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This paper considers the problem of the market with restricted
information. By constructing a restricted information market
model, the explicit relation of arbitrage and the minimal
martingale measure between two different information markets
are discussed. Also a link among all equivalent
martingale measures under restricted information market is given.

BACKGROUND: Patient compliance is essential to the effectiveness of brace treatment for adolescent idiopathic scoliosis (AIS) patients. Subjective measurements like questionnaires and inquiries proved to be arguably inaccurate. Although some scholars have applied temperature/force monitors to measuring patient compliance objectively, few studies to date could monitor patient compliance in real time. The objective of this study is to describe and evaluate a compliance real-time monitoring system of the brace usage in AIS patients. METHODS: A compliance real-time monitoring system (specifically consisting of a compliance monitor, a WeChat Mini Program, a cloud-based storage system and a website backstage management system) was designed to manage the brace treatment. Thirty patients receiving brace treatment were enrolled. They were told to upload the data at least once a day. Clinicians downloaded the compliance data and communicated with the patients online based on their analysis of data at least once every 3 months. The measured force, quality compliance (measured force / baseline force), measured time, and quantity compliance (measured time/ prescribed time) were used to evaluate patient compliance. Patients were also asked to rate their satisfaction at the final follow-up. RESULTS: Twenty-eight patients were included in the final analysis. The mean baseline force was 1.23 ± 0.28 N. The mean measured force was 0.79 ± 0.29 N. The mean quality compliance was 64.8 ± 22.2%. The prescribed time of all patients was 23 h. The mean measured time was 14.1 ± 2.9 h. The mean quantity compliance was 61.3 ± 12.6%. Both the quality and quantity compliance during the first 3 months of treatment was significantly lower than the latter 3 months. In this study, 96.4% (27/28) patients were satisfied with the use of the monitoring system, among whom 21.4% (6/28) are very satisfied and 75.0% (21/28) are somewhat satisfied. CONCLUSIONS: The compliance real-time monitoring system, without evaluating the clinical and radiographic ...