The equilibrium configurations of N Coulomb charges confined by a harmonic potential in two dimensions are found to exhibit a wide variety of patterns that are pleasing to the eye, when adjacent points are joined up. We present a selection of these for N=50. The patterns are reminiscent of early examples of algorithmic or computer-generated art, and might be of use for psycho-physical studies of the perception of structure and randomness. They could also find applications in the generation of recognisable symbols in an alphabet of infinite extent, easily generated and varied using the software that is provided here.

In previous studies, we constructed a theoretical framework via 5-D homogeneous processing to enable the uniform visualization of 4-D information in an interactive environment and succeeded in imparting generality to 4-D graphics. Furthermore, we developed advanced methods for 4-D geometric element definitions and interference via 5-D homogeneous processing. In the 4-D projective space, 5-D homogeneous processing can express a variety of transformations using 5×5 matrices and 5×5 determinants, which can be applied to all points, including points at infinity. Based on this perspective, I consider unified representations of point, line, plane, and hyperplane using 5-D homogeneous processing while investigating the geometric relations between the geometric element definitions and interferences in 4-D space. Subsequently, I describe strict duality of 4-D projective space. The proposed scheme provided more uniform geometric calculations than those described in our previous study.

In a lecture that J.K.Moser gave in 1968, he pointed out the possibility that the periodic orbit with period q=3 (period-3 orbit) appears through anomalous rotation bifurcation (ARB). There are two different types of rotation bifurcation, the ordinary rotation bifurcation (ORB) and ARB. In order to study ORB and ARB, the map T_m (y_n+1=y_n+a(x_n−x_n^m), x_n+1=x_n+y_n+1 (a≥0, m≥2)) is introduced. It is proved that the period-3 orbit in T_m (m≥2) and the period-4 orbit in T_m (m≥3) appear through ARB and the period-4 orbit in T₂ appears through ORB.

Olfaction is generally evaluated using sensory evaluation. Objective evaluation has recently been performed using electrogastrogram (EGG). In this study, EGGs were measured with and without exposure to the lavender odor, and power spectra were obtained from the frequency analysis of the EGGs. Principal component analysis (PCA) was conducted to extract dimension-compressed data in the frequency space. A linear support vector machine (SVM) was then applied to classify the EGGs into those observed in the odorless condition and those recorded with exposure to the lavender odor. Binary classification by the SVM was evaluated by the correct rate and F value that were 100% resulted from this artificial intelligence analysis for all participants.

Almost 400 years ago a sheet of the world map was manufactured in Japan by someone related to Catholic Missions. In 1986 in Tokyo a Japanese private collector gave this map to Kenneth Nebenzahl, an American map-dealer, and the map is still in the United States. The primary study was done by Alfredo Pinheiro Marques, a Portuguese historian of cartography, but this map must be examined by Japanese scholars in cartography and Kakure Kirishitan.