Perimeter search is a bidirectional search algorithm consisting of two phases. In the first phase, a limited regression search computes the perimeter, a region which must necessarily be passed in every solution. In the second phase, a heuristic forward search finds an optimal plan from the initial state to the perimeter. The drawback of perimeter search is the need to compute heuristic estimate...

Multiform glioblastoma is the most common primary, highly invasive, malignant tumor of the central nervous system, with an extremely poor prognosis. The median survival of patients following surgical resection, radiation therapy and chemotherapy does not exceed 12-15 months and thus, novel approaches for the treatment of the disease are required. The phenomenon of the directed migration of stem...

In the class of Carnot groups we study fine properties of sets of finite perimeter. Improving a recent result by Ambrosio-Kleiner-Le Donne, we show that the perimeter measure is local, i.e., that given any pair of sets of finite perimeter their perimeter measures coincide on the intersection of their essential boundaries. This solves a question left open in [4]. As a consequence we prove a gene...