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Background: The Rotation Invariant Vision Transformer (RViT) is a novel deep learning model tailored for brain tumor classification using MRI scans. Methods: RViT incorporates rotated patch embeddings to enhance the accuracy of brain tumor identification. Results: 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. Conclusion: RViT outperforms the standard Vision Transformer model and several existing techniques, highlighting its efficacy inmedical 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. [ABSTRACT FROM AUTHOR]

Deep learning has proven promising in biological and chemical applications, aiding in accurate predictions of properties such as atomic forces, energies, and material band gaps. Traditional methods with rotational invariance, one of the most crucial physical laws for predictions made by machine learning, have relied on Fourier transforms or specialized convolution filters, leading to complex model design and reduced accuracy and efficiency. However, models without rotational invariance exhibit poor generalization ability across datasets. Addressing this contradiction, this work proposes a rotationally invariant graph neural network, named RotNet, for accurate and accelerated quantum mechanical calculations that can overcome the generalization deficiency caused by rotations of molecules. RotNet ensures rotational invariance through an effective transformation and learns distance and angular information from atomic coordinates. Benchmark experiments on three datasets (protein fragments, electronic materials, and QM9) demonstrate that the proposed RotNet framework outperforms popular baselines and generalizes well to spatial data with varying rotations. The high accuracy, efficiency, and fast convergence of RotNet suggest that it has tremendous potential to significantly facilitate studies of protein dynamics simulation and materials engineering while maintaining physical plausibility. [ABSTRACT FROM AUTHOR]

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BackgroundThe Rotation Invariant Vision Transformer (RViT) is a novel deep learning model tailored for brain tumor classification using MRI scans.MethodsRViT incorporates rotated patch embeddings to enhance the accuracy of brain tumor identification.ResultsEvaluation 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.ConclusionRViT 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.

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis. [ABSTRACT FROM AUTHOR]

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership. [ABSTRACT FROM AUTHOR]

We present a method for determining which of a large set of pixels are inside or on the boundary of a polygon. The method works much quicker than the standard method used for points in general and also provides an ordering of the boundary pixels. Once the edge pixels have been chosen and ordered, we move on to the characterization of the edge. We present a method for characterizing the edge slope of digitized images, which is—to a desired tolerance—invariant to rotation. We demonstrate that this characterization is good enough for subsequent use in edge identification and matching algorithms. This allows us to continue, e.g., to juxtaposing corresponding pieces of a jigsaw puzzle, or "sewing" back together, ripped pieces of material, paper or glass. [ABSTRACT FROM AUTHOR]

Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry. [ABSTRACT FROM AUTHOR]

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis.

The topic of joint angle and frequency estimation (JAFE) has aroused extensive interests in the past decades. Current estimation algorithms mainly rely on the Nyquist sampling criterion. In order not to cause ambiguity for parameter estimation, the space–time intervals must be smaller than given thresholds, which results in complicated hardware costs and a huge computational burden. This paper aims to reduce the complexity for JAFE, and a novel sparsity-aware framework is proposed. Unlike the current uniform sampling architectures, the incoming narrow-band singles are sampled by a series of space–time coprime samplers. An improved rotational invariance estimator is introduced, which offers closed-form solutions for both angle and frequency estimation. The mathematical treatments indicate that our methodology is inherent in larger spatial/temporal aperture than the uniform sampling architectures; hence, it provides more accurate JAFE compared to alternative approaches relying on uniform sampling. Additionally, it attains nearly the same complexity as the current rotational invariance approach. Numerical results agree with the theoretical advantages of our methodology. [ABSTRACT FROM AUTHOR]

A novel concept of quaternionic fuzzy sets (QFSs) is presented in this paper. QFSs are a generalization of traditional fuzzy sets and complex fuzzy sets based on quaternions. The novelty of QFSs is that the range of the membership function is the set of quaternions with modulus less than or equal to one, of which the real and quaternionic imaginary parts can be used for four different features. A discussion is made on the intuitive interpretation of quaternion-valued membership grades and the possible applications of QFSs. Several operations, including quaternionic fuzzy complement, union, intersection, and aggregation of QFSs, are presented. Quaternionic fuzzy relations and their composition are also investigated. QFS is designed to maintain the advantages of traditional FS and CFS, while benefiting from the properties of quaternions. Cuts of QFSs and rotational invariance of quaternionic fuzzy operations demonstrate the particularity of quaternion-valued grades of membership.

