc.). Here we consider an adaptation of this kind
of analysis to the space of convex bodies in Euclidean space. As
applications we obtain, e.g., approximation theorems that preserve
special geometric properties such as constant width or brightness. The
ideas that provided our initial motivation us include papers of Carlos
Berenstein and his collaborators on spectral synthesis and spectal
analysis.
^back^
Network Tomography: From Resistors to the Internet
J. S. Baras
mailto: baras@isr.umd.edu
Network Tomography
addresses a large and varied class of problems where measurements at the
edge of the network are used to infer various properties of the
internals of the network, including topology structure, flow parameters
and characterization, anomalous behavior. Initially we describe the
inverse problem in the discrete and simply to state but difficult to
solve classic case of identifying a network of resistors from voltage
and current measurements at the edge nodes. We then describe the key
problem of electrical impedance tomography and the associated
fundamental inverse boundary value problem first analyzed extensively by
Alberto Calderon, as well as the well known parametric dependence of
the Dirichlet to Neumann Map. Finally, we describe current problems of
network tomography for modern communication networks and the Internet.
We formulate precisely and analytically (including also algebraic
methods) several inference problems as true network tomography problems,
involving tomography on graphs. We describe methods for solving some of
these problems and describe a broad range of challenging and important
open problems ranging from on-line identification of routing and
bottlenecks to security threats. Much of the analytical work reported
is joint with Carlos Berenstein.
^back^
Performance Metrics and Related
Complexities in Energy-Efficient Wireless
Networking for Routing and Security
R. Poovendran
mailto: radha@ee.washington.edu
In this talk, I consider the problem of routing and secure multicasting in an ad hoc wireless network that consists of energy constrained wireless devices. I assume that the devices are equiped with omnidirectional antenna. I then introduce the problem of securing the communicaiton and then show why the problem is not a direct extension of a conventional approach. I then show that under the contraint that the storage is unbounded, this problem is NP-hard. I also discuss the approximations that will be within the factor of two of the optimal solution. Many questions remain open in this problem first introduced by me in 2002.
Networking for Routing and Security
R. Poovendran
mailto: radha@ee.washington.edu
In this talk, I consider the problem of routing and secure multicasting in an ad hoc wireless network that consists of energy constrained wireless devices. I assume that the devices are equiped with omnidirectional antenna. I then introduce the problem of securing the communicaiton and then show why the problem is not a direct extension of a conventional approach. I then show that under the contraint that the storage is unbounded, this problem is NP-hard. I also discuss the approximations that will be within the factor of two of the optimal solution. Many questions remain open in this problem first introduced by me in 2002.
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