Recent Developments in Mathematical, Statistical and Computational Sciences: The V AMMCS International Conference, Waterloo, Canada, August 18–23, ... Proceedings in Mathematics & Statistics, 343)

Preface
Contents
Advances in Mathematical Modelling and Theory
A Moving Horizon State Estimator for Real-Time Stabilization of a Double Inverted Pendulum
	1 Introduction
	2 A Proximal Point Moving Horizon Estimator for Linear Time Invariant Systems
		2.1 Centered Proximal Point Observer
	3 Mathematical Model of the Double Inverted Pendulum
	4 Power Series Stabilization Controller
	5 Real Time Stabilization of a Double Inverted Pendulum
	References
Spontaneous Symmetry-Breaking in Deterministic Queueing Models with Delayed Information
	1 Introduction
	2 Preliminaries
	3 Results
		3.1 Local Stability of the Fully Symmetric Equilibrium
		3.2 Symmetry-Breaking Hopf Bifurcations
		3.3 Numerical Simulations
	4 Summary and Conclusions
	References
Algebraic Structure of the Varikon Box
	1 Introduction
	2 Review of the 15-Puzzle
	3 Reachable Configurations of the Varikon Box
	4 Group Structure of the 2 times 2 times 2 Varikon Box
	5 The A5 and A6 Shortest Word Problem
	6 Conclusion and Future Work
	References
A Bestiary of Transformation Semigroups for the Holonomy Decomposition
	1 Introduction
	2 The Holonomy Method
	3 Bestiary of Examples for Image Sets in the Skeleton
	4 Bestiary of Examples for Holonomy Groups
	5 Conclusion
	References
Spatial Iterated Prisoner's Dilemma as a Transformation Semigroup
	1 Introduction
	2 Spatial Algebraic Model
	3 Complexity Regimes
		3.1 Regime A
		3.2 Regime B
		3.3 Regime C
		3.4 Regime D
	4 Conclusion
	References
Oscillations and Periodic Solutions  in a Two-Dimensional Differential Delay Model
	1 Introduction
	2 Preliminaries
		2.1 Assumptions and Basics
		2.2 Linearization and Characteristic Equation
		2.3 Oscillation
		2.4 Ejective Fixed Point Theorem
	3 Main Results
		3.1 Invariant Cone, Slow Oscillation, and Nonlinear Mapping
		3.2 Ejectivity
	4 Conclusion
	References
Exploring Tetris as a Transformation Semigroup
	1 Introduction
	2 Tetris as a Transformation Semigroup
	3 Analysis
		3.1 Tri-Tris
		3.2 Aperiodicity
	4 Periodic Tri-Tris
		4.1 Periodic Tri-Tris: 3 times3 Case
		4.2 Periodic Tri-Tris: 3 times4 Case with Reduced Generating Set
	5 SNAGs and Computation in Tetris
	6 Conclusion
	References
Differential Equations Using Generalized Derivatives on Fractals
	1 Introduction: Derivatives with Respect to a Fractal Measure
	2 The Weak Formulation and H1µ(K)
	3 Some Basics of Iterated Function Systems
	4 Convergence of Solutions
	5 Conclusion
	References
Revisiting Path-Following to Solve the Generalized Nash Equilibrium Problem
	1 The Generalized Nash Equilibrium Problem
	2 A Pathway to the GNEP
	3 Examples of Pathways
		3.1 Smoothing of C-Functions
		3.2 Interior-Point Method
	4 How to Follow the Path
	References
Properties of the Zeros of the Scale-Delay Equation and Its Time-Variant ODE Realization
	1 Introduction
	2 Time-Variant Differential Annihilators
	3 General Results
	4 Extensions: From (α,β) to mathbbR
	5 Application: Scale-Delay Equation
	References
Advances in Statistical Modelling and Data Analysis
Covering Large Complex Networks by Cliques—A Sparse Matrix Approach
	1 Introduction
	2 Compact Representation and Edge Clique Cover
		2.1 Intersection Matrix
		2.2 A Heuristic for Clique Cover
	3 Numerical Testing
	4 Conclusion
	References
Comparing Regularization Techniques Applied to a Perceptron
	1 Introduction
	2 Background
		2.1 The Simple Perceptron Model
	3 Finding Weights and Biases
		3.1 The Loss Function
		3.2 Gradient Descent
	4 Overfitting and Regularization
	5 Results and Discussion
	References
Key Performance Indicators and Individual Factors on Penalty Kicks
	1 Introduction
	2 Data Set and Variables Definition
		2.1 Variable Clarification
	3 Methodology
