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...

An unsupervised method for megakaryocyte detection and analysis is proposed, in order to validate supplementary tools which can be of help in supporting the pathologist in the classification of Philadelphia negative chronic myeloproliferative disorders with thrombocytosis. The experiment was conducted on high power magnification photomicrographs taken from hematoxylin-and-eosin 3 micrometer thi...

Candidates to the least perimeter partition of a disk into N planar connected regions are calculated for N ≤ 43. A Voronoi construction is used to randomly create the candidates and then the perimeter of each is found with the Surface Evolver. Formulae for the perimeter and number of peripheral regions are given, and the candidates classified according to their topology. The simulation techniqu...

Web services security is becoming a critical concern for any organization adopting the XML-based Web services approach to application integration. While many access control techniques for Web services are becoming available, several issues still need to be solved in order to correctly split the burden of securing Web services between the perimetral and the service level. In this paper, a techni...

The square decomposition problem has applications in a number of areas such as bin packing of flexible objects of fixed area and circuit layout with minimum communication requirements. Our interest in the square decomposition problem arises from the following problem in parallel computation [1]. One wishes to compute a table of all values of a binary function f on the Cartesian product S x T, w...

We give the first polynomial-time algorithm for the problem of finding a minimumperimeter k-gon that encloses a given n-gon. Our algorithm is based on a simple structural result, that an optimal k-gon has at least one “flush” edge with the ngon. This allows one to reduce the problem to computing the shortest k-link path in a simple polygon. As a by-product we observe that the minimum-perimeter ...

We propose an explanation for the commonly-seen fading in the density of a stain remaining after a droplet has dried on a surface. The density decreases as a power p of the distance from the edge. For thin, dilute drops of general shape this power is determined by a flow stagnation point in the distant interior of the drop. The power p depends on the local evaporation rate J(0) at the stagnatio...

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In this article, we study the regularity of the boundary of sets minimizing a quasi perimeter T (E) = P (E,Ω) + G (E) with a volume constraint. Here Ω is any open subset of Rn with n ≥ 2, G is a lower semicontinuous function on sets of finite perimeter satisfying a condition that G (E) ≤ G (F ) + C |E∆F | among all sets of finite perimeter with equal volume. We show that under the condition β >...

As 3-point shooting in the NBA continues to increase, importance of perimeter defense has never been greater. Perimeter defenders are often evaluated by their ability tightly contest shots, but how exactly does contesting a jump shot cause decrease expected percentage, and can we use this insight better assess defender ability? In paper analyze over 50,000 trajectories from explain why, terms i...