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IMA Newsletter #341

March 2005

2004-2005 Program

Mathematics of Materials and Macromolecules

See http://www.ima.umn.edu/matter for a full description of the 2004-2005 program on
Mathematics of Materials and Macromolecules: Multiple Scales, Disorder, and Singularities
and http://www.ima.umn.edu/schedule for schedule updates.

News and Notes

The third IMA Career Workshop on Minorities and Applied Mathematics will take place April 22-24, 2005. This workshop will focus on the problems that confront the small, but growing, number of under-represented minority mathematicians in academia, government laboratories and industry. The workshop will offer tutorials with practical applications, intended primarily for researchers in the early to mid-career stages of their professional development, and provide opportunities for networking. A limited number of general interest technical talks will be presented. Senior professionals will provide insight on things they wish someone had told them before they left graduate school, some of the surprises they found upon entering the workplace, and how they managed to overcome the difficulties encountered. Small breakout groups will allow for further exploration of ideas, which will then be shared with the entire group. In addition, poster sessions will showcase the work of selected attendees.

The allied workshop Career Options for Women in Mathematical Sciences, which took place February 4-5, provided more than seventy women mathematicians with an opportunity to share experiences and insights. Graduate student Yelda Aydin wrote “Getting to know these women who were very successful and happy with their different choices made me feel more optimistic.” Postdoc Suzanne Lynch Hruska elaborated “I learned (to my pleasant surprise) that obtaining a job in industry is very possible for an academic with a pure math background. I left many of the talks feeling as though I could quite happily be an employee in the speaker’s company in the future,” while senior researcher Pam Binns found “the candor of the participants was exceptionally impressive—providing insight into ‘real’ experiences—opposed to the marketing pitches typically presented.” Graduate student Paola Vera Licona captured the spirit of the meeting: “One thing that I have learned from this workshop is that I am capable of helping other women by sharing my experiences and that I can learn so much from listening to others’ experiences. In fact, after the workshop I decided to enroll in the AWM Mentor Network.”

IMA Events

IMA Tutorial

Tutorial: New Paradigms in Computation

March 28-30, 2005


The primary goal of this workshop is to facilitate the use of the best computational techniques in important industrial applications. Key developers of three of the most significant recent or emerging paradigms of computation—fast multipole methods, level set methods, and multiscale computation— will provide tutorial introductions to these classes of methods. Presentations will be particularly geared to scientists using or interested in using these approaches in industry. In addition the workshop will include research reports, poster presentations, and problem posing by industrial researchers, and offer ample time for both formal and informal discussion, related to the use of these new methods of computation.

Public Lecture

Dr. Thomas C. Hales, Computers and the Future of Mathematical Proof

March 30, 2005


Computers crash, hang, succumb to viruses, run buggy programs, and harbor spyware. By contrast, mathematics is free of all imperfection. Why are imperfect computational devices so vital for the future of mathematics?

Tuesday, March 1

Wednesday, March 2

11:15a-12:15pStable and finite Morse index solutions on bounded domains with small diffusionNorman Dancer
University of Sydney
Lind Hall 409 MS

Thursday, March 3

11:15a-12:15pNatural cost functions for contact point selection in graspingPaul R Schrater
University of Minnesota
Lind Hall 409 MS

Friday, March 4

11:15a-12:15pMathematical models for biaxial liquid crystals phasesEpifanio G. Virga
Universita di Pavia
Lind Hall 409 MS
1:25p-2:25pMedical image segmentation using deformable modelsChenyang Xu
Siemens Corporate Research
Vincent Hall 570 IPS

Tuesday, March 8

11:15a-12:15pHigher order corrections to the KdV approximation for water wavesDoug Wright
University of Minnesota
Lind Hall 409 PS
2:30p-3:30pMultiscale approaches to molecular dynamics and samplingJesus A. Izaguirre
University of Notre Dame
Lind Hall 409 MS

Wednesday, March 9

11:15a-12:15pCritical intensities for phase transitions in a 3D Smoluchowski equationHailiang Liu
Iowa State University
Lind Hall 409 MS
2:30p-3:30pInformal discussion of molecular dynamicsJesus A. Izaguirre
University of Notre Dame
Brian Laird
University of Kansas
Lind Hall 409 MS

Thursday, March 10

12:25p-1:25pMultiscale photon-limited image analysisRebecca Willett
University of Minnesota
Lind Hall 409 iPAWS
2:30p-3:30pDirect calculation of crystal-melt interfacial free energies from molecular simulationBrian Laird
University of Kansas
Lind Hall 409 MS

Monday, March 14

11:15a-12:15pA variational model of dislocations in the line tension limitStefan Mueller
Max Planck Institute for Math in the Sciences
Lind Hall 409 MS

