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In order to stop and reverse land degradation and curb the loss of biodiversity, the United Nations 2030 Agenda for Sustainable Development proposes to combat desertification. In this paper, a fractional vegetation–water model in an arid flat environment is studied. The pattern behavior of the fractional model is much more complex than that of the integer order. We study the stability and Turing instability of the system, as well as the Hopf bifurcation of fractional order α , and obtain the Turing region in the parameter space. According to the amplitude equation, different types of stationary mode discoveries can be obtained, including point patterns and strip patterns. Finally, the results of the numerical simulation and theoretical analysis are consistent. We find some novel fractal patterns of the fractional vegetation–water model in an arid flat environment. When the diffusion coefficient, d, changes and other parameters remain unchanged, the pattern structure changes from stripes to spots. When the fractional order parameter, β , changes, and other parameters remain unchanged, the pattern structure becomes more stable and is not easy to destroy. The research results can provide new ideas for the prevention and control of desertification vegetation patterns. [ABSTRACT FROM AUTHOR]

Background: Our previous studies have reported the down-regulation of EGFL8 correlates to the development and prognosis of colorectal and gastric cancer. The present study is carried out to explore the expression pattern and role of EGFL8 in hepatocellular carcinoma (HCC).Methods and Materials: EGFL8 expression in 102 cases of HCC tissues matched with adjacent non-tumorous liver tissues, a normal liver cell line and three liver cancer cell lines with different metastatic capacity was detected by reverse transcription-quantitative polymerase chain reaction (RT-qPCR) and Western blot. Moreover, the clinicopathological features and prognosis of HCC patients were correlated with expression of EGFL8. Subsequently, the gain-and loss-of-function experiments were carried out to investigate the biological function of EGFL8 in HCC. We also used N-[N-(3,5-Difluorophenacetyl-L-alanyl)]-(S)- phenylglycine t-butyl ester (DAPT), an inhibitor for Notch signaling pathway, in these experiments to verify the involvement of Notch signaling pathway in the effects of EGFL8. Additionally, a mouse model was established to investigate the effect of EGFL8 on metastasis of HCC cells. The expression of Notch signaling pathway in HCC cells and xenograft mouse tumors were detected by Western blot and immunohistochemistory.Results: The expression of EGFL8 was significantly decreased in HCC tissues and cell lines and EGFL8 down-regulation correlated to multiple nodules, vein invasion, high TNM stage and poor prognosis of HCC. Interestingly, the expression levels of EGFL8 in three liver cancer cell lines were negatively associated with their metastatic capacity. In vitro and in vivo experiments indicated that EGFL8 obviously suppressed metastasis and invasion of HCC cells but slightly promoted apoptosis. Meanwhile, the expression of Notch signaling pathway was obviously suppressed in EGFL8 overexpressed HCCLM3 cells and xenograft mouse tumors generated from these cells but markedly elevated in EGFL8 depleted Hep3B cells. Furthermore, the up-regulated expression of Notch signaling pathway and effects induced by EGFL8 knockdown in Hep3B cells could be counteracted by DAPT treatment.Conclusion: The down-regulation of EGFL8 was correlated to progression and poor prognosis of HCC and regulates HCC cell migration, invasion and apoptosis through activating the Notch signaling pathway, suggesting EGFL8 as a novel therapeutic target and a potential prognostic marker for HCC. [ABSTRACT FROM AUTHOR]

Due to the non-locality of fractional derivative, the analytical solution and good approximate solution of fractional partial differential equations are usually difficult to get. Reproducing kernel space is a perfect space in studying this type of equations, however the numerical results of equations by using the traditional reproducing kernel method (RKM) isn't very good. Based on this problem, we present the piecewise technique in the reproducing kernel space to solve this type of equations. The focus of this paper is to verify the stability and high accuracy of the present method by comparing the absolute error with traditional RKM and study the effect on absolute error for different values of α. Furthermore, we can study the distribution of entire space at a particular time period. Three numerical experiments are provided to verify the efficiency and stability of the proposed method. Meanwhile, it is tested by experiments that the change of the value of α has little effect on its accuracy. [ABSTRACT FROM AUTHOR]

The key of the reproducing kernel method (RKM) to solve the initial boundary value problem is to construct the reproducing kernel meeting the homogenous initial boundary conditions of the considered problems. The usual method is that the initial boundary conditions must be homogeneous and put them into space. Another common method is to put homogeneous or non-homogeneous conditions directly into the operator. In addition, we give a new numerical method of RKM for dealing with initial boundary value problems, homogeneous conditions are put into space, and for nonhomogeneous conditions, we put them into operators. The focus of this paper is to further verify the reliability and accuracy of the latter two methods. Through solving three numerical examples of integral-differential equations and comparing with other methods, we find that the two methods are useful. [ABSTRACT FROM AUTHOR]