In the special case “cost=squared distance” on R, the problem was solved by Caffarelli [Caf1, Caf2, Caf3, Caf4], who proved the smoothness of the map under suitable assumptions on the regularity of the densities and on the geometry of their support. However, a major open problem in the theory was the question of regularity for more general cost functions, or for the case “cost=squared distance”...

The geographical scope of travel varies from short distances in urban areas to long distances across cities and countries. While urban travel has been widely analysed in the literature, travel over longer distances and particularly across countries, has received much less attention. While this may be justified due to the number of travellers it cannot be justified when looking at the mileage co...

vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...

Clickstream analysis provides valuable insight into the behavior of users and can be translated into better business opportunities and increased user satisfaction. A fundamental problem in clickstream analysis is the computation of the distance (or the similarity) between two clickstreams. While, there exists a considerable amount of literature which propose methods of computing path similariti...

[Purpose] This study aimed to determine which clinical measures of walking performance and lower limb muscle strength would predict energy cost during stair ascent and descent in community-dwelling individuals with stroke. [Subjects and Methods] Regression analysis of cross-sectional data from 55 individuals between one and five years post-stroke was used to investigate the measures of walking ...