The K-hull of a compact set A⊆Rd, where K⊆Rd is fixed convex body, the intersection all translates K that contain A. A called K-strongly if it coincides with its K-hull. We propose general approach to analysis facial structure sets, similar well developed theory for polytopes, by introducing notion k-dimensional faces, k=0,…,d−1. then apply our in case when A=Ξn sample n points picked uniformly...

Heavy-tailed random samples, as well their sum or average, are encountered in a number of signal processing applications radar, communications, finance, and natural sciences. Modeling such data through the Pareto distribution is particularly attractive due to its simple analytical form, but may lead infinite variance and/or mean, which not physically plausible: fact, samples always bounded prac...

Abstract Consider two independent random walks. By chance, there will be spells of association between them where the processes move in same direction, or opposite direction. We compute probabilities length longest spell such for a given sample size, and discuss measures like mean mode exact distributions. observe that long (relative to small sizes) occur frequently, which explains why nonsense...

Photoplethysmography (PPG) devices are widely used for monitoring cardiovascular function. However, these devices require skin contact, which restricts their use to at-rest short-term monitoring. Photoplethysmographic imaging (PPGI) has been recently proposed as a non-contact monitoring alternative by measuring blood pulse signals across a spatial region of interest. Existing systems operate in...