Advanced Mathematical Sciences Course
29

Mathematical Modeling andAnalysis of Phenomena― In Pursuit of Introduction of Science and Engineering ―The essence of science is to derive principles from observations, thereby
revealing the simple structures that underlie what appear to be complex
phenomena.
Mathematical sciences, in particular, use mathematical approaches toinvestigate "mathematical models", which are derived throughexperimentation.
The modern frontier of mathematical sciences considers various newmathematical models, including those for biological and social phenomena,in addition to more traditional models in natural sciences. These models areinvestigated through analytical approaches as well as numerical simulations
in order to understand the phenomena.
The knowledge thus obtained is employed to develop innovative technologies
or to predict future developments, and new methodologies are devised fordeeper understanding of phenomena.
In its research and educational activities, our course pays particularattention to large-scale and/or highly non-linear complex phenomena.
Particularly in education, we aim at providing students with both scientificperspectives, which help them to understand principles, and engineering
perspectives which are useful in solving real problems in manufacturing.
This two-pronged approach gives students comprehensive overviews on
both science and engineering in mathematical sciences.

Advanced Mathematical Sciences Course

An Invitation to Mathematical Sciences

Advanced Mathematical Sciences Course

In Graduate School of Informatics, we regard "mathematical modeling and analysis
of natural, social and biological phenomena" as an important foundation of what we
aim at; i.e., "informatics" in the broad sense of the term, which includes not only
traditional computer science but also related disciplines such as mathematicalsciences, applied physics, etc.
Indeed, we have placed importance on research and education in mathematicalsciences since the establishment of our school in 1998 because they are considered toform the academic basis of our disciplines. At the time of inauguration of the school,
we considered it appropriate to name ourselves the "Department of Applied Analysis
and Complex Dynamical Systems", since "complex dynamical systems" was the phrasethat symbolized the advanced mathematical sciences of the time. However, therelentless advancement of mathematical sciences gradually made "complex dynamicalsystems" not necessarily the best phrase to express what we are. Meanwhile,development of computers and networks has made it possible to deal more easily
with so-called “big data,” thus making computers and networks increasingly
important in social life as well as in research and education in mathematical modelingand analysis of natural, social and biological phenomena. With these developments in
mind, we have decided to change the name of our department to "Department ofAdvanced Mathematical Sciences," as of April 2017. We believe that the new namereaffirms and clarifies our directions for both education and research.
In the broad research area of "advanced mathematical sciences," we are particularlyinterested in "mathematical modeling and computer simulations of phenomena,"
which constitute the basis of our activities. Computer simulations and data analyses
are now vitally important in several branches of science and engineering. New
applications of computational methods are found in biology, social sciences, etc. and,of course, as more conventional applications in mechanics. These new trends inmathematical modeling of phenomena call for new methodologies, including
probabilistic and fractal approaches in addition to classical differential equations anddiscrete models. New developments in computer simulation include large-scale,
high-performance computing, use of new computational environments such as
multiple-precision arithmetics, etc. Our course conducts research and education insuch new and advanced areas of mathematical sciences.
Traditionally in Japan, fundamental education in mathematical sciences has been
carried out in schools of science and more application-oriented education has been
provided by engineering schools. However, despite its small size, our course has somefaculty members with science backgrounds and others with engineering backgrounds.
Our aim is to "integrate science and engineering" and develop students withcomprehensive perspectives of advanced
mathematical sciences. We also emphasize
individualized teaching as well as independent
learning by each student, in line with Kyoto
University’s principle of "self-learning based on
dialogue."

Toshio Aoyagi

Professor, Advanced Mathematical Sciences Course

Toshio Aoyagi, Sc.D., earned his doctoral degree from Kyoto University Graduate
School of Science in 1993. Since graduating, he has held such positions as Research
Associate, Department of Applied Mathematics and Physics, Kyoto University Faculty ofEngineering and Lecturer and then Associate Professor, Department of Applied
Analysis and Complex Dynamical Systems, Kyoto University Graduate School ofInformatics, before assuming his present position in 2014. His research specialties are
non-linear physics and theoretical neuroscience, with a focus on the analysis ofrhythmic phenomena and research into coupled dynamical systems on networks. He isa member of the Physical Society of Japan, Japan Neuroscience Society, JapaneseSociety for Mathematical Biology, and Japanese Neural Network Society. 2023
Chairperson of Course.

