Numerical quadrature on the intersection of planar disks

We provide an algorithm that computes algebraic quadrature formulas with cardinality not exceeding the dimension of the exactness polynomial space, on the intersection of any number of planar disks with arbitrary radius. Applications arise for example in computational optics and in wireless networks analysis. By the inclusion-exclusion principle, we can also compute algebraic formulas for the union of a small number of disks. The algorithm is implemented in Matlab, via subperiodic trigonometric Gaussian quadrature and compression of discrete measures

Impact of overlapping in the radio coverage areas of multiple Wi-Fi access points on detecting encounters

Understanding the potential role of Smartphones and other portable wireless devices as relay nodes in message dissemination and content delivery in Delay Tolerant and Opportunistic networks depend on the knowledge about patterns and the number of encounter events among mobile nodes. One of the main challenges for extracting encounters is overlapping in the radio coverage areas of nearby access points (APs). Data about the usage of Wi-Fi networks can be used to perform an analysis of encounters among mobile devices. A realistic estimation of the number of encounters among mobile nodes is now a big challenge. In this paper, the effects of overlapping of radio coverage area among multiple APs for extracting realistic encounters among mobile devices has been discussed, and also an analytical approach has been proposed for extracting realistic encounters from overlapping in the coverage areas of multiple nearby APs. A significant difference was observed between the number of encounters by considering and ignoring overlapping. Our study finds that Wi-Fi datasets are not reliable source to estimate the number of encounters when there are overlapping in radio coverage areas of multiple APs