Variant Construction from Theoretical Foundation to Applications

Description

This open access book presents theoretical framework and sample applications of variant construction. The first part includes the components variant logic, variant measurements, and variant maps, while the second part covers sample applications such as variation with functions, variant stream ciphers, quantum interference, classical/quantum random sequences, whole DNA sequences, and multiple-valued pulse sequences. Addressing topics ranging from logic and measuring foundation to typical applications and including various illustrated maps, it is a valuable guide for theoretical researchers in discrete mathematics; computing-, quantum- and communication scientists; big data engineers; as well as graduate and upper undergraduate students. Front Matter ....Pages i-xxiv Front Matter ....Pages 1-1 Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic (Jeffrey Zheng)....Pages 3-21 Hierarchical Organization of Variant Logic (Jeffrey Zheng)....Pages 23-35 Front Matter ....Pages 37-38 Elementary Equations of Variant Measurement (Jeffrey Zheng)....Pages 39-50 Triangular Numbers and Their Inherent Properties (Chris Zheng, Jeffrey Zheng)....Pages 51-65 Symmetric Clusters in Hierarchy with Cryptographic Properties (Jeffrey Zheng)....Pages 67-94 Front Matter ....Pages 95-96 Variant Maps of Elementary Equations (Jeffrey Zheng)....Pages 97-104 Variant Map System of Random Sequences (Jeffrey Zheng)....Pages 105-131 Stationary Randomness of Three Types of Six Random Sequences on Variant Maps (Jeffrey Zheng, Yamin Luo, Zhefei Li, Chris Zheng)....Pages 133-156 Front Matter ....Pages 157-158 Meta Model on Concept Cell (Jeffrey Zheng, Chris Zheng)....Pages 159-167 Voting Theory for Two Parties Under Approval Rule (Jeffrey Zheng)....Pages 169-190 Front Matter ....Pages 191-192 Biometrics and Knowledge Management Information Systems (Jeffrey Zheng, Chris Zheng)....Pages 193-202 Recursive Measures of Edge Accuracy on Digital Images (Jeffrey Zheng, Chris Zheng)....Pages 203-215 2D Spatial Distributions for Measures of Random Sequences Using Conjugate Maps (Qingping Li, Jeffrey Zheng)....Pages 217-235 Permutation and Complementary Algorithm to Generate Random Sequences for Binary Logic (Jie Wan, Jeffrey Zheng)....Pages 237-245 3D Visual Method of Variant Logic Construction for Random Sequence (Huan Wang, Jeffrey Zheng)....Pages 247-261 Front Matter ....Pages 263-263 Synchronous Property—Key Fact on Quantum Interferences (Jeffrey Zheng)....Pages 265-277 The nth Root of NOT Operators of Quantum Computers (Jeffrey Zheng)....Pages 279-286 Front Matter ....Pages 287-288 Novel Pseudorandom Number Generation Using Variant Logic Framework (Jeffrey Zheng)....Pages 289-295 RC4 Cryptographic Sequence on Variant Maps (Zhonghao Yang, Jeffrey Zheng)....Pages 297-306 Refined Stationary Randomness of Quantum Random Sequences on Variant Maps (Jeffrey Zheng, Yamin Luo, Zhefei Li)....Pages 307-320 Using Information Entropy to Measure Stationary Randomness of Quantum Random Sequences (Weizhong Yang, Yamin Luo, Zhefei Li, Jeffrey Zheng)....Pages 321-331 Visual Maps of Variant Combinations on Random Sequences (Jeffrey Zheng, Jie Wan)....Pages 333-350 Front Matter ....Pages 351-352 Variant Map System to Simulate Complex Properties of DNA Interactions Using Binary Sequences (Jeffrey Zheng, Weiqiong Zhang, Jin Luo, Wei Zhou, Ruoyu Shen)....Pages 353-377 Whole DNA Sequences of Cebus capucinus on Variant Maps (Yuyuan Mao, Jeffrey Zheng, Wenjia Liu)....Pages 379-388 Front Matter ....Pages 389-389 Successful Creation of Regular Patterns in Variant Maps from Bat Echolocation Calls (D. M. Heim, O. Heim, P. A. Zeng, Jeffrey Zheng)....Pages 391-400 Visual Analysis of ECG Sequences on Variant Maps (Zhihui Hou, Jeffery Zheng)....Pages 401-409