Wavelet-Galerkin Method for Identifying an Unknown Source Term in a Heat Equation

We consider the problem of identification of the unknown source in a heat equation. The problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. Meyer wavelets have the property that their Fourier transform has compact support. Therefore, by expanding the data and the solution in the basis of the Meyer wavelets, high-frequency components can be filtered away. Under the additional assumptions concerning the smoothness of the solution, we discuss the stability and convergence of a wavelet-Galerkin method for the source identification problem. Numerical examples are presented to verify the efficiency and accuracy of the method

MicroRNA-200c overexpression inhibits tumorigenicity and metastasis of CD117+CD44+ ovarian cancer stem cells by regulating epithelial-mesenchymal transition

BACKGROUND: Cancer stem cells (CSCs) are believed to be ‘seed cell’ in cancer recurrence and metastasis. MicroRNAs (miRNAs) can play an important role in the progression of primary tumor towards metastasis by regulating the epithelial-mesenchymal transition (EMT). The goal of this study was to investigate the effect of miRNA-200c overexpression on the EMT, tumorigenicity and metastasis of epithelial ovarian cancer (EOC) CSCs. METHODS: The EOC CD117(+)CD44(+)CSCs were isolated from the human ovarian cancer cell line SKOV3 by using a magnetic-activated cell sorting system, and the lentivirus miR-200c transduced CSCs were then selected for the study. The assays of colony forming, wound healing, cellular migration in vitro and tumor progression in vivo were performed. RESULTS: The miR-200c expression was reduced in the CD117(+)CD44(+)CSCs compared with the non-CD117(+)CD44(+)CSCs. However, the stable overexpression of the miR-200c in the CD117(+)CD44(+)CSCs resulted in a significant down-regulation of ZEB-1 and the Vimentin expression, an upregulation of the E-cadherin expression as well as a decrease of colony forming, migratory and invasion in vitro. Importantly, the miR-200c overexpression significantly inhibited the CD117(+)CD44(+)CSCs xenograft growth and lung metastasis in vivo in nude mice by inhibition of the EMT. In addition, the down-regulation of ZEB-1 showed the same efficacy as the miR-200c overexpression in the CD117(+)CD44(+)CSCs. CONCLUSION: These findings from this study suggest that the miR-200c overexpression may be considered a critical approach for the EOC CD117(+)CD44(+)CSCs in clinical trials

Incidence and Etiology of Drug-Induced Liver Injury in Mainland China

Background & Aims: We performed a nationwide, retrospective study to determine the incidence and causes of drug-induced liver injury (DILI) in mainland China.Methods: We collected data on a total of 25,927 confirmed DILI cases, hospitalized from 2012 through 2014 at 308 medical centers in mainland China. We collected demographic, medical history, treatment, laboratory, disease severity, and mortality data from all patients. Investigators at each site were asked to complete causality assessments for each case whose diagnosis at discharge was DILI (n=29,478) according to the Roussel Uclaf Causality Assessment Method.Results: Most cases of DILI presented with hepatocellular injury (51.39%; 95% CI, 50.76–52.03), followed by mixed injury (28.30%; 95% CI, 27.73–28.87) and cholestatic injury (20.31%; 95% CI, 19.80–20.82). The leading single classes of implicated drugs were traditional Chinese medicines or herbal and dietary supplements (26.81%) and anti-tuberculosis medications (21.99%). Chronic DILI occurred in 13.00% of the cases and, although 44.40% of the hepatocellular DILI cases fulfilled Hy’s Law criteria, only 280 cases (1.08%) progressed to hepatic failure, 2 cases underwent liver transplantation (0.01%), and 102 patients died (0.39%). Among deaths, DILI was judged to have a primary role in 72 (70.59%), a contributory role in 21 (20.59%), and no role in 9 (8.82%). Assuming the proportion of DILI in the entire hospitalized population of China was represented by that observed in the 66 centers where DILI capture was complete, we estimated the annual incidence in the general population to be 23.80 per 100,000 persons (95% CI, 20.86–26.74). Only hospitalized patients were included in this analysis, so the true incidence is likely to be higher.Conclusions: In a retrospective study to determine the incidence and causes of drug-induced liver injury (DILI) in mainland China, the annual incidence in the general population was estimated to be 23.80 per 100,000 persons—higher than that reported from western countries. Traditional Chinese medicines, herbal and dietary supplements, and anti-tuberculosis drugs were the leading causes of DILI in mainland Chin

Wavelet-Galerkin Method for Identifying an Unknown Source Term in a Heat Equation

We consider the problem of identification of the unknown source in a heat equation. The problem is ill posed in the sense that the solution if it exists does not depend continuously on the data. Meyer wavelets have the property that their Fourier transform has compact support. Therefore, by expanding the data and the solution in the basis of the Meyer wavelets, high-frequency components can be filtered away. Under the additional assumptions concerning the smoothness of the solution, we discuss the stability and convergence of a wavelet-Galerkin method for the source identification problem. Numerical examples are presented to verify the efficiency and accuracy of the method

A Novel RBF Collocation Method Using Fictitious Centres

© 2019 Elsevier Ltd We propose a simple approach which considerably improves the performance of the well-known Kansa method for the solution of boundary value problems (BVPs). In the proposed approach, in contrast to the traditional Kansa method where the centres are placed in the closure of the domain of the BVP in question, the centres can be located outside it. We also employ a novel hybrid technique for the determination of the shape parameter in the radial basis functions used. Numerical examples in 2D and 3D are presented to demonstrate the effectiveness of the proposed method

The Method of Particular Solutions for Solving Nonlinear Poisson Problems

Based on the recent development in the method of particular solutions, we re-exam three approaches using different basis functions for solving nonlinear Poisson problems. We further propose to simplify the solution procedure by removing the insolvency condition when the radial basis functions are augmented with high order polynomial basis functions. We also specify the deficiency of some of these methods and provide necessary remedy. The traditional Picard method is introduced to compare with the recent proposed methods using MATLAB optimization toolbox solver for solving nonlinear Poisson equations. Ranking on these three approaches are given based on the results of numerical experimen

The MFS and MAFS for Solving Laplace and Biharmonic Equations

The method of fundamental solutions (MFS) has been known as an effective boundary meshless method for solving homogeneous differential equations with smooth boundary conditions and boundary shapes. Despite many attractive features of the MFS, the determination of the source location and the boundaries with sharp corners still pose a certain degree of challenges. In this paper, we revisit another powerful boundary method, the method of approximate fundamental solutions (MAFS), which approximates the fundamental solution using trigonometric functions. In the MAFS, the fundamental solutions for various governed equations can be easily constructed. The placement of the source points is also simple. In this paper, we will apply the MAFS for solving the Laplace equation with non-harmonic boundary conditions and the biharmonic equation with non-biharmonic boundary conditions with highly irregular or non-smooth domains. We will compare the performance of the MAFS and the MFS in these types of problems