	4 Key Performance Factors in Penalty Kick
		4.1 Global Analysis
		4.2 Individual Players
	5 Conclusion
	References
Sparse Covariance and Precision Random Design Regression
	1 Introduction
	2 Estimator Construction
		2.1 Replacing XTX
	3 Numerical Results
		3.1 Simulated Data
		3.2 Forest Fire Data
		3.3 Arizona Crime Data
	4 Discussion
	References
Applying Neural Networks to a Fractal Inverse Problem
	1 Introduction
	2 Mathematical Background
	3 Neural Network Background
	4 Fractal Databases
	5 Results
	6 Conclusions and Future Work
	References
Solving Parameter Identification Problems using the Collage Distance and Entropy
	1 Introduction
	2 Inverse Problems Using the Generalized Collage Theorem
	3 Entropy
	4 Multicriteria Optimization and Our Scalarized Problem
	5 Numerical Results
	6 Conclusions
	References
Mean-Square Stability of Stochastic System with Impulse and Unbounded Delay
	1 Introduction
	2 Problem Formulation
	3 Main Results
	References
BOLD.R: A Software Package to Interface with BOLD Through R
	1 Introduction
	2 Methods and Implementation
	3 Results and Discussion
	4 Conclusions
	References
Analysis of Cortical Spreading Depression in Brain with Multiscale Mathematical Models
	1 Introduction
	2 Mathematical Modeling of CSD
		2.1 Reaction-Diffusion Model of CSD in Two-Space Dimensions
		2.2 One-Dimensional Neuronal Model of CSD
	3 Results and Discussion
		3.1 Reaction-Diffusion Model of CSD in Two-Space Dimensions
		3.2 One-Dimensional Neuronal Model of CSD
	4 Conclusions
	References
Impulsive Consensus of Complex-Valued Multi-agent Systems with Hybrid Protocols
	1 Introduction
	2 Preliminaries
	3 Consensus Results
	4 Numerical Simulations
	5 Conclusion
	References
Input-to-State Stability for Delayed Hybrid Systems and Hinfty Control
	1 Inroduction
	2 Problem Formulation
	3 Main Results
		3.1 Linear Systems
	4 Numerical Examples
	References
Impulsive Distance-Based Formation Tracking Control of Multi-agent Systems
	1 Introduction
	2 Preliminaries and Problem Formulation
		2.1 Graph Theory and Some Useful Lemmas
		2.2 Problem Statement
	3 Main Results
		3.1 Undirected Formations of Double Integrators
	4 Numerical examples
	5 Conclusions
	References
Exponential Stabilization for Markov Jump Neural Networks with Additive Time-Varying Delays via Event-Triggered Impulsive Control
	1 Introduction
	2 Description of problem and preliminaries
	3 Main Results
	4 Numerical Example
	5 Conclusion
	References
Computational Methods for Differential Equations
Development of a Lattice Boltzmann Model for the Solution of Partial Differential Equations, A Performance Comparison Study with that of the Finite Difference Method
	1 Introduction
	2 Description of the Numerical Methods
	3 Results
	4 Conclusion
	References
Using Shooting Approaches to Generate Initial Guesses for ODE Parameter Estimation
	1 Introduction
		1.1 Definitions and Notation
		1.2 Least Squares Parameter Estimation
		1.3 Shooting Approaches
		1.4 Obtaining a suitable po
	2 Proposed method
	3 Numerical Experiments
		3.1 Comparison to random sampling
	4 Conclusions
	References
A Computational Study for Solving Inverse Problems for Mixed Variational Equations on Perforated Domains
	1 Introduction
	2 Basics on Inverse problems for Variational Equations using the Generalized Collage Theorem
	3 Mixed Variational Equations
	4 Inverse Problems on Perforated Domains:  A Computational Study
	5 Conclusion
	References
bacoli_py—A Python Package for the Error Controlled Numerical Solution  of 1D Time-Dependent PDEs
	1 Introduction
	2 Overview of BACOLI and BACOLRI
	3 Description of bacoli_py
		3.1 Basic Usage
	4 Examples
		4.1 One Layer Burgers Equation—Python Callback Functions
		4.2 Two Layer Burgers Equation—Callback Functions  as Compiled Fortran Subroutines
	References
Solving Cardiac Bidomain Problems with B-spline Adaptive Collocation
	1 Introduction
