arXiv subjects
Publications and source records attributed to Xin Zhong.
We establish an explicit correspondence between the Drinfeld current algebra presentation for the two-parameter quantum affine algebra $U_{r, s}(\mathrm{C}_n^{(1)})$ and the $R$-matrix realization á la Faddeev, Reshetikhin and Takhtajan.
We are concerned with the long-time behavior of classical solutions to the isentropic compressible Navier-Stokes equations in $\mathbb R^3$. Our main results and innovations can be stated as follows: Under the assumption that the density $ρ({\bf{x}}, t)$ verifies $ρ({\bf{x}},0)\geq c>0$ and $\sup_{t\geq 0}\|ρ(\cdot,t)\|_{L^\infty}\leq M$, we establish the optimal decay rates of the solutions. This greatly improves the previous result (Arch. Ration. Mech. Anal. 234 (2019), 1167--1222), where the authors require an extra hypothesis $\sup_{t\geq 0}\|ρ(\cdot,t)\|_{C^α}\leq M$ with $α$ arbitrarily small. We prove that the vacuum state will persist for any time provided that the initial density contains vacuum and the far-field density is away from vacuum, which extends the torus case obtained in (SIAM J. Math. Anal. 55 (2023), 882--899) to the whole space. We derive the decay properties of the solutions with vacuum as far-field density. This in particular gives the first result concerning the $L^\infty$-decay with a rate $(1+t)^{-1}$ for the pressure to the 3D compressible Navier-Stokes equations in the presence of vacuum. The main ingredient of the proof relies on the techniques involving blow-up criterion, a key time-independent positive upper and lower bounds of the density, and a regularity interpolation trick.
In this paper, we extend the Reshetikhin-Semenov-Tian-Shansky formulation of quantum affine algebras to the two-parameter quantum affine superalgebra $U_{p, q}(\widehat{\mathfrak{gl}}(m|n))$ and obtain its Drinfeld realization. We also derive its Hopf algebra structure by providing Drinfeld-type coproduct for the Drinfeld generators.
Recently, ternary clathrate hydrides are promising candidates for high-temperature superconductor. However, it is a formidable challenge to effectively hunt high-temperature superconductivity among multinary hydrides due to the expensive computational cost associated with large unit cells and huge stoichiometric choices. Here we present an efficiently data-driven strategy, including generated clathrate frameworks, the quick estimation of stability for each framework and superconducting critical temperature (Tc) for each hydride structure, to accelerate the discovery of high-temperature superconducting hydrides. Our strategy was initialized with more than one million input structures via zeolite databases and our generated dataset. As a result, such a strategy hitherto uncovered 14 prototypical hydrogen frameworks for clathrate hydrides, which is 1.5 times greater than the number (9) of previously reported prototypes. Remarkably, eleven ternary clathrate structures were predicted to have Tcs above 250 K at 300 GPa. Further extensive global structure-searching simulations support that Li2NaH17 and ThY2H24 are thermodynamically stable at 220 and 150 GPa, respectively, with Tcs approaching room temperature of 297 K and 303 K, which are promising for future synthesis. These results offer a platform to explore high-temperature superconductors via a great number of databases.
Garnet has been widely used to decipher the pressure-temperature-time history of rocks, but its physical properties such as elasticity and diffusion are strongly affected by trace amounts of hydrogen. Experimental measurements of H diffusion in garnet are limited to room pressure. We use atomistic simulations to study H diffusion in perfect and defective garnet lattices, focusing on protonation defects at the Si and Mg sites, which are shown to be energetically favored. The ab-initio simulation of H diffusion is computationally challenging due to a transient trapping of H, which is overcome with machine learning techniques by training a deep neural network that encodes the interatomic potential. Our results show high mobility of hydrogen in defect free garnet lattices, whereas H diffusivity is significantly diminished in defective lattices. Tracer simulation focusing on H alone highlights the vital role of atomic vibrations of heavier atoms like Mg in the untrapping of H atoms. Two regimes of H diffusion are identified: a diffuser-dominated regime at high hydrogen content with low activation energies, due to saturation of vacancies by hydrogen, and a vacancy-dominated regime at low hydrogen content with high activation energies, due to trapping of H atoms at vacancy sites. These regimes account for experimental observations, such as a H-concentration dependent diffusivity and the discrepancy in activation energy between deprotonation and D-H exchange experiments. This study underpins the crucial role of vacancies in H diffusion and demonstrates the utility of machine-learned interatomic potentials in studying kinetic processes in the Earth's interior.
