arXiv subjects

Xin Liao

Publications and source records attributed to Xin Liao.

At least 37 records · Page 2Linked to original sources

arXiv2025

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem

We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u\in H_{X,0}^{1}(Ω),\hfill \end{array} \right. \] where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the self-adjoint sub-elliptic operator associated with Hörmander vector fields $X=(X_{1},X_{2},\ldots,X_{m})$, $Ω$ is an open bounded subset in $\mathbb{R}^n$, and $H_{X,0}^{1}(Ω)$ denotes the weighted Sobolev space. We establish multiplicity results for sign-changing solutions using a perturbation method alongside refined techniques for invariant sets. The pivotal aspect lies in the estimation of the lower bounds of min-max values associated with sign-changing critical points. In this paper, we construct two distinct lower bounds of these min-max values. The first one is derived from the lower bound of Dirichlet eigenvalues of $-\triangle_{X}$, while the second one is based on the Morse-type estimates and Cwikel-Lieb-Rozenblum type inequality in degenerate cases. These lower bounds provide different sufficient conditions for multiplicity results, each with unique advantages and are not mutually inclusive, particularly in the general non-equiregular case. This novel observation suggests that in some sense, the situation for sub-elliptic equations would have essential difference from the classical elliptic framework.

math.AP↗

arXiv2025

A Nonlinear Low-rank Representation Model with Convolutional Neural Network for Imputing Water Quality Data

The integrity of Water Quality Data (WQD) is critical in environmental monitoring for scientific decision-making and ecological protection. However, water quality monitoring systems are often challenged by large amounts of missing data due to unavoidable problems such as sensor failures and communication delays, which further lead to water quality data becoming High-Dimensional and Sparse (HDS). Traditional data imputation methods are difficult to depict the potential dynamics and fail to capture the deep data features, resulting in unsatisfactory imputation performance. To effectively address the above issues, this paper proposes a Nonlinear Low-rank Representation model (NLR) with Convolutional Neural Networks (CNN) for imputing missing WQD, which utilizes CNNs to implement two ideas: a) fusing temporal features to model the temporal dependence of data between time slots, and b) Extracting nonlinear interactions and local patterns to mine higher-order relationships features and achieve deep fusion of multidimensional information. Experimental studies on three real water quality datasets demonstrate that the proposed model significantly outperforms existing state-of-the-art data imputation models in terms of estimation accuracy. It provides an effective approach for handling water quality monitoring data in complex dynamic environments.

cs.LG↗

arXiv2025

MetaSSL: A General Heterogeneous Loss for Semi-Supervised Medical Image Segmentation

Semi-Supervised Learning (SSL) is important for reducing the annotation cost for medical image segmentation models. State-of-the-art SSL methods such as Mean Teacher, FixMatch and Cross Pseudo Supervision (CPS) are mainly based on consistency regularization or pseudo-label supervision between a reference prediction and a supervised prediction. Despite the effectiveness, they have overlooked the potential noise in the labeled data, and mainly focus on strategies to generate the reference prediction, while ignoring the heterogeneous values of different unlabeled pixels. We argue that effectively mining the rich information contained by the two predictions in the loss function, instead of the specific strategy to obtain a reference prediction, is more essential for SSL, and propose a universal framework MetaSSL based on a spatially heterogeneous loss that assigns different weights to pixels by simultaneously leveraging the uncertainty and consistency information between the reference and supervised predictions. Specifically, we split the predictions on unlabeled data into four regions with decreasing weights in the loss: Unanimous and Confident (UC), Unanimous and Suspicious (US), Discrepant and Confident (DC), and Discrepant and Suspicious (DS), where an adaptive threshold is proposed to distinguish confident predictions from suspicious ones. The heterogeneous loss is also applied to labeled images for robust learning considering the potential annotation noise. Our method is plug-and-play and general to most existing SSL methods. The experimental results showed that it improved the segmentation performance significantly when integrated with existing SSL frameworks on different datasets. Code is available at https://github.com/HiLab-git/MetaSSL.

