Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall 207 Church Street SE Minneapolis, MN 55455 
Worcester Polytechnic Institute has joined the IMA as a Participating Institution. WPI's representative on the Participating Institutions Council is Bogdan Vernescu, chairman of the Mathematical Sciences Department.
The symmetries studied in the Summer Program naturally arise in several different ways. Firstly, there are the symmetries of a differential geometric structure. By definition, these are the vector fields that preserve the structure in question—the Killing fields of Riemannian differential geometry, for example. Secondly, the symmetries can be those of another differential operator. For example, the Riemannian Killing equation itself is projectively invariant whilst the ordinary Euclidean Laplacian gives rise to conformal symmetries. In addition, there are higher symmetries defined by higher order operators. Physics provides other natural sources of symmetries, especially through string theory and twistor theory.
These symmetries are usually highly constrained—viewed as differential operators, they themselves are overdetermined or have symbols that are subject to overdetermined differential equations. As a typical example, the symbol of a symmetry of the Laplacian must be a conformal Killing field (or a conformal Killing tensor for a higher order symmetry). The Summer Program considers the consequences of overdeterminacy and partial differential equations of finite type.
There will be six teams participating in the workshop. The mentors and projects are: Douglas C. Allan (Corning), Birefringence data analysis; Thomas Grandine (Boeing), WEBspline Finite Elements; SuPing Lyu (Medtronic), CellForeign Particle Interactions; Klaus Wiegand (ExxonMobil), How smart do "smart fields" need to be?; Brendt Wohlberg (Los Alamos National Laboratory), Blind Deconvolution of Motion Blur in Static Images; Chai Wah Wu (IBM), Algorithms for the Carpool Problem.
8:45a9:00a  Coffee  EE/CS 3176  SP7.178.4.06  
9:00a9:45a  Overdetermined elliptic boundary value problems  Jukka Tuomela (University of Joensuu)  EE/CS 3180  SP7.178.4.06 
9:45a10:00a  Break  EE/CS 3180  SP7.178.4.06  
10:00a10:45a  Geometric integration and control  Debra Lewis (University of Minnesota Twin Cities)  EE/CS 3180  SP7.178.4.06 
10:45a11:15a  Break  EE/CS 3176  SP7.178.4.06  
11:15a12:00p  Overdetermined systems, invariant connections, and short detour complexes  A. Rod Gover (University of Auckland)  EE/CS 3180  SP7.178.4.06 
12:00p2:00p  Lunch  SP7.178.4.06  
2:00p2:45p  Higher spin gauge theories and unfolded dynamics  Mikhail Vasiliev (P. N. Lebedev Physics Institute)  EE/CS 3180  SP7.178.4.06 
2:45p3:15p  Break  EE/CS 3176  SP7.178.4.06  
3:15p4:00p  Special polynomials associated with rational solutions of the Painleve equations and applications to soliton equations  Peter A. Clarkson (University of Kent at Canterbury)  EE/CS 3180  SP7.178.4.06 
8:45a9:00a  Coffee  EE/CS 3176  SP7.178.4.06  
9:00a9:45a  CRmanifolds, differential equations and multicontact structures (tentative)  Gerd Schmalz (University of New England)  EE/CS 3180  SP7.178.4.06 
9:45a10:00a  Break  EE/CS 3176  SP7.178.4.06  
10:00a10:45a  Wünsch's calculus for parabolic geometries  Jan Slovak (Masaryk University)  EE/CS 3180  SP7.178.4.06 
10:45a11:15a  Break  EE/CS 3176  SP7.178.4.06  
11:15a12:00p  Differential equations and conformal structures  Pawel Nurowski (University of Warsaw)  EE/CS 3180  SP7.178.4.06 
12:00p2:00p  Lunch  SP7.178.4.06  
2:00p2:45p  Symmetry algebras for even number of vector fields and for linearly perturbed complex structures  ChongKyu Han (Seoul National University)  EE/CS 3180  SP7.178.4.06 
2:45p3:15p  Break  EE/CS 3176  SP7.178.4.06  
3:15p4:00p  Superintegrable systems and the solution of a S. Lie problem  Vladimir S. Matveev (Katholieke Universiteit Leuven)  EE/CS 3180  SP7.178.4.06 
8:45a9:00a  Coffee  EE/CS 3176  SP7.178.4.06  
9:00a9:45a  The Work of Thomas P. Branson (Michael Eastwood, moderator)  Michael Eastwood (University of Adelaide)  EE/CS 3180  SP7.178.4.06 
10:00a10:45a  Break  EE/CS 3176  SP7.178.4.06  
10:00a10:45a  Geometric analysis in parabolic geometries  Bent Orsted (Aarhus University)  EE/CS 3180  SP7.178.4.06 
10:45a11:15a  Break  EE/CS 3176  SP7.178.4.06  
