
Mathematical Aspects of Computer and Information Sciences
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The 28 revised papers and 8 short papers presented were carefully reviewed and selected from 67 submissions. The papers are organized in the following topical sections: foundation of algorithms in mathematics, engineering and scientific computation; combinatorics and codes in computer science; data modeling and analysis; and mathematical aspects of information security and cryptography.
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Content
- Intro
- Preface
- Organization
- Contents
- Foundation of Algorithms in Mathematics, Engineering and Scientific Computation
- Automated Reasoning for Knot Semigroups and -orbifold Groups of Knots
- 1 Main Definitions
- 1.1 Arcs and Crossings
- 1.2 Cancellative Semigroups and Knot Semigroups
- 1.3 Keis
- 1.4 -orbifold Groups and Two-fold Groups
- 1.5 Putting These Constructions Together
- 1.6 Other Constructions: Knot Groups and Quandles
- 2 Trivial Knots
- 2.1 How to Test if a Knot Semigroup Is Cyclic
- 2.2 Cyclic Knot Semigroups
- 2.3 Non-cyclic Knot Semigroups: Small Knots
- 2.4 Non-cyclic Knot Semigroups: Sums of Knots
- 2.5 Efficiency Comparison
- 3 4-plats
- 3.1 Defining Relations for an Alternative Sum Semigroup
- 3.2 Experiments
- 4 Future Research
- 5 Technical Details
- References
- Balancing Expression Dags for More Efficient Lazy Adaptive Evaluation
- 1 Introduction
- 2 Theoretical Foundation
- 2.1 Addition
- 2.2 Multiplication
- 3 Implementation
- 4 Experiments
- 5 Caveats
- 5.1 Evaluation Order
- 5.2 Operands Matter
- 5.3 Overhead
- 6 Conclusion
- 7 Future Work
- References
- Certification Using Newton-Invariant Subspaces
- 1 Introduction
- 1.1 Smale's alpha-theory
- 2 Newton-Invariant Sets
- 2.1 Finding Newton-Invariant Sets
- 3 Certification Algorithm for Square Systems
- 4 Systems Constructed from Newton-Invariant Sets
- 5 Implementation Details and Examples
- 5.1 Implementation in alphaCertified
- 5.2 A Basic Example
- 5.3 An Example from Griewank and Osborne
- 5.4 A System with Embedded Points
- 5.5 Four-Bar Linkages Using Isotropic Coordinates
- 6 Discussion and Summary
- References
- Decomposition of Low Rank Multi-symmetric Tensor
- 1 Introduction
- 2 Partial Symmetric Tensor Decomposition Problem
- 2.1 Solving Polynomial Equations by Eigenvector Computation
- 2.2 Artinian Gorenstein Algebra of a Multivariate Hankel Operator
- 3 Multilinear Tensor Decomposition Problem
- 3.1 Algorithm
- 4 Example
- References
- Dimension Quasi-polynomials of Inversive Difference Field Extensions with Weighted Translations
- 1 Introduction
- 2 Preliminaries
- 3 Dimension Quasi-polynomials of Subsets of Nm and Zm
- 4 The Main Theorem
- References
- Efficient Certification of Numeric Solutions to Eigenproblems
- 1 Introduction
- 2 Notations
- 2.1 Matrix Norms
- 2.2 Clustering
- 2.3 Diagonal Matrices
- 3 Eigenproblems for Perturbed Diagonal Matrices
- 3.1 The Linearized Equation
- 3.2 The Fundamental Iteration
- 3.3 Convergence of the Fundamental Iteration
- 4 Algorithms
- 4.1 Clustering
- 4.2 Certification in the Case of Perturbed Diagonal Matrices
- 4.3 Certification of Approximate Eigenvectors and Eigenvalues
- 5 Possible Extensions
- References
- Fast Chinese Remaindering in Practice
- 1 Introduction
- 2 Chinese Remaindering
- 2.1 The Chinese Remainder Theorem
- 2.2 Modular Arithmetic
- 2.3 Naive Multi-modular Reduction and Reconstruction
- 3 Gentle Moduli
- 3.1 The Naive Algorithms Revisited for Special moduli
- 3.2 Combining Special Moduli into Gentle moduli
- 4 The Gentle Modulus Hunt
