3,319 research outputs found
A differential approach for bounding the index of graphs under perturbations
This paper presents bounds for the variation of the spectral radius (G) of
a graph G after some perturbations or local vertex/edge modifications of G. The
perturbations considered here are the connection of a new vertex with, say, g vertices
of G, the addition of a pendant edge (the previous case with g = 1) and the addition
of an edge. The method proposed here is based on continuous perturbations and
the study of their differential inequalities associated. Within rather economical
information (namely, the degrees of the vertices involved in the perturbation), the
best possible inequalities are obtained. In addition, the cases when equalities are
attained are characterized. The asymptotic behavior of the bounds obtained is
also discussed.Postprint (published version
High-order regularized regression in Electrical Impedance Tomography
We present a novel approach for the inverse problem in electrical impedance
tomography based on regularized quadratic regression. Our contribution
introduces a new formulation for the forward model in the form of a nonlinear
integral transform, that maps changes in the electrical properties of a domain
to their respective variations in boundary data. Using perturbation theory the
transform is approximated to yield a high-order misfit unction which is then
used to derive a regularized inverse problem. In particular, we consider the
nonlinear problem to second-order accuracy, hence our approximation method
improves upon the local linearization of the forward mapping. The inverse
problem is approached using Newton's iterative algorithm and results from
simulated experiments are presented. With a moderate increase in computational
complexity, the method yields superior results compared to those of regularized
linear regression and can be implemented to address the nonlinear inverse
problem
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