Neuroendoscopy treats intracranial pathologies through millimeter-scale channels using endoscopes introduced along a straight trajectory from a cranial entry point to the target. The entry point acts as a Remote Center of Motion (RCM), which must remain fixed to follow the surgical plan and avoid damage around the entry point. Existing robotic RCM platforms rely on rigid multi-link structures, increasing complexity and footprint. To mitigate these limitations, we propose a compact dual-joint compliant mechanism for neuroendoscopic manipulation. Building on the Tetra II flexure architecture, we redesigned and optimized the joint for neurosurgical use. The end-effector holder is moved from the central axis to the side to improve visual access, facilitate sterile draping and allow rapid instrument exchange while preserving the RCM constraint. The mechanical design targets directionally uniform stiffness in the working plane while minimizing parasitic RCM displacements. The mechanism uses two identical compliant joints in series, with the connection angle treated as a design variable. For each angle, the response is obtained by analyzing each joint separately in FEM and combining their contributions via rotation matrices. An angular offset of 300° yields near-isotropic stiffness, with a root-mean-square error of 0.90 N/m from an ideal isotropic behavior. A PA12 prototype was tested under 0 . 1 ± 0 . 01 N radial loads. Experimental stiffness differed by ≤ 19% from FEM. The parasitic RCM displacement was 0.032 ± 0.018 mm for a 4.5°shaft rotation, well within the 1 mm neurosurgical tolerance. This dual-joint compliant RCM mechanism offers a practical alternative to conventional rigid-link designs. • Brain endoscopy needs millimetric pivoting to avoid hurting delicate tissue. • Compliant joints keep a stable pivot and remove footprint, friction, wear, backlash. • Dual-compliant joint for robotics neuroendoscopy. • New hybrid methodology for finding stiffness using FEM and rotation matrices.

Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.

To address the bottlenecks of accuracy in head pose estimation caused by occlusion and rotational representation ambiguities, we propose Deep6DHead, a 6-degree-of-freedom (6DoF) head pose estimation method based on deep feature enhancement. This method innovatively integrates RGB and depth information to construct a four-channel input and achieves feature fusion of RGB-D through a dual-branch network. First, a Squeeze-and-Excitation (SE) module adaptively weights the depth geometric features of key anatomical regions to achieve channel recalibration. Second, based on the 6DoF rotation representation framework, we introduce an anatomical constraint loss using the nasal bridge normal. This constraint corrects rotation deviations caused by noise by enforcing consistency in local geometric orientation. Finally, the model outputs the rotation matrix end-to-end for final pose estimation. Experiments on the 300W-LP, BIWI, and AFLW2000 datasets demonstrate that our method significantly improves robustness and accuracy, particularly under extreme head poses. Notably, it achieves state-of-the-art performance on the roll axis (lowest error: 2.05) and a competitive overall MAE of 3.45, providing an effective solution for head pose estimation in complex real-world scenarios including extreme viewing angles.

The field of Dynamic Multi-Objective Optimization (DMOO) has witnessed a surge of interest from both academia and industry, as numerous time-evolving real-world applications can be naturally formulated as Dynamic Multi-Objective Optimization Problems (DMOPs). This growing demand thus necessitates advanced benchmarks to rigorously evaluate optimization algorithms under realistic conditions. This paper introduces a comprehensive and principled framework for constructing highly realistic and challenging DMOO benchmarks. The proposed framework incorporates several novel components, including: a generalized formulation that allows the Pareto-optimal Set (PS) to change on hypersurfaces; a mechanism for creating controlled variable contribution imbalances to generate heterogeneous landscapes; and dynamic rotation matrices for inducing time-varying variable interactions and non-separability. Furthermore, we incorporate a temporal perturbation mechanism to simulate irregular environmental changes and propose a generalized time-linkage mechanism that systematically embeds historical solution quality into future problems, thereby capturing critical real-world phenomena such as error accumulation and time-deception. Extensive experimental results validate the effectiveness of the proposed framework, demonstrating its superiority over conventional benchmarks in terms of realism, complexity, and its capability for discriminating state-of-the-art algorithmic performance. Thus, this work establishes a new standard for dynamic multi-objective optimization benchmarking and provides a powerful tool for the development and evaluation of next-generation algorithms capable of addressing the complexities of real-world dynamic systems. • Proposes a novel, comprehensive framework for generating highly realistic DMOO benchmarks. • Introduces hypersurface-based Pareto Set changes, controlled imbalance, and dynamic rotation. • Incorporates irregular temporal perturbations and a generalized time-linkage mechanism. • Establishes a new DMOO benchmark standard and demonstrates algorithm discrimination effectiveness.

