Three-dimensional architecture of ESCRT-III flat spirals on the membrane.

The endosomal sorting complexes required for transport (ESCRTs) are responsible for membrane remodeling in many cellular processes, such as multivesicular body biogenesis, viral budding, and cytokinetic abscission. ESCRT-III, the most abundant ESCRT subunit, assembles into flat spirals as the primed state, essential to initiate membrane invagination. However, the three-dimensional architecture of ESCRT-III flat spirals remained vague for decades due to highly curved filaments with a small diameter and a single preferred orientation on the membrane. Here, we unveiled that yeast Snf7, a component of ESCRT-III, forms flat spirals on the lipid monolayers using cryogenic electron microscopy. We developed a geometry-constrained Euler angle-assigned reconstruction strategy and obtained moderate-resolution structures of Snf7 flat spirals with varying curvatures. Our analyses showed that Snf7 subunits recline on the membrane with N-terminal motifs α0 as anchors, adopt an open state with fused α2/3 helices, and bend α2/3 gradually from the outer to inner parts of flat spirals. In all, we provide the orientation and conformations of ESCRT-III flat spirals on the membrane and unveil the underlying assembly mechanism, which will serve as the initial step in understanding how ESCRTs drive membrane abscission.

Optimal 3D angular sampling with applications to cryo-EM problems.

The goal of cryo-EM experiments in the biological sciences is to determine the atomic structure of a molecule and deduce insights into its functions and mechanisms. Despite improvements in instrumentation for data collection and new software algorithms, in most cases, individual atoms are not resolved. Model building of proteins, nucleic acids, or molecules in general, is feasible from the experimentally determined density maps at resolutions up to the range of 3-4 Angstroms. For lower-resolution maps or parts of maps, fitting smaller structures obtained by modelling or experimental techniques with higher resolution is a way to resolve the issue. In practice, we have an atomic structure, generate its density map at a given resolution, and translate/rotate the map within a region of interest in the experimental map, computing a measure-of-fit score with the corresponding areas of the experimental map. This procedure is computationally intensive since we work in 6D space. An optimal ordered list of rotations will reduce the angular error and help to find the best-fitting positions faster for a coarse global search or a local refinement. It can be used for adaptive approaches to stop fitting algorithms earlier once the desired accuracy has been achieved. We demonstrate how the performance of some fitting algorithms can be improved by grouping sets of rotations. We present an approach to generate more efficient 3D angular sampling, and provide the computer code to generate lists of optimal orientations for single and grouped rotations and the lists themselves.

Quaternion-Based Attitude Estimation of an Aircraft Model Using Computer Vision.

Investigating aircraft flight dynamics often requires dynamic wind tunnel testing. This paper proposes a non-contact, off-board instrumentation method using vision-based techniques. The method utilises a sequential process of Harris corner detection, Kanade-Lucas-Tomasi tracking, and quaternions to identify the Euler angles from a pair of cameras, one with a side view and the other with a top view. The method validation involves simulating a 3D CAD model for rotational motion with a single degree-of-freedom. The numerical analysis quantifies the results, while the proposed approach is analysed analytically. This approach results in a 45.41% enhancement in accuracy over an earlier direction cosine matrix method. Specifically, the quaternion-based method achieves root mean square errors of 0.0101 rad/s, 0.0361 rad/s, and 0.0036 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. Notably, the method exhibits a 98.08% accuracy for the pitch rate. These results highlight the performance of quaternion-based attitude estimation in dynamic wind tunnel testing. Furthermore, an extended Kalman filter is applied to integrate the generated on-board instrumentation data (inertial measurement unit, potentiometer gimbal) and the results of the proposed vision-based method. The extended Kalman filter state estimation achieves root mean square errors of 0.0090 rad/s, 0.0262 rad/s, and 0.0034 rad/s for the dynamic measurements of roll rate, pitch rate, and yaw rate, respectively. This method exhibits an improved accuracy of 98.61% for the estimation of pitch rate, indicating its higher efficiency over the standalone implementation of the direction cosine method for dynamic wind tunnel testing.

