Search Results (62)

Nonlinear systems of equations arise across engineering, physics, and biological modeling; however, classical Newton-type methods may fail when the initial approximation lies outside the convergence region of the NJN local solver. This work proposes a two-stage hybrid framework that couples Particle Swarm Optimization (PSO) for global exploration with the fifth-order Newton–Jarratt (NJN) iterative method for local refinement. The fifth-order convergence of the NJN phase, established through a complete Fréchet-derivative Taylor expansion with explicitly computed error constants, guarantees rapid local convergence once PSO delivers a sufficiently close starting point. The framework is validated on four test problems with increasing numbers of dimensions ($n=2,5,20,40$): a two-dimensional benchmark algebraic system, a five-dimensional metabolic network model for ethanol production in Saccharomyces cerevisiae, and two large-scale Hammerstein integral equation systems. Over 30 independent runs per method and under the tested conditions, PSO-NJN achieves 100% convergence with mean final residuals of order ${10}^{-14}$–${10}^{-16}$, while pure PSO fails completely on the high-dimensional Hammerstein cases ($n=20,40$) and achieves only 10% success on the metabolic model. These results confirm that combining global metaheuristic search with high-order local refinement yields a robust, scalable solver for complex biological and engineering nonlinear systems, though performance on problems with dense high-dimensional Jacobians may require further adaptation. Full article

Limited sample diversity poses a major challenge for deep learning-based coal–gangue recognition using mineral laser speckle images under complex industrial conditions. To address this issue, we propose an improved data augmentation framework based on a Deep Convolutional Generative Adversarial Network (DCGAN). Dense Blocks are introduced to enhance high-dimensional feature representation without significantly increasing network complexity, while self-attention modules strengthen multiscale feature interactions between localized flare features and global speckle distributions. Residual-based sampling modules and the Wasserstein GAN with Gradient Penalty (WGAN-GP) objective are further employed to improve gradient propagation and adversarial training stability. Experimental results on synthesizing 512 × 512 mineral laser speckle images show that the proposed model reduces the Fréchet Inception Distance (FID) by 72.75% relative to the baseline DCGAN. Furthermore, the YOLOv5 detectors trained on the augmented datasets achieve a peak mean Average Precision (mAP) of 99.3%, significantly outperforming conventional geometric transformation methods and typical generative baselines including StyleGAN2-ADA and SAGAN. These results demonstrate that the proposed method effectively improves alignment between the synthetic and real distributions, enhances speckle feature diversity and boosts the accuracy and robustness of coal–gangue recognition under limited-sample conditions. Full article

Intelligent fault diagnosis of rotating machinery is essential for ensuring the safety and reliability of industrial systems. While hypergraph neural networks (HGNNs) have recently shown promise for modeling high-order dependencies beyond pairwise graph methods, most existing variants operate in Euclidean space, which is not explicitly aligned with hierarchical fault-response structure (root cause to fault mode to observed response). To address this limitation, we propose Hyperbolic Hypergraph Neural Network (H²GNN), a framework that integrates hyperbolic geometry with hypergraph neural networks for fault diagnosis. Specifically, H²GNN constructs fault-response-aware hyperedges over diagnostic views of vibration signals and performs message passing in the Poincaré ball model, a Riemannian manifold of constant negative curvature commonly used for hierarchical representation learning. We introduce Poincaré hyperedge aggregation via an iterative Fréchet-mean solver, a learnable curvature parameter for adaptive manifold fitting, and a tangent-space classification head. Experiments are conducted on two public benchmarks, namely the Case Western Reserve University (CWRU) bearing dataset and the Machinery Failure Prevention Technology (MFPT) bearing dataset, and report mean accuracies of 99.87% and 99.75%, respectively, outperforming six competing methods, including CNN, GCN, HGNN, dynamic-HGNN, contrastive-HGNN, and spatial-temporal HGNN. Ablation studies indicate that hyperbolic geometry and the adaptive curvature mechanism both contribute to the observed performance gain. Full article

