Study of Togo -Matsuzaki Hot Springs, Tottori Prefecture

1. Layers containing thermal water in this district are thin, and lie at different depths (about 35, 55, and 60 meters) from the ground surface. There are evidences to show that these layers are intimately connected with one another. 2. The authors may suppose the existence of a structurally weak zone, along the line from Matsuzaki to Asozu, within which the issuing spots of thermal springs are located. 3. The head water levels of the thermal springs in this district are closely related with that of Lake Togo. Keeping pace with the variations of the water levels of Lake Togo and of artesian wells in its vicinity, the rate of flow of thermal springs vary; and the correlation between these variations is apparent. 4. The pumping suction of thermal water at one spring affects the flow of water at other springs within distances of 150 to 200 meters therefrom, though the direct sources of thermal water supply for the latter springs may be different from that of the former. 5. The spring water in this district is considered to be a mixture of hot water, containing sodium, calcium, chloride, and sulfate ions, and cold water, containing bicarbonate ion. The diversity of chemical constitutions of different spring waters is explained as due to the difference in proportion in which the hot and cold waters are mixed

A method of identifying influential data in fuzzy clustering

In multivariate statistical methods, it is important to identify influential observations for a reasonable interpretation of the data structure. In this paper, we propose a method for identifying influential data in the fuzzy C-means (FCM) algorithm. To investigate such data, we consider a perturbation of the data points and evaluate the effect of a perturbation. As a perturbation, we consider two cases: one is the case in which the direction of a perturbation is specified and the other is the case in which the direction of a perturbation is not specified. By computing the change in the clustering result of FCM when given data points are slightly perturbed, we can look for data points that greatly affect the result. Also, we confirm an efficacy of the proposed method by numerical examples

Kernel-Induced Sampling Theorem

A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the orthogonal projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points

Theoretical analyses for a class of kernels with an invariant metric

One of central topics of kernel machines in the field of machine learning is a model selection, especially a selection of a kernel or its parameters. In our previous work, we discussed a class of kernels whose corresponding reproducing kernel Hilbert spaces have an invariant metric and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the optimal model. However, discussions for properties that make the metrics of reproducing kernel Hilbert spaces invariant are insufficient. In this paper, we show a necessary and sufficient condition that makes the metrics of reproducing kernel Hilbert spaces invariant

A study of erosion due to low-energy sputtering in the discharge chamber of the Kaufman ion thruster

SIGLEAvailable from British Library Document Supply Centre- DSC:DN056633 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Integrated kernels and their properties

Kernel machines are widely considered to be powerful tools in various fields of information science. By using a kernel, an unknown target is represented by a function that belongs to a reproducing kernel Hilbert space (RKHS) corresponding to the kernel. The application area is widened by enlarging the RKHS such that it includes a wide class of functions. In this study, we demonstrate a method to perform this by using parameter integration of a parameterized kernel. Some numerical experiments show that the unresolved problem of finding a good parameter can be neglected