Defining bone-embedded local coordinate systems (LCSs) is fundamental in shoulder biomechanics, yet multiple scapular LCSs exist, hindering data comparison. Although the International Society of Biomechanics (ISB) has published recommendations, alternative definitions based on distinct anatomical landmarks remain often used. To address these inconsistencies, average rotation matrices were recently proposed to convert between the three most common scapular LCSs, thereby facilitating comparison, merging, and interoperability between datasets. Building upon this, we have extended the approach to 11 scapular LCSs reported in the literature, including scapula- and glenoid-based systems. Using statistical shape models derived from 80 participants (asymptomatic and pathological shoulders), 1000 scapulae were generated to quantify geometric transformations between LCSs. Average rotation matrices were computed for each alternative system relative to the ISB-recommended LCS, and accuracy was assessed using helical angles. The application of the average rotation matrices substantially reduced the maximal discrepancies between LCSs, from 21.9° to 5.2°. Scapula-based systems exhibited lower discrepancies than glenoid-based ones, reflecting greater morphological variability in the glenoid region. Comparisons with previously published matrices showed minimal differences (<3°), supporting the robustness of the approach across various datasets and population. These findings confirm that average rotation matrices provide a reliable means of harmonising scapular kinematic data across studies, even if experimenters initially chose a different LCS. This work offers a simple framework, for bridging existing scapular kinematic datasets and promoting interoperability datasets in shoulder biomechanics research.

ABSTRACT The high‐precision multi‐scale fracture network model serves as the crucial geometric prerequisite for studying the permeability of fractured zones and ensuring the safety of urban underground rail projects. However, the practical application of multi‐scale fracture networks is hindered by challenges in cross‐scale integration. This study examines the three‐dimensional structure of a fractured zone at a metro station in Guangzhou, using borehole core data and CT images. A macro–micro data coupling method for 3D geological structure reconstruction is proposed, integrating multi‐point statistics (MPS) and deep learning techniques. The macroscopic model is constructed using an Adaptive Fully‐Connected Deep Neural Network (AFCDNN) and MPS, while a multi‐scale Expectation Maximisation (EM)‐like iterative optimisation method resolves issues such as stratigraphic sequence disruption and boundary ambiguity. U‐Net networks identify fractures in core CT images, while a quaternion rotation matrix corrects borehole disturbances, restoring fracture topology under real in situ stress conditions and constructing a microscopic DFN model. By coupling the meshed macroscopic model with the upscaled DFN model, a refined 3D geological model is created. The results demonstrate that this method generates high‐precision models with a 1‐m resolution, clearly depicting the spatial distribution of fault zones (e.g., soil‐like fractured zones, block‐like fractured zones and moderately weathered fault rock) and bedrock characteristics (exhibiting a ‘west‐low, east‐high’ pattern). After rotation correction, the DFN model's fracture orientations, initially scattered, clustered into three dominant groups. Given the significant variation in fracture volume, Lambert W transformation was applied to preserve the characteristics of both large and small fractures. This method improved the goodness of fit of the fracture volume distribution from 0.68 to 0.96. The macro–micro coupling method proposed in this study overcomes the limitations of traditional single‐scale modelling. It addresses previous constraints where large‐scale simulations used only homogeneous media, while heterogeneous media were limited to small‐scale simulations. This approach avoids the homogenisation of macroscopic models for microscopic fractures, overcomes the challenges of scaling microscopic models to engineering applications, and provides crucial technical support for deep rock mass heterogeneous modelling and metro engineering safety management.

