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Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial}$ closed $(0,1)$-form $f\in L^p_{(0,1)}(D^n)$ solving the Cauchy-Riemain equation $\overline{\partial} u=f$ on the product domains $D^n$ and obtain the $L^p$-estimates for all $1

Currently, Si vacancy ($\mathrm{V}_\mathrm{Si}$) color centers in SiC are of significant interest due to their potential applications in quantum sensing and quantum communication. Meanwhile, the qualities of laser-induced color centers are well guaranteed. Femtosecond laser processing suffices for increasing the yield of $\mathrm{V}_\mathrm{Si}$ color centers in bulk materials and forms crater-shaped enriched regions on the surface. However, there is a notable absence of existing simulation methods to explain the mechanisms behind laser-assisted $\mathrm{V}_\mathrm{Si}$ color center generation. In this work, we design a three-dimensional molecular dynamics (3D-MD) model using an integral hemi-ellipsoidal shell mathematical model to simulate the interaction of Gaussian laser beams with bulk materials. Furthermore, we calculate the transmittance, absorption coefficient, refractive index, and reflectivity of $4H$-SiC. Then, the absorptance of a 1030 nm laser in 350 {\mu}m-thick $4H$-SiC material is abtained to simulate the energy loss during the actual processing. Finally, the study analyzes the movement trajectories of $\mathrm{V}_\mathrm{Si}$ color centers and explains the source of $\mathrm{V}_\mathrm{Si}$ on the surface. This analysis explains the reasons for the enrichment of color centers in the crater-shaped regions formed after laser deposition. Our work provides an effective 3D-MD modeling approach to study the processing mechanisms of laser interaction with semiconductor materials, offering insights into efficient $\mathrm{V}_\mathrm{Si}$ color center creation processes., Comment: 7 pages, 5 figures

Graph prompt tuning has emerged as a promising paradigm to effectively transfer general graph knowledge from pre-trained models to various downstream tasks, particularly in few-shot contexts. However, its susceptibility to backdoor attacks, where adversaries insert triggers to manipulate outcomes, raises a critical concern. We conduct the first study to investigate such vulnerability, revealing that backdoors can disguise benign graph prompts, thus evading detection. We introduce Krait, a novel graph prompt backdoor. Specifically, we propose a simple yet effective model-agnostic metric called label non-uniformity homophily to select poisoned candidates, significantly reducing computational complexity. To accommodate diverse attack scenarios and advanced attack types, we design three customizable trigger generation methods to craft prompts as triggers. We propose a novel centroid similarity-based loss function to optimize prompt tuning for attack effectiveness and stealthiness. Experiments on four real-world graphs demonstrate that Krait can efficiently embed triggers to merely 0.15% to 2% of training nodes, achieving high attack success rates without sacrificing clean accuracy. Notably, in one-to-one and all-to-one attacks, Krait can achieve 100% attack success rates by poisoning as few as 2 and 22 nodes, respectively. Our experiments further show that Krait remains potent across different transfer cases, attack types, and graph neural network backbones. Additionally, Krait can be successfully extended to the black-box setting, posing more severe threats. Finally, we analyze why Krait can evade both classical and state-of-the-art defenses, and provide practical insights for detecting and mitigating this class of attacks., Comment: Previously submitted to CCS on 04/29

Star clusters were historically considered simple stellar populations, with all stars sharing the same age and initial chemical composition. However, the presence of chemical anomalies in globular clusters (GCs), called multiple stellar populations (MPs), has challenged star formation theories in dense environments. Literature studies show that mass, metallicity, and age are likely controlling parameters for the manifestation of MPs. Identifying the limit between clusters with/without MPs in physical parameter space is crucial to reveal the driving mechanism behind their presence. In this study, we look for MP signals in Whiting 1, traditionally considered a young GC. Using the Magellan telescope, we obtained low-resolution spectra within $\rm \lambda\lambda = 3850-5500 \r{A}$ for eight giants of Whiting 1. We measured the C and N abundances from the CN and CH spectral indices. C and N abundances have variations comparable with their measurement errors ($\sim0.1$ dex), suggesting that MPs are absent from Whiting 1. Combining these findings with literature studies, we propose a limit in the metallicity vs. cluster compactness index parameter space, which relatively clearly separates star clusters with/without MPs (GCs/open clusters). This limit is physically motivated. On a larger scale, the galactic environment determines cluster compactness and metallicity, leading to metal-rich, diffuse, old clusters formed ex situ. Our proposed limit also impacts our understanding of the formation of the Sagittarius dwarf galaxy: star clusters formed after the first starburst (age$\lesssim 8-10$ Gyr). These clusters are simple stellar populations because the enriched galactic environment is no longer suitable for MP formation., Comment: 11 pages, 4 figures, SCPMA accepted

