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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 $\rho({\bf{x}}, t)$ verifies $\rho({\bf{x}},0)\geq c>0$ and $\sup_{t\geq 0}\|\rho(\cdot,t)\|_{L^\infty}\leq M$, 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 $\sup_{t\geq 0}\|\rho(\cdot,t)\|_{C^\alpha}\leq M$ with $\alpha$ 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., Comment: We add a Ref. [24] and Remark 1.5 in this revision

Summarization is a fundamental task in natural language processing (NLP) and since large language models (LLMs), such as GPT-4 and Claude, come out, increasing attention has been paid to long-form summarization whose input sequences are much longer, indicating more information contained. The current evaluation metrics either use similarity-based metrics like ROUGE and BERTScore which rely on similarity and fail to consider informativeness or LLM-based metrics, lacking quantitative analysis of information richness and are rather subjective. In this paper, we propose a new evaluation metric called EVA-Score using Atomic Fact Chain Generation and Document-level Relation Extraction together to automatically calculate the informativeness and give a definite number as an information score. Experiment results show that our metric shows a state-of-the-art correlation with humans. We also re-evaluate the performance of LLMs on long-form summarization comprehensively from the information aspect, forecasting future ways to use LLMs for long-form summarization., Comment: 16 pages, 3 figures, submitted to EMNLP

We establish the realization of the Reshetikhin-Semenov-Tian-Shansky (RS) superalgebra for two parameter quantum affine superalgebra $U_{p, q}(\widehat{\mathfrak{gl}(m|n))}$. We find a simple coproduct for the Drinfeld generators and obtain a Hopf superalgebra structure for this quantum affine superalgebra., Comment: 28 pages, added two related references

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 \'a la Faddeev, Reshetikhin and Takhtajan.

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.

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 {\sigma}-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 {\sigma}-bonded boron framework for the design of high-Tc superconducting borides that may expand to a broader variety of lightweight compounds., Comment: 5 pages

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.

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.

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., Comment: This paper was accepted for publication by the MDPI Applied Sciences journal

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., Comment: The paper has been accpeted for publication by IEEE Access

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., Comment: 19 pages

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., Comment: This paper has been accepted for publication by the IEEE Access

Supervised object detection methods provide subpar performance when applied to Foreign Object Debris (FOD) detection because FOD could be arbitrary objects according to the Federal Aviation Administration (FAA) specification. Current supervised object detection algorithms require datasets that contain annotated examples of every to-be-detected object. While a large and expensive dataset could be developed to include common FOD examples, it is infeasible to collect all possible FOD examples in the dataset representation because of the open-ended nature of FOD. Limitations of the dataset could cause FOD detection systems driven by those supervised algorithms to miss certain FOD, which can become dangerous to airport operations. To this end, this paper presents a self-supervised FOD localization by learning to predict the runway images, which avoids the enumeration of FOD annotation examples. The localization method utilizes the Vision Transformer (ViT) to improve localization performance. The experiments show that the method successfully detects arbitrary FOD in real-world runway situations. The paper also provides an extension to the localization result to perform classification; a feature that can be useful to downstream tasks. To train the localization, this paper also presents a simple and realistic dataset creation framework that only collects clean runway images. The training and testing data for this method are collected at a local airport using unmanned aircraft systems (UAS). Additionally, the developed dataset is provided for public use and further studies., Comment: This paper has been accepted for publication by the 2022 International Conference on Computational Science & Computational Intelligence (CSCI'22), Research Track on Signal & Image Processing, Computer Vision & Pattern Recognition

In recent years, crowd counting has become an important issue in computer vision. In most methods, the density maps are generated by convolving with a Gaussian kernel from the ground-truth dot maps which are marked around the center of human heads. Due to the fixed geometric structures in CNNs and indistinct head-scale information, the head features are obtained incompletely. Deformable convolution is proposed to exploit the scale-adaptive capabilities for CNN features in the heads. By learning the coordinate offsets of the sampling points, it is tractable to improve the ability to adjust the receptive field. However, the heads are not uniformly covered by the sampling points in the deformable convolution, resulting in loss of head information. To handle the non-uniformed sampling, an improved Normed-Deformable Convolution (\textit{i.e.,}NDConv) implemented by Normed-Deformable loss (\textit{i.e.,}NDloss) is proposed in this paper. The offsets of the sampling points which are constrained by NDloss tend to be more even. Then, the features in the heads are obtained more completely, leading to better performance. Especially, the proposed NDConv is a light-weight module which shares similar computation burden with Deformable Convolution. In the extensive experiments, our method outperforms state-of-the-art methods on ShanghaiTech A, ShanghaiTech B, UCF\_QNRF, and UCF\_CC\_50 dataset, achieving 61.4, 7.8, 91.2, and 167.2 MAE, respectively. The code is available at https://github.com/bingshuangzhuzi/NDConv

The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and singular in the vacuum region. In particular, it is unknown whether the entropy remains its boundedness. In the present paper, we investigate the Cauchy problem to the three-dimensional (3D) compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity only. We show that the uniform boundedness of the entropy and the $L^2$ regularities of the velocity and temperature can be propagated provided that the initial density decays suitably slow at infinity. The main tools are based on singularly weighted energy estimates and De Giorgi type iteration techniques developed by Li and Xin (arXiv:2111.14057) for the 3D full compressible Navier-Stokes system. Some new mathematical techniques and useful estimates are developed to deduce the lower and upper bounds on the entropy., Comment: 33 pages. arXiv admin note: text overlap with arXiv:2111.14057 by other authors

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., Comment: To appear in Discrete Contin. Dyn. Syst. Ser. B. arXiv admin note: substantial text overlap with arXiv: 2203.06658

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., Comment: To appear in Communications in Contemporary Mathematics

We investigate global well-posedness to the Cauchy problem of three-dimensional compressible viscous and heat-conducting micropolar fluid equations with zero density at infinity. By delicate energy estimates, we establish global existence and uniqueness of strong solutions under some smallness condition depending only on the parameters appeared in the system and the initial mass. In particular, the initial mass can be arbitrarily large. This improves our previous work [23]. Moreover, we also generalize the result [13] to the case that vacuum is allowed at infinity., Comment: 28 pages