[Mathematical Information Platform]Year Started : 2019

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Kenji Kajiwara

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

Research Director
Collaborators
Makoto Ohsaki
Toshio Honma
Takashi Maekawa
Kenjiro T. Miura
Jun Mitani
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

Research Director
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

Research Director
Collaborators
Gen Kurosawa
Hiroya Nakao
Kenichi Bannai
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

Research Director
Collaborators
Toshiaki Omori
Nobuki Takayama
Hiroaki Yoshimura
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.

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