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This paper is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilisation in distribution). This is the first paper in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilisation in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design the feedback controls in two structure cases: state feedback and output injection.

The backward Euler method is employed to approximate the invariant measure of a class of stochastic differential equations(SDEs) driven by α-stable processes. The existence and uniqueness of the numerical invariant measure is proved. Then the numerical invariant measure is shown to converge to the underlying invariant measure. Numerical examples are provided to demonstrate the theoretical results.

This paper is concerned with the stochastic stabilization problem for nonlinear systems by $G$ -Brownian motion with feedback control based on discrete-time state observations with a time delay. By constructing an auxiliary system, which is a continuous-time stochastic system driven by $G$ -Brownian motion, we establish a sufficient criterion in terms of the observation gap $\tau $ and the time delay $\tau _{0}$ to ensure the quasi-surely exponential stability of the stochastic controlled system. Moreover, implementation of the control strategy is provided. Finally, an example is given to demonstrate the theoretical result.

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of H∞ stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

In this paper, stationary distribution of stochastic differential equations (SDEs) with Markovian switching is approximated by numerical solutions generated by the stochastic θ method. We prove the existence and uniqueness of stationary distribution of the numerical solutions firstly. Then, the convergence of numerical stationary distribution to the underlying one is discussed. Numerical simulations are conducted to support the theoretical results.

Recently, a kind of feedback control based on discrete-time state observations was proposed to stabilize continuous-time hybrid stochastic systems in the mean-square sense. We find that the feedback control there still depends on the continuous-time observations of the mode. However, it usually costs to identify the current mode of the system in practice. So we can further improve the control to reduce the control cost by identifying the mode at discrete times when we make observations for the state. In this paper, we aim to design such a type of feedback control based on the discrete-time observations of both state and mode to stabilize the given hybrid stochastic differential equations (SDEs) in the sense of mean-square exponential stability. Moreover, a numerical example is given to illustrate our results.

This paper aims to stabilize hybrid stochastic differential equations (SDEs) with norm bounded uncertainties by feedback controls based on the discrete-time observations of both state and mode. The control structure appears only in the drift part (the deterministic part) of an SDE and the controlled system will be robustly exponentially stable in mean-square. Our stabilization criteria are in terms of linear matrix inequalities (LMIs) whence the feedback controls can be designed more easily in practice. An example is given to illustrate the effectiveness of our results.

Background Baihu-Guizhi decoction (BHGZD) has been extensively used for the treatment of rheumatoid arthritis (RA) with a satisfying therapeutic effect. However, the material basis and the underlying mechanisms of BHGZD against RA have not been fully elucidated. Purpose To investigate the chemical profile and the pharmacological mechanisms of BHGZD against RA. Methods The chemical constituents containing in BHGZD were identified using UFLC-Q-TOF-MS/MS system, and the corresponding putative targets were predicted. Then, the differentially expressed genes (DEGs) between adjuvant-induced arthritis (AIA) and normal control groups were identified using microarray analysis. After constructing the interaction network of “RA-related gene-BHGZD putative target”, BHGZD candidate targets against RA were screened by topological analysis and further experimentally validated based on AIA rat model. Results A total of 41 chemical constituents were identified in the water extract of BHGZD, which were predicted to hit 1312 putative targets. Additionally, 26 DEGs between the AIA and normal control groups were defined as “RA-related genes”, which were functionally involved into the imbalance of “inflammation-immune” system during RA progression. On the basis of the topological importance in the network of “RA-related gene-BHGZD putative target”, 177 BHGZD candidate targets against RA were identified. Among them, TLR4, c-Fos/AP-1, IL2 and TNF had direct interactions with each other and also function as crucial components of toll-like receptor and T cell receptor signaling pathways, which may play important roles in maintaining the balance of "inflammation-immune" system. Experimentally, we verified that BHGZD dose-dependently attenuated the severity, pathological changes, as well as mechanical, cold, and heat hypersensitivities during RA progression based on the AIA rat model. Further western blot analysis demonstrated that BHGZD significantly reduced the protein levels of TLR4, c-Fos/AP-1, IL2 and TNF, which were induced by RA modeling, in the inflamed joints of AIA rats (all p Conclusion This study combining the chemical and transcriptomic profilings, target prediction, network calculation and experimental validations identifies the chemical constituents containing in BHGZD and offers the convincing evidence that BHGZD may ameliorate RA partially by restoring the balance of "inflammation-immune" system and subsequently reversing the pathological events during RA progression through regulating the TLR4-c-Fos-IL2-TNF axis.

