Search Results (9,656)

Affine invariance is one of the most fundamental properties of free-form curves, ensuring that transformations such as translation, scaling, rotation, and shearing preserve the essential characteristics of the geometric shape. It is exploited by almost every software that uses such curves. However, this property only holds in a theoretical, mathematical sense. The transformation of a curve calculated and displayed on computers using finite precision arithmetic and representation may not be fully identical to the curve calculated from the transformed control points. This deviation, even pixel-level inaccuracy, can cause problems in various applications, such as Computer-Aided Geometric Design, medical image processing, numerical computations, and font design, where this level of error can have serious consequences. In this paper, we study and demonstrate the extent and nature of this deviation using geometric and statistical tools on a cubic Bézier curve. We provide practical methods to mitigate this inaccuracy and decrease the error level using fast and simple alternative computations of the curve, taking advantage of the symmetry of the basis functions, elevating the degree of the curve, and using reparametrization to evaluate the curve on integer values. The effectiveness of these alternatives is evaluated by statistical methods based on 500,000 transformations. Full article

The application prospects of photorealistic 3D reconstruction are broad in smart cities, cultural heritage preservation, and related domains. However, existing methods face persistent challenges in balancing reconstruction accuracy, computational efficiency, and robustness, particularly in complex scenes characterized by reflective surfaces, vegetation, sparse viewpoints, or large-scale structures. In this study, an enhanced 3D Gaussian Splatting (3DGS) framework that integrates three key innovations is proposed: (i) a depth-aware regularization module that leverages metric depth priors from the pre-trained Depth-Anything V2 model, enabling geometrically informed optimization through a dynamically weighted hybrid loss; (ii) a gradient-driven adaptive densification mechanism that triggers Gaussian adjustments based on local gradient saliency, reducing redundant computation; and (iii) a neighborhood density-based floating artifact detection method that filters outliers using spatial distribution and opacity thresholds. Extensive evaluations are conducted across four diverse datasets—ranging from architectures, urban scenes, natural landscapes with water bodies, and long-range linear infrastructures. Our method achieves state-of-the-art performance in both reconstruction quality and efficiency, attaining a PSNR of 34.15 dB and SSIM of 0.9382 on medium-sized scenes, with real-time rendering speeds exceeding 170 FPS at a resolution of 1600 × 900. It demonstrates superior generalization on challenging materials such as water and foliage, while exhibiting reduced overfitting compared to baseline approaches. Ablation studies confirm the critical contributions of depth regularization and gradient-sensitive adaptation, with the latter improving training efficiency by 38% over depth supervision alone. Furthermore, we analyze the impact of input resolution and depth model selection, revealing non-trivial trade-offs between quantitative metrics and visual fidelity. While aggressive downsampling inflates PSNR and SSIM, it leads to loss of high-frequency detail; we identify 1/4–1/2 resolution scaling as an optimal balance for practical deployment. Among depth models, Vitb achieves the best reconstruction stability. Despite these advances, memory consumption remains a challenge in large-scale scenarios. Future work will focus on lightweight model design, efficient point cloud preprocessing, and dynamic memory management to enhance scalability for industrial applications. Full article

Objectives: The emergence of SARS-CoV-2 variants with enhanced immune evasion capabilities poses ongoing challenges for maintaining population-level immunity. This study aim to evaluate neutralizing antibody responses to the wild-type (WT) strain and the Omicron sublineage XBB.1.9 in the Israeli population using serum samples collected between August 2022 and January 2023, prior to widespread circulation of XBB.1.9. Methods: Pseudovirus-based microneutralization assays incorporating variant-specific spike proteins were employed to measure neutralizing geometric mean titers (GMTs) across subgroups categorized by age, gender, socioeconomic status, and geographic region. Results: Neutralizing titers against XBB.1.9 were significantly lower than those against WT across all demographic groups, with a 29-fold reduction in neutralization activity against XBB.1.9, underscoring the immune escape potential of XBB.1.9. For WT, older adults (≥65 years) exhibited higher titers than younger individuals (p < 0.01), whereas no significant age-related differences were observed for XBB.1.9 (p > 0.05). Regional disparities in WT immunity were identified, with higher titers in Northern Israel compared to Jerusalem and Southern regions. By contrast, XBB.1.9 neutralization showed no significant regional variation. Conclusions: These findings demonstrate substantially reduced neutralization of XBB.1.9 compared to WT and reveal disparities in WT immunity by age and region. The results emphasize the need for updated vaccines targeting immune-evasive variants and for tailored vaccination strategies to address regional and demographic gaps in protection. Full article