Graduate School of Informatics30

Advanced Mathematical Sciences Course

Outline■Laboratory and Teaching Staff
Laboratory

Teaching Staff

Yuusuke Iso/Professor Jun Kigami/Professor Hiroshi Fujiwara/Associate Professor
Daisuke Shiraishi/Associate Professor Masayoshi Kubo/Senior Lecturer
Li Douglas/Program-Specific Senior Lecturer Daisuke Kawagoe/Assistant Professor

Applied Analysis
Nonlinear Physics(Nonlinear Dynamics andComputational Statistical Physics)

Nonlinear Physics

Syuji Miyazaki/Senior Lecturer Kenji Harada/Assistant Professor(Non-equilibrium Physics andTheoretical Neuroscience)

Toshio Aoyagi/Professor Jun-nosuke Teramae/Associate Professor
Hiroki Tutu/Assistant Professor

Computational Mechanics

Hitoshi Yoshikawa/Associate Professor Kazuki Niino/Assistant Professor

Industrial Mathematics

Satoshi Taguchi/Professor Tetsuro Tsuji/Associate Professor

Statistical Signal
Processing

Kazunori Hayashi/Professor (Secondary appointment : Institute of Liberal Arts and Sciences)■Curriculum of 㻯㼡㼞㼞㼕㼏㼡㼘㼡㼙㻌㼛㼒㻌㻭㼐㼢㼍㼚㼏㼑㼐㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟㻌㻯㼛㼡㼞㼟㼑
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㻿㼡㼎㼖㼑㼏㼠㼟㻌㼜㼞㼛㼢㼕㼐㼑㼐㻌㼎㼥㻌㼠㼔㼑㻌㻯㼛㼡㼞㼟㼑㻌㻔㻻㼜㼠㼕㼛㼚㼍㼘㻌㻤㻌㼏㼞㼑㼐㼕㼠㼟㻌㼛㼞㻌㼙㼛㼞㼑㻕㻿㼑㼙㼕㼚㼍㼞㻌㻿㼡㼎㼖㼑㼏㼠㼟㻌㻭㼐㼢㼍㼚㼏㼑㼐㻌㻿㼡㼎㼖㼑㼏㼠㼟䠄㻭㻌㼍㼚㼐㻌㻮㻌㼍㼞㼑㻌㼛㼒㼒㼑㼞㼑㼐㻌㼑㼢㼑㼞㼥㻌㼛㼠㼔㼑㼞㻌㼥㼑㼍㼞䠅㻌㻿㼑㼙㼕㼚㼍㼞㻌㼛㼚㻌㻭㼜㼜㼘㼕㼑㼐㻌㻭㼚㼍㼘㼥㼟㼕㼟ϩ㻿㼑㼙㼕㼚㼍㼞㻌㼕㼚㻌㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻼㼔㼥㼟㼕㼏㼟ϩ㻿㼑㼙㼕㼚㼍㼞㻌㼕㼚㻌㻭㼜㼜㼘㼕㼑㼐㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟ϩ䠄㼀㼔㼛㼟㼑㻌㼜㼘㼍㼚㼚㼕㼚㼓㻌㼠㼛㻌㼜㼞㼛㼏㼑㼑㼐㻌㼠㼛㻌㼐㼛㼏㼠㼛㼞㼍㼘㻌㼜㼞㼛㼓㼞㼍㼙㻦㻭㼟㼟㼕㼓㼚㼑㼐㻌㼠㼛㻌㻹㻞㻘㻌㻠㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔䠅㼀㼛㼜㼕㼏㼟㻌 㼕㼚㻌 㻰㼕㼒㼒㼑㼞㼑㼚㼠㼕㼍㼘㻌 㻱㼝㼡㼍㼠㼕㼛㼚㼟㻌 㻭㻘㻮㻌 㻔㻞㻌 㼏㼞㼑㼐㼕㼠㼟㻌 