Search Results (156)

The purpose of this paper is to generalise the rate-differential relations and general integrals, originally derived for Einstein’s particle energy expression, to a family of Lorentz-invariant power-law particle energies characterised by an arbitrary constant $\kappa$ such that the Einstein energy is included through the special case $\kappa =0$. By Lorentz invariance, we refer to invariance under the combined special relativistic space–time and energy–momentum transformations. The power-law particle energy expressions are important and potentially fundamental since they share the same relationship with an extension of the Planck–de Broglie energy–momentum relations, as does Einstein’s energy expression with the conventional Planck–de Broglie relations. The particle–wave approach is again adopted to determine the structure of the general integrals that apply to the power-law energies, except that here an independent derivation is also provided and from which the necessary conditions are apparent for the validity of the integral. A simple similarity solution is given that demonstrates the correctness of the general integrals, and the case of non-constant initial rest energy (non-constant rest mass) is incorporated in the analysis. An appendix provides an independent derivation of the Lorentz force expressions, from which the precise conditions of their validity become apparent. Full article

Crop residue cover (CRC) plays a crucial role in sustainable farming systems by improving soil structure, regulating water retention, and reducing soil erosion. Accurate CRC monitoring is therefore important for evaluating field management practices at scale. Existing field methods (e.g., line-transect and visual estimation) are labor-intensive and difficult to scale, while optical retrievals are often confounded by soil moisture. Moisture introduces nonlinear spectral distortions that can bias residue estimates, particularly in the shortwave infrared range. We propose a Deep Moisture-Invariant Autoencoder (DMIA) framework that performs conditional spectral normalization—referred to as moisture normalization (dry-equivalent spectral transformation)—before linear spectral unmixing. The workflow has two stages: (1) a conditional autoencoder that transforms moisture-affected spectra to dry-equivalent spectra, and (2) fully constrained linear unmixing on dry-equivalent spectra. The experiment included 63 controlled wheat-residue scenes at a semi-arid site in Morocco, spanning three moisture levels and seven residue proportions (0–100%) measured with ASD spectroscopy. Within this controlled experimental dataset, DMIA achieved a global coefficient of determination of R² = 0.93, outperforming ordinary least squares (R² = 0.65), fully constrained least squares (R² = 0.68), and ELMM (R² = 0.71), and matching the performance of MESMA (R² = 0.93) while requiring only a single forward pass at inference rather than iterative library matching. Although both methods showed similar overall accuracy, a closer analysis reveals that DMIA’s advantage over MESMA widens under wetter, coarser-resolution conditions, which are highly representative of operational monitoring. This finding is further validated by a Monte Carlo uncertainty propagation, proving the results are unaffected by reference noise. Using spectrally resampled ground data to simulate satellite responses, performance remained robust for PRISMA (R² = 0.93) and Sentinel-2 simulation (R² = 0.87). Reconstruction diagnostics (mean SAM below 5°) support the physical plausibility of the learned transformation. These results suggest that conditional spectral normalization can reduce moisture-related distortions while preserving compositional signals under controlled experimental conditions; however, the use of three discrete moisture levels represents an experimental simplification; in open operational fields, soil moisture varies continuously and pixel-level states are unknown. This framework provides a proof-of-concept basis for further investigation across diverse soils, residue types, and operational sensor configurations. Full article

