Masaaki Ohkita

An application of rationalized Haar functions to solution of linear differential equations

Rationalized Haar functions (RHFs) [1]-[5] are applied for solving linear differential equations (LDEs). In this algorithm, the first derivatives of the solutions of LDEs are expanded into rationalized Haar series with unknown coefficients. It is because an integration of a rationalized Haar approximation of its derivative in terms of time variable yields a piecewise-linear approximation (PWLA) of the solution. In a process of the solution, the given LDEs are rewritten in the RHF system and are expressed in a form of matrix equations. The PWLAs of the solutions can be obtained by using solutions of their matrix equations. In such a case, coefficient values of the PWLAs can be efficiently computed along flowgraphs for inverse fast rationalized Haar transforms.

Control of the autonomous mobile robot DREAM-1 for a parallel parking

The fuzzy control theory is used for controlling an autonomous mobile robot for the parallel parking, and the fuzzy rules can be derived by modeling driving actions of the conventional car. Loci of the robot for the parking are drawn through the computer simulation. In such a simulation, the forward and reverse movements of the robot can be controlled smoothly by using simple membership functions.

An application of rationalized Haar functions to solution of linear partial differential equations

Rationalized Haar functions (RHFs, for short) are applied for solving linear first- and second-order partial differential equations (PDEs, for short). For this purpose, new operational matrices of integration and differentiation based on a double rationalized Haar series are derived. By using these operational matrices for their solution, the PDEs are transformed into matrix equations quite easily. Coefficients of double rationalized Haar series related to their solutions can be obtained by solving these matrix equations. Some numerical examples are also included.

Application of the Haar functions to solution of differential equations

In this paper, it is proposed that Haar functions should be used for solving ordinary differential equations of a time variable in facility. This is because integrated forms of Haar functions of any degree can be illustrated by linear- and linear segment-functions like as triangles. Fortunately, since they are placed where Haar functions are defined in a specified form respectively, these functions are computable by algebraic operations of quasi binary numbers. Therefore, when a given function is approximated in a form of stairsteps on a Haar function system their integration can be termwise executed by shift and add operations of coefficients of the approximation. The use of this system is comparable with an application using the midpoint rule in numerical integration. In this line, nonlinear differential equations can be solved like as linear differential equations.

Construction of a General Physical Condition Judgment System Using Acceleration Plethysmogram Pulse-Wave Analysis

Among the popular lifestyle-related diseases are smoking, overweight and stress. A daily health check is important because there is no clear objective symptom for these diseases. We developed diagnotic software which shows the state of the blood vessels using a Basic SOM model, and performs synthetic plethysmogram analysis of 4 components using the map location (the state of the blood vessel, vascularity), looseness, pulse/minute, and pulse stability.

Spherical and Torus SOM Approaches to Metabolic Syndrome Evaluation

One of the threatening trends of health to the youth in recent years has been the metabolic syndrome. Many associate this syndrome to how big the fatty tissue around the belly is. Self-organizing maps (SOM) can be viewed as a visualization tool that projects high-dimensional dataset onto a two-dimensional plane making the complexity of the data be simplified and in the process disclose much of the hidden details for easy analyzes, clustering and visualization. This paper focuses on the analysis, visualization and prediction of the syndrome trends using both spherical and Torus SOM with a view to diagnose its trends, inter-relate other risk factors as well as evaluating the responses obtained from the two approaches of SOM.

Evaluation of analytic functions by generalized digital integration

An integral of Haar functions yields triangular waveforms at subintervals where the Haar functions initially exist. These waveforms can be expressed by Haar series. Coefficients of their series can be given in quasi binary numbers. If the solutions of ordinary differential equations(ODE) are expressed by Haar series with unknown coefficients, given ODE can be written in a Haar function system by using Haar coefficients for the triangular waveforms and variable coefficients of the ODE. They are given in terms of matrix equations. Unknown Haar coefficients can be determined by solving such matrix equations. Haar approximations of their solutions can be obtained through a consistent procedure of computation.

Classification using topologically preserving spherical self-organizing maps

A new classification method is proposed with which a multidimensional data set was visualized. The phase distance on the spherical surface for the labeled data was computed and a dendrogram constructed using this distance. Then, the data can be easily classified. To this end, the color-coded clusters on the spherical surface were represented based on the distance between each node and the labels on the sphere. Thus, each cluster can have a separate color. This method can be applied to a variety of data. As a first-example, we considered the iris benchmark data set. A boundary between the clusters was clearly visualizible with this coloring method. As a second example, the velocity (first derivative) mode of a Plethysmogram pulse-wave data set was analyzed using the distance measure on the spherical surface.

Traveling control of the autonomous mobile wheel-chair DREAM-3 considering correction of the initial position

The aim to develop DREAM-3 is make it travel in indoor environments such as in hospitals and/or welfare facilities for their practical use and serve to take care of old people and physically handicapped person. The autonomous mobile robot DREAM-3 has loaded an environmental map for the safety driving, where various sensor information is integrated. In this paper, method to collect the initial position of the robot on the environmental map is described with the traveling control.

Fractional power approximation and its generation

For an analog simulating system, an approximating system is proposed. Its mathematical form is expressed by an algebraic equation: ƒ (x) ≈ α + β χ + γχk with four parameters given by real numbers. Their values can be determined so as to satisfy a best fit in a Chebyshev sense. Then, the accuracy is of the same order with that obtained by any kind of ordinary power series up to terms o f the third order. It is noticeable that a given function can be accurately approximated by this equation without destroying its uniform continuity.