㼑㼍㼏㼔㻕㻘㻌 㼀㼛㼜㼕㼏㼟㻌㼕㼚㻌㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻭㼚㼍㼘㼥㼟㼕㼟㻌㻭㻘㻮㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻌㻘㼀㼛㼜㼕㼏㼟㻌 㼕㼚㻌 㻭㼜㼜㼘㼕㼑㼐㻌 㻭㼚㼍㼘㼥㼟㼕㼟䊠㻘䊡㻔㻝㻌 㼏㼞㼑㼐㼕㼠㻌 㼑㼍㼏㼔㻕㻘㻌㻌㼀㼛㼜㼕㼏㼟㻌㼕㼚㻌㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻰㼥㼚㼍㼙㼕㼏㼟㻌㻭㻘㻮㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻌㻘㼀㼛㼜㼕㼏㼟㻌 㼕㼚㻌 㻺㼛㼚㼑㼝㼡㼕㼘㼕㼎㼞㼕㼡㼙㻌 㻼㼔㼥㼟㼕㼏㼟㻌㻭㻘㻮㻌 㻔㻞㻌 㼏㼞㼑㼐㼕㼠㼟㻌 㼑㼍㼏㼔㻕㻌 㼀㼛㼜㼕㼏㼟㻌㼕㼚㻌㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻼㼔㼥㼟㼕㼏㼟䊠㻘䊡㻔㻝㻌㼏㼞㼑㼐㼕㼠㻌㼑㼍㼏㼔㻕㻘㻌㼀㼛㼜㼕㼏㼟㻌 㼕㼚㻌㻯㼛㼙㼜㼡㼠㼍㼠㼕㼛㼚㼍㼘㻌 㻹㼑㼏㼔㼍㼚㼕㼏㼟㻌 㻭㻘㻮㻌 㻔㻞㻌 㼏㼞㼑㼐㼕㼠㼟㻌 㼑㼍㼏㼔㻕㻌 㼀㼛㼜㼕㼏㼟㻌㼕㼚㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟㻌㻭㻘㻮㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻘㻌㼀㼛㼜㼕㼏㼟㻌㼕㼚㻌㻭㼜㼜㼘㼕㼑㼐㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟䊠㻘䊡㻔㻝㻌㼏㼞㼑㼐㼕㼠㻌㼑㼍㼏㼔㻕㻮㼍㼟㼕㼏㻌㻿㼡㼎㼖㼑㼏㼠㼟(㻭㻌㼍㼚㼐㻌㻮㻌㼍㼞㼑㻌㼛㼒㼒㼑㼞㼑㼐㻌㼑㼢㼑㼞㼥㻌㼛㼠㼔㼑㼞㻌㼥㼑㼍㼞㻕st1㻭㼜㼜㼘㼕㼑㼐㻌 㻭㼚㼍㼘㼥㼟㼕㼟㻌 㻭㻘㻮㻌 㻔㻞㻌 㼏㼞㼑㼐㼕㼠㼟㻌 㼑㼍㼏㼔㻕㻘㻌 㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻼㼔㼥㼟㼕㼏㼟㻌㻭㻘㻮㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻌㻘㻌㻭㼜㼜㼘㼕㼑㼐㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟㻌㻭㻘㻮㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻳㼑㼚㼑㼞㼍㼘㻌 㻿㼡㼎㼖㼑㼏㼠㼟㻌 㼜㼞㼛㼢㼕㼐㼑㼐㻌 㼎㼥㻌 㼠㼔㼑㻌 㻿㼏㼔㼛㼛㼘䠄㻯㼛㼙㼜㼡㼘㼟㼛㼞㼥㻌 㼑㼘㼑㼏㼠㼕㼢㼑㻌㻌㻌㻌㻌㻌㻌㻞㻌㼛㼞㻌㼙㼛㼞㼑㻌㼏㼞㼑㼐㼕㼠㼟㻌㼍㼚㼐㻌㻠㻌㼏㼞㼑㼐㼕㼠㼟㻌㼛㼞㻌㼘㼑㼟㼟㻌㼒㼛㼞㻌䖂㻌㼟㼡㼎㼖㼑㼏㼠㼟䠅㻌㻵㼚㼠㼑㼞㼐㼕㼟㼏㼕㼜㼘㼕㼚㼍㼞㼥㻌㻿㼡㼎㼖㼑㼏㼠㼟㻌㼛㼒㻌㼠㼔㼑㻌㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻝㻌䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻞㻌䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻟㻌䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻠㻌䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻡㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻕㻼㼞㼕㼛㼞㻌㼠㼛
㼍㼐㼙㼕㼟㼟㼕㼛㼚31㻯㼍㼘㼏㼡㼘㼡㼟