- 4.1 The Sieving Procedure
- 4.2 Influence of the Parameters s, w and w'
- 4.3 Application to Matrix Multiplication
- References
- Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets
- 1 Introduction
- 2 Construction of Homotopies
- 3 Isolated Points of Images
- 4 Computing Critical Points of Projections
- 5 Example
- 6 Conclusion
- References
- Implementing Fast Carryless Multiplication
- 1 Introduction
- 1.1 Related Work
- 1.2 Results and Outline of the Paper
- 2 Prerequisites
- 3 Fast Reduction from F2 [x] to F260[x]
- 3.1 Variant of the Frobenius DFT
- 3.2 Frobenius Encoding
- 3.3 Direct Transforms
- 3.4 Inverse Transforms
- 3.5 Multiplication in F2 [x]
- 4 Implementation Details
- 4.1 Packed Representations
- 4.2 Matrix Transposition
- 4.3 Frobenius Encoding
- 5 Timings
- 6 Conclusion
- References
- Improving Enclosure of Interval Scalar Projection Operation
- 1 Introduction
- 2 Interval Extensions
- 3 Interval Scalar Projection in Rn
- 3.1 Lower and Upper Bounds of Interval Scalar Projection in Rn
- 4 Computation of Interval Scalar Projection in R2
- 4.1 Natural Interval Extension Method
- 4.2 Improved Algorithm
- 4.3 Interval Enclosure Quality Comparison
- 5 Applications
- 6 Conclusion and Future Work
- References
- Integrating Algebraic and SAT Solvers
- 1 Introduction
- 2 Algorithms for Basic Operations with Order Ideals
- 3 Linear Interreduction for Boolean Polynomials
- 4 The Boolean Border Basis Algorithm
- 5 The Integration of the BBBA with a SAT Solver
- 6 Design of the Communication
- 7 Modifications of the SAT Solver
- 8 Experiments and Timings
- 8.1 Manual Combination of the Information
- 8.2 Automatic Combination of the Information
- References
- Isabelle Formalization of Set Theoretic Structures and Set Comprehensions
- 1 Introduction
- 1.1 Related Work
- 1.2 Contributions and Outline
- 2 Preliminaries
- 3 Structures
- 3.1 Structure Preliminaries
- 3.2 Structure Operations
- 3.3 Structure Prototype Introduction
- 3.4 Inheritance and Multiple Inheritance
- 4 Set Comprehension
- 5 Case Studies
- 5.1 Algebraic Structures
- 5.2 SCM Computer Model
- 6 Conclusion
- References
- Jordan Canonical Form with Parameters from Frobenius Form with Parameters
- 1 Introduction
- 2 Some Prior Work
- 3 Preliminaries
- 3.1 Regular Chain Theory
- 3.2 Regular Chain Representation of a Splitting Field
- 3.3 The Frobenius Canonical Form
- 3.4 The Jordan Canonical Form
- 4 JCF over a Splitting Field
- 4.1 Jordan Form of a Companion Matrix
- 4.2 Frobenius Form to Jordan Form
- 4.3 Example
- 5 JCF of a Matrix with Parameters
- 5.1 Square-Free Factorization of a Parametric Polynomial
- 5.2 JCF of a Companion Matrix with Parameters
- 5.3 Frobenius Form to JCF with Parameters
- 6 Experimentation
- 6.1 Kac-Murdock-Szegö matrices
- 6.2 The Belousov-Zhabotinskii Reaction
- 6.3 Nuclear Magnetic Resonance
- 6.4 Bifurcation Studies
- References
- Knowledge-Based Interoperability for Mathematical Software Systems
- 1 Introduction
- 2 Math-in-the-Middle Interoperability
- 2.1 The MitM Ontology
- 2.2 Specifying System Dialects
- 2.3 MitM-Based Distributed Computation
- 3 The MitM Ontology for Computational Group Theory
- 3.1 Type Theory and Logic
- 3.2 Group Theory
- 4 The System Dialects of GAP, SageMath, and Singular
- 4.1 SageMath
- 4.2 GAP
- 4.3 Singular
- 4.4 Alignments
- 5 Distributed Computational Group Theory
- 6 Conclusion
- References
- On Interval Methods with Zero Rewriting and Exact Geometric Computation
- 1 Introduction
- 2 Exact Geometric Computation Paradigm
- 3 Variants of Interval Methods with Zero Rewriting
- 4 Experiments
- 5 Conclusions
- References