We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation theory, we establish the global existence and uniqueness of strong solutions, which may be of possibly large oscillations, provided that the initial data are of small total energy. Furthermore, we also derive algebraic decay estimates of the solution. This improves our previous results (Z. Angew. Math. Phys. 71: Paper No. 188, 2020; J. Differential Equations 336: 456--478, 2022) where viscosity coefficients should additionally satisfy $3μ>λ$. To our best knowledge, this is the first result on time-decay rates of solutions to the Cauchy problem of multi-dimensional compressible non-isentropic MHD equations with vacuum.
In this work, we introduce a novel deep learning-based approach to text-in-image watermarking, a method that embeds and extracts textual information within images to enhance data security and integrity. Leveraging the capabilities of deep learning, specifically through the use of Transformer-based architectures for text processing and Vision Transformers for image feature extraction, our method sets new benchmarks in the domain. The proposed method represents the first application of deep learning in text-in-image watermarking that improves adaptivity, allowing the model to intelligently adjust to specific image characteristics and emerging threats. Through testing and evaluation, our method has demonstrated superior robustness compared to traditional watermarking techniques, achieving enhanced imperceptibility that ensures the watermark remains undetectable across various image contents.
The rapid advancement of Large Language Models (LLMs) has significantly enhanced the capabilities of text generators. With the potential for misuse escalating, the importance of discerning whether texts are human-authored or generated by LLMs has become paramount. Several preceding studies have ventured to address this challenge by employing binary classifiers to differentiate between human-written and LLM-generated text. Nevertheless, the reliability of these classifiers has been subject to question. Given that consequential decisions may hinge on the outcome of such classification, it is imperative that text source detection is of high caliber. In light of this, the present paper introduces DeepTextMark, a deep learning-driven text watermarking methodology devised for text source identification. By leveraging Word2Vec and Sentence Encoding for watermark insertion, alongside a transformer-based classifier for watermark detection, DeepTextMark epitomizes a blend of blindness, robustness, imperceptibility, and reliability. As elaborated within the paper, these attributes are crucial for universal text source detection, with a particular emphasis in this paper on text produced by LLMs. DeepTextMark offers a viable "add-on" solution to prevailing text generation frameworks, requiring no direct access or alterations to the underlying text generation mechanism. Experimental evaluations underscore the high imperceptibility, elevated detection accuracy, augmented robustness, reliability, and swift execution of DeepTextMark.
This paper presents a comprehensive survey on deep learning-based image watermarking, a technique that entails the invisible embedding and extraction of watermarks within a cover image, aiming to offer a seamless blend of robustness and adaptability. We navigate the complex landscape of this interdisciplinary domain, linking historical foundations, current innovations, and prospective developments. Unlike existing literature, our study concentrates exclusively on image watermarking with deep learning, delivering an in-depth, yet brief analysis enriched by three fundamental contributions. First, we introduce a refined categorization, segmenting the field into Embedder-Extractor, Deep Networks as a Feature Transformation, and Hybrid Methods. This taxonomy, inspired by the varied roles of deep learning across studies, is designed to infuse clarity, offering readers technical insights and directional guidance. Second, our exploration dives into representative methodologies, encapsulating the diverse research directions and inherent challenges within each category to provide a consolidated perspective. Lastly, we venture beyond established boundaries to outline emerging frontiers, offering a detailed insight into prospective research avenues.