Accurate and transferable land cover mapping from satellite imagery is a prerequisite for national-scale agrienvironmental monitoring and climate change impact assessment. The joint use of Sentinel-1 synthetic aperture radar (SAR) and Sentinel-2 multispectral imagery offers complementary structural and spectral information, yet systematic evaluation of fusion strategies and their geographic transferability remains limited. We trained and tested five U-Net fusion architectures S1-only, S2-only, early (input-level), feature-level (middle), and decision-level (late) alongside a SegFormer-b2 transformer baseline over two German cities (Munich and Berlin) using the Multi-Sensor Land Cover Classification (MSLCC) dataset (single-date 2017 Sentinel-1B/Sentinel-2A acquisitions) at 10 m resolution. Three cross-city transfer protocols (Munich → Berlin, Berlin → Munich, and combined training) quantify model transferability across contrasting urban–rural gradients. Early fusion achieved the highest in-city macro-averaged F1 score among U-Net variants (0.8278), a small but statistically significant improvement over the optical-only baseline (0.8236; patch-level paired bootstrap, $p=0.006$); feature-level (middle, 0.8164) and decision-level (late, 0.8196) fusion were, by contrast, significantly worse than the optical-only baseline ($p<0.001$ and $p=0.030$, respectively), and the SAR-only model (0.6864) trailed substantially. The built-up class was the primary beneficiary of SAR inclusion under early fusion. SegFormer-b2 (0.8214) was numerically close to, but statistically significantly below, the best convolutional configuration ($p=0.005$), and exhibited strong cross-city transfer (0.8632–0.8608 macro-F1), consistent with the geographic invariance conferred by its ImageNet-pretrained encoder. Combined training across both cities improved over the single-direction transfer average by 0.012 macro-F1 points for U-Net and 0.006 points for SegFormer, offering a practical route to national-scale deployment without requiring explicit domain adaptation. Spectral index augmentation (NDVI, NDWI, ExG) and SE channel attention did not significantly improve over plain early fusion when derived from percentile-normalized inputs, with the best variant statistically indistinguishable from the baseline at macro-F1 = 0.8268 ($p=0.365$); the result is attributable to a specific preprocessing dependency: NDVI, NDWI, and ExG are only physically meaningful when computed from calibrated reflectance, whereas here they were derived after scene-level 2nd–98th percentile stretching, which strips the absolute radiometric referencing the indices rely on; practitioners combining spectral indices with percentile-normalized (rather than physically calibrated, e.g., Level-2A surface-reflectance) inputs should expect a similar null result. Full article

Background/Objectives: Timely and accurate medical imaging in pre-hospital emergency care is crucial for improving the effectiveness of emergency medical rescue. Methods: In this study, a portable endoscopic system was developed for image acquisition and intelligent analysis. The core innovation lies in a dedicated image processing framework that integrates an improved U-Net neural network for real-time image dehazing and an enhanced Scale-Invariant Feature Transform (SIFT) algorithm for precise image stitching. Results: Experimental results demonstrated the exceptional performance of our method: the dehazing U-Net achieved a Structural Similarity Index (SSIM) of 0.98, a Peak Signal-to-Noise Ratio (PSNR) of 31.05, and a processing speed exceeding 70 frames per second (fps), while the enhanced SIFT algorithm effectively minimized stitching artifacts and vessel misalignment, yielding an SSIM of 0.9367 and a PSNR of 35.9768. Conclusions: This system significantly enhanced image quality and processing speed, enabling the acquisition of precise imaging information to support rapid diagnosis at the emergency scene. The findings establish a solid foundation for advancing pre-hospital emergency medical imaging and suggest promising avenues for future validation with diverse datasets and long-term clinical evaluations to further improve algorithmic robustness and applicability. Full article

This work is devoted to the practical application of the geometric theory of dynamical systems to find invariants of a set of symmetric time series. Such series are often encountered in information systems processing large volumes of financial data, where spikes, outliers, and fluctuations are visually similar to each other, which can be explained, for example, by identical seasonal cycles or the type of economic activity. Although absolute values, amplitudes, and deviations may differ, the qualitative behaviour of such series is the same, as in oscillatory physical systems under different initial conditions and parameters. The discovered geometric invariant represents a structuring model that can be applied to the entire group of symmetric time series, providing a foundation for robust interval forecasting and the clustering of structurally similar dynamical systems. A theorem is proved establishing that the curvature of the jet space curve is a complete invariant under the group of affine transformations of the jet space coordinates and rotations. The use of translation, scaling, and rotation transformations applied to the locus of points of integral curves makes it possible to identify series that have the same qualitative behaviour up to a weak violation of symmetry. Experimental validation is performed on 25 daily bank account balance series. The proposed method achieves consistent alignment across all series. Full article