Wednesday, March 16

11:15a-12:15pTBAMaria-Carme Calderer
University of Minnesota
Lind Hall 409 MS

Friday, March 18

11:15a-12:15pStretching of polymers on sub-Kolmogorov scales in a turbulent flowJoerg Schumacher
Philipps University Marburg
Lind Hall 409 MS

Thursday, March 24

12:25p-1:25pVolumetric computed tomography and its applicationsXiaochuan Pan
University of Chicago
Lind Hall 409 iPAWS

Friday, March 25

1:25p-2:25pSolid modeling: Math at work in designJan Vandenbrande
Vincent Hall 570 IPS

Monday, March 28

8:30a-9:15aCoffee and RegistrationEE/CS 3-176 T3.28-30.05
9:15a-9:30aWelcome and IntroductionDouglas N. Arnold
University of Minnesota
Robert V. Kohn
New York University - Courant Institute
EE/CS 3-180 T3.28-30.05
9:30a-10:30aLecture 1: Advances in advancing interfaces: Level set methods, fast marching methods, and beyond James A. Sethian
University of California
EE/CS 3-180 T3.28-30.05
10:30a-11:00aCoffee EE/CS 3-176 T3.28-30.05
11:00a-12:00pLecture 1: Fast multipole methods and their applicationsLeslie F. Greengard
New York University
EE/CS 3-180 T3.28-30.05
12:00p-1:30pLunch T3.28-30.05
1:30p-2:30pLecture 1: Overview of multiscale methods Weinan E
Princeton University
EE/CS 3-180 T3.28-30.05
2:30p-3:00pCoffee EE/CS 3-176 T3.28-30.05
3:00p-4:30pIndustrial problems presentationsEE/CS 3-180 T3.28-30.05

Tuesday, March 29

8:45a-9:00a Coffee T3.28-30.05
9:30a-10:30aMore industrial problem presentationsEE/CS 3-180 T3.28-30.05
10:30a-11:00aCoffeeEE/CS 3-176 T3.28-30.05
11:00a-12:00pLecture 2: Advances in advancing interfaces: Level set methods, fast marching methods, and beyond James A. Sethian
University of California
EE/CS 3-180 T3.28-30.05
12:00p-1:30pLunch T3.28-30.05
1:00p-2:30pLecture 2: Fast multipole methods and their applicationsLeslie F. Greengard
New York University
EE/CS 3-180 T3.28-30.05
2:30p-3:00pCoffeeEE/CS 3-176 T3.28-30.05
3:00p-4:00pGroup Photo EE/CS 3-180 T3.28-30.05
3:00p-4:00pLecture 2: Problems with multiple time scalesWeinan E
Princeton University
EE/CS 3-180 T3.28-30.05
4:00p-5:30pIMA Tea and more (with POSTER SESSION) 400 Lind HallLind Hall 400 T3.28-30.05
A graph-theoretic method for the discretization of gene expression measurements Elena Dimitrova
Virginia Tech
Phase field modeling and simulation of cell membranesQiang Du
Pennsylvania State University
High-dimensional finite elements for elliptic problems with multiple scalesViet Ha Hoang
Cambridge University
Generalized Galerkin variational integrators: Lie group, multiscale and spectral methodsMelvin Leok
University of Michigan

Wednesday, March 30

8:50a-9:00aCoffeeEE/CS 3-176 T3.28-30.05
9:00a-12:00pStructured discussion of industrial problem areasEE/CS 3-180 T3.28-30.05
12:00p-1:30pLunch T3.28-30.05
1:30p-3:00pBreakout sessionsEE/CS 3-180 T3.28-30.05
5:00p-6:30pReception for Thomas C. HalesLind Hall 400 PUB3.30.05
7:00p-8:00pIMA Public Lecture: Computers and the Future of Mathematical Proof Thomas C. Hales
University of Pittsburgh
EE/CSci 3-210 PUB3.30.05

Thursday, March 31

12:25p-1:25pCentroidal Voronoi tesselations and their applicationsQiang Du
Pennsylvania State University
Lind Hall 409 iPAWS
Elena Dimitrova (Virginia Tech) A graph-theoretic method for the discretization of gene expression measurements
Abstract: The paper introduces a method for the discretization of experimental data into a finite number of states. While it is of interest in various fields, this method is particularly useful in bioinformatics for reverse engineering of gene regulatory networks built from gene expression data. Many of these applications require discrete data, but gene expression measurements are continuous. Statistical methods for discretization are not applicable due to the prohibitive cost of obtaining sample sets of sufficient size. We have developed a new method of discretizing the variables of a network into the same optimal number of states while at the same time maintaining high information content. We employ a graph-theoretic clustering method to affect the discretization of gene expression measurements. Our C++ program takes as an input one or more time series of gene expression data and discretizes these values into a number of states that best fits the data. The method is being validated by incorporating it into the recently published computational algebra approach to the reverse engineering of gene regulatory networks by Laubenbacher and Stigler.
Qiang Du (Pennsylvania State University) Phase field modeling and simulation of cell membranes
Abstract: Recently, we have produced a series of works on the phase field modeling and simulation of vesicle bio-membranes formed by lipid bilayers. We have considered both the shape deformation of vesicles minimizing the elastic bending energy with volume and surface area constraints and those moving in an incompressible viscous fluid. Rigorous mathematical analysis have been carried out along with extensive numerical experiments. We have also developed useful computational techniques for detecting the topological changes within a broad phase field framework. References: 1. A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, Q. Du, C. Liu and X. Wang, J. Computational Physics, 198, pp. 450-468, 2004 2.Retrieving topological information for phase field models, Q. Du, C. Liu and X. Wang, 2004, to appear in SIAM J. Appl. Math 3. Phase field modeling of the spontaneous curvature effect in cell membranes, Q. Du C. Liu, R. Ryham and X. Wang, 2005, to appear in CPAA 4. A phase field formulation of the Willmore problem. Q. Du, C. Liu, R. Ryham and X. Wang, 2005, to appear in Nonlinearity
Weinan E (Princeton University) Lecture 1: Overview of Multiscale Methods
Abstract: We will begin by reviewing the basic issues and concepts in multiscale modeling, including the various models of multi-physics, serial and concurrent coupling strategies, and the essential features of the kind of multiscale problems that we would like to deal with. We then discuss some representative examples of successful multiscale methods, including the Car-Parrinello method and the quasi-continuum method. Finally we discuss several general methodologies for multiscale, multi-physics modeling, such as the domain decomposition methods, adaptive model refinement and heterogeneous multiscale methods. These different methodologies are illustrated on one example, the contact line problem. Throughout this presentation, we will emphasize the interplay between physical models and numerical methods, which is the most important theme in modern multiscale modeling.
Weinan E (Princeton University) Lecture 2: Problems with multiple time scales
Abstract: We will discuss the mathematical background and numerical techniques for three types of problems with multiple time scales: stiff ODEs, Markov chains with disparate rates and rare events.
Ryan S. Elliott (University of Michigan) Bifurcation and stability of multilattices with applications to martensitic transformations in shape memory alloys
Abstract: Some of the most interesting and technologically important solid--solid transformations are the first order diffusionless transformations that occur in certain ordered multi-atomic crystals. These include the reconstructive martensitic transformations (where no group--subgroup symmetry relationship exists between the phases) found in steel and ionic compounds such as CsCl, as well as the thermally-induced, reversible, proper (group--subgroup relationships exist) martensitic transformations that occur in shape memory alloys such as NiTi. Shape memory alloys are especially interesting, for engineering applications, due to their strong thermomechanical (multi-physics) coupling. The mechanism responsible for these temperature-induced transformations is a change in stability of the crystal's lattice structure as the temperature is varied. To model these changes in lattice stability, a continuum-level thermoelastic energy density for a bi-atomic multilattice is derived from a set of temperature-dependent atomic potentials. The Cauchy-Born kinematic assumption is employed to ensure, by the introduction of internal atomic shifts, that each atom is in equilibrium with its neighbors. Stress-free equilibrium paths as a function of temperature are numerically investigated, and an asymptotic analysis is used to identify the paths emerging from "multiple bifurcation" points that are encountered. The stability of each path against all possible bounded perturbations is determined by calculating the phonon spectra of the crystal. The advantage of this approach is that the stability criterion includes perturbations of all wavelengths instead of only the long wavelength information that is available from the stability investigation of homogenized continuum models. The above methods will be reviewed, and results corresponding to both reconstructive and proper martensitic transformations will be presented. Of particular interest is the prediction of a transformation that has been experimentally observed in CuAlNi, AuCd, and other shape memory alloys.
