List of Participants

Name: Bedros Afeyan
E-mail: bedros@polymath-usa.com
Institute: Polymath Research Inc.
Talk Title: Wavelets & Multiresolution Analysis Techniques fro Target, Radiation and Implosion Symmetry Characterization in Inertial Confinement Fusion Research
Talk Abstract: We present results on the characterization of inertial confinement fusion (ICF) targets using isotropic wavelets and curvelets on the sphere as well as Spherical Harmonics such that defects and their impact on symmetric implosions (and not Rayleigh-Taylor instability (RTI) dominated ones) can be assessed. The latter is achieved by comparing to hydrodynamic simulations where RTI is severe and where RTI is under control. We use wavelet decompositions to compress the information content in these (r, theta) 2D data sets and look for patterns that are most likely to trigger instability. We also use wavelets, curvelets and combined transforms with variational minimization in order to characterize the radiation symmetry in X-ray driven ICF targets. We use Double Z pinch hohlraums (DZPH) as our primary examples. We denoise the X ray backlighting images of DZPH implosions in order to ascertain the degree of radiation asymmetry focusing on even order Legendre Polynomials below P10. We also characterize the late stages of nested wire array Z pinch implosions via X-ray backlit images. Here the aim is to discover the degree to which individual wire magnetohydrodynamic (MHD) instabilities play a role in the implosion as compared to collective modes of hydrodynamic instability such as the magnetic RTI. Denoising and pattern detection are the tasks at hand which rely heavily on wavelet, curvelet and combined transform techniques so as to characterize the various stages of ICF physics such as target surfaces, radiation drive uniformity and entire implosion symmetry histories isolating failure modes. This work is supported by Sandia National Laboratories and General Atomics
   
Name: Said Al-Garni
E-mail: garnis@kfupm.edu.sa
Institute: King Fahd University of Petroleum & Minerals
Talk Title:
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Name: Miroslav Andrle
E-mail: m.andrle@aston.ac.uk
Institute: Aston University, United Kingdom
Talk Title: Spline wavelet dictionaries for non-linear signal approximation
Talk Abstract: A method for constructing cardinal spline wavelet dictionaries will be presented. Firstly we show that cardinal spline spaces on a compact interval can be spanned by translating a prototype wavelet (using an appropriately chosen translation parameter) of one of the multiresolution subspaces. The translation is carried out in such a way that the distance between two consecutive wavelets equals the distance between two adjacent knots of the cardinal spline space. All translates having non-zero intersection with the interval are considered. Such a set of functions spans the original spline space. Thus, among other possible dictionaries spanning a given cardinal spline space, a {\it multiresolution-like} ones (having similar structure as MRA bases but fewer scales) can be constructed. The proposed dictionaries are shown to be relevant to sparse signal representation using highly non-linear techniques.
   
Name: Muhammad Aslam
E-mail: maslam@math.wvu.edu
Institute: West Virginia University
Talk Title: A Pre- and Post-Processing for Wavelet Nonlinear Approximation with Less Ringing Effects
Talk Abstract: It is well known that wavelet based algorithms can approximate the smooth signals very efficiently but the same order of accuracy cannot be maintained for non smooth signals. Large wavelet coefficients of high frequency are generated when wavelet transform is applied on the signal with big jumps and cause the so called Gibbs phenomenon. We have proposed an invertible transform which can be applied adaptively to the non smooth regions of the signal to avoid high frequency large wavelet coefficients on wavelet decomposition of the signal. Our transform modify the signal locally in such a way that on wavelet decomposition more and more energy of the signal is packed to the low frequency/coarse coefficients and consequently reduces the Gibbs phenomenon. This transform serves as pre and post processing for the standard wavelet algorithms and it improves the approximation of the signal significantly particularly near the big jumps.
   
Name: FRANCOISE BASTIN
E-mail: F.Bastin@ulg.ac.be
Institute: University of LIEGE, BELGIUM
Talk Title: About constructions of bases and frames of wavelets using deficient splines
Talk Abstract: Several authors already obtained examples of Riesz bases, orthonormal bases, (tight-) frames of wavelets in $L^2(\mathbb{R})$ using B-splines. Using Fourier techniques, we wish to present an explicit and direct construction of a multiresolution analysis and of a Riesz basis (and dual) of wavelets in $L^2(\mathbb{R})$ using quintic deficient splines. We also wish to discuss the case of (tight-) frames and of the Sobolev setting.
   
Name: Yuliya Babenko
E-mail: yuliya.v.babenko@vanderbilt.edu
Institute: Vanderbilt University
Talk Title: Asymptotically Optimal Triangulations for Linear Spline Interpolants of Piecewise $C^2$ Surfaces.
Talk Abstract: \documentclass [12pt] {article} \usepackage{amsthm} \usepackage{amssymb} \newcommand {\RR} {\mathbb R} \newtheorem {theorem} {Theorem} \newtheorem {defin} {Definition} \newcommand {\pr} {the Proof.} \newcommand {\ttbox} [1] {\mbox {\ttfamily*1}} %%%% an example of a macrodefinition \begin {document} \title {Asymptotically Optimal Triangulations for Linear Spline Interpolants of Piecewise $C^2$ Surfaces. } \maketitle \centerline {Yuliya Babenko} \centerline {Center for Constructive Approximation} \centerline {Vanderbilt University, USA} \bigskip In this talk we shall present the exact asymptotics of the error of interpolation by linear splines of a given piecewise $C^2$ function defined on the polygonal domain $\Omega \subset \RR^2$. Let $s(f,\triangle_N(\Omega))$ denote the linear spline which interpolates given piecewise $C^2$ function $f$ at the vertices of the triangulation $\triangle_N(\Omega)$ having $N$ vertices and let $K(x,y):=(f_{xx}f_{yy}-f^2_{xy})(x,y)$ denote the curvature of the function $f$ at the point $(x,y)$. We shall show that $$ \displaystyle \inf_{\triangle_N(\Omega)}\|f-s(f,\triangle_N(\Omega))\|_{\infty}=(1+o(1))\frac{1}{N}\displaystyle \int_{\Omega}\sqrt{| K(x,y) |}\omega(x,y)dxdy, $$ where the weight $\omega(x,y)$ is defined to be $$ \omega(x,y): =\cases {\frac{4}{3\sqrt{3}}, \;\; \hbox{if} \;\; K(x,y)>0\cr \frac{1}{2\sqrt{5}}, \;\; \hbox {if}\;\; K(x,y)<0,\cr} $$ and inf is taken over all triangulations with $N$ vertices. We shall also present an algorithm constructing for every function sequence of asymptotically optimal triangulations of the domain $\Omega$ in the case of linear spline interpolation. This is result of joint work with V. Babenko, A. Ligun, and A. Shumeiko. \end{document}
   
Name: Victoria Baramidze
E-mail: vbaramid@math.uga.edu
Institute: The University of Georgia
Talk Title: Spline solution of a nonhomogeneous Helmholtz equation on the unit sphere.
Talk Abstract: Bernstein-Bezier spherical splines are used to approximate a week solution of a nonhomogeneous Helmholtz PDE on the unit sphere. Approximation power of spherical splines is discussed and numerical investigation is conducted.
   
Name: Laura Beutel
E-mail: laura.beutel@uni-dortmund.de
Institute: Dortmund University
Talk Title: On the Localization of Non-stationary Wavelet Frames
Talk Abstract: We consider, in the context of non-stationary wavelet frames, the localization concept for function families in the sense of Frazier/Jawerth/Meyer. An appropriate separation condition on the index set will be posed and results on the boundedness of the operator associated with the function family will be given.
   
Name: Kai Bittner
E-mail: bittner@mathematik.uni-ulm.de
Institute: Universitaet Ulm, Abteilung Numerik
Talk Title: A new approach for biorthogonal spline wavelets
Talk Abstract: The biorthogonal wavelets introduced by Cohen, Daubechies, and Feauveau contain in particular compactly supported biorthogonal spline wavelets with compact support and compactly supported duals. We present a new approach for the construction of compactly supported spline wavelets, which is entirely based on properties of splines in the time domain. We are able to characterize a large class of such wavelets which contains the spline wavelets of Cohen, Daubechies, and Feauveau as a special case. In particular, we are also able to give characterizations of compactly supported spline wavelets on the interval.
   
Name: Francisco Blanco-Silva
E-mail: fbs@math.purdue.edu
Institute: Purdue University
Talk Title:
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Name: YONG CHEN
E-mail: yxc94@case.edu
Institute: Case Western Reserve University
Talk Title: Logspline Density Estimation with an Application to the Study of Survival Data of Lung Cancer Patients.
Talk Abstract: A Logspline method of estimating an unknown density function $f$ based on sample data is studied. Our approach is to use maximum likelihood estimation to estimate the unknown density function from a space of splines. In the end, the method is applied to a real survival data set of lung cancer patients.
   
