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To compare two different imaging modalities, magnetic resonance (MR), and three-dimensional sonography (3DUS), in order to evaluate the specific role in preoperative work-up of deep infiltrating endometriosis. 33 women with endometriosis underwent 3DUS and MR followed by surgical and histopathological investigations. Investigators described the disease extension in the following sites: torus uterinus and uterosacral ligaments (USL), vagina, rectovaginal-septum, rectosigmoid, bladder, ovaries. Results were compared with surgical and histopathological findings. Ovarian and deep pelvic endometriosis were found by surgery and histology in, respectively, 24 (72.7%) and 22 (66.6%) of the 33 patients. Sensitivity and specificity values of 3DUS for the diagnosis of endometrial cysts were 87.5% and 100%, respectively; those of MRI were 96.8% and 91.1%, respectively. Sensitivity and specificity of 3DUS for the diagnosis of deep infiltrating endometriosis in specific sites were: USL 50% and 94.7%; vagina 84% and 80%; rectovaginal-septum 76.9% and 100%; rectosigmoid 33.3% and 100%; bladder 25% and 100%. Those of MR were: USL 69.2% and 94.3%; vagina 83.3% and 88.8%; rectovaginal-septum 76.4% and 100%; restosigmoid 75% and 100%; bladder 83.3% and 100%. MR accurately diagnoses deep infiltrating endometriosis; 3DUS accurately diagnoses deep infiltrating endometriosis in specific locations.

Let a pure state \psi be chosen randomly in an NM-dimensional Hilbert space, and consider the reduced density matrix \rho of an N-dimensional subsystem. The bipartite entanglement properties of \psi are encoded in the spectrum of \rho. By means of a saddle point method and using a "Coulomb gas" model for the eigenvalues, we obtain the typical spectrum of reduced density matrices. We consider the cases of an unbiased ensemble of pure states and of a fixed value of the purity. We finally obtain the eigenvalue distribution by using a statistical mechanics approach based on the introduction of a partition function., Comment: 15 pages, 4 figures