arXiv subjects

Guodong Wang

Publications and source records attributed to Guodong Wang.

At least 19 recordsLinked to original sources

arXiv2026

Global persistence of nearly radial concentrated vortices in a bounded domain

In this paper, we study the evolution of nearly radial concentrated vortices for the incompressible Euler equation in a bounded planar domain. We prove that if a single vortex is initially concentrated near a strict local minimum point of the Robin function of the domain and is close, up to translation, to its symmetric decreasing rearrangement, then both its shape and location remain uniformly controlled for all time. We also establish an analogous result for a pair of opposite-sign vortices near a strict local minimum point of the corresponding Kirchhoff--Routh function. No symmetry is imposed on the domain or the initial data, and the initial data need not be close to any steady state. To prove these results, we develop a new Lyapunov mechanism for the evolution of vorticity governed by the Euler equation starting from such initial data, providing quantitative control of both vortex shape and location. Specifically, we combine kinetic-energy conservation and vorticity equimeasurability with several fixed-time estimates to obtain a conditional estimate, and then use a set-valued first-exit argument to propagate it globally in time.

math.AP↗

arXiv2026

ImputeECG: Deep Learning Reconstruction of Complete 12-Lead Electrocardiograms from Incomplete Recordings for Cardiac Assessment

Complete digital 12-lead electrocardiograms (ECGs) are essential for AI-enabled cardiovascular assessment, yet many clinical ECG records, particularly those digitized from ECG images, remain incomplete because of short display formats, incomplete waveform digitization, lead loss, or signal corruption. We developed ImputeECG, a mask-conditioned one-dimensional Transformer autoencoder that completes 12-lead, 10-s ECGs while retaining all observed samples. The model was trained on PTB-XL and evaluated on PTB-XL and CPSC2018 under simulated incomplete settings, with additional real-world validation in a 43,633-record Kailuan clinical cohort after ECG image digitization. Metrics were computed over originally missing regions, with analyses of morphology and downstream diagnostic utility. On PTB-XL, ImputeECG reduced missing-region MAE by 41.7-51.0% and MSE by 54.0-63.7% versus the strongest baseline, with lower errors in R-peak timing, RR interval, QRS duration, QT interval, and P-wave, QRS-complex, and T-wave reconstruction. On CPSC2018, ImputeECG reduced MAE by 49.7-51.9%, supporting external generalization. In downstream multi-label classification, ImputeECG restored performance to 92.28% AUROC and 33.88% AUPRC in the most incomplete PTB-XL setting, approaching complete-ECG performance. On CPSC2018, completed ECGs achieved 94.75-95.89% AUROC and 78.83-81.86% AUPRC across settings. In Kailuan, ECG completion improved zero-shot sex prediction AUROC from 82.6% to 85.8% and reduced age prediction MAE from 10.72 to 9.87 years after image-based ECG digitization. These findings support ECG completion as a practical strategy for converting incomplete ECG records into AI-ready 12-lead, 10-s digital signals and extending the usable scope of ECG archives for digital cardiac assessment.

cs.LG↗

arXiv2026

Quantitative Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus

In this paper, we establish quantitative estimates for the orbital stability of the first Laplacian eigenstates of the incompressible Euler equation on a two-dimensional flat torus. We focus mainly on the hexagonal torus, where the first Laplacian eigenspace has a more intricate structure and the Casimir functionals may exhibit strong degeneracy at special amplitude and phase configurations. The main novelty of the proof is to reduce the estimates for the amplitude parameters of the perturbed solution to a root-stability problem for a cubic polynomial under coefficient perturbations, thereby overcoming the strong degeneracy in an effective way. These estimates appear to indicate that stronger degeneracy in the amplitude-phase configuration leads to weaker stability.

math.AP↗

arXiv2026

Think Like a Pilot: Fine-Grained Long-Horizon UAV Navigation

Language-guided UAV agents must execute long-horizon semantic instructions while producing smooth, physically feasible continuous flight commands, yet existing Vision-Language Navigation (VLN) benchmarks typically use discrete or coarse actions and existing UAV Vision-Language-Action (VLA) tasks focus on short, atomic maneuvers. To address this gap in UAV task settings, we introduce \textbf{FLIGHT}, a \textbf{F}ine-grained \textbf{L}ong-horizon \textbf{I}nstruction-\textbf{G}uided benchmark for \textbf{H}ybrid UAV navigation and reasoning \textbf{T}asks, which combines multi-stage instructions with dense 6-DoF trajectory annotations across two dataset splits: Fine-grained VLN and Long-horizon Flow. To endow the UAV agent with the capability of real-time in-flight reasoning over task execution status and mission planning, while simultaneously accommodating high-frequency, real-time precise control, we further propose \textbf{FLIGHT VLA}, an asynchronous architecture that decouples a low-frequency Streaming Pilot Vision-Language Model (VLM) for task-state reasoning from a high-frequency diffusion action model for continuous control, supervised by explicit \textbf{Pilot Reasoning} texts that summarize the current flight state and anticipate the next subgoal. In closed-loop evaluation, FLIGHT VLA consistently surpasses representative VLN and VLA baselines on our FLIGHT benchmarks, achieving stronger multi-stage completion, subgoal adherence, and terminal control. Its trained Streaming Pilot Reasoning VLM further improves UAV video reasoning, validating the effectiveness of our design.

