Optimized derivation of transfer functions and a software giving it. Application to biological systems

• Published in: Applied mathematics and computation Vol. 184; no. 2; pp. 823 - 841
• Main Authors: Varón, R., García-Moreno, M., Valero, E., Fuentes, M.E., Amo, M.L.L., Arias, E., Arribas, E., García-Sevilla, F.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.01.2007; Elsevier
• Subjects: Dynamic systems; Exact sciences and technology; Flowgram; Global analysis, analysis on manifolds; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Node; Numerical analysis. Scientific computation; Sciences and techniques of general use; Signal-flow graph; Software; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Transfer function; Transmission; Dynamic systems; Node; Transmission; Signal-flow graph; Software; Transfer function; Flowgram; Error estimation; Probability distribution; Dynamical system; Graph flow; Biological system; Numerical analysis; Bypass; Applied mathematics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.06.073

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 the Mason’s rules, both of them being manual, tedious in many cases procedures and therefore prone to human errors. In this paper we facilitate the derivation of the transfer function in two different ways. The first one consists on reducing, when it were 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 in deriving the transfer function using a user friendly software developed by us in this paper and that apply in an automatic form the Mason’s rules to the flowgram under study to derive any of the possible transfer function 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.