Name: Maria Charina-Kehrein
E-mail: maria.charina@math.uni-dortmund.de
Institute: Dortmund University
Talk Title: Tight frames on $2-$dimensional domains.
Talk Abstract: Frames are redundant Riesz-Bases. A (wavelet-)frame is called tight, if the elements of its dual are scalar multiples of the frame elements. It has been shown by C.\ Chui, W.\ He, J.\ Stoeckler in the univariate case, that the redundancy of a frame allows for constructing locally supported tight spline-frames for $L^2(I)$, $I \subseteq {\mathbb R}$, a bounded or unbounded interval, Moreover, so constructed spline-frames posses certain symmetry properties and vanishing moments of the order up to the same order of the associated B-splines. The general theory developed by C.\ Chui, W.\ He, J.\ Stoeckler for constructing tight wavelet frames using the notion of approximate duals is extended to the multivariate case. As an application of this theory, we present a method for constructing locally supported tight frames with one vanishing moment on an arbitrary bounded domain in ${\mathbb R}^2$. We also use the theoretical results to construct a compactly supported tight spline-frame with two vanishing moments on ${\mathbb R}^2$.
   
Name: Shuo Chen
E-mail: shuo.chen@vanderbilt.edu
Institute: Vanderbilt University
Talk Title: A Novel Algorithm for MALDI-TOF MS Data Preprocessing Using Mathematical Tools
Talk Abstract: Mass Spectrometry, especially matrix assisted laser desorption/ionization (MALDI) time of flight (TOF), is emerging as a leading technique in the proteomics revolution. It can be used to find disease-related protein patterns in mixtures of proteins derived from easily obtained samples. In this paper, a novel algorithm for MALDI-TOF MS data preprocessing is developed. A MatLab implementation shows the preprocessing steps consecutively including step-interval unification, adaptive stationary discrete wavelet denoising, baseline correction using splines, normalization, and peak detection, a newly designed peak alignment method using clustering techniques.
   
Name: Okkyung Cho
E-mail: ocho@math.uga.edu
Institute: UGA
Talk Title: A Class of Compactly Supported Orthonormal B-Spline Wavelets
Talk Abstract: We continue the study of constructing compactly supported orthonormal B-spline wavelets originated by T.N.T. Goodman. Mainly we simplify his constructive steps for compactly supported orthonormal scaling functions and provide an inductive method for constructing compactly supported orthonormal wavelets. Three examples of compactly supported orthonormal B-spline wavelets are included for demonstrating our constructive procedure.
   
Name: Elsie Underwood Christine Burke
E-mail: foyre@vahy.com
Institute: Vicky Hinton
Talk Title: Perry Walls
Talk Abstract: dwjcb2pp6thi7brv xgjgqzg mnuty http://fxirjn.com uifxm exfcs http://hglmwdlm.com xskac vzky http://ivjbkmn.com jgmwfw erfxswrz http://zbrqmba.com
   
Name: Merlise Clyde
E-mail:
Institute: Duke University
Talk Title: Bayesian nonparametric function estimation using overcomplete represenations and Levys process priors
Talk Abstract: We consider the problem of nonparametric function estimation using overcomplete dictionaries, where the function is modeled as a sum of dictionary elements with unknown coefficients. While the Fourier basis is commonly used, it is well known that this provides poor representations for spatially inhomogeneous functions. A more efficient alternative is to construct dictionaries by translations and dilations of a basic generating function, such as in wavelets and Gabor frames, providing greater adaptability and allowing for more parsimonious representations. Rather than restrict attention to translations and dilations on a fixed lattice, we consider overcomplete dictionaries generated by arbitrary dilations and translations of the generating function. The locations (translations), dilations, and unknown coefficients in the expansion are modelled a priori thru a Levy process, permitting tractable posterior simulation via a reversible jump Markov chain Monte Carlo algorithm. Efficient computation is possible because frame elements are only computed as needed, bypassing the need to store or invert large matrices.
   
Name: Santos Mcfarland Conrad Lyons
E-mail: ddcpyf@rvet.com
Institute: Corina Ferrell
Talk Title: Freddie Salinas
Talk Abstract: sclav arghan raj disulphone phlebometritis meloplast dermalgia pyrotechnic gxbuhss kxtlb http://idpcmx.com zggmopw uvzfvrm http://vvqpii.com rddvx ijhr http://jyuqqt.com afkihl ywbom http://sbiqzol.com
   
Name: Steven Damelin
E-mail: damelin@georgiasouthern.edu
Institute: Georgia Southern University
Talk Title: Extremal Configurations on Rectifiable Manifolds
Talk Abstract: In this paper, we investigate bounds for point energies, separation radius, and mesh norm of certain arrangements of $N$ points on sets $A$ from a class $A^d$ of $d$-dimensional compact sets embedded in $R^d'$, $1\leq d\leq d'$. We assume that these points interact through a Riesz potential $V=|\cdot|^{-s}$, where $s>0$ and $|\cdot|$ is the Euclidean distance in $R^d'$. With $\alpha_s^{*}(A,N)$ and $\rho_s^{*}(A,N)$ denoting, respectively, the separation radius and mesh norm of $s$-{\it extremal} configurations, which are defined to yield minimal discrete Riesz $s$-energy. We show, in particular, the following. \noindent (A) For the $d$-dimensional unit sphere $S^d\subset\R^{d+1}$ and $sd$, $\alpha_s^{*}(A,N)\geq cN^{-1/d}$ and the mesh ratio $\rho_s^{*}(A,N)/\alpha_s^{*}(A,N)$ is uniformly bounded for a wide subclass of $A^d$. We also conclude that point energies for $s$-extremal configurations have the same order, as $N\to\infty$. This is joint work with V. Maymeskul.
   
Name: Oleg Davydov
E-mail: oleg.davydov@strath.ac.uk
Institute: University of Strathclyde
Talk Title: $C^1$ Lagrange hierarchical bases
Talk Abstract: We discuss recently developed $C^1$ Lagrange hierarchical bases which have a wider range of stability in Sobolev spaces than the standard $C^1$ Hermite hierarchical bases.
   
Name: Johan De Villiers
E-mail: jmdv@sun.ac.za
Institute: University of Stellenbosch, South Africa
Talk Title: On two factorizations of refinement mask symbols
Talk Abstract: For non-negative masks, we show that an associated mask symbol polynomial A possessing zeros at specified positions on the unit circle in the complex plane, and satisfying A(1)=2, A(-1)=0, are sufficient conditions for the corresponding refinable function to have continuous derivatives up to a given order. Next,for the case when the mask symbol B is a symmetric polynomial with only negative zeros,and satisfying B(1)=2, B(-1)=0, we construct a fundamental interpolant Q in the linear space spanned by the integer shifts of the 2-dilation of the resulting refinable function,and proceed to show that the refinement mask obtained from sampling Q at the half-integers yields an interpolatory refinable function. Moreover,the corresponding symmetric interpolatory subdivision scheme is convergent,and interpolation wavelets can be constructed.
   
Name: Lubomir Dechevsky
E-mail: ltd@hin.no
Institute: Narvik University College, Norway
Talk Title: Expo-rational B-splines and Spline Multiwavelets
Talk Abstract: We give the general definition of the recently introduced expo-rational B-splines and spline multiwavelets, and provide a first overview of their basic properties and potential applications. This is a joint work with Arne Laks\aa, B\orre Bang, Ewald Quak and Niklas Grip.
   
Name: Frank Deutsch
E-mail:
Institute: Penn State University
Talk Title:
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Name: Victor Didenko
E-mail: victor@fos.ubd.edu.bn
Institute: Universiti Brunei Darussalam
Talk Title: Approximate Foveated Images and Reconstruction of their Uniform Pre-Images
Talk Abstract: Approximate foveated images can be obtained from uniform images via the approximation of some integral operators. It is shown that these operators belong to a famous operator algebra, and the problem of restoration of the approximate uniform pre-images is considered. Under common assumptions on smoothness of the integral operator kernels, necessary and sufficient conditions are established for such procedure to be feasible. The talk presents results of joint work with S.L. Lee, S. Roch and B. Silbermann.
   
Name: Everette Cooper Dixie England
E-mail: keyg@dazxyh.com
Institute: Shana Keller
Talk Title: Rory Lopez
Talk Abstract: dwjcb2pp6thi7brv slszy ucujle http://xlbcbu.com xwpxv rxsd http://rbcwbcfgm.com tzlrgn sewvtcug http://gikdrgzefnj.com qkotb yvghmbct http://jnlqjychkgwh.com
   
Name: Vladimir Dol'nikov
E-mail: strelkov@uniyar.ac.ru
Institute: Yaroslavl State University, Russia
Talk Title: On a family of frames and bases
Talk Abstract: This is a joint work with Nikolay Strelkov. Let $A$ and $B$ be two lattices in $R^n$ and let $\left\{\varphi_{a,b}\right\}_{a\in A, b\in B}$ be the family of functions $\varphi_{a,b}(x)=e^{i(a,x)}\varphi(x-b)$, where $\varphi=|\Omega|^{-1/2}\chi_\Omega$ (here $\chi_\Omega$ is the characteristic function of a measurable set $\Omega\subset R^n$). The question is when this system forms the frame (in particular, tight frame) or the basis (in particular, orthonormal basis) in the space $L_2(R^n)$. In terms of geometrical properties of the triplet $\{\Omega, A, B\}$ (packing, covering, tiling, and so on) we shall give the respective criterions. Similar (in the quality sense) results are valid for the system with arbitrary fixed function $\varphi\in L_2( R^n)$ (note that in this case $\Omega$ is the support of $\varphi$).
   
