Abstract The identification of knitted fabric patterns is a critical component in modern textile manufacturing processes. Traditionally, manual identification remains the predominant method, but it often incurs significant labor costs and suffers from low efficiency. Machine learning-based approaches, though promising, require labor-intensive feature engineering and fail to achieve satisfactory accuracy. To address these limitations, we propose the frequency domain weighted DenseNet (FW-DenseNet), a novel architecture tailored for fabric pattern recognition. The conventional DenseNet architecture accumulates features across channel dimensions, often leading to redundancy. In our approach, each channel in DenseNet is assigned a learnable weight, enabling the model to selectively prioritize meaningful feature maps while disregarding redundant information. This design not only minimizes information redundancy but also expands the model’s search space for optimal features. Given that the distinct textures in knitted fabric patterns arise from variations in weaving techniques, capturing detailed texture information is paramount. The frequency domain provides richer and more comprehensive descriptions of texture, making it particularly effective for capturing fine-grained details. Accordingly, we convert knitted fabric images into the frequency domain for feature extraction, ensuring robust texture representation. To address the scarcity of publicly available datasets for knitted fabrics, we constructed a custom dataset for this study. Experimental results demonstrate that FW-DenseNet outperforms existing methods, effectively mitigating the impact of factors such as rotation, positional shifts, and lighting variations, while achieving high accuracy in fabric recognition.

Vision Transformers have demonstrated remarkable performance in image classification and structural modeling; however, fixed patch partitioning and static positional encoding often disrupt spatial continuity, thereby limiting their ability to represent rotated structures and irregular boundary regions. To address these limitations, we propose the Moore-curve Vision Transformer (MViT), a Vision Transformer (ViT) framework based on a recursive Moore curve. The proposed framework comprises three key components. First, a multi-order fractal mapping is employed to optimize patch reordering and enhance the spatial coherence of the token sequence. Second, a 7×7 dynamic partitioning template together with a boundary compensation algorithm jointly optimizes dense structural representation and resolution adaptability. Third, a period-aware positional encoding module integrates fractal periodic parameters with convolutional features to align positional embeddings with the fractal traversal pattern. This design significantly enhances the structural adaptability of the model to complex image layouts. Experimental results show that MViT improves classification accuracy over ViT-B/16 by 0.52% and 0.31% on the CIFAR-100 and ImageNet-21k datasets, respectively, while also achieving noticeable improvements in PSNR and SSIM. Ablation and rotational perturbation experiments further confirm its robustness to rotation and localized focus variations. Moreover, MViT exhibits strong structural compatibility, maintaining stable performance across different Transformer backbones and diverse visual tasks.

Vision Transformers have demonstrated remarkable performance in image classification and structural modeling; however, fixed patch partitioning and static positional encoding often disrupt spatial continuity, thereby limiting their ability to represent rotated structures and irregular boundary regions. To address these limitations, we propose the Moore-curve Vision Transformer (MViT), a Vision Transformer (ViT) framework based on a recursive Moore curve. The proposed framework comprises three key components. First, a multi-order fractal mapping is employed to optimize patch reordering and enhance the spatial coherence of the token sequence. Second, a 7×7 dynamic partitioning template together with a boundary compensation algorithm jointly optimizes dense structural representation and resolution adaptability. Third, a period-aware positional encoding module integrates fractal periodic parameters with convolutional features to align positional embeddings with the fractal traversal pattern. This design significantly enhances the structural adaptability of the model to complex image layouts. Experimental results show that MViT improves classification accuracy over ViT-B/16 by 0.52% and 0.31% on the CIFAR-100 and ImageNet-21k datasets, respectively, while also achieving noticeable improvements in PSNR and SSIM. Ablation and rotational perturbation experiments further confirm its robustness to rotation and localized focus variations. Moreover, MViT exhibits strong structural compatibility, maintaining stable performance across different Transformer backbones and diverse visual tasks.

