Among scaling analysis methods based on the root-mean-square deviation from the estimated trend, it has been demonstrated that centered detrending moving average (DMA) analysis with a simple moving average has good performance when characterizing long-range correlation or fractal scaling behavior. Furthermore, higher-order DMA has also been proposed; it is shown to have better detrending capabilities, removing higher-order polynomial trends than original DMA. However, a straightforward implementation of higher-order DMA requires a very high computational cost, which would prevent practical use of this method. To solve this issue, in this study, we introduce a fast algorithm for higher-order DMA, which consists of two techniques: (1) parallel translation of moving averaging windows by a fixed interval; (2) recurrence formulas for the calculation of summations. Our algorithm can significantly reduce computational cost. Monte Carlo experiments show that the computational time of our algorithm is approximately proportional to the data length, although that of the conventional algorithm is proportional to the square of the data length. The efficiency of our algorithm is also shown by a systematic study of the performance of higher-order DMA, such as the range of detectable scaling exponents and detrending capability for removing polynomial trends. In addition, through the analysis of heart-rate variability time series, we discuss possible applications of higher-order DMA.

In recent years, materials for ARVR have been actively developed, and high Refractive Index (R.I.) materials are required to achieve high performance and a wide field of view. In addition, AR display is a fine display, therefore the display is needed the materials that can be embedded in fine structures. Since AR has a fine structure, it is formed by nanoimprint (NIL) or gap fill processes. In short, materials with a high R.I., high transparency, and NIL and gap filling properties are required for AR waveguide. High R.I. formulation with high fluidity and low volatility are required for NIL and gap fill process, however, in the case of conventional organic materials, there is the trade-off to obtain high fluidity with low volatility. We designed from the molecular structure and realized to solve the trade-off parameters. With that organic material technology and our unique formulation technology, we have realized products that can perform NIL and gap fill even if it contains a large amount of inorganic nano-filler. In addition, by using organic materials for organic EL, it is possible to obtain effective characteristics such as solvent-free materials with high light extraction efficiency. Products using this technology are expected to be applied to AR and OLED.

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