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2014基礎工学部要覧_英文

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28Division ofMathematical ScienceArea ofMathematical ModellingThe Area of Mathematical Modelling comprised of the following two research groups is concerned with research and education of mathematical theory and applications on modelling phenomena occured in sev-eral elds of natural science, social science and engi-neering.Dietential Equation Group■Assoc.Prof.：Mitsuru SHIBAYAMA■Assis.Prof.：Yohei FUJISHIMAHere we study nonlinear partial dierential equations appearing in the various elds of Mathematical Sci-ences. For example, we are focusing on the follow-ing topics:1: LASER beam propagation in a nonlinear medium.2: Bifurcation analysis to innite dimensional dynami-cal systems and its application to pattern formation problem.3: Development of computational topology methods applied to dynamical system theories.Applied Analysis Group■Prof.：Takashi SUZUKI■Assis.Prof.：Ryo TAKAHASHIThis group is engaged in the following study and education.1. Mathematical formulation of problems in natural science, engineering, economics, and medical science based on physical principle and phenom-ena.2. Numerical simulation, numerical scheme, and mathematical analysis based on the theory of par-tial dierential equations and nonlinear functional analysis.3. Investigation of mathematical structure for self-interacting particles and biological functions such as the kinetic equation, system of chemotaxis, and tumour growth model.Area of Statistical ScienceThe Area of Statistical Science comprised of the following two research groups is concerned with research and education on analyzing and modelling statistical data with errors, correlations and complex nonlinear structures.Statistical Analysis Group■Prof.：Hidetoshi SHIMODAIRA■Assoc.Prof.：Fuyuhiko TANAKA■Assis.Prof.：Kei HIROSEStatistical｠science,｠machine｠learning,｠and｠Bioinfor-matics｠are｠studied in｠this｠group.｠Statistical｠analy-sis｠of｠complex｠networks｠is｠also｠an important｠topic.｠You｠can｠easily｠nd｠groups｠of｠good｠friends｠in｠social networks｠with｠one｠hundred｠people,｠but｠it｠is｠yet｠a｠big｠challenge｠to understand｠the｠structure｠of｠very｠big｠networks.｠We｠also｠work｠on statistical｠analysis｠of｠DNA｠sequences｠and｠gene｠expressions.｠For estimating｠the｠evolutionary｠tree｠of｠life｠from｠DNA｠sequences,｠in particular,｠a｠statistical｠method｠developed｠by｠our｠group｠has｠been｠used in｠labs｠worldwide.Data Science Research Group■Prof.：Yutaka KANO■Assoc.Prof.：Etsuo KUMAGAI■Assis.Prof.：Kengo KAMATANIAn important purpose of multivariate analysis is to identify any relations among many variables based on statistical data. The recent topics in this eld are new modeling and statistical causal inference. In this research group, we apply mathematics and comput-ers extensively to study structural equation model-ing, graphical modeling, and independent component analysis as well as statistical analysis for stochastic processes. Our research includes methodological and application aspects.Mathematical Science is the science in which mathematical and statistical models are constructed, developed mathematically and diagnosed empirically in order to understand practical phenomena which occur in the elds of natural science, social science, technology, biology and so forth. For the purpose, one needs to utilize computers with advanced levels to make computer simulations, computer graphics and to develop algorithms, among others. This area consists of two large groups. One is a group of applied mathematics and the other a group of statistical science, each having two smaller subgroups. In this area, emphasis is placed on research and education of dierential equations, mathematical physics, statistical analysis and data science.28Division ofMathematical ScienceArea ofMathematical ModellingThe Area of Mathematical Modelling comprised of the following two research groups is concerned with research and education of mathematical theory and applications on modelling phenomena occured in sev-eral elds of natural science, social science and engi-neering.Dietential Equation Group■Assoc.Prof.：Mitsuru SHIBAYAMA■Assis.Prof.：Yohei FUJISHIMAHere we study nonlinear partial dierential equations appearing in the various elds of Mathematical Sci-ences. For example, we are focusing on the follow-ing topics:1: LASER beam propagation in a nonlinear medium.2: Bifurcation analysis to innite dimensional dynami-cal systems and its application to pattern formation problem.3: Development of computational topology methods applied to dynamical system theories.Applied Analysis Group■Prof.：Takashi SUZUKI■Assis.Prof.：Ryo TAKAHASHIThis group is engaged in the following study and education.1. Mathematical formulation of problems in natural science, engineering, economics, and medical science based on physical principle and phenom-ena.2. Numerical simulation, numerical scheme, and mathematical analysis based on the theory of par-tial dierential equations and nonlinear functional analysis.3. Investigation of mathematical structure for self-interacting particles and biological functions such as the kinetic equation, system of chemotaxis, and tumour growth model.Area of Statistical ScienceThe Area of Statistical Science comprised of the following two research groups is concerned with research and education on analyzing and modelling statistical data with errors, correlations and complex nonlinear structures.Statistical Analysis Group■Prof.：Hidetoshi SHIMODAIRA■Assoc.Prof.：Fuyuhiko TANAKA■Assis.Prof.：Kei HIROSEStatistical｠science,｠machine｠learning,｠and｠Bioinfor-matics｠are｠studied in｠this｠group.｠Statistical｠analy-sis｠of｠complex｠networks｠is｠also｠an important｠topic.｠You｠can｠easily｠nd｠groups｠of｠good｠friends｠in｠social networks｠with｠one｠hundred｠people,｠but｠it｠is｠yet｠a｠big｠challenge｠to understand｠the｠structure｠of｠very｠big｠networks.｠We｠also｠work｠on statistical｠analysis｠of｠DNA｠sequences｠and｠gene｠expressions.｠For estimating｠the｠evolutionary｠tree｠of｠life｠from｠DNA｠sequences,｠in particular,｠a｠statistical｠method｠developed｠by｠our｠group｠has｠been｠used in｠labs｠worldwide.Data Science Research Group■Prof.：Yutaka KANO■Assoc.Prof.：Etsuo KUMAGAI■Assis.Prof.：Kengo KAMATANIAn important purpose of multivariate analysis is to identify any relations among many variables based on statistical data. The recent topics in this eld are new modeling and statistical causal inference. In this research group, we apply mathematics and comput-ers extensively to study structural equation model-ing, graphical modeling, and independent component analysis as well as statistical analysis for stochastic processes. Our research includes methodological and application aspects.Mathematical Science is the science in which mathematical and statistical models are constructed, developed mathematically and diagnosed empirically in order to understand practical phenomena which occur in the elds of natural science, social science, technology, biology and so forth. For the purpose, one needs to utilize computers with advanced levels to make computer simulations, computer graphics and to develop algorithms, among others. This area consists of two large groups. One is a group of applied mathematics and the other a group of statistical science, each having two smaller subgroups. In this area, emphasis is placed on research and education of dierential equations, mathematical physics, statistical analysis and data science.

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