This paper deals with the robust stabilization of continuous-time hybrid stochastic systems with time-varying delay by feedback controls based on discrete-time state observations. By employing the Razumikhin technique, delay-independent criteria to determine controllers and time lags are established just under a weaker condition that the time-varying delay should be a bounded function. Meanwhile, for the nondelay system, we obtain a better bound on the duration τ between two consecutive state observations. The new theory developed in this paper improves the existing results. Numerical examples are provided to demonstrate the effectiveness of our results.

The present study developed a systematic method for the degradation products and dynamics of valtrate in artificial intestinal fluid and gastric fluid. HPLC-electrospray tandem mass spectrometry (HPLC-ESI-MSn) was applied to separate the degradation products of valtrate and identify structures of the main degradation products. Samples were separated on an Agilent Extend-Cl8 by gradient elution using acetonitrile and water–acetic acid (0.25%, v/v). Analysis was performed in positive ion mode with 3000 V of capillary voltage, 40 psi of atomization pressure, 10 L min−1 dry nitrogen gas velocity, and m/z 100–1000 of scan range. Six degradation products were all identified to own the stem-nucleus structures of baldrinals. Two of them were identified through the reference substances. An HPLC method with isocratic elution using acetonitrile and water (68:32, v/v) at 254 nm was established to determine content change of valtrate in artificial intestinal fluid and gastric fluid at different time points. The method...

Recently, Mao (2013) discusses the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao (2013) also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will consider a couple of important classes of hybrid SDEs. Making full use of their special features, we will be able to establish a better bound on τ. Our new theory enables us to observe the system state less frequently (so costs less) but still to be able to design the feedback control based on the discrete-time state observations to stabilize the given hybrid SDEs in the sense of mean-square exponential stability.

Ixeris sonchifolia Hance, a normal perennial herb, has effects on appendicitis, headache, menstruation, blood circulation, blood stasis, pain, fibrinolytic enzymes, thrombus formation, coronary artery, myocardial infarct size, PGI2, ET, TXA2, TNF-,?IL-6 and IL-8, etc . However, there was no full coverage about the molecular basis and gene targets of Ixeris sonchifolia injection. PubChem Database and DAVID Database had been used conjunctively to detect the gene IDs, gene targets and their functions. There were 3008 genes found in the final results, 16 kinds of definite functions had been detected, 9 of which had been proved and the effects were focused on the psychological, immune, neurological, metabolic, cardiovascular and cancer functions. Ixeris sonchifoliahad a wide effects on various symptoms, which had been reported by previous experiments and verified by this research; however its influences on aging, chemdependency, developmental, normalvariation, reproduction, pharmacogenomic and psychologic functions should be confirmed in the future experiments.

Dianbaizhu, a folk medicine from Gaultheria leucocarpa BLUME var. yunnanensis (FRANCH.) T. Z. HSU & R. C. FANG (Ericaceae) used as an antirheumatic, has multiple plant origins and officinal parts. A rapid high-performance liquid chromatography with diode array detector (HPLC-DAD) method was established for the simultaneous determination of the characteristic ingredient methyl benzoate-2-O-β-D-glucopyranosyl(1 → 2) [O-β-D-xylopyranosyl(1 → 6)]-O-β-D-glucopyranoside and seven bioactive constituents in eight Gaultheria species. This chromatographic method is precise, accurate, and stable. Kruskal-Wallis analysis, hierarchical cluster analysis, and factor analysis were used to analyze the content of reference compounds in different Gaultheria species and officinal parts. The analyses showed significant differences (p 0.05) in their medicinal parts. G. leucocarpa var. yunnanensis appeared to the best among the Gaultheria species tested for the treatment of rheumatic diseases. Taken together, the results show that this simultaneous quantification of multiple active constituents using HPLC-DAD combined with chemometrics can be reliably applied to evaluate the quality of Dianbaizhu.

