Geometric Langlands in prime characteristic

Let $G$ be a semisimple algebraic group over an algebraically closed field $k$, whose characteristic is positive and does not divide the order of the Weyl group of $G$, and let $\breve G$ be its Langlands dual group over $k$. Let $C$ be a smooth projective curve over $k$. Denote by \Bun_G the moduli stack of $G$-bundles on $C$ and \Loc_{\breve G} the moduli stack of $\breve G$-local systems on $C$. Let D_{\Bun_G} be the sheaf of crystalline differential operators on \Bun_G. In this paper we construct an equivalence between the bounded derived category D^b(\on{QCoh}(\Loc_{\breve G}^0)) of quasi-coherent sheaves on some open subset \Loc_{\breve G}^0\subset\Loc_{\breve G} and bounded derived category D^b(D_{\Bun_G}^0\on{-mod}) of modules over some localization D_{\Bun_G}^0 of D_{\Bun_G}. This generalizes the work of Bezrukavnikov-Braverman in the \GL_n case.Comment: 57 pages, corrected some arguments in section 3.6 and 3.7, to appear in Compositio Mat

Non-abelian Hodge theory for algebraic curves in characteristic p

Let G be a reductive group over an algebraically closed field of positive characteristic. Let C be a smooth projective curve over k. We give a description of the moduli space of flat G-bundles in terms of the moduli space of G-Higgs bundles over the Frobenius twist C' of C. This description can be regarded as the non-abelian Hodge theory for curves in positive characteristic.Comment: The introduction and the example for GL_n are partially rewritten. Section 3 is re-organized. Various typos are corrected. To appear in GAF

Quantization of Hitchin integrable system via positive characteristic

In a celebrated unpublished manuscript Beilinson and Drinfeld quantize the Hitchin integrable system by showing that the global sections of critically twisted differential operators on the moduli stack of G-bundles on an algebraic curve is identified with the ring of regular functions on the space of G-opers; they deduce existence of an automorphic D-module corresponding to a local system carrying a structure of an oper. In this note we show for G=GL(n) that those results admit a short proof by reduction to positive characteristic, where the result is deduced from generic Langlands duality established earlier by the first author and A. Braverman. The appendix contains a proof of some properties of the p-curvature map restricted to the space of opers.Comment: paper by Roman Bezrukavnikov and Roman Travkin with an appendix by Roman Bezrukavnikov, Tsao-Hsien Chen and Xinwen Zhu. 13 page

Recover Triggered States: Protect Model Against Backdoor Attack in Reinforcement Learning

A backdoor attack allows a malicious user to manipulate the environment or corrupt the training data, thus inserting a backdoor into the trained agent. Such attacks compromise the RL system's reliability, leading to potentially catastrophic results in various key fields. In contrast, relatively limited research has investigated effective defenses against backdoor attacks in RL. This paper proposes the Recovery Triggered States (RTS) method, a novel approach that effectively protects the victim agents from backdoor attacks. RTS involves building a surrogate network to approximate the dynamics model. Developers can then recover the environment from the triggered state to a clean state, thereby preventing attackers from activating backdoors hidden in the agent by presenting the trigger. When training the surrogate to predict states, we incorporate agent action information to reduce the discrepancy between the actions taken by the agent on predicted states and the actions taken on real states. RTS is the first approach to defend against backdoor attacks in a single-agent setting. Our results show that using RTS, the cumulative reward only decreased by 1.41% under the backdoor attack

Gypenosides protect against cardiac ischemia-reperfusion injury by inhibiting mitochondria-dependent apoptosis

Purpose: To investigate the effect of gypenoside (Gyp) on myocardial ischemia-reperfusion (I/R), focusing on mitochondrial function and oxidative stress.Methods: A 3-(4,5-Dimethyl-2-thiazolyl)-2,5-diphenyl-2H-tetrazolium bromide methylthiazolyldiphenyltetrazolium bromide (MTT) assay was employed to measure the protective effect of Gyp pre-treatment against I/R injury. Flow cytometry was used to detect cellular reactive oxygen species (ROS) content and mitochondrial membrane potential (MMP) levels. Additionally, cytochrome C release was observedby laser scanning confocal microscopy. Finally, Annexin V staining and western blot were applied to analyse cell apoptosis.Results: MTT assay results showed that Gyp pre-treatment protected H9C2 cells against I/R injury in a Gyp concentration-dependent manner. Moreover, Gyp treatment inhibited intracellular ROS production, repressed cytochrome C transposition induced by I/R treatment, and recovered MMP to almost normal levels. Furthermore, the expression of apoptosis-related proteins included cleaved caspase-3, -9 and Bax which were decreased by Gyp treatment after I/R injury.Conclusion: These results suggest that Gyp treatment prior to injury can help maintain normal mitochondrial function and inhibit ROS production during I/R injury, ultimately leading to the suppression of I/R-induced cell apoptosis. Thus, Gyp may be a promising drug for the treatment of myocardial I/R.Keywords: Gynostemma pentaphyllum, Ischemia-reperfusion, Mitochondria damage, Oxidative stress, Apoptosi

Recombinant adenovirus, a powerful vector to transfer gene

Recombinant adenovirus has been used extensively to express foreign genes because of its high infection efficiency and its ability to infect a broad spectrum of cell-types. In this review, we describe these advantages and how it works by using a recombinant adenovirus to study the NS2 of Hepatitis C virus (HCV) and focal adhesion kinase(FAK)- related non-kinase(FRNK). Taken the research we have done together recombinant adenovirus demonstrates a very useful vector for transferring genes of interest from the outside

Do matrix metalloproteinase and cathepsin K inhibitors work synergistically to reduce dentin erosion?

