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Optimized derivation of transfer functions and a software giving it. Application to biological systems. (English) Zbl 1112.92002

Summary: Today, the transfer function between any two nodes of any linear flowgram are obtained either by applying the step-by-step classical elimination of nodes and branches or by applying S. J. Mason’s [Proc. IRE 41, 1144–1156 (1953)], rules, both of them being manual, tedious in many case procedures and therefore prone to human errors. We facilitate the derivation of the transfer function in two different ways. The first one consists of reducing, when it is possible, the flowgram obtaining, manually, a simpler but equivalent subflowgram to which we apply the above mentioned procedures. Thus the time elapsed in the process as well as the probability of mistakes commission diminishes. The second way consists of deriving the transfer function using a user friendly software developed by us in this paper that applies in an automatic form Mason’s rules to the flowgram under study to derive any of the possible transfer functions without errors and in a very short process time. In each case, the software works on the equivalent subflowgram obtained during the computer process in the same form as it is manually obtained. Finally, we apply the tool here presented to some examples of biological systems.

MSC:

92B05 General biology and biomathematics
92-04 Software, source code, etc. for problems pertaining to biology
93A30 Mathematical modelling of systems (MSC2010)
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