Supersymmetric KdV equation: Darboux transformation and discrete systems

For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related B\"{a}cklund transformation are used to construct integrable super differential-difference and difference-difference systems. The continuum limits of these discrete systems and of their Lax pairs are also considered.Comment: 13pages, submitted to Journal of Physics

Effect of gene transfer of Chlorella vulgaris n-3 fatty acid desaturase on mouse breast cancer cells

Chlorella vulgaris had the gene of n-3 fatty acid desaturase (CvFad3) which can synthesize the precursor of n-3 polyunsaturated fatty acids (PUFAs) or to convert n-6 to n-3 PUFAs. The objective of this study was to examine whether the CvFad3 gene from C. vulgaris can be functionally expressed in mammalian cells and whether its expression can exert a significant effect on cellular fatty acid composition. CvFad3 gene was inserted into plasmid pEGFP-C3 to construct eukaryotic expression vector pEGFP-C3-n-3 and expressed the n-3 Fad gene in mouse breast cancer cells (4T1 cells). Transfection of recombinant vector into 4T1 cells resulted in a high expression of n-3 fatty acid desturase. Lipid analysis indicated a remarkable increase in the level of n-3 PUFAs accompanied with a large decrease in the contents of n-6 PUFAs. Accordingly, CvFad3 gene significantly decreased the ratio of n-6/n-3 PUFAs of 4T1 cells membrane. The expression of CvFad3 gene decreased cellular proliferation and promoted cellular apoptosis. This study demonstrates that CvFad3 gene could dramatically balance the ratio of n-6/n-3 PUFAs. It would be an effective approach to modifying fatty acid composition of mammalian cells and also provided a basis for potential applications of this gene transfer in experimental and clinical settings.Key words: Chlorella vulgaris, CvFad3 gene, fatty acid desaturase, recombinant expression vector, fatty acid composition

Bihamiltonian Cohomologies and Integrable Hierarchies I: A Special Case

We present some general results on properties of the bihamiltonian cohomologies associated to bihamiltonian structures of hydrodynamic type, and compute the third cohomology for the bihamiltonian structure of the dispersionless KdV hierarchy. The result of the computation enables us to prove the existence of bihamiltonian deformations of the dispersionless KdV hierarchy starting from any of its infinitesimal deformations.Comment: 43 pages. V2: the accepted version, to appear in Comm. Math. Phy

Defocus Image Deblurring Network with Defocus Map Estimation as Auxiliary Task

Different from the object motion blur, the defocus blur is caused by the limitation of the cameras’ depth of field. The defocus amount can be characterized by the parameter of point spread function and thus forms a defocus map. In this paper, we propose a new network architecture called Defocus Image Deblurring Auxiliary Learning Net (DID-ANet), which is specifically designed for single image defocus deblurring by using defocus map estimation as auxiliary task to improve the deblurring result. To facilitate the training of the network, we build a novel and large-scale dataset for single image defocus deblurring, which contains the defocus images, the defocus maps and the all-sharp images. To the best of our knowledge, the new dataset is the first large-scale defocus deblurring dataset for training deep networks. Moreover, the experimental results demonstrate that the proposed DID-ANet outperforms the state-of-the-art methods for both tasks of defocus image deblurring and defocus map estimation, both quantitatively and qualitatively. The dataset, code, and model is available on GitHub: https://github.com/xytmhy/DID-ANet-Defocus-Deblurring

An α-Matte Boundary Defocus Model-Based Cascaded Network for Multi-Focus Image Fusion

Capturing an all-in-focus image with a single camera is difficult since the depth of field of the camera is usually limited. An alternative method to obtain the all-in-focus image is to fuse several images that are focused at different depths. However, existing multi-focus image fusion methods cannot obtain clear results for areas near the focused/defocused boundary (FDB). In this article, a novel α -matte boundary defocus model is proposed to generate realistic training data with the defocus spread effect precisely modeled, especially for areas near the FDB. Based on this α -matte defocus model and the generated data, a cascaded boundary-aware convolutional network termed MMF-Net is proposed and trained, aiming to achieve clearer fusion results around the FDB. Specifically, the MMF-Net consists of two cascaded subnets for initial fusion and boundary fusion. These two subnets are designed to first obtain a guidance map of FDB and then refine the fusion near the FDB. Experiments demonstrate that with the help of the new α -matte boundary defocus model, the proposed MMF-Net outperforms the state-of-the-art methods both qualitatively and quantitatively