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Compartmental systems and generating functions

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Abstract

Compartmental systems can be represented by direct graphs in which each node corresponds to a generating function and each arm to a transfer generating function. A homomorphism is established between a compartmental system and this representation, in analogy with that obtained through the use of the Laplace transformation.

From the values obtained experimentally in a given compartment, through the solution of a difference equation, the generating function for the corresponding node can be calculated and the graph of the system can be built up within the degrees of freedom of the model.

From the graph it is possible to calculate the transfer generating function between any two connected nodes, the mean permanence time in a given node, the mean transit time between two nodes, and their precursor-successor order.

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Authors and Affiliations

  1. Department of Pharmacology, University of Camerino, Italy

    Giorgio Segre

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  1. Giorgio Segre
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Segre, G. Compartmental systems and generating functions. Bulletin of Mathematical Biophysics 27 (Suppl 1), 49–63 (1965). https://doi.org/10.1007/BF02477261

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  • DOI: https://doi.org/10.1007/BF02477261

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