University campuses feature spatially diverse environments where thermal performance varies seasonally and spatially. In this study, we integrate field measurements with ENVI-met simulations to evaluate how sky view factor (SVF) influences microclimate and outdoor thermal comfort-quantified via air temperature (Ta), mean radiant temperature (Tmrt), wind speed (WS), relative humidity (RH), physiologically equivalent temperature (PET), and the Universal Thermal Climate Index (UTCI)-within urban street and urban building spaces on a temperate Chinese campus. The results reveal contrasting thermal responses: in summer, low-SVF urban street spaces (SVF_avg 0.075) exhibit moderate heat stress (PET_avg 34.5–39.5 °C) due to radiative trapping and limited ventilation, whereas high-SVF urban building spaces (SVF_avg 0.159) face greater heat load and stronger thermal stress, with peak PET exceeding 49.9 °C. In winter, high-SVF urban building spaces benefit from solar gain, improving thermal comfort. Statistical analyses indicate non-linear threshold effects of SVF on comfort indices, with summer comfort positively correlated at SVF > 0.2, and winter comfort negatively associated at SVF ≤ 0.4. These findings identify SVF as a key geometric predictor of seasonal thermal comfort in distinct campus spatial types, provide quantitative thresholds to guide climate-resilient campus planning in warm temperate zone. Full article

In this study, a neural network was developed to predict the aerodynamic characteristics of fixed-wing aircraft with two lifting surfaces of various aerodynamic configurations. The proposed neural network model can incorporate 23 parameters to describe the aerodynamic configuration of an aircraft. A methodology for discrete geometric parameterization of aerodynamic configurations is introduced, enabling coverage of various combinations of relative positions of aircraft components. This study presents an approach to database construction and automated sample generation for neural network training. Furthermore, a procedure is provided for data preprocessing and correlation analysis of the input variables. The optimization process of the hyperparameters of the multilayer perceptron (MLP) architecture is described. The neural network models are validated through comparison with numerical simulations. Finally, several aerodynamic design problems are addressed, and the key advantages of the developed MLP-based surrogate aerodynamic models are demonstrated. Full article

This paper investigates the dynamics of quantum and classical geometric correlations in the hyperfine structure of the hydrogen atom under pure dephasing noise, focusing on the interplay between entangled initial states and environmental effects. We employ the Lindblad master equation to model dephasing, deriving differential equations for the density matrix elements to capture the evolution of the system. The study explores various entangled initial states, characterized by parameters $a_1$, $a_2$, and $a_3$, and their impact on correlation dynamics under different dephasing rates $\Gamma$. A trace distance approach is utilized to quantify classical and quantum geometric correlations, offering comparative insights into their behavior. Numerical analysis reveals a transition point where classical and quantum correlations equalize, followed by distinct decay and stabilization phases, influenced by initial coherence along the z-axis. Our results reveal a universal sudden transition from classical to quantum decoherence, consistent with observations in other open quantum systems. They highlight how initial state preparation and dephasing strength critically influence the stability of quantum and classical correlations, with direct implications for quantum metrology and the development of noise-resilient quantum technologies. By focusing on the hyperfine structure of hydrogen, this study addresses a timely and relevant problem, bridging fundamental quantum theory with experimentally accessible atomic systems and emerging quantum applications. Full article

