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IMA Newsletter #358

August 2006

News and Notes

Worcester Polytechnic Institute joins the IMA

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.

IMA Events

Symmetries and Overdetermined Systems of Partial Differential Equations

July 17 - August 4, 2006

Organizers: Michael Eastwood (University of Adelaide) and Willard Miller Jr. (University of Minnesota Twin Cities)

This summer program is dedicated to the memory of Thomas P. Branson, who played
a leading role in its conception and organization, but did not live to see its realization.

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.

Mathematical Modeling in Industry X - A Workshop for Graduate Students

August 9-18, 2006

Organizers: Richard J. Braun (University of Delaware),
Fernando Reitich (University of Minnesota Twin Cities),
Fadil Santosa (University of Minnesota Twin Cities)
The 10-day workshop on Mathematical Modeling in Industry is designed to provide graduate students and qualified advanced undergraduates with first hand experience in industrial research. Students will work in teams of up to six students under the guidance of a mentor from industry. The mentor will guide the students in the modeling process, analysis and computational work associated with a real-world industrial problem.

There will be six teams participating in the workshop. The mentors and projects are: Douglas C. Allan (Corning), Birefringence data analysis; Thomas Grandine (Boeing), WEB-spline Finite Elements; SuPing Lyu (Medtronic), Cell-Foreign 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.

Schedule

Tuesday, August 1

8:45a-9:00aCoffeeEE/CS 3-176 SP7.17-8.4.06
9:00a-9:45aOverdetermined elliptic boundary value problemsJukka Tuomela (University of Joensuu)EE/CS 3-180 SP7.17-8.4.06
9:45a-10:00aBreak EE/CS 3-180 SP7.17-8.4.06
10:00a-10:45aGeometric integration and control Debra Lewis (University of Minnesota Twin Cities)EE/CS 3-180 SP7.17-8.4.06
10:45a-11:15aBreakEE/CS 3-176 SP7.17-8.4.06
11:15a-12:00pOverdetermined systems, invariant connections, and short detour complexesA. Rod Gover (University of Auckland)EE/CS 3-180 SP7.17-8.4.06
12:00p-2:00pLunch SP7.17-8.4.06
2:00p-2:45pHigher spin gauge theories and unfolded dynamicsMikhail Vasiliev (P. N. Lebedev Physics Institute)EE/CS 3-180 SP7.17-8.4.06
2:45p-3:15pBreakEE/CS 3-176 SP7.17-8.4.06
3:15p-4:00pSpecial polynomials associated with rational solutions of the Painleve equations and applications to soliton equationsPeter A. Clarkson (University of Kent at Canterbury)EE/CS 3-180 SP7.17-8.4.06

Wednesday, August 2

8:45a-9:00aCoffeeEE/CS 3-176 SP7.17-8.4.06
9:00a-9:45aCR-manifolds, differential equations and multicontact structures (tentative) Gerd Schmalz (University of New England)EE/CS 3-180 SP7.17-8.4.06
9:45a-10:00aBreakEE/CS 3-176 SP7.17-8.4.06
10:00a-10:45aWünsch's calculus for parabolic geometriesJan Slovak (Masaryk University)EE/CS 3-180 SP7.17-8.4.06
10:45a-11:15aBreakEE/CS 3-176 SP7.17-8.4.06
11:15a-12:00pDifferential equations and conformal structuresPawel Nurowski (University of Warsaw)EE/CS 3-180 SP7.17-8.4.06
12:00p-2:00pLunch SP7.17-8.4.06
2:00p-2:45pSymmetry algebras for even number of vector fields and for linearly perturbed complex structuresChong-Kyu Han (Seoul National University)EE/CS 3-180 SP7.17-8.4.06
2:45p-3:15pBreakEE/CS 3-176 SP7.17-8.4.06
3:15p-4:00pSuperintegrable systems and the solution of a S. Lie problemVladimir S. Matveev (Katholieke Universiteit Leuven)EE/CS 3-180 SP7.17-8.4.06

