Norbert Wiener Center Archives for Academic Year 2014


Organizational meeting

When: Tue, September 3, 2013 - 2:30pm
Where: Math 3206
Speaker: N/A () -

Pseudo-differential operators on fractals and some applications

When: Tue, September 10, 2013 - 2:00pm
Where: Math 3206
Speaker: Marius Ionescu (Department of Mathematics, Colgate University) - http://math.colgate.edu/~mionescu/
Abstract: In this talk that is based on joint work with Luke Rogers and Robert Strichartz, I present a definition and and basic properties of pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators have kernels that decay and, in the constant coefficient case, are smooth off the diagonal. Our analysis can be extended to product of fractals. I will present some application to the study of elliptic, hypoelliptic, and quasi-elliptic operators, Hormander hypoelliptic operators as well as the study of wavefront sets and microlocal analysis on p.c.f. fractals.

Composite Dilation Wavelets

When: Tue, September 17, 2013 - 2:00pm
Where: MATH 3206
Speaker: Ben Manning (UMCP) -
Abstract: Composite dilation wavelets are a class of directional multi scale representations developed by K.Guo, D. Labate, W.-Q. Lim, G. Weiss, and E. Wilson. They are a class of basis generated by the action of a lattice group and dilations from a set of matrices $B$. In particular, this class includes shearletswhen $B$ is a group of shearing matrices. We will focus on composite dilation wavelets with finite group $B$ and, unlike the shearlet case, is non-commutative. These type of wavelets can be thought of as usual wavelets except the group of integer translates $\mathbb{Z}$ is replaced with a non-commutative group.We will mention the contributions to the theory of these type of wavelets along with constructions of MRA composite wavelets.

Dirichlet Forms and Derivations on Fractals

When: Tue, September 24, 2013 - 2:00pm
Where: MATH 3206
Speaker: Luke Rogers (UConn) - http://www.math.uconn.edu/~rogers/
Abstract: The classical Dirichlet energy is the L^2 norm of the gradient of a function. Its study was initially motivated by problems from physics. There is also an abstract notion of a Dirichlet energy on a space of functions, and it is natural to wonder to what extent such an energy may be thought of as an integral of some sort of "gradient". In an abstract sense this problem was solved by Beurling-Deny and LeJan, who gave a structure which has the Leibniz (product rule) property of a gradient and is endowed with a Hilbert norm corresponding to the energy. I will describe joint work with Marius Ionescu and Sasha Teplyaev in which we give a concrete description of this structure on certain types of fractal sets and use this to give simple proofs of some results about Fredholm modules in this context. I will also discuss some consequences from work of Michael Hinz and Alexander Teplyaev.

Sampling In Image Representation and Compression

When: Tue, October 1, 2013 - 2:00pm
Where: MATH 3206
Speaker: Alfredo Nava-Tudela (University of Maryland) - http://terpconnect.umd.edu/~ant/
Abstract: In recent years, interest has grown in the study of sparse solutions to underdetermined systems of linear equations because of their many potential applications. In particular, these types of solutions can be used to describe images in a compact form, provided one is willing to accept an imperfect representation. We shall develop this approach in the context of sampling theory, and for problems in image compression. We use various error estimation criteria - PSNR, SSIM, and MSSIM - to conduct a presentation that is phenomenological and computational, as opposed to theoretical. This machinery leads naturally to a compressed sensing problem that can be seen as a non-uniform sampling reconstruction problem with promising applications. Joint work with John J. Benedetto.

Analysis and detection of singularities

When: Tue, October 8, 2013 - 2:00pm
Where: MATH 3206
Speaker: Matthew Begué (UMD-CP) - http://www2.math.umd.edu/~begue/
Abstract: How can one formally detect the location of a jump discontinuity in a function? One very successful tool in detecting singularities is the continuous wavelet transform, which I will present. However, the continuous wavelet transform provides no information about the orientation or geometry of the singularity. This is something that we would desire, especially for shape recognition or image restoration/enhancement. Shearlets have proven to be address these weaknesses of wavelets. I will introduce the continuous shearlet transform in R2 and give a brief overview of some recent results in the field. The entire talk is based on a minicourse taught by Demetrio Labate (University of Houston).