This paper investigates the dynamic disturbances affecting weapon systems mounted on unmanned ground vehicles (UGVs), which pose a significant challenge in maintaining aiming accuracy when moving across uneven terrain. These disturbances arise from terrain-induced vibrations, complex hull movements, suspension-induced vibrations, and cross-inertial interactions between the gun barrel and the turret, particularly under asymmetrical road excitations. This research aims to develop a comprehensive mathematical model describing the dynamic disturbances caused by mass imbalances and cross-inertial effects in weapon-UGV systems and to analyse the influence of asymmetrical and non-uniform road surfaces on weapon system vibrations. The proposed nonlinear dynamic model is constructed using Euler rotation matrices and coordinate transformation methods, incorporating suspension-induced disturbances. An uneven road model with varying roughness heights between the left and right sides and asymmetrical profiles was introduced, including sequential semi-sinusoidal, trapezoidal, and rectangular ridge shapes to represent battlefield-like terrain conditions. The governing equations were solved in MATLAB-Simulink to evaluate weapon vibrations, angular deviations, and disturbance torques. The simulation results showed that asymmetrical road excitation significantly amplified the disturbances to the weapon system during aiming. A scaled UGV model was used to conduct experiments on vehicle body vibrations while moving over a rough terrain section, assessing the effect of suspension and uneven road surfaces on the weapon system. The results demonstrate that the developed dynamic disturbance model provides a solid basis for future stabilisation and compensation control strategies. It improves the firing accuracy of weapon systems mounted on unmanned ground vehicles operating in real-world conditions.

Leaf orientation (posture) influences photosynthesis and plant responses to environmental cues. However, existing methods for quantifying posture typically compress its inherently three-dimensional structure into scalar values or single vectors, leaving the 3D aspects of leaf movement poorly understood. For a more complete geometric description, we propose representing leaf-blade posture by an orthonormal basis (ONB), defined as three perpendicular unit vectors aligned with the developmental axes of the leaf. This ONB serves as a local coordinate system and corresponds to rotation matrices used to represent orientation in three-dimensional space, embedding leaf posture within the mathematical structure of the special orthogonal group SO(3). Using three-dimensional point-cloud data, we reconstructed an ONB aligned with the three axes of the leaf blade and quantified elevation and azimuth angles. When applied to diurnal posture changes, the resulting angular patterns were consistent with previous observations. We then visualized posture changes after gravitational perturbation as continuous rotational trajectories. These trajectories could be compared with mathematically defined geodesic shortest paths and used to simulate alternative reorientation routes that satisfy constraints. The rotational trajectories could also be separated into swing and twist components, which reflect distinct deformation modes. ONB can be obtained not only from three-dimensional point clouds but also from other measurement tools, making the approach broadly applicable. Conceptually, ONB representation places leaf posture within the geometric structure of SO(3), enabling the use of well-established mathematical tools such as rotational distance and geodesics for analyzing leaf reorientation.

Semi-global exponential convergence nonlinear control of the quadrotor unmanned aerial vehicle based on Lie algebra so(3).

A comparative analysis of oncoplastic reconstruction techniques post resection of upper inner quadrant breast tumours: Hemibatwing mastopexy vs Dermoglandular matrix rotation vs MICAP flap

Abstract Mixed reality-guided minimally invasive surgery (MRG-MIS) has shown great potential for clinical application, as it provides surgeons with direct and accurate intraoperative guidance, leading to improved treatment outcomes. Optical trackers play an important role in MRG-MIS and can influence the accuracy and effectiveness of these surgeries. In this research, we present a novel optical tracker based on visible light for MRG-MIS. A stereo-matching algorithm based on circular pose estimation reprojection was proposed to reduce the ghost reconstructed marker in stereo tracking. A marker identification algorithm based on the distance coding matrix was proposed to quickly find the target marker and obtain its pose in real time. A registration method was proposed to find the optimal rotation matrix between mixed reality coordinates and optical tracker coordinates. The 95% confidence interval for tracking distance accuracy was 0.11 mm, and the registration error in the phantom experiment using mixed reality guidance was 1.45 mm. The experimental results suggest that this present system achieves clinically acceptable accuracy and robustness compared with other MRG-MIS approaches.