Thursday, August 3

8:45a-9:00aCoffeeEE/CS 3-176 SP7.17-8.4.06
9:00a-9:45aThe Work of Thomas P. Branson
(Michael Eastwood, moderator)
Michael Eastwood (University of Adelaide)EE/CS 3-180 SP7.17-8.4.06
10:00a-10:45aBreakEE/CS 3-176 SP7.17-8.4.06
10:00a-10:45aGeometric analysis in parabolic geometriesBent Orsted (Aarhus University)EE/CS 3-180 SP7.17-8.4.06
10:45a-11:15aBreakEE/CS 3-176 SP7.17-8.4.06
11:15a-12:00pEquivariant differential operators, classical invariant theory, unitary representations, and Macdonald polynomialsSiddhartha Sahi (Rutgers University)EE/CS 3-180 SP7.17-8.4.06
12:00p-2:00pLunch SP7.17-8.4.06
2:00p-2:45pThe Uniqueness of the Joseph Ideal for the Classical GroupsPetr Somberg (Karlovy (Charles) University)EE/CS 3-180 SP7.17-8.4.06
2:45p-3:15pBreakEE/CS 3-176 SP7.17-8.4.06

Friday, August 4

9:00a-10:00aCoffeeEE/CS 3-176 SP7.17-8.4.06
10:00a-10:45aFinal Discussion Group
Willard Miller Jr., moderator
Willard Miller Jr. (University of Minnesota Twin Cities)EE/CS 3-180 SP7.17-8.4.06

Wednesday, August 9

All DayWorkshop Outline: Posing of problems by the 6 industry mentors. Half-hour 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 3-180 MM8.9-18.06
9:00a-9:30aCoffee and RegistrationEE/CS 3-176 MM8.9-18.06
9:30a-9:40aWelcome and IntroductionDouglas 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 3-180 MM8.9-18.06
9:40a-10:00aTeam 1: Birefringence data analysisDouglas C. Allan (Corning)EE/CS 3-180 MM8.9-18.06
10:00a-10:20aTeam 2: WEB-spline Finite ElementsThomas Grandine (The Boeing Company)EE/CS 3-180 MM8.9-18.06
10:20a-10:40aTeam 3: Cell-Foreign Particle InteractionsSuping Lyu (Medtronic)EE/CS 3-180 MM8.9-18.06
10:40a-11:00aBreakEE/CS 3-176 MM8.9-18.06
11:00a-11:20aTeam 4: How smart do "smart fields" need to be?Klaus D. Wiegand (ExxonMobil)EE/CS 3-180 MM8.9-18.06
11:20a-11:40aTeam 5: Blind Deconvolution of Motion Blur in Static ImagesBrendt Wohlberg (Los Alamos National Laboratory)EE/CS 3-180 MM8.9-18.06
11:40a-12:00pTeam 6: Algorithms for the Carpool ProblemChai Wah Wu (IBM Thomas J. Watson Research Center)EE/CS 3-180 MM8.9-18.06
12:00p-1:30pLunch MM8.9-18.06
1:30p-4:30pafternoon - start work on projectsEE/CS 3-180 MM8.9-18.06

Thursday, August 10

All DayStudents work on the projects. Mentors guide their groups through the modeling process, leading discussion sessions, suggesting references, and assigning work.EE/CS 3-180 MM8.9-18.06