cs.RO↗

arXiv2026

LIBERO-X: Robustness Litmus for Vision-Language-Action Models

Reliable benchmarking is critical for advancing Vision-Language-Action (VLA) models, as it reveals their generalization, robustness, and alignment of perception with language-driven manipulation tasks. However, existing benchmarks often provide limited or misleading assessments due to insufficient evaluation protocols that inadequately capture real-world distribution shifts. This work systematically rethinks VLA benchmarking from both evaluation and data perspectives, introducing LIBERO-X, a benchmark featuring: 1) A hierarchical evaluation protocol with progressive difficulty levels targeting three core capabilities: spatial generalization, object recognition, and task instruction understanding. This design enables fine-grained analysis of performance degradation under increasing environmental and task complexity; 2) A high-diversity training dataset collected via human teleoperation, where each scene supports multiple fine-grained manipulation objectives to bridge the train-evaluation distribution gap. Experiments with representative VLA models reveal significant performance drops under cumulative perturbations, exposing persistent limitations in scene comprehension and instruction grounding. By integrating hierarchical evaluation with diverse training data, LIBERO-X offers a more reliable foundation for assessing and advancing VLA development.

cs.CV↗

arXiv2025

A voltage-responsive strongly dipolar-coupled macrospin network with emergent dynamics for computing

Emergent behavior, which arises from local interactions between simple elements, is pervasive in nature. It underlies the energy-efficient computing in our brains. However, realizing such dynamics in artificial materials, particularly under low-energy stimuli, remains a fundamental challenge. While dipole-dipole interactions are typically suppressed in magnetic storage, here we harness and amplify them to construct a strongly dipolar-coupled network of SmCo5 macrospins at wafer scale, which can exhibit intrinsic interaction-driven collective dynamics in response to voltage pulses. The network combines three essential ingredients: strong dipolar coupling by large single-domain macrospin, giant voltage control of coercivity over nearly 1000-fold, and disordered network topology with frustrated Ising-like energy landscape. When stimulated by 1 V pulses, the network enters a regime where interaction-driven magnetic behaviors emerge, including spontaneous demagnetization, greatly enhanced magnetization modulation, reversible freeze and resume evolution and stochastic convergence toward low-energy magnetic configurations. All these behaviors are completely absent at the single-nanomagnet level. Furthermore, by constructing micromagnetic models of the strongly dipolar-coupled macrospin networks, we show that the resulting nonlinear, high-dimensional collective dynamics, intrinsic to strongly-interacting systems, can enable accurate chaotic Mackey-Glass prediction and multiclass drone-signal classification. Our work establishes the voltage-responsive strongly-coupled SmCo5 network as a mesoscopic platform for probing emergent magnetic dynamics previously inaccessible under ambient conditions. It also suggests a fundamental distinct route towards scalable, low-voltage computing, one rooted in native physical interaction-driven collective dynamics at the network level.

cond-mat.mtrl-sci↗

arXiv2025

New Constructions of Non-GRS MDS Codes, Recovery and Determination Algorithms for GRS Codes

In this paper, we propose a new method for constructing a class of non-GRS MDS codes. The lengths of these codes can reach up to $\frac{q+3}{2}$ (for finite fields of odd characteristic) and $\frac{q+4}{2}$ (for even characteristic), respectively. Owing to their special structure, we can use the Cauchy matrix method to obtain the necessary and sufficient conditions for these codes to be MDS codes and non-GRS MDS codes. Additionally, the inequivalence between these codes and twisted GRS codes is analyzed. Furthermore, we analyze the relationships among several existing classes of codes used for constructing non-GRS MDS codes, propose explicit constructions, and discuss the lengths of non-GRS MDS codes based on these constructions. Finally, we design two efficient algorithms to address two main problems in GRS code research, i.e., determining whether an unknown code $C$ is a GRS code from its generator matrix $G$, and recovering the key vectors $\bmα$ and $\bm{v}$ such that $C = \GRS_{n,k}(\bmα, \bm{v})$ if $C$ is indeed a GRS code. A computational complexity comparison of the proposed algorithms ($O(nk+n)$) with that of the Sidelnikov-Shestakov attack (exceeding $O(qk^2n+qk^3)$) shows that our methods offer superior computational efficiency.

