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BIPOLAR LINEAR ALGEBRA AND YINYANG-N-ELEMENT CELLULAR NETWORKS FOR EQUILIBRIUM-BASED BIOSYSTEM SIMULATION AND REGULATION

WEN-RAN ZHANG

Department of Computer Sciences, Georgia Southern University, 1100 I. T. Drive, Statesboro, GA 30460-7998, USA

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JANE H. ZHANG

Department of Mathematical Sciences, Georgia Southern University, 1100 I. T. Drive, Statesboro, GA 30460-7998, USA

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YONG SHI

Research Center on Fictitious Economy and Data Science, The Chinese Academy of Sciences, Beijing 100080, China

College of Information Science and Technology, University of Nebraska at Omaha, Omaha, NE 68118, USA

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, and

SU-SHING CHEN

CAS-MPG Partner Institute of Computational Biology, Shanghai Institutes of Biological Sciences, The Chinese Academy of Sciences, 320 YueYang Road, Shanghai 200031, China

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https://doi.org/10.1142/S0218339009002958Cited by:56 (Source: Crossref)

Abstract

Bipolar linear algebra (BLA) and YinYang-N-Element bipolar cellular networks (BCNs) are presented for equilibrium-based biological simulation and regulation at the system, molecular, and genetic levels. Bipolar fusion, interaction, oscillation, and quantum entanglement with growing, aging, degenerating, equilibrium, and non-equilibrium properties are mathematically characterized; bipolar dynamic equations with metabolic nourishing and regulating relations are formulated; global and local equilibrium conditions are established and proved. Two families of YinYang-N-Element BCNs are compared and analyzed: one family has predefined nourishing and regulation cycles following the classical YinYang-5-Element protocol in Traditional Chinese Medicine (TCM); another family has random connectivity and link weights. Applicability of the theory is illustrated in equilibrium and non-equilibrium simulation of bio-agent interaction and regulation. The significance of this work is two-fold: (1) BLA provides a unique and unifying mathematical foundation for bipolar fusion, interaction, and oscillation in biophysics and bioeconomics; (2) YinYang-N-Element BCNs provide a unique and unifying architecture for modeling equilibrium and non-equilibrium processes at the system, molecular, and genetic levels.

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