The temporal course of neuronal electric activity within brain networks, or neurodynamics, reflects the structural and functional properties of the neuronal populations that generate it. Using intracranial stereo-electroencephalography (sEEG) recordings from the public Montreal Neurological Institute (MNI) atlas, we investigated neurodynamics in the primary motor (M1), somatosensory (S1), and auditory (A1) cortices. We tested whether modifying the Higuchi fractal dimension (HFD) by replacing the Euclidean distance with the Fréchet distance could improve sensitivity to local neurodynamics by incorporating trajectory-based similarities in signal evolution. Using a conservative within-subject approach established in the previous literature, we compared signals recorded from different cortical areas within the same individuals (M1 vs. S1: # of people = 16; M1 vs. A1: # = 9; S1 vs. A1: # = 6). To delve deeper into the new measure’s meaning, it was tested on sequences with known fractal properties, the Brownian motion and the Weierstrass function. Results showed that the newly introduced Fréchet-based HFD (HFDf), similarly to standard HFD, consistently discriminated cortical areas at the intra-subject level, confirming the robustness of fractal dimension as a descriptor of region-specific neurodynamics. Contrary to our hypothesis, HFDf did not provide additional sensitivity across areas and notably, it displayed less evident reduction of values in sleep than awake. While cortical regions may share common governing principles across spatiotemporal scales, these do not necessarily translate into strict similarity in temporal signal morphology. We suggest that these findings support that the free-scale nature of neurodynamics is not a self-similar one. This refinement of quantitative tools for cortical neurodynamic mapping paves the way towards novel tools for neuroimaging-informed neuromodulation strategies. Full article

Side-scan sonar images play an important role in underwater target detection, seabed mapping, and marine environment monitoring. However, the performance of deep learning-based detectors is often limited by the small scale of available sonar datasets, the high cost of data acquisition, and class imbalance among target categories. To address these issues, this paper proposes a diffusion-model-based data augmentation method for side-scan sonar target detection. A FLUX.1 diffusion model is adopted as the base generative framework and is fine-tuned using low-rank adaptation (LoRA) to adapt the pretrained model to the side-scan sonar image domain under limited training data conditions. The generated samples are further filtered and added only to the training set, while the validation and test sets are kept unchanged and contain only real sonar images. To ensure a fair evaluation of the augmentation strategy, all detection experiments are conducted using a fixed YOLOv8n (You Only Look Once version 8 nano) detector under the same training hyperparameters and three random seeds. Compared with training on the original dataset, the proposed FLUX+LoRA augmentation improves mean average precision (mAP)@0.5 from 0.7400 ± 0.0132 to 0.8582 ± 0.0328 and mAP@0.5:0.95 from 0.3994 ± 0.0187 to 0.5115 ± 0.0164. It also outperforms conventional augmentation methods under the same real-only validation/test protocol. In addition, Fréchet Inception Distance (FID)/Kernel Inception Distance (KID)-based image quality evaluation, generated-sample amount ablation, screening-strategy ablation, LoRA-rank sensitivity analysis, and a controlled 600-sample diffusion-backbone comparison are conducted. The results show that the 600-sample manually annotated FLUX+LoRA subset selected from generated samples achieves better image quality and detection performance than FLUX-base and SD1.5+LoRA under the same annotation budget. These findings demonstrate that FLUX+LoRA-generated sonar images can provide useful structural diversity for detector training and improve target detection performance under limited-data conditions. Full article

Batch effects arising from variations in hardware, acquisition protocols, and reconstruction parameters present a critical challenge in radiomics, limiting the generalizability of models across multicentre studies. Existing harmonization methods, such as ComBat, CovBat, z-score normalization, and Generative Adversarial Networks, exhibit significant limitations when applied to high-dimensional radiomic data. ComBat assumes a linear feature space and tends to leave residual center-specific information recoverable by downstream classifiers. This paper introduces RiTex (Riemannian Texture Harmonization), a framework that solves a generalized eigenvalue problem between class-aware biological scatter and Ledoit–Wolf-regularized per-batch covariances, with the SPD-manifold Fréchet mean used as a principled averaging step. We evaluate RiTex on the 50-dataset radMLBench benchmark and on a new four-center head-and-neck benchmark with known center labels ($n$ = 380 patients, k = 4 centers from TCIA: HGJ, MDACC, Maastro, QIN). On radMLBench, RiTex reduces the batch auto-detection AUC in 48/50 (96%) datasets, 42/50 (84%) reductions remain significant after Benjamini–Hochberg correction; the mean Batch AUC reduction is ΔBatch = −0.365 (95% bootstrap CI [−0.418, −0.312]), with no significant degradation in biological AUC (mean ΔBio = +0.018, 95% CI [−0.011, +0.047]). On the H&N benchmark with real center labels, RiTex reduces the Batch AUC from 0.74 to 0.59, while ComBat and CovBat leave it at ≈0.98. A component-wise ablation shows that the dominant source of empirical performance is the GEVD step, together with Ledoit–Wolf shrinkage. The SPD Fréchet mean acts as a theoretical scaffold with a negligible empirical contribution (ΔBatch AUC = −0.014 vs. arithmetic mean). Full article

