Variant Construction from Theoretical Foundation to Applications.

• Author: Zheng, Jeffrey.
• Place / Publishing House: Singapore : : Springer Singapore Pte. Limited,, 2019.; ©2019.
• Year of Publication: 2019
• Edition: 1st ed.
• Language: English
• Physical Description: 1 online resource (415 pages)

Table of Contents

Intro -- Foreword -- Preface -- Purpose of This Book -- The Need for a New Logic System -- Overview of Modern Group Theory -- Brief History on 0-1 Logic Systems -- Modern 0-1 Vector Algebra -- Introduction to Variant Construction -- The Organization of This Book -- Suitable Readers of This Book -- Acknowledgements -- Contents -- Contributors -- Theoretical Foundation-Variant Logic -- Variant Logic Construction Under Permutation and Complementary Operations on Binary Logic -- 1 Introduction -- 1.1 Western and Eastern Logic Traditions -- 1.2 Logic and Dynamic Systems -- 2 Truth Table Representation for a Logic Function Space -- 2.1 Basic Definitions -- 2.2 Permutation Invariants -- 3 Fourth Level of Organisation -- 3.1 Complementary Operation -- 3.2 Invariant Logic Functions Under Permutation and Complementary -- 3.3 Logic Functional Spaces -- 4 Different Coding Schemes: One- and Two-Dimensional Representations -- 4.1 G Coding -- 4.2 W Coding -- 4.3 F Coding -- 4.4 C Coding -- 5 Two-Variable Cases -- 6 Conclusion -- References -- Hierarchical Organization of Variant Logic -- 1 Laws of Logic Systems -- 1.1 Laws in Classical Logic Systems -- 1.2 Current Logic Systems -- 2 Truth Valued Representation in Boolean Logic Systems -- 3 Cellular Automata Representations -- 4 Variant Construction -- 4.1 Four Variation Forms -- 4.2 Complement and Variant Operators -- 4.3 Other Global Coding Schemes -- 4.4 Sizes of Variant Spaces -- 5 Invariant Properties of Variant Constructions -- 6 Comparison -- 7 Conclusion -- References -- Theoretical Foundation-Variant Measurement -- Elementary Equations of Variant Measurement -- 1 Introduction -- 2 Elementary Equation -- 2.1 Type A Measures -- 2.2 Type B Measures -- 3 Partition -- 4 Variation Space -- 5 Invariant Combination -- 5.1 Type A Invariants -- 5.2 Type B Invariants.

6 Combinatorial Expressions of Type B Invariants -- 7 Two Combinatorial Formula and Quantitative Distributions -- 7.1 Case I. {m-p}{p} -- 7.2 Case II. {2q}{m-2q} -- 7.3 Result Analysis -- 8 Conclusion -- References -- Triangular Numbers and Their Inherent Properties -- 1 Introduction -- 1.1 Geometric Arrangement of Combinatorial Data -- 1.2 Previous Work -- 2 Definitions and Sample Cases -- 2.1 Definitions -- 2.2 Sample Cases -- 3 Elementary Equations -- 4 Local Propensities -- 4.1 Nontrivial Areas -- 4.2 Trivial Areas -- 5 Projection Properties -- 5.1 Linear Projection -- 5.2 Triangular Sequence -- 5.3 Linear Sequence -- 6 Sample Cases -- 7 Conclusion -- References -- Symmetric Clusters in Hierarchy with Cryptographic Properties -- 1 Introduction -- 1.1 Symmetric Functions-Combinatorial Invariant -- 1.2 Crossing Number - Topological Invariant -- 1.3 Rotation Symmetric Functions - Geometric Invariant -- 1.4 Trinomial Coefficients -- 1.5 Variant Symmetric Schemes - Variant Invariants -- 1.6 Organization of the Chapter -- 2 Symmetric Clusters in Measuring Phase Spaces -- 2.1 Basic Symbols -- 2.2 Primary Definitions -- 2.3 Counting Properties on Rotation Clusters -- 2.4 Counting Properties on Measuring Phase Spaces -- 3 Variant Symmetric Clusters -- 3.1 Variant Trinomial Coefficients - Elementary Equation -- 3.2 Combinatorial Projection on Variant Clusters -- 3.3 Crossing Projection on Variant Clusters -- 3.4 Relationships of Four Symmetric Clusters -- 4 Four Number Sets of Symmetric Clusters -- 4.1 Four Approximates on Numbers of Clusters -- 4.2 Four Approximates on Numbers of Vectors -- 5 Symmetric Boolean Functions for Selected Clusters -- 5.1 Four Numbers on Symmetric Boolean Functions -- 5.2 Four Numbers of Balanced Symmetric Clusters -- 5.3 Four Numbers of Balanced Symmetric Boolean Functions.

