Rotational Invariance Research Articles

Discriminating between Babcock–Leighton-type Solar Dynamo Models by Torsional Oscillations

The details of the dynamo process in the Sun are an important aspect of research in solar-terrestrial physics and astrophysics. The surface part of the dynamo can be constrained by direct observations, but the subsurface part lacks direct observational constraints. The torsional oscillations, a small periodic variation of the Sun's rotation with the solar cycle, are thought to result from the Lorentz force of the cyclic magnetic field generated by the dynamo. In this study, we aim to discriminate between three Babcock–Leighton dynamo models by comparing the zonal acceleration of the three models with the observed one. The property that the poleward and equatorward branches of the torsional oscillations originate from about ±55° latitudes with their own migration time periods serves as an effective discriminator that could constrain the configuration of the magnetic field in the convection zone. The toroidal field, comprising poleward and equatorward branches separated at about ±55° latitudes, can generate the two branches of the torsional oscillations. The alternating acceleration and deceleration bands in time are the other property of the torsional oscillations that discriminates between the dynamo models. To reproduce this property, the phase difference between the radial (B r ) and toroidal (B ϕ ) components of the magnetic field near the surface should be about π/2.

Analysis of banana plant health using machine learning techniques

The Indian economy is greatly influenced by the Banana Industry, necessitating advancements in agricultural farming. Recent research emphasizes the imperative nature of addressing diseases that impact Banana Plants, with a particular focus on early detection to safeguard production. The urgency of early identification is underscored by the fact that diseases predominantly affect banana plant leaves. Automated systems that integrate machine learning and deep learning algorithms have proven to be effective in predicting diseases. This manuscript examines the prediction and detection of diseases in banana leaves, exploring various diseases, machine learning algorithms, and methodologies. The study makes a contribution by proposing two approaches for improved performance and suggesting future research directions. In summary, the objective is to advance understanding and stimulate progress in the prediction and detection of diseases in banana leaves. The need for enhanced disease identification processes is highlighted by the results of the survey. Existing models face a challenge due to their lack of rotation and scale invariance. While algorithms such as random forest and decision trees are less affected, initially convolutional neural networks (CNNs) is considered for disease prediction. Though the Convolutional Neural Network models demonstrated impressive accuracy in many research but it lacks in invariance to scale and rotation. Moreover, it is observed that due its inherent design it cannot be combined with feature extraction methods to identify the banana leaf diseases. Due to this reason two alternative models that combine ANN with scale-invariant Feature transform (SIFT) model or histogram of oriented gradients (HOG) combined with local binary patterns (LBP) model are suggested. The first model ANN with SIFT identify the disease by using the activation functions to process the features extracted by the SIFT by distinguishing the complex patterns. The second integrate the combined features of HOG and LBP to identify the disease thus by representing the local pattern and gradients in an image. This paves a way for the ANN to learn and identify the banana leaf disease. Moving forward, exploring datasets in video formats for disease detection in banana leaves through tailored machine learning algorithms presents a promising avenue for research.

The object detection model uses combined extraction with KNN and RF classification

Object detection plays an important role in various fields. Developing detection models for 2D objects that experience rotation and texture variations is a challenge. In this research, the initial stage of the proposed model integrates the gray-level co-occurrence matrix (GLCM) and local binary patterns (LBP) texture feature extraction to obtain feature vectors. The next stage is classifying features using k-nearest neighbors (KNN) and random forest (RF), as well as voting ensemble (VE). System testing used a dataset of 4,437 2D images, the results for KNN accuracy were 92.7% and F1-score 92.5%, while RF performance was lower. Although GLCM features improve performance on both algorithms, KNN is more consistent. The VE approach provides the best performance with an accuracy of 93.9% and an F1-score of 93.8%, this shows the effectiveness of the ensemble technique in increasing object detection accuracy. This study contributes to the field of object detection with a new approach combining GLCM and LBP as feature vectors as well as VE for classification.