cs.IT↗

arXiv2025

Shortest self-orthogonal embeddings of binary linear codes

There has been recent interest in the study of shortest self-orthogonal embeddings of binary linear codes, since many such codes are optimal self-orthogonal codes. Several authors have studied the length of a shortest self-orthogonal embedding of a given binary code $\mathcal C$, or equivalently, the minimum number of columns that must be added to a generator matrix of $\mathcal C$ to form a generator matrix of a self-orthogonal code. In this paper, we use properties of the hull of a linear code to determine the length of a shortest self-orthogonal embedding of any binary linear code. We focus on the examples of Hamming codes and Reed-Muller codes. We show that a shortest self-orthogonal embedding of a binary Hamming code is self-dual, and propose two algorithms to construct self-dual codes from Hamming codes $\mathcal H_r$. Using these algorithms, we construct a self-dual $[22, 11, 6]$ code, called the shortened Golay code, from the binary $[15, 11, 3]$ Hamming code $\mathcal H_4$, and construct a self-dual $[52, 26, 8]$ code from the binary $[31, 26, 3]$ Hamming code $\mathcal H_5$. We use shortest SO embeddings of linear codes to obtain many inequivalent optimal self-orthogonal codes of dimension $7$ and $8$ for several lengths. Four of the codes of dimension $8$ that we construct are codes with new parameters such as $[91, 8, 42],\, [98, 8, 46],\,[114, 8, 54]$, and $[191, 8, 94]$.

cs.IT↗

arXiv2025

Improved Decoding Algorithms for MDS and Almost-MDS Codesfrom Twisted GRS Codes

In this paper, firstly, we study decoding of a general class of twisted generalized Reed-Solomon (TGRS) codes and provide a precise characterization of the key equation for TGRS codes and propose a decoding algorithm. Secondly, we further study decoding of almost-MDS TGRS codes and provide a decoding algorithm. These two decoding algorithms are more efficient in terms of performance compared with the decoding algorithms presented in [Sun et al., IEEE-TIT, 2024] and [Sui et al., IEEE-TIT, 2023] respectively.

cs.IT↗

arXiv2025

Quantitative stability of a class of explicit steady Euler flows in a disk

We provide a short proof of the $L^2$-orbital stability of a class of explicit steady Euler flows in a disk by establishing a quantitative estimate. The main idea is to exploit the conserved quantities of the Euler equation, including the kinetic energy, the enstrophy, and the moment of fluid impulse. Our result seems to suggest that more radial symmetry leads to stronger instability.

math.AP↗

arXiv2025

On the positive constant in Arnold's second stability theorem for a bounded domain

For a steady flow of a two-dimensional ideal fluid, the gradient vectors of the stream function $ψ$ and its vorticity $ω$ are collinear. Arnold's second stability theorem states that the flow is Lyapunov stable if $0<\nablaω/\nablaψ 0$. In this paper, we show that, for a bounded domain, $C_{ar}$ can be taken as the first eigenvalue $\bmΛ_1$ of a certain Laplacian eigenvalue problem. When $\nablaω/\nablaψ$ reaches $\bmΛ_1$, instability may occur, as illustrated by a non-circular steady flow in a disk; however, a certain form of structural stability still holds. Based on these results, we establish a theorem on the rigidity and orbital stability of steady Euler flows in a disk.

math.AP↗

arXiv2025

Orbital Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus

On a two-dimensional flat torus, Laplacian eigenfunctions admit explicit trigonometric representations. It is known that every first eigenstate on a rectangular or square torus is stable under the incompressible Euler dynamics modulo translations. We extend this result to flat tori of arbitrary shape and thereby obtain, to the best of our knowledge, the first family of orbitally stable sinusoidal Euler flows on a hexagonal torus. The proof uses a Burton-type stability criterion and has two main ingredients: (i) a variational characterization of each equimeasurable class in the first eigenspace and (ii) the finiteness of the number of translational orbits contained in each such class. The second ingredient is particularly delicate in the hexagonal case, where it reduces to the analysis of a polynomial system reflecting both the symmetry of the torus and the structure of its first eigenspace.

math.AP↗

arXiv2025

Stability of a class of exact solutions of the incompressible Euler equation in a disk

We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument.

math.AP↗

arXiv2025

Nonlinear stability of plane ideal flows in a periodic channel

In this paper, we establish two stability theorems for steady or traveling solutions of the two-dimensional incompressible Euler equation in a finite periodic channel, extending Arnold's classical work from the 1960s. Compared to Arnold's approach, we employ a compactness argument rather than relying on the negative definiteness of the energy-Casimir functional. The isovortical property of the Euler equation and Burton's rearrangement theory play an essential role in our analysis. As a corollary, we prove for the first time the existence of a class of stable non-shear flows when the ratio of the channel's height to its length is less than or equal to $\sqrt{3}/2.$ Two rigidity results are also obtained as byproducts.

