Search Results (94)

Binary Waring decomposition seeks to express a homogeneous binary form as a minimal sum of powers of linear forms. In the binary setting, Sylvester’s theorem gives a classical algebraic route for rank determination and parameter recovery through structured Hankel/catalecticant matrices. Although this procedure is exact and interpretable in ideal arithmetic, practical rank identification may become unstable when the input coefficients are contaminated by noise or when the underlying roots are close to degenerate configurations. This paper develops a data-driven rank inference framework coupled with certified Sylvester reconstruction for robust binary Waring decomposition. The proposed method first converts the coefficient sequence into a Hankel-aware graph that captures recurrence-induced dependencies among polynomial coefficients. A graph neural network is then used to infer plausible rank candidates from this structured representation. Instead of accepting a single prediction directly, the framework performs explicit Sylvester reconstruction and algebraic residual verification for candidate ranks. To further improve decision reliability, a lightweight meta-verification module integrates reconstruction residuals, model confidence scores, and stability-related indicators to select the most credible rank. Experiments on large-scale synthetic binary forms show that the proposed meta-guided variant improves rank identification and verified reconstruction success relative to the one-shot hybrid solver under low-to-moderate noise while maintaining the transparency and auditability of classical symbolic–numeric computation. Additional stress tests indicate that performance can degrade under shifted sampling regimes; so, the method should be interpreted as a robust decision layer within the modeled problem class rather than as unconstrained real-world validation. Full article

Accurate maize yield prediction across diverse environments is pivotal for modern breeding programs. While machine learning (ML) excels at capturing non-linear environmental effects, Genomic Best Linear Unbiased Prediction (GBLUP) remains a benchmark for modeling polygenic small-effect contributions. However, principled integration of these paradigms—while explicitly accounting for genotype-by-environment interaction (G×E)—remains a formidable challenge. We propose a two-step framework evaluated on the Genomes to Fields (G2F) 2022 dataset. In Step 1, ML models are employed to fit environmental main effects; in Step 2, genomic residuals are modeled via additive-dominance relationship matrices, augmented by an explicit low-rank G×E matrix. Candidate interaction markers were screened through plasticity-based genome-wide association studies (GWAS) across six phenotypic stability metrics and used to construct a low-rank candidate G×E representation, with a cross-validation-selected scaling parameter applied to control the contribution of the predicted G×E component. TwoStep_G×E_alpha0.33, achieved a within–environment Pearson correlation coefficient (PCC) of 0.376, outperformed both GBLUP and the competition-winning model (PCC = 0.357) in within-environment ranking. Furthermore, environment-adaptive selection yielded a genetic gain of 0.454 Mg ha⁻¹, representing a 34.7% improvement over GBLUP. Overall, the proposed framework provides a practical approach for environment-specific yield prediction and adaptive selection in maize breeding. Full article

Foreign plastic objects (FPOs) in poultry products present significant food safety risks and cause economic losses for the industry. Conventional detection methods, including X-rays and color imaging, often struggle to identify small or low-density plastics. Hyperspectral imaging (HSI) offers both spatial and spectral information but suffers from high computational cost when applied for FPO identification in industrial environments. This study introduces a parameter-efficient and computationally efficient spatial–spectral transformer framework for pixel-level classification of FPOs on broiler meat using NIR-HSI (1000–1700 nm). The framework integrates three innovations: (1) center-focused linear attention (CFLA) to reduce computational complexity from $O\left(n^2\right)$ to $O\left(n\right)$; (2) patch-local mixed-axis 2D rotary position embedding to preserve geometric relationships within hyperspectral patches; and (3) low-rank factorized projection (LRP) matrices to reduce parameters by approximately 50% within projection weight matrices. The framework was trained and evaluated on a dataset of 52 chicken fillets, comprising 295,340 labeled target hyperspectral pixels from 12 common polymer types and 1 fillet class. The model achieved 99.39% overall accuracy, 99.57% average accuracy, and a 99.31 Kappa coefficient across 248,540 test pixels. Per-class precision, recall, and F1-score exceeded 98.05%, 98.59%, and 98.76%, respectively, across all classes. Efficiency analyses showed an 83% reduction in multiply–accumulate operations (MACs), a 22% reduction in trainable parameters, and a model size reduction from 1.72 MB to 1.35 MB relative to the baseline configuration. These gains also translated into practical inference benefits, with the final model achieving a throughput of 212,971.5 hyperspectral patch cubes/s and a 4.19× speedup over the baseline. These results demonstrate that the proposed framework combines strong classification performance with high efficiency, supporting high-throughput inference for real-time monitoring and enabling contamination source traceability and preventive quality control in industrial poultry processing. The approach provides a benchmark for applying transformer-based models to food safety inspection tasks. Full article