The rise of novel materials such as graphene compounds or carbon nanotubes recently revived the interest on the role of symmetries upon electrical properties. Among possible solids, symmetrical polytopes, widely realized in natural and artificial matter, deserve particular attention. When equal resistors are attached between neighbouring nodes of Perfect (Platonic) solids (PS) along the edges, the two-point resistance between any pair of nodes was established in the 1990s by van Steenwijk using an elegant and efficient method. Using van Steenwijk’s method, Moddy and Aravind subsequently derived the resistance values for two Archimedean and two Catalan solids. Here, with the same method, we derive the exact expression for the two-point resistance between any two nodes for resistor networks made of equal resistors placed along the edges of the thirteen Archimedean solids (AS). While the calculation remains elementary for the simplest AS, a dedicated method using computer assistance was developed for the Snub Cube, the Snub Dodecahedron and the three AS with three different rotation symmetries (the Great Rhombicuboctahedron, the Small Rhombicosidodecahedron and the Great Rhombicosidodecahedron). The largest resistance value (191/90) is obtained between the two opposite nodes of the Truncated Dodecahedron, and the second largest (42815/21114) is obtained between the two opposite nodes of the Great Rhombicosidodecahedron. The smallest resistance value (14137/38016) is obtained between some of the neighbouring nodes of the Snub Cube, whereas the resistance between neighbouring nodes of the Icosahedron (11/30) is slightly smaller. Some general symmetry relations between two-point resistances in AS networks are also derived, as well as some relations with two-point resistances in PS networks. The complete set of exact two-point resistance values for PS and AS networks can be used to check numerical codes or to evaluate the capacity of regular solids to provide appropriate models for given experimental situations.

Sun, P.; Zhou, J.; Liu, Y., and Wang, Y., 2022. Lattice Boltzmann method for simulations of nozzle flows in coastal environments. Journal of Coastal Research, 38(1), 204–217. Coconut Creek (Florida), ISSN 0749-0208. A better understanding of flow in pipes is considered to be critical for marine equipment because it helps to improve pipe performance related to vibration and structure problems. In this study, flow simulations were conducted using a large–eddy-simulation lattice Boltzmann method (LES-LBM) in a nozzle under various Reynolds numbers (Re) and the effect of the three-dimensional cubic lattice models D3Q15, D3Q19, and D3Q27 was examined. The results show that when Re < 200 (i.e. the asymmetry of the results calculated using lattice models D3Q15 and D3Q19 is below 5%) or when the lattice model D3Q27 is adopted, computational results can satisfy the requirement of rotational invariance. When 250 < Re < 300 or the flow suddenly traverses an abrupt expansion, the isotropy of lattice models D3Q15 and D3Q19 experience "collapse". Defective planes cannot be used to completely solve complex flows and accurately transfer flow information. The resultant problems in the computational results include preference in the circumferential distribution of axial velocity and contraction effects of the phase portrait of axial and radial velocities. More complex flows (e.g., for situations with large Re or fluid traversing abrupt expansion) universally cause more significant lattice model effects, where nonlinear flow phenomena become dominant. Therefore, it is necessary to ensure that solutions in the entire computational domain are independent of lattice orientation during flow simulation using LBM. Overall, the results in this paper have important potential applications in predicting flow characteristics for pipe flows in marine structures such as marine risers in coastal environments and zones farther out to sea. [ABSTRACT FROM AUTHOR]

