Point configurations, phylogenetic trees, and dissimilarity vectors.

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

Characterization of ferromagnetic or conductive properties of metallic foreign objects embedded within the human body with magnetic iron detector (MID): Screening patients for MRI.

PURPOSE: A preliminary assessment of the MRI-compatibility of metallic object possibly embedded within the patient is required before conducting the MRI examination. The Magnetic Iron Detector (MID) is a highly sensitive susceptometer that uses a weak magnetic field to measure iron overload in the liver. MID might be used to perform a screening procedure for MRI by determining the ferromagnetic/conductive properties of embedded metallic objects. METHODS: The study was composed by: (i) definition of MID sensitivity threshold; (ii) application of MID in a procedure to characterize the ferromagnetic/conductive properties of metallic foreign objects in 958 patients scheduled for MID examination. RESULTS: The detection threshold for ferromagnetic objects was found to be the equivalent of a piece of wire of length 2 mm and gauge 0.8 mm(2) and, representing purely conductive objects, an aluminum sheet of area 2 × 2 cm(2) . Of 958 patients, 165 had foreign bodies of unknown nature. MID was able to detect those with ferromagnetic and/or conducting properties based on fluctuations in the magnetic and eddy current signals versus control. CONCLUSION: The high sensitivity of MID makes it suitable for assessing the ferromagnetic/conductive properties of metallic foreign objects embedded within the body of patients scheduled for MRI.