Evaluating conditional time-series generation models remains challenging in battery research, where degradation data are often limited and experiments cover only a small number of operating conditions. The widely used Fréchet Inception Distance (FID) summarizes all conditions into a single score, which can obscure failures under rare but safety-critical conditions. Several condition-aware extensions of FID, including Conditional Fréchet Inception Distance (CFID), partially address this limitation by evaluating each condition separately. However, these approaches do not assess whether physically meaningful relationships between operating conditions are preserved, and their reliability deteriorates when only a few samples are available for each condition. To address these issues, we propose a three-layer diagnostic framework for evaluating conditional generative models under limited-data conditions. The first layer, Stratified Fréchet Distance, identifies the specific operating conditions and degradation phases where generation quality degrades. The second layer, based on Conditional Response Consistency (CRC), Conditional Distance Ratio (CDR), and Mean-Order Preservation (MOP), evaluates whether the model preserves the distance structure and ordering between conditions. MOP detects condition-ordering defects that CRC cannot identify when the real data distance matrix is non-monotone. This layer also enables statistically meaningful comparisons even when only a small number of samples are available. The third layer detects strata where statistical estimates are unreliable and provides a more stable alternative for evaluation. We validate the framework on four battery degradation datasets using two generative model architectures. The proposed approach reveals condition-specific failures that are not captured by conventional FID. It localizes generation errors to the late-stage high-temperature degradation regime that is most relevant to battery safety. The framework also detects structural distortions with statistical significance. In addition, it consistently ranks physics-informed model variants across quality differences spanning seven orders of magnitude. These results demonstrate that the proposed framework provides a practical and physically interpretable evaluation methodology for conditional generative modeling in battery degradation analysis. Full article

Graph-based fraud detection in multi-relational social networks must capture heterogeneous relation semantics and diverse fraud patterns while preserving geometric consistency and remaining scalable. Existing methods often either force all relations into a shared Euclidean or single-curvature space, or fuse relation-wise embeddings after mapping them to tangent coordinates, which weakens curvature-dependent metric information. We propose Relation-Specific Curvature Fields on Product Manifolds (RSCF-PM), a geometry-consistent framework that learns relation-specific curvature and represents each node as a tuple on a Riemannian product manifold. Each relation is encoded in its own hyperbolic space, and cross-relation fusion is performed directly through the product metric rather than Euclidean concatenation. On top of this representation, we introduce a multi-prototype classifier to model multiple fraud modes within each class. To support large-scale training, we adopt tangent-space aggregation as an efficient approximation to the Fréchet mean. Experiments on four public fraud detection benchmarks, including the 5.78M-node T-Social network, show that RSCF-PM achieves the best results on T-Social, FDCompCN, and YelpChi, while remaining highly competitive on Amazon, with up to 4.96% AUC improvement over strong baselines. Ablation and efficiency studies further confirm the complementary value of each component and the practical scalability of the framework. Full article

Cone-beam computed tomography (CBCT) is widely used in image-guided radiotherapy because of its low radiation dose and on-board acquisition capability. However, CBCT images often suffer from scatter artifacts, increased noise, reduced soft-tissue contrast, and inaccurate Hounsfield Unit (HU) values, which limit their direct use for accurate dose calculation and quantitative analysis. To address this limitation, we propose a CBCT-to-CT synthesis framework based on 2.5D context encoding (concatenating five adjacent slices along the channel dimension) and latent-space variational diffusion. The proposed method combines a Vector Quantized Variational Autoencoder (VQ-VAE) and a U-shaped Vision Transformer (U-ViT)-based latent-space Variational Diffusion Model (VDM) to translate CBCT images into synthetic CT (sCT) images in a compressed latent space. To incorporate inter-slice anatomical context while preserving the computational efficiency of 2D processing, five adjacent CBCT slices are concatenated along the channel dimension and used as input. We evaluated the proposed method on the SynthRAD2025 paired CBCT-CT dataset covering head-and-neck, thoracic, and abdominal regions. Under the provided benchmark setting, quantitative evaluation on the validation set showed that the proposed 2.5D model improved peak signal-to-noise ratio (PSNR) from 25.39 dB to 27.44 dB (averaged across regions), structural similarity index measure (SSIM) from 0.813 to 0.846, reduced mean squared error (MSE) from 0.00313 to 0.00200, and lowered Fréchet inception distance (FID) from 1009.33 to 869.53 compared with the 2D baseline. Qualitative results also showed improved anatomical consistency and reduced artifact-related distortions. These findings suggest that neighboring-slice context can enhance HU fidelity and overall image quality in a computationally practical synthesis framework, supporting the usefulness of efficient AI-based cross-modality reconstruction for radiotherapy-related imaging workflows. Full article

