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We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner-Nordstr\"om geometry using the Newman Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function $\Psi_4$, as is well known, but for the electromagnetic signal the information is encoded in the function $\chi$ which relates the perturbations of the radiative Maxwell scalars $\varphi_2$ and the Weyl scalar $\Psi_3$. In deriving the perturbation equations we do not impose any gauge condition and our analysis contains as a limiting case the results obtained previously for instance in Chandrashekhar's book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on a basis of spin weighted spherical harmonics and the Reissner-Nordstr\"om spacetime in Kerr-Schild type coordinates a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we solve completely a system which generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitating the gravitational wave detection via the electromagnetic signal., Comment: 21 pages, 6 figures, 1 table

Wireless Capsule Endoscope (WCE) is an innovative imaging device that permits physicians to examine all the areas of the Gastrointestinal (GI) tract. It is especially important for the small intestine, where traditional invasive endoscopies cannot reach. Although WCE represents an extremely important advance in medical imaging, a major drawback that remains unsolved is the WCE precise location in the human body during its operating time. This is mainly due to the complex physiological environment and the inherent capsule effects during its movement. When an abnormality is detected, in the WCE images, medical doctors do not know precisely where this abnormality is located relative to the intestine and therefore they can not proceed efficiently with the appropriate therapy. The primary objective of the present paper is to give a contribution to WCE localization, using image-based methods. The main focus of this work is on the description of a multiscale elastic image registration approach, its experimental application on WCE videos, and comparison with a multiscale affine registration. The proposed approach includes registrations that capture both rigid-like and non-rigid deformations, due respectively to the rigid-like WCE movement and the elastic deformation of the small intestine originated by the GI peristaltic movement. Under this approach a qualitative information about the WCE speed can be obtained, as well as the WCE location and orientation via projective geometry. The results of the experimental tests with real WCE video frames show the good performance of the proposed approach, when elastic deformations of the small intestine are involved in successive frames, and its superiority with respect to a multiscale affine image registration, which accounts for rigid-like deformations only and discards elastic deformations.

Several explanations can be found in the literature about the origin of colorectal cancer. There is however some agreement on the fact that the carcinogenic process is a result of several genetic mutations of normal cells. The colon epithelium is characterized by millions of invaginations, very small cavities, called crypts, where most of the cellular activity occurs. It is consensual in the medical community, that a potential first manifestation of the carcinogenic process, observed in conventional colonoscopy images, is the appearance of Aberrant Crypt Foci (ACF). These are clusters of abnormal crypts, morphologically characterized by an atypical behavior of the cells that populate the crypts. In this work an homogenization model is proposed, for representing the cellular dynamics in the colon epithelium. The goal is to simulate and predict, in silico, the spread and evolution of ACF, as it can be observed in colonoscopy images. By assuming that the colon is an heterogeneous media, exhibiting a periodic distribution of crypts, we start this work by describing a periodic model, that represents the ACF cell-dynamics in a two-dimensional setting. Then, homogenization techniques are applied to this periodic model, to find a simpler model, whose solution symbolizes the averaged behavior of ACF at the tissue level. Some theoretical results concerning the existence of solution of the homogenized model are proven, applying a fixed point theorem. Numerical results showing the convergence of the periodic model to the homogenized model are presented., Comment: 26 pages, 4 figures