cs.CV↗

arXiv2025

Radio-Frequency Quantum Rectification in Kagome Superconductor CsV3Sb5

Rectification of electromagnetic fields into direct current (DC) is pivotal for energy harvesting, wireless charging, and next-generation communication technologies. The superconducting diode effect, which exploits the nonreciprocal transport of dissipationless superconducting currents, offers ultra-low power consumption and high rectification ratios. Combining the superconducting diode effect with the AC Josephson effect holds promise for converting radio-frequency (rf) irradiation into a quantized DC output. However, experimental realization has been hindered by challenges in achieving the necessary symmetry breaking and fabricating high-performance Josephson junctions. Here we demonstrate the quantum rectification in kagome superconductor CsV3Sb5, which hosts emergent Josephson effects and a zero-field Josephson diode. Under rf irradiation, a DC voltage emerges without applied bias, scaling linearly with frequency as V = hf/2e, where h is Planck's constant, f is the microwave frequency, and e is the electron charge. Furthermore, the rectified voltage exhibits quantized steps with increasing rf power, consistent with Shapiro step quantization. Our work establishes CsV3Sb5 as a versatile platform for wireless quantum power supplies and charging, and underscores the intertwined order parameters as a promising pathway for precise quantum matter control.

cond-mat.supr-con↗

arXiv2025

Towards Imperceptible JPEG Image Hiding: Multi-range Representations-driven Adversarial Stego Generation

Image hiding fully explores the hidden potential of deep learning-based models, aiming to conceal image-level messages within cover images and reveal them from stego images to achieve covert communication. Existing hiding schemes are easily detected by the naked eyes or steganalyzers due to the cover type confined to the spatial domain, single-range feature extraction and attacks, and insufficient loss constraints. To address these issues, we propose a multi-range representations-driven adversarial stego generation framework called MRAG for JPEG image hiding. This design stems from the fact that steganalyzers typically combine local-range and global-range information to better capture hidden traces. Specifically, MRAG integrates the local-range characteristic of the convolution and the global-range modeling of the transformer. Meanwhile, a features angle-norm disentanglement loss is designed to launch multi-range representations-driven feature-level adversarial attacks. It computes the adversarial loss between covers and stegos based on the surrogate steganalyzer's classified features, i.e., the features before the last fully connected layer. Under the dual constraints of features angle and norm, MRAG can delicately encode the concatenation of cover and secret into subtle adversarial perturbations from local and global ranges relevant to steganalysis. Therefore, the resulting stego can achieve visual and steganalysis imperceptibility. Moreover, coarse-grained and fine-grained frequency decomposition operations are devised to transform the input, introducing multi-grained information. Extensive experiments demonstrate that MRAG can achieve state-of-the-art performance.

cs.CV↗

arXiv2025

Adaptive Cubic Regularized Second-Order Latent Factor Analysis Model

High-dimensional and incomplete (HDI) data, characterized by massive node interactions, have become ubiquitous across various real-world applications. Second-order latent factor models have shown promising performance in modeling this type of data. Nevertheless, due to the bilinear and non-convex nature of the SLF model's objective function, incorporating a damping term into the Hessian approximation and carefully tuning associated parameters become essential. To overcome these challenges, we propose a new approach in this study, named the adaptive cubic regularized second-order latent factor analysis (ACRSLF) model. The proposed ACRSLF adopts the two-fold ideas: 1) self-tuning cubic regularization that dynamically mitigates non-convex optimization instabilities; 2) multi-Hessian-vector product evaluation during conjugate gradient iterations for precise second-order information assimilation. Comprehensive experiments on two industrial HDI datasets demonstrate that the ACRSLF converges faster and achieves higher representation accuracy than the advancing optimizer-based LFA models.

cs.LG↗

arXiv2025

OpenPath: Open-Set Active Learning for Pathology Image Classification via Pre-trained Vision-Language Models

Pathology image classification plays a crucial role in accurate medical diagnosis and treatment planning. Training high-performance models for this task typically requires large-scale annotated datasets, which are both expensive and time-consuming to acquire. Active Learning (AL) offers a solution by iteratively selecting the most informative samples for annotation, thereby reducing the labeling effort. However, most AL methods are designed under the assumption of a closed-set scenario, where all the unannotated images belong to target classes. In real-world clinical environments, the unlabeled pool often contains a substantial amount of Out-Of-Distribution (OOD) data, leading to low efficiency of annotation in traditional AL methods. Furthermore, most existing AL methods start with random selection in the first query round, leading to a significant waste of labeling costs in open-set scenarios. To address these challenges, we propose OpenPath, a novel open-set active learning approach for pathological image classification leveraging a pre-trained Vision-Language Model (VLM). In the first query, we propose task-specific prompts that combine target and relevant non-target class prompts to effectively select In-Distribution (ID) and informative samples from the unlabeled pool. In subsequent queries, Diverse Informative ID Sampling (DIS) that includes Prototype-based ID candidate Selection (PIS) and Entropy-Guided Stochastic Sampling (EGSS) is proposed to ensure both purity and informativeness in a query, avoiding the selection of OOD samples. Experiments on two public pathology image datasets show that OpenPath significantly enhances the model's performance due to its high purity of selected samples, and outperforms several state-of-the-art open-set AL methods. The code is available at \href{https://github.com/HiLab-git/OpenPath}{https://github.com/HiLab-git/OpenPath}..

cs.CV↗

arXiv2025

Sharp Stability of Global Compactness on the Heisenberg Group

In this paper, we establish a sharp stability inequality on the Heisenberg group for functions that are close to the sum of m weakly interacting Jerison-Lee bubbles. As a consequence, we obtain a sharp quantitative stability of global compactness for non-negative functions on Heisenberg group.

math.AP↗

arXiv2025

A Causal Convolutional Low-rank Representation Model for Imputation of Water Quality Data

The monitoring of water quality is a crucial part of environmental protection, and a large number of monitors are widely deployed to monitor water quality. Due to unavoidable factors such as data acquisition breakdowns, sensors and communication failures, water quality monitoring data suffers from missing values over time, resulting in High-Dimensional and Sparse (HDS) Water Quality Data (WQD). The simple and rough filling of the missing values leads to inaccurate results and affects the implementation of relevant measures. Therefore, this paper proposes a Causal convolutional Low-rank Representation (CLR) model for imputing missing WQD to improve the completeness of the WQD, which employs a two-fold idea: a) applying causal convolutional operation to consider the temporal dependence of the low-rank representation, thus incorporating temporal information to improve the imputation accuracy; and b) implementing a hyperparameters adaptation scheme to automatically adjust the best hyperparameters during model training, thereby reducing the tedious manual adjustment of hyper-parameters. Experimental studies on three real-world water quality datasets demonstrate that the proposed CLR model is superior to some of the existing state-of-the-art imputation models in terms of imputation accuracy and time cost, as well as indicating that the proposed model provides more reliable decision support for environmental monitoring.

cs.LG↗

arXiv2025

Academic Network Representation via Prediction-Sampling Incorporated Tensor Factorization

Accurate representation to an academic network is of great significance to academic relationship mining like predicting scientific impact. A Latent Factorization of Tensors (LFT) model is one of the most effective models for learning the representation of a target network. However, an academic network is often High-Dimensional and Incomplete (HDI) because the relationships among numerous network entities are impossible to be fully explored, making it difficult for an LFT model to learn accurate representation of the academic network. To address this issue, this paper proposes a Prediction-sampling-based Latent Factorization of Tensors (PLFT) model with two ideas: 1) constructing a cascade LFT architecture to enhance model representation learning ability via learning academic network hierarchical features, and 2) introducing a nonlinear activation-incorporated predicting-sampling strategy to more accurately learn the network representation via generating new academic network data layer by layer. Experimental results from the three real-world academic network datasets show that the PLFT model outperforms existing models when predicting the unexplored relationships among network entities.