BackgroundAccurate classification and segmentation of brain tumors in MRI scans are essential for diagnosis and treatment planning. However, the heterogeneous morphology of brain tumors, including irregular shapes, sizes, and spatial variability, makes this task highly challenging. Traditional convolutional neural networks (CNNs) lack rotational and translational invariance, which limits their ability to generalize across different orientations.MethodsThis study introduces a geometric deep learning framework called Modified Special Euclidean (Mod-SE(2)), which integrates geometric priors to enhance spatial consistency and reduce reliance on data augmentation. By incorporating symmetry-preserving group convolutions and spatial priors, Mod-SE(2) improves the robustness in tumor classification (namely Mod-Cls-SE(2)) and segmentation (mentioned as Mod-Seg-SE(2)). Unlike conventional CNNs, geometric deep learning encodes roto-translation symmetry directly into the architecture. This addresses the spatial variability and orientation sensitivity that are common in MRI-based diagnostics. Mod-SE(2) was evaluated on three MRI datasets and two other medical image datasets for classification and segmentation tasks. It incorporates lifting layers, group convolutions, and feature recalibration. It was benchmarked against U-Net, NN U-Net, VGG16, VGG19, and ResNet architectures.ResultsMod-Cls-SE(2) achieved an average classification accuracy of 0.914, outperforming ResNet101 with 0.682, VGG16 with 0.705, and their variants. In the binary classification of five tumor types (AVM, Meningioma, Pituitary, Metastases, and Schwannoma) from the private dataset, the model achieved an accuracy of 0.935 and a precision of 0.960 for pituitary tumors and a precision of 0.96. For segmentation tasks, Mod-Seg-SE(2) achieved a dice coefficient of 0.9503 and an IoU of 0.9616 on the BraTS2020 dataset. This result exceeds those of U-Net and NN U-Net with dice scores of 0.797 and 0.815, respectively. The model also reduced inference time and demonstrated strong computational performance.ConclusionsMod-SE(2) uses geometric priors to improve the spatial consistency, efficiency, and interpretability in brain tumor analysis. Its symmetry-aware design enables better generalization across tumor shapes and outperforms traditional methods across all key metrics. The Mod-SE(2) CNN ensures accurate boundary delineation, supporting neurosurgical planning, intraoperative navigation, and downstream applications such as Monte Carlo-based radiotherapy simulations and PET-MRI co-registration. Future work will extend the model to 3D volumes and validate its clinical readiness.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12929-025-01213-y.

As a key task in 3D scene understanding, point cloud semantic segmentation has broad application prospects in fields such as autonomous driving and robot navigation. Existing point cloud segmentation methods suffer from insufficient local feature extraction and a lack of effective integration of global contextual information, leading to inaccurate recogni-tion and incomplete segmentation of categories with similar surface textures and geometric structures. In view of this, this paper proposes an improved point cloud segmentation method for RandLA-Net : (1) Local polar coordinate posi-tion encoding module is introduced to eliminate the impact of Z-axis rotation on feature learning; (2) Global information acquisition module composed of attention mechanisms is constructed to enhance the network's contextual perception ability; (3) Hybrid pooling mechanism is integrated to improve the extraction of local features. The proposed method is evaluated on the self-built HPU dataset and public datasets S3DIS and Toronto-3D. The results show that the improved network achieves mean intersection over union (mIoU) values of 90.7%, 71.2%, and 76.4% respectively, demonstrating improvements compared to other algorithms. The model exhibits excellent generalization and segmentation perfor-mance in different types of point cloud scenes.

Influence of rotational spatial variability in geotechnical parameters on the rainfall-induced stability of soil-like slopes

The stochastic rotational invariance of an integration by parts formula inspired by the Bismut approach to Malliavin calculus is proved in the framework of the Lie symmetry theory of stochastic differential equations. The non-trivial effect of the rotational invariance of the driving Brownian motion in the derivation of the integration by parts formula is discussed and the invariance property of the formula is shown via applications to some explicit two-dimensional Brownian motion-driven stochastic models.

