A note on the growth factor in Gaussian elimination for generalized Higham matrices

The Higham matrix is a complex symmetric matrix A=B+iC, where both B and C are real, symmetric and positive definite and $\mathrm{i}=\sqrt{-1}$ is the imaginary unit. For any Higham matrix A, Ikramov et al. showed that the growth factor in Gaussian elimination is less than 3. In this paper, based on the previous results, a new bound of the growth factor is obtained by using the maximum of the condition numbers of matrixes B and C for the generalized Higham matrix A, which strengthens this bound to 2 and proves the Higham's conjecture.Comment: 8 pages, 2 figures; Submitted to MOC on Dec. 22 201

Establishment of a male Wistar rat model of nanobacteriainduced kidney stones

Purpose: To establish a male Wistar rat model of nanobacteria (NB)-induced kidney stones. Methods: Sixty male Wistar rats were randomly divided into control group (NC group) given caudal vein injection of saline + saline gavage, and NB-induced stone group (NBS group) given caudal vein injection of NB + saline gavage. Results: Compared with NC, serum creatinine, blood uric acid, urea nitrogen and urinary calcium levels in NBS group increased between weeks 3 and 8 (p < 0.05). Kidney index (kidney weight/body weight ratio) in the NBS group was higher than that in NC group from weeks 8-10. At week 8, urine pH and serum phosphorus in NBS group were higher than those in NC group (p < 0.05). Between weeks 6 and 7, serum calcium in NBS group was higher than that in NC group (p < 0.05). Calcium crystals in NBS rats were distributed mostly in the distal and proximal convoluted tubules. However, no such crystals were observed in NC rats. Similarly, no such pathological changes were seen in the renal tissue of NC group. Calculus analysis showed that stone formation was higher in NBS group than in NC group (p < 0.05). There was no significant difference in micro-CT between the two groups (p ˃ 0.05). Conclusion: The successful establishment of the Wistar rat kidney stone model using NB cultured from urine of upper urinary tract stone patient is potentially useful for further etiological studies on kidney stone formation

InstructEdit: Improving Automatic Masks for Diffusion-based Image Editing With User Instructions

Recent works have explored text-guided image editing using diffusion models and generated edited images based on text prompts. However, the models struggle to accurately locate the regions to be edited and faithfully perform precise edits. In this work, we propose a framework termed InstructEdit that can do fine-grained editing based on user instructions. Our proposed framework has three components: language processor, segmenter, and image editor. The first component, the language processor, processes the user instruction using a large language model. The goal of this processing is to parse the user instruction and output prompts for the segmenter and captions for the image editor. We adopt ChatGPT and optionally BLIP2 for this step. The second component, the segmenter, uses the segmentation prompt provided by the language processor. We employ a state-of-the-art segmentation framework Grounded Segment Anything to automatically generate a high-quality mask based on the segmentation prompt. The third component, the image editor, uses the captions from the language processor and the masks from the segmenter to compute the edited image. We adopt Stable Diffusion and the mask-guided generation from DiffEdit for this purpose. Experiments show that our method outperforms previous editing methods in fine-grained editing applications where the input image contains a complex object or multiple objects. We improve the mask quality over DiffEdit and thus improve the quality of edited images. We also show that our framework can accept multiple forms of user instructions as input. We provide the code at https://github.com/QianWangX/InstructEdit.Comment: Project page: https://qianwangx.github.io/InstructEdit