Blow-up analysis for a periodic two-component μ-Hunter–Saxton system

Abstract The two-component μ-Hunter–Saxton system is considered in the spatially periodic setting. Firstly, two wave-breaking criteria are derived by employing the transport equation theory and the localization analysis method. Secondly, a sufficient condition of the blow-up solutions is established by using the classic method. The results obtained in this paper are new and different from those in previous works

Full-Information Optimal-Stopping Problems: Providing People with the Optimal Policy Does Not Improve Performance

In optimal-stopping problems, people encounter options sequentially with the goal of finding the best one; once it is rejected, it is no longer available. Previous research indicates that people often do not make optimal choices in these tasks. We examined whether additional information about the task's environment enhances choices, aligning people's behaviour closer to the optimal policy. Our study implemented two additional-information conditions: (1) a transparent presentation of the underlying distribution and (2) a provision of the optimal policy. Our results indicated that while choice patterns varied weakly with additional information when providing the optimal policy, it did not significantly enhance participants' performance. This finding suggests that the challenge in following the optimal strategy is not only due to its computational complexity; even with access to the optimal policy, participants often chose suboptimal options. These results align with other studies showing people's reluctance to rely on algorithmic or AI-generated advice

Full-Information Optimal-Stopping Problems: Providing People with the Optimal Policy Does not Improve Performance

In optimal-stopping problems, people encounter options sequentially with the goal of finding the best one; once it is rejected, it is no longer available. Previous research indicates that people often do not make optimal choices in these tasks. We examined whether additional information about the task's environment enhances choices, aligning people's behaviour closer to the optimal policy. Our study implemented two additional-information conditions: (1) a transparent presentation of the underlying distribution and (2) a provision of the optimal policy. Our results indicated that while choice patterns varied weakly with additional information when providing the optimal policy, it did not significantly enhance participants' performance. This finding suggests that the challenge in following the optimal strategy is not only due to its computational complexity; even with access to the optimal policy, participants often chose suboptimal options. These results align with other studies showing people's reluctance to rely on algorithmic or AI-generated advice