共同利用

Fiber Topology Meets Applications


種別 一般研究-研究集会(II)
研究計画題目 Fiber Topology Meets Applications
研究代表者 櫻井大督(九州大学 汎オミクス計測・計算科学センター・准教授)
研究分野のキーワード 特異点論,ファイバーのトポロジー,可視化,地球温暖化問題,半導体,オペレーションズリサーチ
目的と期待される成果 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. It has been proven powerful for understanding today’s data whose size and complexity are overwhelming (Takahashi, 2004; Hamada & Chiba, 2017).

In the proposed meeting, we gather researchers from academia and the industry. The meeting aides the interaction among mathematics, computation, and applications. For this, participants gather from a broad spectra of research disciplines, including not only mathematics and computer science, but also operational research, environmental sciences and semiconductors.

The operational research, conducted by Naoki Hamada (Fujitsu Research Institute), Daisuke Sakurai (Kyushu University Pan-Omics Data-Driven Research Innovation Center) et al., is a project with assembly scheduling workers in Fujitsu. Together, we have been designing software products that offer optimal schedules based on characterization implied by fiber topology.

Environmental scientists from Hiroshi Yamashita and Bastian Kern (German Aerospace Center, Germany) have some history of joint-research with Sakurai while he was in Germany at Zuse Institute Berlin (Germany). Their current research project by these environmental scientists focus 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.

Finally, the application in semiconductor research employs fiber topology for understanding the potential fields of atomic configurations. For simulation outputs done with Japan’s next-generation supercomputer Fugaku, we extract the landscape of the high-dimensional potential fields. Fiber topology gives a concise and parameter-free representation of the landscape, which is also robust against numerical errors.

All of the applications pose a challenge to the current state-of-the-art analysis of fiber topology. Especially, the high spatial dimensionality in the data is something that requires an update to the numerical methods. The current, rather loose, mathematics found in the computer science literature meets a more rigorous treatment by Takahiro Yamamoto (Tokyo Gakugei University).

OUTCOME

In this first meeting that gathers all of our collaboration teams, we set interdisciplinary milestones of progress in the coming years. Sakurai has so far held discussions with each member face-to-face, and this meeting establishes a coherent grand strategy among the international team. 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.

Theorists not only provide solutions, but get feedback about desirable expansions. We discuss how fiber topology should let us extract information about the energy potential of atomic configurations, robustness of the assembly schedule against errors, and the impact of the inter-governmental decisions towards the aviation industry and air pollution.
While our progress in computation has seen a success, there are theoretical questions left, such as how the mathematical results translate to and from numerical representations.
What directions in mathematical theories benefit numerical ones, and vice versa, is another question.

The collaboration is also a part of the interdisciplinary data-driven activities taking place at Kyushu University. Sakurai and Osamu Saeki are with Pan-Omics Data-Driven Research Innovation Center, which co-managed by the Institute of Mathematics for Industry together with other four research centers in the university. Further gatherings will take place in the coming years in order to evaluate and surpass the milestones set this time.
組織委員(研究集会)
参加者(短期共同利用)
山本卓宏(東京学芸大学・准教授)
Hamish Carr(英国 Univeristy of Leeds・Senior Lecturer (准教授相当))
佐伯 修(IMI・教授,部局長)
櫻井 大督(汎オミクス計測・計算科学センター・准教授)
濱田 直希((株)富士通研究所・研究員)
高橋 成雄(会津大学・教授)