- Sparse Rational Function Interpolation with Finitely Many Values for the Coefficients
- 1 Introduction
- 2 Preliminary Algorithms
- 3 Univariate Rational Function Interpolation
- 3.1 A Basic Interpolation Algorithm
- 3.2 Deterministic Incremental Interpolation
- 3.3 Deterministic Incremental Interpolation with Two Points
- 3.4 Probabilistic Univariate Rational Function Interpolation
- 4 Multivariate Rational Function Interpolation
- 4.1 Multivariate Polynomial Interpolation with Kronecker Substitution
- 4.2 Probabilistic Multivariate Rational Function Interpolation
- 5 Experimental Results
- 6 Conclusion
- References
- Virtual Theories - A Uniform Interface to Mathematical Knowledge Bases
- 1 Introduction
- 2 Virtual Research Environments for Mathematics: The Math-in-the-Middle Approach
- 3 Example: The API and Structure of LMFDB
- 3.1 The Structure of LMFDB
- 3.2 An API for LMFDB Objects
- 4 LMFDB as a Set of Virtual Theories
- 5 Accessing Virtual Theories
- 5.1 Concrete Encodings of Mathematical Objects
- 5.2 Choosing Encodings in Schema Theories
- 6 Translating Queries
- 7 Conclusion
- References
- On Real Roots Counting for Non-radical Parametric Ideals
- 1 Introduction
- 2 Preliminary
- 2.1 Multivariate Real Roots Counting
- 2.2 Comprehensive Gröbner System
- 2.3 CGS-QE Algorithm
- 3 New Multivariate Real Roots Counting
- 3.1 Main Result
- 4 Conclusion and Remarks
- References
- On the Bit-Size of Non-radical Triangular Sets
- 1 Introduction
- 2 Interpolation Formula
- 3 Bit-Size Consideration
- References
- Rapidly Convergent Integrals and Function Evaluation
- 1 Introduction
- 2 First Integral
- 2.1 Trapezoidal Rule
- 2.2 Convergence Rate
- 3 Second Integral
- References
- Stirling Numbers, Lambert W and the Gamma Function
- 1 Introduction
- 2 First Expansion
- 3 Second Expansion
- 4 Concluding Remarks
- References
- The Potential and Challenges of CAD with Equational Constraints for SC-Square
- 1 Introduction
- 1.1 Cylindrical Algebraic Decomposition
- 1.2 New Applications: SC2
- 2 Potentials
- 2.1 Equational Constraint
- 2.2 Multiple Equational Constrains
- 2.3 Equational Constraints of Sub-formulae
- 3 Challenges
- 3.1 Need for Primitivity
- 3.2 Well-Orientedness
- 3.3 Incremental CAD
- References
- Combinatorics and Codes in Computer Science
- New Small 4-Designs with Nonabelian Automorphism Groups
- 1 Introduction
- 2 Construction Method
- 3 Designs with 18 Points
- 4 Designs with 19 Points
- References
- On Classifying Steiner Triple Systems by Their 3-Rank
- 1 Introduction
- 2 The Triple System Supported by Cn
- 3 Counting STS(27) Supported by the Code C3
- 4 A Class of STS(27) Invariant Under a Group of Order 3
- References
- Right-Justified Characterization for Generating Regular Pattern Avoiding Permutations
- 1 Introduction
- 2 A Characterization for Right-Justified Permutation Patterns
- 3 Regular Patterns
- 4 c-Regular patterns
- 5 Constant Amortized Time Algorithms
- 6 Conclusion and Open Problems
- References
- Experimental Study of the Ehrhart Interpolation Polytope
- 1 Introduction
- 2 The Ehrhart Interpolation Polytope
- 3 Experiments and Statistics
- 4 Conclusion
- References
- On Testing Isomorphism of Graphs of Bounded Eigenvalue Multiplicity
- 1 Introduction
- 2 Permutation Representations and Projections
- 3 Bounding Vertex Partitions
- References
- Data Modeling and Analysis
- A Simple Streaming Bit-Parallel Algorithm for Swap Pattern Matching
- 1 Introduction
- 2 Basic Definitions and the Graph Theoretic Model
- 2.1 Notations and Basic Definitions
- 2.2 A Graph Theoretic Model
- 2.3 Using Graph Theoretic Model for Matching
