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Discrete Structure Analysis

Department Head: Professor Akihiro Munemasa

In the Department of Discrete Structure Analysis, we mostly work on the mathematical analysis of combinational structures and their application. Specifically, we work on the paradigm of building an analysis for discrete structures with the utilization of big data at the forefront of our research. We work to contribute to the reliability of communications by creating a new theory of algebraic coding through our work on quantum codes and DNA codes.

New developments in algebraic coding theory

One of our new developments in algebraic coding theory is to use not only algebraic approaches to quantum codes and DNA codes, but to also incorporate computer-aided combinatorial analysis approaches to large, yet finite, objects. In doing this, we hope to create a completely new paradigm for the mathematical analysis for combinational structures.

New developments in the algebraic coding theory

Mathematical approach to large networks

We contribute to the mathematical foundation of large complex networks, its structure and dynamics, by combining both discrete and continuous mathematics. Applications are explored, for example, in gene expression in biological science, decision-making in social science, network-type big data in information science, and so forth.

Normalized joint spectral distributions of Cartesian powers of Paley graphs Paley(q) and their complements

Games and Combinatorial Structures

We aim to discover new values of combinatorial structures by using unconventional methods with games. For example, we will study combinatorial structures such as designs and codes by embedding them into combinatorial games so that they become winning position sets.

Games and Combinatorial Structures