Search Results (1,931)

This work presents a comprehensive study of weakly B-symmetric warped product manifolds ${\left(WBS\right)}_n$, a natural extension of several classical curvature-restricted geometries including B-flat, B-parallel, and B-recurrent manifolds. We begin by formulating the fundamental properties of the B-tensor $B(X,Y)=aS(X,Y)+brg(X,Y)$, where S is the Ricci tensor, r the scalar curvature, and $a,b$ are smooth non-vanishing functions. The warped product structure is then exploited to obtain explicit curvature identities for base and fiber manifolds under various geometric constraints. Detailed characterizations are established for Einstein conditions, Codazzi-type tensors, cyclic parallel tensors, and the behavior of geodesic vector fields. The weakly B-symmetric condition is analyzed through all possible projections of vector fields, leading to sharp criteria describing the interaction between the warping function and curvature. Several applications are discussed in the context of Lorentzian geometry, including perfect fluid and generalized Robertson–Walker spacetimes in general relativity. These results not only unify different curvature-restricted frameworks but also reveal new geometric and physical implications of warped product manifolds endowed with weak B-symmetry. Full article

In recent years, inverse reinforcement learning algorithms have garnered substantial attention and demonstrated remarkable success across various control domains, including autonomous driving, intelligent gaming, robotic manipulation, and automated industrial systems. Nevertheless, existing methodologies face two persistent challenges: (1) finite or non-optimal expert demonstration and (2) ambiguity in which different reward functions lead to same expert strategies. To improve and enhance the expert demonstration data and to eliminate the ambiguity caused by the symmetry of rewards, there has been a growing interest in research on developing inverse reinforcement learning based on the maximum entropy method. The unique advantage of these algorithms lies in learning rewards from expert presentations by maximizing policy entropy, matching expert expectations, and then optimizing the policy. This paper first provides a comprehensive review of the historical development of maximum entropy-based inverse reinforcement learning (ME-IRL) methodologies. Subsequently, it systematically presents the benchmark experiments and recent application breakthroughs achieved through ME-IRL. The concluding section analyzes the persistent technical challenges, proposes promising solutions, and outlines the emerging research frontiers in this rapidly evolving field. Full article

Hyperspectral imaging (HSI) systems often suffer from complex noise degradation during the imaging process, significantly impacting downstream applications. Deep learning-based methods, though effective, rely on impractical paired training data, while traditional model-based methods require manually tuned hyperparameters and lack generalization. To address these issues, we propose SS³L (Self-Supervised Spectral-Spatial Subspace Learning), a novel HSI denoising framework that requires neither paired data nor manual tuning. Specifically, we introduce a self-supervised spectral–spatial paradigm that learns noisy features from noisy data, rather than paired training data, based on spatial geometric symmetry and spectral local consistency constraints. To avoid manual hyperparameter tuning, we propose an adaptive rank subspace representation and a loss function designed based on the collaborative integration of spectral and spatial losses via noise-aware spectral-spatial weighting, guided by the estimated noise intensity. These components jointly enable a dynamic trade-off between detail preservation and noise reduction under varying noise levels. The proposed SS³L embeds noise-adaptive subspace representations into the dynamic spectral–spatial hybrid loss-constrained network, enabling cross-sensor denoising through prior-informed self-supervision. Experimental results demonstrate that SS³L effectively removes noise while preserving both structural fidelity and spectral accuracy under diverse noise conditions. Full article