	2 The Bidomain Model in
		2.1 B-spline Basis Expansion
		2.2 Collocation Equations
		2.3 Error Control
	3 Numerical Experiments
		3.1 Initiation of Pulse Solutions
		3.2 Reference Solution and Error
		3.3 Numerical Solutions
	4 Results
	5 Conclusions
	References
A Computational Comparison of Three Methods for Solving a 1D Boundary Value Inverse Problem
	1 Introduction
	2 Regularization Methods
		2.1 Tikhonov Regularization
		2.2 An Example Problem
	3 Iteration Schemes
		3.1 Landweber-Fridman Iteration
		3.2 Revisited: An Example Problem
	4 Collage-Coding Methods
		4.1 Revisited: An Example Problem
	5 Conclusions and Future Work
	References
A Comparison of Turbulence Generated by 3DS Sparse Grids with Different Blockage Ratios and Different Co-frame Arrangements
	1 Introduction
	2 Direct Numerical Simulations
	3 Results on Turbulence Intensity
	4 Conclusions
	References
Mathematical Modelling in Engineering, Physical and Chemical Sciences
An Extended Pseudo Potential Multiphase Lattice Boltzmann Model with Variable Viscosity Ratio
	1 Introduction
	2 Pseudopotential Model
	3 Model Validation
		3.1 Static Droplet
		3.2 Immiscible Two-Phase Poiseuille Flow
		3.3 Droplet Splashing
	4 Conclusion
	References
Approximating Dispersive Materials with Parameter Distributions in the Lorentz Model
	1 Introduction
	2 Background
		2.1 Maxwell's Equations
		2.2 Lorentz Model
		2.3 Random Polarization
	3 Frequency Domain
		3.1 Frequency Domain Inverse Problem
		3.2 Bimodal Data
	4 Time Domain Discretization
		4.1 FDTD Discretization
	5 Time Domain Inverse Problem
	6 Conclusion
	References
Coulomb Explosion Imaging: Super-Resolution by Optical Properties of Electrostatics Lenses
	1 Introduction
	2 Paraxial Approximation
	3 Optical Property and Time Dispersion
	4 Conclusion
	References
Error Correction for Correlated Quantum Systems
	1 Introduction
	2 Freedom in the Operator-Sum Representation
	3 Modeling Open Quantum Systems
	4 Reversing a Quantum Operation Corresponding  to a Completely Positive Map
	5 Reversing a Quantum Operation that Is Not  a Completely Positive Map
	6 Discussion/Conclusions
	References
Numerical Investigation of VAWT Airfoil Shapes on Power Extraction and Self-starting Purposes
	1 Introduction
	2 Selected Airfoils and Characteristics of VAWT
	3 Methodology
		3.1 Setup, Boundary Conditions, and Flow Modeling
		3.2 Mesh
		3.3 Validation
	4 Evaluation of Power Coefficients (CP)
	5 Analysis of Self-starting
	6 Conclusion
	References
Stability and Stabilization of T–S Fuzzy Systems with Aperiodic Sampling
	1 Introduction
	2 Preliminaries
	3 Main Results
	4 Conclusion
	References
A New Method of Modelling Tuneable Lasers with Functional Composition
	1 Introduction
	2 Previous Modelling Efforts
		2.1 Discrete Component Models
	3 A New Model
		3.1 Components
		3.2 Non-dimensionalization
		3.3 Combining the Effects of Each Block of the Model
	4 Conclusion
	References
Algebraic Structure and Complexity  of Bootstrap Percolation with External Inputs
	1 Introduction
	2 The Modified Bootstrap Percolation Model with External Inputs
	3 Holonomy Decomposition and Modeling the Process  as a Transformation Semigroup
	4 Methods, Results and Discussion
	5 Conclusion
	References
Simulations of Realistic Trombone Notes in the Time-Domain
	1 Introduction
	2 Computational Model
		2.1 Numerical Test Case
		2.2 Initial and Boundary Conditions
		2.3 Computational Trombone Geometry
	3 Simulation Results
	4 Conclusion
	References
The Impact of External Features on Prediction Accuracy in Short-Term Energy Forecasting
	1 Introduction
	2 Notable Multivariate and Univariate Machine Learning Time Series Algorithms
	3 Implementation Methodology
	4 Experimental Results
	5 Conclusion
	References
Toral Diffeomorphisms Induce Quantum Superoperators via TAQS
	1 Introduction
	2 The Method of TAQS
		2.1 Q-Transform Mediated Equivalence Between Functions and Operators
