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

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.