We study a class of perturbed tridiagonal problems in the form of a rank-one update of a symmetric tridiagonal Toeplitz matrix. We derive computable formulas for up to eighth-order polynomial approximations or closed formulas for quartic approximation. Moreover, we study some symmetries that characterise the coefficients of these polynomials. Numerical testing suggested that the error is close to machine accuracy in the former case and surprising low in the latter, whereas for big matrices the computational time is clearly lower compared to the MATLAB’s eig function. Full article

Despite offering rich complementary information, multimodal remote sensing images collected by diverse sensors increase the computational burden in clustering. To alleviate this issue, we devise an efficient multimodal clustering approach (MCSM) on superpixel manifolds formed by superpixel segmentation. The MCSM jointly learns cluster representation of all modalities and a consensus cluster membership graph that fuses the multimodal representation to yield clusters. To capture the local geometric structure of the superpixel manifolds, the optimization is constrained by manifold regularization of the consensus graph. In contrast to vanilla multiview subspace clustering techniques, the proposed approach does not rely on spectral clustering, and only involves element-wise product and multiplication on small-scale matrices. In addition, we prove that the MSCM is a special case of classic low-rank subspace clustering models, providing a perspective for understanding the learned cluster graphs. Extensive experiments are conducted on three popular multimodal remote sensing datasets, showing that the proposed method achieves competitive clustering performance compared to state-of-the-art methods, and significantly outperforms the latter in computational efficiency. Full article

Low-rank sparse decomposition models have become the mainstream optimization framework for multiframe infrared small target detection. Existing low-rank matrix decomposition approximations typically pre-decompose infrared videos into the product of two low-rank matrices to capture the background’s low-rank characteristics. However, such approximations are not optimal and often result in suboptimal background recovery. To achieve more accurate low-rank recovery, we exploit the intrinsic relationship between low-rank matrices and their generalized inverse matrices, thereby improving conventional decomposition approximations. Moreover, to address the high computational cost of applying low-rank and sparse decomposition models to multi-frame infrared videos, we introduce a robust column-row (CUR) decomposition to accelerate the iterative process, thereby significantly improving computational efficiency. The experimental results show that the proposed method achieves fast detection of small targets in infrared videos while maintaining competitive detection performance. Full article

Structural damage detection using the finite element method is inherently formulated as an inverse problem, often suffering from ill-posedness and high sensitivity to measurement noise. This study introduces a novel damage detection methodology by applying low-rank adaptation (LoRA), originally developed for fine-tuning large language models, to inverse problems in structural mechanics for the first time. The proposed approach exploits the physically inherent low-rank nature of structural damage: damage is typically localized, and the contribution of each finite element to the stiffness matrix is limited by its degrees of freedom. Accordingly, the stiffness change matrix is factorized into two low-rank matrices, reducing the number of parameters and providing implicit regularization against full-rank measurement noise. Physical consistency is ensured through sparsity and symmetry constraints. Numerical experiments on cantilever beam and L-shaped plate structures across five damage scenarios demonstrated that the proposed method achieved superior noise robustness compared with baseline methods. At a signal-to-noise ratio of 20 dB, representative of practical field conditions, LoRA achieved stiffness errors below 2%, whereas the baseline methods failed to provide reliable results. The proposed framework achieved a 100% success rate in damage zone localization (Precision@n ≥ 80%) with over 60% parameter reduction, presenting a promising solution for practical structural health monitoring. Full article

Aspect-based sentiment analysis (ABSA) plays a vital role in deriving fine-grained sentiment from textual content. As large language models (LLMs) are increasingly adopted for automated data annotation in natural language processing (NLP), concerns have emerged regarding the accuracy of their outputs. Despite their capacity to generate large volumes of labeled data, LLMs often suffer from overconfidence in predictions, high uncertainty in complex contexts, and difficulty capturing nuanced meanings, which compromise the quality of annotations and, in turn, the performance of downstream models. This underscores the need to enhance LLM adaptability while maintaining annotation accuracy. To address these limitations, we integrated low-rank adaptation (LoRA) with parameter-efficient fine-tuning (PEFT) for adapting Qwen2.5 to ABSA. LoRA reduces the number of trainable parameters by decomposing weight updates into low-rank matrices, while PEFT introduces modular adapter layers with scaled gradient updates and dynamic rank allocation. Using the standard SemEval 2014 Laptop dataset, Qwen2.5-3B fine-tuned with LoRA and PEFT achieves 64.50% accuracy, outperforming its baseline of 24.05%. Likewise, Qwen2.5-7B attains 77.50%, compared with a baseline of 34.63%. These results highlight the potential of parameter-efficient methods to improve the accuracy of LLMs in ABSA annotation tasks, especially under resource constraints. Such results lay the groundwork for scalable, reproducible LLM deployment and open avenues for future research in cross-domain adapter transferability and dynamic rank optimization. Full article

