Abstract: Whole-body Positron Emission Tomography (PET) scanners are required in order to span large Fields of View (FOV). Therefore, reaching the sensitivity and spatial resolution required for early stage breast tumor detection is not straightforward. MAMMI is a dedicated breast PET scanner with a ring geometry designed to provide PET images with a spatial resolution as high as 1.5 mm, being able to detect small breast tumors ( < 1 cm). The patient lays down in prone position during the scan, thus making possible to image the whole breast, up to regions close to the base of the pectoral without the requirement of breast compression. Attenuation correction (AC) for PET data improves the image quality and the quantitative accuracy of radioactivity distribution determination. In dedicated, high resolution breast cancer scanners, this correction would enhance the proper diagnosis in early disease stages. In whole-body PET scanners, AC is usually taken into account with the use of transmission scans, either by external radioactive rod sources or by Computed Tomography (CT). This considerably increases the radiation dose administered to the patient and time needed for the exploration. In this work we propose a method for breast shape identification by means of PET image segmentation. The breast shape identification will be used for the determination of the AC. For the case of a specific breast PET scanner the procedure we propose should provide AC similar to that obtained by transmission scans as we take advantage of the breast anatomical simplicity. Experimental validation of the proposed approach with a dedicated breast PET prototype is also presented. The main advantage of this method is an important dose reduction since the transmission scan is not required.

Abstract: In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and s-wave. An example, requiring only experimental data, is shown for the rho meson indicating that it is not a composite particle of pi pi and K (K) over bar but something else.

Abstract: We study static, spherically symmetric solutions with an electric field in an extension of general relativity containing a Ricci-squared term and formulated in the Palatini formalism. We find that all the solutions present a central core whose area is proportional to the Planck area times the number of charges. Far from the core, curvature invariants quickly tend to those of the usual Reissner-Nordstrom solution, though the structure of horizons may be different. In fact, besides the structures found in the Reissner-Nordstrom solution of general relativity, we find black hole solutions with just one nondegenerate horizon (Schwarzschild-like) and nonsingular black holes and naked cores. The charge-to-mass ratio of the nonsingular solutions implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density. We discuss the physical implications of these results for astrophysical and microscopic black holes, construct the Penrose diagrams of some illustrative cases, and show that the maximal analytical extension of the nonsingular solutions implies a bounce of the radial coordinate.

Abstract: We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius r(core) approximate to N(q)(1/2)l(P)/3, where l(P) is the Planck length and N-q is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition M-0(2) approximate to m(P)(2)alpha N-3/2(em)q(3)/2, where m(P) is the Planck mass and alpha(em) is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.

Abstract: We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of general relativity (GR) formulated a la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.