Bergman complexes are polyhedral complexes associated to matroids. Faces of these complexes are certain matroids, called matroid types, too. In order to understand the structure of these faces we decompose matroid types into direct summands. Ardila/Klivans proved that the Bergman Complex of a matroid can be subdivided into the order complex of the proper part of its lattice of flats. Beyond tha...

We study the expected size of the 2D visibility complex of randomly distributed objects in the plane. We prove that the expected asymptotic number of free bitangents (which correspond to the 0-faces of the visibility complex) among unit discs or polygons of bounded aspect ratio is linear and exhibit bounds in terms of the density of the objects. We also make an experimental assessment of the si...

We report the case of a patient referred to our prenatal diagnostic unit due to the suspicion of spina bifida at 24 weeks gestation. Morphological assessment revealed rachischisis associated with Chiari type II, single kidney and anorectal malformation. The nonvisualization of the anal sphincter complex (ASC) on ultrasound led to the diagnosis of suspected high-type anorectal malformation (A,B ...