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#ref(intro.gif,nowrap,nolink); Research and education in this Department deal with modeling, analysis, and control of complicated and large-scaled systems, not necessarily confined to artificial ones, and optimization of their performances together with basic methodologies such as discrete and applied mathematics, dynamical system theory, and statistical physics. The aim of the Department is to bring up scientists or engineers who can cope with various problems encountered in highly organized and informatized modern societies, based on flexible conception, sharp insight, and high competence for searching solutions, resulting from profound attainments in mathematics and mathematical physics and from a general background in computer sciences. #br #ref(logo_outline_e.jpg,nowrap,nolink); ----- #br The Department has 3 divisions, each with 2 or 3 sub-divisions, and consists of 7 chairs. 21 graduate students are accepted into the Master's Program annually and 7 into the Doctoral program. **&size(21){Applied Mathematical Analysis};　　　&size(12){ - Developing algorithms from integrable systems };[#sc84cb37] #ref(01.gif,nolink,around,nowrap,left); &br; We carry out research in the areas of contemporary soliton research and integrable system research, not only regarding the applied analysis of orthogonal polynomials and special functions that are closely associated with integrable systems, but also regarding the application of the mathematical methods developed by integrable system studies to the solution of various problems hitherto thought to be unrelated to integrable systems (such as numerical calculation and algorithm development). Our Group is a pioneer in this research field, and conducts studies into the applied analysis of integrable systems in the development of algorithms and other new branches of mathematics from the perspective of computer science.&br; （Professor: NAKAMURA Yoshimasa, Associate Professors: TSUJIMOTO Satoshi , Program Specific Associate Professor: KIMURA Kinji, Assistant Professor: KAMIOKA Shuhei） #clear **&size(21){Discrete Mathematics};　　　&size(12){ -Exploring the complexity of discrete mathematics problems and developing algorithms}; [#w71aad75] #ref(02.gif,nolink,around,nowrap,right); &br; Topics in discrete mathematics, such as the graphs and network used to represent systems, schedules to enhance the efficiency of production, and the logical analysis of large volumes of data, are closely related to applications of research results. We explore the complexity of the calculations used to solve these problems; design logical approximation algorithms; develop taboo search algorithms, genetic algorithms and other metaheuristic algorithms; and apply them to solving actual problems. &br; （Professor: NAGAMOCHI Hiroshi, Senior Lecturer: ZHAO Liang, Assistant Professor: FUKUNAGA Takuro） #clear **&size(21){System Optimization};　　　&size(12){ - Optimization is the keyword for solving problems}; [#ab315b65] #ref(03.gif,nolink,around,nowrap,left); &br; We conduct education and research regarding the theory and methodology of system optimization, which plays an important role as a mathematical approach that is used to resolve many different kinds of practical problems. In particular, we develop efficient mathematical optimization approaches to actual large-scale systems, complex nonlinear systems, and systems with uncertainty, as well as basic research regarding mathematical programming. &br; （Professor: FUKUSHIMA Masao, Associate Professor: YAMASHITA Nobuo, Assistant Professor: HAYASHI Shunsuke） #clear **&size(21){Control Systems Theory};　　　&size(12){ - Mathematical approaches to modeling and control }; [#o9515ff3] #ref(04.gif,nolink,around,nowrap,right); &br; We carry out teaching and research regarding the mathematical methodologies of modeling, analysis and design of control systems, and their application with the aim of developing practical and expansive control theories. Our main research themes are robust control, control systems with input/output constraints, networked control systems, algebraic system theory, mathematical optimization in control, stochastic realization and system identification. &br; （Professor: OHTA Yoshito, Assistant Professor: Kentaro OHKI） #clear **&size(21){Physical Statisticsprocessing}; &size(12){ - The mathematical studies on dynamics of coupled multi-element systems and information processing}; [#p5eb59df] #ref(06.gif,nolink,around,nowrap,left); &br; We aim to gain a mathematical and unified understanding of the complex and diverse phenomena that arise out of the intense mutual interactions of multiple elements (units) in a system and apply this understanding to information processing. For example, we will use stochastic process theory, statistical physics, computer simulations, dynamical system theory, agent models, and large-scale data processing techniques to analyze information processing in simple threshold systems, neurons, and their networks; the structure of the Internet and other complex networks, and the propagation of information within them; and the dynamical properties of price change, stock markets and other economic phenomena. &br; （ Professor: UMENO Ken ,Associate Professor: IGARASHI Akito, Assistant Professor: SATO Akihiro） #clear **&size(21){Dynamical System Theory};　　　&size(12){ - Looking into systems through dynamical systems theory }; [#j17f08be] #ref(07.gif,nolink,around,nowrap,right); &br; We apply differential geometry and other branches of mathematics in our analysis of the mathematical physical structure of dynamical systems. Examples include reduction theory and chaos in dynamical systems, the differential geometric structure of many-body systems, quantum-classical correspondence, and the analysis of orbital instability. In our research into engineering applications, we use the concepts of differential geometry to analyze problems of how to control dynamical systems with non-holonomic constraints. We are also involved with differential geometric techniques in quantum computation theory. &br; (Professor: IWAI Toshihiro, Associate Professor: TANIMURA Shogo, Assistant Professor: YAMAGUCHI Yoshiyuki)&br; #clear **&size(21){Applied Mathematical Modeling Adjunct Unit}; (in collaboration with Hitachi, Ltd.)　　　&size(12){ - Infusing information systems with intelligence}; [#ca90345d] #ref(outline05.gif,nolink,around,nowrap,left); &br; To make information systems useful to our day-to-day lives and industry at large, we need to be able to mathematically model both the behavior of people and the movements of objects that these systems deal with. The form of these models ranges from the conceptual to the numerically precise. We will examine case studies from industry in our research of modeling technology, including methods of using human knowledge (structural modeling) and methods using actual data (multivariate analysis). &br; （Professor: YAMAMOTO Akira, Associate Professor: KURISU Hiromitsu）