Metal borides have been considered as potential high-temperature superconductors since the discovery of record-holding 39 K superconductivity in bulk MgB2. In this work, we identified a superconducting yet thermodynamically stable F43m Sr2B5 at 40 GPa with a unique covalent sp3-hybridized boron framework through extensive first-principles structure searches. Remarkably, solving the anisotropic Migdal-Eliashberg equations resulted in a high superconducting critical temperature (Tc) around 100 K, exceeding the boiling point (77 K) of liquid nitrogen. Our in-depth analysis revealed that the high-temperature superconductivity mainly originates from the strong coupling between the metalized σ-bonded electronic bands and E phonon modes of boron atoms. Moreover, anharmonic phonon simulations suggest that F43m Sr2B5 might be recovered to ambient pressure. Our current findings provide a prototype structure with a full σ-bonded boron framework for the design of high-Tc superconducting borides that may expand to a broader variety of lightweight compounds.
Image watermarking involves embedding and extracting watermarks within a cover image, with deep learning approaches emerging to bolster generalization and robustness. Predominantly, current methods employ convolution and concatenation for watermark embedding, while also integrating conceivable augmentation in the training process. This paper explores a robust image watermarking methodology by harnessing cross-attention and invariant domain learning, marking two novel, significant advancements. First, we design a watermark embedding technique utilizing a multi-head cross attention mechanism, enabling information exchange between the cover image and watermark to identify semantically suitable embedding locations. Second, we advocate for learning an invariant domain representation that encapsulates both semantic and noise-invariant information concerning the watermark, shedding light on promising avenues for enhancing image watermarking techniques.
We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a finite number of two-dimensional connected components. We derive the global existence and uniqueness of classical solutions provided that the initial total energy is suitably small. Our result generalizes the Cauchy problems of compressible Navier-Stokes equations with Coulomb force (J. Differential Equations 269: 8468--8508, 2020) and compressible MHD equations (SIAM J. Math. Anal. 45: 1356--1387, 2013) to the case of bounded domains although tackling many surface integrals caused by the slip boundary condition are complex. The main ingredient of this paper is to overcome the strong nonlinearity caused by Coulomb force, magnetic field, and rotation effect of micro-particles by applying piecewise-estimate method and delicate analysis based on the effective viscous fluxes involving velocity and micro-rotational velocity.
We investigate compressible nematic liquid crystal flows in three-dimensional (3D) bounded domains with slip boundary condition for velocity and Neumann boundary condition for orientation field. By applying piecewise-estimate method and delicate analysis based on the effective viscous flux and vorticity, we derive the global existence and uniqueness of strong solutions provided that the initial total energy is suitably small. Our result is an extension of the works of Huang-Wang-Wen (J. Differential Equations 252: 2222-2265, 2012) and Li-Xu-Zhang (J. Math. Fluid Mech. 20: 2105-2145, 2018), where the local strong solutions in three dimensions and the global strong solutions for 3D Cauchy problem were established, respectively. Moreover, it also shows that blow up mechanism for local strong solutions obtained by Huang-Wang-Wen (Arch. Ration. Mech. Anal. 204: 285-311, 2012) cannot occur if the initial total energy is sufficiently small.
Joint Embedding Architecture-based self-supervised learning methods have attributed the composition of data augmentations as a crucial factor for their strong representation learning capabilities. While regional dropout strategies have proven to guide models to focus on lesser indicative parts of the objects in supervised methods, it hasn't been adopted by self-supervised methods for generating positive pairs. This is because the regional dropout methods are not suitable for the input sampling process of the self-supervised methodology. Whereas dropping informative pixels from the positive pairs can result in inefficient training, replacing patches of a specific object with a different one can steer the model from maximizing the agreement between different positive pairs. Moreover, joint embedding representation learning methods have not made robustness their primary training outcome. To this end, we propose the ViewMix augmentation policy, specially designed for self-supervised learning, upon generating different views of the same image, patches are cut and pasted from one view to another. By leveraging the different views created by this augmentation strategy, multiple joint embedding-based self-supervised methodologies obtained better localization capability and consistently outperformed their corresponding baseline methods. It is also demonstrated that incorporating ViewMix augmentation policy promotes robustness of the representations in the state-of-the-art methods. Furthermore, our experimentation and analysis of compute times suggest that ViewMix augmentation doesn't introduce any additional overhead compared to other counterparts.