(-)-Epicatechin (EC), an optical antipode of (+)-catechin (C), possesses many potential significant health benefits. However, the in vivo metabolic pathway of EC has not been clarified yet. In this study, an efficient strategy based on ultra-high performance liquid chromatography coupled with a linear ion trap-Orbitrap mass spectrometer was developed to profile and characterize EC metabolites in rat urine, faeces, plasma, and various tissues. Meanwhile, post-acquisition data-mining methods including high-resolution extracted ion chromatogram (HREIC), multiple mass defect filters (MMDFs), and diagnostic product ions (DPIs) were utilized to screen and identify EC metabolites from HR-ESI-MS

The Chinese folk medicine Dianbaizhu, consisting of Gaultheria species, is widely used for the treatment of rheumatoid arthritis by several minority nationalities. The species and plant parts of this genus used as Dianbaizhu in clinical application are confused. In order to elucidate the species and the medicinal parts, as well as to ascertain the effective components and the probable optimal source of Dianbaizhu, the different plant parts and polarity fractions of its mainstream species, G. leucocarpa var. yunnanensis were investigated. The inhibition of nitric oxide and tumor necrosis factor produced in macrophage J774 were used to assess the anti-inflammatory effect of those samples. G. leucocarpa var. yunnanensis may be the preferred species for anti-RA effect. The underground parts of this taxon showed the best anti-inflammatory and anti-RA activities; the n-butanol and water fractions of the underground parts may be the most anti-RA active.

Recently, Mao [Automatica J. IFAC, 49 (2013), pp. 3677--3681] initiated the study the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. In the same paper Mao also obtains an upper bound on the duration $\tau$ between two consecutive state observations. However, it is due to the general technique used there that the bound on $\tau$ is not very sharp. In this paper, we will be able to establish a better bound on $\tau$ making use of Lyapunov functionals. We will discuss the stabilization not only in the sense of exponential stability (as Mao does in [Automatica J. IFAC, 49 (2013), pp. 3677--3681]) but also in other sense---that of $H_\infty$ stability or asymptotic stability. We will consider not only the mean square stability but also the almost sure stability.

Dianbaizhu, a folk medicine from Gaultheria leucocarpa BLUME var. yunnanensis (FRANCH.) T. Z. HSUR. C. FANG (Ericaceae) used as an antirheumatic, has multiple plant origins and officinal parts. A rapid high-performance liquid chromatography with diode array detector (HPLC-DAD) method was established for the simultaneous determination of the characteristic ingredient methyl benzoate-2-O-β-D-glucopyranosyl(1 → 2) [O-β-D-xylopyranosyl(1 → 6)]-O-β-D-glucopyranoside and seven bioactive constituents in eight Gaultheria species. This chromatographic method is precise, accurate, and stable. Kruskal-Wallis analysis, hierarchical cluster analysis, and factor analysis were used to analyze the content of reference compounds in different Gaultheria species and officinal parts. The analyses showed significant differences (p0.05) in Gaultheria species but few differences (p0.05) in their medicinal parts. G. leucocarpa var. yunnanensis appeared to the best among the Gaultheria species tested for the treatment of rheumatic diseases. Taken together, the results show that this simultaneous quantification of multiple active constituents using HPLC-DAD combined with chemometrics can be reliably applied to evaluate the quality of Dianbaizhu.

The Chinese folk medicine Dianbaizhu, consisting of Gaultheria species, is widely used for the treatment of rheumatoid arthritis by several minority nationalities. The species and plant parts of this genus used as Dianbaizhu in clinical application are confused. In order to elucidate the species and the medicinal parts, as well as to ascertain the effective components and the probable optimal source of Dianbaizhu, the different plant parts and polarity fractions of its mainstream species, G. leucocarpa var. yunnanensis were investigated. The inhibition of nitric oxide and tumor necrosis factor produced in macrophage J774 were used to assess the anti-inflammatory effect of those samples. G. leucocarpa var. yunnanensis may be the preferred species for anti-RA effect. The underground parts of this taxon showed the best anti-inflammatory and anti-RA activities; the n-butanol and water fractions of the underground parts may be the most anti-RA active.