Leslie F. Greengard (New York University) Lecture 1: Fast multipole methods and their applications
Abstract: In these lectures, we will describe the analytic and computational foundations of fast multipole methods (FMMs), as well as some of their applications. They are most easily understood, perhaps, in the case of particle simulations, where they reduce the cost of computing all pairwise interactions in a system of N particles from O(N²) to O(N) or O(N log N) operations. FMMs are equally useful, however, in solving partial differential equations by first recasting them as integral equations. We will present examples from electromagnetics, elasticity, and fluid mechanics.
Thomas C. Hales (University of Pittsburgh) IMA Public Lecture: Computers and the Future of Mathematical Proof
Abstract: Computers crash, hang, succumb to viruses, run buggy programs, and harbor spyware. By contrast, mathematics is free of all imperfection. Why are imperfect computational devices so vital for the future of mathematics?
Viet Ha Hoang (Cambridge University) High-dimensional finite elements for elliptic problems with multiple scales
Abstract: Joint work with Christoph Schwab. Elliptic homogenization problems in a d dimensional domain with n+1 separated scales are reduced to elliptic one-scale problems in dimension (n+1)d. These one-scale problems are discretized by a sparse tensor product finite element method (FEM). We prove that this sparse FEM has accuracy, work and memory requirement comparable to standard FEM for single scale problems in while it gives numerical approximations of the correct homogenized limit as well as of all first order correctors, throughout the physical domain with performance independent of the physical problem's scale parameters. Numerical examples for model diffusion problems with two and three scales confirm our results.
Jesus A. Izaguirre (University of Notre Dame) Multiscale approaches to molecular dynamics and sampling
Abstract: In the first part of this talk, I will survey some approaches for producing multiscale models for molecular dynamics (MD) and sampling. I will consider two parts of the problem: finding coarsened variables, and then integrating or propagating the coarsened model. I will discuss the approach of Brandt and collaborators to semi-automatically determine the coarsened variables, and the more ad-hoc approach of Gear and collaborators, who assume a reaction-coordinate is known which produces a natural separation of scales. Both methods attempt to sample the fast scales, and then to do an accurate integration of the slow scales. Related approaches will be mentioned, such as Leimkuhler's and Reich's reversible integrators.
Brian Laird (University of Kansas) Direct calculation of crystal-melt interfacial free energies from molecular simulation
Abstract: The crystal-melt interfacial free energy, the work required to create a unit area of interface between a crystal and its own melt, is a controlling property in the kinetics and morphology of crystal growth and nucleation, especially in the case of dendritic growth. Despite the technological importance of this quantity, accurate experimental data is difficult to obtain. The paucity of experimental measurements has motivated the development of a variety of novel computational methods to determine the interfacial free energy via molecular simulation. After a short tutorial on thermodynamic integration techniques for free energy calculation, I will introduce our method of cleaving walls for the calculation of the crystal-melt interfacial free energy, and a competing method based on fluctuation spectra. Results for a variety of simple systems will be presented to give a broad picture of the interaction and crystal structure dependence of the interfacial free energy. The results will be discussed in relation to popular empirical theories of the interfacial free energy.
Melvin Leok (University of Michigan) Generalized Galerkin variational integrators: Lie group, multiscale and spectral methods
Abstract: Geometric mechanics involves the study of Lagrangian and Hamiltonian mechanics using geometric and symmetry techniques. Computational algorithms obtained from a discrete Hamilton's principle yield a discrete analogue of Lagrangian mechanics, and they exhibit excellent structure-preserving properties that can be ascribed to their variational derivation. We propose a natural generalization of discrete variational mechanics, whereby the discrete action, as opposed to the discrete Lagrangian, is the fundamental object. This is achieved by appropriately choosing a finite dimensional function space to approximate sections of the configuration bundle and numerical quadrature techniques to approximate the action integral. We will discuss how this general framework allows us to recover high-order Galerkin variational integrators, asynchronous variational integrators, and symplectic-energy-momentum integrators. In addition, we will also introduce generalizations such as high-order symplectic-energy-momentum integrators, Lie group integrators, high-order Euler-Poincare integrators, multiscale variational integrators, and pseudospectral variational integrators. This framework will be illustrated by an application of Lie group variational integrators to rigid body dynamics wherein the discrete trajectory evolves in the space of 3x3 matrices, while automatically staying on the rotation group, without the use of local coordinates, constraints, or reprojection. This is joint work with Taeyoung Lee and Harris McClamroch.