Despite remarkable success in diverse web-based applications, Graph Neural Networks(GNNs) inherit and further exacerbate historical discrimination and social stereotypes, which critically hinder their deployments in high-stake domains such as online clinical diagnosis, financial crediting, etc. However, current fairness research that primarily craft on i.i.d data, cannot be trivially replicated to non-i.i.d. graph structures with topological dependence among samples. Existing fair graph learning typically favors pairwise constraints to achieve fairness but fails to cast off dimensional limitations and generalize them into multiple sensitive attributes; besides, most studies focus on in-processing techniques to enforce and calibrate fairness, constructing a model-agnostic debiasing GNN framework at the pre-processing stage to prevent downstream misuses and improve training reliability is still largely under-explored. Furthermore, previous work on GNNs tend to enhance either fairness or privacy individually but few probe into their interplays. In this paper, we propose a novel model-agnostic debiasing framework named MAPPING (\underline{M}asking \underline{A}nd \underline{P}runing and Message-\underline{P}assing train\underline{ING}) for fair node classification, in which we adopt the distance covariance($dCov$)-based fairness constraints to simultaneously reduce feature and topology biases in arbitrary dimensions, and combine them with adversarial debiasing to confine the risks of attribute inference attacks. Experiments on real-world datasets with different GNN variants demonstrate the effectiveness and flexibility of MAPPING. Our results show that MAPPING can achieve better trade-offs between utility and fairness, and mitigate privacy risks of sensitive information leakage., Comment: Finished May last year. Remember to submit all papers to arXiv early without compromising the principles of conferences

Medical image registration is a critical task that estimates the spatial correspondence between pairs of images. However, current traditional and deep-learning-based methods rely on similarity measures to generate a deforming field, which often results in disproportionate volume changes in dissimilar regions, especially in tumor regions. These changes can significantly alter the tumor size and underlying anatomy, which limits the practical use of image registration in clinical diagnosis. To address this issue, we have formulated image registration with tumors as a constraint problem that preserves tumor volumes while maximizing image similarity in other normal regions. Our proposed strategy involves a two-stage process. In the first stage, we use similarity-based registration to identify potential tumor regions by their volume change, generating a soft tumor mask accordingly. In the second stage, we propose a volume-preserving registration with a novel adaptive volume-preserving loss that penalizes the change in size adaptively based on the masks calculated from the previous stage. Our approach balances image similarity and volume preservation in different regions, i.e., normal and tumor regions, by using soft tumor masks to adjust the imposition of volume-preserving loss on each one. This ensures that the tumor volume is preserved during the registration process. We have evaluated our strategy on various datasets and network architectures, demonstrating that our method successfully preserves the tumor volume while achieving comparable registration results with state-of-the-art methods. Our codes is available at: \url{https://dddraxxx.github.io/Volume-Preserving-Registration/}., Comment: ICCV 2023 Poster

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in $n$-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on a bounded product domain $\Omega^n$, where $\Omega$ is any bounded domain in $\mathbb{C}$ with $C^{1,\alpha}$ boundary for some $\alpha>0$., Comment: arXiv admin note: substantial text overlap with arXiv:2211.01507

Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the Fubini-Study metric of the complex projective space of infinite dimension. Several new domains with surprising curvature properties for their Bergman metrics are constructed. A new conjecture is also formulated at the end of the paper.

In this paper we present a chemical and kinematic analysis of two ultra-faint dwarf galaxies (UFDs), Aquarius II (Aqu~II) and \text{Bo\"{o}tes II} (Boo~II), using Magellan/IMACS spectroscopy. We present the largest sample of member stars for Boo~II (12), and the largest sample of red-giant-branch members with metallicity measurements for Aqu~II (8). In both UFDs, over 80\% of targets selected based on $Gaia$ proper motions turned out to be spectroscopic members. In order to maximize the accuracy of stellar kinematic measurements, we remove the identified binary stars and RR Lyrae variables. For Aqu~II we measure a systemic velocity of $-65.3 \pm 1.8$ km s$^{-1}$ and a metallicity of [Fe/H] = $-2.57^{+0.17}_{-0.17}$. When compared with previous measurements, these values display a $\sim 6$ km s$^{-1}$ difference in radial velocity and a decrease of 0.27 dex in metallicity. Similarly for Boo~II, we measure a systemic velocity of $-130.4^{+1.4}_{-1.1}$ km s$^{-1}$, more than 10 km s$^{-1}$ different from the literature, a metallicity almost 1 dex smaller at [Fe/H] = $-2.71^{+0.11}_{-0.10}$, and a velocity dispersion 3 times smaller at $\sigma_{v_{\rm hel}} = 2.9^{+1.6}_{-1.2}$ km s$^{-1}$. Additionally, we derive systemic proper motion parameters and model the orbits of both UFDs. Finally, we highlight the extremely dark matter dominated nature of Aqu~II and compute the J-factor for both galaxies to aid searches of dark matter annihilation. Despite the small size and close proximity of Boo~II, it is an intermediate target for the indirect detection of dark matter annihilation due to its low velocity dispersion and corresponding low dark matter density., Comment: 21 pages, 7 figures, 5 tables. Submitted to AAS Journal

