Keita Iida

Mathematical Framework for Biological Dynamics Control

Grant No.：JPMJPR24K1

Researcher

Keita Iida

Outline

This study aims to understand the operational principles of biological systems, which consist of hierarchically interconnected molecules, cells, and tissues. Constructing a mathematical framework that comprehensively captures disease transformation mechanisms from the perspective of gene regulation, I aim to enable disease prediction, optimal control, and applications in medicine. I also seek to develop versatile computational tools by integrating mathematical and data sciences, defining spaces that represent multimodal data.

Noriyasu Iwamoto

Deformation Modeling and Control of Closed Surface Structures with Piecewise Constant Mean Curvature

Grant No.：JPMJPR24K2

Researcher

Noriyasu Iwamoto

Outline

Real-time shape control of surface-like structures could enable innovations such as adaptive clothing, architecture, and furniture that respond to individual needs and environmental conditions. Achieving this requires shape models that are computationally efficient for use in both prediction and control. However, modeling the shape of closed surface structures poses significant challenges. This project investigates the mathematical representation of closed surface structures based on the assumption of piecewise constant mean curvature, with the goal of achieving shape control for these structures.

Yuzuru Kato

Quantum nonlinear dynamics theory for understanding, prediction, and control of quantum dynamics

Grant No.：JPMJPR24K3

Researcher

Yuzuru Kato

Outline

This research aims to develop quantum nonlinear dynamics theory for understanding, analyzing, predicting, and controlling the complex phenomena of quantum systems. This research will open up new academic research areas of quantum nonlinear dynamics from the viewpoints of nonlinear dynamics analysis, nonlinear data analysis, and nonlinear control. This research will provide a fundamental theory for developing a new technology for quantum information science, quantum machine learning, and quantum measurement and control, thereby contributing to the development of quantum information processing and quantum device technologies.

Hiroshi Kera

Computational algebra and machine learning theory for large-scale algebraic computation

Grant No.：JPMJPR24K4

Researcher

Hiroshi Kera

Outline

This research aims to drastically accelerate high-cost algebraic and symbolic computation algorithms (particularly, Gröbner basis computation) using machine learning techniques, thereby establishing a practical computational method for large-scale algebraic equations. Specifically, we will focus on developing the foundational computational algebraic algorithms and machine learning models and theories. If this objective is achieved, it will enable the implementation of exact solutions through algebraic methods in large-scale control systems.

Tasuku Soma

Towards Submodular Optimization on Subspaces

Grant No.：JPMJPR24K5

Researcher

Tasuku Soma

Outline

Submodular optimization is an extremely powerful framework with efficient algorithms and a wide range of modeling capabilities to represent various problems involving discrete objects such as graphs and networks in a unified manner. In this project, we extend classical submodular optimization on subsets to submodular optimization on subspaces. We develop a new combinatorial optimization framework with a wide range of modeling capabilities and efficient algorithms based on matrix computation.

Han Bao

Interplay between loss function design and optimization dynamics

Grant No.：JPMJPR24K6

Researcher

Han Bao

Outline

This research project aims to extend calibration analysis, a framework to verify whether a surrogate loss leads to the optimal performance under a given evaluation metric, and integrate it with optimization dynamics. Therein, a general recipe to choose an appropriate loss function depending on optimization budget (on the whole computational time or error tolerance) is provided. This framework is going to be applied to classification with abstention, where a reasonable proper loss is chosen given optimization budget.

Shogo Nakakita

Change Point Detection in High-Dimensional Stochastic Differential Equation Models for Prediction and Control

Grant No.：JPMJPR24K7

Researcher

Shogo Nakakita

Outline

High-dimensional stochastic differential equation models are important in the prediction and control of complex phenomena with uncertainty; however, prediction and control by a single model can fail under regime shifts of systems. To address this problem, this project regards regime shifts as change points of models and develops methods to detect them properly.