TBA

When: Tue, October 15, 2013 - 2:00pm
Where: MATH 3206
Speaker: Xuemei Chen (UMD) -

Transition operators on trees, boundaries and spectra

When: Tue, October 22, 2013 - 2:00pm
Where: MATH 3206
Speaker: Massimo Picardello (University of Roma ``Tor Vergata'' and UMD-CP) - http://www.mat.uniroma2.it/~picard/
Abstract: Since infinite homogeneous trees are discrete analogues of the hyperbolic disc,
these trees are a natural environment for studying free group actions and also spectra of transition operators.
We outline their introduction in harmonic analysis, discrete potential theory and random walks, and review old and new results
on strictly related subjects: the spectrum of the Laplace operator on a homogeneous tree, uniformly bounded representations of free groups, boundary behaviour of harmonic functions,
nearest neighbour and finite step transition operators, and the Poisson and Martin boundaries.

A great amount of deep progress on representations of free groups and on spectra of transition operators on groups and graphs has followed these
preliminary steps in the course of the years: substantial results have been obtained by K. Aomoto, T. Steger, S. Lalley, W. Woess, V. Kajmanovich, L. Saloff-Coste, Th. Coulhon, N.Th. Varopoulos, T. Nagnibeda and many others, not to mention the deep theory of Gromov and hyperbolic graphs, but all these results are beyond the scope of this presentation.

Multiresolution analysis on zero-dimensional abelian group and wavelets bases

When: Tue, October 29, 2013 - 2:00pm
Where: MATH 3206
Speaker: Wei-Hsuan Yu (UMD) -
Abstract: I will present the paper written by S.F. Lukomskii with title
"Multiresolution analysis on zero-dimensional abelian group and
wavelets bases". In this paper, authors builds a MRA on locally
compact zero-dimensional group and put forward an algorithm for
constructing orthogonal wavelet bases.

Motion Correction and Pharmacokinetic Analysis in Dynamic Positron Emission Tomography

When: Tue, November 5, 2013 - 2:00pm
Where: MATH 3206
Speaker: Hassan Mohy-ud-Din (JHU) -
Abstract: Abstract: My talk will focus on two important aspects of Positron Emission Tomography (PET): (i)

Motion-compensation, and (ii) Pharmacokinetic analysis of dynamic PET images.

Recovering a Representative Conformational Ensemble from Underdetermined Macromolecular Structural Data

When: Tue, November 12, 2013 - 2:00pm
Where: MATH 3206
Speaker: Konstantin Berlin (UMD) - https://sites.google.com/site/kberlin/
Abstract: Structural analysis of proteins and nucleic acids is complicated by their inherent flexibility, conferred, for example, by linkers between their contiguous domains. Therefore, the macromolecule needs to be represented by an ensemble of conformations instead of a single conformation. Determining this ensemble is challenging because the experimental data are a convoluted average of contributions from multiple conformations. As the number of the ensemble degrees of freedom generally greatly exceeds the number of independent observables, directly deconvolving experimental data into a representative ensemble is an ill-posed problem. Recent developments in sparse approximations and compressive sensing have demonstrated that useful information can be recovered from underdetermined (ill-posed) systems of linear equations by using sparsity regularization. Inspired by these advances, we designed the Sparse Ensemble Selection (SES) method for recovering multiple conformations from a limited number of observations. SES is more general and accurate than previously published minimum-ensemble methods, and we use it to obtain representative conformational ensembles of Lys48-linked diubiquitin, characterized by the residual dipolar coupling data measured at several pH conditions. These representative ensembles are validated against NMR chemical shift perturbation data and compared to maximum-entropy results. The SES method reproduced and quantified the previously observed pH dependence of the major conformation of Lys48-linked diubiquitin, and revealed lesser-populated conformations that are preorganized for binding known diubiquitin receptors, thus providing insights into possible mechanisms of receptor recognition by polyubiquitin. SES is applicable to any experimental observables that can be expressed as a weighted linear combination of data for individual states.