The enhancement of production yield is a continuous challenge in semiconductor manufacturing. Analyzing the spatial defect patterns of previously processed wafers is a key step in identifying the root causes of yield degradation. Predictive modeling approaches have been successful in automated wafer map pattern classification. The classification performance depends significantly on the quantity and diversity of data that can be acquired, which are often limited in practice. In this study, we demonstrate that rotation-based data augmentation can effectively improve wafer map pattern classification when training data are scarce. As rotation is a label-preserving transformation for wafer maps, we construct a convolutional neural network with rotation-augmented training data to render the classification invariant with respect to rotation. This enables us to provide consistent predictions for rotational variations of new wafer maps, thereby achieving higher classification performance. The effectiveness of our method is verified based on real-word data from a semiconductor manufacturer.

Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry.

The topic of joint angle and frequency estimation (JAFE) has aroused extensive interests in the past decades. Current estimation algorithms mainly rely on the Nyquist sampling criterion. In order not to cause ambiguity for parameter estimation, the space–time intervals must be smaller than given thresholds, which results in complicated hardware costs and a huge computational burden. This paper aims to reduce the complexity for JAFE, and a novel sparsity-aware framework is proposed. Unlike the current uniform sampling architectures, the incoming narrow-band singles are sampled by a series of space–time coprime samplers. An improved rotational invariance estimator is introduced, which offers closed-form solutions for both angle and frequency estimation. The mathematical treatments indicate that our methodology is inherent in larger spatial/temporal aperture than the uniform sampling architectures; hence, it provides more accurate JAFE compared to alternative approaches relying on uniform sampling. Additionally, it attains nearly the same complexity as the current rotational invariance approach. Numerical results agree with the theoretical advantages of our methodology.

We consider the problem of computationally fast extraction of rotationally invariant features for object detection procedures based on the sliding window. The central point of interest are Zernike moments (ZMs), which can serve to generate rotationally invariant features. However, the definition-based computations of ZMs are linear with respect to the number of pixels in the image window, and therefore are too slow to be applied directly. The method, we have proposed, computes each feature in constant-time — O(1), and thereby does not depend on the number of pixels. This is owed to a suitable construction of complex-valued integral images that we perform prior to the detection procedure. The approach can be referred to extraction of well known Haar-like features (HFs), but our actual computations are more intricate, and obviously the HFs are not rotationally invariant. This paper constitutes a follow-up study and a refinement of our former research. We enrich our initial ideas by proposing an extended space of Zernike invariants backed with integral images. This feature space includes not only the moduli of Zernike moments but also real and imaginary parts of suitable moment products. We demonstrate the rotational invariance property of these products and provide all necessary algorithmic details, such as: a suitable indexation scheme, feature extraction procedures, and feature counts. Finally, we present a road sign detection experiment confirming that the extended space of features contributes to more accurate detection of objects regardless of their rotation. [ABSTRACT FROM AUTHOR]

Complex fuzzy sets (CFSs) are a new extension of fuzzy sets, whose membership grades are vectors in the unit circle of the complex plane. Complex fuzzy operations are of high importance in both theoretical and applied studies of CFSs. The property of rotational invariance is highly pertinent to complex fuzzy operations. To enhance and extend the applicability of complex fuzzy operations, this article develops new types of rotational invariance for complex fuzzy operations. These rotational invariances are raised by different rotation operations of the arguments of complex fuzzy operations. After that, rotational invariance of several complex fuzzy operations is studied. [ABSTRACT FROM AUTHOR]

To improve the resolution of the numerical results for the 2D Euler equations, a hybrid scheme of rotational flux was proposed. The algorithm was built under the quasi-1D idea of the rotational flux method, and the flux function was given in the form of a hybrid scheme coupling the entropy stable numerical flux satisfying the 2nd law of thermodynamics with the HLL numerical flux of good robustness. The time was advanced with the 3rd?order strongly stable Runge-Kutta method. The hybrid scheme of rotational flux has the advantages of simple structure and high resolution. Numerical results show good characteristics of the algorithm. [ABSTRACT FROM AUTHOR]

