Normalized solutions for some quasilinear elliptic equation with critical Sobolev exponent

Consider the equation \begin{equation*} -\Delta_p u =\lambda |u|^{p-2}u+\mu|u|^{q-2}u+|u|^{p^\ast-2}u\ \ {\rm in}\ \R^N \end{equation*} under the normalized constraint $$\int_{ \R^N}|u|^p=c^p,$$ where $-\Delta_pu={\rm div} (|\nabla u|^{p-2}\nabla u)$, $1<p<N$, $p0$ and $\lambda\in\R$. In the purely $L^p$-subcritical case, we obtain the existence of ground state solution by virtue of truncation technique, and obtain multiplicity of normalized solutions. In the purely $L^p$-critical and supercritical case, we drive the existence of positive ground state solution, respectively. Finally, we investigate the asymptotic behavior of ground state solutions obtained above as $\mu\to0^+$

Brain MRI Super Resolution Using 3D Deep Densely Connected Neural Networks

Magnetic resonance image (MRI) in high spatial resolution provides detailed anatomical information and is often necessary for accurate quantitative analysis. However, high spatial resolution typically comes at the expense of longer scan time, less spatial coverage, and lower signal to noise ratio (SNR). Single Image Super-Resolution (SISR), a technique aimed to restore high-resolution (HR) details from one single low-resolution (LR) input image, has been improved dramatically by recent breakthroughs in deep learning. In this paper, we introduce a new neural network architecture, 3D Densely Connected Super-Resolution Networks (DCSRN) to restore HR features of structural brain MR images. Through experiments on a dataset with 1,113 subjects, we demonstrate that our network outperforms bicubic interpolation as well as other deep learning methods in restoring 4x resolution-reduced images.Comment: Accepted by ISBI'1

Exploring virus relationships based on virus-host protein-protein interaction network

<p>Abstract</p> <p>Background</p> <p>Currently, several systems have been proposed to classify viruses and indicate the relationships between different ones, though each system has its limitations because of the complexity of viral origins and their rapid evolution rate. We hereby propose a new method to explore the relationships between different viruses.</p> <p>Method</p> <p>A new method, which is based on the virus-host protein-protein interaction network, is proposed in this paper to categorize viruses. The distances between 114 human viruses, including 48 HIV-1 and HIV-2 viruses, are estimated according to the protein-protein interaction network between these viruses and humans.</p> <p>Conclusions/significance</p> <p>The results demonstrated that our method can disclose not only relationships consistent with the taxonomic results of currently used systems of classification but also the potential relationships that the current virus classification systems have not revealed. Moreover, the method points to a new direction where the functional relationships between viruses and hosts can be used to explore the virus relationships on a systematic level.</p

Efficient and Accurate MRI Super-Resolution using a Generative Adversarial Network and 3D Multi-Level Densely Connected Network

High-resolution (HR) magnetic resonance images (MRI) provide detailed anatomical information important for clinical application and quantitative image analysis. However, HR MRI conventionally comes at the cost of longer scan time, smaller spatial coverage, and lower signal-to-noise ratio (SNR). Recent studies have shown that single image super-resolution (SISR), a technique to recover HR details from one single low-resolution (LR) input image, could provide high-quality image details with the help of advanced deep convolutional neural networks (CNN). However, deep neural networks consume memory heavily and run slowly, especially in 3D settings. In this paper, we propose a novel 3D neural network design, namely a multi-level densely connected super-resolution network (mDCSRN) with generative adversarial network (GAN)-guided training. The mDCSRN quickly trains and inferences and the GAN promotes realistic output hardly distinguishable from original HR images. Our results from experiments on a dataset with 1,113 subjects show that our new architecture beats other popular deep learning methods in recovering 4x resolution-downgraded im-ages and runs 6x faster.Comment: 10 pages, 2 figures, 2 tables. MICCAI 201

Azido­(methanol)[N,N′-(o-phenyl­ene)bis­(pyridine-2-carboxamidato)]manganese(III)

In the title complex, [Mn(C18H12N4O2)(N3)(CH4O)], the MnIII ion is in a distorted octa­hedral coordination environment. In the crystal structure, inter­molecular O—H⋯O hydrogen bonds connect mol­ecules into centrosymmetric dimers