t. This paper surveys some of the work our group has done in electrical impedance tomography.

Electrical Impedance Tomography

We review theoretical and numerical studies of the inverse problem of electrical impedance tomography which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.

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Electrical impedance tomography

Commutative ring theory: Regular rings

This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in one, two, and three dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the code's parallel performance, and discuss the Enzo collaboration's code development methodology.

/pdf/enzo-an-adaptive-mesh-refinement-code-for-astrophysics-2cgbpdu97q.pdf

Enzo: An Adaptive Mesh Refinement Code for Astrophysics

Linear Inverse Problems.- Large-Scale Inverse Problems in Imaging.- Regularization Methods for Ill-Posed Problems.- Distance Measures and Applications to Multi-Modal Variational Imaging.- Energy Minimization Methods.- Compressive Sensing.- Duality and Convex Programming.- EM Algorithms.- Iterative Solution Methods.- Level Set Methods for Structural Inversion and Image Reconstructions.- Expansion Methods.- Sampling Methods.- Inverse Scattering.- Electrical Impedance Tomography.- Synthetic Aperture Radar Imaging.- Tomography.- Optical Imaging.- Photoacoustic and Thermoacoustic Tomography: Image Formation Principles.- Mathematics of Photoacoustic and Thermoacoustic Tomography.- Wave Phenomena.- Statistical Methods in Imaging.- Supervised Learning by Support Vector Machines.- Total Variation in Imaging.- Numerical Methods and Applications in Total Variation Image Restoration.- Mumford and Shah Model and its Applications in Total Variation Image Restoration.- Local Smoothing Neighbourhood Filters.- Neighbourhood Filters and the Recovery of 3D Information.- Splines and Multiresolution Analysis.- Gabor Analysis for Imaging.- Shaper Spaces.- Variational Methods in Shape Analysis.- Manifold Intrinsic Similarity.- Image Segmentation with Shape Priors: Explicit Versus Implicit Representations.- Starlet Transform in Astronomical Data Processing.- Differential Methods for Multi-Dimensional Visual Data Analysis.- Wave fronts in Imaging, Quinto.- Ultrasound Tomography, Natterer.- Optical Flow, Schnoerr.- Morphology, Petros.- Maragos.- PDEs, Weickert. - Registration, Modersitzki. - Discrete Geometry in Imaging, Bobenko, Pottmann.-Visualization, Hege.- Fast Marching and Level Sets, Osher.- Couple Physics Imaging, Arridge.- Imaging in Random Media, Borcea.- Conformal Methods, Gu.- Texture, Peyre.- Graph Cuts, Darbon.- Imaging in Physics with Fourier Transform (i.e. Phase Retrieval e.g Dark field imaging), J. R. Fienup.- Electron Microscopy, Oktem Ozan.- Mathematical Imaging OCT (this is also FFT based), Mark E. Brezinski.- Spect, PET, Faukas, Louis.

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Handbook of mathematical methods in imaging

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Reseaux électriques planaires II.

Let G be a bipartite graph. We show some algebraic properties of blowup algebras associated to the ideal of vertex covers of G.

Blowup algebras of ideals of vertex covers of bipartite graphs

We study irreducible representations of Rees cones and char- acterize the max-flow min-cut property of clutters in terms of the nor- mality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and com- mutative algebra. As a byproduct we obtain an eective method, based

/pdf/a-note-on-rees-algebras-and-the-mfmc-property-3s348bjett.pdf

A Note on Rees Algebras and the MFMC Property

Ring graphs and complete intersection toric ideals

Let G be a simple graph with |V(G)| = n and no isolated vertices. Let α be its stability number. We study invariants of the edge-ring of G that can be interpreted as invariants of G. If G has a cover by maximum stable sets we are able to prove the inequality . As a byproduct we prove that if G is vertex-critical, then α ≤ (n − |A|)/2, where A is the intersection of all the minimum vertex covers of G. We estimate the smallest number of vertices in any maximal stable set of G to obtain a bound for the depth of the edge-ring of G. #Communicated by R. Villarreal.

Isidoro Gitler

Papers

Reseaux électriques planaires II.

Blowup algebras of ideals of vertex covers of bipartite graphs

A Note on Rees Algebras and the MFMC Property

Ring graphs and complete intersection toric ideals

Bounds For Invariants of Edge-Rings