Hailiang Liu (Iowa State University) Critical intensities for phase transitions in a 3D Smoluchowski equation
Abstract: We study the structure of equilibrium solutions to a Smoluchowski equation on a sphere, which arises in the modelling of rigid rod-like molecules of polymers. A complete classification of intensities for phase transitions to equilibrium solutions is obtained. It is shown that the number of equilibrium solutions hinges on whether the potential intensity crosses two critical values alpha_1 approximately 6.731393 and alpha_2 = 7.5. Furthermore, we present explicit formulas for all equilibrium solutions. These solutions consist of a set of axially symmetric functions and all those which are obtained from this set by rotation. In this joint work with Hui Zhang and Pingwen Zhang, we solve the Onsager's 1949 conjecture on phase transitions in rigid rodlike polymers.
Stefan Mueller (Max Planck Institute for Math in the Sciences) A variational model of dislocations in the line tension limit
Abstract: We study the (Gamma) limit of a dislocation model proposed by Ortiz et al., in which slip occurs only on one plane. Mathematically the core is an extension of the Alberti-Bouchitte-Seppecher results for 1/eps nonconvex two-well energy + H^{1/2} norm squared to an periodic array of wells (hence no naive coercivity). From the analysis point of view H^{1/2} is interesting since it leads to a logarithnmic rescaling.
Xiaochuan Pan (University of Chicago) Volumetric computed tomography and its applications
Abstract: Computed tomography (CT) is one of the most widely used imaging modality in medicine and other areas. In this lecture, following the introduction of the basic principle of CT, I will describe what physical quantity is measured and how an image is reconstructed from the measured data in CT. Based upon such knowledge about CT, I will tour recent advances of CT technology and their new biomedical applications. One of such important advances is the advent of helical cone-beam CT and the breakthroughs in imaging theory associated with it. These technological and theoretical advances in CT have brought immediate important impact on medical and other applications of CT, offering tremendous opportunities to design innovative imaging protocols and applications that are otherwise impossible. One of the important trends in CT imaging is the so-called targeted imaging of a region of interest (ROI) within the subject from truncated data. Such a strategy for targeted imaging would substantially reduce the radiation dose delivered to the subject and scanning effort. I will discuss the theory and algorithms that we have developed recently for exact reconstruction of ROI images. Finally, I will touch upon the implications of these new developments in CT imaging theory for other tomographic imaging modalities.
Paul R Schrater (University of Minnesota) Natural cost functions for contact point selection in grasping
Abstract: When reaching to touch or lift an object, how are contact points visually selected? In this talk I will formulate the issue as a statistical decision theory problem that requires minimizing the expectation over a suitable loss function. However, it is the nature of this loss function that is the heart of the presentation. In the first part of the talk, I will show how contact points for two fingered grasp can be optimally chosen, given a plan for the grasped object's motion. The basic assumption is that the minimum control framework used to predict hand trajectories should also apply to the control of the grasped object. The cost function on the object's motion can then be rewritten in terms of finger placement and contact, inducing a cost function on finger contact points. I will present human reaching data that supports this idea. In the second part of the talk, I will present evidence for a decomposition of the natural cost function for reaching into task completion and motor control components. The issue can be framed as follows: In many reaching tasks there are a set of contact points that are equivalent in terms of task completion cost -- touching a line, for example. In generating a path, the ambiguity is broken by motor control cost, which distinguishes the minimum control point of the set (e.g. the closest point on the line). This unique target point could be selected to generate a simple feedback control strategy of minimizing distance to the target. Alternatively, a feedback control strategy could be based directly on a lumped cost function. These two strategies behave differently under a perturbing force field mid-reach: the first corrects the perturbations, while the second "goes with the flow" to contact the new minimum control point within the task completion set. I will present data supports the idea that reaches "go with the flow", adapting to external perturbations. This suggests that the brain visually encodes and adaptively uses the set of viable contact points. Finally, I will discuss why the contact point selection problem is important for understanding the sensory demands made by the motor control system during reaching.
Joerg Schumacher (Philipps University Marburg) Stretching of polymers on sub-Kolmogorov scales in a turbulent flow
Abstract: First results on numerical studies of the stretching of Hookean dumbbells on scales below the viscous length of the advecting turbulent flow are presented. Direct numerical simulations of the Navier-Stokes turbulence are combined with Brownian dynamics simulations for simple polymer chains. The role of extreme stretching events on the overall statistics is discussed. Our findings are compared with recent analytical models for the polymer advection in Gaussian random flow without time-correlation.