Although Deep Neural Networks (DNNs), such as the convolutional neural networks (CNN) and Vision Transformers (ViTs), have been successfully applied in the field of computer vision, they are demonstrated to be vulnerable to well-sought Adversarial Examples (AEs) that can easily fool the DNNs. The research in AEs has been active, and many adversarial attacks and explanations have been proposed since they were discovered in 2014. The mystery of the AE's existence is still an open question, and many studies suggest that DNN training algorithms have blind spots. The salient objects usually do not overlap with boundaries; hence, the boundaries are not the DNN model's attention. Nevertheless, recent studies show that the boundaries can dominate the behavior of the DNN models. Hence, this study aims to look at the AEs from a different perspective and proposes an imperceptible adversarial attack that systemically attacks the input image boundary for finding the AEs. The experimental results have shown that the proposed boundary attacking method effectively attacks six CNN models and the ViT using only 32% of the input image content (from the boundaries) with an average success rate (SR) of 95.2% and an average peak signal-to-noise ratio of 41.37 dB. Correlation analyses are conducted, including the relation between the adversarial boundary's width and the SR and how the adversarial boundary changes the DNN model's attention. This paper's discoveries can potentially advance the understanding of AEs and provide a different perspective on how AEs can be constructed.
We investigate the Cauchy problem to the compressible planar non-resistive magnetohydrodynamic equations with zero heat conduction. The global existence of strong solutions to such a model has been established by Li and Li (J. Differential Equations 316: 136--157, 2022). However, to our best knowledge, so far there is no result on the behavior of the entropy near the vacuum region for this model. The main novelty of this paper is to give a positive response to this problem. More precisely, by a series of a priori estimates, especially the singular type estimates, we show that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density.
During the last decades, many studies have been dedicated to improving the performance of neural networks, for example, the network architectures, initialization, and activation. However, investigating the importance and effects of learnable padding methods in deep learning remains relatively open. To mitigate the gap, this paper proposes a novel trainable Padding Module that can be placed in a deep learning model. The Padding Module can optimize itself without requiring or influencing the model's entire loss function. To train itself, the Padding Module constructs a ground truth and a predictor from the inputs by leveraging the underlying structure in the input data for supervision. As a result, the Padding Module can learn automatically to pad pixels to the border of its input images or feature maps. The padding contents are realistic extensions to its input data and simultaneously facilitate the deep learning model's downstream task. Experiments have shown that the proposed Padding Module outperforms the state-of-the-art competitors and the baseline methods. For example, the Padding Module has 1.23% and 0.44% more classification accuracy than the zero padding when tested on the VGG16 and ResNet50.
Incorporating geometric transformations that reflect the relative position changes between an observer and an object into computer vision and deep learning models has attracted much attention in recent years. However, the existing proposals mainly focus on the affine transformation that is insufficient to reflect such geometric position changes. Furthermore, current solutions often apply a neural network module to learn a single transformation matrix, which not only ignores the importance of multi-view analysis but also includes extra training parameters from the module apart from the transformation matrix parameters that increase the model complexity. In this paper, a perspective transformation layer is proposed in the context of deep learning. The proposed layer can learn homography, therefore reflecting the geometric positions between observers and objects. In addition, by directly training its transformation matrices, a single proposed layer can learn an adjustable number of multiple viewpoints without considering module parameters. The experiments and evaluations confirm the superiority of the proposed layer.