Multiplicities of Eigenvalues of the Diffusion Operator with Random Jumps from the Boundary

This paper deals with a non-self-adjoint differential operator which is associated with a diffusion process with random jumps from the boundary. Our main result is that the algebraic multiplicity of an eigenvalue is equal to its order as a zero of the characteristic function $\Delta(\lambda)$. This can be used to determine the multiplicities of eigenvalues for concrete operators

Eupatilin attenuates diabetic nephropathy by upregulating matrix metalloproteinase-9 expression in diabetic rat kidney

Purpose: To evaluate the nephro-protective effect of eupatilin in diabetic nephropathic (DN) rats.Method: Diabetes was induced by intraperitoneal administration of streptozotocin (STZ, 55 mg/kg) and confirmed by fasting blood glucose results, while DN was determined by measuring serum urea and creatinine levels on day 40 after STZ administration. The eupatilin-treated group received eupatilin at 50 and 100 mg/kg, p.o. for 20 days, after which blood levels of some biochemical parameters, glomerulosclerosis index, eosinophilic cast index, and expression of MMP-9 were determined using standard procedures.Results: Treatment with eupatilin significantly decreased serum levels of glucose, creatinine and urea, and increased creatinine clearance, compared to the negative control group. Moreover, eupatilin attenuated changes in kidney histopathology, and significantly enhanced the expression of MMP-9 in the kidney tissues of the DN rats, relative to negative control group.Conclusion: These results indicate that eupatilin attenuates renal failure in STZ-induced DN rats by upregulating the expression of MMP-9.Keywords: Eupatilin, Streptozotocin, Diabetic nephropathy, MMP-

Li-rich and super Li-rich giants produced by element diffusion

Context. About 0.2-2% of giant stars are Li-rich, whose lithium abundance (A(Li)) is higher than 1.5 dex. Among them, near 6% are super Li-rich with A(Li) exceeding 3.2 dex. Meanwhile, the formation mechanism of these Li-rich and super Li-rich giants is still under debate. Aims. Considering the compact He core of red giants, attention is paid to the effect of element diffusion on A(Li). In particular, when the He core flash occurs, the element diffusion makes the thermohaline mixing zone extend inward and connect to the inner convection region of stars. Then, a large amount of 7Be produced by the He flash can be transferred to stellar surface, finally turning into 7Li. Thus, the goal of this work is to propose the mechanism of A(Li) enrichment and achieve the consistency between the theoretical and observation data. Methods. Using the Modules for Experiments in Stellar Astrophysics (MESA), we simulate the evolution of low-mass stars, with considering the effects of element diffusion on the Li abundances. The timescale ratio of Li-rich giants to normal giants is estimated by population synthesis method. Then we get the theoretical value of A(Li) and make a comparison with observations. Results. Considering the influence of element diffusion in the model results in the increase of lithium abundance up to about 1.8dex, which can reveal Li-rich giants. Simultaneously, introducing high constant diffusive mixing coefficients (Dmix) with the values from 10e11 to 10e15in the model allows A(Li) to increase from 2.4 to 4.5dex, which can explain the most of Li-rich and super Li-rich giant stars. The population synthesis method reveals that the amount of Li-rich giants among giants is about 0.2-2%, which is consistent with observation estimated levels

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Interaction Embeddings for Prediction and Explanation in Knowledge Graphs

Knowledge graph embedding aims to learn distributed representations for entities and relations, and is proven to be effective in many applications. Crossover interactions --- bi-directional effects between entities and relations --- help select related information when predicting a new triple, but haven't been formally discussed before. In this paper, we propose CrossE, a novel knowledge graph embedding which explicitly simulates crossover interactions. It not only learns one general embedding for each entity and relation as most previous methods do, but also generates multiple triple specific embeddings for both of them, named interaction embeddings. We evaluate embeddings on typical link prediction tasks and find that CrossE achieves state-of-the-art results on complex and more challenging datasets. Furthermore, we evaluate embeddings from a new perspective --- giving explanations for predicted triples, which is important for real applications. In this work, an explanation for a triple is regarded as a reliable closed-path between the head and the tail entity. Compared to other baselines, we show experimentally that CrossE, benefiting from interaction embeddings, is more capable of generating reliable explanations to support its predictions.Comment: This paper is accepted by WSDM201

Robust H∞ finite-horizon filtering with randomly occurred nonlinearities and quantization effects

The official published version of this article can be found at the link below.In this paper, the robust H∞ finite-horizon filtering problem is investigated for discrete time-varying stochastic systems with polytopic uncertainties, randomly occurred nonlinearities as well as quantization effects. The randomly occurred nonlinearity, which describes the phenomena of a nonlinear disturbance appearing in a random way, is modeled by a Bernoulli distributed white sequence with a known conditional probability. A new robust H∞ filtering technique is developed for the addressed Itô-type discrete time-varying stochastic systems. Such a technique relies on the forward solution to a set of recursive linear matrix inequalities and is therefore suitable for on-line computation. It is worth mentioning that, in the filtering process, the information of both the current measurement and the previous state estimate is employed to estimate the current state. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany