Uniform regularity in the low Mach number and inviscid limits for the full Navier-Stokes system in domains with boundaries

Motivated by the studies on the low Mach number limit problem, this manuscript establishes uniform regularity estimates with respect to the Mach number for the non-isentropic compressible Navier-Stokes system in smooth domains with Navier-slip boundary conditions, in the general case of ill-prepared initial data. The thermal conduction is taken into account and the large variation of temperature is allowed. Moreover, the obtained regularity estimates are also uniform in the Reynolds number $\text{Re}\in[1,+\infty),$ P\'eclet number $\text{Pe}\in [1,+\infty),$ provided $$\big|\frac{1}{\text{Re}}-\frac{\iota_0}{\text{Pe}}\big|\lesssim \frac{1}{\text{Pe}^{\frac{1}{2}}}\frac{1}{\text{Re}},$$ where $\iota_0$ is a fixed constant independent of Mach number, Reynolds number and P\'eclet number. The convergence to the limit system when the Mach number tends to zero is then justified for an exterior domain outside a smooth compact set in $\mathbb{R}^3$ in the spirit of \cite{MR2106119}.Comment: Comments are welcome

Linear asymptotic stability of small-amplitude periodic waves of the generalized Korteweg--de Vries equations

In this note, we extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg--de Vries equation in \cite{JFA-R} to small-amplitude periodic traveling waves of the generalized Korteweg-de Vries equations that are not subject to Benjamin--Feir instability. With the adapted notion of stability, this provides for such waves, global-in-time bounded stability in any Sobolev space, and asymptotic stability of dispersive type. When doing so, we actually prove that such results also hold for waves of arbitrary amplitude satisfying a form of spectral stability designated here as dispersive spectral stability.Comment: 15 page

Estimating a Large Drive Time Matrix between Zip Codes in the United States: A Differential Sampling Approach

Estimating a massive drive time matrix between locations is a practical but challenging task. The challenges include availability of reliable road network (including traffic) data, programming expertise, and access to high-performance computing resources. This research proposes a method for estimating a nationwide drive time matrix between ZIP code areas in the U.S.--a geographic unit at which many national datasets such as health information are compiled and distributed. The method (1) does not rely on intensive efforts in data preparation or access to advanced computing resources, (2) uses algorithms of varying complexity and computational time to estimate drive times of different trip lengths, and (3) accounts for both interzonal and intrazonal drive times. The core design samples ZIP code pairs with various intensities according to trip lengths and derives the drive times via Google Maps API, and the Google times are then used to adjust and improve some primitive estimates of drive times with low computational costs. The result provides a valuable resource for researchers

Suppression of MHC class I surface expression by calreticulin's P-domain in a calreticulin deficient cell line

AbstractCalreticulin (CRT) is an important chaperone protein, comprising an N-domain, P-domain and C-domain. It is involved in the folding and assembly of multi-component protein complexes in the endoplasmic reticulum, and plays a critical role in MHC class I antigen processing and presentation. To dissect the functional role and molecular basis of individual domains of the protein, we have utilized individual domains to rescue impaired protein assembly in a CRT deficient cell line. Unexpectedly, both P-domain fragment and NP domain of CRT not only failed to rescue defective cell surface expression of MHC class I molecules but further inhibited their appearance on the surface of cells. Formation of the TAP-associated peptide-loading complex and trafficking of the few detectable MHC class I molecules were not significantly impaired. Instead, this further suppression of MHC class I molecules on the cell surface appears due to the complex missing antigenic peptides, the third member of fully assembled MHC class I molecules. Therefore the P-domain of calreticulin appears to play a significant role in antigen presentation by MHC class I molecules

Automatic segmentation of meniscus based on MAE self-supervision and point-line weak supervision paradigm

Medical image segmentation based on deep learning is often faced with the problems of insufficient datasets and long time-consuming labeling. In this paper, we introduce the self-supervised method MAE(Masked Autoencoders) into knee joint images to provide a good initial weight for the segmentation model and improve the adaptability of the model to small datasets. Secondly, we propose a weakly supervised paradigm for meniscus segmentation based on the combination of point and line to reduce the time of labeling. Based on the weak label ,we design a region growing algorithm to generate pseudo-label. Finally we train the segmentation network based on pseudo-labels with weight transfer from self-supervision. Sufficient experimental results show that our proposed method combining self-supervision and weak supervision can almost approach the performance of purely fully supervised models while greatly reducing the required labeling time and dataset size.Comment: 8 pages,10 figure