6 Cryptographic Properties of Symmetric Boolean Functions in Hierarchy -- 7 Conclusion -- References -- Theoretical Foundation-Variant Map -- Variant Maps of Elementary Equations -- 1 Introduction -- 2 Measures and Maps -- 2.1 Case 1. {m-p}{p} -- 2.2 Case 2. {2q}{m-2q} -- 3 Visual Results -- 3.1 Case 1. Maps -- 3.2 Case 2. Maps -- 4 Result Analysis -- 5 Conclusion -- Variant Map System of Random Sequences -- 1 Introduction -- 1.1 Pseudo-Random Sequences -- 1.2 Truly Random Sequences from Hardware Devices and Speckle Patterns -- 1.3 Statistic Testing Packages on Cryptographic Sequences -- 1.4 Gaussian Distribution and Speckle Pattern -- 1.5 Controlling Deterministic Chaos -- 1.6 Poincaré Map -- 1.7 Variant Framework -- 1.8 Proposed Scheme -- 1.9 Organization of the Chapter -- 2 Framework of Variant Map System -- 2.1 Framework -- 2.2 Shift Segment Measurement SSM -- 2.3 Measuring Sequence Combination MSC -- 2.4 Projective Color Map PCM -- 3 Sequence Analysis -- 3.1 Ideal Condition -- 3.2 General Condition -- 3.3 Brief Discussion -- 4 Sample Maps -- 4.1 Dramatically Changing the Segment Lengths: 1DP, 1DQ, 2DP, 2DQ, and 2DPQ Maps m={8,16,128}, r=0 -- 4.2 Small Changes in Segment Lengths: 2DP Maps -- Variation Series in Lengths of Segments m={125,126,127}, r=0 -- 4.3 Changing the Lengths of Shift Displacement: 2DP Maps Change on Displacement Series m= 128, r={1,2,8} -- 4.4 Enlarged Maps: 2DP Maps on m= {125,127,128}, r={0,8} -- 5 Result Analysis -- 5.1 Figures 3, 4 and 5 -- 5.2 Figure 6 -- 5.3 Figure 7 -- 5.4 Figures 8-9 -- 6 Conclusion -- References -- Stationary Randomness of Three Types of Six Random Sequences on Variant Maps -- 1 Introduction -- 1.1 Pseudorandom Sequences from Linear Stream Ciphers -- 1.2 Pseudorandom Sequences from Nonlinear Stream Ciphers -- 1.3 Truly Random Sequences from Hardware Devices.