Quasicrystals and Harmonic Analysis

When: Tue, November 19, 2013 - 2:00pm
Where: MATH 3206
Speaker: Michael Kreisel (UMD) -
Abstract: When attempting to discretize the Fourier transform (or STFT), lattices are the clear first choice. They have a duality theory that culminates in the Poisson summation formula and support an elegant theory of periodic functions. Thus when trying to extend sampling results to non-uniform point sets, it is natural to try to preserve as many of these properties of lattices as is possible. Quasicrystals (also called cut and project sets) were developed for precisely this purpose. They also have a natural duality theory culminating in a version of the Poisson
summation formula, and they support a theory of almost-periodic functions. I will discuss some of these properties, along with recent results of Meyer about sampling on quasicrystals.

TBA

When: Tue, November 26, 2013 - 2:00pm
Where: MATH 3206
Speaker: Jameson Cahill (Duke) -

TBA

When: Tue, December 3, 2013 - 2:00pm
Where: MTH 3206
Speaker: Mishko Mitkovski (Clemson University ) -

Neural Networks: Topologies and Preprocessing

When: Tue, December 10, 2013 - 2:00pm
Where: MATH 3206
Speaker: Frederick W. Chen (Signal Systems Corporation) -
Abstract: Neural networks are capable of learning complicated mathematical
relationships and quickly computing approximations of computationally
intensive physical models. The choice of topology and preprocessing are
important to neural network learning. In this talk, I will describe a
building-block-based framework for understanding the range of functions
that a neural network can approximate given a topology. I will also show
how well-chosen preprocessing methods can reduce the complexity needed to
solve a problem. As examples, I will present some problems involving
functions of circular data (e.g. time and geolocation).

N/A

When: Tue, February 4, 2014 - 2:00pm
Where: MATH 3206
Speaker: ORGANIZATIONAL MEETING (UMD) -
Abstract: N/A

FFT 2014

When: Thu, February 20, 2014 - 9:00am
Where: Math 3206
Speaker: February Fourier Talks 2014 () -
Abstract: FFT 2014 http://www.norbertwiener.umd.edu/FFT/2014/schedule.html

Necessary and sufficient conditions for operator identification

When: Tue, February 25, 2014 - 2:00pm
Where: MATH 3206
Speaker: Gokhan Civan (UMD ) -
Abstract: We discuss the work of Pfander and Walnut on the sampling of operators, which deals with the identification of a class of operators from their action on a single properly chosen input signal. We describe the case of Hilbert-Schmidt operators whose time-frequency spread is confined to a common support. The area of the support decides the identifiability of these operators.

Topologies and Preprocessing

When: Tue, March 4, 2014 - 2:00pm
Where: MATH 3206
Speaker: Frederick W. Chen (Signal Systems Corporation) -
Abstract:
Neural networks are capable of learning complicated mathematical
relationships and quickly computing approximations of computationally
intensive physical models. The choice of topology and preprocessing are
important to neural network learning. In this talk, I will describe a
building-block-based framework for understanding the range of functions
that a neural network can approximate given a topology. I will also show
how well-chosen preprocessing methods can reduce the complexity needed to
solve a problem. As examples, I will present some problems involving
functions of circular data (e.g. time and geolocation).