The accurate prediction of protein function from raw amino acid sequences and structural data remains a central challenge in computational biology, essential for advancing drug discovery and understanding cellular mechanisms. While sequence-based methods have historically dominated the field due to data abundance, they often fail to capture the functional implications of distant homology where sequence similarity is low but structural conservation is high. With the advent of highly accurate structure prediction systems, the availability of 3D protein structures has exploded, necessitating novel architectures capable of leveraging this geometric data. This paper introduces GeoProtNet, a comprehensive framework that utilizes Geometric Deep Learning (GDL) to predict protein function, specifically Gene Ontology (GO) terms. We propose a hybrid architecture that processes the protein as a geodesic graph on a Riemannian manifold to capture local chemical environments, while simultaneously integrating global context through a higher-order Protein-Protein Interaction (PPI) graph. By enforcing SE(3)-equivariance within the message-passing mechanism, our model ensures robustness against rotational and translational variations inherent in coordinate data. Experimental results demonstrate that GeoProtNet significantly outperforms state-of-the-art sequence-based and structure-based baselines, particularly in the twilight zone of low sequence identity.

ABSTRACT Most spin density functionals are collinear, assuming the spin magnetization has only one nonzero component. However, a fully defined functional should be noncollinear, treating all three components of the spin magnetization vector as variables. The multicollinear approach is introduced to bridge this gap by generalizing an arbitrary collinear functional to a noncollinear one. In contrast to the traditional scheme, which adopts the local projection of the spin magnetization vector field, the multicollinear method employs a global projection scheme. It offers several key advantages, including recovering the collinear limit, ensuring global spin rotational invariance, maintaining numerical stability, and providing nonzero local torque. Its broad applicability spans relativistic and nonrelativistic cases, molecular and periodic systems, ground and excited states, as well as static and dynamic simulations. Furthermore, for collinear systems, it provides capabilities that go beyond standard collinear functionals by establishing a rigorous framework for spin‐flip TDDFT. This makes it a powerful tool for treating challenging problems such as double excitations, conical intersections, bond dissociation, and diradicals. Overall, the multicollinear approach provides a unified and versatile framework for quantum chemistry. This article is categorized under: Electronic Structure Theory > Density Functional Theory

MotivationImaging-based spatially resolved transcriptomics (imSRT) technologies provide high-throughput molecular-resolution spatial characterization of genes within cells. Conventional analysis methods to identify cell-types and states in imSRT data rely on gene count matrices derived from tallying the number of mRNA molecules detected for each gene per segmented cell, thereby overlooking subcellular heterogeneity that can be useful in defining cell states.ResultsTo take advantage of the molecular-resolution information in imSRT data and potentially identify cell-states based on subcellular heterogeneity, we developed STARIT (Spatial Transcriptomics As Rasterized Image Tensors). STARIT converts transcripts within segmented cells in imSRT data into an image-based tensor representation that can be combined with deep learning computer vision models for downstream analysis. Using simulated data, we demonstrate that STARIT distinguishes transcriptionally distinct cell-types and further separates cell states based on subcellular transcript localization, which conventional gene count analysis fails to capture. Likewise, using real imSRT data, we demonstrate how STARIT identifies comparable cell-types to conventional gene count analysis as well as delineate rotational variation. By providing a standardized framework to encode subcellular molecular information in imSRT data, STARIT will enable deeper insights into subcellular heterogeneity and enhance the identification and characterization of cell-types and states that are overlooked by gene count representations.Availability and ImplementationSTARIT is available as a Python package on GitHub at https://github.com/JEFworks-Lab/STARIT.

Abstract Attitude and heading reference systems (AHRSs) are widely used in aviation and navigation to provide reliable attitude and heading information. While traditional AHRS relied on mechanical gyroscopes, advancements in micro-electro-mechanical systems technology have enabled the development of cost-effective AHRS solutions utilizing magnetic, angular rate, and gravity sensors. However, the accuracy of AHRS is often compromised by internal sensor errors, such as non-orthogonality, sensitivity, and bias errors, as well as coordinate inconsistencies between sensors. Existing calibration methods, such as the ellipsoid fitting and dot product invariance methods, effectively address internal sensor errors but are limited in correcting coordinate inconsistencies, particularly in reference-free environments or with sensors of different types. This paper proposes a novel, reference-free method for calibrating coordinate inconsistencies in AHRS. By leveraging the normal vector invariance of plane rotation in tri-axial field sensors, the proposed approach achieves accurate calibration without the need for auxiliary precision equipment or external references, offering a cost-effective and practical solution for improving AHRS reliability and performance. The feasibility and effectiveness of the method are validated through field experiments, which were conducted using precision rigs to ensure accuracy, demonstrating that it significantly enhances AHRS accuracy. This advancement holds great potential for applications in resource-constrained systems, such as unmanned aerial vehicles and autonomous underwater vehicles (AUVs).