In recent years, convolutional neural network-based object detectors have achieved extensive applications in remote sensing (RS) image interpretation. While multi-scale feature modeling optimization remains a persistent research focus, existing methods frequently overlook the symmetrical balance between feature granularity and morphological diversity, particularly when handling high-aspect-ratio RS targets with anisotropic geometries. This oversight leads to suboptimal feature representations characterized by spatial sparsity and directional bias. To address this challenge, we propose the Parallel Interleaved Convolutional Kernel Network (PICK-Net), a rotation-aware detection framework that embodies symmetry principles through dual-path feature modulation and geometrically balanced operator design. The core innovation lies in the synergistic integration of cascaded dynamic sparse sampling and symmetrically decoupled feature modulation, enabling adaptive morphological modeling of RS targets. Specifically, the Parallel Interleaved Convolution (PIC) module establishes symmetric computation patterns through mirrored kernel arrangements, effectively reducing computational redundancy while preserving directional completeness through rotational symmetry-enhanced receptive field optimization. Complementing this, the Global Complementary Attention Mechanism (GCAM) introduces bidirectional symmetry in feature recalibration, decoupling channel-wise and spatial-wise adaptations through orthogonal attention pathways that maintain equilibrium in gradient propagation. Extensive experiments on RSOD and NWPU-VHR-10 datasets demonstrate our superior performance, achieving 92.2% and 84.90% mAP, respectively, outperforming state-of-the-art methods including EfficientNet and YOLOv8. With only 12.5 M parameters, the framework achieves symmetrical optimization of accuracy-efficiency trade-offs. Ablation studies confirm that the symmetric interaction between PIC and GCAM enhances detection performance by 2.75%, particularly excelling in scenarios requiring geometric symmetry preservation, such as dense target clusters and extreme scale variations. Cross-domain validation on agricultural pest datasets further verifies its rotational symmetry generalization capability, demonstrating 84.90% accuracy in fine-grained orientation-sensitive detection tasks. Full article

Many parametric models can be enriched by introducing additional parameters through transmutation, mixing, or compounding techniques. In this paper, we develop the framework of doubly generalized transmutation models (DGTMs), obtained by the repeated application of rank transmutation maps and their generalizations. We show that several flexible families already available in the literature can be reinterpreted as instances of double or multiple transmutation, thus unifying apparently disparate constructions under a common perspective. A key feature of DGTMs is their ability to flexibly control symmetry through parameterization, enabling more accurate modeling of asymmetric or heavy-tailed phenomena. We also discuss the potential extension of these models to the bivariate case. In addition, we introduce the gentransmuted R package, Version 1.0, which provides routines for data generation, parameter estimation, and model comparison for generalized transmutation models. Two real data applications illustrate the practical advantages of this approach, highlighting improved model fit relative to classical alternatives. Our results underscore the value of transmutation-based methods as a systematic tool for generating flexible probability distributions and advancing their computational implementation. Full article

In the digital transformation of public services, reliable and secure data handling has become central to effective E-government operations. This study introduces a symmetry-driven neural network architecture tailored for secure, scalable, and energy-efficient data processing. The model integrates weight-sharing and symmetrical configurations to enhance efficiency and resilience. Experimental validation on three E-government datasets (95,000–230,000 records) demonstrates that the proposed model improves processing speed by up to 40% and enhances adversarial robustness by maintaining accuracy reductions below 2.5% under attack scenarios. Compared with baseline neural networks, the architecture achieves higher accuracy (up to 95.1%), security (up to 98% attack prevention), and efficiency (processing up to 1600 records/sec). These results confirm the model’s applicability for large-scale, real-time E-government systems, providing a practical path for sustainable and secure digital public administration. Full article

