Variant Construction from Theoretical Foundation to Applications.

Variant Construction from Theoretical Foundation to Applications.

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

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