Mitsuhiko Toda

Methods for Visual Understanding of Hierarchical System Structures

Two kinds of new methods are developed to obtain effective representations of hierarchies automatically: theoretical and heuristic methods. The methods determine the positions of vertices in two steps. First the order of the vertices in each level is determined to reduce the number of crossings of edges. Then horizontal positions of the vertices are determined to improve further the readability of drawings. The theoretical methods are useful in recognizing the nature of the problem, and the heuristic methods make it possible to enlarge the size of hierarchies with which we can deal. Performance tests of the heuristic methods and several applications are presented.

Trace inequalities involving Hermitian matrices

Abstract Some trace inequalities for Hermitian matrices and matrix products involving Hermitian matrices are presented.

Brief paper: Bounds on performance of nonstationary continuous-time filters under modelling uncertainty

A method for obtaining quantitative measures of the performance of non-stationary Kalman type filters for time-varying, linear, continuous-time systems with modelling errors is described. The performance measures consist of upper and lower bounds on the trace of the estimation error covariances (the mean squared error) of suboptimal filters. Errors in system configuration, noise statistics, and prior information are treated and the resulting bounds are expressed in terms of the model matrices and the range of errors in these matrices.

A method for aggregating ordinal assessments by a majority decision rule

Abstract A new method for aggregating ordinal assessments of individuals is proposed to obtain a collective preference ordering of alternatives. The method converts the ordinal assessments to collective pairwise comparisons of the alternatives and incorporates a deduction process to yield transitively consistent pairwise comparisons with respect to majority principle, and hence yields a linear order of the alternatives. Its algorithm is presented and its properties are studied. The method is applied to an opinion survey concerning quality of life, and a collective ordering of items pertaining to the quality of life is obtained with respect to their importance.

VISUAL Q-ANALYSIS (I): A CASE STUDY OF FUTURE COMPUTER SYSTEMS DEVELOPMENT IN JAPAN

Abstract A novel method called Visual Q-Analysis (VQA) is proposed to analyze structures of complex systems, where the structure of a system is represented by simplicial complex in topology and analyzed in terms of q-connectivity. Two different types of hierarchies, Q-hierarchy and F-hierarchy, are introduced and algorithms are given. In order to draw these hierarchies in a visually understandable form, SKETCH system is used. By inspecting the combination of the drawings and measures such as Q-vector, eccentricity and concentricity we can grasp readily the structural information embedded in the complex. This method is applied to a structural study of technological development of future computers of Japan in terms of relationships between social needs and technological requirements (seeds). Results of the application not only show the effectiveness of VQA to support in planning technological developments but also suggest wide applicabilities of VQA to various other fields.

VISUAL Q-ANALYSIS (II): STRATEGY ANALYSIS FOR FUTURE COMPUTER SYSTEMS DEVELOPMENT IN JAPAN

Abstract Visual Q-Analysis (I) proposed in Part I are extended to evaluate strategies of technological developments. The method for extension is based on F-Hieraichies generated by Visual Q-Analysis (I), which is a method for structural analysis. Utility indicators of technologies are first computed by taking account of their relevancy to social needs, and then preferred paths of technological developments are determined by utilizing the indicators. Algorithms to obtain the indicators and the paths are presented and their properties are studied. The method is applied to analyze strategies for developing future computers in Japan.

Algorithms for adaptive stochastic control for a class of linear systems

Abstract This paper is concerned with the control of linear, discrete-time, stochastic systems with unknown control gain parameters. Two suboptimal adaptive control schemes are derived: One is based on underestimating future control and the other is based on overestimating future control. Both schemes require little on-line computation and incorporate in their control laws some information on estimation errors. The performance of these laws is studied by Monte Carlo simulations on a computer. Two single-input, third-order systems are considered, one stable and the other unstable, and the performance of the two adaptive control schemes is compared with that of the scheme based on enforced certainty equivalence and the scheme where the control gain parameters are known.