Financial markets exhibit fundamental asymmetries in temporal causality, where policy interventions create asymmetric transmission patterns that traditional symmetric modeling approaches fail to capture. This work introduces a mathematical framework that exploits the inherent symmetries of transformer architectures while preserving essential asymmetric temporal relationships in financial causal inference. We develop CausalFormer, a symmetry-aware neural architecture that maintains the permutation equivariance properties of self-attention mechanisms while enforcing strict temporal asymmetry constraints for causal discovery. The framework incorporates three mathematically principled components: (1) a symmetric attention matrix construction with asymmetric temporal masking that preserves the mathematical elegance of transformer operations while ensuring causal consistency, (2) a multi-scale convolution module with symmetric kernel initialization but asymmetric temporal receptive fields that captures policy transmission effects across heterogeneous time horizons, and (3) enhanced Nelson–Siegel decomposition that maintains the symmetric factor structure while modeling the evolution dynamics of asymmetric factors. Our mathematical formulation establishes the formal symmetry properties of the attention mechanism under temporal transformations while proving asymmetric convergence behaviors in policy transmission scenarios. The integration of symmetric optimization landscapes with asymmetric causal constraints enables simultaneous achievement of mathematical elegance and economic interpretability. Comprehensive experiments on monetary policy datasets demonstrate that the symmetry-aware design achieves a 15.3% improvement in the accuracy of causal effect estimations and a 12.7% enhancement in the predictive performance compared to those for existing methods while maintaining 91.2% causal consistency scores. The framework successfully identifies asymmetric policy transmission mechanisms, revealing that monetary tightening exhibits 40% faster propagation than easing policies, establishing new mathematical insights into the temporal asymmetries in financial systems. This work demonstrates how principled exploitation of architectural symmetries combined with domain-specific asymmetric constraints opens up new directions for mathematically rigorous yet economically interpretable deep learning in financial econometrics, with broad applications spanning computational finance, economic forecasting, and policy analysis. Full article

Electromyography (EMG) signals reflect hand motion intention and exhibit a certain degree of amplitude symmetry. Nowadays, recognition of hand motion intention based on EMG has enriched its burgeoning promotion in various applications, such as rehabilitation, prostheses, and intelligent supply chains. For instance, the motion intentions of humans can be conveyed to logistics equipment, thereby improving the level of intelligence in a supply chain. To enhance the recognition accuracy of multiple hand motion intentions, this paper proposes a hand motion intention recognition method that decodes EMG signals based on improved long short-term memory (LSTM). Firstly, we performed preprocessing and utilized overlapping sliding windows on EMG segments. Secondly, we chose LSTM and improved it so as to capture features and enable prediction of hand motion intention. Specifically, we introduced the optimal key hyperparameter combination in the LSTM model using a genetic algorithm (GA). We found that our proposed method achieved relatively high accuracy in detecting hand motion intention, with average accuracies of 92.0% (five gestures) and 89.7% (seven gestures), while the highest accuracy reached 100.0% (seven gestures). Our paper may provide a way to predict the motion intention of the human hand for intention communication. Full article

This paper investigates the quasi-concircular curvature tensor on sequential warped product manifolds, which extend the classical singly warped product structure. We examine various curvature conditions associated with this tensor, including quasi-concircular flatness, quasi-concircular symmetry, and the divergence-free quasi-concircular condition, and we explore the properties of related soliton structures. In addition, we analyze the implications of these results in Lorentzian geometry by deriving explicit expressions for the Ricci tensor and scalar curvature of the considered manifolds. The study concludes with an illustrative example that emphasizes the geometric significance and potential applications of the investigated structures. Full article

With the iterative evolution of SLAM (Simultaneous Localization and Mapping) technology in the robotics domain, the SLAM paradigm based on three-dimensional Gaussian distribution models has emerged as the current state-of-the-art technical approach. This research proposes a novel MSGS-SLAM system (Monocular Semantic Gaussian Splatting SLAM), which innovatively integrates monocular vision with three-dimensional Gaussian distribution models within a semantic SLAM framework. Our approach exploits the inherent spherical symmetries of isotropic Gaussian distributions, enabling symmetric optimization processes that maintain computational efficiency while preserving geometric consistency. Current mainstream three-dimensional Gaussian semantic SLAM systems typically rely on depth sensors for map reconstruction and semantic segmentation, which not only significantly increases hardware costs but also limits the deployment potential of systems in diverse scenarios. To overcome this limitation, this research introduces a depth estimation proxy framework based on Metric3D-V2, which effectively addresses the inherent deficiency of monocular vision systems in depth information acquisition. Additionally, our method leverages architectural symmetries in indoor environments to enhance semantic understanding through symmetric feature matching. Through this approach, the system achieves robust and efficient semantic feature integration and optimization without relying on dedicated depth sensors, thereby substantially reducing the dependency of three-dimensional Gaussian semantic SLAM systems on depth sensors and expanding their application scope. Furthermore, this research proposes a keyframe selection algorithm based on semantic guidance and proxy depth collaborative mechanisms, which effectively suppresses pose drift errors accumulated during long-term system operation, thereby achieving robust global loop closure correction. Through systematic evaluation on multiple standard datasets, MSGS-SLAM achieves comparable technical performance to existing three-dimensional Gaussian model-based semantic SLAM systems across multiple key performance metrics including ATE RMSE, PSNR, and mIoU. Full article

