Delay dependent stability of highly nonlinear hybrid stochastic systems

There are lots of papers on the delay dependent stability criteria for differential delay equations (DDEs), stochastic differential delay equations (SDDEs) and hybrid SDDEs. A common feature of these existing criteria is that they can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions (namely, satisfy the linear growth condition). In other words, there is so far no delay-dependent stability criterion on nonlinear equations without the linear growth condition (we will refer to such equations as highly nonlinear ones). This paper is the first to establish delay dependent criteria for highly nonlinear hybrid SDDEs. It is therefore a breakthrough in the stability study of highly nonlinear hybrid SDDE

Structured robust stability and boundedness of nonlinear hybrid delay systems

Taking different structures in different modes into account, the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations (SDDEs) without the linear growth condition. A new Lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes. Moreover, a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition

Female chromosome X mosaicism is age-related and preferentially affects the inactivated X chromosome

To investigate large structural clonal mosaicism of chromosome X, we analysed the SNP microarray intensity data of 38,303 women from cancer genome-wide association studies (20,878 cases and 17,425 controls) and detected 124 mosaic X events >2 Mb in 97 (0.25%) women. Here we show rates for X-chromosome mosaicism are four times higher than mean autosomal rates; X mosaic events more often include the entire chromosome and participants with X events more likely harbour autosomal mosaic events. X mosaicism frequency increases with age (0.11% in 50-year olds; 0.45% in 75-year olds), as reported for Y and autosomes. Methylation array analyses of 33 women with X mosaicism indicate events preferentially involve the inactive X chromosome. Our results provide further evidence that the sex chromosomes undergo mosaic events more frequently than autosomes, which could have implications for understanding the underlying mechanisms of mosaic events and their possible contribution to risk for chronic diseases

Female chromosome X mosaicism is age-related and preferentially affects the inactivated X chromosome

To investigate large structural clonal mosaicism of chromosome X, we analysed the SNP microarray intensity data of 38,303 women from cancer genome-wide association studies (20,878 cases and 17,425 controls) and detected 124 mosaic X events42Mb in 97 (0.25%) women. Here we show rates for X-chromosome mosaicism are four times higher than mean autosomal rates; X mosaic events more often include the entire chromosome and participants with X events more likely harbour autosomal mosaic events. X mosaicism frequency increases with age (0.11% in 50-year olds; 0.45% in 75-year olds), as reported for Y and autosomes. Methylation array analyses of 33 women with X mosaicism indicate events preferentially involve the inactive X chromosome. Our results provide further evidence that the sex chromosomes undergo mosaic events more frequently than autosomes, which could have implications for understanding the underlying mechanisms of mosaic events and their possible contribution to risk for chronic diseases

Detectable clonal mosaicism and its relationship to aging and cancer

In an analysis of 31,717 cancer cases and 26,136 cancer-free controls from 13 genome-wide association studies, we observed large chromosomal abnormalities in a subset of clones in DNA obtained from blood or buccal samples. We observed mosaic abnormalities, either aneuploidy or copy-neutral loss of heterozygosity, of >2 Mb in size in autosomes of 517 individuals (0.89%), with abnormal cell proportions of between 7% and 95%. In cancer-free individuals, frequency increased with age, from 0.23% under 50 years to 1.91% between 75 and 79 years (P = 4.8 × 10(-8)). Mosaic abnormalities were more frequent in individuals with solid tumors (0.97% versus 0.74% in cancer-free individuals; odds ratio (OR) = 1.25; P = 0.016), with stronger association with cases who had DNA collected before diagnosis or treatment (OR = 1.45; P = 0.0005). Detectable mosaicism was also more common in individuals for whom DNA was collected at least 1 year before diagnosis with leukemia compared to cancer-free individuals (OR = 35.4; P = 3.8 × 10(-11)). These findings underscore the time-dependent nature of somatic events in the etiology of cancer and potentially other late-onset diseases

Health Assessment of a Small Watershed on the Loess Plateau *

Abstract: A health ecosystem is the aim of building a nice Loess Plateau with green mountain and clear river. This paper, taking Zhifanggou small watershed as an example, by using the AHP (Analytic Hierarchy Process) selecting the woodland and pasture cover, area of fundamental cropland, soil anti-scourability, soil organic matter, output/input, crop yield, net incomes of per capita and benefit of reducing the soil erosion etc. analyzed the improvement process in ecosystem rehabilitation. The result showed that after about 20 years of soil conservation practice and restoration, the ecosystem health index of the watershed has improved from 0.178 in 1985 to 0.707 in 1999 experiencing initial restoration, stable improvement and coming to fine development period. This research introduced the new indicators of soil anti-scourability, soil organic matter content and gave the different weight value of indicators in health index calculation in restoration process

Advances in the truncated Euler-Maruyama method for stochastic differential delay equations

Guo et al. [GMY17] are the first to study the strong convergence of the explicit numerical method for the highly nonlinear stochastic differential delay equations(SDDEs) under the generalised Khasminskii-type condition. The method used there is the truncated Euler–Maruyama (EM) method. In this paper we will point out that a main condition imposed in [GMY17] is somehow restrictive in the sense that the condition could force the step size to be so small that the truncated EM method would be inapplicable. The key aim of this paper is then to establish the convergence rate without this restriction

Investigation of inter-rater and test-retest reliability of Y balance test in college students with flexible flatfoot

Abstract Background The Lower Quarter Y Balance Test (YBT-LQ) has been widely used to assess dynamic balance in various populations. Dynamic balance in flexible flatfoot populations is one of the risk factors for lower extremity injuries, especially in college populations in which more exercise is advocated. However, no study has demonstrated the reliability of the YBT-LQ in a college student flexible flatfoot population. Methods A cross-sectional observational study. 30 college students with flexible flatfoot were recruited from Beijing Sports University. They have been thrice assessed for the maximal reach distance of YBT under the support of the lower limb on the flatfoot side. Test and retest were performed with an interval of 14 days. The outcome measures using the composite score and normalized maximal reach distances in three directions (anterior, posteromedial, and posterolateral). The relative reliability was reported as the Intraclass Correlation Coefficient (ICC). Minimal Detectable Change (MDC), Smallest worthwhile change (SWC), and Standard Error of Measurement (SEM) were used to report the absolute reliability. Results For inter-rater reliability, the ICC values for all directions ranged from 0.84 to 0.92, SEM values ranged from 2.01 to 3.10%, SWC values ranged from 3.67 to 5.12%, and MDC95% values ranged from 5.58 to 8.60%. For test-retest reliability, the ICC values for all directions ranged from 0.81 to 0.92, SEM values ranged from 1.80 to 2.97%, SWC values ranged from 3.75 to 5.61%, and MDC95% values ranged from 4.98 to 8.24%. Conclusions The YBT-LQ has “good” to “excellent” inter-rater and test-retest reliability. It appears to be a reliable assessment to use with college students with flexible flatfoot. Trial registration This trial was prospectively registered at the Chinese Clinical Trial Registry with the ID number ChiCTR2300075906 on 19/09/2023