11:15a12:00p  Equivariant differential operators, classical invariant theory, unitary representations, and Macdonald polynomials  Siddhartha Sahi (Rutgers University)  EE/CS 3180  SP7.178.4.06 
12:00p2:00p  Lunch  SP7.178.4.06  
2:00p2:45p  The Uniqueness of the Joseph Ideal for the Classical Groups  Petr Somberg (Karlovy (Charles) University)  EE/CS 3180  SP7.178.4.06 
2:45p3:15p  Break  EE/CS 3176  SP7.178.4.06 
9:00a10:00a  Coffee  EE/CS 3176  SP7.178.4.06  
10:00a10:45a  Final Discussion Group Willard Miller Jr., moderator  Willard Miller Jr. (University of Minnesota Twin Cities)  EE/CS 3180  SP7.178.4.06 
All Day  Workshop Outline: Posing of problems by the 6 industry mentors. Halfhour introductory talks in the morning followed by a welcoming lunch. In the afternoon, the teams work with the mentors. The goal at the end of the day is to get the students to start working on the projects.  EE/CS 3180  MM8.918.06  
9:00a9:30a  Coffee and Registration  EE/CS 3176  MM8.918.06  
9:30a9:40a  Welcome and Introduction  Douglas N. Arnold (University of Minnesota Twin Cities) Richard J. Braun (University of Delaware) Fernando Reitich (University of Minnesota Twin Cities) Fadil Santosa (University of Minnesota Twin Cities)  EE/CS 3180  MM8.918.06 
9:40a10:00a  Team 1: Birefringence data analysis  Douglas C. Allan (Corning)  EE/CS 3180  MM8.918.06 
10:00a10:20a  Team 2: WEBspline Finite Elements  Thomas Grandine (The Boeing Company)  EE/CS 3180  MM8.918.06 
10:20a10:40a  Team 3: CellForeign Particle Interactions  Suping Lyu (Medtronic)  EE/CS 3180  MM8.918.06 
10:40a11:00a  Break  EE/CS 3176  MM8.918.06  
11:00a11:20a  Team 4: How smart do "smart fields" need to be?  Klaus D. Wiegand (ExxonMobil)  EE/CS 3180  MM8.918.06 
11:20a11:40a  Team 5: Blind Deconvolution of Motion Blur in Static Images  Brendt Wohlberg (Los Alamos National Laboratory)  EE/CS 3180  MM8.918.06 
11:40a12:00p  Team 6: Algorithms for the Carpool Problem  Chai Wah Wu (IBM Thomas J. Watson Research Center)  EE/CS 3180  MM8.918.06 
12:00p1:30p  Lunch  MM8.918.06  
1:30p4:30p  afternoon  start work on projects  EE/CS 3180  MM8.918.06 
All Day  Students work on the projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.  EE/CS 3180  MM8.918.06 
All Day  Students work on the projects.  EE/CS 3180  MM8.918.06 
All Day  Students and mentors work on the projects.  EE/CS 3180  MM8.918.06 
All Day  Students and mentors work on the projects.  MM8.918.06 
9:30a9:50a  Team 1 Progress Report  EE/CS 3180  MM8.918.06  
9:50a10:00a  Team 2 Progress Report  EE/CS 3180  MM8.918.06  
10:10a10:30a  Team 3 Progress Report  EE/CS 3180  MM8.918.06  
10:30a11:00a  Break  EE/CS 3176  MM8.918.06  
11:00a11:20a  Team 4 Progress Report  EE/CS 3180  MM8.918.06  
11:20a11:40a  Team 5 Progress Report  EE/CS 3180  MM8.918.06  
11:40a12:00p  Team 6 Progress Report  EE/CS 3180  MM8.918.06  
12:00p2:00p  Picnic  TBA  MM8.918.06 
All Day  Students and mentors work on the projects.  MM8.918.06 
All Day  Students and mentors work on the projects.  MM8.918.06 
All Day  Students and mentors work on the projects.  MM8.918.06 
9:00a9:30a  Team 1 Final Report  EE/CS 3180  MM8.918.06  
9:30a10:00a  Team 2 Final Report  EE/CS 3180  MM8.918.06  
10:00a10:30a  Team 3 Final Report  EE/CS 3180  MM8.918.06  
10:30a11:00a  Break  EE/CS 3176  MM8.918.06  
11:00a11:30a  Team 4 Final Report  EE/CS 3180  MM8.918.06  
11:30a12:00p  Team 5 Final Report  EE/CS 3180  MM8.918.06  
12:00p12:30p  Team 6 Final Report  EE/CS 3180  MM8.918.06  
12:30p2:00p  Pizza party  EE/CS 3176  MM8.918.06 
Event Legend: 

MM8.918.06  Mathematical Modeling in Industry X  A Workshop for Graduate Students 
SP7.178.4.06  Symmetries and Overdetermined Systems of Partial Differential Equations 
Douglas C. Allan (Corning)  Team 1:Birefringence data analysis 
Abstract: The goal of this project is to develop a set of algorithms implemented in software (such as Matlab) that reads and analyzes a birefringence map for a glass sample after exposure to a UV laser. The purpose of the analysis is to characterize how much strain (density change) has been produced in the glass by the laser exposure. This result can be reduced to a single number (the density change) but should be accompanied by some kind of error bar or quality of fit assessment. The analysis is to be performed in several steps, each of which offers opportunities for algorithm design and optimization: 1. A baseline measurement is read from a data file. This gives the birefringence of the glass sample prior to any laser exposure. 