Variant Construction from Theoretical Foundation to Applications
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 cipher...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore
Springer Nature
2019
Springer Singapore Pte. Limited Springer |
| Ausgabe: | 1 |
| Schlagworte: | |
| ISBN: | 9789811322815, 9811322813, 9789811322822, 9811322821 |
| Online-Zugang: | Volltext |
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Inhaltsangabe:
- 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
- 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
- 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 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