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Reverse Engineering Of The Nk Boolean Network And Its Extension — Fuzzy Logic Network

Author

Listed:
  • YINGJUN CAO

    (Department of Mathematics and Computer Science, North Carolina Central University, 1801 Fayetteville Street, Durham, North Carolina 27707, USA)

  • PAUL P. WANG

    (Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA)

  • GERMANO RESCONI

    (Department of Mathematics and Physics, Catholic University, Via Musei 41, I-25121 Brescia, Italy)

Abstract

In this paper, we first propose a reverse engineering solution to decode theNKBoolean dynamic network given the input and output of the system. This theory utilizes basis functions and dynamic matrices, through which the network's evolutionary behavior can be simulated in a rigorous mathematical manner. Then, a general network model, fuzzy logic network (FLN), is presented as the extension of the Boolean network. This novel network model assigns variable values in a continuous domain, and it can accommodate internal conflicts among variables. In addition, the FLN uses fuzzy logical functions instead of Boolean logical functions, which enables it to model highly non-linear relationships and periodicity. Using the approach of annealed approximations, we proved important theorems concerning the dynamic property of the FLN. Combined with the Zipf's law, the criteria of applying FLN to the modeling of gene regulatory networks were achieved.

Suggested Citation

  • Yingjun Cao & Paul P. Wang & Germano Resconi, 2007. "Reverse Engineering Of The Nk Boolean Network And Its Extension — Fuzzy Logic Network," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 69-87.
    • Handle: RePEc:wsi:nmncxx:v:03:y:2007:i:01:n:s179300570700063x
    DOI: 10.1142/S179300570700063X
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