Symmetric Transformation Research Articles

PhysFiT: Physical-aware 3D Shape Understanding for Finishing Incomplete Assembly

Understanding the part composition and structure of 3D shapes is crucial for a wide range of 3D applications, including 3D part assembly and 3D assembly completion. Compared to 3D part assembly, 3D assembly completion is more complicated which involves repairing broken or incomplete furniture that miss several parts with a toolkit. The primary challenge persists in how to reveal the potential part relations to infer the absent parts from multiple indistinguishable candidates with similar geometries, and complete for well-connected, structurally stable and aesthetically pleasing assemblies. This task necessitates not only specialized knowledge of part composition but, more importantly, an awareness of physical constraints, i.e. , connectivity, stability, and symmetry. Neglecting these constraints often results in assemblies that, although visually plausible, are impractical. To address this challenge, we propose PhysFiT, a physical-aware 3D shape understanding framework. This framework is built upon attention-based part relation modeling and incorporates connection modeling, simulation-free stability optimization and symmetric transformation consistency. We evaluate its efficacy on 3D part assembly and 3D assembly completion, a novel assembly task presented in this work. Extensive experiments demonstrate the effectiveness of PhysFiT in constructing geometrically sound and physically compliant assemblies.

Symmetrical Transformer Design for Suppressing Even-Order Components in CM Noise Applied to Converter With Fixed-Frequency PWM Strategy

Symmetrical Transformer Design for Suppressing Even-Order Components in CM Noise Applied to Converter With Fixed-Frequency PWM Strategy

Metric ultraproducts of groups — Simplicity, perfectness and torsion

We characterise the simplicity of metric ultraproducts of a family of metric groups. We also present several new examples of simple groups, such as metric ultraproducts of finite and infinite symmetric groups, linear groups, and interval exchange transformation groups. Using similar methods, we also examine concepts such as genericity, perfectness, and torsion.

Effect of temperature on the nanoindentation behavior of monocrystalline silicon by molecular dynamics simulations

Monocrystalline silicon (Si) undergoes complex phase transformations under external loads, significantly affecting its performance and processing. In this study, molecular dynamics (MD) simulations are performed from 1 to 900 K to explore temperature effects on the mechanical properties and deformation behavior of monocrystalline silicon during nanoindentation. Results indicate that hardness and elastic modulus decrease with rising temperature. At lower temperature, the activation of plastic deformation is delayed. The suddenly release of stored elastic energy manifests as a pop-in event. The indentation creates a quadruple symmetric phase transformation zone, primarily consisting of Si-II at the core, flanked by Si-XIII and bct-5. Increasing temperature advances the plastic deformation of the sample. High temperatures facilitate the formation and subsequent phase transformation of Si-XIII, reduce the stability of bct-5 during unloading, and promote the amorphization of silicon. At high temperatures, the dislocation of silicon nucleates at the subsurface, resulting in the formation of a substable phase. The anisotropy of deformation is evident from the atomic perspective, based on the orientation dependence of the phase transformation. This research provides new insights into the deformation behavior and phase transformations of monocrystalline silicon, supporting manufacturing and application of silicon products.

On the symmetric transformation with geometric constraints

ABSTRACT Coordinate transformation is a fundamental issue in the related studies of measurement. However, existing methodologies often need to pay more attention to the available spatial information, leading to suboptimal results. This paper addresses this issue by incorporating geometric constraints into the symmetric coordinate transformation. We propose the so-called geo-constrained transformation method based on the joint adjustment of the coordinate transformation in conjunction with the geometric constraints over a set of points. By formulating the geometric constraints as the conditional model, we analyze the effects of geometric constraints on the estimated transformation parameters and point locations. By removing such effects during the symmetric transformation algorithm, the results show better statistical performance and satisfy geometric constraints. Two numerical examples are given to demonstrate the expected improvement in the statistical accuracy. It is shown that the improvement of the point determination accuracy can go beyond 50%.