The eighteenth data release of the Sloan Digital Sky Surveys (SDSS) is the first one for SDSS-V, the fifth generation of the survey. SDSS-V comprises three primary scientific programs, or "Mappers": Milky Way Mapper (MWM), Black Hole Mapper (BHM), and Local Volume Mapper (LVM). This data release contains extensive targeting information for the two multi-object spectroscopy programs (MWM and BHM), including input catalogs and selection functions for their numerous scientific objectives. We describe the production of the targeting databases and their calibration- and scientifically-focused components. DR18 also includes ~25,000 new SDSS spectra and supplemental information for X-ray sources identified by eROSITA in its eFEDS field. We present updates to some of the SDSS software pipelines and preview changes anticipated for DR19. We also describe three value-added catalogs (VACs) based on SDSS-IV data that have been published since DR17, and one VAC based on the SDSS-V data in the eFEDS field., Comment: Accepted to ApJS

In this paper, the author solves the long term open problem of Kerzman on sup-norm estimate for Cauchy-Riemann equation on polydisc in $n$-dimensional complex space. The problem has been open since 1971. He also extends and solves the problem on a bounded product domain $\Omega^n$, where $\Omega$ either is simply connected with $C^{1,\alpha}$ boundary or satisfies a uniform exterior ball condition with piecewise $C^1$ boundary.

Currently, the engineering of miniature spectrometers mainly faces three problems: the mismatch between the number of filters at the front end of the detector and the spectral reconstruction accuracy; the lack of a stable spectral reconstruction algorithm; and the lack of a spectral reconstruction evaluation method suitable for engineering. Therefore, based on 20 sets of filters, this paper classifies and optimizes the filter array by the K-means algorithm and particle swarm algorithm, and obtains the optimal filter combination under different matrix dimensions. Then, the truncated singular value decomposition-convex optimization algorithm is used for high-precision spectral reconstruction, and the detailed spectral reconstruction process of two typical target spectra is described. In terms of spectral evaluation, due to the strong randomness of the target detected during the working process of the spectrometer, the standard value of the target spectrum cannot be obtained. Therefore, for the first time, we adopt the method of joint cross-validation of multiple sets of data for spectral evaluation. The results show that when the random error of positive or negative 2 code values is applied multiple times for reconstruction, the spectral angle cosine value between the reconstructed curves becomes more than 0.995, which proves that the spectral reconstruction under this algorithm has high stability. At the same time, the spectral angle cosine value of the spectral reconstruction curve and the standard curve can reach above 0.99, meaning that it realizes a high-precision spectral reconstruction effect. A high-precision spectral reconstruction algorithm based on truncated singular value-convex optimization, which is suitable for engineering applications, is established in this paper, providing important scientific research value for the engineering application of micro-spectrometers., Comment: 22pages 11figures

Arbitrary-oriented object detection (AOOD) plays a significant role for image understanding in remote sensing scenarios. The existing AOOD methods face the challenges of ambiguity and high costs in angle representation. To this end, a multi-grained angle representation (MGAR) method, consisting of coarse-grained angle classification (CAC) and fine-grained angle regression (FAR), is proposed. Specifically, the designed CAC avoids the ambiguity of angle prediction by discrete angular encoding (DAE) and reduces complexity by coarsening the granularity of DAE. Based on CAC, FAR is developed to refine the angle prediction with much lower costs than narrowing the granularity of DAE. Furthermore, an Intersection over Union (IoU) aware FAR-Loss (IFL) is designed to improve accuracy of angle prediction using an adaptive re-weighting mechanism guided by IoU. Extensive experiments are performed on several public remote sensing datasets, which demonstrate the effectiveness of the proposed MGAR. Moreover, experiments on embedded devices demonstrate that the proposed MGAR is also friendly for lightweight deployments., Comment: 13 pages, 9 figures, 14 tables