Soil aggregates are critical determinants of soil erosion resistance and nutrient retention capacity, while freeze–thaw cycles (FTCs) induce the structural reorganization of soil aggregates, thereby altering soil stability and influencing soil organic carbon (SOC) sequestration. This study was located in the Minjia River Basin in the typical seasonal freeze–thaw areas of the Loess Plateau and aimed to quantify the effects of FTCs on soil aggregate stability and SOC content under different land use types. Farmland, grassland, and forestland with more than 20 years of usage in the region were selected, and a 0–20 cm soil layer was subjected to seven FTCs (−8 °C to 20 °C), followed by wet and dry sieving classification, focusing on soil aggregate distribution, aggregate stability, mean weight diameter (MWD), geometric mean diameter (GMD), aggregate particle fractal dimension (APD), and SOC content of the aggregate. The results showed that soil aggregates in all land use types were dominated by macroaggregates (>2 mm), with the proportion in forestland (61–63%) > grassland (54–58%) > farmland (38–51%). FTCs enhanced aggregate stability across all land use types, especially in farmland. Concurrently, FTCs reduced the SOC content in all aggregate size fractions, with reduction rates ranging from farmland (9.00–21%) to grassland (4–26%) to forestland (5–31%). Notably, FTCs significantly increased the contribution of 2–5 mm water-stable (WS) aggregates to SOC sequestration, with increment rates of 86% (farmland), 80% (grassland), and 86% (forestland). Furthermore, FTCs altered the correlation between SOC content and aggregate stability. Specifically, the positive correlations of SOC with MWD and GMD were strengthened in aggregates < 0.5 mm but weakened in aggregates >0.5 mm. These findings advance our understanding of the coupled mechanisms underlying soil erosion and carbon cycling across land uses under freeze–thaw, providing a theoretical basis for ecosystem restoration and optimized soil carbon management in cold regions. Full article

Background: The COVID-19 pandemic has been associated with increased sedentary behavior in children, raising concerns about posture and spinal health. This study compared standardized measures of sitting spinal alignment in two independent cohorts assessed before (2017) and after (2024) the pandemic and examined correlations among alignment parameters across different sitting postures. Methods: This cross-sectional study included healthy children aged 9–13 years. The sternal angle, sacral angle, lumbar lordosis, thoracic kyphosis, trunk tilt, and lateral deviation were measured using a Saunders digital inclinometer and a DIERS Formetric 4D rasterstereographic system in passive, forced, and corrected sitting postures. Results: No statistically significant differences were observed between the 2017 and 2024 cohorts (p > 0.05). Within each cohort, significant posture-related differences were found for the sternal and sacral angles, lumbar lordosis, and lateral deviation (p < 0.05), while thoracic kyphosis and trunk inclination differed between passive and corrected sitting (p < 0.05). The sternal angle correlated moderately to strongly with thoracic kyphosis (r = 0.657–0.695, p < 0.001), and the sacral angle correlated with lumbar lordosis (r = 0.679–0.743, p < 0.001). Conclusions: Similar alignment parameters across time-separated cohorts suggest no major cohort-level shifts in standardized sitting posture; however, behavioral factors were not directly assessed. Strong correlations among sagittal angles emphasize the consistent geometric relationship between the sternum, sacrum, and spinal curvatures. A sternal angle of approximately 65° was consistently associated with physiologically favorable spinal alignment and may serve as a practical reference value for posture assessment and education. Full article

Existing pneumatic artificial muscle (PAM) static geometrical models based on the principle of virtual work provide only approximate force predictions since they neglect the effects of volume change and radial bladder deformation work loss. In this study, we propose an improved geometrical static model called the Accurate Volume and Bladder Deformation Loss (AVBDL) model. This model introduces a physically consistent calculation of muscle volume at different contractions and pressures and incorporates a new way of describing work losses due to radial deformation of the bladder. The hyperelastic properties of the bladder were experimentally characterized and modeled using the Mooney–Rivlin formulation. The AVBDL model was validated against experimental data from four types of pneumatic muscles and compared with three established analytical models. Results show that the AVBDL model significantly improves force prediction accuracy, achieving a normalized root mean square (NRMS) error of 6.7–16.4%, compared to 20–68% for existing models. Due to its analytical transparency, reduced error, and broad applicability, the AVBDL model provides a robust basis for accurate simulation and control of pneumatic artificial muscles. Full article