Friday, August 11

All DayStudents work on the projects.EE/CS 3-180 MM8.9-18.06

Saturday, August 12

All DayStudents and mentors work on the projects.EE/CS 3-180 MM8.9-18.06

Sunday, August 13

All DayStudents and mentors work on the projects. MM8.9-18.06

Monday, August 14

9:30a-9:50aTeam 1 Progress ReportEE/CS 3-180 MM8.9-18.06
9:50a-10:00aTeam 2 Progress ReportEE/CS 3-180 MM8.9-18.06
10:10a-10:30aTeam 3 Progress ReportEE/CS 3-180 MM8.9-18.06
10:30a-11:00aBreakEE/CS 3-176 MM8.9-18.06
11:00a-11:20aTeam 4 Progress ReportEE/CS 3-180 MM8.9-18.06
11:20a-11:40aTeam 5 Progress ReportEE/CS 3-180 MM8.9-18.06
11:40a-12:00pTeam 6 Progress ReportEE/CS 3-180 MM8.9-18.06
12:00p-2:00pPicnicTBA MM8.9-18.06

Tuesday, August 15

All DayStudents and mentors work on the projects. MM8.9-18.06

Wednesday, August 16

All DayStudents and mentors work on the projects. MM8.9-18.06

Thursday, August 17

All DayStudents and mentors work on the projects. MM8.9-18.06

Friday, August 18

9:00a-9:30aTeam 1 Final ReportEE/CS 3-180 MM8.9-18.06
9:30a-10:00aTeam 2 Final ReportEE/CS 3-180 MM8.9-18.06
10:00a-10:30aTeam 3 Final ReportEE/CS 3-180 MM8.9-18.06
10:30a-11:00aBreakEE/CS 3-176 MM8.9-18.06
11:00a-11:30aTeam 4 Final ReportEE/CS 3-180 MM8.9-18.06
11:30a-12:00pTeam 5 Final ReportEE/CS 3-180 MM8.9-18.06
12:00p-12:30pTeam 6 Final ReportEE/CS 3-180 MM8.9-18.06
12:30p-2:00pPizza partyEE/CS 3-176 MM8.9-18.06
Abstracts
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 post-exposure field. The alignment involves a two-dimensional translation (no rotation or scale change), but the translation may well be a sub-pixel 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 laser-induced 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 sub-pixel shift, and then a best-fit 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 laser-exposed 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. Sub-pixel 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:

  1. J. Moll, D. C. Allan, and U. Neukirch, “Advances in the use of birefringence to measure laser-induced density changes in fused silica,” SPIE 5377, 1721-1726 (2004)
  2. N.F. Borrelli, C. Smith, D.C. Allan, T.P. Seward III, “Densification of fused silica under 193-nm excitation”, J. Opt. Soc. Am. B 14 (7), 1606-1615 (1997).

Prerequisites:
Required: computing skills, including familiarity with FFTs, manipulating data arrays, and plotting two-dimensional data fields.
Desired: some optics (not required), some physics (not required), familiarity with continuum elastic theory (stress and strain)

Keywords: strain-induced birefringence, laser damage of silica, data analysis algorithms

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 Korteweg-de Vries, modified Korteweg-de Vries, classical Boussinesq and nonlinear Schrodinger equations. The Painleve equations (PI-PVI) 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 Yablonskii-Vorob'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 Korteweg-de Vries equation is described by a constrained Calogero-Moser system describes the motion of the poles of rational solutions of the Korteweg-de 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 Korteweg-de Vries, modified Korteweg-de Vries and classical Boussinesq equations, and the motion of zeroes and poles of rational and new rational-oscillatory 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 (tractor-type) 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: WEB-spline Finite Elements
Abstract:

One of the more intriguing choices of finite elements in the finite element method is B-splines. B-splines 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 B-splines for ODEs is de Boor - Swartz collocation at Gauss points. Until recently, however, extensions to more than one variable were hard to come by.

cylinder

That changed with the publication of "Finite Element Methods with B-Splines", by Klaus Hoellig in 2003. He introduces weighted, extended B-splines (WEB-splines) 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 WEB-splines. We will test the code on a fairly simple cylindrical beam that comes from an established multi-disciplinary design optimization problem. If time permits, we will perform the actual design optimization on the given part using the WEB-spline code that we will have developed.