Abstract Background: There is growing evidence supporting the benefits of the Mediterranean diet in breast cancer (BC) prevention, but their contribution to prognosis remains unclear. Our objective is to investigate whether adherence to the Mediterranean dietary patterns before diagnosis is associated with the risk of BC recurrence and tumor proliferation in an exploratory cohort of the multicenter case-control EpiGEICAM study. Methods: Transcriptome-wide gene expression was assessed using the nCounter Breast Cancer 360 panel (NanoString). Formalin-fixed paraffin-embedded tumor tissues from an exploratory cohort of 89 pre- or perimenopausal BC patients from the EpiGEICAM study were used. The PAM50 gene expression signature was employed to classify tumors into the gold-standard BC intrinsic molecular subtypes, and to compute both the PAM50 risk of recurrence (ROR) and PAM50 proliferation scores. Dietary patterns over the five years prior to diagnosis were identified in the control population of the EpiGEICAM study, applying principal components analysis without rotation of the variance-covariance matrix over 26 inter-correlated food groups. The association between adherence to Mediterranean dietary patterns and both ROR and proliferation scores was analyzed using linear regression models with continuous outcomes. All models were adjusted for age and adherence to a Western dietary pattern, with additional adjustment for PAM50 molecular subtype in the proliferation score analysis. Results: The mean age was 44 years and 28% had a family history of BC. Regarding molecular subtypes, 49.4% corresponded to Luminal A, 22.5% to Luminal B, 13.5% to HER2-enriched and 14.6% to Basal-like subtype. High adherence to the Mediterranean dietary pattern was observed in 56% of participants, with higher prevalence among women with Luminal A and Luminal B subtypes. The mean ROR score was 51 (95%CI=46-57) in women with low adherence to the Mediterranean diet, and 46 (95%CI=40-51) in those with high adherence. Mean proliferation scores were 4.8 (95%CI=4.6-5.1) and 4.5 (95%CI=4.3-4.8), respectively. Although no statistically significant associations were observed, women with high adherence to the Mediterranean dietary pattern showed lower mean ROR score (β=-5.8; 95%CI=-14.0-2.5) and a reduced proliferation score (β=-0.14; 95%CI=-0.40-0.12) compared to those with low adherence. Conclusion: The present EpiGEICAM exploratory analysis showed that adherence to a Mediterranean dietary pattern prior to diagnosis may be associated with lower breast cancer PAM50 proliferation and risk of recurrence scores. Studies with larger sample sizes are needed to confirm these results and to clarify the effect of the Mediterranean diet on the biology and prognosis of this tumor. Citation Format: V. Lope, P. Fernández, Á. Guerrero-Zotano, P. Sánchez-Rovira, A. Antón-Torres, M. Benavent-Viñuales, J. Baena-Cañada, S. Antolín, M. Muñoz, L. Paris, J. Chacón, C. Olier, S. González, J. García-Sáenz, Á. Jimenez-Arranz, A. Oltra, J. Brunet, M. Marin-Alcala, A. De Juan, B. Pérez-Gómez, R. Rincón, R. Caballero, B. Bermejo, M. Martín, M. Pollan. Association between adherence to the mediterranean dietary pattern and PAM50-derived breast cancer proliferation and recurrence risk scores. Exploratory analysis from the Epigeicam study [abstract]. In: Proceedings of the San Antonio Breast Cancer Symposium 2025; 2025 Dec 9-12; San Antonio, TX. Philadelphia (PA): AACR; Clin Cancer Res 2026;32(4 Suppl):Abstract nr PS3-01-27.

Optical digital computing, leveraging optical signals for high-speed, efficient, and high-precision discretized digital computations and information processing, is widely applied in artificial intelligence, communication, and network. However, the development of multiplication/division, pivotal components within digital optical computing systems, has been constrained by the absence of effective computational physical dimensions conducive to manipulating optical signals and the stringent requirement for precise operational control. We propose a fixed-base multiplication and division scheme based on orbital angular momentum (OAM) modes using optical diffractive neural networks (ODNNs). Utilizing the OAM mode as the computational physical dimension, and employing ODNN to perform mode-parallel and independent transformations on it for achieving numerical equivalent shifts, it is feasible to realize 2n-fold multiplication and division operations. Using this mechanism, we have constructed a 3-layer ODNN to realize OAM mode fixed-base multiplication and division for n = 1, 2, and 3, with mode purities of the operation outputs reaching 99%. Furthermore, a dynamic switching between multiplication and division operations has been achieved within the same system through rotation of the phase matrix. Our design suggests a feasible pathway for fixed-base optical multiplication and division, and may offer useful insights for future research on optical digital computing architectures.