2. An experimental data file is read in, giving the birefringence field of the same sample after laser exposure. It is necessary to align the two fields of data so that the baseline can be subtracted from the postexposure field. The alignment involves a twodimensional translation (no rotation or scale change), but the translation may well be a subpixel value. (Typically the data sets are on a uniform grid of 0.5 mm spacing, which is a little coarser than some of the features we hope to study.) After subtraction, the resulting field of data represents only the laserinduced birefringence, without artifacts due to the initial birefringence of the sample. 3. A theoretical birefringence field is read in. This has been calculated assuming a nominal fractional density change (e.g. 1ppm ) and takes into account the sample boundary conditions and exposure geometry. The theoretical birefringence field must be aligned with the subtracted file calculated above, again with a subpixel shift, and then a bestfit value of the density should be deduced to give the best agreement between theory and measurement. Theory and experiment are compared in Figure 1.
Figure 1. Calculated (left) and measured (right) birefringence maps for a laserexposed sample. Small lines show slow axis orientation, blue regions have low birefringence and green regions have higher birefringence. There are several features of this problem that makes it mathematically more interesting: 1. Birefringence (defined as the difference in optical index of refraction for orthogonal polarizations of light) is a quantity with both magnitude and direction, but is not a vector. Manipulating and calculating birefringence fields offers some challenges. 2. Subpixel alignment of data sets requires some kind of interpolation scheme, such as Fourier interpolation by use of FFTs or something else. Optimizing the alignment with slightly noisy data offers some challenges. 3. The underlying physics of birefringence and why the birefringence fields look as they do (e.g. zero in the center of the exposed region, peak value just outside the exposed region) is interesting to study and understand. References:
Prerequisites: 

Peter A. Clarkson (University of Kent at Canterbury)  Special polynomials associated with rational solutions of the Painleve equations and applications to soliton equations 
Abstract: In this talk I shall discuss special polynomials associated with rational solutions for the Painleve equations and of the soliton equations which are solvable by the inverse scattering method, including the Kortewegde Vries, modified Kortewegde Vries, classical Boussinesq and nonlinear Schrodinger equations. The Painleve equations (PIPVI) are six nonlinear ordinary differential equations that have been the subject of much interest in the past thirty years, which have arisen in a variety of physical applications. Further they may be thought of as nonlinear special functions. Rational solutions of the Painleve equations are expressible in terms of the logarithmic derivative of certain special polynomials. For PII these polynomials are known as the YablonskiiVorob'ev polynomials, first derived in the 1960's by Yablonskii and Vorob'ev. The locations of the roots of these polynomials is shown to have a highly regular triangular structure in the complex plane. The analogous special polynomials associated with rational solutions of PIV are described and it is shown that their roots also have a highly regular structure. It is well known that soliton equations have symmetry reductions which reduce them to the Painleve equations. Hence rational solutions of soliton equations arising from symmetry reductions of the Painleve equation can be expressed in terms of the aforementioned special polynomials. Also the motion of the poles of the rational solutions of the Kortewegde Vries equation is described by a constrained CalogeroMoser system describes the motion of the poles of rational solutions of the Kortewegde Vries equation, as shown by Airault, McKean, and Moser in 1977. The motion of the poles of more general rational solutions of equations in the Kortewegde Vries, modified Kortewegde Vries and classical Boussinesq equations, and the motion of zeroes and poles of rational and new rationaloscillatory solutions of the nonlinear Schrodinger equation will be discussed.  