Evaluation and comparison of lattice-based digital signature of the "Digital Signature Schemes" PQC NIST competition

Over the past decade, post-quantum cryptography has reached a tipping point; institutional bodies and stakeholders have initiated standardization and deployment, and various projects have achieved a reasonably high level of progress and even deployment and implementation. In July 2022, at the end of Round 3 of the NIST's PQC competition, 3 candidates were proposed for the NIST standardization for post-quantum digital signatures scheme: one signature scheme based on MLWE (Crystals-Dilithium), one signature based on NTRU (Falcon), and one signature based on hash (Sphincs+). Although the performance profiles and “black-box” security of these schemes are well understood, resistance to side-channel attacks remains a weak point for all of them. After that, the NIST announced that the PQC standardization process is continuing with a fourth round, with the following KEMs still under consideration: BIKE, Classic McEliece, HQC, and SIKE. However, there are no candidates of digital signature schemes left for consideration. As such, the NIST has issued a call for additional digital signature proposals to be considered in the PQC standardization process. Acceptance of documents ended on June 1, 2023. As a result, 40 candidates were selected for the role of DS standard, namely: 6 DS algorithms based on codes, one DS algorithm based on isogenies, 7 DS algorithms based on lattice operations, 7 candidates for the role of DS algorithm based on the MPC method -in-the-Head and 10 algorithms based on multivariate transformations, 4 DS schemes were selected based on symmetric cryptographic transformations, and 5 more candidates based on other types of cryptographic transformations. The NIST is primarily interested in additional general purpose signature schemes that are not based on structured lattices. For certain applications, such as certificate transparency, the NIST may also be interested in signature schemes that have short signatures and fast verification. The NIST is open to receiving additional materials based on structured lattices, but intends to diversify post-quantum signature standards. Therefore, any structured array-based signature proposal would need to significantly outperform CRYSTALS-Dilithium and FALCON in relevant applications and/or provide significant additional security properties to be considered for standardization. Thus, the purpose of this paper is to analyze, evaluate, and compare digital signature algorithms based on lattice cryptography, an additional PQC NIST competition, and compare them with already standardized lattice-based DS mechanisms, such as CRYSTALS-Dilithium and FALCON.

SrSNet: Accurate segmentation of stroke lesions by a two-stage segmentation framework with asymmetry information

Ischemic stroke is a common neurological disease with a high mortality rate. Accurate stroke segmentation is crucial to evaluating patients’ disease outcomes. Stroke segmentation suffers from variable lesion size and noise interference due to similar image contrast characteristics of tissue structures. In this work, we propose a novel two-stage framework named Segmentation–reSegmentation Net (SrSNet) that mainly considers the bilateral symmetric comparison of brain hemispheres to locate pathological abnormalities. The whole framework includes two stages, the coarse segmentation stage and the fine segmentation stage. In the coarse segmentation stage, the brain images are first divided into three patches according to their spatial information to learn the local-level feature and then fed into a 2D Triplet Multi-scale Symmetric Transformer (TMSFormer) with a feature fusion module. This module facilitates the TMSFormer to generate detailed coarse segmentation results. In the fine segmentation stage, we refine the coarse segmentations with a 2D ResUNet. Extensive experiments are conducted using the two ischemic stroke lesion segmentation datasets, and the results are compared with other advanced models. Experiment results on two datasets show that SrSNet achieves state-of-the-art (SOTA) performance. Moreover, on the Ischemic Stroke Lesion Segmentation 2022 (ISLES’22) dataset, the recall score for stroke lesions that the maximum cross-sectional diameter is larger than 5 cm is 83.80%, and the recall score for strokes that the number of lesions of more than five is 79.05%. Overall, our method provides a potentially successful tool for improving the diagnosis of ischemic stroke.

The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules.

Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.