Classification of rotation-invariant biomedical images using equivariant neural networks

Transmission electron microscopy (TEM) is an imaging technique used to visualize and analyze nano-sized structures and objects such as virus particles. Light microscopy can be used to diagnose diseases or characterize e.g. blood cells. Since samples under microscopes exhibit certain symmetries, such as global rotation invariance, equivariant neural networks are presumed to be useful. In this study, a baseline convolutional neural network is constructed in the form of the commonly used VGG16 classifier. Thereafter, it is modified to be equivariant to the p4 symmetry group of rotations of multiples of 90° using group convolutions. This yields a number of benefits on a TEM virus dataset, including higher top validation set accuracy by on average 7.6% and faster convergence during training by on average 23.1% of that of the baseline. Similarly, when training and testing on images of blood cells, the convergence time for the equivariant neural network is 7.9% of that of the baseline. From this it is concluded that augmentation strategies for rotation can be skipped. Furthermore, when modelling the accuracy versus amount of TEM virus training data with a power law, the equivariant network has a slope of − 0.43 compared to − 0.26 of the baseline. Thus the equivariant network learns faster than the baseline when more training data is added. This study extends previous research on equivariant neural networks applied to images which exhibit symmetries to isometric transformations.

Manufacture and performance test of suspended batch centrifuge for extraction of glucomannan from porang (Amorphophallus muelleri Blume)

Abstract Porang is a potential local agricultural commodity in Indonesia for future food. This commodity contains ingredients beneficial for health, namely glucomannan, but also contains calcium oxalate, which is dangerous for the skin and kidneys. For this reason, it needs treatment to remove the oxalate content and other impurities in it. This research aims to manufacture and carry out performance tests on centrifuge equipment to remove oxalate and other impurities from porang flour. In the tubers porang glucomannan extracting process, the centrifuges machine separates the solvent (ethanol) and other impurities, such as the oxalate and starch, centrifugation principle. The type of centrifuge manufactured is the suspended batch centrifuge type, where the solids will remain in the walls of the centrifuge while the liquid solvent and other fine particles are thrown out of the centrifuge. The machine’s overall dimensions are 1049 mm × 697 mm in height and width, with a designed capacity of 2 kg of porang flour per batch. The main components of the centrifuge consist of a material intake system equipped with a suction pump, a centrifuge tube equipped screen, a centrifuge housing static tube equipped slurry outlet, a drive motor, a mounting frame, and a control panel. Functional and performance tests have been carried out on centrifuges with rotation variations speeds of 500, 750, and 1000 rpm. The response parameters observed were energy consumption, machine vibration, and effectiveness of solids and slurry extraction. Data analysis for response parameters using ANOVA. Increasing centrifuge rotation in the range of 500-1000 rpm did not significantly affect extraction effectiveness (P>0.05) however, energy consumption and vibration showed significant differences (P<0.05) due to differences in centrifuge rotation speed.

A novel focus measure algorithm for three-dimensional microscopic vision measurement based on focus stacking

The three-dimensional (3D) microscopic vision measurement methods based on focus stacking are widely used because of their outstanding advantages such as noncontact, high accuracy, high flexibility, and low cost. On-site focus stacking 3D microscopic measurement is susceptible to environmental disturbances, surface dirt, illumination occlusion, and the shape of the object itself. This leads to the difficulty of obtaining the focus position accurately, stably, and quickly with the existing focus measure function. To improve the ability to extract the focus signals from the image, high-pass mask operators and band-pass mask operators are designed. A new high-pass and band-pass energy weighting focus measure function with rotation invariance is proposed. A focus stacking microscopic measurement system is constructed to validate the proposed focus measure function. Six classical and latest focus measure functions are selected for the quantitative performance comparison experiments. The experimental results show that the proposed algorithm has the best performance in accuracy, sensitivity, unimodality, and monotonic interval range. This measure function has a high operational efficiency, nearly three times the computational efficiency of the frequency domain measure function. The measure function also drastically reduces the evaluation curve fluctuation, peak collapse, and other anomalies, and shows good robustness.