Michael Eastwood (University of Adelaide)  The Work of Thomas P. Branson (Michael Eastwood, moderator) 
Abstract: Tom Branson played a leading role in the conception and organization of this Summer Program. Tragically, he passed away in March this year and the Summer Program is now dedicated to his memory. This session will be devoted to a discussion of his work. The format will be decided in consultation with others during the earlier part of the Program and anyone wishing to present material is asked to contact the moderator.  
A. Rod Gover (University of Auckland)  Overdetermined systems, invariant connections, and short detour complexes 
Abstract: With mild restrictions, each overdetermined differential operator is equivalent to a (tractortype) connection on a prolonged system, and this connection depends only on the operator concerned. On the other hand in Riemannian geometry (for example), natural conformally invariant overdetermined operators may, given suitable curvature restrictions, be extended to an elliptic conformally invariant complex that we term a short detour complex. (These complexes yield an approach to studying deformations of various structures, and these complexes and their hyperbolic variants also have a role in gauge theory.) These constructions are intimately related.  
Thomas Grandine (The Boeing Company)  Team 2: WEBspline Finite Elements 
Abstract: One of the more intriguing choices of finite elements in the finite element method is Bsplines. Bsplines can be constructed to form a basis for any space of piecewise polynomial functions, including those which have specified continuity conditions at the junctions between the individual polynomial pieces. The classical finite element method based on Bsplines for ODEs is de Boor  Swartz collocation at Gauss points. Until recently, however, extensions to more than one variable were hard to come by.
That changed with the publication of "Finite Element Methods with BSplines", by Klaus Hoellig in 2003. He introduces weighted, extended Bsplines (WEBsplines) as a means addressing boundary conditions and numerical conditioning problems. Results presented by Hoellig and his collaborator Ulrich Reif look very promising. This project is straightforward: We will attempt to implement a finite element method for an elliptical PDE using WEBsplines. We will test the code on a fairly simple cylindrical beam that comes from an established multidisciplinary design optimization problem. If time permits, we will perform the actual design optimization on the given part using the WEBspline code that we will have developed. References
Prerequisites: Required: One semester of numerical analysis,
knowledge of programming Keywords: WEBspline, Bspline, finite element method, collocation 

ChongKyu Han (Seoul National University)  Symmetry algebras for even number of vector fields and for linearly perturbed complex structures 
Abstract: We discuss the existence of solutions and the dimension of the solution spaces for infinitesimal symmeries of the following two cases: firstly, even number (2n) of vector fields in a manifold of dimension 2n+1, and secondly, almost complex manifold with linearly perturbed structure. We use the method of complete prolongation for thses overdetermined linear pde systems of first order and checking the integrability of the associated Pfaffian systems.  
Debra Lewis (University of Minnesota Twin Cities)  Geometric integration and control 
Abstract: The global trivializations of the tangent and cotangent bundles of Lie groups significantly simplifies the analysis of variational problems, including Lagrangian mechanics and optimal control problems, and Hamiltonian systems. In numerical simulations of such systems, these trivializations and the exponential map or its analogs (e.g. the Cayley transform) provide natural mechanisms for translating traditional algorithms into geometric methods respecting the nonlinear structure of the groups and bundles. The interaction of some elementary aspects of geometric mechanics (e.g. noncommutativity and isotropy) with traditional methods for vector spaces yields new and potentially valuable results.  
Suping Lyu (Medtronic)  Team 3: CellForeign Particle Interactions 
Abstract:
Cell membrane forms a closed shell separating the cell content (cytoplasm) from the extra cellular matrix, both of which are simply aqueous solutions of electrolytes and neutral molecules. Typically, there is a net positive charge in the outside surface (extracellular) of the membrane and a net negative charge in the inside surface (cytoplamic) of the membrane. As such, there is a voltage drop from the outside surface to the inside surface across the membrane. However, the membrane itself is hydrophobic and deformable. When there is an external electric field, e.g. by a charged foreign particle, the surface charge densities of the membrane could be disturbed. Because the system is in electrolyte solutions, the static interactions need to be modeled with the PoissonBoltzmann equation. The problems proposed here are: (1) How are the surface charge densities of the membrane disturbed by a charged particle? What are the interactions between the particle and the membrane? (2) If the particle is smaller than the cell, when it touches the membrane surface, how does it deform the membrane and can it pass through the membrane? Consider the following variables for the above analysis: the size and charge of the particle, surface charge density and surface tension of the membrane, membrane curvature and rigidity, and particlemembrane distance. One can assume that both the particle and the cell are spheres. The electrolyte solutions both inside and outside of the cell are the same. The membrane thickness (about 5 nm) is much smaller than cell size (1 to 10 micron). References
Required: None Desired: Familiarity with electromagnetics, statistical mechanics Keywords: surfacecharged membrane, PoissonBoltzmann equation for electrolyte solution, interfacial tension. 

