Fiber Topology Meets Applications 2
| Reference No. | 20210013 |
|---|---|
| Type/Category | Grant for General Research-Workshop（Ⅱ） |
| Title of Research Project | Fiber Topology Meets Applications 2 |
| Principal Investigator | Daisuke Sakurai（Kyushu University Pan-Omics Data-Driven Innovation Research Center in Research Institute for Information Technology・Associate Professor） |
| Research Period |
December 1,2021. ～
December 3,2021. |
| Keyword(s) of Research Fields | Fiber Topology, Singularity Theory, Topological Analysis, Morse Theory, Visualization, Multiobjective Optimization |
| Abstract for Research Report |
PURPOSE In differential topology, the study of the topology of fibers, known as fiber topology, extends the Morse theory, of functions, to that of maps (Saeki, 2004). This establishes a thorough exploration of topological transitions of inverse images. The topological analysis of the level set, from which fiber topology-based data analysis originates, has been proven powerful for understanding today’s data whose size and complexity are overwhelming (Takahashi, 2004; Hamada & Chiba, 2017). We have worked on establishing data analysis utilizing fiber topology with regard to theory and computation, and now are on the stage to co-design applications and further developments for them. Continuing the effort in the previous meeting, we propose to gather researchers from academia and the industry to discuss the future directions. The participants included mathematics, computation, and applications. For this, participants bring themes from broad spectra of practitioners including those from mathematics, topological analysis in visualization, the game industry and environmental sciences. The research project by the environmental scientists, Hiroshi Yamashita and Bastian Kern (German Aerospace Center, Germany), focuses on proposing a new tax incentive for balancing the environmental costs against the operational cost in the aviation industry. Fiber topology is employed for understanding the high-dimensional space spanned by different kinds of subcosts. The application for the game industry, conducted mainly by Naoki Hamada (KLab), Takahiro Yamamoto (Tokyo Gakugei University) and Daisuke Sakurai (Kyushu University Pan-Omics Data-Driven Research Innovation Center), aims at designing and automating game music developments. A key problem is to formalize activities of industrial artists, for which fiber topology can contribute by designing and understanding benchmarks of multiobjective optimization. All these applications pose a challenge to state-of-the-art algorithms. The current, rather loose, mathematics found in the computer science literature meets a more rigorous treatment by mathematicians. OUTCOME In this second meeting that gathers the key players, we check interdisciplinary milestones of progress, which was agreed on in the first meeting. This builds a network of researchers who talk to different fields from the point of view of theories, computation, and problems in the society. The participants include senior researchers experienced in their fields and junior researchers who are building new research areas. |
| Organizing Committee Members (Workshop) Participants (Short-term Joint Usage) |
Daisuke Sakurai（Kyushu University Pan-Omics Data-Driven Innovation Research Center in Research Institute for Information Technology・Associate Professor） Osamu Saeki（Institute of Mathematics for Industry Kyushu University・Professor） Shigeo Takahashi（University of Aizu・Professor） Hamish Carr（University of Leeds (UK)・Professor） Takahiro Yamamoto（Tokyo Gakugei University・Associate Professor） Naoki Hamada（KLab・博士研究員） |