An active learning workflow for predicting hydrogen atom adsorption energies on binary oxides based on local electronic transfer features

Machine learning combined with density functional theory (DFT) enables rapid exploration of catalyst descriptors space such as adsorption energy, facilitating rapid and effective catalyst screening. However, there is still a lack of models for predicting adsorption energies on oxides, due to the complexity of elemental species and the ambiguous coordination environment. This work proposes an active learning workflow (LeNN) founded on local electronic transfer features (e) and the principle of coordinate rotation invariance. By accurately characterizing the electron transfer to adsorption site atoms and their surrounding geometric structures, LeNN mitigates abrupt feature changes due to different element types and clarifies coordination environments. As a result, it enables the prediction of ∗H adsorption energy on binary oxide surfaces with a mean absolute error (MAE) below 0.18 eV. Moreover, we incorporate local coverage (θl) and leverage neutral network ensemble to establish an active learning workflow, attaining a prediction MAE below 0.2 eV for 5419 multi-∗H adsorption structures. These findings validate the universality and capability of the proposed features in predicting ∗H adsorption energy on binary oxide surfaces.

Influence Of Job Rotation, Work Discipline, And Workload On Employee Productivity At PT. Bank Bengkulu (Persero) KC Karang Tinggi Bengkulu Tengah

This study aims to analyze the impact of job rotation on work productivity, the impact of work discipline on work productivity, the impact of workload on work productivity, and the combined impact of job rotation, work discipline, and workload on work productivity. The research population comprises 34 employees of PT. Bank Bengkulu (Persero) KC Karang Tinggi. The sample consists of 34 respondents, selected using the census method. Data analysis was conducted using multiple regression and hypothesis testing, utilizing SPSS version 25. The results of this study concluded that job rotation does not affect employee productivity (significance 0.729 0.05), work discipline has a significant positive effect on productivity (significance 0.001 0.05), and workload does not affect productivity (significance 0.186 0.05). The combined variables of job rotation, work discipline, and workload have a significant impact on productivity (significance 0.000 0.05).

Enhancing brain tumor detection in MRI with a rotation invariant Vision Transformer.

The Rotation Invariant Vision Transformer (RViT) is a novel deep learning model tailored for brain tumor classification using MRI scans. RViT incorporates rotated patch embeddings to enhance the accuracy of brain tumor identification. Evaluation on the Brain Tumor MRI Dataset from Kaggle demonstrates RViT's superior performance with sensitivity (1.0), specificity (0.975), F1-score (0.984), Matthew's Correlation Coefficient (MCC) (0.972), and an overall accuracy of 0.986. RViT outperforms the standard Vision Transformer model and several existing techniques, highlighting its efficacy in medical imaging. The study confirms that integrating rotational patch embeddings improves the model's capability to handle diverse orientations, a common challenge in tumor imaging. The specialized architecture and rotational invariance approach of RViT have the potential to enhance current methodologies for brain tumor detection and extend to other complex imaging tasks.

Accelerate rotation invariant sliced Gromov-Wasserstein distance by an alternative optimization method

The traditional Wasserstein distance is inadequate for comparing two distributions in different metric spaces. The Gromov-Wasserstein distance (GWD), which evolves from the Gromov-Hausdorff distance, constructs intraspace pairs to ensure comparability. However, solving the GWD requires tackling a complex nonconvex quadratic problem, a process that typically demands significant time and space complexity. The sliced Gromov-Wasserstein distance (SGW) addresses the efficiency issues of GWD by employing a projection-slice method. Unfortunately, slicing destroys the crucial rotation invariance property of GWD. The rotation invariant sliced Gromov-Wasserstein distance (RISGW) restores it by enumerating the alignments of the distributions. Inspired by our observations, we introduce BRISGW, a novel batch rotation invariant sliced Gromov-Wasserstein distance that alternately iterates and approximates the underlying best alignment both effectively and efficiently. We theoretically prove the feasibility the proposed our approach. Moreover, significant experimental results show that the proposed method outperforms the state-of-the-art methods.

