In this area, by means of mathematical modelling, we strive to gain an understanding of analytic and algebraic structures behind the phenomena occurring in nature, social, or engineering problems. Based on these fundamentals, we are conducting and providing research and education in developing, validating and relating such models to reality.
■ Professor: Takayuki Kobayashi ■ Associate Professor: Hajime Koba ■ Assistant Professor: Masato Hashidume (concurrent)
Differential Equation Group's WebsiteWe research and provide education in the field related to mathematical structure of nonlinear partial differential equations, which often appear in the studies of fluid mechanics or nonlinear fiber optics. In connection with this, we are developing an analytical method using the topological computation based on functional analysis, stochastic differential equation, and infinite-dimensional mechanical systems.
■ Professor: Michinori Ishiwata ■ Assistant Professor: Masato Hashidume (concurrent)
Applied Analysis Group's WebsiteBy means of mathematical analysis composed of numerical methods, nonlinear partial differential equation, nonlinear functional analysis, we elucidate the mathematical structure of problems in fields of natural science, engineering, medical science, and provide education and research on topics concerning many-body problem, biological functions, condensations, algorithms for numerical methods, and so on.
In this area, we offer education and research related to the development of analytical methods and applications of data-based modelling, concerning the analysis of phenomena that have a complex correlation and a strongly nonlinear structure along with errors and fluctuations, such as biological phenomena or social phenomena.
■ Professor: Joe Suzuki ■ Associate Professor: Yoshikazu Terada ■ Assistant Professor: Youzou Tonaki
Statistical Analysis Group's WebsiteWe consider the study and application of fields of computational statistics including machine learning, information theory, and Bayesian statistics. Usually, we propose a learning algorithm, implement it by a software, apply it to a real data set, and then evaluate its accuracy and computation time, though, whenever possible, we also try to make an understanding of its meaning by knowledge of information geometry, or to think of whether we got a reasonable estimate result compared to the number of samples (i.e., model selection). As an example of applications of the field, one of our accomplishments includes a learning algorithm based on undirected forest or Bayesian network that is used to analyze the probabilistic relationship among multiple variables, such as that of genomic analysis or stock price analysis. Apart from that, we are also interested in the topic related to statistical inference of quantum system.
■ Professor: Tomoyuki Sugimoto ■ Lecturer: Futoshi Futami
Data Science Research Group's WebsiteThe situation surrounding data science has become more active with the recent development of information and AI technologies. In order to contribute to biostatistics such as survival time analysis, automation of intellectual activities and new value creation through data analysis and utilization, and statistical summarization to make AI results interpretable, our research group is developing new statistical method or machine learning method to obtain new knowledge from multivariate data set and also studying mathematical statistics or learning theory of developed methods, using mathematical science and computational power as fundamental tools.