Symmetry plays a key role in the study of stress and strain analysis of spherical tanks, as described in detail in the main text. The inherent geometric symmetry of a spherical tank–being uniform in all directions from its center–allows for significant simplification of finite element models. This radial symmetry means that the stress and strain fields under uniform internal pressure are also symmetrical, reducing the computational domain to a small, representative portion of the tank rather than the entire structure. By using these symmetry principles, the study not only ensures the accuracy of its predictions but also achieves a high degree of computational efficiency, making complex engineering problems easier and more accessible. The application of symmetry, therefore, is not just a theoretical concept but a practical tool that underlies the methodology and success of this analysis. This study investigates the mechanical behavior of a spherical tank subjected to internal fluid pressure, utilizing the finite element method (FEM) as a primary analytical tool. Spherical tanks are widely used for the storage of various fluids, including liquefied natural gas (LNG), compressed gases, and water. Their design is critical to ensure structural integrity and safety. This research aims to provide a comprehensive stress and strain analysis of a typical spherical tank, focusing on the hoop and meridian stresses, and their distribution across the tank’s geometry. A 3D finite element model of a spherical tank will be developed using commercial FEA software. The model will incorporate realistic material properties (e.g., steel alloy) and boundary conditions that simulate the support structure and internal fluid pressure. The analysis will consider both linear elastic and potentially non-linear material responses to explore the tank’s behavior under various operational and overpressure scenarios. The primary objectives of this study are as follows: (1) determine the maximum principal stresses and strains within the tank wall, (2) analyze the stress concentration at critical points, such as support connections and nozzle penetrations, and (3) validate the FEM results against classical analytical solutions for thin-walled spherical pressure vessels. The findings will provide valuable insights into the structural performance of these tanks, highlighting potential areas of concern and offering a robust numerical approach for design optimization and safety assessment. This research demonstrates the power and utility of FEM in engineering design, offering a more detailed and accurate analysis than traditional analytical methods. Full article

A novel polarization-reconfigurable 1 × 8 array beam-scanning antenna based on a switchable vertically crossed balanced feed (VCBF) structure is presented. The designed VCBF structure can provide a stable 180° phase difference by utilizing spatial symmetry, enabling the synthesis of two linear polarizations (LP). The parasitic patch layer loaded directly above the VCBF can effectively enhance the operating frequency bandwidth of the antenna. In the array design, by controlling the amplitude and phase input at each port, scanning angles of ±45°, ±40°, and ±30° can be achieved under two LP at 3.0, 3.5, and 4.0 GHz. The simulation and measurement results indicate that the designed antenna has a wideband characteristic with a relative bandwidth of 28.6% and stable polarization reconfigurability. Benefiting from the advantages of polarization reconfigurability and beam-scanning capabilities, the antenna is highly suitable for applications in wireless communication systems that require polarization anti-interference. Full article

