This paper addresses the fixed-time leader-follower consensus problem for second-order multiagent systems without velocity measurement. A new continuous fixed-time distributed observer-based consensus protocol is developed to achieve consensus in a bounded finite time fully independent of initial condition. A rigorous stability proof of the multiagent systems by output feedback control is presented based on the bi-limit homogeneity and the Lyapunov technique. Finally, the efficiency of the proposed methodology is illustrated by numerical simulation.

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Epidemiological studies have found obesity to be a risk factor for women's breast cancer. The present study was to investigate whether there is a relationship between serum levels of leptin, insulin, and lipids and breast cancer incidence, in order to find experimental evidence that would be helpful in the diagnosis and prevention of breast cancer. Blood samples were collected from 130 patients with mammary disease and 103 healthy control subjects. Serum leptin, insulin, and lipids were determined by radioimmunoassay (RIA), enzyme-linked immunosorbent assays (ELISA), and Biochemistry Auto-analyzer, respectively. The data analysis was performed by use of the SPSS10.0 computer software. We found that the serum levels of leptin, insulin, and triglyceride (TG) were clearly higher in patients with breast cancer than in patients with benign breast disease and healthy controls, while serum HDL-C levels were lower in breast cancer patients (p < 0.03). Moreover, serum leptin levels were significantly correlated with BMI (body mass index) among three groups, whereas serum insulin levels were unrelated to BMI among three groups. Furthermore, the serum levels of leptin and insulin were not associated with menopausal status in patients with mammary disease (p > 0.05); however, the serum levels of F-Chol, T-Chol, TG, LDL-C, and APOB were significant higher in postmenopausal cases than those in premenopausal cases (p < 0.025). Interestingly, logistic regression analysis showed that subjects with elevated serum levels of leptin, insulin, TG, APOA1, and reduced level of serum HDL-C displayed increased risk of developing breast cancer than those with the normal levels, respectively. In conclusion, the present study suggested that aberrant serum levels of leptin, insulin, and lipids might play an important role in carcinogenesis of breast cancer. The elevated serum levels of leptin, insulin, TG, APOA1, and reduced level of serum HDL-C may be correlated with increased risk of breast cancer, suggesting that one way of preventing breast cancer would be carried out by controlling the intake of food.

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We evaluated the relationship among the leptin receptor (LEPR) gene Gln223Arg polymorphism, body mass index (BMI), waist and hip circumference ratio (WHR), dietary structure, lifestyle, and other biomarkers with breast cancer and determined whether they could be effective for the prevention and treatment of breast cancer. The Gln223Arg polymorphisms in the LEPR gene were investigated in blood deoxyribonucleic acid (DNA) available for 240 breast cancer cases and 500 controls. Genotyping was performed by polymerase chain reaction-restriction fragment length polymorphism. Leptin, insulin were determined by enzyme-linked immunosorbent assays. We found that the serum levels of leptin, insulin, triglyceride (TG), free cholesterol (FCH), apolipoprotain (APO) A1, and BMI were significantly higher in breast cancer cases than the controls, while physical activity was clearly less in breast cancer cases (P < 0.02 approximately P < 0.001, respectively). Moreover, there were significant association between the Gln223Arg genotype and breast cancer risk; homozygotes for AA and heterozygotes for AG,AG + GG genotypes had been proved to increase the risk of breast cancer, and their corresponding odds ratio were 7.14 (95% confidence interval [CI] = 1.92-25.64), 1.33(95% CI = 1.03-2.70), and 2.04 (95% CI = 1.09-3.82). Interestingly, logistic regression analysis showed that LEPR gene Gln223Arg polymorphism and elevated leptin, insulin, TG, FCH, APOA1, WHR, and reduced APOB increased the risk of developing breast cancer, respectively. And, it also suggested that LEPR gene Gln223Arg polymorphisms, elevated leptin, insulin, TG, FCH, APOA1, WHR, and reduced APOB should play a major role in the development of breast cancer.

SummaryA continuous multivariable output feedback control scheme is developed for trajectory tracking and attitude stabilization of quadrotor helicopters. The whole closed-loop system is composed by position loop and attitude loop. The homogeneous technique is used to design finite-time stabilizing controller and observer in each loop. The virtual control is introduced in position loop to ensure that the real control is smooth enough such that it can be tracked by attitude loop. The finite-time stability of the closed-loop system is guaranteed through homogeneity and Lyapunov analysis. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.

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