Vladimir S. Matveev (Katholieke Universiteit Leuven)  Superintegrable systems and the solution of a S. Lie problem 
Abstract: I present a solution of a classical problem posed by Sophus Lie in 1882. One of the main ingredients comes from superintegrable systems. Another ingredient is a study of the following question and its generalizations: when there exists a Riemannian metric with a given a projective connection.  
Willard Miller Jr. (University of Minnesota Twin Cities)  Final Discussion Group Willard Miller Jr., moderator 
Abstract: A primary aim of this Summer Program is to promote fruitful interaction between various research groups and individuals currently working, perhaps unwittingly, on overlapping themes. This session will be devoted to a public discussion of problems and possible directions for future research and collaboration. The format will be decided in consultation with others during the earlier part of the Program and anyone wishing to present material is asked to contact the moderator.  
Pawel Nurowski (University of Warsaw)  Differential equations and conformal structures 
Abstract: We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a onetoone correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact transformations of variables and (local) 3dimensional conformal Lorentzian geometries. The second example shows that every point equivalent class of 3rd order ODEs satisfying the Wuenschmann and the Cartan conditions define a 3dimensional Lorentzian EinsteinWeyl geometry. The third example associates to each point equivalence class of 3rd order ODEs a 6dimensional conformal geometry of neutral signature. The fourth example exhibits the onetoone correspondence between point equivalent classes of 2nd order ODEs and 4dimensional conformal Feffermanlike metrics of neutral signature. The fifth example shows the correspondence between undetermined ODEs of the Monge type and conformal geometries of signature (3,2). The Cartan normal conformal connection for these geometries is reducible to the Cartan connection with values in the Lie algebra of the noncompact form of the exceptional group G2. All the examples are deeply rooted in Elie Cartan's works on exterior differential systems.  
Bent Orsted (Aarhus University)  Geometric analysis in parabolic geometries 
Abstract: Many aspects of parabolic geometries are by now well understood, especially those related to differential geometry and the symmetries of natural differential operators associated with these geometries. In this talk we shall see how some aspects of geometric analysis may be generalized from the bestknown cases, namely Riemannian and conformal geometry, resp. CR geometry, to more general geometries. In particular we shall give results about Sobolev spaces and inequalities, and also mention results about unitary representations of the natural symmetry groups.  
Siddhartha Sahi (Rutgers University)  Equivariant differential operators, classical invariant theory, unitary representations, and Macdonald polynomials 
Abstract: The various subjects in the title are connected by a common strand! In my talk, which is introductory in nature, I will give an overview of the subjects, and describe this fascinating connection.  
Gerd Schmalz (University of New England)  CRmanifolds, differential equations and multicontact structures (tentative) 
Abstract: Cartan's method of moving frames has been successfully applied to the study of CRmanifolds, their mappings and invariants. For some types of CRmanifolds there is a close relation to the pointwise or contact geometry of differential equations. This can be used to find CRmanifolds with special symmetries. The recently introduced notion of multicontact structures provides a general framework comprising certain geometries of differential equations and CRmanifolds which in turn give examples with many symmetries.  
Jan Slovak (Masaryk University)  Wünsch's calculus for parabolic geometries 
Abstract: The conformally invariant objects were always understood as affine invariants of the underlying Riemannian connections which did not depend on the choice within the conformal class. Although this definition is so easy to understand, the description of such invariants is a difficult task and many mathematicians devoted deep papers to this problem in the last 80 years. The classical approach coined already by Veblen and Schouten was to elaborate special tensorial objects out of the curvatures, designed to eliminate the transformation rules of the Riemannian connections under conformal rescaling. The most complete treatment of such a procedure was given in a series of papers by Günther and Wünsch in 1986. They provide a version of calculus which allows to list all invariants in low homogeneities explicitly. The aim of this talk is to present a concise version of a similar calculus for all parabolic geometries, relying on the canonical normal Cartan connections.  
Petr Somberg (Karlovy (Charles) University)  The Uniqueness of the Joseph Ideal for the Classical Groups 
Abstract: The Joseph ideal is a unique ideal in the universal enveloping algebra of a simple Lie algebra attached to the minimal coadjoint orbit. For the classical groups, its uniqueness  in a sense of the noncommutative graded deformation theory  is equivalent to the existence of tensors with special properties. The existence of these tensors is usually concluded abstractly via algebraic geometry, but we present explicit formulae. This allows a rather direct computation of a special value of the parameter in the family of ideals used to determine the Joseph ideal.  
