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Seminar Evolution and Physics, jannuary 2008, Bad Honnef, Germany

Evolution of Citation Webs modelled by Neural Networks

According to Lotka's law Citation webs exhibit a Pareto-Zipf distribution for citation frequences.

This type of longtailed distribution is found for all evolving self-organized systems in Astrophysics, Geophysics, biochemistry, biology, economics, sociology and linguistics (second law of genesis).

A citation web can be modelled as a hierarchical multilayer feedforward Neural Network with cyclic backpropagation. (Multilayer Perceptron). Neural Networks of this topology are known to have memory (web topology and respective weights of individual processors); they can learn through error optimization via gradient descent striving to minimize the overall system's error.

In a first approximation the hierarchical levels of a citation web are: single citation (a pointer to an idea) feeding into the paper level, which feeds into the referee level (peer-system) which feeds into the conference proceedings or journal publication level, which feeds into the book-editor level, which feeds into the book level, feeding the institute library level and finally feeding the Library of Congress level. Backpropagation are the respective reference lists of citations fed down the levels of the hierarchy. On each level there are binary threshold processors, which can be only on or off. Paper in progrees vs. Paper written, paper submitted for conference vs. Paper accepted for conference, paper submitted to journal vs. Paper published by journal, book sumitted to editor vs. Book published by editor Book proposed to library vs. Book acquired by library ... All these binary threshold automata of the web are interlinked in a hierarchical way and undergo a cyclic feedforward process with consecutive backpropagation. If the Neural Network analogy holds we come to the following conclusions:

1) Citationwebs have memory. It is the topology of the web's authors and their respective links which constitute the memory of the self-organized system.

  1. Citationwebs are learning through a cyclic feedback process of reference lists through the different hierarchical levels of the system. An author 's weight is proportional to the number of citations in the citation index.

  2. Citationwebs are « intelligent », the cyclic self-organisation process (feed forward and consecutive backpropagation) optimizes the overall coherence of the system. Thus the system is striving to an extremum of an objective function (goal).