Minisymposia Abstracts
Speaker:  Jeremi Darde Universit'e Paris 7, France 
Title:  The exterior approach to solve an inverse obstacle problem in electric impedance tomography 
Abstract:  We introduce a technique based on duality in optimization
for approximating the Cauchy data of an electromagnetic potential from the
corresponding electrode currents and potentials in the framework of the complete
electrode model of impedance tomography. We then demonstrate that this approach
can be combined with the socalled "exterior approach", a quasireversibility
level set method to solve the inverse obstacle problem with ideally
conducting inhomogeneity using (only a few) electrode measurements of
electrical impedance tomography. We present numerical results highlighting
the efficiency of the method.

Speaker:  Martin Simon Johannes GutenbergUniversity of Mainz 
Title:  Probabilistic Interpretation of CurrenttoVoltageMaps within the Complete Electrode Model of EIT 
Abstract:  In this talk we consider currenttovoltage maps arising
in the complete electrode model of EIT. A probabilistic representation formula
in terms of reflected diffusion processes and their boundary local times is
presented, which coincides with the wellknown FeynmanKac formula if the
conductivity is constant. In the second part of the talk we discuss the
numerical simulation of the corresponding processes. We will point out difficult
ies in extending onedimensional simulation schemes to the multidimensional
case. In the third part of the presentation a formulation of the inverse problem
of EIT in terms of the diffusion processes and their generators is given. This
talk is based on joint work with Martin HankeBourgeois, University of Mainz,
Germany.

Speaker:  Nuutti Hyvonen Aalto University, Finland 
Title:  Electrical impedance tomography with two electrodes 
Abstract: 
Electrical impedance tomography is a noninvasive imaging technique for
recovering the conductivity distribution inside a body from boundary measurements
of current and voltage. In this talk, we consider impedance tomography in the
special case that the measurements are carried out with two electrodes that
can be moved along the boundary of the (twodimensional) object of interest.
Two different types of data are considered: The backscatter data is obtained
by using a small probe consisting of two electrodes for driving currents and
measuring voltage differences subsequently at various neighboring locations on
the boundary of the object. The scan data is gathered by fixing the location of
one electrode and measuring the voltage difference required for maintaining a
unit current as a function of the position of the other. A reconstruction
algorithm for locating conductivity inhomogeneities in homogeneous background
from such data sets is introduced and tested numerically. 
Speaker:  Armin Lechleiter
Ecole Polytechnique, France 
Title:  Explicit Characterization of the Support of NonLinear Inclusions 
Abstract:  We consider two inverse problems related to nonlinear and
penetrable media: An inverse scattering problem for a nonlinear medium and
the impedance tomography problem for a nonlinear conductivity. The nonlinear
measurement operators of these two problems (that is, the farfield operator
and the DirichlettoNeumann operator) satisfy factorizations that are suitable
to derive an explicit characterization of the support of a weakly nonlinear
inhomogeneity from the measurement operator. The technique is related to the
socalled infimum criterion and the Factorization method for inverse problems.

Speaker:  Peter Monk University of Delaware 
Title:  The Linear Sampling method in the Time Domain 
Abstract:  We present an extension of the frequency domain linear sampling
method to the time domain nearfield inverse scattering problem for the wave
equation of finding the shape of a Dirichlet scattering object from time domain
measurements of scattered waves. The inversion algorithm works directly on
timedomain data without using a Fourier transformation. This feature allows
us to naturally incorporate multiple (in fact, a continuum of) frequencies in
the inversion algorithm. Consequently, it offers the potential of improving the
quality of the reconstruction compared to frequency domain methods working with
a single frequency. We demonstrate this potential by several numerical examples.

Speaker:  John Sylvester University of Washington 
Title:  Transmission Eigenvalues and Upper Triangular Compactness 
Abstract:  The interior transmission eigenvalue problem can be formulated
as a 2x2 system of pdes, where one of the two unknown functions must satisfy too
many boundary conditions, and the other too few. The system is not selfadjoint
and the resolvent is not compact. Under the hypothesis that the contrast satisfies a coercivity condition on the boundary of the domain, we show that the corresponding operator has Upper Triangular Compact Resolvent and that the analytic Fredholm theorem holds for such operators. As a corollary, we can show that the set of (complex) interior transmission eigenvalues is a (possibly empty) discrete set. This is different from previous results because the contrast need not have a constant sign (or be real valued) in the interior of the domain. 
Speaker:  Marcel Ullrich University of Mainz, Germany 
Title:  A Monotony Based Method for EIT 
Abstract: 
The aim of Electrical Impedance Tomography (EIT) is to reconstruct the spatially dependent conductivity σ: Ω → R
in the inside of a conductive object Ω ⊆ R^{n} on the basis of a sequence of currentvoltage measurements on the outside of that object.
The relation between the electric potential u: Ω → R and the conductivity σ is modeled by the equation A well known monotony relation for the dependence of Λ on σ is given by: From both relations we then obtain a monotony based method that is capable of exactly reconstructing the outer support of a conductivity change. We show that this method holds even for the indefinite case, i.e. for conductivities, which are respectively higher and lower than the background conductivity on separated areas. 
Speaker:  Ting Zhou University of Washington 
Title:  Reconstructing Electromagnetic Obstacles by the Enclosure Method 
Abstract:  We show that one can determine Perfectly Magnetic Conductor
obstacles, Perfectly Electric Conductor obstacles and obstacles satisfying
impedance boundary condition, embedded in a known electromagnetic medium, by
making electromagnetic measurements at the boundary of the medium. The boundary
measurements are encoded in the impedance map that sends the tangential
component of the electric field to the tangential component of the magnetic
field. We do this by probing the medium with complex geometrical optics solutions
to the corresponding Maxwells equations and extend the enclosure method to this
case. Moreover, using complex spherical waves, constructed by the inversion
transformation with respect to a sphere, the enclosure method can recover some
nonconvex part of the obstacle.

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