PHASE ANGLE SHIFT AND SLOPE BASED RESTRAINT FOR INDIRECT SYMMETRICAL PHASE SHIFT TRANSFORMER PROTECTION

This study presents a method to limit the functioning of the differential relay during the different operating conditions of an Indirect Symmetrical Phase Shift Transformer (ISPST). The proposed method depends on two thresholds; phase angle shift (PAS) between two ends of an ISPST to discriminate internal faults and inrush conditions from normal, over-excitation, and external fault conditions and slope of differential current helps to discriminate the situation of internal fault from inrush. In the first step of the algorithm, the PAS-based threshold discriminates normal, over-excitation, and external fault conditions from magnetizing inrush and internal fault conditions. In the second step, the slope-based threshold discriminates magnetizing inrush from internal fault conditions. The reliability of the proposed method has also been examined under the condition of current transformer saturation due to heavy external faults. Additionally, the comparison of the suggested and conventional methods is discussed to check the superiority of the proposed method. The proposed method eliminates the need for phase angle shift correction in the suggested method. A variety of faults in the series and excitation unit are simulated using the PSCAD/EMTDC platform to verify the approach method.

Symmetry and symmetric transformations in mathematical imaging

The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of polynomial equations. Galois theory, a cornerstone of modern algebra, connects symmetries, permutations, and solvability of equations. Group theory finds practical applications in cryptography, physics, and coding theory. Sophus Lie extends group theory to continuous spaces with Lie Group Theory, offering a powerful framework for studying continuous symmetries. Lie groups find applications in robotics and control theory, streamlining the representation of transformations. Benoit Mandelbrots fractal geometry, introduced in the late 20th century, provides a mathematical framework for understanding complex, self-similar shapes. The applications of fractal geometry range from computer graphics to financial modeling. Symmetrys practical applications extend to data visualization and cryptography. The article concludes by emphasizing symmetrys foundational role in physics, chemistry, computer graphics, and beyond. A deeper understanding of symmetry not only enriches perspectives across scientific disciplines but also fosters interdisciplinary collaborations, unveiling hidden order and structure in the natural and designed world. The exploration of symmetry promises ongoing discoveries at the intersection of mathematics and diverse fields of study.

SBIT-Fuse: Infrared and visible image fusion based on Symmetrical Bilateral interaction and Transformer

Infrared and visible image fusion, as a typical image enhancement task, aims to generate an image containing complementary information. Existing deep learning-based methods usually use a dual-stream model to extract features, which suffers from insufficient feature interaction in the feature extraction process. In order to effectively utilize information, this work proposes a Symmetrical Bilateral Interaction and Transformer fusion method (SBIT-Fuse) that is simple and efficient for constructing a dual-stream interaction network. Specifically, inspired by the problem of dead ReLU, we propose a Symmetrical Bilateral Interaction (SBI) module which consists of a certain number of cascaded cross domain activation interaction (CDAI) layers, where the deactivation information of the ReLU rectifier is transferred from one flow to another instead of being discarded. The proposed module exploits the drawbacks of ReLU to efficiently build the interaction of two streams and combine spatial and channel attention mechanisms, achieving the enhancement of feature extraction. Besides, our network is end-to-end and a transformer module is employed for extracting long-range semantic information. Moreover, combining a novel designed loss function, the proposed method can generate higher-quality fusion images. The comparative experiments with existing advanced methods and ablation studies on publicly datasets demonstrate the effectiveness of the proposed approach. Our code can be found at https://github.com/ljx111790/SBIT-Fuse.

Boosting deep neural networks with geometrical prior knowledge: a survey

Deep neural networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and—in the case of supervised learning—labelling the data is expensive and time-consuming. Additionally, assessing the networks’ generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods.

Single open‐phase fault detection and tolerant control for wye‐connected three‐phase induction machine drives

SummaryThis paper proposes open‐phase fault detection (FD) and tolerant control strategies for wye‐connected three‐phase induction machines (WCTPIMs). The FD mechanism is based on the comparison between predicted and actual values of stator currents, and the control approach is derived from the field‐oriented control (FOC). In the proposed fault‐tolerant control (FTC) method, an asymmetrical current transformation is used for stator current components, and the conventional symmetrical voltage transformation is employed for stator voltage components. It is shown that using these transformations, a modified FOC can be employed for the faulty WCTPIM. The suggested scheme is able to control WCTPIM drives under normal and single open‐phase fault (SOPF) modes with minor adjustments. Experimental results achieved from a laboratory prototype confirm the possibility and good performance of the proposed open‐phase FD and tolerant control for the WCTPIM under different operating conditions.