cs.LG↗

arXiv2025

Stability of the second non trivial eigenvalue of the Neumann Laplacian

In this paper, building on the ideas of Brasco and Pratelli (Geom. Funct. Anal., 22 (2012), 107-135), we establish a stability estimate for Bucur and Henrot's inequality (Acta Math., 222 (2019), 337-361). Their inequality asserts that, among regular sets of given measure, the disjoint union of two balls with the same radius maximizes the second non trivial eigenvalue of the Neumann Laplacian. Last week I was informed of the same result of this paper has been published by Wang K, Wu H. A quantitative Bucur Henrot inequality. Mathematische Nachrichten, 2022, 295(12): 2436-2451. So thearticle has been deprecated.

math.SP↗

arXiv2025

Self-stabilized charge states in a double-decker molecular magnet on Pb(111)

Electron charging play key roles in physiochemical processes, whose intrinsic stabilization in single molecules is desirable for tailoring molecular functionality and developing molecular devices, but remains elusive on surfaces. Here, we show molecular charge states can be self-stabilized via intramolecular distortion in single bis(phthalocyaninato)terbium(III) (TbPc2) double-decker molecules, that were grown on Pb(111) substrate. Using scanning tunneling microscopy and spectroscopy, we identify fractions of TbPc2 molecules reduce to 2-fold symmetry, expressing energy-split molecular orbitals and two types of different spin states. Our first principles calculations unveil that the symmetry reduction is induced by charging-triggered Jahn-Teller distortions, which lifts the degenerate orbitals into two 2-fold symmetric orbitals. Single or double occupancy of the lower-energy orbital results in different molecular spin states. Such intramolecular distortion traps the excess electrons stably without explicit involvement of the substrate, in contrast to previously observed molecular charge states. These charged single molecule can be manipulated with the tip individually. This study offers a new avenue for tailoring the charge and spin states of molecules.

cond-mat.mes-hall↗

arXiv2025

Charge density wave modulated third-order nonlinear Hall effect in 1$T$-VSe$_2$ nanosheets

We report the observation of a pronounced third-order nonlinear Hall effect (NLHE) in 1$T$-phase VSe$_2$ nanosheets, synthesized using chemical vapor deposition (CVD). The nanosheets exhibit a charge density wave (CDW) transition at $\sim$77 K. Detailed angle-resolved and temperature-dependent measurements reveal a strong cubic relationship between the third-harmonic Hall voltage $V_{3ω}^\perp$ and the bias current $I_ω$, persisting up to room temperature. Notably, the third-order NLHE demonstrates a twofold angular dependence and significant enhancement below the CDW transition temperature, indicative of threefold symmetry breaking in the CDW phase. Scaling analysis suggests that the intrinsic contribution from the Berry connection polarizability tensor is substantially increased in the CDW phase, while extrinsic effects dominate at higher temperatures. Our findings highlight the critical role of CDW-induced symmetry breaking in modulating quantum geometric properties and nonlinear transport phenomena in VSe$_2$, paving the way for future explorations in low-dimensional quantum materials.

cond-mat.mes-hall↗

arXiv2025

LDR-Net: A Novel Framework for AI-generated Image Detection via Localized Discrepancy Representation

With the rapid advancement of generative models, the visual quality of generated images has become nearly indistinguishable from the real ones, posing challenges to content authenticity verification. Existing methods for detecting AI-generated images primarily focus on specific forgery clues, which are often tailored to particular generative models like GANs or diffusion models. These approaches struggle to generalize across architectures. Building on the observation that generative images often exhibit local anomalies, such as excessive smoothness, blurred textures, and unnatural pixel variations in small regions, we propose the localized discrepancy representation network (LDR-Net), a novel approach for detecting AI-generated images. LDR-Net captures smoothing artifacts and texture irregularities, which are common but often overlooked. It integrates two complementary modules: local gradient autocorrelation (LGA) which models local smoothing anomalies to detect smoothing anomalies, and local variation pattern (LVP) which captures unnatural regularities by modeling the complexity of image patterns. By merging LGA and LVP features, a comprehensive representation of localized discrepancies can be provided. Extensive experiments demonstrate that our LDR-Net achieves state-of-the-art performance in detecting generated images and exhibits satisfactory generalization across unseen generative models. The code will be released upon acceptance of this paper.

cs.CV↗

arXiv2025

Current-induced magnetoresistance hysteresis in the kagome superconductor CsV$_3$Sb$_5$