This study examines the relationship between the Potts model in statistical mechanics and mathematical knots. This is done by transforming the Potts model into knot polynomials. The knot polynomial in the Kauffman square brackets is used. Temperley–Lieb algebra is used to obtain the dichromatic polynomial of a graph. A special family of knots called Zengi knots (links) is considered, consisting of four different models. We reveal the partition functions of these knots (links) by using a strain factor corresponding to the particles in the Potts model. One of the deep connections between physics and mathematics is the existence of the relationship between the Potts model and similar models developed for some algebras and knot and link invariants. This is clearly stated here by the given applications. Full article

We construct a connection-theoretic framework for parallel transport of spectral components along parameter families of signals on the similarity group $\tilde{G}=\mathbb{R}\times \mathrm{SO}\left(2\right)$. Let ${\left\{f_t\right\}}_{t\in I}$ be a signal family that evolves under a $C^1$ group trajectory. The frequency support of the associated scale-rotation transforms produces three Hilbert subbundles over the parameter interval, and the trajectory velocity induces a covariant derivative on each subbundle. The standard spectral viewpoint treats transformation behavior at individual parameter values. Our formulation instead organizes the propagation of spectral components along the entire parameter path and provides closed-form transport operators together with error bounds on each subbundle. We derive three explicit parallel transport formulas. On the equivariant subbundle the transport is an exact isometric translation. On the coupled subbundle, the transport combines log-scale translation with a phase factor $e^{i{n}_0\Delta \theta }$. On the invariant subbundle, the transport is approximate, with the quantitative bound $\parallel {\mathsf{\Pi }}^{\mathrm{inv}}F-F\parallel \le \epsilon |\Delta \tau |\parallel F\parallel$, where ${\mathsf{\Pi }}^{\mathrm{inv}}$ denotes the parallel transport operator on that subbundle. We introduce the notion of non-parallelism rate as a pointwise measure of deviation from parallel evolution, and we prove that cumulative deviation along the path is bounded by the path integral of this quantity. The bound separates into two parts. One part is controlled by trajectory estimation error and reflects geometric mismatch. The other part is controlled by intrinsic appearance variation and reflects non-geometric drift. We also show that regularity transfers from the signal family to the spectral sections, and we establish a discrete transport theorem whose finite-sum error bounds recover the continuous estimates in the small-step limit. The framework provides a quantitative geometric tool for multi-scale feature evolution under continuous scale-rotation transformations. Full article

Adversarial examples reveal critical vulnerabilities in deep neural networks, posing significant risks in real-world deployment. In black-box settings, transferable targeted attacks rely on surrogate models but often suffer from low success rates. We argue that this limitation arises not only from surrogate-boundary overfitting but also from insufficient alignment with the target semantic space, which restricts the ability of adversarial examples to encode target-specific characteristics. To address this issue, we propose Cosine-Based Logit Alignment (CBLA), a unified framework for transferable targeted attacks. CBLA replaces the conventional cross-entropy loss with a cosine similarity objective to enhance directional alignment in logit space and alleviate gradient saturation. In addition, a semantic-invariant transformation strategy is introduced to improve structural consistency and cross-model generalization. Experiments on the ImageNet validation set demonstrate that CBLA consistently improves targeted attack success rates, achieving an average gain of 4.55% over strong baselines across multiple architectures. Full article

