Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise

Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and $L_{1}$-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations.Comment: 33 page

Cross-Model Conjunctive Queries over Relation and Tree-structured Data

Conjunctive queries are the most basic and central class of database queries. With the continued growth of demands to manage and process the massive volume of different types of data, there is little research to study the conjunctive queries between relation and tree data. In this paper, we study Cross-Model Conjunctive Queries (CMCQs) over relation and tree-structured data (XML and JSON). To efficiently process CMCQs with bounded intermediate results we first encode tree nodes with position information. With tree node original label values and encoded position values, it allows our proposed algorithm CMJoin to join relations and tree data simultaneously, avoiding massive intermediate results. CMJoin achieves worst-case optimality in terms of the total result of label values and encoded position values. Experimental results demonstrate the efficiency and scalability of the proposed techniques to answer a CMCQ in terms of running time and intermediate result size.Peer reviewe

Wound Segmentation with Dynamic Illumination Correction and Dual-view Semantic Fusion

Wound image segmentation is a critical component for the clinical diagnosis and in-time treatment of wounds. Recently, deep learning has become the mainstream methodology for wound image segmentation. However, the pre-processing of the wound image, such as the illumination correction, is required before the training phase as the performance can be greatly improved. The correction procedure and the training of deep models are independent of each other, which leads to sub-optimal segmentation performance as the fixed illumination correction may not be suitable for all images. To address aforementioned issues, an end-to-end dual-view segmentation approach was proposed in this paper, by incorporating a learn-able illumination correction module into the deep segmentation models. The parameters of the module can be learned and updated during the training stage automatically, while the dual-view fusion can fully employ the features from both the raw images and the enhanced ones. To demonstrate the effectiveness and robustness of the proposed framework, the extensive experiments are conducted on the benchmark datasets. The encouraging results suggest that our framework can significantly improve the segmentation performance, compared to the state-of-the-art methods