Yuji Hirono

Development of topological control theory

Grant No.：JPMJPR24K8

Researcher

Yuji Hirono

Outline

This research aims to elucidate the relationship between robust control in complex systems and network topology, with the goal of establishing a new “topological control theory”. We will mathematically formalize a framework that characterizes robust control in various systems, such as chemical reaction networks and electrical circuits, using topological invariants. Additionally, we aim to develop efficient algorithms for detecting control mechanisms, with potential applications in fields like synthetic biology.

Yoshihiro Maruyama

Categorical Machine Learning and Applications to Chemical Information Processing

Grant No.：JPMJPR24K9

Researcher

Yoshihiro Maruyama

Outline

Category theory is an abstract mathematical language allowing us to shed light on compositional structural aspects of various systems and processes in the sciences. In this project we apply category theory in artificial intelligence and machine learning, thus developing the novel paradigm of categorical machine learning for the next generation of artificial intelligence that integrates symbolic reasoning and statistical inference capabilities. In this project we focus inter alia upon the theoretical foundations of categorical machine learning and explore potential applications to chemical information processing in particular.

Yuta Mizuno

Quantum Computing for Operator-Theoretic Analysis of Dynamical Systems

Grant No.：JPMJPR24KA

Researcher

Yuta Mizuno

Outline

Simulating every conceivable scenario and guiding optimal decision-making—to achieve such ideal prediction and control, this project aims to develop quantum software. Specifically, grounded in the operator-theoretic approach to dynamical systems theory, I will develop a suite of quantum programs for dynamical systems analysis. These programs will simulate a wide variety of possible scenarios in parallel using a quantum differential equation solver, extract essential dynamical information through quantum dynamic mode decomposition, and construct reduced-order models useful for understanding and controlling dynamic phenomena.

Hiroki Miyazako

Functional control of bioartificial muscle tissue based on topology of cell alignment

Grant No.：JPMJPR24KB

Researcher

Hiroki Miyazako

Outline

Muscle tissue engineering has been widely developed as biotechnology for many social problems, including regenerative medicine and drug discovery. However, design principles for engineered muscle heavily depend on rules of thumb or trial and error. Based on theories of cell alignment based on complex analysis, this study aims to develop new mathematical theories for predictive design and control of muscular functions from viewpoints of (1) mechanical contraction, (2) self-repairing, and (3) propagation of excitation.

Hiroshi Morioka

Data-driven prediction and decoding of complex systems via representation learning

Grant No.：JPMJPR24KC

Researcher

Hiroshi Morioka

Outline

This project aims to realize prediction and control of high-dimensional complex systems by developing novel data-driven frameworks combining representation learning, seeking fundamental latent representation of those systems, and control law designing based on such latent representation.

Toshiaki Yachimura

Developing a Mathematical Framework for Inferring and Controlling Cell Differentiation Dynamics via Optimal Transport Theory

Grant No.：JPMJPR24KD

Researcher

Toshiaki Yachimura

Outline

This research aims to develop a method based on optimal transport theory to estimate cell differentiation dynamics using time-series scRNA-seq data. We will construct a mathematical framework to infer and control Waddington’s epigenetic landscape and the underlying gene regulatory networks in gene expression space. Furthermore, we aim to reconstruct spatiotemporal gene expression patterns in actual three-dimensional tissues from time-series scRNA-seq data.

Hidekazu Yoshioka

Establishment of non-Markovian biological resource management models

Grant No.：JPMJPR24KE

Researcher

Hidekazu Yoshioka

Outline

We will describe environmental and resource dynamics in a unified manner as a polynomial process based on the Markovian lifts. We will also analyze the presence or absence of turning points and their precursors. Furthermore, by tracking the changes in the Orlicz space that correspond to data fluctuations and memories, we will work on prediction and control to avoid and mitigate turning points and even try to revitalize systems that have reached a turning point. In addition to developing mathematical methods, we will apply the proposed methods by installing an environmental measurement system in cities at risk of vanishing.