Research on an Adaptive Method for the Angle Calibration of Roadside LiDAR Point Clouds.

Light Detection and Ranging (LiDAR), a laser-based technology for environmental perception, finds extensive applications in intelligent transportation. Deployed on roadsides, it provides real-time global traffic data, supporting road safety and research. To overcome accuracy issues arising from sensor misalignment and to facilitate multi-sensor fusion, this paper proposes an adaptive calibration method. The method defines an ideal coordinate system with the road's forward direction as the X-axis and the intersection line between the vertical plane of the X-axis and the road surface plane as the Y-axis. This method utilizes the Kalman filter (KF) for trajectory smoothing and employs the random sample consensus (RANSAC) algorithm for ground fitting, obtaining the projection of the ideal coordinate system within the LiDAR system coordinate system. By comparing the two coordinate systems and calculating Euler angles, the point cloud is angle-calibrated using rotation matrices. Based on measured data from roadside LiDAR, this paper validates the calibration method. The experimental results demonstrate that the proposed method achieves high precision, with calculated Euler angle errors consistently below 1.7%.

Optimization of Gradient Descent Parameters in Attitude Estimation Algorithms.

Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment of the algorithm parameters, which is often overlooked in the literature. Here, we present the effects of the step size, the maximum number of iterations, and the initial quaternion, as well as different propagation methods on the quality of the estimation in noiseless and noisy conditions. A novel figure of merit and termination criterion that defines the algorithm's accuracy is proposed. Furthermore, the guidelines for selecting the optimal set of parameters in order to achieve the highest accuracy of the estimate using the fewest iterations are proposed and verified in simulations and experimentally based on the measurements acquired from an in-house developed model of a satellite attitude determination and control system. The proposed attitude estimation method based on the gradient descent algorithm and complementary filter automatically adjusts the number of iterations with the average below 0.5, reducing the demand on the processing power and energy consumption and causing it to be suitable for low-power applications.

Posture Monitoring and Correction Exercises for Workers in Hostile Environments Utilizing Non-Invasive Sensors: Algorithm Development and Validation.

Personal protective equipment (PPE) is an essential key factor in standardizing safety within the workplace. Harsh working environments with long working hours can cause stress on the human body that may lead to musculoskeletal disorder (MSD). MSD refers to injuries that impact the muscles, nerves, joints, and many other human body areas. Most work-related MSD results from hazardous manual tasks involving repetitive, sustained force, or repetitive movements in awkward postures. This paper presents collaborative research from the School of Electrical Engineering and School of Allied Health at Curtin University. The main objective was to develop a framework for posture correction exercises for workers in hostile environments, utilizing inertial measurement units (IMU). The developed system uses IMUs to record the head, back, and pelvis movements of a healthy participant without MSD and determine the range of motion of each joint. A simulation was developed to analyze the participant's posture to determine whether the posture present would pose an increased risk of MSD with limits to a range of movement set based on the literature. When compared to measurements made by a goniometer, the body movement recorded 94% accuracy and the wrist movement recorded 96% accuracy.

A coordinate-system-independent method for comparing joint rotational mobilities.

Three-dimensional studies of range of motion currently plot joint poses in a 'Euler space' whose axes are angles measured in the joint's three rotational degrees of freedom. Researchers then compute the volume of a pose cloud to measure rotational mobility. However, pairs of poses that are equally different from one another in orientation are not always plotted equally far apart in Euler space. This distortion causes a single joint's mobility to change when measured based on different joint coordinate systems and precludes fair comparison among joints. Here, we present two alternative spaces inspired by a 16th century map projection - cosine-corrected and sine-corrected Euler spaces - that allow coordinate-system-independent comparison of joint rotational mobility. When tested with data from a bird hip joint, cosine-corrected Euler space demonstrated a 10-fold reduction in variation among mobilities measured from three joint coordinate systems. This new quantitative framework enables previously intractable, comparative studies of articular function.

Attitude Estimation of Underwater Vehicles Using Field Measurements and Bias Compensation.

