This paper concerns a priori second order derivative estimates of solutions the Neumann problem for Monge-Amp\`ere type equations in bounded domains n dimensional Euclidean space. We first establish double normal estimate on boundary under an appropriate notion domain convexity. Then, assuming barrier condition linearized operator, we provide complete proof global elliptic solutions, as previou...

The tropical Grassmannian parameterizes tropicalizations of ordinary linear spaces, while the Dressian parameterizes all tropical linear spaces in TP. We study these parameter spaces and we compute them explicitly for n ≤ 7. Planes are identified with matroid subdivisions and with arrangements of trees. These representations are then used to draw pictures.

In this paper, we study how human observers judge image similarity. To do so, we have conducted two psychophysical scaling experiments and have compared the results to two algorithmic image similarity metrics. For these experiments, we selected a set of 97 digitized photographic images which represent a range of semantic categories, viewing distances, and colors. We then used the two perceptual...