Prefabricated H-section steel composite wall columns (PHSWCs) are crucial for advancing modular steel construction, yet their elastic buckling performance lacks a universally accurate predictive model due to the complex interplay between section interaction and semi-rigid bolted connections. To address this, a comprehensive theoretical framework for elastic buckling analysis is developed in this study. The model integrates Euler–Bernoulli beam theory for the H-sections, a three-dimensional spring system to represent the stiffness of bolted connections, and the Green strain tensor to account for geometric nonlinearity. Validation against ABAQUS (2020) and ANSYS (2021 R1) shows high accuracy (average errors: 1.0% and 1.2%, respectively). Furthermore, a unified formula for the normalized slenderness ratio is derived via stepwise regression, which elegantly degenerates to the classical Euler solution under limiting conditions. The main conclusion is that this framework enables rapid and precise buckling analysis, reducing parametric study time by 95% compared to detailed finite element modeling. It establishes a bolt density coefficient threshold of η = 0.5 that separates composite from independent section behavior, with an optimal design range of η = 0.2 to 0.25, thereby offering a robust theoretical basis for PHSWC design. Full article

Heat exchangers are key components of advanced waste-heat recovery energy systems that operate on low-boiling working fluids. The efficiency and cost of power plants depend directly on their design characteristics. Increasing the heat-transfer surface area, on the one hand, reduces temperature differences and improves cycle efficiency, but on the other hand increases material consumption and equipment cost. For given fluid parameters and heat-exchanger duty, the required surface area is determined by the type of heat exchanger, the choice of device, the shape of the enhanced heating surface, and the methods of heat-transfer intensification. This paper provides a comprehensive analysis of the current state of heat exchangers for low-boiling working fluids and discusses their areas of application. A methodology has been developed for optimizing the main design characteristics of heat exchangers, including a search algorithm aimed at minimizing the total costs of equipment production and operation. Using this methodology, computational studies were carried out for advanced energy cycles with low-boiling working fluids (organic Rankine cycles, recompression supercritical CO₂ (s-CO₂) Brayton cycle). The relationships of weight, size, and cost parameters of heat exchangers for waste-heat recovery cycles using low-boiling fluids to exhaust-gas temperatures and external economic factors were obtained. Optimal channel geometric parameters and heat-exchanger design types were identified that ensure minimal material consumption and cost while delivering the required heat-transfer performance. Recommendations are formulated for selecting and designing heat exchangers for waste-heat recovery power plants using low-boiling working fluids, the implementation of which will improve their efficiency and reduce costs. Full article

This study is aimed at developing and verifying a method that uses a digital holographic camera to measure the gas volumetric flux, which is relevant for the monitoring of gas emissions, in particular methane in the Arctic seas. The method is based on the analysis of histograms of cross-sectional areas of gas bubbles and their velocities obtained from holographic data. The result of the study is the determination of a constant calibration factor k = 2, taking into account the geometric factor of the camera and the deformation of the bubbles. The coefficient is determined in laboratory conditions, taking into account the area of the gas-generating site of a bubble generator simulating a gas flare. It is found that k remains stable in a wide range of a gas volumetric flux from 5 × 10⁻⁴ m³·m⁻²·s⁻¹ to 15 × 10⁻⁴ m³·m⁻²·s⁻¹ that limits the applicability of a working formula. Verification of the method in the field conditions of the Arctic expedition showed good agreement with the data obtained by the standard trap method: the discrepancy was only 5%. It was shown that the method is applicable for quantitative assessment of weak gas emissions, in particular methane, in the Arctic seas, where the measured volumetric fluxes are orders of magnitude lower than the established upper limit of the method. Full article