Questions of recognizing images of multiple objects whose dimensions are close to the resolution limit of recording equipment - groups of point objects (GPO) - are investigated. Images in the form of GPOs are found in radar images, whereas images of large-scale objects represented by characteristic points, clusters of data in a feature space, and events in mass service systems and automated control systems can be reduced to them. GPO recognition is complicated by disconnectedness of constituent elements, the narrowness of the image autocorrelation function in terms of the geometric transform parameters, spatial fluctuations of elements, false markings and omissions of signal markings. The most promising approaches to the image recognition of this type are based on the transformation of the GPO into a connected object - an associated continuous image (ACI) - and the analysis of its secondary features. However, for GPO with a non-stationary configuration and / or partially masked GPO, the recognition issues are still poorly investigated. The paper proposes an approach to the recognition of GPO based on the marking of their elements - the identification of point objects to within a metaclass (family, type) that is stable for nonstationary and partially masked GPOs. Four metaclasses are proposed: the extreme and inner points of the GPO with a chain structure, the outer and inner points of clusters. The essence of the approach to marking point marks is the recognition of complex-valued contour codes composed of samples of the cylindrical sections of an associated continuous image (ASI) around the GPO elements. To form the ASI, a vector field with partial sources in the elements of the GPO is used. Evaluations of the reliability of marking under various observation conditions are obtained. The results of marking are both of independent significance for various applied problems and suited for the subsequent recognition of GPO. Approaches to GPO recognition based on the results of marking of their elements are suggested.

Due to the lack of rotation invariance in traditional convolution operations, even acting a slight rotation on the input can severely degrade the performance of Convolutional Neural Networks (CNNs). To address this, we propose a Rotation-Invariant Coordinate Convolution (RIC-C), which achieves natural invariance to arbitrary rotations around the input center without additional trainable parameters or data augmentation. We first evaluate the rotational invariance of RIC-C using the MNIST dataset and compare its performance with most previous rotation-invariant CNN models. RIC-C achieves state-of-the-art classification on the MNIST-rot test set without data augmentation and with lower computational costs. Then, the interchangeability of RIC-C with traditional convolution operations is demonstrated by seamlessly integrating it into common CNN models like VGG, ResNet, and DenseNet. We conduct remote sensing image classification on the NWPU VHR-10, MTARSI and AID datasets and patch matching experiments on the UBC benchmark dataset, showing that RIC-C significantly enhances the performance of CNN models across different applications, especially when training data is limited. Our codes can be downloaded from https://github.com/HanlinMo/Rotation-Invariant-Coordinate-Convolutional-Neural-Network.git. • We propose RIC-C: a novel convolutional operation naturally invariant to all input center rotations, no extra parameters or data augmentation. • Without data augmentation, RIC-CNN shows superior performance on MNIST compared to previous rotation invariant CNNs. • RIC-C is successfully deployed to popular CNN models, and enhances their performance in various tasks, particularly with limited training data. [ABSTRACT FROM AUTHOR]