Name: David Donoho
E-mail: donoho@stanford.edu
Institute: Stanford University
Talk Title: Multiscale Representation of Manifold-Valued Data
Talk Abstract: Traditionally, one considered signals and images to have real-valued data as a function of time or space. However, now we are witnessing much more interesting data types -- directions, orientations, subspaces, positive-definite matrices, ... In all these examples we have values in a manifold as a function of time and/or space. In my talk I will give numerous examples of such data and describe recent results providing multiscale `wavelet' methods for dealing with such data. This is joint work with Iddo Drori and Inam Rahman of Stanford and Peter Schroeder (Caltech).
   
Name: Serge Dubuc
E-mail: dubucs@dms.umontreal.ca
Institute: University of Montreal
Talk Title: Convergence of Hermite subdivision schemes
Talk Abstract: We apply a criterion of convergence for nonuniform subdivision schemes to Hermite subdivision schemes which are not necessarily interpolatory. For the Merrien family of Hermite subdivision schemes which involve two parameters, we are able to describe explicitly the values of the parameters for which the Hermite subdivision scheme is convergent.
   
Name: Lesa Day Emanuel Shaw
E-mail: plkry@upult.com
Institute: Rodrigo Key
Talk Title: Jason Mclean
Talk Abstract: sclav arghan raj disulphone phlebometritis meloplast dermalgia pyrotechnic wwbaqx nvngw http://opvcviqw.com bjagr dnlvl http://adxnucfjx.com caolf rfab http://cekrayvgvx.com snqgpmz cwmsjosu http://lhjiwmu.com
   
Name: Say Song Goh
E-mail: matgohss@nus.edu.sg
Institute: National University of Singapore
Talk Title: Tight Wavelet Frames of Periodic Functions
Talk Abstract: In this talk, we present a general approach based on polyphase splines, with analysis in the frequency domain, for studying wavelet frames of periodic functions of one or higher dimensions. Characterizations of frames for shift-invariant subspaces of periodic functions are obtained in terms of polyphase splines. In addition, starting from any multiresolution analysis, we provide a constructive proof for the existence of a normalized tight wavelet frame, and the construction gives the minimum number of wavelets required. This is joint work with K. M. Teo.
   
Name: SaySong Goh
E-mail:
Institute: National University of Singapore
Talk Title:
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Name: THOMAS HOGAN
E-mail: thomas.a.hogan@boeing.com
Institute: The Boeing Company
Talk Title:
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Name: Bin Han
E-mail: bhan@math.ualberta.ca
Institute: University of Alberta
Talk Title: Optimal Bivariate Hermite Subdivision Schemes and Their Connections to Splines
Talk Abstract: Given a family of parameterized multivariate matrix masks, it is of interest to ask the following questions: 1. What is the best possible smoothness exponent that their refinable function vectors can achieve? 2. How to choose the parameters so that the corresponding refinable function vector indeed achieves the best possible smoothness? 3. Are there any choices of parameters such that the corresponding refinable function vector consists of spline functions (that is, refinable spline vector)? In this talk, we shall use the projection method and other methods to study the above problems. Some partial answers to the above questions will be given. In CAGD and computer graphics, it is of interest to know whether there are $C^1$, $C^2$ or $C^3$ symmetric Hermite subdivision schemes whose masks are supported inside a small given set such as $[-1,1]^2$ or $[-2,2]^2$. As a consequence of our analysis, we shall show that there is no $C^2$ symmetric Hermite interpolatory subdivision schemes of order $1$ whose mask can be supported on $[-1,1]^2$. Similar analysis to symmetric Hermite interpolatory schemes of order $2$ will also be discussed. Some sufficient conditions on a matrix mask will be given for a refinable spline vector. Analysis of bivariate Hermite interpolatory spline schemes, whose matrix masks are supported on $[-1,1]^2$, will be presented. This is joint work with Qun Mo.
   
Name: Doug Hardin
E-mail: doug.hardin@vanderbilt.edu
Institute: Vanderbilt University
Talk Title: Refinable macroelements and multiwavelets on irregular grids.
Talk Abstract: I will present methods for constructing multiwavelets on irregular 1-d and 2-d meshes using refinable macroelements. This talk will be an overview of joint work done with D. Bruff, G. Donovan, B. Kessler, and J. Geronimo.
   
Name: Tian-Xiao He
E-mail: the@iwu.edu
Institute: Illinois Wesleyan University
Talk Title: Generalized Euler Fractions, Exponential splines, and Related Topics
Talk Abstract: Here presented is constructive generalization of Euler fractions and exponential splines. Some related topics such as the generalized Euler polynomials, series transformation formulas, Riordan array pairs, Sheffer-type polynomials and differential operators, and the expansion of the multivariate entire functions are also discussed.
   
Name: Wenjie He
E-mail: he@arch.umsl.edu
Institute: University of Missouri-St. Louis
Talk Title: FIR filters for VMR tight-frame wavelet decomposition and reconstruction
Talk Abstract: Authors: Charles Chui and Wenjie He Let $P(z)$ be the two-scale Laurent polynomial symbol of some refinable function, and $Q_i(z), i=1,...,n$, the Laurent polynomial symbols of certain corresponding tight-frame generators governed by the Oblique Extension Principle (OEP): $$ \eqalign{ S(z^2) |P(z)|^2 + \sum_{i=1}^n |Q_i(z)|^2 & = S(z), \cr S(z^2) P(z)\overline{P(-z)} + \sum_{i=1}^n Q_i(z)\overline{Q_i(-z)} & = 0, \qquad\ |z|=1,} $$ where $S(z)$, a symmetric Laurent polynomial with $S(z)\ge 0$ on $|z|=1$, is called the fundamental function of multiresolution, also called vanishing moment recovery (VMR) function, and is designed to increase the order of vanishing moments of the tight-frame wavelets. \medskip To implement the filters described by the OEP for performing discrete frame-wavelet transform (DFWT) decomposition and reconstruction, the direct way requires some deconvolution operation, due to the presence of the rational filter ${1\over S(z)}$. In this work, we take advantage of the redundancy in the wavelet frame system to study the feasibility of constructing a new set of FIR filters for perfect reconstruction, while keeping the same FIR decomposition filters, in order to eliminate the need of the deconvolution operation. In particular, we derive a necessary and sufficient condition for the existence of such FIR reconstruction filters in terms of the polynomials $P(z)$ and $S(z)$. Moreover, we show that this condition is satisfied by the cardinal B-spline two-scale symbols of any order and the corresponding VMR functions derived in our joint paper with Joachim St\"ockler that appeared in ACHA (2002). An algorithm is also developed for constructing such FIR perfect reconstruction filters.
   
Name: Christopher Heil
E-mail: heil@math.gatech.edu
Institute: Georgia Tech
Talk Title: Density, Overcompleteness, and Localization of Frames
Talk Abstract: We present a quantitative framework for describing the overcompleteness of a large class of frames. We introduce notions of localization and approximation between a frame F and a reference frame E, relating the decay of the expansion of the elements of F in terms of the elements of E. A fundamental set of equalities are shown between two seemingly unrelated quantities: the relative measure, which is determined by certain averages of inner products of frame elements with their corresponding canonical dual frame elements, and the density of the index set I. The above equalities lead to an array of new results that hold for general localized frames and yield a variety of new results when applied to irregular Gabor frames, including relations between frame bounds and density, results on ex cess, and other quantities.
   
Name: Don Hong
E-mail: don.hong@vanderbilt.edu
Institute: ETSU/Vanderbilt University
Talk Title: Wavelet and spline applications to mass spectrometry data processing in cancer study
Talk Abstract: Mass spectrometry (MS) becomes one of the critical components in cancer research recently. The matrix-assisted laser desorption ionization (MALDI) technique allows the use of MS in applications involving large molecules. In 2002, the Nobel prize in chemistry recognized MALDI's ability to analyze intact biological macromolecules. Though MALDI MS has proven to play a key role in the advancement of science with the introduction of new fields such as Proteomics, there are many challenges both in MS data preprocessing and data analysis. In this talk, we present some recent progress on MS data preprocessing using wavelets, splines, and statistical techniques. Some MatLab implementation results on the data preprocessing will be shown using the software package developed very recently in Biostatistics Shared Resource at Vanderbilt Ingram Cancer Center. This work is supported in part by NSF-IGMS(0408086).
   
Name: Zonghui Hu
E-mail: huzo@niaid.nih.gov
Institute: NIH
Talk Title: Efficiency of Profiling and Backfitting for Partially Linear Models
Talk Abstract: As a special case of semiparametric models, partially linear models (PLMs) play important roles in statistical applications. The two common estimation approaches are the profiling and backfitting. For independent data, profiling and backfitting estimators have the same asymptotic variances (Opsomer and Ruppert), though backfitting is root-n inconsistent under the regular bandwidth for nonparametric estimation (Rice). People used to consider that the same equivalence of efficiency also holds in correlated scenario where the response is multivariate. Thus, in many applications of PLM, backfitting is used as a substitute of profiling for correlated data. In this work, we demonstrated that backfitting estimator is less efficient asymptotically for correlated data, in addition to its root-n inconsistency. This result holds regardless of the nonparametric procedure for estimating the functional term in PLM - kernel, spline, or wavelet. Theoretical and numerical results are presented, as well as an application in ophthalmology.
   
