Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations

Asymptotic stability and boundedness have been two of most popular topics in the study of stochastic functional differential equations (SFDEs) (see e.g. Appleby and Reynolds (2008), Appleby and Rodkina (2009), Basin and Rodkina (2008), Khasminskii (1980), Mao (1995), Mao (1997), Mao (2007), Rodkina and Basin (2007), Shu, Lam, and Xu (2009), Yang, Gao, Lam, and Shi (2009), Yuan and Lygeros (2005) and Yuan and Lygeros (2006)). In general, the existing results on asymptotic stability and boundedness of SFDEs require (i) the coefficients of the SFDEs obey the local Lipschitz condition and the linear growth condition; (ii) the diffusion operator of the SFDEs acting on a C2,1-function be bounded by a polynomial with the same order as the C2,1-function. However, there are many SFDEs which do not obey the linear growth condition. Moreover, for such highly nonlinear SFDEs, the diffusion operator acting on a C2,1-function is generally bounded by a polynomial with a higher order than the C2,1-function. Hence the existing criteria on stability and boundedness for SFDEs are not applicable andwesee the necessity to develop new criteria. Our main aim in this paper is to establish new criteria where the linear growth condition is no longer needed while the up-bound for the diffusion operator may take a much more general form

Stochastic population dynamics under regime switching II

AbstractThis is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69–84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population

Stabilisation of hybrid stochastic differential equations by feedback control based on discrete-time observations of state and mode

Mao [10] recently initiated the study of the mean-square exponential stabilisation of continuous-time hybrid stochastic differential equations (SDEs) by the feedback controls based on the discrete-time observations of the state. However, the feedback controls still depend on the continuous-time observations of the mode. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the discrete-time observations of both state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE

Stochastic population dynamics under regime switching II

This is a continuation of our paper [Q. Luo, X. Mao, Stochastic population dynamics under regime switching, J. Math. Anal. Appl. 334 (2007) 69-84] on stochastic population dynamics under regime switching. In this paper we still take both white and color environmental noise into account. We show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population. In some special but important situations we precisely describe the limit of the average in time of the population

Emotional abuse and depressive symptoms among the adolescents: the mediation effect of social anxiety and the moderation effect of physical activity

BackgroundChildhood maltreatment has been identified as a risk factor for depressive symptoms. Social anxiety is closely associated with depression. Physical activity has been regarded as an underlying protective factor. Little is known about the complex relations among these factors in Chinese middle school students. This study aimed to explore whether social anxiety mediated the association between childhood maltreatment and depressive symptoms and investigate whether physical activity moderated the indirect or direct effect of the mediation model.MethodsA total of 1,570 middle school students were recruited and measured for childhood maltreatment (measured by Childhood Trauma Questionnaire—Short Form Chinese version), social anxiety (as the mediator, measured by the Chinese simplified version of Social Anxiety Scale for Adolescents), depressive symptoms (measured by the Chinese version of Depression Anxiety Stress Scales-21), physical activity (as the moderator), and covariates such as age, sex, and nationality. The proposed relationships were tested using mediation and moderated mediation models.ResultsEmotional abuse was directly associated with depression, and the association between emotional abuse and depression was partially mediated by social anxiety. The associations between emotional abuse with depression and with social anxiety were moderated by physical activity.ConclusionThis study revealed the mediating role of social anxiety and the moderating role of physical activity between emotional abuse and depression, which emphasizes the potential benefits of sufficient physical activity to reduce social anxiety and depressive symptoms, and more intervention studies should be conducted to explore the direct influence of sufficient physical activity in the future

Noise suppresses or expresses exponential growth

In this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially. On the other hand, we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially. In other words, we reveal that the noise can suppress or expresses exponential growth

Effect of Adenosine 5’-Diphosphate Ribosylation on Meat Quality of Qinchuan Cattle

