Some Remarks on Regularity Criteria of Axially Symmetric Navier-Stokes Equations

Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a $log$ supercritical assumption on the horizontally radial component $u^r$ and vertical component $u^z$, accompanied by a $log$ subcritical assumption on the horizontally angular component $u^\theta$ of the velocity. Second, the precise Green function for the operator $-(\Delta-\frac{1}{r^2})$ under the axially symmetric situation, where $r$ is the distance to the symmetric axis, and some weighted $L^p$ estimates of it will be given. This will serve as a tool for the study of axially symmetric Navier-Stokes equations. As an application, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a critical (or a subcritical) assumption on the angular component $w^\theta$ of the vorticity.Comment: Final version, to appear in Comm. Pure Appl. Ana

Constrained large solutions to Leray's problem in a distorted strip with the Navier-slip boundary condition

In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution will be investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. The main novelty is the total flux of the velocity can be relatively large (proportional to the {\it slip length}) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case.Comment: 45 pages. arXiv admin note: text overlap with arXiv:2204.10578. A remark is added to state the independent accomplishment of solving the 2D Leray's problem with the Navier-slip boundary condition by our group and Professor Chunjing Xie's grou

A Novel Driver Distraction Behavior Detection Based on Self-Supervised Learning Framework with Masked Image Modeling

Driver distraction causes a significant number of traffic accidents every year, resulting in economic losses and casualties. Currently, the level of automation in commercial vehicles is far from completely unmanned, and drivers still play an important role in operating and controlling the vehicle. Therefore, driver distraction behavior detection is crucial for road safety. At present, driver distraction detection primarily relies on traditional Convolutional Neural Networks (CNN) and supervised learning methods. However, there are still challenges such as the high cost of labeled datasets, limited ability to capture high-level semantic information, and weak generalization performance. In order to solve these problems, this paper proposes a new self-supervised learning method based on masked image modeling for driver distraction behavior detection. Firstly, a self-supervised learning framework for masked image modeling (MIM) is introduced to solve the serious human and material consumption issues caused by dataset labeling. Secondly, the Swin Transformer is employed as an encoder. Performance is enhanced by reconfiguring the Swin Transformer block and adjusting the distribution of the number of window multi-head self-attention (W-MSA) and shifted window multi-head self-attention (SW-MSA) detection heads across all stages, which leads to model more lightening. Finally, various data augmentation strategies are used along with the best random masking strategy to strengthen the model's recognition and generalization ability. Test results on a large-scale driver distraction behavior dataset show that the self-supervised learning method proposed in this paper achieves an accuracy of 99.60%, approximating the excellent performance of advanced supervised learning methods

Mimicry of a Non-ribosomally Produced Antimicrobial, Brevicidine, by Ribosomal Synthesis and Post-translational Modification

Zhao et al. describe a strategy to synthesize mimics of the recently discovered antimicrobial non-ribosomal peptide, brevicidine. The engineered mimics show antimicrobial activities against pathogens susceptible to brevicidine, which demonstrate that conversion of NRPs to RiPPs is feasible and offer great opportunities for engineering a wide range of effective antibiotics

In situ structures of the genome and genome-delivery apparatus in a single-stranded RNA virus.

Packaging of the genome into a protein capsid and its subsequent delivery into a host cell are two fundamental processes in the life cycle of a virus. Unlike double-stranded DNA viruses, which pump their genome into a preformed capsid, single-stranded RNA (ssRNA) viruses, such as bacteriophage MS2, co-assemble their capsid with the genome; however, the structural basis of this co-assembly is poorly understood. MS2 infects Escherichia coli via the host 'sex pilus' (F-pilus); it was the first fully sequenced organism and is a model system for studies of translational gene regulation, RNA-protein interactions, and RNA virus assembly. Its positive-sense ssRNA genome of 3,569 bases is enclosed in a capsid with one maturation protein monomer and 89 coat protein dimers arranged in a T = 3 icosahedral lattice. The maturation protein is responsible for attaching the virus to an F-pilus and delivering the viral genome into the host during infection, but how the genome is organized and delivered is not known. Here we describe the MS2 structure at 3.6 Å resolution, determined by electron-counting cryo-electron microscopy (cryoEM) and asymmetric reconstruction. We traced approximately 80% of the backbone of the viral genome, built atomic models for 16 RNA stem-loops, and identified three conserved motifs of RNA-coat protein interactions among 15 of these stem-loops with diverse sequences. The stem-loop at the 3' end of the genome interacts extensively with the maturation protein, which, with just a six-helix bundle and a six-stranded β-sheet, forms a genome-delivery apparatus and joins 89 coat protein dimers to form a capsid. This atomic description of genome-capsid interactions in a spherical ssRNA virus provides insight into genome delivery via the host sex pilus and mechanisms underlying ssRNA-capsid co-assembly, and inspires speculation about the links between nucleoprotein complexes and the origins of viruses