James A. Sethian (University of California) Lecture 1: Advances in advancing interfaces: Level set methods, fast marching methods, and beyond
Abstract: Propagating interfaces occur in a variety of settings, including semiconductor manufacturing in chip production, the fluid mechanics of ink jet plotters, segmentation in cardiac medical imaging, computer-aided-design, optimal navigation in robotic assembly, and geophysical wave propagation. Over the past 25 years, a collection of numerical techniques have come together, including Level Set Methods and Fast Marching Methods for computing such problems in interface phenomena in which topological change, geometry-driven physics, and three-dimensional complexities play important roles. These algorithms, based on the interplay between schemes for hyperbolic conservation laws and their connection to the underlying theory of curve and surface evolution, offer a unified approach to computing a host of interface prn this tutorial, the author will cover (i) the development of these methods, (ii) the fundamentals of Level Set Methods and Fast Marching Methods, including efficient, adaptive versions, and the coupling of these schemes to complex physics, and (iii) new approaches to tackling more demanding interface problems. The emphasis in this tutorial will be on a practical, "hands-on" view, and the methods and algorithms will be discussed in the context of on-going collaborative projects, including work on semiconductor processing, industrial ink jet design, and medical and bio-medical imaging.
Jan Vandenbrande (Boeing) Solid modeling: Math at work in design
Abstract: Design is the art of creating something new and predicting how it will perform before it is ever build. One of the major breakthroughs in the last 25 years is the ability to describe a design as a virtual artifact in a computer, and simulate its physical characteristics accurately to enable designers to make better decisions. The core technology that underlies these mechanical Computer Aided Design and Manufacturing (CAD/CAM) systems is solid modeling, whose theoretical underpinnings are grounded in mathematics. This talk will cover some of these mathematical concepts, including point set topology, regularized set operations, Constructive Solid Geometry (CSG), representation schemes, algorithms and geometry. We will cover the impact of solid modeling in industry, and discuss some of the remaining open issues such as the ambiguity between the topological representation and the computed geometric boundary.
Epifanio G. Virga (Universita di Pavia) Mathematical models for biaxial liquid crystals phases
Abstract: The search for thermotropic biaxial phases has recently found some firm evidence of their existence. It has rightly been remarked that this "announcement has created considerable excitement, for it opens up new areas of both fundamental and applied research. It seems that a Holy Grail of liquid-crystal science has at last been found" (see G.R. Luckhurst, Nature 430, 413 (2004)). In this lecture, I shall present a mean-field model that has the potential to describe such an evanescent phase of matter. More specifically, I show the outcomes of a bifurcation analysis of the equilibrium equations and I illuminate the complete phase diagram, which exhibits two tricritical points. The predictions of this analysis are also qualitatively confirmed by a Monte Carlo simulation study. One of the main conclusions is that two order parameters suffice to label all equilibrium phases, though they exhibit different bifurcation patterns.
Rebecca Willett (University of Minnesota) Multiscale photon-limited image analysis
Abstract: Many critical scientific and engineering applications rely upon the accurate reconstruction of spatially or temporally distributed phenomena from photon-limited data. However, a number of information processing challenges arise routinely in these problems: Sensing is often indirect in nature, such as tomographic projections in medical imaging, resulting in complicated inverse reconstruction problems. Limited system resources, such as data acquisition time and image storage requirements, lead to complex tradeoffs between communications, sensing and processing. Furthermore, the measurements are often "noisy" due to low photon counts. In addition, the behavior of the underlying photon intensity functions can be very rich and complex, and consequently difficult to model a priori. All of these issues combine to make accurate reconstruction a complicated task, involving a myriad of system-level and algorithm tradeoffs. In this talk, I will demonstrate that nonparametric multiscale reconstruction methods can overcome all the challenges above and provide a theoretical framework for assessing tradeoffs between reconstruction accuracy and system resources. First, the theory supporting these methods facilitates characterization of fundamental performance limits. Examples include lower bounds on the best achievable error performance in photon-limited image reconstruction and upper bounds on the data acquisition time required to achieve a target reconstruction accuracy. Second, existing reconstruction methods can often be enhanced with multiscale techniques, resulting in significant improvements in a number of application domains. Underlying these methods are ideas drawn from the theory of multiscale analysis, statistical learning, nonlinear approximation theory, and iterative reconstruction algorithms. I will demonstrate the effectiveness of the theory and methods in several important applications, including superresolution imaging and medical image reconstruction.
