Clustering is indispensable to obtain a general view of series data from a number of data such as gene expression profiles. We propose a novel metric for clustering. The proposed metric automatically normalizes data to minimize a logarithmic scale distance between the data series.

A new concept for a navigation and communication satellite system has been proposed. The navigation satellite system that forms the basis of the proposed system has been studied by one of the authors and extended to add a mobile communication function to the system. The satellite system consists of 15 satellites in quasi-geostationary orbit (QGEO) that have a geostationary altitude and high inclination and provide global coverage and positioning capability to the observer through only reception of the range measurement signals generated at the satellites, which are in the same configuration as the satellites in Global Positioning System (GPS), Three satellites out of the 15 satellite are designated to install a subsystem for mobile satellite communication in order to satisfy mobile communication convenience as required in a Future Air Navigation System's (FANS) concept of International Civil Aviation Organization (ICAO). The case studies of 15-satellites constellations demonstrate not only an acceptable positioning accuracy over the whole globe, but also an accuracy distribution weighted on the north pole region as an example of a weighted accuracy distribution. The addition of a mobile communication function suggests a unified system of satellite navigation and communication, which might provide convenience for the civil aviation industry, because the two functions currently depend on different systems.