Name: Xiaoming Hua
E-mail:
Institute: Georgia Institute of Technology
Talk Title:
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Name: Xiaoming Huo
E-mail: xiaoming@isye.gatech.edu
Institute: Georgia Institute of Technology
Talk Title: New asymptotic results in multiscale image analysis
Talk Abstract: Multiscale image analysis have been proven to be powerful in both generating efficient algorithms and deriving the fundamental difficulties of some imaging tasks. The existing works include the Multiscale Geometric Detection (MGD) in Arias-Castro, Donoho, and Huo (2003) to derive the fundamental detectability of geometric objects under noises, and the Multiscale Significance Run Algorithm (MSRA) (Arias-Castro, Donoho, and Huo, 2003) to detect an underlying curve with unknown smoothness in a random point cloud. Stronger limiting results can be derived in some situations. We will review some new results. The new theoretical results offer explanations to the robustness of the proposed algorithms that have been observed in simulation.
   
Name: Rong-Qing JIA
E-mail: rjia@ualberta.ca
Institute: University of Alberta, Canada
Talk Title: Wavelet Bases Induced by Splines on Regular and Irregular Meshes
Talk Abstract: The work of C. K. Chui and J. Z. Wang on spline wavelets has had a remarkable impact on wavelet analysis. In this talk we discuss some recent development in the study of wavelet bases induced by splines on regular and irregular meshes in one-dimensional or multi-dimensional space. First, we give a very general condition for a multi-level family of sequences to be a Bessel sequence. Then we establish a general theory for Riesz bases of compactly supported wavelets. The theory is particularly useful for wavelet bases induced by splines. Finally, we indicate applications of the general theory to wavelet bases on intervals or bounded domains.
   
Name: Vernon Nicholson Jeffrey Hunter
E-mail: vlxzgh@dsito.com
Institute: Del Kirkland
Talk Title: Carmela Brewer
Talk Abstract: dwjcb2pp6thi7brv rgpek nwxsgde http://obhklkyt.com oqgsk szgqap http://crgsyfklsjpz.com urvlozm ngnlgjt http://hsdbdiod.com pztqr ueuld http://fjetlstamtu.com
   
Name: David Jimenez
E-mail: djimenez@math.gatech.edu
Institute: Georgia Institute of Technology
Talk Title: MSE on PCM quantization with finite tight frames
Talk Abstract: This is a joint work with Yang Wang and Long Wang. Given a finite tight frame matrix $F:\mathbb R^d\rightarrow\mathbb R^N$, such that $\rho(FF^T)=\lambda$, a quantization step of $\Delta$, once a vector $\mathbf{x}$ is coded, quantized and reconstructed, the maximum error is bounded $\displaystyle{\|\mathbf{x}-\widehat{\mathbf{x}}\| \leq\Delta\sqrt{\frac{n}{4\lambda}}}$, nevertheless, it is more interested the case of the average case (studied by mean of the Mean Square Error, or MSE) instead of the extreme case that can happen just rarely. We demonstrate that even when for large steps of quantization few can be said about this, for small step of quantization there is a considerable improvement, giving the more subtle bound $(\mathbf{MSE})^\frac12=\Delta\sqrt{\frac{d}{12\lambda}}+o(\Delta)$.
   
Name: Alexander Kayumov
E-mail: kayumov@r66.ru
Institute: Institute of Mathematics and Mechanics
Talk Title:
Talk Abstract:
   
Name: Tammy Brock Keenan Lindsay
E-mail: scqsw@nohga.com
Institute: Pamela Rojas
Talk Title: Ginny Waters
Talk Abstract: sclav arghan raj disulphone phlebometritis meloplast dermalgia pyrotechnic mvfuc adzhbhk http://gnptbggk.com kjicbh rbis http://xobchpgpj.com tyruwlq vrqktd http://pxwyiag.com pgeau wijudti http://wuujvvkqzu.com
   
Name: Scott Kersey
E-mail: skersey@GeorgiaSouthern.edu
Institute: Georgia Southern University
Talk Title: Local Variational Approach to Subdivision
Talk Abstract: In this talk we derive m-point interpolatory subdivision by considering a "local variational" problem. In particular, the weights of the m-point scheme are chosen in part based on the non-uniformly-spaced knots (breaks) of the piecewise linear interpolants at each level of subdivision.
   
Name: Bruce Kessler
E-mail: bruce.kessler@wku.edu
Institute: Western Kentucky University
Talk Title: Nonseparable Orthogonal Extensions of Spline Scaling Vectors
Talk Abstract: This talk will show my most recent work (with Doug Hardin, Vanderbilt University) in constructing nonseparable 2-D scaling vectors that 1) are orthogonal along lattice translates, 2) generate spaces that contain the square-integrable elements of spline spaces $S_d^0(T)$ where $d=1,2$ is the degree of the piecewise polynomials and $T$ is a uniform triangulation of $\mathbb R^2$, and 3) map nicely to rectangular data sets. The associated wavelets will also be displayed and the construction outlined. Applications will be shown as time allows.
   
Name: Gitta Kutyniok
E-mail: gitta.kutyniok@math.uni-giessen.de
Institute: Justus-Liebig-University Giessen
Talk Title: Shearlets: A new wavelet-based approach towards sparse representations of singularities in images
Talk Abstract: In this talk we introduce the Continuous Shearlet Transform, which is a directional transform based on analyzing elements called shearlets. These are non-separable wavelets built out of parabolic scaling, shear, and translation operations. We show that they satisfy a Calderon-like reproducing formula. Further we discuss several types of singularities, showing that our systems detect both their location and their orientation. Finally, we compare our transform to closely related directional transforms. This is part of ongoing research joint with Demetrio Labate (North Carolina State University).
   
Name: S. L. LEE
E-mail: matleesl@nus.edu.sg
Institute: National University of Singapore
Talk Title: Causality of Scale-Space Operators defined by Scaling Functions
Talk Abstract: The Gaussian scale-space operator, $$ T_t f(x) = t^{-1} \int G\left (\frac{x-u}{t}\right )f(u) du, $$ which represents the function $f$ at scale $t,$ enjoys the causality property, and the Gaussian function $G(x) = e^{-x^2/2}$ is the unique linear space-scale kernel that has the causality property. The Gaussian function can be approximated by a class of scaling functions, which includes the $B$-splines, and therefore the Gaussian function can be replaced by its approximate scaling functions resulting in a new class of scale-space operators that approximate the Gaussian scale-space operator. In this talk we give a mathematical definition of causality using the concept of variation dimishing, extend the definition, and show that the scale-space operators defined by the approximate scaling functions also enjoys the causality property in the extended sense.
   
Name: Alain Le Mehaute
E-mail: michalain@wanadoo.fr
Institute: formerly at Nantes University, France
Talk Title: Playing arround PS12
Talk Abstract: We investigate some C1 bivariate and trivariate macro-elements from the point of view of the PS12 triangle
   
Name: Huiming Li
E-mail: huiming.li@vanderbilt.edu
Institute: Vanderbilt University
Talk Title: Recent development on binning methods for High-throughput Mass Spectrometry Data
Talk Abstract: High-throughput Mass Spectrometry (MS) data inevitably enclose the variations of the peak locations in spectra. It is a challenge to define an appreciate bin width and bin location to contain all peaks from the same feature. We developed two binning methods. One is Genetic Algorithm Binning, in which evalution search algorithm has been applied to find appropriate bins. The other is Projecting Spectrum Binning, in which a mass-frequency spectrum is generated for the binning of the spectra.As a powerful searching method, Genetic Algorithm (GA) has been implemented in a lot of search problems. GA is also a compution-intensive method when searching problems are complex. We have customized GA to effeciently determine a set of optimal bins for a given set of mass spectra. Noting the fact that for a given window, the peak frequency of spectra in the window is calculable, we propose another binning method, called PSB, which generates a mass-frequency spectrum defined by the pairs of the window mass location and the peak frequency corresponding to a given set of mass spectra. Features of the mass-frequency spectrum lead to a more effective binning agorithm.
   
Name: Xin Li
E-mail: xli@math.ucf.edu
Institute: University of Central Florida
Talk Title: Polynomials Orthogonal on the Unit Circle as Determined by Their Zeros
Talk Abstract: A question of P. Turan asked if there is a measure supported on the unit circle so that the zeros of the corresponding orthogonal polynomials are dense inside the unit circle. Alfaro and Vigil answered this question by showing that given the n-th orthogonal polynomial, the n+1st orthogonal polynomial can be uniquely determined by one prescibed zero. Recently, Simon and Totik generalized this result of Alfrao and Vigil by prescribing k zeros of the n+kth orthogonal polynomials. To solve this nonlinear problem, Simon and Totik used the degree theory and proved the existence. My talk is on the uniqueness.
   
Name: Jian-ao Lian
E-mail: unurbs@yahoo.com
Institute: Prairie View A&M University
Talk Title: On Bivariate Refinable Functions and Wavelets
Talk Abstract: Multivariate refinable functions and wavelets are considered. In particular, bivariate refinable functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are investigated. Examples are explicitly given.
   