References

  1. Hoellig, Klaus. Finite Element Methods with B-splines. Philadelphia: SIAM Frontiers and Applied Mathematics Series, 2003.
  2. de Boor, C. and B. Swartz. "Collocation at Gaussian points," SIAM Journal of Numerical Analysis 10, pp. 582-606 (1973).

Prerequisites:

Required: One semester of numerical analysis, knowledge of programming
Desired: One semester of partial differential equations.

Keywords: WEB-spline, B-spline, finite element method, collocation

Chong-Kyu 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. non-commutativity and isotropy) with traditional methods for vector spaces yields new and potentially valuable results.
Suping Lyu (Medtronic) Team 3: Cell-Foreign 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 Poisson-Boltzmann 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 particle-membrane 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

  1. W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions, Cambridge Univ Pr., 1992
  2. Jacob N. Israelachvili, Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, Elsevier Science & Technology Books, 1992
  3. Miles D. Houslay, Keith K. Stanley, Dynamics of Biological Membrane: Influence on Synthesis Structure and Functions, Wiley, John & Sons, 1982
Prerequisites:
Required: None
Desired: Familiarity with electromagnetics, statistical mechanics

Keywords: surface-charged membrane, Poisson-Boltzmann 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 one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact transformations of variables and (local) 3-dimensional 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 3-dimensional Lorentzian Einstein-Weyl geometry. The third example associates to each point equivalence class of 3rd order ODEs a 6-dimensional conformal geometry of neutral signature. The fourth example exhibits the one-to-one correspondence between point equivalent classes of 2nd order ODEs and 4-dimensional conformal Fefferman-like 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 best-known 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) CR-manifolds, differential equations and multicontact structures (tentative)
Abstract: Cartan's method of moving frames has been successfully applied to the study of CR-manifolds, their mappings and invariants. For some types of CR-manifolds there is a close relation to the point-wise or contact geometry of differential equations. This can be used to find CR-manifolds with special symmetries. The recently introduced notion of multicontact structures provides a general framework comprising certain geometries of differential equations and CR-manifolds 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 non-commutative 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 Shapiro-Lopatinski 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 inf-sup 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 one-dimensional 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?

Under what conditions will smart field technologies provide the anticipated uplift in profitability? In other words, given the uncertainty in field description, development and operational parameters, commodity prices, and model inaccuracies, how can we best quantify the benefits of smart field technology? Ideas will be tested using simplified reservoir modeling techniques. It will not be necessary to have/develop expertise in reservoir simulation. This project is intended to be able to develop interesting and useful results without needing an in-depth understanding of geostatistics. On the other hand, if the team's interests head in that direction, this could be added. A "classical" reference in this area is "An Introduction to Applied Geostatistics" by E. H. Isaaks and R. M. Srivastava. A reference on uncertainty is "Sensitivity and Uncertainty Analysis", Volume 1: Theory (Hardcover) by Dan G. Cacuci. A reference on optimization is "Integer and Combinatorial Optimization" by G. L. Nemhauser and L. A. Wolsey.

References:

  1. Steve Begg, Reidar Bratvold, and John Campbell, "The Value of Flexibility in Managing Uncertainty in Oil and Gas Investments", SPE 77586, presented at the SPE annual technical conference and exhibition held in San Antonio, Texas, Sept 29 - Oct 2, 2002.
  2. V. Demyanov, S. Subbey, and M. A. Christie, "Uncertainty Assessment in PUNQ-S3 - Neighbourhood Algorithm Framework for Geostatistical Modeling," Proceedings, 2004 European Conference on the Mathematics of Oil Recovery Cannes, France (2004).
  3. P. Sarma, K. Aziz, L. J. Durlofsky, "Efficient Closed-Loop Production Optimization under Uncertainty", SPE 94241, presented at the SPE Europec/EAGE Annual Conference held in Madrid, Spain, 13-16 June, 2005.