Summary: In the present paper, we describe a new simple stereological method of estimating volume tensors in 3D from vertical sections. The volume tensors provide information about particle shape in 3D. In a model‐based setting, the method requires that the particle distribution is invariant under rotations around the vertical axis. In a design‐based approach, where the vertical section is uniformly rotated around the vertical axis, the method provides information about an index of elongation of the particles in the direction of the vertical axis. The method has been implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus of Brodmann Area 46. In the actual implementation, the new estimator shows similar precision as an earlier estimator, based on an optical rotator design, but it is a factor 3 faster to collect the measurements for the new estimator. Furthermore, the calculations needed for determining the new estimator are much simpler. Lay Description: A new method is described for estimating volume tensors in 3 dimensions based on the stereological method: planar rotator. In general, volume tensors may provide information about particle volume, shape and direction. The new estimator was implemented on human brain tissue for the analysis of neurons in layer III of the medial frontal gyrus on Brodmann Area 46 and compared to a previous published method, based on an optical rotator design. The new estimator shows similar precision as the earlier estimator, but it is a factor 3 faster to collect the measurements. Besides, the calculations behind the new estimator are simpler and easier to implement to a software program. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) are one of the deep learning architectures capable of learning complex set of nonlinear features useful for effectively representing the structure of input to the network. Existing CNN architectures are invariant to small distortions, translations, scaling but are sensitive to rotations. In this paper, unlike the approaches where training samples with different orientations are included, we propose a new architecture in which addition of a rotational invariant map gives few folds of improvement towards rotational invariance to the network. We also propose an improved architecture where rotational invariance is achieved by rotationally varying the convolutional maps. We show that the proposed methods give better invariance towards rotations as compared to conventional training of CNN architecture (where the network is trained without considering the different orientation of training samples). The methods achieve rotation-independent classification by introducing few modifications in conventional CNNs, but do not add any trainable parameter to the network, thus keeping the number of free parameters/weights constant. We demonstrate the performance of proposed rotation invariant architectures for handwritten digits and texture data sets. [ABSTRACT FROM AUTHOR]

This paper investigates whether rotational variance and information exchange affect the performance of Particle Swarm Optimization (PSO) algorithms. Four PSO versions which include the presence or absence of rotational variance, and the fast or late information exchange among particles are under evaluation. The goal is to highlight the best approach and principal benefits of each PSO version based on numerical simulations. To accomplish the aforesaid, the algorithms were evaluated on CEC 2017 benchmark optimization problems. Additionally, a method to estimate a reliable number of algorithms executions was also proposed. Statistical measurements based on Clerc's rules were used to strengthen the analyses. The results indicated the rotationally variant PSO as the overall winner, and the fast information exchange was statistically significant better than the late one, according to Friedman's and Wilcoxon's tests. • Rotation and information exchange among particles impact the results of PSO algorithm. • Clerc's rules are used to strengthen the obtained numerical simulation results. • A proposed method based on the Law of Large Numbers determines the minimum number of algorithms' executions. • Rotationally variant PSO version and fast information exchange are suggested as the best combination. [ABSTRACT FROM AUTHOR]

Spatially confined magnetic inhomogeneities were revealed by measuring nuclear forward scattering time spectra on the same sample in two different geometric arrangements. They differ by 180° rotation of the sample around one of the polarization axes. A basic theoretical description of this phenomenon and its relation to a spatial distribution of nuclei featuring different magnetic moments is provided. From an experimental point of view, the violation of rotational invariance was observed for an inhomogeneous Fe81Mo8Cu1B10 metallic glass. The development of magnetic inhomogeneities and their relation to the evolution of time spectra was studied during thermal annealing. [ABSTRACT FROM AUTHOR]

Abstract We study a space-fractional Allen-Cahn phase-field model in which the fractional Laplacian is defined to be an infinitesimal generator of an α -stable Lévy process with 0 < α < 2. Compared with the Allen-Cahn model using the Riemann-Liouville (R-L) fractional derivatives in the literature, the current model enjoys the following advantages: (1) it can control the sharpness and the decaying behavior of the interface via the tunable order parameter α as the Riemann-Liouville fractional model does; (2) it generates numerical solutions with sharper interfaces than the Riemann-Liouville fractional Allen-Cahn model with the same 1 < α < 2 , and it can generate numerical solutions with even sharper interfaces as it also applies to the case for 0 < α < 1 ; (3) as α → 2 − , it provides good approximations to the classical Allen-Cahn model as the fractional Riemann-Liouville model does; (4) it is rotational invariant; and (5) it has a much slower mass decaying rate than the Riemann-Liouville fractional model. We also propose and analyze a first order in time and second order in space energy stable finite difference scheme. Highlights • A space-fractional Allen-Cahn model with fractional Laplacian as an infinitesimal generator of an α -stable Lévy process is studied. • The studied model can control the interface sharpness and mass decaying behavior through the tunable fractional order. • The model is rotationally invariant and exhibits slower mass decaying rate and sharper interfaces than the R-L fractional model. • A first order in time and second order in space finite difference scheme along with its fast implementation is proposed. • Rigorous analysis is provided to show the discrete energy stability and investigate the accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]

