Minisymposia Abstracts
Speaker:  Antonio Leitao Federal University of St. Catarina, Brazil 
Title:  On new levelset type approaches for solving illposed problems 
Abstract:  We investigate levelset type approaches for solving illposed inverse
problems, under the assumption that the solution is a piecewise
constant function. Our goal is to identify the level sets as well as the level values of the unknown parameter function. Two distinct levelset frameworks are proposed for solving the inverse problem. In both of them the levelset function is assumed to be in L^{2}. Corresponding Tikhonov regularization approaches are derived and analyzed. Existence of minimizers for the Tikhonov functionals is proven. Moreover, convergence and stability results of the variational approaches are established, characterizing the Tikhonov approaches as regularization methods. 
Speaker:  Benedikt Wirth
Institute for Numerical Simulation, University of Bonn 
Title:  Fast Willmore flow time stepping for shape reconstruction from apparent contour 
Abstract:  Given a smooth threedimensional object, its Huffman labeling is a
twodimensional image. Its value at each point is given by the number of
times that the object surface is traversed by the ray emanating from the
image point orthogonally to the image. To reconstruct from a given
Huffman labeling the corresponding threedimensional object, we apply a
variational approach: We minimize the sum of a fitting energy (the
squared L²difference between the given and the actual Huffman
labeling) and the Willmore energy of the object surface as a
regularizer. The implementation of the above energy is based on a novel phase field model for Willmore type functionals, which itself consists of a nested variational formulation. Instead of using a direct approximation of the involved mean curvature in space, a suitable approximation is extracted from a timediscrete curvature motion model. More precisely, the mean curvature is replaced by the approximate speed of mean curvature motion, which is computed via a fully implicit variational model. The minimization of the reconstruction functional is then performed in a nested fashion: The minimization of the actual functional is treated in an outer variational approach which contains the above approximation of the mean curvature as an inner variational problem. This results in a PDEconstrained optimization in which the actual surface geometry as well as the geometry resulting from the implicit curvature motion time step are represented by phase field functions. 
Speaker:  Wolfgang Ring University of Graz 
Title:  Shape of optimally harmonic vibrating strings in tempered tuning 
Abstract: 
Harmonic vibrating strings are characterized by harmonic eigenvalues or
overtones λ_{n} = n λ_{0} with some
fundamental frequency λ_{0} (the pitch of the string). Simultaneously
sounding strings are perceived as
consonant (as opposed to dissonant) if the overtones of the two strings coincide
to a large extend. This
concept has led—already in ancient Greece—to the definition of consonant
intervals based on small integer
ratios between the pitches of two strings. A problem arise if one aims to build
up a coherent harmonic system
from the fact that already the two most fundamental intervals, the octave 2:1
and the pure fifth 3:2 are incompatible
in the sense that stacking pure fifth over a base tone never brings you exactly
(only approximately) to an octave and the
celebrated cycle of fifths does not close. As a remedy, welltempered tuning was
introduced in the Baroque age
were the octave is divided into 12 equal intervals defined by the irrational
factor ^{12}√2. Doing so a consistent harmonic
system without a distinguished central tone and the possibility to modulate
between different keys can be build up, however at
the expense of giving up purely consonant intervals with exactly matching
overtone. In other words, tempered tuned instruments
sound slightly out of tune.
By making the diameter of a vibrating string variable over the length of the string, the sequence of overtones can be shifted away from the harmonic sequence (n λ_{0})_{n ∈ N}. We aim to find a diameterprofile of a string such that the overtones of an array of geometrically identical strings in tempered tuning satisfy—as much as possible—the requirements of consonant agreement of common overtones. We present numerical and acoustical experiments for a piano in tempered tuning with harmonically matching overtones. 
Speaker:  Esther Klann Johannes Kepler University, Austria 
Title:  A Mumford–Shah like approach for limited tomography 
Abstract:  In this article the Mumford–Shah like method of Ramlau and Ring for complete
tomographic data is generalized and applied to limited angle and region of
interest tomography data. With the Mumford– Shah like method, one reconstructs a
piecewise constant function and simultaneously a segmentation from its
(complete) Radon transform data. For limited data, the ability of the
Mumford–Shah like method to find a segmentation, and by that the singularity set
of a function, is exploited. The method is applied to generated data from a
torso phantom. The results demonstrate the performance of the method in
reconstructing the singularity set, the density distribution itself for limited
angle data and also some quantitative information about the density distribution
for region of interest data. As a second example limited angle region of
interest tomography is considered as a simplified model for electron tomography.
For this problem we combine Lambda tomography and the MumfordShah like method.
The combined method is applied to simulated ET data.

Please address administrative questions to aipc@math.tamu.edu. Scientific questions should be addressed to the chair of the Scientific Program Committee: rundell AT math.tamu.edu