Prerequisites:
Required: computing experience, some background in optimization and/or statistical modeling
Desired: geostatistics, control, reservoir simulation

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:

  • Develop a theoretical and practical understanding (via computational experiments) of classical approaches to blind deconvolution.
  • Perform a literature survey to become acquainted with some of the more recent advanced approaches to this problem. For example, those based on total variation regularization ("Total Variation Blind Deconvolution", Tony F. Chan and Chiu-Kwong Wong, ftp://ftp.math.ucla.edu/pub/camreport/cam96-45.ps.gz, wavelet methods ("ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems Ramesh Neelamani", Hyeokho Choi, and Richard Baraniuk,http://www-dsp.rice.edu/publications/pub/neelshdecon.pdf), or nonnegative matrix factorization ("Single-frame multichannel blind deconvolution by nonnegative matrix factorization with sparseness constraints", Ivica Kopriva,http://ol.osa.org/abstract.cfm?id=86353)
  • Devise one or two new or modified approaches to implement and pursue via computational experiment.

Figure 1. Motion-blurred image and deconvolved image. From Maximum Entropy Data Consultants Ltd (UK) http://www.maxent.co.uk/example_1.htm

References:

  1. Deepa Kundur and Dimitrios Hatzinakos, Blind image deconvolution", IEEE Signal Processing Magazine, May 1996. PDF available at http://www.ece.tamu.edu/~deepa/pdf/KunHat96a.pdf (Also see their followup article at http://www.ece.tamu.edu/~deepa/pdf/00543976.pdf
  2. Ming Jiang and Ge Wang, Development of blind image deconvolution and its applications, Journal of X-Ray Science and Technology, 11, 2003 PDF available at http://www.uiowa.edu/~mihpclab/papers/096-Jiang-Wang%20blind.pdf
  3. Matlab Image Processing Toolbox tutorial on Image Deblurring, at http://www.mathworks.com/access/helpdesk/help/toolbox/images/deblurri.html

Prerequisites:
Required: 1 semester of Fourier analysis, good computing skills (Matlab, C, or Python preferred)
Desired: Some background in mathematics of digital signal processing.
Beneficial: Familiarity with convex optimization and regularization methods, wavelet analysis

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:

  1. M. Ajtai, J. Aspnes, M. Naor, Y. Rabani, L. J. Schulman, and O. Waarts, Fairness in scheduling, Journal ofAlgorithms, 29(2), 306-357, 1998.
  2. S. K. Baruah, N. K. Cohen, C. G. Plaxton, and D. A. Varvel, Proportionate progress: A notion of fairness in resource allocation, Algorithmica, 15, 600-625, 1996.
  3. R. Fagin and J. H. Williams, A fair carpool scheduling algorithm, IBM Journal of Research and Development, 27(2),133-139, 1983.

Prerequisites:
Required: 1 semester of computer science or computer programming course
Desired: 1 semester of optimization/mathematical programming course.

Keywords: Analysis of algorithms, computer simulation.

Visitors in Residence
Douglas C. Allan Corning 8/8/2006 - 8/18/2006
Jung-Ha 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 Humboldt-Universität 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
Chong-Kyu 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
Song-Hwa Kwon University of Minnesota Twin Cities 8/30/2005 - 8/31/2007
Niels Lauritzen Aarhus University 8/28/2006 - 6/30/2007
Guang-Tsai 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 Verge-Rebelo 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 Bio-Key International 7/16/2006 - 8/5/2006
Legend: Postdoc or Industrial Postdoc Long-term Visitor

Participating Institutions: Air Force Research Laboratory, Carnegie-Mellon University, Consiglio Nazionale delle Ricerche, Georgia Institute of Technology, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Michigan State University, Mississippi State University, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Seoul National University, Texas A & M University, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at 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, University of Wisconsin, University of Wyoming, Wayne State University, Worcester Polytechnic Institute
Participating Corporations: 3M, Boeing, Corning, ExxonMobil, Ford, General Electric, General Motors, Honeywell, IBM, Johnson & Johnson, Lockheed Martin, Medtronic, Motorola, Schlumberger, Siemens, Telcordia