Environment and Power Quality International Conference on Renewable Energies and Power Quality (ICREPQ’09) Valencia (Spain), 15th to 17th April, 2009 Evaluation of Different Methods for Voltage Sag Source Detection Based on Positive-Sequence Componen

This paper evaluates methods for voltage sag source detection, which are based either on energy, current or impedance criteria. It is shown that some methods known from the literature do not work well, particularly in cases of asymmetrical voltage sags. Furthermore, some methods require measurements of instantaneous values, which is not always feasible. Therefore, symmetrical component transformation is applied, whereas only positive-sequence components are used. All the discussed methods were tested by applying extensive simulations and field tests. The obtained results show that all methods which are based on positive-sequence components are highly effective also in cases of asymmetrical voltage sags.

Application of Discrete Wavelet Transform and Chebyshev Neural Network for Differential Protection of Indirect Symmetrical Phase Shift Transformer

The Indirect Symmetrical Phase Shift Transformer (ISPST) stands out from a power transformer due to its combination of electrically connected and magnetically coupled circuits. Hence in this work, an intelligent differential protection algorithm, based on Discrete Wavelet Transform (DWT) and Chebyshev Neural Network (ChNN), is proposed as main classifier to discriminate internal fault and inrush. Half cycle thee phase post fault differential current is considered for the proposed algorithm. PSCAD/EMTDC software is utilized to simulate different operating conditions of ISPST, resulting in the simulation of a significant amount of internal faults and inrush cases. The algorithm under consideration has undergone extensive evaluation across numerous cases, resulting in an accuracy rate exceeding 99%. The results indicate that the classifier based on DWT - ChNN yields extremely promising results, even when dealing with a noisy signal, current transformer (CT) saturation, and varying ISPST ratings. Superiority of the proposed algorithm is also compared with Multilayer Perceptron (MLP), Radial Basis Function Neural Network (RBFNN) and Probabilistic Neural Network (PNN) based approaches under the same conditions and it is found that proposed classifier is the most efficient and rapid among all alternative classifiers for the differential protection scheme of an ISPST under the considered conditions.

Statistical robust estimation of spatial symmetric transformations based on Mahalanobis distance

Statistical robust estimation of spatial symmetric transformations based on Mahalanobis distance

Rolling bearing fault diagnosis method using time-frequency information integration and multi-scale TransFusion network

Advances in deep learning methods have demonstrated remarkable development in diagnosing faults of rotating machinery. The currently popular deep neural networks suffer from design flaws in their network structure, leading to issues of long-term dependencies in fault diagnosis models built upon conventional deep neural networks. Consequently, such models exhibit insufficient global perceptual capabilities towards fault features. Furthermore, how accurately pre-trained models can diagnose faults is hugely impacted by changes in bearings’ working conditions. To tackle the aforementioned issues, this study puts forth a multi-scale TransFusion (MSTF) model for diagnosing faults in rolling bearings under multiple operating conditions. Firstly, a time-frequency symmetric dot pattern transformation technique is designed to transform the original vibration signals into two-dimensional representations. This method can effectively highlight the distinctions between different fault types. Secondly, a multi-scale feature fusion module is established, which fully extracts low-level features from the time-frequency signals and reduces the complexity of the subsequent attention calculations. Meanwhile, relying on the advantages of the Transformer model in capturing global dependencies, the long-range periodic fault information is deeply mined. Finally, multi-head and multi-layer attention are visualized to enhance the interpretability of the model. After analyzing two case studies with both public and experimental datasets, the examination demonstrated that the developed model outperformed other state-of-the-art models. The diagnostic model developed in this study exhibits the ability to accurately diagnose bearing faults across multiple operating conditions while maintaining high robustness to signals contaminated with noise.

CPFTransformer: transformer fusion context pyramid medical image segmentation network.