㻸㼕㼚㼑㼍㼞㻌㻭㼘㼓㼑㼎㼞㼍㻲㼡㼚㼐㼍㼙㼑㼚㼠㼍㼘㼟㻌㼛㼒㻌㻻㼞㼐㼕㼚㼍㼞㼥㻌㻰㼕㼒㼒㼑㼞㼑㼚㼠㼕㼍㼘㻌㻱㼝㼡㼍㼠㼕㼛㼚㼟㻿㼑㼙㼕㼚㼍㼞㻌㼛㼚㻌㻭㼜㼜㼘㼕㼑㼐㻌㻭㼚㼍㼘㼥㼟㼕㼟Ϩ㻿㼑㼙㼕㼚㼍㼞㻌㼕㼚㻌㻺㼛㼚㼘㼕㼚㼑㼍㼞㻌㻼㼔㼥㼟㼕㼏㼟Ϩ㻿㼑㼙㼕㼚㼍㼞㻌㼕㼚㻌㻭㼜㼜㼘㼕㼑㼐㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟Ϩ㻭㼟㼟㼕㼓㼚㼑㼐㻌㼠㼛㻌㻹㻝㻘㻌㻠㻌㼏㼞㼑㼐㼕㼠㼟㻌㼑㼍㼏㼔㻿㼑㼙㼕㼚㼍㼞㼟㻌㼍㼚㼐㻌㼑㼤㼑㼞㼏㼕㼟㼑㼟㻌㼒㼛㼞㻌㻹㼍㼟㼠㼑㼞䇻㼟㻌㼠㼔㼑㼟㼕㼟㻌㻔㻹㼍㼚㼐㼍㼠㼛㼞㼥㻌㻤㻌㼏㼞㼑㼐㼕㼠㼟㻕㻭㼐㼢㼍㼚㼏㼑㼐㻌㻿㼠㼡㼐㼥㻌㼕㼚㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟㻌㻞㻌㻔㻭㼟㼟㼕㼓㼚㼑㼐㻌㼠㼛㻌㻹㻞㻘㻌㻢㻌㼏㼞㼑㼐㼕㼠㼟㻕㻭㼐㼢㼍㼚㼏㼑㼐㻌㻿㼠㼡㼐㼥㻌㼕㼚㻌㻹㼍㼠㼔㼑㼙㼍㼠㼕㼏㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㼟㻌㻝㻌㻔㻭㼟㼟㼕㼓㼚㼑㼐㻌㼠㼛㻌㻹㻝㻘㻌㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕䖂㻼㼑㼞㼟㼜㼑㼏㼠㼕㼢㼑㼟㻌㼕㼚㻌㻼㼘㼍㼠㼒㼛㼞㼙㻌㻿㼠㼡㼐㼕㼑㼟㻌㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻯㼛㼙㼜㼡㼠㼍㼠㼕㼛㼚㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㻘㻌㻵㼚㼠㼞㼛㼐㼡㼏㼠㼕㼛㼚㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻯㼛㼙㼜㼡㼠㼍㼠㼕㼛㼚㼍㼘㻌㻿㼏㼕㼑㼚㼏㼑㻘㻌㻱㼤㼑㼞㼏㼕㼟㼑㻌㻭㻌㻔㻝㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌㻌䖂㻵㼚㼒㼛㼞㼙㼍㼠㼕㼛㼚㻌㼍㼚㼐㻌㻵㼚㼠㼑㼘㼘㼑㼏㼠㼡㼍㼘㻌㻼㼞㼛㼜㼑㼞㼠㼥㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻵㼚㼚㼛㼢㼍㼠㼕㼛㼚㻌㼍㼚㼐㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼛㼚㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼛㼚㻭㼚㼍㼘㼥㼟㼕㼟㻌 㼍㼚㼐㻌 㻹㼍㼚㼍㼓㼑㼙㼑㼚㼠㻔㻞㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌 㻵㼚㼒㼛㼞㼙㼍㼠㼕㼛㼚㻭㼚㼍㼘㼥㼟㼕㼟㻌㼍㼚㼐㻌㻹㼍㼚㼍㼓㼑㼙㼑㼚㼠㻘㻌㻱㼤㼑㼞㼏㼕㼟㼑㻌㻔㻝㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻿㼛㼏㼕㼍㼘㻯㼛㼚㼠㼞㼕㼎㼡㼠㼕㼛㼚㼟㻌㼠㼔㼞㼛㼡㼓㼔㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻔㻝㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻌㻵㼚㼠㼑㼞㼚㼟㼔㼕㼜㻌㼕㼚㼠㼔㼑㻌㻲㼕㼑㼘㼐㻌㼛㼒㻌㻵㼚㼒㼛㼞㼙㼍㼠㼕㼏㼟㻌㻔㻝㻌㼏㼞㼑㼐㼕㼠㼟㻕㻘㻹㼑㼏㼔㼍㼚㼕㼏㼟㻌㼛㼒㻌㻼㼍㼞㼠㼕㼏㼘㼑㼟㻘㻌㻿㼥㼟㼠㼑㼙㼟㻌㼛㼒㻌㻼㼍㼞㼠㼕㼏㼘㼑㼟㻘㻌㼍㼚㼐㻌㻾㼕㼓㼕㼐㻌㻮㼛㼐㼕㼑㼟㻿㼜㼑㼏㼕㼒㼕㼏㻌㼟㼡㼎㼖㼑㼏㼠㼟㻌㼜㼞㼛㼢㼕㼐㼑㼐㻌㼎㼥㻌㼠㼔㼑㻌㼟㼏㼔㼛㼛㼘㻭㼏㼍㼐㼑㼙㼕㼏㻌㻲㼛㼡㼚㼐㼍㼠㼕㼛㼚㼟㻌㼍㼠㻌㼁㼚㼐㼑㼞㼓㼞㼍㼐㼡㼍㼠㼑㻌㻸㼑㼢㼑㼘㻌㼒㼛㼞㻌㻿㼠㼡㼐㼥㻌㼍㼠㻌㼠㼔㼑㻌㻯㼛㼡㼞㼟㼑㻺㼛㼠㼑㻦㻌㻿㼡㼎㼖㼑㼏㼠㼟㻌㼙㼍㼞㼗㼑㼐㻌㼣㼕㼠㼔㻌㼠㼔㼑㻌㼘㼑㼠㼠㼑㼞㻌䇾㻱䇿㻌㼣㼕㼘㼘㻌㼎㼑㻌㼜㼞㼛㼢㼕㼐㼑㼐㻌㼕㼚㻌㻱㼚㼓㼘㼕㼟㼔㻚㻲㼡㼚㼐㼍㼙㼑㼚㼠㼍㼘㼟㻌㼛㼒㻌㻯㼛㼙㼜㼘㼑㼤㻌㻭㼚㼍㼘㼥㼟㼕㼟

