- JST Home
- /
- Strategic Basic Research Programs
- /
- PRESTO
- /
- project/
- Elucidating mathematical structures in real/virtual world objects and their utilization/
- [Math-Structure] Year Started : 2020

Associate professor

Institute for Advanced Study

Kyoto University

With the recent rapid development of biotechnology, a variety of genetic information has been converted into data, and key principles of life are being elucidated by the analysis of such data. In this study, we will develop a novel analysis system that extracts multi-resolution cell differentiation structures of cell populations and single cells from gene expression data to uncover the design principles of life. This system utilizes mathematical theories such as high-dimensional statistics, statistical causal discovery, topology, and dynamical systems from multiple perspectives.

Senior Research Scientist

Department of Information Technology and Human Factors

National Institute of Advanced Industrial Science and Technology

Formal methods have been studied to provide mathematically rigorous techniques to verify the correctness of programs, and have been applied to the verification of various software. This project studies formal methods for verifying statistical software in a mathematically rigorous way. In particular, the project aims to develop techniques for the automated verification of statistical programs in order to improve the reliability of statistical software.

Associate Professor

Graduate School of Information Science and Technology

The University of Tokyo

In mathematics, physics, informatics, etc., we are required to solve problems of finding “optimal” configurations of a finite number of points in regions in Euclidean spaces. For such problems, various optimization methods are considered in many cases. However, any general theory and algorithms for them have not been established. In this study, we provide mathematical foundation for these methods and find a viewpoint called “approximate convexity” unifying them to establish general theory and algorithms for problems of optimal point configurations.

Associate Professor

National Institute of Informatics

Research Organization of Information and Systems

Meta-complexity refers to the complexity of problems asking for computational complexity (= resources needed to solve a problem). Examples of meta-complexity theoretic problems include the Minimum Circuit Size Problem and the problem of computing the time-bounded Kolmogorov complexity. Recently, meta-complexity has been widely studied and recognized as an important topic in complexity theory. In this research, we view computational complexity theory through the lens of meta-complexity theory, and aim to make progress on challenging open questions of complexity theory.

Associate professor

Graduate School of Science and Technology

Nara Institute of Science and Technology

This project aims to develop sparse modeling and visualization techniques for a geometric transformation field, which extends a vector field to have a geometric transformation at each point. Algebra on geometric transformations stands on multiplication, not addition. Therefore, the conventional techniques defined by addition are unsuitable for analyzing geometric transformation fields. Meanwhile, the sparse modeling techniques defined by multiplication can guarantee that the analysis result interprets as a geometric transformation.

Assistant Professor

Medical Institute of Bioregulation

Kyushu University

In this project, I propose a data analysis framework by utilizing combinatorial Hodge decomposition as the key concept to obtain the qualitative understanding behind large scale data. I aim to obtain a qualitative interpretation of data through the structure of flows, a human-friendly concept using omics data measured biological systems at a molecule, cell, and tissue level.

Associate Professor

Faculty of Engineering

Kindai University

Near infrared imaging is an imaging modality without radiation exposure but with a compact device. In addition to medicine, the technology can potentially be utilized in different fields of science and engineering. However, its inverse problem to obtain tomographic images is nonlinear and moreover severely ill posed. My research focuses on this inverse problem. I will obtain high quality tomographic images by using the radiative transport equation without relying on the diffusion approximation and achieve a fast computation by making use of inverse series. Furthermore, I will establish a new data driven approach for the time series of successive measurements by exploring the inverse problem with the help of information science.

Research scientist

Center for Advanced Intelligence Project (AIP)

RIKEN

This project aims to reveal the unknown mechanisms underlying higher-order dynamic functions occasionally expressed in many types of large-scale networks. To that end, I develop a nonlinear representation learning framework applicable to large-scale network-structural time series, based on novel theoretical backgrounds, which extracts the hidden representation of the nonlinear network dynamics and the hidden factors organizing it in data-driven manner.

Professor

Graduate School of Economics

Hitotsubashi University

The aim of this project is to develop new computational methods for high dimensional partial differential equations (PDEs) using higher order weak approximation of stochastic differential equations with Malliavin calculus and deep learning. Efficient numerical schemes will be provided for various linear and nonlinear PDEs and large scale simulation models.