Kenji Kajiwara

ED3GE: Evolving Design and Discrete Differential GEometry - towards Mathematics Aided Computer Design

Grant No.：JPMJCR1911

Research Director

Kenji Kajiwara

Collaborator

Makoto Ohsaki	Professor Graduate School of Engineering Kyoto University
Tadatoshi Sekine	Associate Professor Faculty of Engineering Shizuoka University
Kenji Takizawa	Professor Faculty of Science and Engineering Waseda University
Jun Mitani	Professor Faculty of Engineering University of Tsukuba
Yohei Yokosuka	Associate Professor Graduate School of Science and Engineering Kagoshima University

Outline

We originate a novel geometry of discrete surfaces having the surfaces with good properties, such as developable surfaces, as the shape elements, incorporate the theory of aesthetic shapes and construct the technique of structural analysis/optimization on it. Under this framework, we develop an innovative software platform that enables structural design with high efficiency and low cost, endowed with beauty and artisticity, and guaranteeing security and safety. We integrate the knowledge in various areas of design to the geometry of shapes by the power of mathematics, and provide it as a basis of the regeneration of Japanese manufacturing which creates precise and beautiful products but with currently high cost.

Yoshiyuki Kabashima

Deciphering intracellular phenomena through information flow

Grant No.：JPMJCR1912

Research Director

Yoshiyuki Kabashima

Collaborator

Shinsuke Uda	Associate Professor Center for Information and Data Science Education Yamaguchi University
Yasushi Sako	Chief Scientist Cluster for Pioneering Research RIKEN
Atsushi Hatano	Assistant Professor Graduate School of Medical and Dental Sciences Niigata Uiversity

Outline

With the goal of deciphering intracellular phenomena, we develop data-driven methods to identify mechanisms that control information flow in living cells, and methods to assess the reliability of the obtained results. Our key concept is “information quantity”. The developed methods are to be employed to characterize the chain reactions of a few molecular species associated with carcinogenesis, as information flow, and to identify gene expression networks related to the immune system. By comparison of healthy and disordered systems, we aim to acquire knowledge that will lead to more effective diagnosis and treatment of cancer and immune disorders.

Yoshinobu Kawahara

Operator theoretic data analysis of complicated dynamics and its itegerated utilization with mathematical models

Grant No.：JPMJCR1913

Research Director

Yoshinobu Kawahara

Collaborator

Gen Kurosawa	Researcher Interdisciplinary Theoretical and Mathematical Sciences Program RIKEN
Hiroya Nakao	Professor School of Engineering Institute of Science Tokyo
Kennichi Bannai	Professor Faculty of Science and Technology Keio University

Outline

We develop based on representations of nonlinear dynamical systems with operators, such as transfer operators, (1)methods for identifying important dynamics in complex systems using statistical schemes, (2)theories for physical interpretations/usages of the identified dynamics and (3)methods for prediction/leaning by utilizing those with mathematical models. And we apply the developed methods/theories to data analyses in various fields to verify those effectiveness. We study these problems with the participation of researchers on machine learning, mathematics, nonlinear physics and theoretical biology.

Takaharu Yaguchi

Structure Preserving System Modeling and Simulation Basis Based on Geometric Discrete Mechanics

Grant No.：JPMJCR1914

Research Director

Takaharu Yaguchi

Collaborator

Toshiaki Oomori	Associate Professor Graduate School of Engineering Kobe University
Nobuki Takayama	Professor Graduate School of Science Kobe University
Hiroaki Yoshimura	Professor Faculty of Science and Engineering Waseda University

Outline

In this research, a discrete version of Lagrangian Dirac mechanics is constructed. This mechanics is integrated with various technologies of mathematical sciences and information sciences such as symplectic geometry, automatic differentiation, computational algebra, sparse modeling, and neural differential equations to construct new theories and new technologies that will be the foundation of modeling and simulation of various systems. We also implement these techniques as computer programs and develop a library for robust modeling and simulation.