Rotation invariance and equivariance in 3D deep learning: a survey

Deep neural networks (DNNs) in 3D scenes show a strong capability of extracting high-level semantic features and significantly promote research in the 3D field. 3D shapes and scenes often exhibit complicated transformation symmetries, where rotation is a challenging and necessary subject. To this end, many rotation invariant and equivariant methods have been proposed. In this survey, we systematically organize and comprehensively overview all methods. First, we rewrite the previous definition of rotation invariance and equivariance by classifying them into weak and strong categories. Second, we provide a unified theoretical framework to analyze these methods, especially weak rotation invariant and equivariant ones that are seldom analyzed theoretically. We then divide existing methods into two main categories, i.e., rotation invariant ones and rotation equivariant ones, which are further subclassified in terms of manipulating input ways and basic equivariant block structures, respectively. In each subcategory, their common essence is highlighted, a couple of representative methods are analyzed, and insightful comments on their pros and cons are given. Furthermore, we deliver a general overview of relevant applications and datasets for two popular tasks of 3D semantic understanding and molecule-related. Finally, we provide several open problems and future research directions based on challenges and difficulties in ongoing research.

Influence of Tire-Enveloping Model Complexity on High-Frequency Simulations

ABSTRACT Race tires are subject to high speeds and high vertical loads during cornering. They are also subject to extreme stress when they are driven over high-frequency and low-amplitude curbs, often leading to tire failures. Research and development by D. C. Davis and P. W. A. Zegelaar has shown that when the tire moves over high-frequency, low-amplitude, and short-wavelength obstacles, it exhibits obstacle-enveloping properties. Tire response over such obstacles includes vertical force variation, longitudinal force variation, and rotational speed variation. Additionally, such road inputs excite tire belt dynamics that include high-frequency modes. Therefore, a single-contact-point model is no longer sufficient to predict tire response over such obstacles. To better capture the tire obstacle-enveloping behavior, advanced contact patch models such as the tandem-cam model by P. W. A. Zegelaar, the radial–interradial spring model by J. M. Badalmenti and G. R. Davis Jr., and the flexible ring model by S. Gong have been developed. To capture high-frequency tire belt dynamics, the rigid-ring model has been developed by P. W. A. Zegelaar. Previous work combines the rigid-ring model with the tandem-cam model to capture obstacle-enveloping behavior and tire belt dynamics up to 60–100 Hz. This paper presents a comparative study of different tire–road contact models to simulate high-frequency curbs typically found at racetracks. The curb profile of the Singes corner at the Paul Ricard racetrack is chosen for simulations as it is known to be extremely demanding on the tires, often causing failures. An advanced four-wheel model is used to simulate a race car at high speeds. Metrics to quantify the tire response over these high-frequency curbs are created and an investigation is conducted to quantify the influence of tire model complexity on the metrics.

Stochastic Quantization of Two-Dimensional $$P(\Phi )$$ Quantum Field Theory

AbstractWe give a simple and self-contained construction of the $$P(\Phi )$$ P ( Φ ) Euclidean quantum field theory in the plane and verify the Osterwalder–Schrader axioms: translational and rotational invariance, reflection positivity and regularity. In the intermediate steps of the construction, we study measures on spheres. In order to control the infinite volume limit, we use the parabolic stochastic quantization equation and the energy method. To prove the translational and rotational invariance of the limit measure, we take advantage of the fact that the symmetry groups of the plane and the sphere have the same dimension.

