The Chevalley-Gras formula over global fields

In this article we give an adelic proof of the Chevalley-Gras formula for global fields, which itself is a generalization of the ambiguous class number formula. The idea is to reduce the formula to the Hasse norm theorem, the local and global reciprocity laws. We also give an adelic proof of the Chevalley-Gras formula for $0$-th divisor class group in the function field case, which extends a result of Rosen.Comment: minor revisio

Multi-scale 3D Convolution Network for Video Based Person Re-Identification

This paper proposes a two-stream convolution network to extract spatial and temporal cues for video based person Re-Identification (ReID). A temporal stream in this network is constructed by inserting several Multi-scale 3D (M3D) convolution layers into a 2D CNN network. The resulting M3D convolution network introduces a fraction of parameters into the 2D CNN, but gains the ability of multi-scale temporal feature learning. With this compact architecture, M3D convolution network is also more efficient and easier to optimize than existing 3D convolution networks. The temporal stream further involves Residual Attention Layers (RAL) to refine the temporal features. By jointly learning spatial-temporal attention masks in a residual manner, RAL identifies the discriminative spatial regions and temporal cues. The other stream in our network is implemented with a 2D CNN for spatial feature extraction. The spatial and temporal features from two streams are finally fused for the video based person ReID. Evaluations on three widely used benchmarks datasets, i.e., MARS, PRID2011, and iLIDS-VID demonstrate the substantial advantages of our method over existing 3D convolution networks and state-of-art methods.Comment: AAAI, 201

Novel Role of Intestinal Lipid Transport in Food Allergy and Cholesterol Homeostasis

The small intestine is the main organ for food digestion and nutrient absorption. It is constantly exposed to antigen and immunomodulatory agents from diet and commensal microbiota. Thus, the intestine is the largest compartment of the immune system in the body. Peanuts and many other allergen resources contain triglycerides, which may affect the antigen absorption through the intestine, but their effects on sensitization and anaphylaxis are unknown. We found that medium chain triglycerides (MCT) promoted antigen absorption into Peyer’s Patches, rather than into the blood directly. Both gavage and feeding of MCT plus peanut protein induced spontaneous allergic sensitization. MCT-sensitized mice experienced the IgG-dependent anaphylaxis from systemic challenges and the IgE-dependent anaphylaxis from oral challenges. Furthermore, MCT alone had direct pharmaceutical effect on enterocytes, like stimulating Jejunal-epithelial Th2 cytokine responses compared with what was seen in the long chain triglycerides (LCT) treated group. Moreover, the oral challenges conducted with peanut protein in MCT significantly exacerbated anaphylaxis compared with the LCT challenges. The intestine also plays an important role in whole body cholesterol homeostasis due to its exclusive function in cholesterol absorption. The researchers found that the intestine function in cholesterol secretion and elimination, but it has not been proven directly until recently. This pathway that facilitate the cholesterol secretions through intestine was named the Transintestinal Cholesterol Efflux (TICE) and has not been well studied yet. To find the possible transporter candidates involved in TICE, we compared both biliary and intestinal cholesterol excretion rates in wild-type (WT) and G5G8 deficient (KO) mice of both sexes. All mice were maintained on a plant-sterol free diet beginning at weaning to prevent the development of secondary phenotypes associated with Sitosterolemia. We found that WT mice had higher biliary cholesterol excretion rates compared to their G5G8 KO littermates as previously reported. However, this difference is significantly greater in females compared to males. Interestingly, intestinal cholesterol excretions increased in female KO mice compared to their WT littermates, a difference not observed in males. This data suggests a sexually dimorphic adaptive mechanism to maintain cholesterol elimination in the absence of G5G8. Whereas male mice maintain a greater level of biliary output in the absence of G5G8, female mice upregulate an alternate intestinal elimination route. To determine the origin of intestinally secreted cholesterol, we compared both hepatobiliary and intestinal cholesterol secretion rates in male wild-type (WT) and CETP transgenic (CETP TG) mice at the age of 12 weeks. Cholesteryl ester transfer protein (CETP) facilitates the transport of cholesteryl esters and triglycerides between lipoproteins in plasma and alters the lipoprotein distribution of plasma cholesterol. We found that WT and CETP TG mice did not differ in either biliary or intestinal cholesterol secretion rates when maintained on a standard chow diet. However, CETP TG mice showed increased biliary cholesterol secretion rates and decreased intestinal cholesterol secretion rates compared to the WT group in response to a Western diet. We next determined the effect of CETP on the delivery of radiolabeled HDL-cholesterol ester to bile and intestinal lumen. Unlike bulk cholesterol secretions, HDL-derived cholesterol esters were preferentially delivered to the intestine in CETP TG mice. This data suggests that CETP alter the routes of total and HDL cholesterol elimination from the body in mice

Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model

In this paper, a novel observation is made on a one-dimensional compressible Navier--Stokes model for the dynamic combustion of a reacting mixture of $\gamma$-law gases ($\gamma>1$) with discontinuous Arrhenius reaction rate function, on both bounded and unbounded domains. We show that the mass fraction of the reactant (denoted as $Z$) satisfies a weighted gradient estimate $Z_y/ \sqrt{Z} \in L^\infty_t L^2_y$, provided that at time zero the density is Lipschitz continuous and bounded strictly away from zero and infinity. Consequently, the graph of $Z$ cannot form cusps or corners near the points where the reactant in the combustion process is completely depleted at any instant, and the entropy of $Z$ is bounded from above. The key ingredient of the proof is a new estimate based on the Fisher information, first exploited by [2, 7] with applications to PDEs in chemorepulsion and thermoelasticity. Along the way, we also establish a Lipschitz estimate for the density.Comment: 18 page