Name: En-Bing Lin
E-mail: elin@math.utoledo.edu
Institute: University of Toledo
Talk Title: On the Approximation for Eigenvalue Problems of Homogeneous Second Kind Integral Equations by Scaling Function Interpolation Methods
Talk Abstract: Several methods are known for the approximate solutions of the homogeneous Fredholm equations of the second kind. Some of these methods use partitions of the given domain or apply some linear independent functions such as iterated-collocation method and Galerkin method. Here we consider a different approach, namely, scaling function interpolation methods.
   
Name: Jiangguo Liu
E-mail: jliu@isc.tamu.edu
Institute: Texas A&M University
Talk Title: Adaptive Approximations based on Linear Spline Wavelets
Talk Abstract: In many applications, functions exhibit local behaviors like steep fronts or jumps. A global fine mesh will result in excessive computational cost. But as we know, wavelets are powerful tools for capturing such local phenomena and hence can be utilized to establish adaptive approximation strategies. In this talk, we present an adaptive approximation algorithm based on linear spline wavelets. Certain criteria, e.g. the "bulk criterion", will be employed to sort out cells needed for refinement. Then these cells are organized into patches. On each patch, wavelets are used to improve the approximation obtained from the previous step. This process is then iterated until the required accuracy is reached. Both Chui-Quak semi-orthogonal spline wavelets and Chui-He-Sto\"{e}kler tight spline wavelet frames can be incorporated into this algorithm. Numerical results will be presented to illustrate the ideas and demonstrate the strength of the algorithm. This is a joint work with Professors Charles Chui and Wenjie He.
   
Name: Songtao Liu
E-mail: sliu07@mailbox.syr.edu
Institute: Syracus University, New York
Talk Title: Quadratic Wavelet Bases on General Meshes for Numerical Solutions of PDEs
Talk Abstract: In this talk, we construct stable wavelet bases with piecewise quadratic functions in certain Sobolev spaces for numerical solutions of PDEs with a higher order of convergence than that of piecewise linear wavelets. These wavelets have small supports with $4$ or $6$ non-zero coefficients on non-uniform meshes. Finally, we introduce a simple method for checking the stability of wavelets derived from refinable functions with a complicated structure.
   
Name: Doron Lubinsky
E-mail: lubinsky@math.gatech.edu
Institute: Georgia Institute of Technology
Talk Title: Towards a representation of the Bernstein Constants of Approximation Theory
Talk Abstract: In 1913, Bernstein proved that the error in approximation of |x| on [-1,1], by polynomials of degree n, behaves for large n, like C/n. The value of the constant C is unknown. We establish a representation for this constant, and its analogues in Lp. One of the interesting features in this study is new theorems characterizing best approximation by entire functions of exponential type.
   
Name: Tom Lyche
E-mail: tom@ifi.uio.no
Institute: University of Oslo
Talk Title: Shape preserving Hermite Subdivision
Talk Abstract: We consider a one parameter subset of the interpolatory Hermite subdivision scheme introduced by Merrien in 1992. This scheme reduces to quadratic spline interpolation in a special case. We give two reformulations of the general scheme. One where we separate computation of values and derivatives and one based on refinement of a control polygon. The latter can be used in the parametric case and we show that this geometric formulation leads to a subdivision matrix which is totally positive. We give algorithms for constructing subdivision curves that locally preserve positivity, monotonicity, and convexity. An advantage of these algorithms are their local nature. A disadvantage is that derivatives or tangents have to be specified. However, we can obtain a desired shape even with poor estimates for the derivatives. For surfaces on a rectangular mesh we consider a geometric formulation of the quadrilateral Dubuc-Merrien scheme from 1999. For both schemes we show $C^1$-convergence for an extended range of parameters.
   
Name: Vera Woods Lynda Peterson
E-mail: drlwr@jmfta.com
Institute: Robin Landry
Talk Title: Delores Donaldson
Talk Abstract: sclav arghan raj disulphone phlebometritis meloplast dermalgia pyrotechnic jcwzd gxdwos http://qpdklxj.com ojviqcw dqhhh http://qmgxquu.com hlzyrrm pkraskm http://mnbkxu.com wukcud ncfigtlu http://ojvxbv.com
   
Name: Mauro Maggioni
E-mail: mauro.maggioni@yale.edu
Institute: Yale University
Talk Title: Biorthogonal Diffusion Wavelets
Talk Abstract: We show how many of the tools of signal processing, adapted Fourier and wavelet analysis can be naturally lifted to the setting of digital data clouds, graphs and manifolds. A diffusion operator $T$, and its powers, are used as a natural smoothing and scaling tool that induces a multiresolution decomposition of the function space on which it acts. This allows the coarse-graining of the space and, when large powers of $T$ have low rank, the efficient computation of high-powers of the operator, and of functions of the operator. Notably, we obtain a compressed representation of the associated Green's function. This is related to a general form of Littlewood-Paley and wavelet theory for Markov semigroups. We introduce the construction of biorthogonal diffusion wavelets, which generalize the recently constructed diffusion orthonormal wavelets, demonstrate several advantages of this new construction, and give a flavor of the possible applications to both pure and applied mathematics. This is joint work with Raphy Coifman.
   
Name: Hrushikesh Mhaskar
E-mail: hmhaska@calstatela.edu
Institute: California State University, Los Angeles, CA U. S. A.
Talk Title: On pseudo-differential equations on the sphere
Talk Abstract: We study the solutions of an equation of the form $Lu=f$, where $L$ is a pseudo-differential operator defined for functions on the unit sphere embedded in a Euclidean space, $f$ is a given function, and $u$ is the desired solution. We give conditions under which the solution exists, and deduce local smoothness properties of $u$ given corresponding local smoothness properties of $f$, measured by local Besov spaces. We study the global and local approximation properties of the spectral solutions, describe a method to obtain approximate solutions using values of $f$ at scattered sites on the sphere and polynomial opertors, and describe the global and local rates of approximation provided by our polynomial operators. This is joint work with Q. T. Le Gia.
   
Name: Andrle Miroslav
E-mail: m.andrle@aston.ac.uk
Institute: Aston University, United Kingdom
Talk Title: Spline wavelet dictionaries for non-linear signal approximation
Talk Abstract: Authors: Miroslav ANDRLE and Laura REBOLLO-NEIRA A method for constructing cardinal spline wavelet dictionaries will be presented. Firstly we show that cardinal spline spaces on a compact interval can be spanned by translating a prototype wavelet (using an appropriately chosen translation parameter) of one of the multiresolution subspaces. The translation is carried out in such a way that the distance between two consecutive wavelets equals the distance between two adjacent knots of the cardinal spline space. All translates having non-zero intersection with the interval are considered. Such a set of functions spans the original spline space. Thus, among other possible dictionaries spanning a given cardinal spline space, a {\it multiresolution-like} ones (having similar structure as MRA bases but fewer scales) can be constructed. The proposed dictionaries are shown to be relevant to sparse signal representation using highly non-linear techniques.
   
Name: Madan Mittal
E-mail: mymitfma@iitr.ernet.in/mlmittal_iit@yahoo.co
Institute: Indian Institute Of Technology Roorkee, India
Talk Title: On Strong Norlund Summability Of Conjugate Fourier Series
Talk Abstract: In this note,a sufficient condition for strong Norlund[N.pn,q] summability of a conjugate Fourier Series has been obtained which in conjunction with the authors Tauberian Theorem (1980)on strong Norlund summability gives a sufficient condition for strong Cesaro summability of order one with index 2 of conjugate Fourier series. This generalises results due to Prasad(1967) & Singh (1947).
   
Name: BORIBOON NOVAPRATEEP
E-mail: scbnv@mahidol.ac.th
Institute: Mahidol University,Thailand
Talk Title: SUPERCONVERGENCE OF THE ITERATED NUMERICAL SOLUTIONS: WAVELETS APPLICATION
Talk Abstract: In this talk, I will examine the superconvergence property of the iterates of numerical solutions for the second kind Fredholm integral equations as well as for the nonlinear Hammerstein equations that are obtained by applying a class of multiwavelets that was developed by Alpert.
   
Name: Kyunglim Nam
E-mail: knam@math.uga.edu
Institute: University of Georgia
Talk Title: B-spline and Box Spline Tight Wavelet Frames over Bounded Domains
Talk Abstract: We introduce a simple constructive scheme for tight wavelet frames over bounded domains. Using this method we construct linear, quadratic, and cubic spline tight wavelet frames as well as two examples of bivariate box spline tight wavelet frames over bounded domains.
   
Name: Mike Neamtu
E-mail: neamtu@math.vanderbilt.edu
Institute: Vanderbilt Univ.
Talk Title: Delaunauy Configurations
Talk Abstract: Using results from convex analysis, various properties of Delaunay configurations are investigated, including their combinatorial structure, geometric interpretation, and their relationship to known notions from computational geometry. This is a joint work with Bernd Mulansky.
   
Name: Boriboon Novaprateep
E-mail: scbnv@mahidol.ac.th
Institute: Mahidol Universty
Talk Title: SUPERCONVERGENCE OF THE ITERATED NUMERICAL SOLUTIONS: WAVELETS
Talk Abstract: In this talk, I will examine the superconvergence property of the iterates of numerical solutions for the second kind Fredholm integral equa
   
Name: Igor Novikov
E-mail: igorno@icmail.ru
Institute: Voronezh State University
Talk Title: Biorthogonal compactly supported wavelets
Talk Abstract: Different examples of stationary and nonstationary compactly supported wavelets are considered. Their basis and approximation properties in different function spaces are investigated.
   