This paper proposes a method of estimating the attitude of an underwater vehicle. The proposed method uses two field measurements, namely, a gravitational field and a magnetic field represented in terms of vectors in three-dimensional space. In many existing methods that convert the measured field vectors into Euler angles, the yaw accuracy is affected by the uncertainty of the gravitational measurement and by the uncertainty of the magnetic field measurement. Additionally, previous methods have used the magnetic field measurement under the assumption that the magnetic field has only a horizontal component. The proposed method utilizes all field measurement components as they are, without converting them into Euler angles. The bias in the measured magnetic field vector is estimated and compensated to take full advantage of all measured field vector components. Because the proposed method deals with the measured field independently, uncertainties in the measured vectors affect the attitude estimation separately without adding up. The proposed method was tested by conducting navigation experiments with an unmanned underwater vehicle inside test tanks. The results were compared with those obtained by other methods, wherein the Euler angles converted from the measured field vectors were used as measurements.

Knot soliton in DNA and geometric structure of its free-energy density.

In general, the geometric structure of DNA is characterized using an elastic rod model. The Landau model provides us a new theory to study the geometric structure of DNA. By using the decomposition of the arc unit in the helical axis of DNA, we find that the free-energy density of DNA is similar to the free-energy density of a two-condensate superconductor. By using the φ-mapping topological current theory, the torus knot soliton hidden in DNA is demonstrated. We show the relation between the geometric structure and free-energy density of DNA and the Frenet equations in differential geometry theory are considered. Therefore, the free-energy density of DNA can be expressed by the curvature and torsion of the helical axis.

Sine Rotation Vector Method for Attitude Estimation of an Underwater Robot.

This paper describes a method for estimating the attitude of an underwater robot. The method employs a new concept of sine rotation vector and uses both an attitude heading and reference system (AHRS) and a Doppler velocity log (DVL) for the purpose of measurement. First, the acceleration and magnetic-field measurements are transformed into sine rotation vectors and combined. The combined sine rotation vector is then transformed into the differences between the Euler angles of the measured attitude and the predicted attitude; the differences are used to correct the predicted attitude. The method was evaluated according to field-test data and simulation data and compared to existing methods that calculate angular differences directly without a preceding sine rotation vector transformation. The comparison verifies that the proposed method improves the attitude estimation performance.

A comment on powder averaging in wide line NMR.

Computer calculations of wide line NMR spectra of powders usually involve numerical evaluation of double integrals over two Euler angles. Practice confirms intuition-based expectations that the integration results should be independent from the choice of the crystal-fixed (or molecule-fixed) coordinate system used in the calculations. However, a closer inspection of the relevant integration formulas may make one wonder why this is so. The present paper provides a rigorous mathematical proof of the validity of these intuitive predictions, by formulating the problem in terms of surface integrals on a sphere, which has presumably no precedence in the NMR literature.

Defining humeral axial rotation with optical motion capture and inertial measurement units during functional task assessment.

Humeral motion can be challenging to measure and analyze. Typically, Euler/Cardan sequences are used for humeral angle decomposition, but choice of rotation sequence has substantial effects on outcomes. A new method called True axial rotation calculation may be more precise. The objective of this study is to compare humeral axial rotation measured from two systems (optical motion capture and inertial measurement units (IMUs)) and calculated with two methods (Euler angles and True axial). Motion of torso and dominant humerus of thirty participants free from any upper limb impairments was tracked using both systems. Each participant performed a functional tasks protocol. Humeral axial rotation was calculated with Euler decomposition and the True axial method. Waveforms were compared with two-way ANOVA statistical parametric mapping. A consistent pattern emerged: axial rotation was not different between motion capture systems when using the True axial method (p > .05), but motion capture systems showed relatively large magnitude differences (~ 20-30°) when using Euler angle calculation. Between-calculation method differences were large for both motion capture systems. Findings suggest that the True axial rotation method may result in more consistent findings that will allow for precise measurements and comparison between motion capture systems. Two methods for calculating humeral axial rotation measured from optical motion capture and inertial measurement units were compared.