Objective: This study investigates whether audit rotation provides incremental informational content for participants in the Brazilian capital market. Method: The value relevance model of Collins et al. (1997) is applied to a sample of 402 companies (2,680 observations) listed on the B3 between 2010 and 2021. The rotation variables were obtained from the firms’ Reference Forms and classified by type (audit firm or audit partner), nature (voluntary or mandatory), and audit firm size (Big 4 or non-Big 4). Results: The results show asymmetrical capital market reactions to audit rotation information. Rotation of signatory partners is positively value relevant, whereas mandatory audit rotation is not. The findings also indicate that replacements from non-Big 4 to Big 4 firms are perceived as value relevant, while any change to a non-Big 4 firm leads to negative investor responses. Contributions: The study contributes by demonstrating that audit firm rotation constitutes a relevant accounting element for value creation in the market, as it functions as an informational mechanism that signals to investors the reliability of the reported accounting figures and the likelihood of detecting and reporting deviations in accounting practices.

Abstract We conduct a systematic robustness analysis of the hybrid machine learning framework USmorph , which integrates unsupervised and supervised learning for galaxy morphological classification. Although USmorph has already been applied to nearly 100,000 I -band galaxy images in the COSMOS field (0.2 < z < 1.2, I mag < 25), the stability of its core modules has not been quantitatively assessed. Our tests show that the convolutional autoencoder achieves the best performance in preserving structural information when adopting an intermediate network depth, 5 × 5 convolutional kernels, and a 40D latent representation. The adaptive polar coordinate transform effectively enhances rotational invariance and improves the robustness of downstream tasks. In the unsupervised stage, a bagging clustering number of K = 50 provides the optimal trade-off between classification granularity and labeling efficiency. For supervised learning, we employ GoogLeNet, which exhibits stable performance without overfitting. We validate the reliability of the final classifications through two independent tests: (1) the t-distributed stochastic neighbor embedding visualization reveals clear clustering boundaries in the low-dimensional space; and (2) the morphological classifications are consistent with theoretical expectations of galaxy evolution, with both true and false positives showing unbiased distributions in the parameter space. These results demonstrate the strong robustness of the USmorph algorithm, providing guidance for its future application to the China Space Station Telescope mission.

Contour-based shape representation is a fundamental task in computer vision, particularly for binary image analysis in technical and industrial applications [1], [2], [14]. While global geometric descriptors such as contour length offer computational efficiency and rotational invariance, they often lack sufficient discriminative power for complex shapes due to the loss of local structural information [1], [13]. This paper presents a local topological contour analysis framework based on a 32-template model, where object boundaries are represented by the distribution of predefined 3×3 neighborhood configurations along the contour. The proposed descriptor encodes local geometric transitions and topological patterns while maintaining low computational complexity. Similarity between objects is evaluated using a metric-based comparison scheme, and classification decisions are obtained via a dominant-folder strategy [3], [12]. Experimental evaluation was conducted on a controlled dataset of planar binary objects under full rotational variation and reconstruction scenarios. The results demonstrate that the proposed 32-template contour descriptor achieves 100% dominant-folder classification accuracy, exhibiting strong diagonal dominance in similarity matrices and stable statistical behavior across samples. The findings confirm that local topological contour representations significantly improve discriminative capability compared to global metrics, while preserving interpretability and computational efficiency. The proposed method provides a practical and training-free solution for real-time shape recognition in binary images and establishes a solid foundation for further development of local contour-based descriptors.