ABSTRACT Complete elemental characterization of Molybdenum sulfide, an electro‐catalyst for hydrogen evolution reactions, is essential without much compromise on the material integrity. Energy dispersive x‐ray fluorescence (EDXRF) spectrometry can non‐destructively determine the chemical composition. Mo and S were determined by EDXRF, after addressing the matrix interferences. The interferences due to attenuation of characteristic low energy x‐rays of S by the Mo‐matrix and overlap of S and Mo characteristic x‐rays, lead to rotational and translational matrix effects. These effects on calibration curves were corrected by adopting multiple standard additions, along with matrix correction factors. Herein, the pragmatic inferences, obtained via optimization of experimental variables, were combined with a theoretically calculated correction factor, to solve the extreme spectral overlap problem, during S determinations in the presence of Mo. The results were validated using QC standards and the methodology was applied for real sample analyses. Accuracies better than ±5% were achieved.

Aim: In recent times, agriculture needs increases in production, which aggravates the use of agrochemical products, exacerbating the effect on the environment and human health. Though different initiatives exist farmers often overlook these safety norms because awareness, knowledge, education and intention are limited. Therefore, this study standardise a tool to depict farmers' perception on health issues related to agrochemical impact. Methods: Research design involved a multi-step process, initiate with construction of items. After content validity test and item refinements were done through judges rating. Refined items were administered among 190 farmers in three different agroclimatic zones of West Bengal, India. The responses of randomly selected participants were used for reliability and validity tests with the help of exploratory factor analysis, Cronbach's alpha, split-half and correlation analysis. Result: In the content validity stage, out of 80 items, only 24 items were secured 85% relevancy score. Exploratory factor analysis determined a satisfactory KMO value of .870. Among 24 items, the Rotated component matrix loaded in 6 components and after exclusion of single item that was loaded in sixth component, a total 5 compnents with 16 items on a 0.50 threshold level has been considered. Reliability test indicated a satisfactory Cronbach's alpha value of .875 and split half coefficient of .822. After correlation analysis results suggested for retention of 16 items for the final scale. Conclusion: The scale confirms items are reliable, valid and effective to assess the perception level of the farmers related to agrochemical usage on human health. These insights will help to refine policies with precision to target aims related to sustainable agriculture and can work as a convenient research tool for researchers.

Recovering polarization-multiplexed QAM signals through carrier-free phase retrieval (CF-PR) remains a significant challenge, as it requires accurate estimation of the 2 × 2 transfer matrix of standard single mode fiber (SSMF) based on the only intensity measurements. In this paper, we propose and experimentally demonstrate a dual-polarization CF-PR (DP-CF-PR) receiver that reconstructs DP-QAM signals based solely on intensity detection. By integrating iterative field reconstruction with training-sequence assisted polarization rotation matrix estimation, the proposed scheme effectively mitigates cross-polarization coupling and enables the full-field recovery of DP-QAM signals. Numerical simulations show the polarization rotation angle and phase difference estimation errors below 0.18 rad under the variable optical signal-to-noise (OSNR) values and various modulation formats. Experimental validation based on 32GBaud DP-QPSK/16QAM signals transmission over 80 km SSMF holds excellent accuracy of phase reconstruction and BER performance, achieving the 20% soft-decision FEC (20% SD-FEC) threshold at OSNR values of 17.4 dB and 27.5 dB, respectively. The proposed DP-CF-PR architecture therefore, offers a practical and cost-efficient solution for dual-polarization optical field recovery based on direct detection, showing strong potential for short-reach and energy-efficient optical interconnects.