The integration of heterogeneous geospatial data, specifically low-cost unmanned aerial vehicle (UAV) imagery and mobile light detection and ranging (LiDAR) system point clouds, presents a significant challenge due to the significant radiometric and structural discrepancies between the two modalities. This study proposes a novel air-to-ground semantic feature matching framework to achieve precise geometric registration between these data sources by effectively incorporating semantic-constraint deep learning-based matching. The methodology transformed the cross-sensor alignment challenge into a robust two-dimensional image matching problem. This was achieved by first using YOLOv11 for semantic segmentation of common road markings in both the UAV orthoimage and the converted LiDAR intensity image to generate highly consistent feature references. Subsequently, the SuperPoint detector and a graph neural network matcher, SuperGlue, were applied to these semantic images to establish reliable geomatics information correspondence points. Experimental results confirmed that this semantic-guided strategy consistently outperformed traditional feature-based matching (i.e., scale-invariant feature transform + fast library for approximate nearest neighbors), particularly by converting the noisy LiDAR intensity image into a stabilized semantic representation. The explicit application of semantic constraints further proved effective in eliminating false matches between geometrically similar but semantically distinct objects. The final object-specific analysis demonstrated that features with clear, complex geometric structures (e.g., pedestrian crossings and directional arrows) provide the most robust matching control. In summary, the proposed framework successfully leverages semantic context to overcome cross-sensor heterogeneity, offering an automated and precise solution for the geometric alignment of mobile LiDAR data. Full article

Significant nonlinear radiation differences and weak texture differences exist between multimodal weak texture remote sensing images (MWTRSIs). When using traditional methods to match MWTRSIs, the low distinguishability of descriptors in weak texture regions results in poor matching performance. A robust matching method is proposed based on normalized structural feature transform (NSFT), which can extract spatial structural features of images while mitigating nonlinear radiation differences between weak texture regions. First, the bilateral filter is used to transform the weak texture remote sensing image into a normalized image, which not only greatly weakens the nonlinear radiation difference but also retains most of the structural information. Then, the UC-KAZE detector is designed to extract many evenly distributed feature points on the normalized image. Subsequently, a multimodal weak texture feature descriptor with rotation invariance is designed based on the self-similarity of the weak texture image. Finally, the initial correspondences are constructed by bilateral matching, and the mismatches are removed by the fast sample consensus (FSC) algorithm. We perform comparison experiments on eight types of MWTRSIs. The results show that the proposed method has good scale and rotation invariance and good resistance to nonlinear radiation differences and weak texture differences. Full article

Water utilities continue to lose a lot of Non-Revenue Water (NRW) because of leaks that go undetected. This makes it necessary to find accurate but easy-to-use monitoring solutions. This paper presents FiT-WST+, a wavelet-guided Frequency-Informed Transformer (FiT) designed for the classification of five distinct leak types utilising accelerometer measurements. The proposed architecture combines the spectral modelling ability of a FIT with the stable translation-invariant representation of the Wavelet Scattering Transform (WST). The model uses a guided attention mechanism to combine spectral and scattering cues that work well together to make classes more distinct, especially for fault types that are similar. On the held-out test set, FiT-WST+ achieves 99.6% accuracy, 99.6% balanced accuracy, and a 99.6% macro-averaged F1-score. Comparative benchmarking against recent methods tested on the same dataset shows that this method works at a low sampling rate (1 kHz), which greatly lowers bandwidth needs and allows for scalable deployment on edge devices with limited resources for real-time monitoring of important water infrastructure. Full article

A class of self-similar solutions to the model of a cylindrical shock wave in non-uniform atmosphere in the presence of monochromatic radiation and gravitation in magneto gas dynamics has been obtained by using a similarity method. The propagation of a cylindrical shock wave in an ideal gas with monochromatic radiation and gravitating effects has been discussed. Through applying similarity transformations to the system of equations, we obtained the symmetry generators of the system. By using the symmetry generators and the surface invariance condition, we obtained the group invariant solution and then, with the help of group invariant solution, we converted the given system of PDEs to the system of ODEs together with the boundary condition. The obtained system of ODEs together with boundary condition has been solved numerically by using Runge–Kutta method of order four. The flow variables are analyzed graphically behind the shock with respect to the variation of parameters. Full article