Bifurcation analysis in the regularized four-sided cavity flow: Equilibrium states in a D2-symmetric fluid system

In this study, we investigate a handful of equilibrium states and their hydrodynamic stability for the incompressible flow in a square cavity driven by the tangential simultaneous motion of all of its lids at the same speed. This problem has been investigated in the recent past, albeit only partially and always disregarding the singular boundary conditions at the corners. The implications of the system symmetries have not been rigorously addressed, either. In our study, we introduce a regularized version of the boundary conditions to avoid the corner singularities, in a way that preserves the main features of the original setup. In addition, the Navier–Stokes equations are discretized by means of highly accurate Chebyshev spectral methods that provide exponential convergence of all computed flows and consistently eliminate any potential source of structural instability of the bifurcation scenario. We employ Newton–Krylov solvers, implemented within continuation algorithms, to accurately compute equilibrium solutions. Linear stability analysis of both the primary symmetric base flow and the secondary asymmetric states uncovers new branches of fully asymmetric steady states. The analysis has allowed identification of six previously undetected bifurcations, all of which are associated with the disruption of either the rotational invariance or the reflection symmetry. Some of these bifurcations have been found to be quite clustered in some regions of the parameter space, which points at the underlying action of higher codimension mechanisms. Notably, all the bifurcations reported occur within the range of low to moderate Reynolds numbers, making the regularized four-sided lid-driven cavity flow a reliable benchmark for assessing different numerical schemes in the context of Navier–Stokes equivariant bifurcation theory.

Suppression mechanism of transient pressure during the turbine runaway of an ultra-high head pump-turbine

Abstract Pressure fluctuation (PF) is a serious issue in transitions of the ultra-high head (UHH) pump-turbines (PTs). To explore the mechanism and control method of PF, the turbine runaway process (TRP) of an UHH PT was simulated using the one- and three-dimensional coupled method. The study suggested that the local backflow (BF) near the high-pressure (HP) inlet of the impeller blocked the impeller channel and induced water hammer. The local BF near the HP inlet of the impeller were closely related to the ratio of rotational speed to PT head. To suppress the BF this study proposed an improved impeller channel with 5 degree spread angle in meridian plane. The study found that the increase of rotational speed and transient pressure variations induced by water hammer could be suppressed successfully by using the improved impeller. The study provided important reference for the design and optimization of the UHH PTs.

A theoretical view of the T-web statistical description of the cosmic web

Context. The objective classification of the cosmic web into different environments is an important aspect of large-scale structure studies, as it can be used as a tool to study the formation of structures (halos and galaxies) in mode detail, and it forms a link between their properties and the large-scale environment; these different environments also offer another class of objects whose statistics contain cosmological information. Aims. In this paper, we present an analytical framework to compute the probability of the different environments in the cosmic web based on the so-called T-web formalism, which classifies structures into four different classes (voids, walls, filaments, and knots) based on the eigenvalues of the Hessian of the gravitational potential, often called the tidal tensor. Methods. Our classification method relies on studying whether the eigenvalues of this Hessian matrix are above or below a given threshold and thus requires knowledge of the joint probability distribution of those eigenvalues. We performed a change of variables in terms of rotational invariants, which are polynomials of the field variables and minimally correlated. We studied the distribution of those variables in the linear and quasi-linear regimes with the help of a so-called Gram-Charlier expansion, using tree-order Eulerian perturbation theory to compute the Gram-Charlier coefficients. This expansion then allowed us to predict the probability of the four different environments as a function of the chosen threshold and at a given smoothing scale and redshift for the density field. We checked the validity regime of our predictions by comparing those predictions to measurements made in the N-body Quijote simulations. Results. Working with fields normalised by their linear variance, we find that scaling the threshold value with the non-linear amplitude of fluctuations allows us to capture almost the entire redshift evolution of the probabilities of the four environments, even if we assume that the density field is Gaussian (corresponding to the linear regime of structure formation). We also show that adding mild non-Gaussian corrections with the help of a Gram-Charlier expansion – hence introducing corrections that depend on third-order cumulants of the field – provides even greater accuracy, allowing us to obtain very precise predictions for cosmic web abundances up to scales of as small as ∼5 Mpc h−1 and redshifts down to z ∼ 0.

