Traveling Wavefronts of Competing Pioneer and Climax Model with Nonlocal Diffusion

We study a competing pioneer-climax species model with nonlocal diffusion. By constructing a pair of upper-lower solutions and using the iterative technique, we establish the existence of traveling wavefronts connecting the pioneer-existence equilibrium and the coexistence equilibrium. We also discuss the asymptotic behavior of the wave tail for the traveling wavefronts as s=x+ct→−∞

SynFundus-1M: A High-quality Million-scale Synthetic fundus images Dataset with Fifteen Types of Annotation

Large-scale public datasets with high-quality annotations are rarely available for intelligent medical imaging research, due to data privacy concerns and the cost of annotations. In this paper, we release SynFundus-1M, a high-quality synthetic dataset containing over one million fundus images in terms of \textbf{eleven disease types}. Furthermore, we deliberately assign four readability labels to the key regions of the fundus images. To the best of our knowledge, SynFundus-1M is currently the largest fundus dataset with the most sophisticated annotations. Leveraging over 1.3 million private authentic fundus images from various scenarios, we trained a powerful Denoising Diffusion Probabilistic Model, named SynFundus-Generator. The released SynFundus-1M are generated by SynFundus-Generator under predefined conditions. To demonstrate the value of SynFundus-1M, extensive experiments are designed in terms of the following aspect: 1) Authenticity of the images: we randomly blend the synthetic images with authentic fundus images, and find that experienced annotators can hardly distinguish the synthetic images from authentic ones. Moreover, we show that the disease-related vision features (e.g. lesions) are well simulated in the synthetic images. 2) Effectiveness for down-stream fine-tuning and pretraining: we demonstrate that retinal disease diagnosis models of either convolutional neural networks (CNN) or Vision Transformer (ViT) architectures can benefit from SynFundus-1M, and compared to the datasets commonly used for pretraining, models trained on SynFundus-1M not only achieve superior performance but also demonstrate faster convergence on various downstream tasks. SynFundus-1M is already public available for the open-source community

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page