Deploying conditional Generative Adversarial Networks (cGANs) for industrial texture synthesis faces two barriers: the prohibitive cost of manual data annotation and the uncertain alignment between automated evaluation metrics and human perception. This study addresses both challenges for marble texture synthesis using 289 high-resolution industrial scans. We adapt an unsupervised segmentation pipeline combining Simple Linear Iterative Clustering (SLIC) superpixels, Gaussian Mixture Models (GMMs), and graph cut optimization to extract vein structures without manual annotation. Four cGAN architectures—baseline cGAN, Pix2Pix, BicycleGAN, and GauGAN—are benchmarked using a dual-evaluation protocol contrasting ten automated metrics with structured human-centered assessment. The results reveal a significant metric–perception discrepancy. Pix2Pix achieved the best Fréchet Inception Distance (FID = 85.3) yet received the lowest human ratings due to periodic texture artifacts. GauGAN produced textures statistically indistinguishable from real marble, achieving a Visual Turing Pass Rate (VTPR) of 0.533 and a Mean Opinion Score on Marble Authenticity (MOS-MA) of 2.89, despite an inferior FID (87.3). These findings make three contributions: an annotation-free segmentation pipeline, empirical evidence that automated metrics alone are insufficient for architecture selection, and a dual-evaluation framework that establishes human-in-the-loop assessment as essential for quality-critical industrial deployment. Full article

Introduction: Optical coherence tomography (OCT) is the gold standard for retinal nerve fibre layer (RNFL) assessment; its high cost and limited accessibility hinder widespread use. This study aims to develop deep learning models that generate RNFL thickness maps from fundus images, providing a cost-effective alternative to OCT. Methods: A dataset of 5000 fundus-OCT image pairs from 5000 unique glaucoma patients was used to train and compare the following four U-Net-based deep learning models: ResU-Net, R2U-Net, Nested U-Net, and Dense U-Net. All models were trained for up to 1000 epochs with early stopping (patience = 50 epochs). Performance was evaluated using Mean Squared Error (MSE), Mean Absolute Error (MAE), Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Fréchet Inception Distance (FID). Results: ResU-Net demonstrated the best performance, achieving MSE = 0.00061, MAE = 0.01877, SSIM = 0.9163, PSNR = 32.19 dB, and FID = 30.08. These results represent a 108% improvement in SSIM and a 67% improvement in PSNR compared to previously published benchmark for this task. Conclusions: This study demonstrates that deep learning models, particularly ResU-Net, can generate high-fidelity RNFL thickness maps from fundus photographs, substantially outperforming prior published benchmarks. This approach represents a potential contribution toward accessible glaucoma assessment, contingent upon prospective clinical validation and regulatory evaluation. Full article

The structural analysis of paper fibers is vital for the noninvasive classification and conservation of traditional handmade paper in cultural heritage. Although digital still cameras (DSCs) offer a low-cost and noninvasive imaging solution, their inferior image quality compared to white-light confocal microscopy (WCM) limits their effectiveness in fiber classification. To address this modality gap, we propose an unpaired image-to-image translation approach using cycle-consistent adversarial networks (CycleGANs). Our study targets a multifiber setting involving kozo, mitsumata, and gampi, using publicly available domain-specific datasets. Generated WCM-style images were quantitatively evaluated using peak signal-to-noise ratio, structural similarity index measure, mean absolute error, and Fréchet inception distance, achieving 8.24 dB, 0.28, 172.50, and 197.39, respectively. Classification performance was tested using EfficientNet-B0 and Inception-ResNet-v2, with F1-scores reaching 94.66% and 98.61%, respectively, approaching the performance of real WCM images (99.50% and 98.86%) and surpassing previous results obtained directly from DSC inputs (80.76% and 84.19%). Furthermore, Grad-CAM visualization confirmed that the translated images retained class-discriminative features aligned with those of the actual WCM inputs. Thus, the proposed CycleGAN-based image conversion effectively bridges the modality gap, enabling DSC images to approximate WCM characteristics and support high-accuracy paper fiber classification, which is a practical alternative for noninvasive material analysis. Full article

