28 June 2014
Since the days of Leonard Euler and till the recent days of complex network theory the distance between two vertices in a graph is taken to be the number of edges in a shortest path connecting them. We propose an alternative approach, where the distance is defined as a "Feynman path integral", in which all possible paths between two vertices in a connected graph of a data base are taken into account, although some paths are more preferable than others. The path integral distance approach to the analysis of databases has proven its efficiency and success, especially on multivariate strongly correlated data where other methods fail to detect structural components. In particular, we report on the analysis of the Maddison historical data that covers population by country, GDP and GDP per capita back to 1820 and demonstrate a possibility to predict the political and economic stability in a country within different global contexts.
1. Volchenkov, D., Ph. Blanchard, “Introduction to Random Walks on Graphs and Databases”, © Springer Series in Synergetics , Vol. 10, Berlin / Heidelberg , ISBN 978-3-642-19591-4, 1st Edition., 340 p. 70 illus., 12 in color; http://dx.doi.org/10.1007/978-3-642-19592-1 (2011).
2. Volchenkov, D., Ph. Blanchard, Mathematical Analysis of Urban Spatial Networks, © Springer Series Understanding Complex Systems, Berlin / Heidelberg. ISBN 978-3-540-87828-5, 181 pages (2009).
Last edited: 11 July 2014
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