Underwater optical images often exhibit severe color distortion, weak texture, and uneven illumination due to light absorption and scattering in water. These issues result in unstable feature detection and inaccurate image registration. To address these challenges, this paper proposes an underwater image stitching method that integrates ORB (Oriented FAST and Rotated BRIEF) feature extraction with a fixed-ratio constraint matching strategy. First, lightweight color and contrast enhancement techniques are employed to restore color balance and improve local texture visibility. Then, ORB descriptors are extracted and matched via a KNN (K-Nearest Neighbors) nearest-neighbor search, and Lowe’s ratio test is applied to eliminate false matches caused by weak texture similarity. Finally, the geometric transformation between image frames is estimated by incorporating robust optimization, ensuring stable homography computation. Experimental results on real underwater datasets show that the proposed method significantly improves stitching continuity and structural consistency, achieving 40–120% improvements in SSIM (Structural Similarity Index) and PSNR (peak signal-to-noise ratio) over conventional Harris–ORB + KNN, SIFT (scale-invariant feature transform) + BF (brute force), SIFT + KNN, and AKAZE (accelerated KAZE) + BF methods while maintaining processing times within one second. These results indicate that the proposed method is well-suited for real-time underwater environment perception and panoramic mapping on low-cost, micro-sized underwater robotic platforms. Full article

In this study, equidistant ruled surfaces generated by the Darboux vector, which has significant kinematic importance and characterizes the instantaneous rotation of a moving frame, are investigated specifically for the Frenet frame. By establishing a structural relationship between a surface and its equidistant ruled surface, transition formulas are provided for shape operators, Gaussian and mean curvatures, and fundamental forms, revealing that the equidistant surface is a scaled transformation of the original one. The obtained results demonstrate that both surfaces are developable and that the geometric properties of the equidistant ruled surfaces can be expressed dependently on each other. Furthermore, it is shown that the geometric character of the equidistant surface, including the invariance of asymptotic lines and the preservation of umbilical points under constant angle conditions, is determined by the rotational dynamics of the base curve. These findings constitute a theoretical foundation for cases involving the use of Darboux axes of different frames in higher dimensions or the investigation of similar structures in different geometric spaces. The geometric interpretation of this theoretical framework is elucidated through the fundamental properties of the surfaces. Finally, a concrete example is presented, where the symmetry of the central planes of the equidistant ruled surfaces at appropriate points is visualized using Maple 2017 software. Full article

Deep learning for semantic segmentation has made significant advances in recent years, achieving state-of-the-art performance. Medical image segmentation, as a key component of healthcare systems, plays a vital role in the diagnosis and treatment planning of diseases. Due to the fractal and scale-invariant nature of biological structures, effective medical image segmentation requires models capable of capturing hierarchical and self-similar representations across multiple spatial scales. In this paper, a Recurrent Neural Network (RNN) is explored within the Convolutional Neural Network (CNN) and Vision Transformer (ViT)-based hybrid U-shape network, named RCV-UNet. First, the ViT-based layer was developed in the bottleneck to effectively capture the global context of an image and establish long-range dependencies through the self-attention mechanism. Second, recurrent residual convolutional blocks (RRCBs) were introduced in both the encoder and decoder to enhance the ability to capture local features and preserve fine details. Third, by integrating the global feature extraction capability of ViT with the local feature enhancement strength of RRCBs, RCV-UNet achieved promising global consistency and boundary refinement, addressing key challenges in medical image segmentation. From a fractal–fractional perspective, the multi-scale encoder–decoder hierarchy and attention-driven aggregation in RCV-UNet naturally accommodate fractal-like, scale-invariant regularity, while the recurrent and residual connections approximate fractional-order dynamics in feature propagation, enabling continuous and memory-aware representation learning. The proposed RCV-UNet was evaluated on four different modalities of images, including CT, MRI, Dermoscopy, and ultrasound, using the Synapse, ACDC, ISIC 2018, and BUSI datasets. Experimental results demonstrate that RCV-UNet outperforms other popular baseline methods, achieving strong performance across different segmentation tasks. The code of the proposed method will be made publicly available. Full article