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We first present a detailed geometric and analytical foundation for intrinsic quantization on the unit sphere, including definitions of great and small circles, spherical triangles, geodesic distance, Slerp interpolation, the Fréchet mean, spherical Voronoi regions, centroid conditions, and quantization dimensions. Building upon this framework, we develop explicit continuous and discrete quantization models on spherical curves, namely great circles, small circles, and great circular arcs—supported by rigorous derivations and pedagogical exposition. For uniform continuous distributions, we compute optimal sets of n-means and the associated quantization errors on these curves; for discrete distributions, we analyze antipodal, equatorial, tetrahedral, and finite uniform configurations, illustrating convergence to the continuous model. The central conclusion is that for a uniform probability distribution supported on a one-dimensional geodesic subset of total length L, the optimal n-means form a uniform partition and the quantization error satisfies $V_n=L^2/\left(12n^2\right)$.The exposition emphasizes geometric intuition, detailed derivations, and clear step-by-step reasoning, making it accessible to beginning graduate students and researchers entering the study of quantization on manifolds. This article is intended as an expository and tutorial contribution, with the main emphasis on geometric reformulation and pedagogical clarity of intrinsic quantization on spherical curves, rather than on the development of new asymptotic quantization theory. Full article

Pre-defined motion command profiles enable precise positioning and dynamic control in mechanical and mechatronic systems, maximizing efficiency and reliability. Real-world applications introduce dynamic factors like mechanical compliance, friction, and external disturbances that significantly impact system performance. Understanding these influences improves motion control strategy accuracy, robustness, and system stability. This study emphasizes the role of systematic and stochastic disturbances in improving motion control and accuracy. It introduces a structured method for evaluating system behavior under realistic operational conditions using advanced vibration analysis and spatio-temporal similarity measures. Using vibration indicators like amplitude, frequency content, phase relationships, crest factor, and acceleration root mean square (RMS) values, a comprehensive framework is created to quantify motion profile deviations. These indicators identify resonant frequencies, transient disturbances, and system inconsistencies, improving compensation strategies and predictive maintenance. A key contribution of this research is the comparison of quantification methods for motion precision and robustness integrating vibration diagnostics and advanced motion similarity analysis to improve motion control and assessment. Multi-faceted motion deviation characterization is achieved by combining displacement, velocity, and acceleration measurements with statistical and mathematical analysis. To assess motion consistency, spatio-temporal similarity measures like Dynamic Time Warping (DTW), Hausdorff distance, and discrete Fréchet distance capture spatial alignment and temporal progression. These measures allow a more nuanced evaluation of motion quality than traditional error metrics, especially in variable-speed dynamics, sampling rate inconsistencies, and complex motion patterns. Frequency-domain methods like FFT and wavelet transforms detect oscillatory behaviors to improve motion analysis reliability. The study uses spectral analysis and time–frequency domain techniques to detect motion inconsistencies that may cause mechanical wear, instability, or energy waste. Crest factor analysis and phase relationship assessment can also detect misalignment, structural resonance, and transient perturbations that conventional metrics miss. Full article

This paper proposes the lower-bounded Fréchet–log-logistic distribution (LFLD), a probability model designed for robust flood frequency analysis (FFA). The LFLD addresses key limitations of traditional distributions (e.g., generalized extreme value (GEV) and log-Pearson Type III (LP3)) by combining bounded support ($\alpha <x<\infty$) to reflect physical flood thresholds, flexible tail behavior via Fréchet–log-logistic fusion for extreme-value accuracy, and maximum entropy characterization, ensuring optimal parameter estimation. Thus, we obtain the LFLD’s main statistical properties (PDF, CDF, and hazard rate), prove its asymptotic convergence to Fréchet distributions, and validate its superiority through simulation studies showing MLE consistency (bias < 0.02 and mean squared error < 0.0004 for $\alpha$) and empirical flood data tests (52- and 98-year AMS series), where the LFLD outperforms 10 competitors (AIC reductions of 15–40%; Vuong test p < 0.01). The LFLD’s closed-form quantile function enables efficient return period estimation, critical for infrastructure planning. Results demonstrate its applicability to heavy-tailed, bounded hydrological data, offering a 20–30% improvement in flood magnitude prediction over LP3/GEV models. Full article