Microseismic source localization is essential for the early warning of disasters in deep rock mass engineering. Traditional time difference methods require a dense sensor network, which is often impractical in large-scale scenarios with low-density sensor placement. Three-component microseismic sensors offer a promising alternative by utilizing multi-axis sensing, but their application depends on accurate sensor attitude estimation—a challenge due to installation deviations, integration errors, magnetic interference, and ambiguity in P-wave polarization direction. This study proposes an attitude calculation and source localization method based on P-wave polarization analysis. For attitude estimation, a unit vector from the sensor to the event is used as a reference; the P-wave polarization direction is extracted via covariance matrix analysis, and a novel “direction–vector–rotation–matrix cross-optimization” method resolves polarization–vector ambiguity. Multi-event data fusion enhances stability and robustness. For source localization, a “1 three-component + 1 single-component” sensor scheme is introduced, combining distance, azimuth, and distance difference constraints to achieve accurate positioning while substantially reducing hardware and energy costs. Field validation at the Yebatan Hydropower Station shows an average reference vector conversion error of 7.72° and an average localization deviation of 10.72 m compared with a conventional high-precision method, meeting engineering early-warning requirements. The proposed approach provides a cost-effective, efficient technical solution for large-scale microseismic monitoring with low sensor density, supporting sustainable infrastructure development through improved disaster risk management.

This article studies the principal component analysis (PCA) estimation of weak factor models with sparse loadings. We uncover an intrinsic near-sparsity preservation property for the PCA estimators of loadings, which comes from the approximately (block) upper triangular structure of the rotation matrix. It suggests an asymmetric relationship among factors: the sparsity of the rotated loadings for a stronger factor can be contaminated by the loadings from weaker ones, but the sparsity of the rotated loadings of a weaker factor is almost unaffected by the loadings of stronger ones. Then, we propose a simple alternative to the existing penalized approaches to sparsify the loading estimators by screening out the small PCA loading estimators directly, and construct consistent estimators for factor strengths. The proposed estimators perform well in finite samples, as shown by a set of Monte Carlo simulations.

Purpose This study aims to improve the mechanical properties of additively manufactured (AM) parts by optimizing the orientation of the model during printing and proposes an exact initial point method to improve the effectiveness of orientation optimization. Design/methodology/approach This study employs a transversely isotropic material model with a rotation matrix, utilizing the moving asymptote method (MMA) for orientation optimization to determine optimal component placement angles for improved mechanical properties. To address the issue of potential local optima in MMA, an improved method for selecting exact initial iteration points is proposed. This method involves fixing the movement direction of MMA, adjusting step sizes and introducing a criterion to select suitable initial iteration points, thereby preventing local optima and improving the solution's efficiency. Additionally, the study evaluates how the print direction influences the mechanical properties of topology-optimized structural parts by integrating AM and structural topology optimization. Findings Research has shown that optimizing the placement angle of the AM model can improve the mechanical properties of the component and that directional optimization also has a significant impact on the mechanical properties of topologically optimized structural parts. In addition, by using an improved method with exact initial iteration points, the local optimal problem of the MMA can be effectively avoided, thus improving the solution efficiency. Originality/value The placement direction of the AM model is linked to the mechanical properties of the model, and the MMA is used to achieve direction optimization to improve the mechanical properties of the AM model. On this basis, an accurate initial point method is proposed to avoid the phenomenon of local optimal solution in the direction optimization process of MMA, which makes up for the shortcomings of MMA in optimization.

To achieve low-cost and flexible wheel angles measurement, we propose a novel strategy that integrates wheel segmentation network with 3D vision. In this framework, a semantic segmentation network is first employed to extract the wheel rim, followed by angle estimation through ICP-based point cloud registration. Since wheel rim extraction is closely tied to angle computation accuracy, we introduce APCS-SwinUnet, a segmentation network built on the SwinUnet architecture and enhanced with ASPP, CBAM, and a hybrid loss function. Compared with traditional image processing methods in wheel alignment, APCS-SwinUnet delivers more accurate and refined segmentation, especially at wheel boundaries. Moreover, it demonstrates strong adaptability across diverse tire types and lighting conditions. Based on the segmented mask, the wheel rim point cloud is extracted, and an iterative closest point algorithm is then employed to register the target point cloud with a reference one. Taking the zero-angle condition as the reference, the rotation and translation matrices are obtained through point cloud registration. These matrices are subsequently converted into toe and camber angles via matrix-to-angle transformation. Experimental results verify that the proposed solution enables accurate angle measurement in a cost-effective, simple, and flexible manner. Furthermore, repeated experiments further validate its robustness and stability.