We construct a set of special complex-valued integral images and an algorithm that allows to calculate Zernike moments fast, namely in constant time. The technique is suitable for dense detection procedures, where the image is scanned by a sliding window at multiple scales, and where rotational invariance is required at the level of each window. We assume no preliminary image segmentation. Owing to the proposed integral images and binomial expansions, the extraction of each feature does not depend on the number of pixels in the window and thereby is an $O(1)$ calculation. We analyze algorithmic properties of the proposition, such as: number of needed integral images, complex-conjugacy of integral images, number of operations involved in feature extraction, speed-up possibilities based on lookup tables. We also point out connections between Zernike and orthogonal Fourier–Mellin moments in the context of computations backed with integral images. Finally, we demonstrate three examples of detection tasks of varying difficulty. Detectors are trained on the proposed features by the RealBoost algorithm. When learning, the classifiers get acquainted only with examples of target objects in their upright position or rotated within a limited range. At the testing stage, generalization onto the full $360^\circ$ angle takes place automatically. [ABSTRACT FROM AUTHOR]

Abstract Several rotational invariant quantities for the lepton angular distributions in Drell–Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam–Tung relation. While the violation of the Lam–Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred. [ABSTRACT FROM AUTHOR]

Summary: In neuroscience, application of widely used stereological local volume estimators, including the planar rotator, is challenged by the combination of a complex tissue organisation and an estimator requirement of either isotropic or vertical sections, i.e. randomly oriented tissue. The spatial rotator is applicable with any tissue orientation but is sensitive to projection artefacts. The challenge is thus to select the most appropriate method for individual analyses. In this study, agreement between estimates of mean cell volume acquired with the vertical planar and the spatial rotator is assessed for two brain regions with different types of cytoarchitecture (motor cortex and hippocampal cornu ammonis 1). The possibility of using the planar rotator in tissues cut in an arbitrary direction is explored and requirements for a theoretically unbiased result as well as histological considerations are provided. Lay Description: Cells may change volume both during disease and with advancing age. Assessment of the volume of individual cells can therefore serve as a useful indicator of general tissue state. Most available methods to estimate cell volume in tissue sections, however, require that the tissue analysed has random orientation. Particularly for complex tissues such as the brain this is a challenge as identification, delineation and subdivision of many brain areas rely heavily on the use of anatomical atlases where illustrations depict the tissue in a few well‐known orientations. In this study, the practical application of two different methods for estimating mean cell volumes in tissues cut in a preferred orientation is evaluated. Requirements for the feasibility of cell volume estimation without random tissue orientation as well as histological considerations are provided. [ABSTRACT FROM AUTHOR]

In modern validity theory, a major concern is the construct validity of a test, which is commonly assessed through confirmatory or exploratory factor analysis. In the framework of Bayesian exploratory Multidimensional Item Response Theory (MIRT) models, we discuss two methods aimed at investigating the underlying structure of a test, in order to verify if the latent model adheres to a chosen simple factorial structure. This purpose is achieved without imposing hard constraints on the discrimination parameter matrix to address the rotational indeterminacy. The first approach prescribes a 2-step procedure. The parameter estimates are obtained through an unconstrained MCMC sampler. The simple structure is, then, inspected with a post-processing step based on the Consensus Simple Target Rotation technique. In the second approach, both rotational invariance and simple structure retrieval are addressed within the MCMC sampling scheme, by introducing a sparsity-inducing prior on the discrimination parameters. Through simulation as well as real-world studies, we demonstrate that the proposed methods are able to correctly infer the underlying sparse structure and to retrieve interpretable solutions. [ABSTRACT FROM AUTHOR]