This study addressed the effect of adenosine 5’-diphosphate (ADP) ribosylation on the mitochondrial function and quality of Qinchuan cattle meat during early postmortem aging. The Longissimus dorsi muscle of Qinchuan cattle treated with 20 µmol/L rucaparib, a poly(ADP-ribose) polymerase 1 (PARP1) inhibitor, were evaluated for mitochondrial indices, myofibrillar fragmentation index (MFI), shear force, pH, and other quality indices after being stored for 0 h, 6 h, 12 h, 2 d, 4 d, and 8 d and the expression levels of PARP1 and desmin were detected using Western blot. The results showed that the content of reactive oxygen species (ROS) in the treated group was significantly lower than that in the control group (P < 0.05) during 0 h–8 d (except 12 h) after slaughter. The caspase-3 activity and MFI in the treated group were significantly lower than those in the control group (P < 0.05) during 0–12 h. Mitochondrial membrane potential during 2–4 d as well as succinate dehydrogenase (SDH) activity during 4–8 d were significantly higher in the treated group than in the control group (P < 0.05). These findings indicate that PARP1 inhibition, which characterizes ADP ribosylation, can slow down the decrease in mitochondrial membrane potential and increase SDH activity, preserving mitochondrial function to some extents and delaying the decrease in MFI and the degradation of desmin and thereby meat tenderization

Epidemiology of Sleep Disturbances and Their Effect on Psychological Distress During the COVID-19 Outbreak: A Large National Study in China

Background: The purpose of the current study was to assess the prevalence of sleep disturbances among Chinese people during the COVID-19 pandemic in a large national survey, analyze the relationship between sleep disturbances and mental health status, and explore the influencing factors of the relationship between sleep disturbances and mental health status.Methods: An online survey was accessed by 19,740 people throughout China from February 14 to 21, 2020. The survey included the Depression Anxiety Stress Scale-21 (DASS-21) to measure psychological distress and two questions about sleep disturbances. Logistic regression analyses and moderation analysis were performed.Results: (1) Among the 14,505 respondents included in analyses, 3,783 (26.08%) reported sleep disturbances at least 3 days during the past week. (2) Sleep disturbances increased the risk of depression, anxiety, and stress (p &lt; 0.05). (3) Gender, age, education, occupation, frequency of attending to epidemic information, nervousness about supplies, receiving provisions of living necessities from the service department during the outbreak, number of correct responses to questions about the epidemic, and isolation/quarantine affected the risk of mental health problems among participants experiencing sleep disturbances (p &lt; 0.05). (4) A moderation analysis found that sleep problems were more likely to affect depression, anxiety, and stress scores in men than women during the COVID-19 outbreak.Conclusion: During the COVID-19 outbreak, 26.08% people surveyed experienced sleep disturbances, and the presence of sleep disturbances was positively related to depression, anxiety, and stress, especially among front-line anti-epidemic workers, younger people, people living in isolation/quarantine, people with a college or greater education, and males

Modeling habitat suitability for Yunnan Snub-nosed monkeys in Laojun Mountain National Park

We provide new information on Yunnan snub-nosed monkey (Rhinopithecus bieti) behavioral ecology, contributing to future conservation efforts within the Laojun Mountain National Park. Habitat evaluation procedures are used to quantify the value of land as a habitat for a species. We analyzed environmental variables hypothesized to influence habitat suitability for Yunnan snub-nosed monkeys, and mapped the distribution of suitable habitats across the study area and adjacent areas. Spatial analysis with GPS data was conducted to investigate home-range change of these monkeys. Predictor variables were generated using ArcMap and R programming language. We prepared 34 environmental variables at 30-m spatial resolution. Maxent was used to analyze environmental variables that contributed to suitability. Using satellite remote sensing and GIS, we modeled the distribution of suitable habitat for Yunnan snub-nosed monkeys in the Jinsichang area of the Laojun Mountains in China. This study did not describe the frequency or intensity of habitat use. Habitat suitability was affected by several variables, the most influential, as determined by permutation importance, being mean diurnal temperature range (31.6%), precipitation during the wettest quarter of the year (30.4%), average annual precipitation (17%), normalized difference vegetation index (5%), wetness (4.6%), and aspect (4.5%). This habitat suitability model provides information about the current distribution of Yunnan snub-nosed monkeys, which is important for appropriate implementation of conservation actions