		2.2 Toral Automorphisms Acting on Functions and Operators
		2.3 Explicit Formulas for the Special TAQS
	3 A few Examples of the Effect of TAQS
	References
Optimal Time Decay Rates for a Chemotaxis Model with Logarithmic Sensitivity
	1 Introduction
	2 Decay Rates for the Transformed System
	3 Decay Rates for the Original System
	References
Mathematical and Statistical Modelling in Life Sciences
An Optimal Control Strategy  for a Malaria Model
	1 Introduction
	2 Formulation of the Optimal Control Model
		2.1 The Optimal Control Problem
		2.2 Analysis of the Optimal Control Problem
		2.3 Optimality System
	3 Numerical Simulations and Results
	4 Discussion
	5 Conclusion
	References
Effect of Genetic Defects in a Cortical Circuit Model Associated with Childhood Absence Epilepsy
	1 Introduction
	2 Model
	3 Isolated Single Neurons
	4 Modeling Impairment of GABA Synapses
	5 Modeling Sodium Channel Mutations
	6 Conclusion and Future Directions
	References
Operator Splitting for the Simulation of Aqueous Humor Thermo-Fluid-Dynamics in the Anterior Chamber
	1 Introduction
	2 Mathematical Model
	3 Numerical Method
	4 Simulation Results
	5 Conclusions
	References
Modelling Thermal Aspects of Decomposition
	1 Introduction
	2 Mathematical Model
	3 Model Implementation
	4 Results
		4.1 Analysis of the Coupling Coefficient
		4.2 Temperature Prediction and Heat Flux Analysis
	5 Conclusion
	6 Future Work
	References
Mathematical Modeling of the Steady-State Behavior of Nitric Oxide in Brain
	1 Introduction
	2 Mathematical Model
	3 Results
	4 Conclusion
	References
Automate Obstructive Sleep Apnea Diagnosis Using Convolutional Neural Networks
	1 Introduction and Background
	2 Cleveland Children's Sleep and Health Study Database
		2.1 Individual Labeling
		2.2 Data Preprocessing
	3 1D-CNN Architecture
	4 Results and Analysis
	5 Conclusion and Discussion
	References
Numerical Analysis of Nanowire Resonators for Ultra-high Resolution Mass Sensing in Biomedical Applications
	1 Introduction
	2 Mathematical Modelling
	3 Solution Procedure
		3.1 FDM
		3.2 Implementation of the FDM for the Nanowire Resonator
	4 Results and Discussion
	5 Conclusion
	References
Contaminant Removal in Ceramic Water Filters by Bacterial Biofilms
	1 Introduction
	2 Mathematical Model
		2.1 Pressure Driven Flow
	3 Numerical Treatment
		3.1 Numerical Method
		3.2 Implementation
	4 Numerical Simulations
	5 Conclusion
	References
Comparison of Fractional-Order and Integer-Order Cancer Tumor Growth Models: An Inverse Approach
	1 Introduction
	2 Existing Models for Cancer Tumor Growth
	3 Fractional Ordinary Differential Equation Models
		3.1 A Quick Introduction to Fractional Calculus
	4 Comparison of Integer and Fractional Order Cancer Tumor Models
		4.1 Inverse Problems via Collage-Coding
		4.2 Examples
	5 Conclusions and Future Work
	References
Numerical Modelling of Drug Delivery in an Isolated Solid Tumor Under the Influence of Vascular Normalization
	1 Introduction
	2 Materials and Methods
		2.1 Governing Equations
		2.2 Model Geometry and Boundary Conditions
		2.3 Solution Procedure
		2.4 The Value of Transport Parameters
	3 Results and Discussion
	4 Conclusion
	References
Quantitative Study of the Coupling Among Cardiovascular System, Lymphatic System and Interstitial Space
	1 Introduction
	2 Methods
	3 Results
	4 Conclusions
	References
Age-Structured Epidemic with Adaptive Vaccination Strategy: Scalar-Renewal Equation Approach
	1 Introduction
	2 Age-Structured Epidemic Model
		2.1 Equilibrium Equation of the Endemic Steady State
		2.2 General Case
		2.3 Special Case of Natural Constant Per-Capita Mortality Rate
	3 Conclusion
	References
On the Modeling of Drug Delivery to Solid Tumors; Computational Viewpoint
	1 Introduction
	2 Material and Methods
		2.1 Mathematical Modeling Approach
		2.2 Model Geometry, Computational Domain, and Boundary Conditions