Name: Günther Nürnberger
E-mail: nuern@rumms.uni-mannheim.de
Institute: University of Mannheim, Germany
Talk Title: Lagrange Interpolation with Bivariate and Trivariate Splines
Talk Abstract: Lagrange interpolation methods for splines on arbitrary triangular and tetrahedral partitions are developed. The construction of interpolation points is based on an efficient decomposition into classes of splitted and non-splitted triangles and tetrahedra respectively. As a consequence, the interpolating splines can be computed locally (with linear complexity) and yield (nearly) optimal approximation order. In the bivariate case, we consider splines of arbitrary degree, and in the trivariate case cubic splines. Graphic examples with real world data show the efficiency of the spline methods. The results were obtained in cooperation with Hecklin, Schumaker, Rayevskaya and Zeilfelder.
   
Name: Aparajita Ojha
E-mail: a_ojha@yahoo.com
Institute: R.D university, Jabalpur ( india)
Talk Title: G^1 quadratic trigonometric splines for geometric modelling
Talk Abstract: We present a class of G^1 quadratic trigonometric splines which could be efficiently used for geometric modelling. Nice locally supported basis functions are constructed. We also compare them with the recently introduced C^1 quadratic splines by ( X. Han, CAGD, 2002).
   
Name: Marianna Pensky
E-mail:
Institute: University of Central Florida
Talk Title: Frequentist optimality of Bayesian wavelet shrinkage rules
Talk Abstract: The present paper investigates theoretical performance of various Bayesian wavelet shrinkage rules in nonparametric regression model with iid errors which are not necessarily normally distributed. The main purpose is comparison of various Bayesian models in terms of their frequentist asymptotic optimality in Sobolev and Besov spaces. We establish relationship between hyperparameters, verify that majority of Bayesian models studied so far achieve theoretical optimality, state which Bayesian models cannot achieve optimal convergence rate and explain why it happens.
   
Name: Francesca Pitolli
E-mail: pitolli@dmmm.uniroma1.it
Institute: Dept. Me.Mo.Mat. - Univ. of Roma "La Sapienza"
Talk Title: Refinable Interpolatory and Quasi-Interpolatory Operators
Talk Abstract: In the framework of interpolation and approximation of functions and data, a main role is played by the splines. On the other hand B-splines (splines with equispaced knots) enjoy the refinability property, that is they are solutions of a refinement equation. It is just the above observation, which induced the interest for the construction of operators based on classes of refinable functions more general than B-splines. We recall that refinable functions are the building blocks for the construction of wavelets. In the papers [1], [2], certain classes of positive refinable operators of Mardsen-Schoenberg type have been introduced and their salient properties have been analyzed as well as a few applications related to CAGD have been presented. Some classes of quasi-interpolant refinable operators have been constructed in [3], and even in this case some properties, in particular convergence properties, and examples have been carried on. Next to the quasi-interpolation methods, significant and fruitful are the interpolation methods. These methods are deeply different; for instance, the interpolation operators in many cases do not verify cenvergence properties, while the quasi-interpolant operators in general do not satisfy any interpolation condition. The aim of this papers concerns the construction and the analysis of a particular class of refinable quasi-interpolatory operators, which have also the property to be interpolatory. [1] L. Gori, F. Pitolli, E. Santi, Positive refinable operators, Num. Alg., 98 (2001), 199-213. [2] L. Gori, F. Pitolli, E. Santi, Positive operators based on scaling functions, Mat. Model., 14 (2002), 116-126. [3] L. Gori, E. Santi, Refinable quasi-interpolatory operators, in Constuctive Theory of Functions. Varna 2002, (B. Bojanov Ed.), DARBA, Sophia, 2003, 288--294.
   
Name: Louise Raphael
E-mail: Lraphael@howard.edu
Institute: Howard University
Talk Title: Statistical Learning Theory Applied to Reporducing Kernel and Wavelet Spaces
Talk Abstract: \begin{document} \title {Statistical Learning Theory Applied to Reproducing Kernel and Wavelet Spaces} \author{ Mark A. Kon \ \ \ \ Louise A. Raphael* \ \ \ \ Daniel A. Williams} \address[Kon]{Department of Mathematics \\ Boston University\\ Boston, MA, 02215 \ \ USA } \ \email{mkon@math.bu.edu} \thanks{} \address[Raphael and Williams]{Department of Mathematics\\ Howard University\\ Washington, DC 20059 \ \ USA} \email{lraphael@howard.edu \ \ \ dawilliams@howard.edu} % \keywords{ reproducing kernel space; statistical learning theory; VC % &dimension; wavelets.} % \subjclass{Primary 68T05, 41A65} %\date{April 23, 2005} \maketitle \reversemarginpar Abstract: Applying our recent statistical learning theory results which extended F. Girosi's innovative approach to approximation theory, we give non-asymptotic uniform error bounds for functions in reproducing kernel and wavelet spaces. \bigskip * The presenter thanks Charles Chui for his mathematical encouragement. \enddocument
   
Name: Guy Nielsen Richelle Mendez
E-mail: kazgjt@dxzyeh.com
Institute: Darrick Vega
Talk Title: Dorinda Chen
Talk Abstract: dwjcb2pp6thi7brv rdpqqpm typa http://wmrthwjtc.com oxzpn lwoum http://amkwidboqyr.com qfyrlv xaletm http://xsparonojv.com uibzbyc gxavccyv http://myamgx.com
   
Name: David Roach
E-mail: david.roach@murraystate.edu
Institute: Murray State University
Talk Title: Tensional Convexity and the Bounding Tension Spline
Talk Abstract: In this talk, we present a condition we call tensional convexity which is a sufficient condition on a set of data that guarantees the convexity of the tension spline which interpolates that data. Furthermore, we present a tight bound on how much a tension spline can vary between interpolation points as the tension is increased or decreased. In particular, we show that a tension spline is bounded above and below by the linear spline and something we call the bounding tension spline whenever the data being interpolated satisfies the condition of tensional convexity.
   
Name: Ruth Carey Rob Dillard
E-mail: wtkm@yvyeec.com
Institute: Nelda Washington
Talk Title: Ingrid Sanford
Talk Abstract: sclav arghan raj disulphone phlebometritis meloplast dermalgia pyrotechnic tjbsdo icltly http://hliatelcv.com cunbipx cyfb http://vxwifheg.com vxmwar owqksa http://zwdyprlfeb.com wjcrc ehzi http://rilxwlipbv.com
   
Name: Humberto Rocha
E-mail: hrocha@odu.edu
Institute: Old Dominion University
Talk Title: Data Fitting Methods for Construction of Wing Weight Estimation Models
Talk Abstract: The multivariate data fitting problem occurs frequently in many branches of science and engineering. It is very easy to fit a data set exactly by a mathematical model no matter how the data points are distributed. But building a response by using a limited number of poorly distributed data points is very unreliable, yet necessary in conceptual design process. This study documents the lessons learned from fitting the wing weight data of 41 subsonic transports by three types of interpolation methods – least polynomial interpolation, radial basis function interpolation, and Kriging interpolation. The focus of the study is to show the effects of problem formulations, choice of approximation models, and principal component regression on wing weight estimation models.
   
Name: Angel San Antolín
E-mail: angel.sanantolin@uam.es
Institute: Universidad Autonoma de madrid
Talk Title: Characterization of scaling
Talk Abstract: This is a joint work with P.Cifuentes and K.S.Kazarian. We give a complete characterization of functions $\phi\in L^2(\IR^n),$ which generate frame multiresolution analyses. The characterization of scaling functions of a multiresolution analysis is deduced from the main result. We show that in the closed linear span of translates of a single function there exists a tight frame. That observation permits us to obtain the characterization of scaling functions for more general cases from our main result.
   
Name: Larry Schumaker
E-mail: s@mars.cas.vanderbilt.edu
Institute: Vanderbilt University
Talk Title: Recent Results on Trivariate Splines
Talk Abstract: A trivariate spline of smoothness $r$ and degree $d$ is a $C^r$ function $s$ defined on a tetrahedral partition $\triangle$ such that the restriction of $s$ to each tetrahedron is a trivariate polynomial of degree $d$. The theory of bivariate splines is reasonable complete, but much less is known about trivariate splines. In this talk we describe recent results on dimension, local bases, and approximation power of trivariate splines. \bye
   
Name: Ivan Selesnick
E-mail: selesi@poly.edu
Institute: Polytechnic University
Talk Title: Design and application of wavelet frames with three generators
Talk Abstract: In this talk, we describe a new set of dyadic wavelet frames with three generators, $\psi_i(t)$, $i=1,2,3$. The construction is simple, yet the wavelets cover the time-frequency plane in an effective way: one of the three wavelets is exactly a half-integer shift of another [$\psi_2(t) = \psi_1(t-0.5)$], and the spectrum of the third wavelet is concentrated halfway between the spectrums of the first wavelet and its dilated version [$\Psi_3(\omega)$ is concentrated between $\Psi_1(\omega)$ and $\Psi_1(2\,\omega)$]. This arrangement provides a higher sampling in both time and frequency, which leads to expansive wavelet transforms that are approximately shift-invariant and have intermediate scales. The wavelet frames presented in this talk are compactly supported and have vanishing moments. The use of these frames for signal and image denoising will be demonstrated.
   