Lead-free perovskite variants have emerged as promising candidates due to their self-trapped exciton emission. However, in ASnX₃ systems, facile oxidation of Sn(II) to Sn(IV) yields A₂SnCl₆ vacancy-ordered derivatives. Paradoxically, despite possessing a direct bandgap, these variants exhibit diminished photoluminescence (PL). Doping engineering thus becomes essential for precise optical tailoring of A₂SnX₆ materials. Herein, through integrated first-principles calculations and spectroscopic analysis, we elucidate the luminescence mechanism in Te⁴⁺-doped (NH₄)₂SnCl₆ lead-free perovskites. Density functional theory, X-ray diffraction (XRD) patterns and X-ray photoelectron spectroscopy (XPS) confirm Te⁴⁺ substitution at Sn sites via favorable chemical potentials. Spectral interrogations, including absorption and emission profiles, reveal that the intense emission originates from the triplet STE recombination (³P₁ → ¹S₀) of Te centers. Temperature-dependent PL spectra further demonstrate strong electron–phonon coupling that induces symmetry-breaking distortions to stabilize STEs. Complementary electronic band structure and molecular orbital calculations unveil the underlying photophysical pathway. Leveraging these distinct thermal responses of PL intensity and peak position, 0.5%Te:(NH₄)₂SnCl₆ emerges as a highly promising candidate for non-contact, dual-parameter optical thermometry over an ultra-broad range (100–400 K). This work provides fundamental insights into the exciton dynamics and thermal engineering of optical properties in this material system, establishing its significant potential for advanced temperature-sensing applications. Full article

The prediction of stock price trends is of vital importance for maintaining the stability of the financial market, optimizing resource allocation and preventing systemic risks. To ensure the practical application value of the prediction model, it is necessary to maintain prediction accuracy while ensuring that the output results of the model are interpretable, enabling decision-makers to understand and verify the prediction basis. Belief Rule Base (BRB) models, grounded in IF-THEN rule semantics, offer inherent interpretability. However, optimizing BRB models can erode this interpretability, and they are susceptible to combinatorial explosion in multi-attribute scenarios, disrupting the structural symmetry and escalating model complexity. To address these challenges while preserving both accuracy and interpretability symmetry, this paper proposes a new method based on hierarchical Belief Rule Base with balanced accuracy and interpretability (HBRB-b) for stock price trend prediction. First, a hierarchical model structure is constructed to overcome the rule combinatorial explosion problem, ensuring initial structural symmetry and interpretability. Second, several interpretability criteria specifically designed for stock prediction and compatible with maintaining model balance during optimization are proposed to guide the modeling process. Finally, an improved Whale Optimization Algorithm is proposed, incorporating constraints to preserve the interpretability symmetry throughout the optimization process. A case study validates the model’s effectiveness in stock price trend prediction. Comparative results demonstrate that the HBRB-b-based model achieves a favorable symmetry between prediction accuracy and model interpretability, offering distinct advantages in both aspects. Full article

This study conducts an in-depth analysis of the dynamical characteristics and solitary wave solutions of the integrable Zhanbota-IIA equation through the lens of planar dynamic system theory. This research applies Lie symmetry to convert nonlinear partial differential equations into ordinary differential equations, enabling the investigation of bifurcation, phase portraits, and dynamic behaviors within the framework of chaos theory. A variety of analytical instruments, such as chaotic attractors, return maps, recurrence plots, Lyapunov exponents, Poincaré maps, three-dimensional phase portraits, time analysis, and two-dimensional phase portraits, are utilized to scrutinize both perturbed and unperturbed systems. Furthermore, the study examines the power frequency response and the system’s sensitivity to temporal delays. A novel classification framework, predicated on Lyapunov exponents, systematically categorizes the system’s behavior across a spectrum of parameters and initial conditions, thereby elucidating aspects of multistability and sensitivity. The perturbed system exhibits chaotic and quasi-periodic dynamics. The research employs the maximum Lyapunov exponent portrait as a tool for assessing system stability and derives solitary wave solutions accompanied by illustrative visualization diagrams. The methodology presented herein possesses significant implications for applications in optical fibers and various other engineering disciplines. Full article