Legal judgment prediction (LJP) increasingly relies on large language models whose full fine-tuning is memory-intensive and susceptible to catastrophic forgetting. We present LawLLM-DS, a two-stage Low-Rank Adaptation (LoRA) framework that first performs legal knowledge pre-tuning with an aggressive learning rate and subsequently refines judgment relations with conservative updates, using dedicated LoRA adapters, 4-bit quantization, and targeted modification of seven Transformer projection matrices to keep only 0.21% of parameters trainable. From a structural perspective, the twenty annotated legal elements form a symmetric label co-occurrence graph that exhibits both cluster-level regularities and asymmetric sparsity patterns, and LawLLM-DS implicitly captures these graph-informed dependencies while remaining compatible with downstream GNN-based representations. Experiments on 5096 manually annotated divorce cases show that LawLLM-DS lifts macro F1 to 0.8893 and achieves an accuracy of 0.8786, outperforming single-stage LoRA and BERT baselines under the same data regime. Ablation studies further verify the contributions of stage-wise learning rates, adapter placement, and low-rank settings. These findings demonstrate that curriculum-style, parameter-efficient adaptation provides a practical path toward lightweight yet structure-aware LJP systems for judicial decision support. Full article

Hyperspectral images present significant challenges for conventional dimensionality reduction methods due to their high dimensionality, spectral redundancy, and complex spatial–spatial dependencies. While kernel-based sparse representation methods have shown promise in handling spectral non-linearities, they often fail to preserve spatial consistency and semantic discriminability during feature transformation. To address these limitations, we propose a novel semantic-guided kernel low-rank sparse preserving projection (SKLSPP) framework. Unlike previous approaches that primarily focus on spectral information, our method introduces three key innovations: a semantic-aware kernel representation that maintains discriminability through label constraints, a spatially adaptive manifold regularization term that preserves local pixel affinities in the reduced subspace, and an efficient optimization framework that jointly learns sparse codes and projection matrices. Extensive experiments on benchmark datasets demonstrate that SKLSPP achieves superior performance compared to state-of-the-art methods, showing enhanced feature discrimination, reduced redundancy, and improved robustness to noise while maintaining spatial coherence in the dimensionality-reduced features. Full article

Federated learning (FL) enables privacy-preserving adaptation of large language models (LLMs) across distributed clients. However, deploying FL in edge environments remains challenging because of the high communication overhead of full-model updates. Recent advances in parameter-efficient fine-tuning (PEFT), particularly low-rank adaptation (LoRA), have substantially reduced update sizes by injecting lightweight trainable matrices into pretrained transformers, thereby making FL with LLMs more feasible. In this paper, we propose LoRaC-GA, a communication-aware optimization framework that dynamically determines the optimal number of clients to participate in each round under a fixed bandwidth constraint. We formulated a max-min objective to jointly maximize the model accuracy and communication efficiency and solved the resulting non-convex problem using a genetic algorithm (GA). To further reduce the overhead, we integrated a structured peer-to-peer collaboration protocol with ${log}_{2}K$ complexity, enabling scalable communication without full connectivity. The simulation results demonstrate that LoRaC-GA adaptively selects the optimal client count, achieving competitive accuracy while significantly reducing the communication cost. The proposed framework is well-suited for bandwidth-constrained edge deployments involving large-scale LLMs. Full article

Background: Autism spectrum disorder (ASD) is a highly heterogeneous neurodevelopmental condition for which accurate and automated diagnosis is crucial to enable timely intervention. Resting-state functional magnetic resonance imaging (rs-fMRI) serves as one of the key modalities for diagnosing ASD and elucidating its underlying mechanisms. Numerous existing studies using rs-fMRI data have achieved accurate diagnostic performance. However, these methods often rely on a single brain atlas for constructing brain networks and overlook the data heterogeneity caused by variations in imaging devices, acquisition parameters, and processing pipelines across multiple centers. Methods: To address these limitations, this paper proposes a multi-view, low-rank subspace graph structure learning method to integrate multi-atlas and multi-center data for automated ASD diagnosis, termed M³ASD. The proposed framework first constructs functional connectivity matrices from multi-center neuroimaging data using multiple brain atlases. Edge weight filtering is then applied to build multiple brain networks with diverse topological properties, forming several complementary views. Samples from different classes are separately projected into low-rank subspaces within each view to mitigate data heterogeneity. Multi-view consistency regularization is further incorporated to extract more consistent and discriminative features from the low-rank subspaces across views. Results: Experimental results on the ABIDE-I dataset demonstrate that our model achieves an accuracy of 83.21%, outperforming most existing methods and confirming its effectiveness. Conclusions: The proposed method was validated using the publicly available Autism Brain Imaging Data Exchange (ABIDE) dataset. Experimental results demonstrate that the M³ASD method not only improves ASD diagnostic accuracy but also identifies common functional brain connections across atlases, thereby enhancing the interpretability of the method. Full article