Effect of Feed Depth on the ProcessMilling Against Surface Roughness Steel 4140 Carbide Endmill Applications

In the metal cutting industry today, milling process applications are still carried out using cutting fluids. One of the criteria for determining machining quality is surface roughness. Surface roughness as a dependent variable is influenced by machining parameters, namely feed depth, cutting speed and feed speed as independent variables. Research activities with the aim of obtaining machined surface roughness of 4140 low alloy steel workpieces due to spindle rotation speed and feed depth using carbide endmill cutting tools. Research activities were carried out with 9 specimens for the vertical milling process using cutting fluid through variations in machine spindle rotation of 1200 rpm, 1400 rpm and 1600 rpm and feed depths of 0.5 mm, 0.75 mm, 1 mm. Data processing was carried out using experimental methods to obtain surface roughness data.

Analytical method for contact characteristics of rubber shaft seals under dynamic eccentricity considering viscous effect

This study introduces a methodology for analyzing the viscous effect on rubber shaft seals under dynamic eccentricity. It models the radial motion of the shaft seal and quantifies the viscous force arising from the viscous effect. A 3-D FEM with a noncircular shaft is established, equating viscous force to the interference distribution equation. Then, simulated mounting yield contact characteristics. Findings indicate increased interference with the viscous effect and heightened sensitivity of contact characteristics to eccentricity and rotational speed variations. This approach enhances precision in calculating rubber shaft seal contact characteristics under dynamic eccentricity.

Walking and Running of Children with Decreased Femoral Torsion.

Understanding the implications of decreased femoral torsion on gait and running in children and adolescents might help orthopedic surgeons optimize treatment decisions. To date, there is limited evidence regarding the kinematic gait deviations between children with decreased femoral torsion and typically developing children, as well as the implications of the same on the adaptation of walking to running. A three-dimensional gait analysis study was undertaken to compare gait deviations during running and walking among patients with decreased femoral torsion (n = 15) and typically developing children (n = 11). Linear mixed models were utilized to establish comparisons within and between the two groups and investigate the relationship between clinical examination, spatial parameters, and the difference in hip rotation between running and walking. Patients exhibited increased external hip rotation during walking in comparison to controls, accompanied by higher peaks for the same as well as for knee valgus and external foot progression angle. A similar kinematic gait pattern was observed during running, with significant differences noted in peak knee valgus. In terms of variations from running to walking, patients internally rotated their initially externally rotated hip by 4°, whereas controls maintained the same internal hip rotation. Patients and controls displayed comparable kinematic gait deviations during running compared to walking. The passive hip range of motion, torsions, and velocity did not notably influence the variation in mean hip rotation from running to walking. This study underlines the potential of 3D gait kinematics to elucidate the functional implications of decreased FT and, hence, may contribute to clinical decision making.

The Effect Of Mutation and Rotation On Employee Performance at The BPJS Employment Office Palu City Branch

Employee performance is one aspect that must be considered in a company. This study aims to test whether Mutation and Rotation Variables affect Employee Performance at the BPJS Employment Office Palu City Branch. The population in the study was 50 employees. While the sample in the study was employees who received mutations and rotations as many as 36 employees. The data collection technique used is a questionnaire. The collected data is analyzed and then fed into multiple linear regression equations. The findings in this study show that some Mutation Variables have a negative insignificant effect on Employee Performance at the BPJS Employment Office Palu City Branch. Conversely, the Rotation Variable shows partial results that Rotation has a positive and significant effect on Employee Performance at the BPJS Employment Office Palu City Branch. While the simultaneous results show that the Mutation Variable and the Rotation Variable together have a positive and significant effect on Employee Performance at the BPJS Employment Office Palu City Branch.