Jukka Tuomela (University of Joensuu)  Overdetermined elliptic boundary value problems 
Abstract: I will first report on some recent work on generalising ShapiroLopatinski condition to overdetermined problems. The technical difficulty in this extension is that the parametrices are no longer pseudodifferential operators, but Boutet de Monvel operators. Then I discuss some numerical work related to these issues, and present one possibility to treat overdetermined problems numerically. In this approach there is no need to worry about infsup condition: for example one can stably compute the solution of the Stokes problem with P1/P1 formulation.  
Mikhail Vasiliev (P. N. Lebedev Physics Institute)  Higher spin gauge theories and unfolded dynamics 
Abstract: I will discuss nonlinear equations of motion of higher spin gauge fields. The driving idea is to study most symmetric field theories, assuming that whatever theory of fundamental interactions is it should be very symmetric. The formulation is based on the unfolded dynamics formalism which is an overdetermined multidimensional covariant extension of the onedimensional Hamiltonian dynamics. General properties of the unfolded dynamics formulation will be discussed in some detail with the emphasize on symmetries and coordinate independence.  
Klaus D. Wiegand (ExxonMobil)  Team 4: How smart do "smart fields" need to be? 
Abstract:
A hot new area in the petroleum industry is "smart" or "intelligent" wells/fields. In relatively simple model (artificial) cases, use of intelligent oilfield technology can lead to large predicted improvements in profitability over the life of a field. However, practical issues are commonly ignored in the published cases, particularly the large uncertainties of several kinds typically encountered. For example, consider the essentially unpredictable wide swings in oil price that have occurred, as shown in the chart below. How does this impact our confidence in the modeled rate of return?
References:
Prerequisites:
Keywords: modeling, optimization, uncertainty 

Brendt Wohlberg (Los Alamos National Laboratory)  Team 5: Blind Deconvolution of Motion Blur in Static Images 
Abstract:
Many kinds of image degradation, including blur due to defocus or camera motion, may be modeled by convolution of the unknown original image by an appropriate point spread function (PSF). Recovery of the original image is referred to as deconvolution. The more difficult problem of blind deconvolution arises when the PSF is also unknown. The goal of the project is to design and implement an effective algorithm for blind deconvolution of images degraded by motion blur (see figures). The project will consist of the following stages:
Figure 1. Motionblurred image and deconvolved image. From Maximum Entropy Data Consultants Ltd (UK) http://www.maxent.co.uk/example_1.htm References:
Prerequisites: Keywords: Image processing, motion blur, blind deconvolution, inverse problems 

Chai Wah Wu (IBM Thomas J. Watson Research Center)  Team 6: Algorithms for the Carpool Problem 
Abstract:
Scheduling problems occur in many industrial settings and have been studied extensively. They are used in many applications ranging from determining manufacturing schedules to allocating memory in computer systems. In this project we study the scheduling problem known as the Carpool problem: suppose that a subset of the people in a neighborhood gets together to carpool to work every morning. What is the fairest way to choose the driver each day? This problem has applications to the scheduling of multiple tasks on a single resource. The goal of this project is to study various aspects of algorithms to solve the Carpool problem, including optimality and performance. References:
Prerequisites: Keywords: Analysis of algorithms, computer simulation. 