math.AP↗

arXiv2025

ONER: Online Experience Replay for Incremental Anomaly Detection

Incremental anomaly detection aims to sequentially identify defects in industrial product lines but suffers from catastrophic forgetting, primarily due to knowledge overwriting during parameter updates and feature conflicts between tasks. In this work, We propose ONER (ONline Experience Replay), an end-to-end framework that addresses these issues by synergistically integrating two types of experience: (1) decomposed prompts, which dynamically generate image-conditioned prompts from reusable modules to retain prior knowledge thus prevent knowledge overwriting, and (2) semantic prototypes, which enforce separability in latent feature spaces at pixel and image levels to mitigate cross-task feature conflicts. Extensive experiments demonstrate the superiority of ONER, achieving state-of-the-art performance with +4.4% Pixel AUROC and +28.3% Pixel AUPR improvements on the MVTec AD dataset over prior methods. Remarkably, ONER achieves this with only 0.019M parameters and 5 training epochs per task, confirming its efficiency and stability for real-world industrial deployment.

cs.CV↗

arXiv2025

Towards Training-free Anomaly Detection with Vision and Language Foundation Models

Anomaly detection is valuable for real-world applications, such as industrial quality inspection. However, most approaches focus on detecting local structural anomalies while neglecting compositional anomalies incorporating logical constraints. In this paper, we introduce LogSAD, a novel multi-modal framework that requires no training for both Logical and Structural Anomaly Detection. First, we propose a match-of-thought architecture that employs advanced large multi-modal models (i.e. GPT-4V) to generate matching proposals, formulating interests and compositional rules of thought for anomaly detection. Second, we elaborate on multi-granularity anomaly detection, consisting of patch tokens, sets of interests, and composition matching with vision and language foundation models. Subsequently, we present a calibration module to align anomaly scores from different detectors, followed by integration strategies for the final decision. Consequently, our approach addresses both logical and structural anomaly detection within a unified framework and achieves state-of-the-art results without the need for training, even when compared to supervised approaches, highlighting its robustness and effectiveness. Code is available at https://github.com/zhang0jhon/LogSAD.

cs.CV↗

arXiv2024

Align-DETR: Enhancing End-to-end Object Detection with Aligned Loss

DETR has set up a simple end-to-end pipeline for object detection by formulating this task as a set prediction problem, showing promising potential. Despite its notable advancements, this paper identifies two key forms of misalignment within the model: classification-regression misalignment and cross-layer target misalignment. Both issues impede DETR's convergence and degrade its overall performance. To tackle both issues simultaneously, we introduce a novel loss function, termed as Align Loss, designed to resolve the discrepancy between the two tasks. Align Loss guides the optimization of DETR through a joint quality metric, strengthening the connection between classification and regression. Furthermore, it incorporates an exponential down-weighting term to facilitate a smooth transition from positive to negative samples. Align-DETR also employs many-to-one matching for supervision of intermediate layers, akin to the design of H-DETR, which enhances robustness against instability. We conducted extensive experiments, yielding highly competitive results. Notably, our method achieves a 49.3% (+0.6) AP on the H-DETR baseline with the ResNet-50 backbone. It also sets a new state-of-the-art performance, reaching 50.5% AP in the 1x setting and 51.7% AP in the 2x setting, surpassing several strong competitors. Our code is available at https://github.com/FelixCaae/AlignDETR.

cs.CV↗

arXiv2024

New Constructions of Optimal Binary LCD Codes

Linear complementary dual (LCD) codes can provide an optimum linear coding solution for the two-user binary adder channel. LCD codes also can be used to against side-channel attacks and fault non-invasive attacks. Let $d_{LCD}(n, k)$ denote the maximum value of $d$ for which a binary $[n,k, d]$ LCD code exists. In \cite{BS21}, Bouyuklieva conjectured that $d_{LCD}(n+1, k)=d_{LCD}(n, k)$ or $d_{LCD}(n, k) + 1$ for any lenth $n$ and dimension $k \ge 2$. In this paper, we first prove Bouyuklieva's conjecture \cite{BS21} by constructing a binary $[n,k,d-1]$ LCD codes from a binary $[n+1,k,d]$ $LCD_{o,e}$ code, when $d \ge 3$ and $k \ge 2$. Then we provide a distance lower bound for binary LCD codes by expanded codes, and use this bound and some methods such as puncturing, shortening, expanding and extension, we construct some new binary LCD codes. Finally, we improve some previously known values of $d_{LCD}(n, k)$ of lengths $38 \le n \le 40$ and dimensions $9 \le k \le 15$. We also obtain some values of $d_{LCD}(n, k)$ with $41 \le n \le 50$ and $6 \le k \le n-6$.

cs.IT↗