Interrelations between Stochastic Equations for Systems with Pair Interactions

Several types of stochastic equations are important in thermodynamics, chemistry, evolutionary biology, population dynamics and quantitative social science. For systems with pair interactions four different types of equations are derived, starting from a master equation for the state space: First, general mean value and (co)variance equations. Second, Boltzmann-like equations. Third, a master equation for the configuration space allowing transition rates which depend on the occupation numbers of the states. Fourth, a Fokker-Planck equation and a ``Boltzmann-Fokker-Planck equation''. The interrelations of these equations and the conditions for their validity are worked out clearly. A procedure for a selfconsistent solution of the nonlinear equations is proposed. Generalizations to interactions between an arbitrary number of systems are discussed.Comment: For related work see http://www.theo2.physik.uni-stuttgart.de/helbing.htm

A new methodological approach to bibliographic coupling and its application to the national, regional and institutional level

In an earlier study the authors have shown that bibliographic coupling techniques can be used to identify 'hot' research topics. The methodology is based on appropriate thresholds for both number of related documents and the strength of bibliographic links. Those papers are called core documents that have more than 9 links of at Least the strength 0.25 according to Salton's measure, provided they are articles, notes or reviews. This choice resulted in a selection of nearly one per cent of all papers of the above types recorded in the 1992 annual cumulation of the SCI. Core documents proved important nodes in the network of documented science communication.status: publishe