Douglas C. Allan  Corning  8/8/2006  8/18/2006 
JungHa An  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Stephen Anco  Brock University  7/15/2006  8/4/2006 
Sasanka Are  University of Massachusetts  8/8/2006  8/18/2006 
Douglas N. Arnold  University of Minnesota Twin Cities  7/15/2001  8/31/2007 
Donald G. Aronson  University of Minnesota Twin Cities  9/1/2002  8/31/2007 
Christopher Bailey  Kent State University  8/8/2006  8/18/2006 
Evgeniy Bart  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Helga Baum  HumboldtUniversität  7/16/2006  8/5/2006 
Gloria Mari Beffa  University of Wisconsin  7/23/2006  8/4/2006 
Joao Pedro Boavida  University of Minnesota Twin Cities  8/8/2006  8/19/2006 
Melisande Fortin Boisvert  McGill University  7/16/2006  8/4/2006 
Richard J. Braun  University of Delaware  8/7/2006  8/18/2006 
Yanping Cao  University of California  8/8/2006  8/19/2006 
Andreas Cap  University of Vienna  7/16/2006  8/4/2006 
Mark Chanachowicz  University of Waterloo  7/16/2006  8/5/2006 
Claudia Chanu  Università di Torino  7/14/2006  8/2/2006 
Jeongoo Cheh  University of St. Thomas  7/17/2006  8/4/2006 
Qianyong Chen  University of Minnesota Twin Cities  9/1/2004  8/31/2006 
Ginmo (Jason) Chung  University of California  8/8/2006  8/18/2006 
Peter A. Clarkson  University of Kent at Canterbury  7/16/2006  8/4/2006 
Benjamin Cook  University of California  8/8/2006  8/18/2006 
Luca Degiovanni  Università di Torino  7/14/2006  8/1/2006 
Brian DiDonna  University of Minnesota Twin Cities  9/1/2004  8/31/2006 
Paul Dostert  Texas A & M University  8/8/2006  8/18/2006 
Boris Doubrov  Belarus State University  7/16/2006  8/5/2006 
Michael Eastwood  University of Adelaide  7/15/2006  8/5/2006 
Bree Ettinger  University of Georgia  8/8/2006  8/18/2006 
Peter Franek  Karlovy (Charles) University  7/16/2006  8/4/2006 
Michal Godlinski  University of Warsaw  7/17/2006  8/4/2006 
A. Rod Gover  University of Auckland  7/25/2006  8/2/2006 
Thomas Grandine  The Boeing Company  8/8/2006  8/18/2006 
Alvaro Guevara  Louisiana State University  8/8/2006  8/19/2006 
Robert Gulliver  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Hazem Hamdan  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
ChongKyu Han  Seoul National University  7/16/2006  8/4/2006 
Sean Hardesty  Rice University  8/8/2006  8/18/2006 
Gloria Haro Ortega  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Kengo Hirachi  University of Tokyo  7/16/2006  8/5/2006 
Evelyne Hubert  Institut National de Recherche en Informatique Automatique (INRIA)  7/15/2006  8/5/2006 
Peter Hydon  University of Surrey  7/14/2006  8/4/2006 
Jens Jonasson  Linköping University  7/17/2006  8/4/2006 
Sookyung Joo  University of Minnesota Twin Cities  9/1/2004  8/31/2006 
Vikram Kamat  Arizona State University  8/8/2006  8/18/2006 
Chiu Yen Kao  University of Minnesota Twin Cities  9/1/2004  8/31/2006 
Tanya Kazakova  University of Notre Dame  8/8/2006  8/19/2006 
Joseph Kenney  University of Minnesota Twin Cities  8/8/2006  8/19/2006 
Joseph Kenney  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Irina Kogan  North Carolina State University  7/16/2006  8/5/2006 
Felix Krahmer  New York University  8/8/2006  8/18/2006 
Jonathan Kress  University of New South Wales  7/14/2006  8/4/2006 
Svatopluk Krysl  Karlovy (Charles) University  7/16/2006  8/5/2006 
SongHwa Kwon  University of Minnesota Twin Cities  8/30/2005  8/31/2007 
Niels Lauritzen  Aarhus University  8/28/2006  6/30/2007 
GuangTsai Lei  GTG Research  7/17/2006  8/4/2006 
Thomas Leistner  University of Adelaide  7/15/2006  8/5/2006 
Felipe Leitner  Universität Stuttgart  7/17/2006  8/5/2006 
Debra Lewis  University of Minnesota Twin Cities  7/15/2004  8/31/2006 
Anton Leykin  University of Illinois  8/16/2006  8/15/2007 
Hstau Liao  University of Minnesota Twin Cities  9/2/2005  8/31/2007 
Youzuo Lin  Arizona State University  8/8/2006  8/19/2006 
Juan Liu  University of Florida  8/8/2006  8/18/2006 
Xiaolong Liu  University of Iowa  7/16/2006  8/4/2006 
Suping Lyu  Medtronic  8/8/2006  8/18/2006 
Pedro Madrid  University of Puerto Rico  8/8/2006  8/18/2006 