Defining repeatability for scapulothoracic and thoracohumeral motion during the novel work-related activities and functional task (WRAFT) protocol.

Upper limb motion can be challenging to measure and analyze during work or daily life tasks. Further, humeral angle calculation method substantially influences angle outcomes. Therefore, the purpose of this study was to assess the repeatability of scapular and humeral kinematics and compare thoracohumeral angle calculation during a work-related and functional task (WRAFT) protocol. Thirty healthy young adults completed the WRAFT protocol (Comb Hair, Wash Axilla, Tie Apron, Overhead Reach, Side Reach, Forward Transfer, Floor Lift, and Overhead Lift) on two separate occasions. Peak humeral angles and select scapular angles were extracted for each task. Intra-class correlation coefficients (ICCs), standard error of measurement, and minimal detectable change (MDC) were examined. Humeral angles were compared using the XZY and ZXY rotation sequences and "true" axial rotation for incidence of gimbal lock and amplitude coherence. Results showed that for scapular kinematics, elevation-based WRAFTs produced overall better ICC scores (0.23-0.90) compared to those tasks primarily driven by lateral humeral motion (0.02-0.84). MDCs ranged from 7°-78°, suggesting some tasks demonstrated good repeatability (Comb Hair, Overhead Reach, Floor Lift), while others had very high variability (Side Reach, Tie Apron). Amplitude coherence for thoracohumeral angles was best for ZXY for all tasks except the Comb Hair and Tie Apron, for which XZY is recommended. "True" axial rotation demonstrated good coherence for all but Tie Apron. The WRAFT protocol may be used for functionally relevant scapular and humeral kinematic assessment for select task and posture combinations.

The Influence of Mathematical Definitions on Patellar Kinematics Representations.

A correlation between patellar kinematics and anterior knee pain is widely accepted. However, there is no consensus on how they are connected or what profile of patellar kinematics would minimize anterior knee pain. Nevertheless, answering this question by merging existing studies is further complicated by the variety of ways to describe patellar kinematics. Therefore, this study describes the most frequently used conventions for defining patellar kinematics, focusing on the rotations. The similarities and differences between the Cardan sequences and angles calculated by projecting axes are analyzed. Additionally, a tool is provided to enable the conversion of kinematic data between definitions in different studies. The choice of convention has a considerable impact on the absolute values and the clinical characteristics of the patello-femoral angles. In fact, the angles that result from using different mathematical conventions to describe a given patello-femoral rotation from our analyses differ up to a Root Mean Squared Error of 111.49° for patellar flexion, 55.72° for patellar spin and 35.39° for patellar tilt. To compare clinical kinematic patello-femoral results, every dataset must follow the same convention. Furthermore, researchers should be aware of the used convention's implications to ensure reproducibility when interpreting and comparing such data.

Three-dimensional intervertebral range of motion in the cervical spine: Does the method of calculation matter?

Intervertebral range of motion (ROM) is commonly calculated using ordered rotations or projection angles. Ordered rotations are sequence-dependent, and projection angles are dependent upon on which orientation vectors are projected. This study assessed the effect of calculation method on intervertebral ROM in the subaxial cervical spine (C3-C7) during in vivo dynamic, three-dimensional, functional movement. Biplane radiographs were collected at 30 images per second while 29 participants performed full ROM flexion/extension, axial rotation and lateral bending movements of their cervical spine. In vivo bone motion was tracked with sub-millimeter accuracy using a validated volumetric model-based tracking technique. Intervertebral rotations were calculated using six Cardan angle sequences and two projection angle combinations. Within-subject comparisons revealed significant differences in intervertebral ROM among calculation methods (all p<0.002). Group mean ROM differences were small, but significantly different among calculation methods (p<0.001). A resampling technique demonstrated that as group size increases, the differences between calculation methods decreases substantially. It is concluded that the method used to calculate intervertebral rotations of the sub-axial cervical spine can significantly affect within-subject and between group comparisons of intervertebral ROM.