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3 years ago

Doshisha University (Private)

Doshisha University (Private)

DNA computing: The

DNA computing: The properties of the chemical reactions of four types of DNA bases are used and optimization theory is applied for devising new computing principles. Rough information image processing analysis: Redundant information occurs when image processing data is handled in a significantly large space. The objective of this research is to develop algorithms with faster computing speeds to take advantage of the large number of zero values even though the number of computing increases. Research Contents The average rate of change can be calculated by taking the displacement of an object as minute changes over time. The limiting operation can be used to obtain the differential (coefficient) from the average rate of change. We are engaged in research that applies this differential concept to various fields. The purpose of our research is analysis of the stability and chaos (complex behavior that is difficult to predict) of trajectories for ordinary differential equations where differentiation is considered on a continuous time axis and difference equations at discrete times and then applying these results. In particular, our aim is to apply these results to price stabilization analysis in economic theory. Also, when the environment surrounding people is modeled, information analysis is needed that incorporates ambiguous meanings (fuzziness) such as "roughly, about" if objectively performing numerical analysis of subjectivity and skilled and experienced intuition. We are also involved in the analysis of fuzzy differential equations that have ambiguity and research into the fuzzy optimization such as bridge location problems that take into account ambiguous road traffic volumes. Keywords Fuzzy differential equation Fuzzy optimization Qualitative theory of ordinary differential equation Chaos/fractal analysis Price adjustment difference equation Optimized DNA computing Sparse decomposition and wavelet transformation

Prof. Yoshihide WATANABE Discrete Mathematics Laboratory http://istc.doshisha.ac.jp/course/environment/labo_68.html Research Topics Maximum likelihood decoding of two-dimensional codes using a Groebner basis The Ikegami-Kaji algorithm that performs two-dimensional maximum likelihood decoding using a Groebner basis requires too much computational time to be of practical use. In view of this problem, in this research we consider whether a Groebner basis of the ideal necessary for maximum likelihood decoding can be derived from combinatorial properties of the codes. Such an attempt might lead to the opening of a new vista on the mathematical structure of codes and the mechanism of maximum likelihood decoding. Groebner basis and the problem of network optimization In many cases, the problem of network optimization can be formulated as an integer programming problem. Consequently, based upon this problem, a toric ideal can be defined. We investigate the relationship between generators or Groebner bases of such toric ideal and network structures. Various problems of combinatorial optimization in bioinformatics In the field of bioinformatics, various combinatorial optimization problems occur that are also of interest from an optimization problem perspective. By formulating such problems as integer programming problems, we study their mathematical structures. Research Contents Optimization refers to the process of either maximizing or minimizing an objective function under a given set of constraints. As such, it represents a typical research topic in applied mathematics. Optimization problems are of two types: a continuous optimization problem in which the treated variable takes continuous values, and a discrete optimization problem in which the variable takes discrete values. Our laboratory is principally devoted to the study of discrete optimization problems, in particular, integer programming problems, in terms of their mathematical structures and from a mathematical point of view. The keyword is either toric ideal or lattice ideal. The tools we use are the Groebner bases of an ideal in the polynomial ring. Specific discrete optimization problems that we are pursuing and that are of considerable interest include the graphical network optimization problem, the problem of maximum likelihood decoding in error correcting codes, and various combinatorial optimization problems in bioinformatics. Keywords Optimization problem Discrete structure Formula manipulation Groebner basis Toric ideal Error correcting code Bioinformatics

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