Alison Malcolm  University of Minnesota Twin Cities  9/1/2005  8/31/2006 
Elizabeth L. Mansfield  University of Kent at Canterbury  7/16/2006  8/4/2006 
Jose Kenedy Martins  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Vladimir S. Matveev  Katholieke Universiteit Leuven  7/17/2006  8/4/2006 
Bonnie McAdoo  Clemson University  8/8/2006  8/18/2006 
Bonnie McAdoo  Clemson University  7/16/2006  8/7/2006 
Ray McLenaghan  University of Waterloo  7/16/2006  8/5/2006 
Willard Miller Jr.  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Darshana Nakum  University of Nevada  8/8/2006  8/19/2006 
Jeremy Neal  Kent State University  8/8/2006  8/18/2006 
Anatoly Nikitin  National Academy of Sciences of Ukraine  7/16/2006  8/4/2006 
Hung (Ryan) Nong  Rice University  8/8/2006  8/18/2006 
Pawel Nurowski  University of Warsaw  7/16/2006  8/5/2006 
Luke Oeding  Texas A & M University  7/16/2006  8/4/2006 
Peter J. Olver  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Bent Orsted  Aarhus University  7/28/2006  8/4/2006 
Katharine Ott  University of Virginia  8/8/2006  8/18/2006 
Saadet S. Ozer  Yeditepe University  7/16/2006  8/4/2006 
Teoman Ozer  Istanbul Technical University  7/15/2006  8/8/2006 
Miguel Pauletti  University of Maryland  8/8/2006  8/18/2006 
Peter Philip  University of Minnesota Twin Cities  8/22/2004  8/18/2006 
Giovanni Rastelli  Università di Torino  7/14/2006  8/2/2006 
Greg Reid  University of Western Ontario  7/30/2006  8/2/2006 
Fernando Reitich  University of Minnesota Twin Cities  8/9/2006  8/18/2006 
Chan Roath  Ministry of Education, Youth and Sport  7/15/2006  8/15/2006 
Siddhartha Sahi  Rutgers University  7/23/2006  8/4/2006 
Fadil Santosa  University of Minnesota Twin Cities  8/9/2006  8/18/2006 
Arnd Scheel  University of Minnesota Twin Cities  7/15/2004  8/31/2007 
Gerd Schmalz  University of New England  7/28/2006  8/4/2006 
Neil Seshadri  University of Tokyo  7/16/2006  8/5/2006 
Sarthok Sircar  Florida State University  8/8/2006  8/18/2006 
Astri Sjoberg  University of Johannesburg  7/16/2006  8/4/2006 
Jan Slovak  Masaryk University  7/17/2006  8/4/2006 
Dalibor Smid  Karlovy (Charles) University  7/16/2006  8/5/2006 
Roman Smirnov  Dalhousie University  7/16/2006  8/5/2006 
Vadim Sokolov  Northern Illinois University  8/8/2006  8/18/2006 
Tatiana Soleski  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Petr Somberg  Karlovy (Charles) University  7/17/2006  8/5/2006 
Vladimir Soucek  Karlovy (Charles) University  7/17/2006  8/5/2006 
Olga Terlyga  Northern Illinois University  8/8/2006  8/18/2006 
Dennis The  McGill University  7/16/2006  8/5/2006 
Carl Toews  University of Minnesota Twin Cities  9/1/2005  8/31/2007 
Jukka Tuomela  University of Joensuu  7/23/2006  8/2/2006 
Francis Valiquette  University of Minnesota Twin Cities  7/17/2006  8/4/2006 
Jon Van Laarhoven  University of Iowa  8/8/2006  8/18/2006 
Mikhail Vasiliev  P. N. Lebedev Physics Institute  7/17/2006  8/6/2006 
Raphael VergeRebelo  University of Montreal  7/16/2006  8/5/2006 
Alfredo Villanueva  University of Iowa  7/16/2006  8/4/2006 
John Voight  University of Sydney  8/15/2006  8/31/2007 
Jiakou Wang  Pennsylvania State University  8/8/2006  8/18/2006 
Xiaoqiang Wang  University of Minnesota Twin Cities  9/1/2005  8/4/2006 
Ben Warhurst  University of New South Wales  7/16/2006  8/5/2006 
Ang Wei  University of Delaware  8/8/2006  8/18/2006 
David Widemann  University of Maryland  8/8/2006  8/18/2006 
Klaus D. Wiegand  ExxonMobil  8/8/2006  8/18/2006 
Brendt Wohlberg  Los Alamos National Laboratory  8/8/2006  8/18/2006 
Thomas Wolf  Brock University  7/16/2006  8/6/2006 
Chai Wah Wu  IBM Thomas J. Watson Research Center  8/8/2006  8/18/2006 
Jianbao Wu  University of Georgia  8/8/2006  8/18/2006 
Guangri Xue  Pennsylvania State University  8/8/2006  8/18/2006 
Keizo Yamaguchi  Hokkaido University  7/16/2006  8/5/2006 
Jin Yue  Dalhousie University  7/16/2006  8/5/2006 
Ping Zhang  University of Kentucky  8/8/2006  8/19/2006 
Xinyi Zhang  University of Delaware  8/8/2006  8/18/2006 
Ruijun Zhao  Purdue University  8/8/2006  8/19/2006 
Renat Zhdanov  BioKey International  7/16/2006  8/5/2006 