Anomalous thresholds and edge singularities in Electrical Impedance Tomography

Studies of models of current flow behaviour in Electrical Impedance Tomography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the technique. This behaviour imposes severe restrictions on the numerical techniques used in image reconstruction algorithms. In this paper we have considered a simple two dimensional case and we have shown how the theory of end point/pinch singularities which was developed for studying the anomalous thresholds encountered in elementary particle physics can be used to give a complete description of the analytic structure of the current density near to the edge of the electrodes. As a byproduct of this study it was possible to give a complete description of the Riemann sheet manifold of the eigenfunctions of the logarithmic kernel. These methods can be readily extended to other weakly singular kernels.Comment: Correction of a misprint which occurred in the unnumbered formula preceding Eq. (14), LaTeX file as an uuencoded file, 40 pages with 12 figures, uses epsf.st

An integral equation method for the inverse conductivity problem

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity. We have used a priori information to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind for the Laplacian of the potential, and then by solving a first order partial differential equation for the regularized conductivity itself. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.Comment: 15 pages, 8 figure

The pion-pion scattering amplitude. III: Improving the analysis with forward dispersion relations and Roy equations

We complete and improve the fits to experimental $\pi\pi$ scattering amplitudes, both at low and high energies, that we performed in the previous papers of this series. We then verify that the corresponding amplitudes satisfy analyticity requirements, in the form of partial wave analyticity at low energies, forward dispersion relations (FDR) at all energies, and Roy equations below$\bar{K}K$ threshold; the first by construction, the last two, inside experimental errors. Then we repeat the fits including as constraints FDR and Roy equations. The ensuing central values of the various scattering amplitudes verify very accurately FDR and, especially, Roy equations, and change very little from what we found by just fitting data, with the exception of the D2 wave phase shift, for which one parameter moves by $1.5 \sigma$. These improved parametrizations therefore provide a reliable representation of pion-pion amplitudes with which one can test various physical relations. We also present a list of low energy parameters and other observables. In particular, we find $a_0^{(0)}=0.223\pm0.009 M^{-1}_\pi$, $a_0^{(2)}=-0.0444\pm0.0045 M^{-1}_\pi$ and $\delta_0^{(0)}(m^2_K)-\delta_0^{(2)}(m^2_K)=50.9\pm1.2^{\rm o}$.Comment: Plain TeX. 29 figures. Version to be published in PRD, with improved P and F wave

Functional Analytic Continuation Techniques with Applications in Field Theory

Often one has data at points inside the holomorphy domain of a Green’s function, or of an Amplitude or Form—Factor, and wants to obtain information about the spectral function i.e. the discontinuity along the cuts. Data may be experimental or theoretical. In QCD for example the perturbation expansion is valid only for unphysicaL values of the energy: one would like to continue this information to the cuts to find the resonance parameters. However, analytic continuation off open contours is extremely unstable. Also, the straightforward continuation of the truncated perturbation expansion will not do, since this is itself analytic and continuation will thus yield exactly the same result. This problem is solved by functional techniques, first by allowing small imprecisions in the data to remove the uniqueness of the continuation, and then by introducing a stabilizing condition suited to the particular physical problem, which will suppress the functions with incorrect behaviour. The stabilizing condition is expressed in terms of a norm giving a measure of the smoothness of the Discrepancy Function -which is the Amplitude with the resonances removed. The minimal norm computed from the data depends on the trial values of the resonance parameters and enables one to select the best values for these. The corresponding optimal amplitude is also constructed. An explicit solution is obtained for the case of a discrete data set; in the continuous case the problem is expressed in terms of a Fredholm integral equation

Litho-sedimentological and morphodynamic characterization of the Pisa Province coastal area (northern Tuscany, Italy)

In this paper litho-sedimentological and morphodynamic maps of the coastal sector belonging to the Pisa Province are presented as an example of how increasing the accessibility to data on lithology, sedimentology, and morphodynamics may lead to a better approach to coastal management. The database used to build the maps includes an original rendering of remote sensing data (aerial imagery) and new field data (geologic survey), as well as data retrieved from the scientific literature (grain-size and past coastline positions). The maps show that the geometry of beach ridges is an indication of the evolution of the Arno River delta in the last 3000 years, highlighting the relationships between geological aspects and morphodynamic features. The maps represent the synthesis of different data available in the database, and they may be a useful support to coastal management as they are more easily understandable and straightforward than the database from which are created

The "Peeking" Effect in Supervised Feature Selection on Diffusion Tensor Imaging Data

We read with great interest the article by Haller et al[1][1] in the February 2013 issue of the American Journal of Neuroradiology . The authors used whole-brain diffusion tensor imaging–derived fractional anisotropy (FA) data, skeletonized through use of the standard tract-based spatia