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This paper formulates the modified least-squares method presented by Mullis in a general form so that weighting can be applied. Then, all algorithm is proposed with which a least-squares approximation can be derived for an IIR digital filter, by solving iteratively a system of equations. The method is extended to a complex Chebyshev approximation that minimizes the maximum magnitude of the complex error, by multiplying the weight, which is newly derived in this paper, with the modified least-squares error. The method is compared with a conventional complex Chebyshev approximation by means of a computer simulation and the effectiveness of the proposed method is demonstrated. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(7): 28–36, 1998 [ABSTRACT FROM AUTHOR]

In this paper, we propose a model of the human head and eyeballs that naturally simulates the movement of its line of sight in computer graphics. We first measure the actual trajectory characteristics of head movement for several angles. From previous research and the data we obtained, we find that moving the head with a sigmoidal angular velocity is an optimal feature. A mathematical moving model of the head and eyeballs based on our finding is proposed. We create several movements, such as furtive, weird, astonished, and glancing facial expressions, by changing the model parameters. We also present a simple and practical model. Finally, we discuss our proposed model based on our evaluation of subjective tests on the model. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 41–50, 1999 [ABSTRACT FROM AUTHOR]

Some methods for synthesizing a protocol specification from a given service specification have been proposed using various computational models. However, the existing methods cannot treat service specifications including both complex control flows and system variables. In this paper, we propose a method for synthesizing a protocol specification automatically from a pair consisting of a service specification and a resource allocation. In our method, service specifications are described in an extended model of Petri nets, which can treat system variables. We have developed a pair consisting of a synthesis system and an execution system, and applied them to CSCW (Computer Supported Cooperative Work). © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 81(8): 18–26, 1998 [ABSTRACT FROM AUTHOR]

Given, a graph G = (V, E), with two vertices s and t specified as the origin and destination, respectively; a positive integer K called the obstruction number; and (positive) weights l (·) on the edges; then, two players P1 and P2 play a game with the following rules. P1 starts from s, and tries to arrive at t by tracing an edge on each move. P2 cuts in his turn, P2 cuts some edges. The maximum total number of edges that P2 can cut is K during the game. It is assumed that both P1 and P2 can see the whole graph. P1 tries to minimize the sum of traveled edge weights (called the path length), and P2 tries to maximize the path length. This paper shows that the path length when the two players do their best can be determined in O(nk-l (m + n log n)) (m = |E| n = (|V|) time. It is also shown that the problem of deciding whether or not the path length when the two players do their best is not greater than a certain positive integer is P-SPACE-complete, even if the weight on each edge is 1. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(2): 13–23, 1998 [ABSTRACT FROM AUTHOR]

This paper discusses the concept of the minimal value set. Based on the number of connected components of the minimal value set, the unimodal function (number of connected components = 1) and the multimodal function (number of connected components ≧ 2) are defined. Several properties are derived from the relation between the connected level set and the minimal value set, and the unimodal region of a certain minimal value set is defined. Three theorems concerning the minimal value set are derived, as follows. (1) The set of local minimal points includes the minimal value set. (2) The minimal value set includes the set of minimal points in the narrow sense. (3) The unimodal function includes the quasi-convex function. The probability that the multistart method, where the local optimization technique is applied to the multiple candidate points, finds the global minimal point, as well as the necessary condition for the local optimization technique so that the points on the unimodal region containing the global minimal point converge correctly to the global minimal point, are discussed. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(1): 42–51, 1998 [ABSTRACT FROM AUTHOR]