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In this paper, the phenomenon of phase transition is studied in an asymmetric tristable model driven by Lévy noise and Gaussian white noise. First, the fourth-order Runge-Kutta algorithm is used to simulate the stationary probability density of the system. Then we observe the shape of the stationary probability density curve by adjusting the system parameters and noise parameters. It has been found that asymmetric parameter, additive noise intensity, multiplicative noise intensity, the stability index, and the skewness parameter can all induce phase transition. Moreover, the influence of additive noise intensity and multiplicative noise intensity on the number and height of stationary probability density peaks is opposite. We also found that under the same asymmetric parameters, the influence of positive and negative skewness parameters on the stationary probability density is different.(讨论了非对称三稳系统在Lévy噪声和高斯白噪声共同驱动下的相转移问题。采用四阶Runge-Kutta算法，计算了系统的稳态概率密度函数，通过改变系统参数和噪声参数观察其稳态概率密度函数曲线形态的变化情况。研究发现，非对称参数、加性噪声强度、乘性噪声强度、稳定性指标、偏斜参数均可诱导系统相转移，当分别改变加性噪声强度和乘性噪声强度时，概率密度函数的峰数与高度的变化情况相反。此外，在相同的非对称参数下，随着偏斜参数正负取值的变化，概率密度曲线图中峰的结构亦呈现不同的现象。)

OBJECTIVE: The main clinical manifestations of knee osteoarthritis are pain, swelling, stiffness, and limited activity, which have a serious impact on the life of patients. Exercise therapy can effectively improve the related symptoms of patients with knee osteoarthritis. This paper uses the method of network meta-analysis to compare the efficacy of different exercise types in the treatment of knee osteoarthritis. METHODS: CNKI, WanFang, PubMed, Embase, Cochrane Library, Web of Science, Scopus, Ebsco, SinoMed, and UpToDate were searched with Chinese search terms “knee osteoarthritis, exercise therapy” and English search terms “knee osteoarthritis, exercise”. Randomized controlled trials on the application of different exercise types in patients with knee osteoarthritis from October 2013 to October 2023 were collected. The outcome measures included visual analog scale, Western Ontario and McMaster Universities Osteoarthritis Index score, Timed Up and Go test, and 36-item short form health survey. Literature quality analysis was performed using the Cochrane Manual recommended tool for risk assessment of bias in randomized controlled trials. Two researchers independently completed the data collection, collation, extraction and analysis. RevMan 5.4 and Stata 18.0 software were used to analyze and plot the obtained data. RESULTS: A total of 29 articles with acceptable quality were included, involving 1 633 patients with knee osteoarthritis. The studies involved four types of exercise: aerobic training, strength training, flexibility/skill training, and mindfulness relaxation training. (1) The results of network meta-analysis showed that compared with routine care/health education, aerobic training could significantly improve pain symptoms (SMD=-3.26, 95%CI: -6.33 to -0.19, P < 0.05); strength training (SMD=-0.79, 95%CI: -1.34 to -0.23, P < 0.05) and mindfulness relaxation training (SMD=-0.79, 95%CI: -1.23 to -0.34, P < 0.05) could significantly improve the function of patients. Aerobic training (SMD=-1.37, 95%CI: -2.24 to -0.51, P < 0.05) and mindfulness relaxation training (SMD=-0.41, 95%CI: -0.80 to -0.02, P < 0.05) could significantly improve the functional mobility of patients. Mindfulness relaxation training (SMD=0.70, 95%CI: 0.21-1.18, P < 0.05) and strength training (SMD=0.42, 95%CI: 0.03-0.81, P < 0.05) could significantly improve the quality of life of patients. (2) The cumulative probability ranking results were as follows: pain: aerobic training (86.6%) > flexibility/skill training (60.1%) > strength training (56.8%) > mindfulness relaxation training (34.7%) > routine care/health education (11.7%); Knee function: strength training (73.7%) > mindfulness relaxation training (73.1%) > flexibility/skill training (56.1%) > aerobic training (39.9%) > usual care/health education (7.6%); Functional mobility: aerobic training (94.7%) > mindfulness relaxation training (65.5%) > strength training (45.1%) > flexibility/skill training (41.6%) > routine care/health education (3.2%); Quality of life: mindfulness relaxation training (91.3%) > strength training (68.0%) > flexibility/skill training (44.3%) > aerobic training (34.0%) > usual care/health education (12.3%). CONCLUSION: (1) Exercise therapy is effective in the treatment of knee osteoarthritis, among which aerobic training has the best effect on relieving pain and improving functional mobility. Strength training and mindfulness relaxation training has the best effect on improving patients’ function. Mindfulness relaxation training has the best effect on improving the quality of life of patients. (2) Limited by the quality and quantity of the included literature, more high-quality studies are needed to verify it. [ABSTRACT FROM AUTHOR]

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Copyright of Nankai Business Review is the property of Nankai Business Review Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

男性≤55岁、女性≤65岁的冠心病患者称为早发冠心病,其常起病较急、无先兆、预后较差。因此,研究对早发冠心病具有高敏感性及特异性的血清学标志物具有重要意义。目前研究较多的血清学标志物主要有纤维蛋白原、尿酸、血小板参数、同型半胱氨酸、红细胞分布宽度、骨保护素等,其在早发冠心病发生、发展及预后等方面均发挥了重要作用。 [ABSTRACT FROM AUTHOR]