Advanced Mathematical Sciences Course
Admission, Curriculum and Other Efforts in Our Course
In study and research of advanced mathematical sciences, one
needs both basic mathematical skills as well as knowledge of
his/her specialist field. Accordingly, in the entrance exam, allapplicants for our Master's course are required to solve basic
problems in linear algebra and calculus together with one problemof their choice related to their respective specialties. Finaldecisions on acceptance are made through interviews with those
applicants who score above a certain level in the written exam,
since it is not desirable to make such decisions based only on the
results of the written exam where one point may be the difference
between a pass mark and failure. The interviews will be conductedby all the faculty members in order to determine if applicant’sinterests match the expertise of our faculties. In the entrance
exam for the Ph.D. course, final decisions on acceptance are madebased on the achievements of each candidate in his/her researchwork, which are evaluated in interviews conducted by all thefaculty members.
Our curriculum for the Master course consists of both generaland specialized subjects. All students are advised to take three
general subjects, which help them to develop both scientific andengineering perspectives in mathematical sciences. Researchadvice is given mainly on a one-to-one basis, taking into accounteach student’s aptitude. For those wishing to go on to Ph.D.
courses, we provide Seminar II (for second-year students), which
is designed to give students opportunities to learn advanced topics
in addition to receiving standard research mentoring. In the Ph.D.
course, students can receive mentoring not only from theiradvisers but also from other professors in our course andaffiliated professors from science and engineering schools. Thissystem gives students access to a broader spectrum ofstate-of-the-art knowledge in the mathematical sciences.
Students thus have opportunities to deepen their expertise and toobtain a broad appreciation of mathematical sciences from boths c i e n t i fi c a n d e n g i n e e r i n g
perspectives, which we believe
to be a unique feature of theeducation provided by ourcourse.
In addition, almost every
year, we offer open, public
seminars on topical subjects.

