Similarity reductions and new nonlinear exact solutions for the 2D incompressible Euler equations

For the 2D and 3D Euler equations, their existing exact solutions are often in linear form with respect to variables x, y, z. In this paper, the Clarkson–Kruskal reduction method is applied to reduce the 2D incompressible Euler equations to a system of completely solvable ordinary equations, from which several novel nonlinear exact solutions with respect to the variables x and y are found.     

Decay properties of solutions to the Cauchy problem for the damped wave equation with absorption

We consider the Cauchy problem for the damped wave equation with absorption

     

Matching fluorescence spectra of oil spills with spectra from suspect sources

Fluorescence spectroscopy is ideally suited to the analysis of oil spills as it allows chemical information of polycyclic aromatic hydrocarbons to be acquired quickly, sensitively and selectively. Unlike infrared spectra which have detailed peak information, many fluorescence spectra have only a few broad peaks. Nine different samples of crude and diesel oils were used for testing point-to-point matching across the spectral range. Five of them were discriminated by point-to-point matching algorithms and the other four very similar samples were not. Principal components analysis (PCA) did successfully discriminate among all similar samples. PCA could also distinguish the extent of weathering of different samples, an important factor in matching environmental spills.     

Effective single-cell clustering through ensemble feature selection and similarity measurements

Single-cell RNA sequencing technologies have revolutionized biomedical research by providing an effective means to profile gene expressions in individual cells. One of the first fundamental steps to perform the in-depth analysis of single-cell sequencing data is cell type classification and identification. Computational methods such as clustering algorithms have been utilized and gaining in popularity because they can save considerable resources and time for experimental validations. Although selecting the optimal features (i.e., genes) is an essential process to obtain accurate and reliable single-cell clustering results, the computational complexity and dropout events that can introduce zero-inflated noise make this process very challenging. In this paper, we propose an effective single-cell clustering algorithm based on the ensemble feature selection and similarity measurements. We initially identify the set of potential features, then measure the cell-to-cell similarity based on the subset of the potentials through multiple feature sampling approaches. We construct the ensemble network based on cell-to-cell similarity. Finally, we apply a network-based clustering algorithm to obtain single-cell clusters. We evaluate the performance of our proposed algorithm through multiple assessments in real-world single-cell RNA sequencing datasets with known cell types. The results show that our proposed algorithm can identify accurate and consistent single-cell clustering. Moreover, the proposed algorithm takes relative expression as input, so it can easily be adopted by existing analysis pipelines. The source code has been made publicly available at https://github.com/jeonglab/scCLUE.     

Quality evaluation of Hypericum ascyron extract by two‐dimensional high‐performance liquid chromatography coupled with the colorimetric 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide method

In this paper, a heart‐cutting two‐dimensional high‐performance liquid chromatography coupled with the 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide (MTT) method was established for controlling the quality of different batches of Hypericum ascyron extract for the first time. In comparison with the common one‐dimensional fingerprint, the second‐dimensional fingerprint compiled additional spectral data and was hence more informative. The quality of H. ascyron extract was further evaluated by similarity measures and the same results were achieved, the correlation coefficients of the similarity of ten batches of H. ascyron extract were ＞0.99. Furthermore, we also evaluated the quality of the ten batches of H. ascyron extract by antibacterial activity. The result demonstrated that the quality of the ten batches of H. ascyron extract was not significantly different by MTT. Finally, we demonstrated that the second‐dimensional fingerprint coupled with the MTT method was a more powerful tool to characterize the quality of samples of batch to batch. Therefore the proposed method could be used to comprehensively conduct the quality control of traditional Chinese medicines.