Abstract: This paper investigates a one-dimensional (1D) descriptor model for image recognition based solely on contour length. The proposed approach represents each planar object by a single scalar value obtained through weighted accumulation of local contour segments. The primary objective is to evaluate the computational efficiency and discriminative capability of this simplified descriptor under rotation and reconstruction scenarios. Contours are extracted using Canny edge detection following binarization and noise suppression. Experimental results on a dataset of original and reconstructed images demonstrate that the contour-length descriptor provides high computational speed and rotational invariance for smooth shapes. However, due to its global nature, the model fails to adequately capture local geometric variations, leading to reduced discrimination for complex contours. The findings confirm that contour length alone is insufficient for robust shape recognition and the integration of higher-dimensional local structural descriptors in future research.

Abstract: This paper investigates a contour-based metric approach for planar object recognition in binary images [1,2,14]. The proposed method represents each object using contour length as a global geometric descriptor and evaluates its effectiveness under rotation and reconstruction scenarios [1,14,15]. Contours are extracted after preprocessing steps including binarization, noise suppression, and morphological filtering. The contour length is computed using a weighted neighborhood scheme that accounts for horizontal, vertical, and diagonal connections. Experiments were conducted on a dataset consisting of original and reconstructed binary images with full rotational variations. The results demonstrate that contour length is computationally efficient and invariant to rotation, making it suitable for real-time image processing applications [1,2,14]. However, statistical analysis using empirical cumulative distribution functions and histogram distributions reveals significant overlap of contour length values among different objects, which limits discriminative performance for complex shapes [14,15]. The study concludes that contour length alone is insufficient for reliable shape recognition but provides a useful baseline for more advanced local and hybrid contour descriptors [14,15].

Spatial distribution similarity analysis has extensive application value in multiple domains including geographic information science, urban planning, and engineering site selection. However, traditional regional similarity analysis methods face three key challenges: high sensitivity to directional changes, limitations in feature interpretability, and insufficient adaptability to multi-type data. Addressing these issues, this paper proposes a rotation-invariant spatial distribution similarity analysis method based on ring vectors. This method comprises three stages. First, the traversal starting point of the ring vector is dynamically selected based on the maximum value point of the regional feature matrix. Next, concentric ring features are extracted according to this starting point to achieve multi-scale characterization. Finally, the bidirectional weighted comprehensive distance of ring vectors between regions is calculated to measure the similarity between regions. Three experimental sets verified the method’s effectiveness in terrain matching, engineering site selection, and urban functional area identification. These results confirm its rotational invariance, feature interpretability, and adaptability to multi-type data. This research provides a new technical approach for spatial distribution similarity analysis, with significant theoretical and practical implications for geographic information science, urban planning, and engineering site selection.

The magneto-optical Kerr effect (MOKE) microscopy is a powerful tool for characterizing magnetic materials, leveraging its high surface sensitivity, nondestructive nature, rapid scanning capability, and real-time imaging functionality. This technique probes surface magnetization states by detecting polarization rotation or intensity variations in reflected polarized light, with three distinct operational modes (polar, longitudinal, transverse) tailored to different magnetization orientations. MOKE applications span diverse magnetic material systems, including metals and alloys, complex oxides, and polymer nanocomposites. This review comprehensively surveys MOKE developments, encompassing fundamental principles, operational modalities, comparative advantages over conventional magnetic characterization techniques, applications across material classes, and recent advancements-such as MOKE for high-resolution spectroscopy of 2D materials and topological magnetic structures.

Abstract This paper presents a method for jointly measuring the number of blades and the opening angle of rotationally symmetric targets based on the orbital angular momentum (OAM) spectral missing effect. We use single-mode vortex beam to illuminate the fan-shaped target. The number of blades is determined by analyzing the intervals of dispersion peaks in the echo OAM spectrum. The single blade’s opening angle is determined by the suppression characteristic of specific OAM modes, enabling simultaneous estimation identification of geometric parameters. We also verified that this method combines rotational invariance and beam parameter robustness, providing a new idea for non-contact detection of structures such as aircraft blades and unmanned aerial vehicle rotors.

F-norm based low-power motion recognition on wearable devices in the presence of outlier motions