Doug Wright (University of Minnesota) Higher order corrections to the KdV approximation for water waves
Abstract: In order to investigate corrections to the common KdV approximation to long waves, we derive modulation equations for the evolution of long wavelength initial data for the water wave and Boussinesq equations. The equations governing the corrections to the KdV approximation are identical for both systems and are explicitly solvable. We prove estimates showing that they do indeed give a significantly better approximation than the KdV equation alone. We also present the results of numerical experiments which show that the error estimates we derive for the correction to the Boussinesq equation are essentially optimal.
Chenyang Xu (Siemens Corporate Research) Medical image segmentation using deformable models
Abstract: In the past four decades, computerized image segmentation has played an increasingly important role in medical imaging. Segmented images are now used routinely in a multitude of different applications, such as the quantification of tissue volumes, diagnosis, localization of pathology, study of anatomical structure, treatment planning, partial volume correction of functional imaging data, and computer-assisted surgery. Image segmentation remains a difficult task, however, due to both the tremendous variability of object shapes and the variation in image quality. In particular, medical images are often corrupted by noise and sampling artifacts, which can cause considerable difficulties when applying classical segmentation techniques such as edge detection and thresholding. As a result, these techniques either fail completely or require some kind of postprocessing step to remove invalid object boundaries in the segmentation results. To address these difficulties, deformable models have been extensively studied and widely used in medical image segmentation, with promising results. Deformable models are curves or surfaces defined within an image domain that can move under the influence of internal forces, which are defined within the curve or surface itself, and external forces, which are computed from the image data. By constraining extracted boundaries to be smooth and incorporating other prior information about the object shape, deformable models offer robustness to both image noise and boundary gaps and allow integrating boundary elements into a coherent and consistent mathematical description. Such a boundary description can then be readily used by subsequent applications. Since its introduction 15 years ago, deformable models have grown to be one of the most active and successful research areas in image segmentation. There are basically two types of deformable models: parametric deformable models and geometric deformable models. Parametric deformable models represent curves and surfaces explicitly in their parametric forms during deformation. This representation allows direct interaction with the model and can lead to a compact representation for fast real-time implementation. Adaptation of the model topology, however, such as splitting or merging parts during the deformation, can be difficult using parametric models. Geometric deformable models, on the other hand, can handle topological changes naturally. These models, based on the theory of curve evolution and the level set method, represent curves and surfaces implicitly as a level set of a higher-dimensional scalar function. Their parameterizations are computed only after complete deformation, thereby allowing topological adaptivity to be easily accommodated. Despite this fundamental difference, the underlying principles of both methods are very similar. In this talk, I will present an overall description of the development in deformable models research and their applications in medical imaging. I will first introduce parametric deformable models, and then describe geometric deformable models. Next, I will present an explicit mathematical relationship between parametric deformable models and geometric deformable models. Finally, I will present several extensions to these deformable models by various researchers and point out future research directions.
Visitors in Residence
Stuart Antman University of Maryland 3/20/2005 - 4/1/2005
Douglas N. Arnold University of Minnesota 7/15/2001 - 8/31/2006
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2005
Gerard Awanou University of Minnesota 9/2/2003 - 8/31/2005
John Ball Oxford University 3/13/2005 - 3/25/2005
Daniel E. Bentil University of Vermont 3/26/2005 - 4/16/2005
Paolo Biscari Politecnico di Milano 3/16/2005 - 4/2/2005
Sandstede Bjorn University of Surrey-England 2/21/2005 - 3/1/2005
Maria-Carme Calderer University of Minnesota 9/1/2004 - 6/30/2005
Carsten Carstensen Humboldt Universität zu Berlin 3/8/2005 - 3/21/2005
Qianyong Chen University of Minnesota 9/1/2004 - 8/31/2006
Giovanni Ciccotti University of Rome "La Sapienza" 3/20/2005 - 4/20/2005
Fabrizio Cleri Universita di Perugia 3/20/2005 - 5/23/2005
L. Pamela Cook University of Delaware 3/18/2005 - 3/20/2005
Norman Dancer University of Sydney 2/20/2005 - 3/22/2005
Antonio DeSimone SISSA-Italy 3/10/2005 - 7/15/2005
Brian DiDonna University of Minnesota 9/1/2004 - 8/31/2006
Elena Dimitrova Virginia Tech 3/27/2005 - 3/30/2005
Charles Doering University of Michigan 3/19/2005 - 3/20/2005
Qiang Du Pennsylvania State University 3/26/2005 - 4/1/2005
Weinan E Princeton University 3/27/2005 - 3/31/2005
Charles M. Elliott University of Sussex 3/20/2005 - 4/15/2005
Ryan S. Elliott University of Michigan 1/1/2005 - 6/30/2005
Ralf Everaers Max-Planck-Institut for Physics of Complex Systems 3/28/2005 - 5/1/2005
Wilfrid Gangbo Georgia Institute of Technology 3/13/2005 - 3/22/2005
Tim Garoni University of Minnesota 8/25/2003 - 8/31/2005