Nitrosamines (NAs) pose a risk due to their carcinogenic properties, especially in processed and cured meats where nitrites and nitrates are widely used. The objective of this study was to develop an integrated Ultra-High-Performance Liquid Chromatography–High-Resolution Mass Spectrometry (UHPLC–HRMS) workflow for detecting both volatile (VNAs) and non-volatile (NVNAs) nitrosamines in meat matrices. Comparison of two ionization techniques showed that heated electrospray ionization (HESI) and atmospheric pressure chemical ionization (APCI) provided complementary coverage and sensitivity. Extraction and cleanup were optimized for meat, although recovery rates remained variable, underscoring the analytical complexity. The method was applied to raw, cooked, cured, and grilled meats, as well as to in vitro gastric digestion and co-digestion with spinach. Results revealed that some NAs were present even in untreated raw meat (≈3.0 µg/kg, N-nitrosodi-n-butylamine), while the addition of nitrites and nitrates significantly increased their levels (more than 10 µg/kg, N-nitrosodiethylamine, N-nitrosodimethylamine, N-nitrosodi-n-butylamine). Gastric digestion was the most critical condition, further promoting nitrosamine formation, particularly for N-nitrosodiethylamine, N-nitrosodi-n-butylamine, and N-nitrosopiperidine. Ascorbate exhibited a dual role, acting as an inhibitor at low nitrite concentrations but becoming pro-oxidant at high levels (300 mg/kg). Cooking alone had limited impact, whereas cooking combined with digestion yielded the highest and most consistent nitrosamine concentrations. The inclusion of spinach during digestion modestly altered nitrosamine levels, reflecting both its nitrate content and polyphenolic profile. Nonparametric ANOVA (aligned rank transform) confirmed that preservative treatment, rather than processing or interaction effects, was the main driver of variability (total nitrosamines: H = 24.15, p = 2.33 × 10⁻⁵), with the combination of preservative ascorbate plus nitrite producing significantly higher levels than other treatments (q = 0.000656). N-nitrosodimethylamine consistently emerged as the most relevant marker for dietary exposure, in agreement with EFSA guidance. Overall, this study underscores both the analytical and biochemical complexity of nitrosamine detection and formation in meat products, while highlighting the importance of preservative formulation and the potential role of dietary antioxidants in mitigating exposure. Full article

In the realm of image classification, the capsule network is a network topology that packs the extracted features into many capsules, performs sophisticated capsule screening using a dynamic routing mechanism, and finally recognizes that each capsule corresponds to a category feature. Compared with previous network topologies, the capsule network has more sophisticated operations, uses a large number of parameter matrices and vectors to express picture attributes, and has more powerful image classification capabilities. However, in the practical application field, the capsule network has always been constrained by the quantity of calculation produced by the complicated structure. In the face of basic datasets, it is prone to over-fitting and poor generalization and often cannot satisfy the high computational overhead when facing complex datasets. Based on the aforesaid problems, this research proposes a novel enhanced capsule network topology. The upgraded network boosts the feature extraction ability of the network by incorporating a multi-scale feature extraction module based on proprietary star structure convolution into the standard capsule network. At the same time, additional structural portions of the capsule network are changed, and a variety of optimization approaches such as dense connection, attention mechanism, and low-rank matrix operation are combined. Image classification studies are carried out on different datasets, and the novel structure suggested in this paper has good classification performance on CIFAR-10, CIFAR-100, and CUB datasets. At the same time, we also achieved 98.21% and 95.38% classification accuracy on two complicated datasets of skin cancer ISIC derived and Forged Face EXP. Full article

This article is proposing a fast version of adaptive iterative matrix designed thresholding (AIMDT) algorithm which is studied in our previous work. In AIMDT algorithm, a designed thresholding operator is studied to the problem of recovering the low-rank matrices. By adjusting the size of the parameter, this designed operator can apply less bias to the singular values of a matrice. Using this proposed designed operator, the AIMDT algorithm has been generated to solve the matrix rank minimization problem, and the numerical experiments have shown the superiority of AIMDT algorithm. However, the AIMDT algorithm converges slowly in general. In order to recover the low-rank matrices more quickly, we present a fast AIMDT algorithm to recover the low-rank matrices in this paper. The numerical results on some random low-rank matrix completion problems and a missing English text completion problem show that the our proposed fast algorithm has much faster convergence than the previous AIMDT algorithm. Full article