Objectives: To evaluate the effects of matrix metalloproteinase (MMP) and cathepsin K (catK) inhibitors on resistance to dentin erosion. Methodology: A total of 96 dentin specimens (3×3×2 mm) were prepared and randomly assigned into four groups (n=24): deionized water (DW); 1 µM odanacatib (ODN, catK inhibitor); 1 mM 1,10-phenanthroline (PHEN, MMP inhibitor); and 1 µM odanacatib + 1 mM 1,10-phenanthroline (COM). Each group was further divided into two subgroups for the application of treatment solutions before (PRE) and after erosive challenges (POST). All specimens were subjected to four daily erosive challenges for 5 d. For each erosive challenge, the specimens in subgroup PRE were immersed in the respective solutions before cola drinks, while the specimens in subgroup POST were immersed in the respective solutions after cola drinks (the immersion duration was 5 min in both cases). All specimens were stored in artificial saliva at 37°C between erosive challenges. The erosive dentin loss (EDL) was measured by profilometry. The residual demineralized organic matrix (DOM) of specimens was removed using type VII collagenase and evaluated by profilometry. Both the EDL and thickness of the residual DOM were statistically analyzed by two-way analysis of variance (ANOVA) and Bonferroni’s test (α=0.05). The surface topography and transverse sections of the specimens were observed using SEM. MMPs and catK were immunolabeled in the eroded dentin and in situ zymography was performed to evaluate the enzyme activity. Results: Significantly lower EDL was found in the groups ODN, PHEN, and COM than in the control group (all p<0.05), while no significant difference in EDL was found among the groups ODN, PHEN, and COM (all p>0.05). The application sequence showed no significant effect on the EDL of the tested groups (p=0.310). A significantly thicker DOM was observed in the group ODN than in the control group regardless of the application sequence (both p<0.05). The treatment with ODN, PHEN, and COM inhibited the gelatinolytic activity by approximately 46.32%, 58.6%, and 74.56%, respectively. Conclusions: The inhibition of endogenous dentinal MMPs and catK increases the acid resistance of human dentin but without an apparent synergistic effect. The inhibition of MMPs and catK is equally effective either before or after the acid challenge

Unsupervised Domain Adaptation GAN Inversion for Image Editing

Existing GAN inversion methods work brilliantly for high-quality image reconstruction and editing while struggling with finding the corresponding high-quality images for low-quality inputs. Therefore, recent works are directed toward leveraging the supervision of paired high-quality and low-quality images for inversion. However, these methods are infeasible in real-world scenarios and further hinder performance improvement. In this paper, we resolve this problem by introducing Unsupervised Domain Adaptation (UDA) into the Inversion process, namely UDA-Inversion, for both high-quality and low-quality image inversion and editing. Particularly, UDA-Inversion first regards the high-quality and low-quality images as the source domain and unlabeled target domain, respectively. Then, a discrepancy function is presented to measure the difference between two domains, after which we minimize the source error and the discrepancy between the distributions of two domains in the latent space to obtain accurate latent codes for low-quality images. Without direct supervision, constructive representations of high-quality images can be spontaneously learned and transformed into low-quality images based on unsupervised domain adaptation. Experimental results indicate that UDA-inversion is the first that achieves a comparable level of performance with supervised methods in low-quality images across multiple domain datasets. We hope this work provides a unique inspiration for latent embedding distributions in image process tasks

Self-Ensemble Protection: Training Checkpoints Are Good Data Protectors

As data become increasingly vital for deep learning, a company would be very cautious about releasing data, because the competitors could use the released data to train high-performance models, thereby posing a tremendous threat to the company's commercial competence. To prevent training good models on the data, imperceptible perturbations could be added to it. Since such perturbations aim at hurting the entire training process, they should reflect the vulnerability of DNN training, rather than that of a single model. Based on this new idea, we seek adversarial examples that are always unrecognized (never correctly classified) in training. In this paper, we uncover them by modeling checkpoints' gradients, forming the proposed self-ensemble protection (SEP), which is very effective because (1) learning on examples ignored during normal training tends to yield DNNs ignoring normal examples; (2) checkpoints' cross-model gradients are close to orthogonal, meaning that they are as diverse as DNNs with different architectures in conventional ensemble. That is, our amazing performance of ensemble only requires the computation of training one model. By extensive experiments with 9 baselines on 3 datasets and 5 architectures, SEP is verified to be a new state-of-the-art, e.g., our small $\ell_\infty=2/255$ perturbations reduce the accuracy of a CIFAR-10 ResNet18 from 94.56\% to 14.68\%, compared to 41.35\% by the best-known method.Code is available at https://github.com/Sizhe-Chen/SEP