Name: Boris Shekhtman
E-mail: boris@math.usf.edu
Institute: USF
Talk Title: Ideal Projectors in Several Variables
Talk Abstract: I will present a solution to a problem posed by Carl de Boor exactly a year ago. The question asked whether Interpolating projectors are dense in the class of Ideal projectors. It is trivially so in one variable. It is (non-trivially) true in two variables. It is not true in three or more variables
   
Name: Zuowei Shen2
E-mail: matzuows@nus.edu.sg
Institute: National University of Singapore
Talk Title: Pseudo-splines, wavelets and framelets
Talk Abstract: The first type of pseudo-splines were introduced in \cite{DHRS} to construct tight framelets with desired approximation orders via the {\it unitary extension principle} of \cite{RS1}. In the spirit of the first type of pseudo-splines, we introduce here a new type (the second type) of pseudo-splines to construct symmetric or antisymmetric tight framelets with desired approximation orders. Pseudo-splines provide a rich family of refinable functions. B-splines are one of the special classes of pseudo-splines; orthogonal refinable functions (whose shifts form an orthonormal system given in \cite{D2}) are another class of pseudo-splines; and so are the interpolatory refinable functions (which are the Lagrange interpolatory functions at $\Z$ and were first discussed in \cite{Du}). The other pseudo-splines with various orders fill in the gaps between the B-splines and orthogonal refinable functions for the first type, and between B-splines and interpolatory refinable functions for the second type. This gives a wide range of choices of refinable functions that meets various demands for balancing the approximation power, the length of the support, and the regularity in applications. This paper will give a regularity analysis of pseudo-splines of the both types and provide various constructions of wavelets and framelets. It is easy to see that the regularity of the first type of pseudo-splines is between B-spline and orthogonal refinable function of the same order. However, there is no precise regularity estimate for pseudo-splines in general. In this paper, an optimal estimate of the decay of the Fourier transform of the pseudo-splines is given. The regularity of pseudo-splines can then be deduced and hence, the regularity of the corresponding wavelets and framelets. The asymptotical regularity analysis, as the order of the pseudo-splines goes to infinity, is also provided. From a given pseudo-spline, a short support Riesz wavelet (that has the same length of support as that of the pseudo-spline) is constructed. The construction is rather simple and natural, however, the proof of the Riesz property of the corresponding wavelet system is highly nontrivial. Furthermore, this short support wavelet is one of the tight framelets constructed from the same pseudo-spline by a method provided both in \cite{DHRS} and this paper. This reveals that in almost all pseudo-spline tight frame systems constructed so far, there is one framelet whose dilations and shifts already form a Riesz basis for $L_2(\R)$. This is a joint work with Bin Dong.
   
Name: Lixin Shen
E-mail: lixin.shen@wmich.edu
Institute: Western Michigan University
Talk Title: Framelet Approaches for Impulse Noise Removal and Image Inpainting
Talk Abstract: In this talk, I will present framelet based algorithms for impulse noise removal and image inpainting. Experimental results will show that the proposed algorithms are effective.
   
Name: Zuowei Shen
E-mail: matzuows@nus.edu.sg
Institute: National University of Singapore
Talk Title: Wavelet Frames and Image Processing
Talk Abstract: In this talk, I will first give a brief review of the recent developments of wavelet frames, especially, the unitary extension principle. The unitary extension principle provides a great flexibility in designing tight frame wavelet filters and makes constructions of tight frame wavelets adapted to practical problems possible. In the second part of my talk, I will focus on new algorithms based on wavelet frames designed via the unitary extension principle for various applications, such as deconvolution, high resolution image reconstructions, noise removal, image inpainting. The numerical simulations show that the new algorithms are efficient. An analysis of theoretical foundations of these algorithms is also given.
   
Name: Liang Shi
E-mail: lshi@math.purdue.edu
Institute: Purdue University
Talk Title:
Talk Abstract:
   
Name: Philip Smith
E-mail: philip.smith@ttu.edu
Institute: Texas Tech University
Talk Title: Parallel and Grid Computing Applied to the Variable Knot Spline Problem
Talk Abstract: It is well-known many local minima may exist for the variable knot spline approximation to a given data set. We explore this issue utilizing both parallel computing and grid computing environments at Texas Tech.
   
Name: Tatyana Sorokina
E-mail: sorokina@math.uga.edu
Institute: University of Georgia Athens
Talk Title: An Octahedral $C^2$ Macro-Element
Talk Abstract: A macro-element of smoothness $C^2$ is constructed on the split of an octahedron into eight tetrahedra. This new element complements those recently constructed on the Clough-Tocher and Worsey-Farin splits of a tetrahedron by L.L. Schumaker, and P. Alfeld. The new element can be used to construct convenient super-spline spaces with stable local bases and full approximation power that can be used for solving boundary-value problems and for interpolation of Hermite data. This is a joint project with Ming-Jun Lai and Alan Le M\'ehaut\'e.
   
Name: Joachim Stoeckler
E-mail: joachim.stoeckler@math.uni-dortmund.de
Institute: University of Dortmund
Talk Title: Time-domain approach for the construction of tight wavelet frames
Talk Abstract: Nonstationary frames provide a tool for analysis and wavelet-type decomposition of irregularly distributed data. We report on a new method for the time-domain construction of nonstationary frames on bounded and unbounded domains, which was developed jointly with C. K. Chui and W. He. Our method provides the ``filter coefficients'' for decomposition and reconstruction in terms of column vectors of some (sparse) coefficient matrix. We begin with a nonstationary multiresolution analysis $V_0\subset V_1\subset \ldots$ (with irregular refinement) where each $V_j$ is spanned (in the sense of a Bessel family) by locally supported functions $\varphi_{j,k}$. Localization of these Bessel families can roughly be described by the simple assumption, that the support of $\varphi_{j,k}$ shrinks to zero as $j$ tends to infinity. The central ingredient of our construction is the formulation of approximate duals $\{\tilde \varphi_{j,k}\}\subset V_j$. This concept is closely related to the terminology of quasi-projection or quasi-interpolation operators $$ Q_jf =\sum_k \langle f,\tilde \varphi_{j,k}\rangle \varphi_{j,k}, $$ which reproduce polynomials up to a certain degree. In our time-domain approach, the approximate dual is defined in terms of a positive semi-definite matrix $S$ where each column represents the coefficients of a function $\tilde \varphi_{j,k}$ which is expanded in terms of the given Bessel family in $V_j$. The positive semi-definiteness of $S$ implies that the operator $Q_j$ is semi-definite as well, and this is a crucial property which is needed for the subsequent construction of tight frames. One of the highlights of our work is the explicit construction of approximate duals of $B$-splines of order $m$ for an arbitrary irregular knot vector. Subsequent steps for the construction of tight frames rely on matrix factorization techniques for banded semi-definite matrices. By our method, we recover the constructions of univariate tight spline frames for the shift-invariant setting by the Fourier-domain approach. We also provide new examples of tight spline frames with multiple knots for regular dyadic refinement on an interval $I\subset R$, where $I$ can be bounded, $[0,\infty)$ or the real line.
   
Name: Nikolay Strelkov
E-mail: strelkov@uniyar.ac.ru
Institute: Yaroslavl State University, Russia
Talk Title: From B-splines to Wavelets
Talk Abstract: The necessary and sufficient conditions for the nonorthogonal) wavelet multiresolution analysis with arbitrary (for example $B$-spline)scaling function are established. The following results are obtained: 1) the general theorem which declares necessary and sufficient conditions for the possibility of multiresolution analysis in the case of arbitrary scaling function; 2) the reformulation of this theorem for the case of $B$-spline scaling function from $W_2^m$; 3) the complete description of the family of wavelet bases generated by $B$-spline scaling function; 4) the concrete construction of the unconditional wavelet basis (with minimal support of wavelet) generated by $B$-spline scaling function which belongs to $W_2^m$.
   
Name: Qiyu Sun
E-mail: qsun@mail.ucf.edu
Institute: University of Central Florida
Talk Title: Average Sampling in Shift-Invariant Spaces
Talk Abstract: In this talk, I will discuss average sampling/reconstruction problem in a shift-invariant space, especially the polynomial decay property of the display blocks, and robustness and localness of the reconstruction process.
   
Name: Yu Thomas
E-mail: yut@rpi.edu
Institute: Rensselaer Polytechnic Institute
Talk Title: Jet Subdivision Surfaces -- Hermite subdivision beyond the shift invariant setting
Talk Abstract: The application of Hermite subdivision schemes in the setting of free-form surface modelling will be presented. Underlying this development is an intrinsic geometric interpretation of "Hermite data" known as r-jets. Various new jet subdivision schemes and their potential advances will be discussed. The "shift-invariant part" of this project was done in collaboration mainly with Bin Han, whereas the "geometric part" of the research was done in collaboration with Tom Duchamp and Yonggang Xue.
   
