Preface
Contents
Part I Introduction
1 Advanced Mathematical Science for Mobility Society
	1.1 Current State of Mobility Society
	1.2 Project Titled Advanced Mathematical Science for Mobility Society
	References
Part II Mathematical Models of Flow
2 Analysis of Autonomous Many-Body Particle Models from Geometric Perspective and Its Applications
	2.1 Introduction
	2.2 Discrete Morse Theory
		2.2.1 Homology
		2.2.2 Morse Theory
		2.2.3 Discrete Morse Theory
	2.3 Application of Discrete Morse Theory to Traffic Flow Models
		2.3.1 Algorithms for Constructing Discrete Morse Functions on Cubical Complexes
		2.3.2 Application to Analysis of the Burgers Cellular Automaton
		2.3.3 Application to Analysis of Pedestrian Flow
	2.4 A Traffic Flow Model Using Quantum Walks
		2.4.1 A Definition of One-Way Multi-particle Quantum Walks
		2.4.2 Probability Distribution of OMQW
		2.4.3 Simulation
	2.5 Pedestrian Flow and Future Perspectives
	References
3 Integrable Systems Related to Matrix LR Transformations
	3.1 Introduction
	3.2 Discrete Hungry Integrable Systems
		3.2.1 Discrete Hungry Toda Equations
		3.2.2 Nonautonomous Discrete Hungry Integrable Systems
	3.3 Discrete Relativistic Toda Equation
		3.3.1 Derivation from the Perspective of a Shifted LR Transformation
		3.3.2 Relationship with the Discrete Hungry Lotka–Volterra System
	3.4 Ultradiscrete Toda Equation
		3.4.1 Min-Plus Algebra
		3.4.2 Relationship with Min-Plus Eigenvalue
	3.5 Numbered Box and Ball System
	3.6 Concluding Remarks
	References
Part III Mathematical Methods for Huge Data and Network Analysis
4 Numerical Analysis for Data Relationship
	4.1 Spectral Methods for Machine Learning
	4.2 Complex Moment-Based Supervised Eigenmap for Dimensionality Reduction
		4.2.1 Dimensionality Reduction Based on a Matrix Trace Optimization
		4.2.2 A Complex Moment-Based Supervised Eigenmap
	4.3 Multi-view Data Analysis
		4.3.1 Multi-Kernel Learning
		4.3.2 Multi-view Graph Clustering
		4.3.3 Multi-view Subspace Clustering
	4.4 Data Collaboration Analysis
		4.4.1 Privacy-Preserving Integrated Data Analysis
		4.4.2 Data Collaboration Analysis
	References
5 Application of Tensor Network Formalism for Processing Tensor Data
	5.1 Introduction
	5.2 Tensor-Network Formalism
		5.2.1 Tensor Contraction and Tensor Network
		5.2.2 Tensor Decomposition and Tensor Compression
	5.3 Generative Model Using a Tree Tensor Network
		5.3.1 Generative Modeling
		5.3.2 Tree Generative Model
		5.3.3 Canonical Form of TTN
		5.3.4 Learning Algorithm
		5.3.5 Network Optimization
	5.4 Tensor Ring Decomposition
		5.4.1 Introduction to Tensor Ring Decompositions
		5.4.2 Redundant Loops
		5.4.3 Entanglement Penalty Algorithm
		5.4.4 Numerical Experiments
	5.5 Exact MERA Network and Quantum Renormalization Group for Critical Spin Models
		5.5.1 Introduction
		5.5.2 Heisenberg Model and Quantum Entanglement
		5.5.3 Construction of Exact MERA Network
		5.5.4 RG Flow
		5.5.5 Concluding Remarks
	5.6 Summary
	References
6 Machine Learning Approach to Mobility Analyses
	6.1 Introduction
	6.2 Deep Learning-Based Multi-animal Tracking
	6.3 Horse Herding Analysis
	6.4 Multi-level Attention Pooling for Graph Neural Networks
	6.5 Conclusions
	References
7 Graph Optimization Problems and Algorithms for DAG-Type Blockchains
	7.1 Introduction
		7.1.1 Related Work
	7.2 Preliminaries
	7.3 Blockchain
		7.3.1 Chain-Type Blockchain
		7.3.2 DAG-Type Blockchain
		7.3.3 PHANTOM Protocol
	7.4 Pathwidth
		7.4.1 Pathwidth and Directed Pathwidth
		7.4.2 DAG-Pathwidth
		7.4.3 Nice DAG-PD
	7.5 Discord k-Independent Set Problem
	7.6 Conclusion
	References
Part IV Algorithms for Mobility Society
8 System-Control-Based Approach to Car-Sharing Systems
	8.1 Introduction
	8.2 Optimization of the Car-Sharing System Considering Demand Shift by Dynamic Pricing
		8.2.1 Modeling
		8.2.2 Control Objective
		8.2.3 Main Result
		8.2.4 Simulation Result
	8.3 Sparse Optimal Control for Networked Systems
		8.3.1 Sparse Optimal Control Problem
		8.3.2 Application to the Rebalancing Problem
	8.4 Communication-Aware Cooperative Car-Sharing Control
		8.4.1 Formulation of Cooperative Rebalancing Control
		8.4.2 Distributed Event-Triggered Optimization
		8.4.3 Event-Triggered Distributed Primal-Dual Algorithm
		8.4.4 Numerical Simulation
	8.5 Optimal Control Problem of Probability Distributions for Rebalancing in One-Way Car-Sharing Service
		8.5.1 Optimal Control Problem of Probability Distributions: Problem Formulation and Optimal Condition
		8.5.2 Application to Rebalancing in One-Way Car-Sharing Services
	8.6 Optimization of One-Way Car-Sharing Services via DC Program
		8.6.1 Problem Formulation
		8.6.2 DC Programming
		8.6.3 Numerical Simulation
	8.7 Conclusion
	References
9 Algorithms for Future Mobility Society
	9.1 Introduction
	9.2 Basic Problems and Algorithms for Mobility Society
		9.2.1 Approaches for Hard Problems
		9.2.2 Reallocation Scheduling
	9.3 Online Optimization for Mobility Society
	9.4 Mechanism Design for Mobility Society
	References
10 Mechanism Design for Mobility
	10.1 Introduction
	10.2 Online Facility Assignment Problems on a Line
		10.2.1 Background and Known Results
		10.2.2 Preliminaries
		10.2.3 Online Facility Assignment with a Small Number of Servers
		10.2.4 Capacity-Insensitive Algorithms
		10.2.5 Conclusions
	10.3 Two-Sided Matching with Flexible Quotas: Student-Project-Resource Matching-Allocation Problem
		10.3.1 Introduction
		10.3.2 Model
		10.3.3 Impossibility Theorems
		10.3.4 Sample and Deferred Acceptance (SDA) Mechanism
		10.3.5 Conclusions
	10.4 Formalizing Station-Based One-Way Car Sharing as Three-Sided Matching
		10.4.1 Background
		10.4.2 Problem Setting and Formulation
		10.4.3 Proposed Mechanism
		10.4.4 Experiment Settings and Simulation Process
		10.4.5 Results
		10.4.6 Conclusions
	References