Characterizing equations for generalized translation invariant systems on LCA groups

When: Tue, March 25, 2014 - 2:00pm
Where: MATH 3206
Speaker: Jakob Lemvig (TU Denmark) -
Abstract: In this talk we consider representations of square integrable functions on locally compact Abelian groups using so-called generalized translation invariant (GTI) frames. These systems are a generalization of generalized shift invariant (GSI) systems introduced by Hernandez, Labate and Weiss, and independently, Ron and Shen, where one translates the generators along co-compact (but not necessarily discrete) subgroups. One advantage of studying GSI and GTI systems is that they provide a unified theory for many of the familiar representations, e.g., wavelets, shearlets, and Gabor systems. This talk gives an introduction to generalized translation invariant (GTI) systems on LCA groups. We focus on characterizations of those generators of GTI systems that lead to convenient reproducing formulas. This talk is based on joint work with M.S. Jakobsen (TU Denmark).

The MUSIC algorithm for line spectral estimation: stability and super-resolution

When: Tue, April 8, 2014 - 2:00pm
Where: MATH 3206
Speaker: Wenjing Liao (Duke) -
Abstract: The problem of spectral estimation, namely – recovering the frequency
contents of a signal – arises in various fields of science and
engineering, including speech recognition, array imaging and remote
sensing. In this talk, I will introduce the MUltiple SIgnal
Classification (MUSIC) algorithm for line spectral estimation and
provide a stability analysis of the MUSIC algorithm. Numerical
comparison of MUSIC with other algorithms, such as greedy algorithms and
L1 minimization, shows that MUSIC combines the advantages of strong
stability and low computational complexity for the detection of
well-separated frequencies on a continuum. Moreover, MUSIC truly shines
when the separation of frequencies drops to one Rayleigh length and
below while all other methods fail. This is a joint work with Albert
Fannjiang at UC Davis.

TBA

When: Tue, April 15, 2014 - 2:00pm
Where: MATH 3206
Speaker: Vahid Reza Ramezan () -

Fourier Analysis on Graphs

When: Wed, April 30, 2014 - 1:00pm
Where: MATH 3206
Speaker: Matt Begue (UMD) - http://www2.math.umd.edu/~begue/
Abstract: Graph theory has developed into a useful tool in applied mathematics as many modern data sets are or can be represented as a graph. Motivated by the classical Harmonic Analysis in the Euclidean domain and empowered with the tools of spectral graph theory, we present some advancements and hurdles of time-frequency analysis on a graph domain as presented by Pierre Vandergheynst and collaborators.

The Mesner-Bhattacharya algebra of Hypermatrices and their spectral decomposition

When: Tue, May 6, 2014 - 2:00pm
Where: MATH 3206
Speaker: Edinah Gnang (Princeton-IAS) -
Abstract: In this talk we will present an overview of the hypermatrix generalization of matrix algebra proposed by Mesner and Bhattacharya in 1990. We will discuss a spectral theorem for hypermatrices deduced from this algebra as well as connections with other tensor spectral decompositions. Finally if time permits we will discuss some applications and related open problems. Joint work with Vladimir Retakh and Ahmed Elgammal.

Alpha-Molecules A Unified Concept for Sparse Approximations

When: Tue, May 13, 2014 - 2:00pm
Where: MATH 3206
Speaker: Sandra Keiper (TU Berlin) -
Abstract: Cartoon-like images are a well-studied class of functions that reasonably approximate natural images. They are typically defined to be functions in R2 (Hölder-) continuous onto two areas separated by an α-Hölder continuous boundary curve.

Well-known results show that both curvelets and shearlets optimally approximate cartoon functions whenever α equals 2. These results have usually been proven for each system separately. Recently, the α-molecules framework has been developed to include all known anisotropic frame constructions based on parabolic scaling, and this framework has unified sparse approximation results for the cartoon-like images.

In this talk we will introduce the concept of α-molecules and their advantages. The main result states that we can identify classes of representation systems which share the same nearly-optimal sparse approximation behavior for cartoon-like images. This is joint work with Philipp Grohs, Gitta Kutyniok and Martin Schöfer.