Applied Analysis Laboratory
Advanced Mathematical Sciences Course

Analysis in the 21st Century■Numerical Analysis of (Partial) Differential Equations, Numerical andMathematical Analyses
I am interested in both mathematical and numerical analyses in research
regarding the determination of unknown coefficients and other inverse
problems, as well as boundary value problems and other forward problems
with respect to partial differential equations that describe mechanical andphysical phenomena.
[Yuusuke Iso]
■Fractal Analysis, Fractal Geometry
I am interested in the mathematical theory of problems concerning heat
and wave propagation in fractal concept models ‒new models for the natural
world.
[Jun Kigami]■Numerical Analysis of Ill-posed Problems, Design and Implementation ofMulti-precision Arithmetic Environments
I am interested in research concerning regularization methods andnumerical analysis of multiple-precision calculations with the aim of solving
inverse problems that occur in mechanics and geophysics. [ Hiroshi Fujiwara]

Numerical Simulation of Light Propagation in a
Human Brain■Structure of Brownian Motion and Random Walk
How does the trace of Brownian motion look like? What can we say about
the structure of random walk trace? Such questions have fascinatedprobabilists and mathematical physicists for a long time, and they continue tobe an unending source of challenging problems. I am interested in the natureof sample paths of these fundamental processes.
[Daisuke Shiraishi]■Inverse Problem Analysis, Numerical Analysis of (Partial) Differential
Equations, Partial Differential Equations, Brain Model Mathematical
Research
I mathematically analyze partial differential equations that appear inmathematical physics and mathematically and numerically analyze theinverse problems found in these partial differential equations, where theunknown coefficients of these inverse problems are determined by observed
data.
[Masayoshi Kubo]

Uniform spanning tree (solid line) and dual path(dotted line)■Numerical Analysis of Differential Equations and Data-Driven Science
I am interested in numerical simulations of differential equations and data driven modelling in natural science, technology andsocial sciences.
[Li Douglas]■Integro-Differential Equations, Spectral Analysis
I study regularity of solutions to integro-differential equations appearing in kinetic theory and optics.
analysis on boundary integral operators which are related to the theory of elasticity.

Also, I work in spectral[Daisuke Kawagoe]

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Advanced Mathematical Sciences Course

OutlineNonlinear Physics Laboratory■Group of Non-equilibrium Physics andTheoretical Neuroscience■From nonlinear physics to theory of networks,
as well as living and neural systems

I am particularly interested in systems composed ofmany simple elements that, through cooperativeinteractions, come to exhibit complex behavior andhigh-level functions, such as not only many physicalsystems, but also biological and social systems.
Co-evolution involving the intricate interplay between the
dynamics of the network and the elements is a key concept
for understanding the self-organized, flexible nature of
real-world network systems. I study such cooperative
phenomena in systems of this kind, focusing on rhythmic
phenomena and chaos from the perspective of nonlinear[Toshio Aoyagi]
dynamics.

Neural systems and social networks are nonlinear dynamic systems
that have a high degree of freedom and develop as their dynamic
elements change the structure of their interconnections.

■Nonlinear physics of computation and learningin the brain

The brain is a highly complex network composed ofabout 100 billion of neurons. Spike propagation along the
network and plasticity of synaptic connection of themcause high-dimensional nonlinear dynamics, which is thenature of neural computation and learning. Central
questions, however, still remain elusive.
What is intelligence? What is underlying principles ofneural computation and learning? Our recent study, fore x a m p l e , r e v e a l s s i g n i fi c a n t r o l e s o f s p o n t a n e o u s
fl u c t u a t i o n i n n e u r a l c o m p u t a t i o n . B y i n t e g r a t i n gneuroscience, computer science, and nonlinear physics,
here we are trying to answer these questions and trying todevelop fully brain-inspire AIs.
[Jun-nosuke Teramae]

Conceptual diagram of neurons (pink) in the brain interacting throughsynapses (green circles) that transmit impulse currents in a process
called “spike firing.” The process can be mathematically analyzed bymodeling the states of neurons and synapses as random variables.