A computational technique called opposition-based learning (OBL) has gained a lot of attention in the field of soft computing. Among the different forms of OBL, the iBetaCOBL variant, which is a stochastic OBL, has shown the best results in improving the performance of differential evolution (DE). However, this approach may not be effective in handling complex problems as it is susceptible to rotations in the coordinate system. To address this issue, we present a new and improved version of iBetaCOBL called iBetaCOBL-eig. This new technique uses an eigenvector-based multiple exponential crossover operator in the partial dimensional change method, making it rotationally invariant. We conducted experiments to evaluate the performance enhancements of DE using iBetaCOBL-eig on 29 challenging benchmark problems. Our results showed that the new algorithm is able to outperform not only ten strong OBL variants but also its previous version iBetaCOBL. • A rotationally invariant stochastic OBL called iBetaCOBL-eig is introduced. • iBetaCOBL-eig can direct the distribution of solutions toward the global optimum. • iBetaCOBL-eig can speed up the convergence of differential evolution variants. [ABSTRACT FROM AUTHOR]

In this study, we show the lack of rotational invariance in the Artificial Bee Colony algorithm (ABC) through numerical experiments. After analysis from the viewpoint of rotational invariance, we develop an ABC with rotational invariance using a hypersphere. The performance of the proposed ABC with rotational invariance is verified through numerical experiments for typical separable benchmark functions without and with rotation. © 2020 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

A non-linear mathematical model of type-II thermoelastic continuum with fine microstructure is developed. The model is described in terms of 4covariant field theoretical formalism attributed to field theories of continuum mechanics. Fine microstructure is introduced by d-vectors and tensors playing role of extra field variables. A Lagrangian density for type-II thermoelastic continuum with fine microstructure is proposed and the least action principle is formulated. Virtual microstructural inertia is added to the considered action density. It is also valid for the thermal inertia. Corresponding 4-covariant field equations of type-II thermoelasticity are obtained. Constitutive equations of type-II microstructural thermoelasticity are discussed. Following the usual procedure for type-II micropolar thermoelastic Lagrangians functionally independent rotationally invariant arguments are obtained. Those are proved to form a complete set. Objective forms of the Lagrangians satisfying the frame indifference principle are given. Those are derived by using extrastrain vectors and tensors.

Quantification of the material internal structure (i.e., microstructure) is central to establishing the highly sought-after process-structure-property (PSP) relationships central to any materials design effort. In recent years, two-point spatial correlations (a subset of the n-point spatial correlations) have garnered significant attention because of their tremendous potential in arriving at practically useful PSP linkages. The central advantage of the two-point spatial correlations is that they capture an exceedingly large number of directionally resolved microstructure statistics. However, they are sensitive to the selection of the observer reference frame. In a number of practical applications, there is a critical need to establish the directionally resolved microstructure statistics, while attaining invariance to the observer reference frame (i.e., the statistics extracted are independent of the selection of the observer frame). A framework for defining and computing such observer-frame invariant two-point spatial correlations does not exist at the present time. This paper addresses this gap by introducing a new form of two-point spatial correlations, hereafter called rotationally invariant two-point spatial correlations . The theoretical framework for these new rotationally invariant two-point spatial correlations is introduced in this paper, and demonstrated through a comprehensive case study. [ABSTRACT FROM AUTHOR]

A model invariant under a supersymmetric extension of the rotation group 0(3) is mapped, using a stereographic projection, from the spherical surface S2 to two-dimensional Euclidean space. The resulting model is not translation invariant. This has the consequence that fields that are supersymmetric partners no longer have a degenerate mass. This degeneracy is restored once the radius of S2 goes to infinity, and the resulting supersymmetry transformation for the fields is now mass dependent. An analogous model on the surface S4 is introduced and its projection onto four-dimensional Euclidean space is examined. This model in turn suggests a supersymmetric model on (3 + 1)-dimensional Minkowski space. [ABSTRACT FROM AUTHOR]