Eugene C. Gartland Jr. Kent State University 1/10/2005 - 6/30/2005
Dmitry Golovaty University of Akron 3/1/2005 - 3/31/2005
Jian Ping Gong Hokkaido University 3/21/2005 - 3/26/2005
Leslie F. Greengard New York University 3/27/2005 - 3/30/2005
Jean-Luc Guermond Texas A & M University 3/25/2005 - 3/31/2005
Robert Gulliver University of Minnesota 9/1/2004 - 6/30/2005
Rohit Gupta University of Minnesota 3/28/2005 - 3/30/2005
Thomas C. Hales University of Pittsburgh 3/29/2005 - 3/31/2005
Chuan-Hsiang Han University of Minnesota 9/1/2004 - 8/31/2005
Viet Ha Hoang Cambridge University 3/5/2005 - 4/16/2005
Jesus A. Izaguirre University of Notre Dame 3/3/2005 - 3/16/2005
Richard D. James University of Minnesota 9/1/2004 - 6/30/2005
Shi Jin University of Wisconsin 1/4/2005 - 6/30/2005
Sookyung Joo University of Minnesota 9/1/2004 - 8/31/2006
Lili Ju University of South Carolina 3/27/2005 - 3/30/2005
Chiu Yen Kao University of Minnesota 9/1/2004 - 8/31/2006
Robert V. Kohn New York University - Courant Institute 3/17/2005 - 3/20/2005
Richard Kollar University of Minnesota 9/1/2004 - 8/31/2005
Matthias Kurzke University of Minnesota 9/1/2004 - 8/31/2006
Brian Laird University of Kansas 3/6/2005 - 3/11/2005
Namyong Lee Mankato State University 3/27/2005 - 3/30/2005
Frederic Legoll University of Minnesota 9/3/2004 - 8/31/2006
Benedict Leimkuhler University of Leicester 2/1/2005 - 6/2/2005
Melvin Leok University of Michigan 3/27/2005 - 3/30/2005
Debra Lewis University of Minnesota 7/15/2004 - 8/31/2006
Xiantao Li University of Minnesota 8/3/2004 - 8/31/2006
Hua Lin Purdue University 3/27/2005 - 3/30/2005
Chun Liu Pennsylvania State University 9/1/2004 - 6/30/2005
Hailiang Liu Iowa State University 1/1/2005 - 6/30/2005
Irene Livshits Ball State University 3/8/2005 - 3/13/2005
Mitchell Luskin University of Minnesota 9/1/2004 - 6/30/2005
Stefan Mueller Max Planck Institute for Math in the Sciences 3/9/2005 - 3/25/2005
David Nicholls University of Notre Dame 3/26/2005 - 4/1/2005
Felix Otto University of Bonn 3/21/2005 - 4/16/2005
Peter Palffy-Muhoray Kent State University 3/15/2005 - 5/15/2005
Xiaochuan Pan University of Chicago 3/24/2005 - 3/24/2005
Alexander Panchenko Washington State University 3/12/2005 - 3/24/2005
Peter Philip University of Minnesota 8/22/2004 - 8/31/2006
Petr Plechac University of Warwick 3/21/2005 - 4/15/2005
Lea Popovic University of Minnesota 9/2/2003 - 8/31/2005
Kumbakonam Rajagopal Texas A & M University 3/14/2005 - 3/20/2005
S.S. Ravindran University of Alabama - Huntsville 3/27/2005 - 3/30/2005
Maria Reznikoff Courant Institute, New York University 3/27/2005 - 4/17/2005
Rolf Ryham Pennsylvania State University 9/1/2004 - 6/30/2005
Arnd Scheel University of Minnesota 7/15/2004 - 8/31/2006
Anja Schloemerkemper University of Stuttgart 3/6/2005 - 3/17/2005
Paul R Schrater University of Minnesota 3/3/2005 - 3/3/2005
Joerg Schumacher Philipps University Marburg 3/18/2005 - 3/18/2005
George R Sell University of Minnesota 9/1/2004 - 6/30/2005
Shaun Sellers Washington University - St. Louis 3/5/2005 - 3/12/2005
James A. Sethian University of California 3/27/2005 - 3/30/2005
Jie Shen Purdue University 3/22/2005 - 4/2/2005
Tien-Tsan Shieh Indiana University 9/1/2004 - 6/30/2005
Devashish Shrivastava University of Minnesota 3/28/2005 - 3/30/2005
Valery P. Smyshlyaev University of Bath-UK 2/1/2005 - 3/3/2005
Daniel Spirn University of Minnesota 9/1/2004 - 6/30/2005
Peter J. Sternberg Indiana University 8/15/2004 - 6/15/2005
Vladimir Sverak University of Minnesota 9/1/2004 - 6/30/2005
Chris R. Sweet University of Leicester 2/7/2005 - 3/15/2005
Eugene Terentjev Cambridge University 3/13/2005 - 4/30/2005
K. Thangavel Gandhigram Rural Institute-Deemed University 3/27/2005 - 3/30/2005
Philippe Tondeur University of Illinois - Urbana-Champaign 3/19/2005 - 3/20/2005
Yoshihiro Tonegawa Hokkaido University 3/16/2005 - 3/25/2005
Miroslav Trajkovic Symbol Technologies 3/31/2005 - 4/1/2005
Igor Tsukerman University of Akron 3/27/2005 - 3/30/2005
Jan Vandenbrande Boeing 3/24/2005 - 3/25/2005
Shankar Venkataramani University of Arizona 2/19/2005 - 3/12/2005
Epifanio G. Virga Universita di Pavia 2/26/2005 - 3/25/2005
Qi Wang Florida State University 1/31/2005 - 5/15/2005
Stephen J. Watson Northwestern University 9/1/2004 - 6/30/2005
Rebecca Willett University of Minnesota 3/10/2005 - 3/10/2005
Ruth Williams University of California - San Diego 3/19/2005 - 3/20/2005
Doug Wright University of Minnesota 2/15/2005 - 8/31/2005
Chenyang Xu Siemens Corporate Research 3/3/2005 - 3/4/2005
Baisheng Yan Michigan State University 9/1/2004 - 6/30/2005
Mihalis Yannakakis Columbia University 3/19/2005 - 3/20/2005
Aaron Nung Kwan Yip Purdue University 1/16/2005 - 6/30/2005
Emmanuel Yomba University of Ngaoundéré 10/6/2004 - 8/31/2005
Pingwen Zhang Peking University 3/16/2005 - 3/31/2005
Erik van der Giessen University of Groningen 3/19/2005 - 3/26/2005
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Carnegie Mellon University, Consiglio Nazionale delle Ricerche (CNR), Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratories, Los Alamos National Laboratory, Michigan State University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Sandia National Laboratories, Seoul National University (BK21), Seoul National University (SRCCS), Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois - Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Texas - Austin, University of Wisconsin, University of Wyoming, Wayne State University
Participating Corporations: 3M, Boeing, Corning, ExxonMobil, Ford Motor Company, General Electric, General Motors, Honeywell, IBM Corporation, Johnson & Johnson, Lockheed Martin, Lucent Technologies, Motorola, Schlumberger-Doll Research, Siemens, Telcordia Technologies