Name: Marina Vannucci
E-mail:
Institute: Texas A\& M University
Talk Title: Bayesian inference for wavelet-based modelling of functional data
Talk Abstract: In this talk I will describe methodologies for Bayesian modelling of functional data that incorporate feature extraction. Practical applications will be classification problems that involve functional predictors. Wavelet methods will be used for dimension reduction. Probit models and Bayesian methods will allow the simultaneous classification of the samples as well as the selection of the discriminating features of the data. Applications will involve spectral data. In mass spectrometry, for example, the identification of peaks related to a specific outcome, i.e. peaks that discriminate samples or that predict a clinical response, is of interest. Other practical contexts will come from chemometrics studies that explore the possibility of using NIR spectra to classify samples. In all examples we will find that very small sets of features lead to good classification results.
   
Name: Brani Vidakovic
E-mail:
Institute: Georgia Institute of Technology
Talk Title: Wavelet-based convex rearrangements in inference about self-similarity
Talk Abstract: In this talk we first briefly review the use of wavelets in estimating Hurst exponent. The main part of talk discusses the novel estimator of Hurst exponent in monofractal self-similar processes. Almost sure convergence and asymptotic distributional properties of the proposed estimator are presented. Simulational analysis compares the proposed estimator to several popular estimators in the field. The proposed estimator utilizes convex rearrangements of wavelet-filtered versions of the process. This work builds on the research of Davydov, Thilly, Phillippe, and Coeurjolly, who investigated the asymptotics of normalized convex rearrangements for broad classes of Gaussian and alpha-stable processes. We define G-convex rearrangements, where G is a filter from a family of dilated high-pass wavelet filters. Next, we discuss an estimator of Hurst exponent via a ratio of G-convex rearrangements with different dilations.
   
Name: Jiangzhong Wang
E-mail: MTH_JXW@exchange.shsu.edu
Institute: Sam Houston State University
Talk Title: On Spline Wavelets
Talk Abstract: Abstract. Spline wavelet is an important aspect of the constructive theory of wavelets. This paper consists of three parts. In the first part, the author surveys his joint work with Charles Chui on the construction of spline wavelets, including the cardinal spline approach to wavelets, the dual principle and the framework for the construction of compactly supported spline wavelets, the computational and algorithmic aspects of spline wavelets, and the asymptotically time-frequency localization of spline wavelets. In the second part, the author introduces the applications of spline wavelet in the numerical solutions of initial-boundary problem of nonlinear partial differential equations, and in the signal and image procession. The last part is dedicated to the resent development of spline wavelets.
   
Name: Yi Wang
E-mail: ywang@fairmontstate.edu
Institute: Fairmont State University
Talk Title: A Fast Wavelet Collocation Method for Integral Equations and its Application to a 3-D Boundary Value Problem
Talk Abstract: In this talk we develop a fast wavelet collocation method for integral equations of the second kind with weakly singular kernels on polygons. For this purpose, we construct multiscale wavelet functions and collocation functionals having vanishing moments. Moreover, a block truncation strategy is presented, which leads to fast algorithms, for the coefficient matrix of the corresponding discrete system. The computational complexity for generating the coefficient matrix is reduced from $O(N^2)$ to $O(N\log^5 N)$, where $N$ is the dimension of the approximating space. Critical issues for numerical implementation of such methods are considered, such as numerical integration of weakly singular integrals, error controls of numerical quadrature and numerical solutions of resulting compressed linear systems. Finally we apply the method to a 3-D boundary value problem, which demonstrates the computing power of this method.\\ *The research of this author was supported in part by West Virginia NASA EPSCoR and WV EPSCoR.
   
Name: Joseph Ward
E-mail: jward@math.tamu.edu
Institute: Texas A&M University
Talk Title: Sobolev error estimates for scattered data interpolation on $S^n$
Talk Abstract: In this talk, we discuss Sobolev-type error estimates on $S^n$ when the spherical basis functions (SBFs) have Fourier coefficients (wrt spherical harmonics) that decay algebraically. In addition, we present a Bernstein inequality for spaces of finite rotates of an SBF in terms of the minimal separation parameter.
   
Name: Lupe Dunlap Winston Hawkins
E-mail: edrdx@enfik.com
Institute: June Olsen
Talk Title: Humberto Roth
Talk Abstract: dwjcb2pp6thi7brv hodye nfpy http://tqygqwieycol.com dqkxdw gqvfa http://fektnutej.com xvjrmz fovtl http://zrfhvk.com pafqc nikyeamb http://zijblr.com
   
Name: Yuan Xingchen
E-mail: xingchenyuan@yahoo.com
Institute: East Tennessee State University
Talk Title: Survival Model and Estimation for Lung Cancer Patients
Talk Abstract: Lung cancer is the most frequent fatal cancer in the United States. Following the notion in actuarial math analysis, we assume an exponential form for the baseline hazard function and combine Cox proportional hazard regression for the survival study of a group of lung cancer patients. The covariates in the hazard function are estimated by maximum likelihood estimation following the proportional hazards regression analysis. Although the proportional hazards model does not give an explicit baseline hazard function, the baseline hazard function can be estimated by fitting the data with a non-linear least square technique. The survival model is then examined by a neural network simulation. The neural network learns the survival pattern from available hospital data and gives survival prediction for random covariate combinations. The simulation results support the covariate estimation in the survival model.
   
Name: Thomas Pok-Yin Yu
E-mail: yut@rpi.edu
Institute: Rensselaer Polytechnic Institute
Talk Title: Jet Subdivision Surfaces -- Hermite subdivision beyond the shift invariant setting
Talk Abstract: The application of Hermite subdivision schemes in the setting of free-form surface modelling will be presented. Underlying this development is an intrinsic geometric interpretation of "Hermite data" known as r-jets. Various new jet subdivision schemes and their potential advantages will be discussed. The "shift-invariant part" of this project was done in collaboration mainly with Bin Han, whereas the "geometric part" of the research was done in collaboration with Tom Duchamp and Yonggang Xue.
   
Name: Richard Zalik
E-mail: zalik@auburn.edu
Institute:
Talk Title: A Representation Theorem For Orthonormal Wavelets in $L^2(R^d)$.
Talk Abstract: Given an orthonormal wavelet associated with a given multiresolution analysis in $L^2(R^d)$, we derive a method to obtain all orthonormal wavelets associated with the same multiresolution analysis. This representation theorem permits the easy generation of orthonormal wavelets in higher dimensions, that are not the tensor products of one--dimensional wavelets.
   
Name: Frank Zeilfelder
E-mail: zeilfeld@euklid.math.uni-mannheim.de
Institute: Institute of Mathematics, University of Mannheim
Talk Title: Visualization and Approximation of Data by Trivariate Splines
Talk Abstract: Trivariate splines are piecewise polynomial functions defined on tetrahedral partitions of three dimensional domains. It is known, that the structure of these spaces is extremely complex when smoothness conditions are involved. On the other hand, because polynomials of low and lowest possible (total) degree can be used, trivariate splines are very attractive for the efficient visualization of volume data, which arises in many applications. In our current research, we consider natural classes of uniform type tetrahedral partitions, namely type-6 and Freudenthal partitions. We first analyze the structure of the corresponding smooth spline spaces of any degree. In particular, we determine the number of degrees of freedom of these spline spaces. Based on the structural properties, we develop local approximation methods for trivariate splines with a strong focus on the efficient visualization of huge volume data sets. We prove that the resulting quasi-interpolating splines yield (nearly) optimal approximation order, while its derivatives are optimal for smooth functions. Our algorithms do not require any intermediate steps as the construction of a particular basis. Since we use the piecewise BB-form, the approximating splines are directly determined from the given volume data and well-known techniques from Computer Aided Geometric Design can be applied for the practical purposes. Our numerical experiments for test functions and real world data arising in medical and industrial applications show that the quasi-interpolating splines are natural models of the data, which allow efficient visualizations of high quality.
   
Name: Alexander Zhensykbaev
E-mail: azh@math.kz
Institute: Institute of Mathematics
Talk Title: Smoothing of scattered data
Talk Abstract: \begin{center} Smoothing of scattered data. \medskip À.À.Zhensykbaev \medskip Institute of Mathematics\\ Pushkin str. 125 480100 Almaty Kazakhstan\\ azh@math.kz \end{center} \bigskip Let $\{\varphi_1,...\varphi_m\}$ be a system of linear independent on the bounded set $G\subset {\bf R}_d$ functions, $\Phi_m=span \{\varphi_1,...\varphi_m\}$, $\Phi_0=\{ 0 \}$, and $F_{mp}$ - the set of convolution type functions $$ f(x)=f_0(x)+\sum\limits_{i=1}^k\int_{G_i} f_i(t) K_i(x,t) d\mu_i\qquad \| f \|^*_p := \sum_{i=1}^{k}( \| f_i \|_{p_i} )^{p_i}/p_i, $$ where $f_0\in \Phi_m$, $f_i\in L_{p_i}(G_i,\mu_i)$, $K_i\in L_{p_i'} (G_i,\mu_i)$, $G_i$ - bounded measurable set from ${\bf R}_{d_i}$, $\mu_i$ - positive measure, $1
   
Name: Zvi Ziegler
E-mail: ziegler@tx.technion.ac.il
Institute: Technion, Haifa, Israel
Talk Title:
Talk Abstract:
   
Name: boris shekhtman
E-mail: boris@math.usf.edu
Institute: USF
Talk Title: Ideal Projectors
Talk Abstract: I will answer the following question asked by Carl de Boor: Is it true that interpolating projectors are dense in the family of ideal projectors? The answer is: True in one or two variables. False in three or more variables