Stability and inviscid limit of the 3D anisotropic MHD system near a background magnetic field with mixed fractional partial dissipation

A main result of this paper establishes the global stability of the three-dimensional MHD equations near a background magnetic field with mixed fractional partial dissipation with $\alpha, \beta\in(\frac{1}{2}, 1]$. Namely, the velocity equations involve dissipation $(\Lambda_1^{2\alpha} + \Lambda_2^{2\alpha}+\sigma \Lambda_3^{2\alpha})u$ with the case $\sigma=1$ and $\sigma=0$. The magnetic equations without partial magnetic diffusion $\Lambda_i^{2\beta} b_i$ but with the diffusion $(-\Delta)^\beta b$, where $\Lambda_i^{s} (s>0)$ with $i=1, 2, 3$ are the directional fractional operators. Then we focus on the vanishing vertical kinematic viscosity coefficient limit of the MHD system with the case $\sigma=1$ to the case $\sigma=0$. The convergent result is obtained in the sense of $H^1$-norm

COMCAT: Towards Efficient Compression and Customization of Attention-Based Vision Models

Attention-based vision models, such as Vision Transformer (ViT) and its variants, have shown promising performance in various computer vision tasks. However, these emerging architectures suffer from large model sizes and high computational costs, calling for efficient model compression solutions. To date, pruning ViTs has been well studied, while other compression strategies that have been widely applied in CNN compression, e.g., model factorization, is little explored in the context of ViT compression. This paper explores an efficient method for compressing vision transformers to enrich the toolset for obtaining compact attention-based vision models. Based on the new insight on the multi-head attention layer, we develop a highly efficient ViT compression solution, which outperforms the state-of-the-art pruning methods. For compressing DeiT-small and DeiT-base models on ImageNet, our proposed approach can achieve 0.45% and 0.76% higher top-1 accuracy even with fewer parameters. Our finding can also be applied to improve the customization efficiency of text-to-image diffusion models, with much faster training (up to $2.6\times$ speedup) and lower extra storage cost (up to $1927.5\times$ reduction) than the existing works.Comment: ICML 2023 Poste

catena-Poly[[tris[silver(I)-μ-4,4′-bi­pyridine-κ2 N:N′]] tris­(perchlorate) di­hydrate]

In the title compound, {[Ag3(C10H8N2)3](ClO4)3·2H2O}n, one of the AgI ions, one of the 4,4′-bipyridine (bipy) ligands and one of the perchlorate anions are each situated on a twofold rotation axis. Each AgI ion is coordinated by two N atoms from two bridging bipy ligands, forming chains along [101]. π–π inter­actions between the pyridine rings [centroid–centroid distances = 3.638 (8) and 3.688 (8) Å] connect the chains. Inter­molecular O—H⋯O hydrogen bonds link the uncoord­inated water mol­ecules and the perchlorate anions

Weekly induction intraperitoneal chemotherapy after primary surgical cytoreduction in patients with advanced epithelial ovarian cancer

BACKGROUND: Traditional intraperitoneal (IP) therapy administered simultaneously with intravenous (IV) chemotherapy in the primary setting has been well documented. This retrospective study was conducted to investigate the role of weekly IP therapy as an inducing intervention before front-line IV chemotherapy, particularly in patients with bulky residual disease after surgery. METHODS: A total of 426 patients with advanced ovarian cancer treated between 1990 and 1999, were reviewed. Follow-up data were available in 409 patients. Of whom, 230 patients received postoperative weekly IP therapy with a median cycles of 4, other 179 patients who did not receive any IP therapy were used as the control group. RESULTS: The median age of the patients was 51 years (range, 20–77 years). One hundred eighty-nine patients with stage III disease and 41 patients with stage IV disease were treated with postoperative IP therapy, respectively. Complications and toxicity were observed in 68 patients (29.5%), but there were no grade 4 toxicities and no patients died of complications or toxicities. In patients with residual disease > 1 cm, the median survival of those with IP delivery of chemotherapy and those without was 21.6 months and 18.8 months, respectively (hazard ratio [HR]= 0.69, P = 0.02). Whereas, in patients with residual disease ≤ 1 cm, the median survival was 46.8 months and 37.6 months, respectively (HR= 0.73, P = 0.09). Multivariate analysis suggested that the factors age ≤ 60 years, stage III, IP therapy and paclitaxel as front-line chemotherapy were associated with a better prognosis for patients with advanced ovarian cancer. CONCLUSION: Weekly postoperative IP therapy as an inducing intervention is practical for both physicians and patients with acceptable complications and associated with a lengthened survival of patients with advanced ovarian cancer. Whether this arm can be used in lieu of a traditional one needs further randomized trial to confirm the preliminary results