Biplot methods provide a framework for the simultaneous graphical representation of both rows and columns of a data matrix. Classical biplots were originally developed for continuous data in conjunction with principal component analysis (PCA). In recent years, several extensions have been proposed for binary and nominal data. These variants, referred to as logistic biplots (LBs), are based on logistic rather than linear response models. However, existing formulations remain insufficient for analyzing ordinal data, which are common in many social and behavioral research contexts. In this study, we extend the biplot methodology to ordinal data and introduce the ordinal logistic biplot (OLB). The proposed method estimates row scores that generate ordinal logistic responses along latent dimensions, whereas column parameters define logistic response surfaces. When these surfaces are projected onto the space defined by the row scores, they form a linear biplot representation. The model is based on a framework, leading to a multidimensional structure analogous to the graded response model used in Item Response Theory (IRT). We further examine the geometric properties of this representation and develop computational algorithms—based on an alternating gradient descent procedure—for parameter estimation and computation of prediction directions to facilitate visualization. The OLB method can be viewed as an extension of multidimensional IRT models, incorporating a graphical representation that enhances interpretability and exploratory power. Its primary goal is to reveal meaningful patterns and relationships within ordinal datasets. To illustrate its usefulness, we apply the methodology to the analysis of job satisfaction among PhD holders in Spain. The results reveal two dominant latent dimensions: one associated with intellectual satisfaction and another related to job-related aspects such as salary and benefits. Comparative analyses with alternative techniques indicate that the proposed approach achieves superior discriminatory power across variables. Full article

In certain mining areas, bauxite ore exhibits high and uneven hardness, causing frequent overloads in the cutting heads of bauxite mining equipment and challenging the dynamic performance and reliability of its gear transmission system. To investigate the influence of macro-geometric parameters, a dynamic model was built using MASTA software (version 13.0.1). This study systematically analyzed the effects of pressure angle, face width, and bottom clearance coefficient on gear meshing characteristics, service life, and vibration noise under various loads. A preferred set of parameters was determined and validated through vibration and noise tests. The results show that increasing the pressure angle and face width improves gear meshing and fatigue life, while the bottom clearance coefficient has an optimal value of 0.4. Increasing the bottom clearance coefficient exacerbates vibration and noise, with other parameters causing fluctuations under different conditions. The optimal parameters of 23° pressure angle, 75 mm face width, and 0.4 bottom clearance coefficient effectively reduce vibration and noise, providing a theoretical and practical basis for improving the cutting transmission system. Full article

Mining-induced subsidence has significantly altered the structure of the vadose zone in coal mining areas, where soil cracks act as preferential pathways controlling water infiltration and redistribution. In this study, a Hydrus-2D dual-domain seepage model incorporating geometric parameterization of cracks was developed to simulate water migration in the vadose zone of a typical subsidence area in the Ordos Basin. The model integrates field-measured crack geometry, soil texture, and rainfall characteristics to quantitatively analyze preferential flow formation under twelve combinations of crack width, soil type, and rainfall intensity. The results show that (i) crack width dominates preferential flow behavior, with wider cracks (≥5 cm) deepening the wetting front from approximately 107 cm to 144 cm within 120 h and sustaining high conductivity after rainfall; (ii) soil texture governs infiltration pathways, as sandy soils promote deeper wetting fronts (up to 99 cm, ~40% deeper than loam) and layered soils induce interface retention or “jump” infiltration; and (iii) rainfall intensity controls infiltration depth, with storm events producing wetting fronts more than four times deeper than those under light rain. Overall, this study demonstrates the feasibility and significance of integrating crack parameterization into vadose-zone hydrological modeling using Hydrus-2D, providing a quantitative basis for understanding rapid infiltration–migration–recharge processes and supporting ecological restoration and water resource management in arid and semi-arid mining regions. Full article