■Mathematical models for molecular machines

Biological molecular motors are amazing machinesthat generate useful movement (as a pump or a porter).
The relationship between the structures of proteins andtheir highly efficient energy conversion, even under afluctuating environment, remains mysterious. I explore
the underlying principles of such molecular machineswith mathematical models.
[Hiroki Tutu]

Rotary ratchet model consisting of arotor (rigid body consisting of four
points) and a rotor housing (potential)that simulates a Wankel rotaryengine■Group of Nonlinear Dynamics and Computational Statistical Physics■Study on powders and charged particles under cyclic
external forces

Inspired by experiments in which several micron-size charged
corpuscles are injected into an AC trap, a simplified version of a
Paul ion trap, and prior studies into the particle model of ionchannels and its anomalous transport, we mainly study collective
motions of granular materials and charged corpuscles, which are
subject to periodic external force. We also propose mathematicalmodels for numerical analysis that faithfully reproduce
experiment settings and analyze critical phenomena incidental tocollective motions of macroscopic charged corpuscles injected
into an AC trap and various types of bifurcations that occur invibrating powder.
[Syuji Miyazaki]■Statistical physics using computational approaches

Using the computational approach, we advance statisticalphysical research for the emerging properties in complex
systems consisting of many elements with nonlinear interactions.
My research areas range from the atomic scale to the real world,e.g.,quantum critical phenomena and infectious diseases. Basedon tensor network formalism, I am also working on informational
processing technology, such as classical and quantum machinelearning.
[Kenji Harada]

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It is known that when two different
powders, one of large and one ofsmall grain size, are horizontally
vibrated, the two powders
separate, causing a stripe pattern
to form.
We discovered that when powders,
one of large and one of small
grain size, each one with a size
distribution centered around its
average grain size, are vibrated
horizontally, the two powders
separate, causing a mesh pattern
to form.

Tensor network

Researchers actively study new compression methods forlarge data sets and deep learning models with exponentiallygrowing parameters using tensor network representation.

Advanced Mathematical Sciences Course

Computational Mechanics Laboratory
Computer simulations:development of fast BIEMs and their applications to engineering problems
Numerical simulations provide powerful tools forsolving various problems in science and engineering.
Computational mechanics, together with theoreticaland experimental mechanics, is an effective method ofinvestigating mechanical phenomena in engineering
based on numerical simulations. Our group specializes
in Boundary Integral Equation Methods (BIEM) which
are among major techniques in computational
mechanics. BIEMs are particularly effective in wave andfracture problems. We focus on fast BIEMs and theirapplications to large-scale problems with special
interest in electromagnetic wave propagations inperiodic structures, which have many applications in
optics. Other topics of interest include shape
optimization problems, eigenvalue problems andinverse problems.
[Hitoshi Yoshikawa , Kazuki Niino]

A nanoporous gold mesh (left) and example of numerical computation of its transverse
photo-induced voltage (right)

Advanced Mathematical Sciences Course

Industrial Mathematics Laboratory
Toward new fluid mechanics for
non-equilibrium flows
In our group we investigate the behavior of non-equilibrium flows based on
kinetic theory describing the collective behavior of innumerable particles.
We aim at understanding mechanical and/or thermodynamic properties ofnon-equilibrium flows both theoretically and numerically. We also aim at
elaborating continuum theory and applying it to non-equilibrium flows, by deriving
suitable mathematical models for non-equilibrium flows.
[Satoshi Taguchi]
Recent advances in micro/nanoscale technologies require theunderstanding of transport phenomena in micro/nanoscale and theircontrol. For this reason there is a growing interest in the research ofnon-equilibrium flows. In particular, we aim at investigating moving
boundary problems for non-equilibrium flows and the motion of tinymaterials (or particles) driven by non-equilibrium effects from the view
point of mathematical sciences and from experimental view points. We
also aim at integrating them in industrial applications.
[Tetsuro Tsuji]

Unidirectional flow around a heated U-shaped body (top left)
Flow caused by a discontinuous wall temperature in a vessel (top right)
Flow caused by a rotating sphere impulsively set into motion (bottom left)
The Magnus effect of a spinning microparticle (bottom right)

Statistical Signal Processing Laboratory
Integration of Model-based and Data-driven Approaches
In the discipline of statistical signal processing, we try to systematize
methodologies for extracting useful information from raw observation data.
This has a wide range of applications in telecommunications, as well as
measurement, image processing, and biological signal processing. Statisticalsignal processing is a valuable tool for tackling various kinds of problems
relating to data science, including data sensing, collection, transmission,
analysis, and utilization. We have recently been studying methods for solving
underdetermined linear inverse problems that make use of the sparsity anddiscreteness of signals.
[Kazunori Hayashi]
Example of optical communication receiver configuration using “deep unfolding”
Combining traditional telecommunications knowledge with a data-driven approach makes it
possible to determine all parameters in an optical communication receiver system at once
based on the loss function at output.

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