We report the observation of current-modulated magnetoresistance hysteresis below the superconducting transition temperature in the kagome superconductor CsV$_3$Sb$_5$. This highly tunable hysteresis behavior is confined to the superconducting state and vanishes when superconductivity is fully suppressed, directly linking magnetoresistance hysteresis to the superconducting order in CsV$_3$Sb$_5$. Additionally, the superconducting diode effect driven by a small magnetic field is observed, indicating the enhanced electronic magnetochiral anisotropy by the chiral domain-wall scattering. Our findings position CsV$_3$Sb$_5$ as a promising platform for exploring nontrivial physical phenomena, including unconventional pairing mechanisms and topological superconductivity.

cond-mat.supr-con↗

arXiv2025

Giant Third-Order Nonlinearity Induced by the Quantum Metric Quadrupole in Few-Layer WTe2

The quantum geometric properties of topological materials underpin many exotic physical phenomena and applications. Quantum nonlinearity has emerged as a powerful probe for revealing these properties. The Berry curvature dipole in nonmagnetic materials and the quantum metric dipole in antiferromagnets have been explored by studying the second-order nonlinear Hall effect. Although the quadrupole moment of the quantum geometric tensor is theoretically predicted to induce higher-order quantum nonlinearity, the quantum metric quadrupole remains experimentally unexplored. Here, we report the quantum metric quadrupole induced third-order nonlinear longitudinal electrical response in few-layer WTe2, persisting up to room temperature. Angle-resolved third-harmonic current-voltage characteristics are found consistent with the intrinsic crystal symmetry of WTe2. Through temperature variation and scaling analysis, we identify the quantum metric quadrupole as the physical origin of the observed third-order longitudinal nonlinearity. Additionally, we determine the angle dependence of the quantum metric quadrupole, establishing third-order nonlinearity as an efficient method for revealing the quantum metric structure.

cond-mat.mes-hall↗

arXiv2024

Nonlinear Valley and Spin Valves in Bilayer Graphene

Nonlinear transport plays a vital role in probing the quantum geometry of Bloch electrons, valley chirality, and carrier scattering mechanisms. The nonlinear Hall effect, characterized by a nonlinear scaling of Hall voltage with longitudinal current, has been explored to reveal the Berry curvature and quantum metric related physics. In this work, we extend the study of nonlinear transport to spin and valley degrees of freedom. Using bilayer graphene devices with Fe3GeTe2 contacts, we observe a second-order nonlinear spin current exhibiting spin valve-like behaviors. By tracking magnetic moment precession under an in-plane magnetic field, we identify a significantly enhanced critical magnetic field required for in-plane rotation, suggesting out-of-plane valley polarization induced by ferromagnetic proximity. These findings offer deep insights into the interplay of valley and spin in second-order nonlinear transport, opening avenues for promising device applications.

cond-mat.mes-hall↗

arXiv2024

Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4

We report on the observation of the linear anomalous Hall effect (AHE) in the nonmagnetic Weyl semimetal TaIrTe4. This is achieved by applying a direct current Idc and an alternating current Iac (Iac<<Idc) in TaIrTe4, where the former induces time-reversal symmetry breaking and the latter probes the triggered AHE. The anomalous Hall resistance VacH/Iac shows a linear dependence on Idc and changes sign with the polarity of Idc. In temperature-dependent measurements, VacH/Iac also experiences a sign reversal at 100 K, consistent with the temperature-dependent nonlinear Hall effect (NLHE). Furthermore, in measurements involving only dc transport, the dc Hall voltage exhibits a quadratic relationship with Idc. When the Idc direction is reversed, the Hall resistance changes sign, demonstrating a colossal nonreciprocal Hall effect (NRHE). Our theoretical calculations suggest that the observed linear AHE, NLHE, and NRHE all dominantly originate from the current-induced orbital magnetization compared to the minor spin contribution. This work provides deep insights into the orbital magnetoelectric effect and nonlinear Hall response, promising precise electric control of out-of-plane polarized orbit flow.

cond-mat.mes-hall↗