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This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

Based on an orthogonal set of product states of two three-state particles, a new quantum secret sharing scheme is proposed, which uses a novel distribution strategy so that continuous and independent measurements, rather than particle-wise coordinated ones, are performed. As a result, it is convenient and efficient to implement. The scheme is also secure against several common attacks and gets rid of partial-information leakage due to the revised coding method. Moreover, the quantitative analysis shows that the security can be further improved by using more product states from appropriate multiple sets.