Center manifold reduction for large populations of globally coupled phase oscillators

A bifurcation theory for a system of globally coupled phase oscillators is developed based on the theory of rigged Hilbert spaces. It is shown that there exists a finite-dimensional center manifold on a space of generalized functions. The dynamics on the manifold is derived for any coupling functions. When the coupling function is $\sin \theta$, a bifurcation diagram conjectured by Kuramoto is rigorously obtained. When it is not $\sin \theta$, a new type of bifurcation phenomenon is found due to the discontinuity of the projection operator to the center subspace

Development of a Gastric Cancer Diagnostic Support System with a Pattern Recognition Method Using a Hyperspectral Camera

Gastric cancer is a completely curable cancer when it can be detected at its early stage. Thus, because early detection of gastric cancer is important, cancer screening by gastroscopy is performed. Recently, the hyperspectral camera (HSC), which can observe gastric cancer at a variety of wavelengths, has received attention as a gastroscope. HSC permits the discerning of the slight color variations of gastric cancer, and we considered its applicability to a gastric cancer diagnostic support system. In this paper, after correcting reflectance to absorb the individual variations in the reflectance of the HSC, a gastric cancer diagnostic support system was designed using the corrected reflectance. In system design, the problems of selecting the optimum wavelength and optimizing the cutoff value of a classifier are solved as a pattern recognition problem by the use of training samples alone. Using the hold-out method with 104 cases of gastric cancer as samples, design and evaluation of the system were independently repeated 30 times. After analyzing the performance in 30 trials, the mean sensitivity was 72.2% and the mean specificity was 98.8%. The results showed that the proposed system was effective in supporting gastric cancer screening