		2.3 Validation
	3 Results and Discussion
	4 Conclusions
	References
Evaluating a Logistic K-mer Based Model for Classifying CO1 Sequences of C. Clupeaformis
	1 Introduction
	2 Model Inspiration and Background Information
		2.1 Inspiration from Natural Language Processing
		2.2 K-mers Based Model
	3 Methods and Implementation Details
		3.1 Logistic Regression
		3.2 K-Fold Cross-Validation
		3.3 Implementation Details
	4 Results
	5 Discussion
	6 Conclusion
	References
Mathematical Modeling of Coupled Electro-thermal Response of Nerve Tissues Subjected to Radiofrequency Fields
	1 Introduction
	2 Computational Modeling Details
	3 Results and Discussion
	4 Conclusion
	References
Ranking Association Rules from Data Mining for Health Outcomes: A Case Study of Effect of Industrial Airborne Pollutant Mixtures on Birth Outcomes
	1 Background
	2 Methods
		2.1 Definitions and Notations
		2.2 Ranking Association Rules
	3 Results
	4 Discussion
	References
Mathematics and Computation in Finance, Economics, and Social Sciences
About the Algorithms of Strategic Management
	1 Introduction
	2 Notations and Definitive Concepts
		2.1 Statement Problem
		2.2 Solution Problem
	3 Result and Discussion
	References
Using Cognitive Fit Theory to Evaluate the Effectiveness of Financial Information Visualization: An Example Using Data to Detect Fraudulent Transactions
	1 Introduction
	2 Research Question
	3 Research Approach
		3.1 Participants
		3.2 Measures
		3.3 Procedure
		3.4 Business Scenarios Design
	4 Results and Discussion
		4.1 Data Reduction and Analysis Plan
		4.2 Speed and Accuracy
		4.3 Discussion
	References
Factors Affecting Sustainable Development and Modelling
	1 Introduction
	2 Structuring the Goal of the System
	3 Assigning Weight to the Goal of the System
	4 Minimization of the Local Goals of the System
	5 Conclusion
	References
On a Generalized Integro-Differential Spatial Model of Economic Growth
	1 Introduction
	2 The Solow-Type Model
	3 The Ramsey-Type Model
	4 The Maximization Algorithm
	5 Numerical Examples
	6 Conclusion
	References
Utilizing Bidirectional Encoder Representations from Transformers for Answer Selection
	1 Introduction
	2 Related Work
	3 Utilizing BERT for Answer Selection
		3.1 Transformer Encoder
		3.2 Pre-training the BERT Model
		3.3 Fine-Tuning BERT for Answer Selection
	4 Experimental Setup
		4.1 Datasets
		4.2 Training Parameters and Evaluation Metrics
	5 Results and Analyses
		5.1 Performance Comparisons
		5.2 Ablation Studies
	6 Conclusions and Future Work
	References
Calibration and Analysis of Structural Credit Risk Models with Occupation Time
	1 Introduction
	2 Occupation-Time Structural Model
	3 Numerical Results
		3.1 Calibration Process
		3.2 Case Studies
	4 Conclusion
	References
Prediction Intervals of Machine Learning Models for Taxi Trip Length
	1 Introduction
	2 Prediction Interval Algorithms
		2.1 Decomposition into Model Variance and Inherent Noise
		2.2 K Nearest Neighbors Inductive Conformal Prediction
	3 Computational Models for Empirical Evaluation
	4 Experimental Results
	5 Conclusion
	References
The Cobb-Douglas Production Function Revisited
	1 Introduction
	2 Theoretical Framework
	3 Main Result
	References
Inferring Rankings from First Order Marginals
	1 Introduction
	2 Background and the Fourier Transform
	3 Main Results
		3.1 Structure of the Matrices
		3.2 `Uniqueness'
	4 Generalizations and Further Directions
	References
High-Frequency Statistical Modelling for Jump-Diffusion Multi-asset Price Processes with a Systemic Component
	1 Introduction
	2 High-Frequency Data Processing
	3 Detecting Common and Disjoint Jumps
	4 Multi-Asset Price Model
	5 Estimation of Parameters for the Systemic Component
	6 Estimation of Model Parameters
		6.1 Assets Model with only Common Jump
		6.2 Assets Model with an Additional Jump Component
	7 Numerical Results
	References