- 2.4 Shift-And Algorithm
- 3 Our Algorithm
- 3.1 Graph Theoretic View of the Shift-And Algorithm
- 3.2 Our Algorithm for Swap Matching Using the Graph Theoretic Model
- 4 Limitations of the Finite Deterministic Automata Approach
- 5 Smalgo Algorithm
- 5.1 Smalgo-I
- 5.2 The Flaw in the Smalgo, Smalgo-I and Smalgo-II
- 6 Experiments
- References
- Epidemic Intelligence Statistical Modelling for Biosurveillance
- 1 Introduction
- 1.1 Objectives/Goals
- 1.2 State of the Art
- 2 Materials and Methods
- 2.1 Sentinel Epidemiological Surveillance System
- 2.2 Two Season Influenza Historical Data
- 2.3 Research Methodology
- 3 Experimental Study
- 4 Concluding Remarks
- References
- Mining Acute Stroke Patients' Data Using Supervised Machine Learning
- 1 Introduction
- 2 Related Work
- 3 Dataset
- 4 Methodology
- 4.1 Defining Classifications Criteria
- 4.2 Pre-processing Data
- 5 Modelling Data
- 5.1 Software Tool
- 5.2 Classification Techniques
- 5.3 Testing Technique
- 5.4 Performance Metrics for Evaluation
- 6 Evaluation Results and Comparison
- 6.1 First Approach
- 6.2 Second Approach
- 7 Conclusion
- References
- Parallel and Robust Empirical Risk Minimization via the Median Trick
- 1 Introduction
- 1.1 Related Work
- 2 Method
- 2.1 Medians
- 2.2 Discussion of Method
- 3 Theorems
- 4 Experiments
- 4.1 Comparison of Accuracy
- 4.2 Group Size
- 4.3 Min-of-Min Counterexample
- 5 Summary
- References
- Mathematical Aspects of Information Security and Cryptography
- Leakage-Resilient Riffle Shuffle
- 1 Introduction
- 1.1 Card Shuffling and Cryptography
- 1.2 Leakage
- 1.3 Our Contribution
- 2 Preliminary
- 2.1 Security Definition
- 2.2 Markov Chains and Rate of Convergence
- 3 RiffleSST- Leakage Resilient Shuffle
- 3.1 General Pseudo-random Permutation Generator
- 3.2 Description of RiffleSST Algorithm
- 4 Proofs
- 5 Sample Execution of RiffleSST Algorithm
- 6 Conclusions
- References
- Ordinary Pairing-Friendly Genus 2 Hyperelliptic Curves with Absolutely Simple Jacobians
- 1 Introduction
- 2 Background
- 3 Constructing Pairing-Friendly Jacobians
- 3.1 Lauter-Shang's Frobenius Elements
- 3.2 Generalized Drylo's Frobenius Elements
- 3.3 Alternative Representation
- 4 Implementation and Numerical Examples
- 5 Conclusion
- References
- Statistical Testing of PRNG: Generalized Gambler's Ruin Problem
- 1 Introduction
- 1.1 Related Work
- 1.2 Our Contribution
- 2 Gambler's Ruin Problem: Explicit Formulas for Winning Probabilities
- 3 BitTracker: Transforming Bit Strings into Intervals
- 3.1 BitTracker - Every Bit Counts
- 4 Testing Procedure
- 4.1 General Approach
- 4.2 Actual Parameters and Testing Procedure
- 4.3 Bit Derivation
- 5 Experimental Results
- 5.1 The 2 Test
- 6 Summary
- References
- Subtleties in Security Definitions for Predicate Encryption with Public Index
- 1 Introduction
- 2 Preliminaries
- 2.1 Predicate-Based Schemes with Public Index
- 3 Indistinguishability Templates for PE and P-KEM
- 4 Handling of User Secret Keys
- 4.1 OK-Security Does Not Imply OU-Security and CK-Security
- 4.2 OU-Security Does Not Imply OK-Security and CK-Security Under Chosen-Ciphertext Attack
- 4.3 Discussion and Recommendation
- 5 When and How to Restrict Challenge Decryptions
- References
- Code-Based Key Encapsulation from McEliece's Cryptosystem
- 1 Introduction
- 2 Preliminaries
- 2.1 The McEliece Cryptosystem
- 2.2 Encapsulation Mechanisms and the Hybrid Framework
- 3 The New KEM Construction
- 4 Conclusions
- A The McEliece Cryptosystem
- B Other Cryptographic Tools
- References
- Author Index
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