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Summary: The fused lasso signal approximator (FLSA) is a smoothing procedure for noisy observations that uses fused lasso penalty on unobserved mean levels to find sparse signal blocks. Several path algorithms have been developed to obtain the whole solution path of the FLSA. However, it is known that the FLSA has model selection inconsistency when the underlying signals have a stair‐case block, where three consecutive signal blocks are either strictly increasing or decreasing. Modified path algorithms for the FLSA have been proposed to guarantee model selection consistency regardless of the stair‐case block. In this paper, we provide a comprehensive review of the path algorithms for the FLSA and prove the properties of the recently modified path algorithms' hitting times. Specifically, we reinterpret the modified path algorithm as the path algorithm for local FLSA problems and reveal the condition that the hitting time for the fusion of the modified path algorithm is not monotone in a tuning parameter. To recover the monotonicity of the solution path, we propose a pathwise adaptive FLSA having monotonicity with similar performance as the modified solution path algorithm. Finally, we apply the proposed method to the number of daily‐confirmed cases of COVID‐19 in Korea to identify the change points of its spread. [ABSTRACT FROM AUTHOR]

Although game‐based learning has been increasingly promoted in education, there is a need to adapt game content to individual needs for personalized learning. Procedural content generation (PCG) offers a solution for difficulty in developing game contents automatically by algorithmic means as it can generate individually customizable game contents applicable to various objectives. In this paper, we advanced a data‐driven PCG approach benefiting from a genetic algorithm and support vector machines to automatically generate educational‐game contents tailored to individuals' abilities. In contrast to other content generation approaches, the proposed method is not dependent on designer's intuition in applying game contents to fit a player's abilities. We assessed this data‐driven PCG approach at length and showed its effectiveness by conducting an empirical study of children who played an educational language‐learning game to cultivate early English‐reading skills. To affirm the efficacy of our proposed method, we evaluated the data‐driven approach against a heuristic‐based approach. Our results clearly demonstrated two things. First, users realized greater performance gains from playing contents tailored to their abilities compared with playing uncustomized game contents. Second, this data‐driven approach was more effective in generating contents closely matching a specific player‐performance target than the heuristic‐based approach. Lay Description: What is already known about this topic Educational games are mostly designed with a fixed task‐progression difficulty. Given the current broad diversity of player background, preferences, and motivations, it is typically difficult to achieve a dynamic difficulty adaptation with any single and fixed progression.Procedural content generation provides a solution for this difficulty by developing game contents automatically through algorithmic means with or without the involvement of a human designer. What this paper adds A data‐driven approach is employed to refine the fitness function for content evaluation and the prediction of players' capabilities.Unlike previous approaches that have predominantly steered the generation process through designer‐defined goals or heuristics, the proposed approach does not depend on the designer intuition in aligning contents with fitness. Implications for practice and/or policy The proposed framework can be applied to other educational games.The proposed approach offers users a different experience with every new game to enhance the game replayability. [ABSTRACT FROM AUTHOR]

A millimetre‐wave cloud radar has limitations for observing heavy rainfall because the short wavelength leads to strong attenuation from raindrops. However, recent studies have attempted to estimate the rain rate using attenuation, which becomes greater as the rain intensity increases. The rain‐rate‐retrieval algorithm is developed in the present paper using the Ka‐band cloud radar (KaCR) installed at the Boseong Global Standard Observatory (BGSO) in the Republic of Korea. First, rain profiles were identified using the threshold of reflectivity (Z) and Doppler velocity (DV) averaged for the analysis of layer that minimized the effects of the receiver saturation and classified as low or high rain‐rate cases using the averaged DV. The reflectivity and rain‐rate (Z‐R) relationship was then derived for low rain‐rate cases that showed insignificant effects for signal attenuation. On the other hand, the attenuation and rain‐rate (A‐R) relationship was derived using high rain‐rate cases that showed the dominant effects of attenuation. The attenuation was calculated using a reflectivity gradient between the upper and lower boundaries of the attenuated layer. Finally, the rain‐rate‐retrieval algorithm was designed using the derived Z‐R and A‐R relationship and then applied back to the KaCR. The estimated rain rate in the KaCR was a similar trend to the observed rain rate in the optical rain gauge (ORG), but slightly underestimated. [ABSTRACT FROM AUTHOR]