The application of U-shaped convolutional neural network (CNN) methods in medical image segmentation tasks has yielded impressive results. However, this structure's single-level context information extraction capability can lead to problems such as boundary blurring, so it needs to be improved. Additionally, the convolution operation's inherent locality restricts its ability to capture global and long-distance semantic information interactions effectively. Conversely, the transformer model excels at capturing global information. Given these considerations, this paper presents a transformer fusion context pyramid medical image segmentation network (CPFTransformer). The CPFTransformer utilizes the Swin Transformer to integrate edge perception for segmentation edges. To effectively fuse global and multi-scale context information, we introduce an Edge-Aware module based on a context pyramid, which specifically emphasizes local features like edges and corners. Our approach employs a layered Swin Transformer with a shifted window mechanism as an encoder to extract contextual features. A decoder based on a symmetric Swin Transformer is employed for upsampling operations, thereby restoring the resolution of feature maps. The encoder and decoder are connected by an Edge-Aware module for the extraction of local features such as edges and corners. Experimental evaluations on the Synapse multi-organ segmentation task and the ACDC dataset demonstrate the effectiveness of our method, yielding a segmentation accuracy of 79.87% (DSC) and 20.83% (HD) in the Synapse multi-organ segmentation task. The method proposed in this paper, which combines the context pyramid mechanism and Transformer, enables fast and accurate automatic segmentation of medical images, thereby significantly enhancing the precision and reliability of medical diagnosis. Furthermore, the approach presented in this study can potentially be extended to image segmentation of other organs in the future.

Tour Route Recommendation Model by the Improved Symmetry-Based Naive Bayes Mining and Spatial Decision Forest Search

In machine learning, classifiers have the feature of constant symmetry when performing the attribute transformation. In the research field of tourism recommendation, tourists’ interests should be mined and extracted by the symmetrical transformation in founding the training dataset and creating the classifier, so as to ensure that the recommendation results meet the individualized interests and needs. In this paper, by applying the feature of constant symmetry in the classifier and analyzing the research background and existing problems of POI tour routes, we propose and construct a tour route recommendation model using improved symmetry-based Naive Bayes mining and spatial decision forest search. First, the POI natural attribute classification model is constructed based on text mining to classify the natural attributes of the destination POIs. Second, the destination POI recommendation model based on the improved symmetry-based Naive Bayes mining and decision forest algorithm is constructed, outputting POIs that match tourists’ interests. On this basis, the POI tour route recommendation model based on a spatial decision tree algorithm is established, which outputs the optimal tour route with the lowest sub-interval cost and route interval cost. Finally, the validation and comparative experiments are designed to output the optimal POIs and tour routes by using the proposed algorithms, and then the proposed algorithm is compared with the commonly used route planning methods, GDM and 360M. Experimental results show that the proposed algorithm can reduce travel costs by 4.56% and 10.36%, respectively, on the optimal tour route compared to the GDM and 360M and by 2.94% and 8.01%, respectively, on the suboptimal tour route compared to the GDM and 360M, which verifies the advantages of the proposed algorithm over the traditional route planning methods.

Composition transformation of terrigenous organic matter resinous-asphaltene components in super-deep wells in Siberia during meso- and apocatagenesis

The evolution of the elemental composition of dispersed organic matter (DOM) heterocyclic components during catagenesis was traced via studying samples from the Tyumen (SG-6) and Srednevylyuy-27 (SV-27) super-deep wells of Siberia. During mesocatagenesis, the composition of terrigenous DOM asphaltenes and resins undergoes directed changes: a decrease in hydrogen and oxygen content, enrichment with carbon, and graphitization of the structure. During apocatagenesis, due to high-temperature destruction, on the one hand, there is a condensation of individual blocks of asphaltenes and their transition to an insoluble form (formation of epiasphaltenic kerogens – EPAK). On the other hand, the lighter part of the asphaltenes goes into the formation of hydrocarbons and gas formation – a relative increase in the concentration of the former in % by mass of residual bitumoids is noted, as well as structural redistributions within benzene and spirit-benzene resins. In all studied parameters of the elemental composition, a symmetrical (unidirectional) transformation of resinous and asphaltene components of bitumoids from the SG-6 and SV-27 wells under harsh thermobaric conditions is noted. The obtained results should be taken into account when predicting new oil and gas accumulation zones in deep-laid horizons.