1.4 P_value Schemes-Statistical Tests on Cryptographic Sequences -- 1.5 Multiple Statistical Probability Distributions -- 1.6 Photon Statistic in Quantum Optics -- 1.7 Stationary and Non-stationary Properties -- 1.8 Datastreams -- 1.9 Variant Framework -- 1.10 Proposed Scheme -- 1.11 Organization of the Chapter -- 2 Testing System -- 2.1 System Architecture -- 2.2 Core Modules -- 3 Association Analysis -- 4 Testing Results -- 5 Result Analysis -- 6 Conclusion -- References -- Theoretical Foundation-Meta Model -- Meta Model on Concept Cell -- 1 Introduction -- 2 Concept Cell Model -- 3 Core Components -- References -- Voting Theory for Two Parties Under Approval Rule -- 1 Introduction -- 1.1 Brief Review of Voting Systems -- 1.2 Problems in the 2000 American Election -- 1.3 Structure of the Chapter -- 2 Simple Ballot Model -- 2.1 Key Words in Election -- 2.2 Definitions -- 2.3 One-Dimensional Feature Distribution -- 2.4 Separable Condition -- 2.5 Uncertain Condition -- 2.6 Balanced Opposites -- 2.7 Four Additional Policies -- 2.8 How Accurate Is Accurate? -- 2.9 Shifting Attentions from Invalid Votes to Valid Votes -- 3 Component Ballot Model -- 3.1 Definitions -- 3.2 Feature Partition -- 3.3 Feature Matrix Representation -- 3.4 Probability Feature Vector -- 3.5 Differences Between Two Probability Vectors -- 3.6 Permutation Invariant Group -- 3.7 Two Probability Vectors and Their Feature Indexes -- 3.8 CBM Construction -- 4 Conclusion and Further Work -- References -- Applications-Global Variant Functions -- Biometrics and Knowledge Management Information Systems -- 1 Introduction -- 2 Different Complexity Issues in Biometrics Applications -- 3 Proper Concepts, Methods and Useful Toolkits -- 4 Demand in Future Society -- 5 Base Strategy of Development -- References -- Recursive Measures of Edge Accuracy on Digital Images -- 1 Introduction.

1.1 Gradient -- 1.2 Laplacian -- 1.3 Gaussian -- 1.4 Mathematical Morphology -- 1.5 Conjugate -- 2 Recursive Model of Edge Accuracy -- 2.1 Question -- 3 Four Types of Edge Accuracy Measures -- 4 Four Sample Groups of Recursive Edge Maps -- 5 Comparison -- 6 Conclusion -- 2D Spatial Distributions for Measures of Random Sequences Using Conjugate Maps -- 1 Introduction -- 2 Traditional Methods and Conjugate Method -- 3 Generate and Measure Mechanism of Time Sequence -- 3.1 Disposal Model -- 3.2 Measure Model -- 3.3 Visualization Model -- 4 Visualization Result -- 5 Analyze -- 6 Conclusion -- References -- Permutation and Complementary Algorithm to Generate Random Sequences for Binary Logic -- 1 Introduction -- 2 Method -- 2.1 Permutation Operation -- 2.2 Complementary Operation -- 2.3 Visualization -- 2.4 Matrix Representation -- 3 Algorithm and Properties -- 3.1 Permutation and Complementary Algorithm -- 3.2 Representation Scheme -- 3.3 W, F, and C -- 4 Coding Simples -- 5 Result Analysis -- 6 Conclusion -- References -- 3D Visual Method of Variant Logic Construction for Random Sequence -- 1 Introduction -- 1.1 The Weakness of RC4 -- 1.2 CA -- 2 Architecture -- 2.1 Architecture -- 2.2 Computation Model of CA (CMCA) -- 2.3 Computation Model of RC4 Keystream (RC4KCM) -- 2.4 Measure Mechanism (MM) -- 2.5 Variant Measure (VM) -- 2.6 Probability Measurement (PM) -- 2.7 Selection Mechanism Module -- 2.8 Visualization Model -- 3 Sample Results on 3D Maps -- 3.1 Visualization Results of Unified Model -- 3.2 Visualization Results of Non-unified Model -- 3.3 Visualization Results of CA with Different Length of Initial Sequence -- 3.4 Visualization Results of RC4 Keystream with Different Segment Strategies -- 4 Analysis of Results -- 5 Conclusions -- References -- Applications-Quantum Simulations -- Synchronous Property-Key Fact on Quantum Interferences.

1 Introduction.