Symmetry Detection Research Articles

Constrained Symmetric Non-Negative Matrix Factorization with Deep Autoencoders for Community Detection

Recently, community detection has emerged as a prominent research area in the analysis of complex network structures. Community detection models based on non-negative matrix factorization (NMF) are shallow and fail to fully discover the internal structure of complex networks. Thus, this article introduces a novel constrained symmetric non-negative matrix factorization with deep autoencoders (CSDNMF) as a solution to this issue. The model possesses the following advantages: (1) By integrating a deep autoencoder to discern the latent attributes bridging the original network and community assignments, it adeptly captures hierarchical information. (2) Introducing a graph regularizer facilitates a thorough comprehension of the community structure inherent within the target network. (3) By integrating a symmetry regularizer, the model’s capacity to learn undirected networks is augmented, thereby facilitating the precise detection of symmetry within the target network. The proposed CSDNMF model exhibits superior performance in community detection when compared to state-of-the-art models, as demonstrated by eight experimental results conducted on real-world networks.

Learning symmetry-aware atom mapping in chemical reactions through deep graph matching

Accurate atom mapping, which establishes correspondences between atoms in reactants and products, is a crucial step in analyzing chemical reactions. In this paper, we present a novel end-to-end approach that formulates the atom mapping problem as a deep graph matching task. Our proposed model, AMNet (Atom Matching Network), utilizes molecular graph representations and employs various atom and bond features using graph neural networks to capture the intricate structural characteristics of molecules, ensuring precise atom correspondence predictions. Notably, AMNet incorporates the consideration of molecule symmetry, enhancing accuracy while simultaneously reducing computational complexity. The integration of the Weisfeiler-Lehman isomorphism test for symmetry identification refines the model’s predictions. Furthermore, our model maps the entire atom set in a chemical reaction, offering a comprehensive approach beyond focusing solely on the main molecules in reactions. We evaluated AMNet’s performance on a subset of USPTO reaction datasets, addressing various tasks, including assessing the impact of molecular symmetry identification, understanding the influence of feature selection on AMNet performance, and comparing its performance with the state-of-the-art method. The result reveals an average accuracy of 97.3% on mapped atoms, with 99.7% of reactions correctly mapped when the correct mapped atom is within the top 10 predicted atoms.Scientific contributionThe paper introduces a novel end-to-end deep graph matching model for atom mapping, utilizing molecular graph representations to capture structural characteristics effectively. It enhances accuracy by integrating symmetry detection through the Weisfeiler-Lehman test, reducing the number of possible mappings and improving efficiency. Unlike previous methods, it maps the entire reaction, not just main components, providing a comprehensive view. Additionally, by integrating efficient graph matching techniques, it reduces computational complexity, making atom mapping more feasible.

Exploring the Molecular Terrain: A Survey of Analytical Methods for Biological Network Analysis

Biological systems, characterized by their complex interplay of symmetry and asymmetry, operate through intricate networks of interacting molecules, weaving the elaborate tapestry of life. The exploration of these networks, aptly termed the “molecular terrain”, is pivotal for unlocking the mysteries of biological processes and spearheading the development of innovative therapeutic strategies. This review embarks on a comprehensive survey of the analytical methods employed in biological network analysis, focusing on elucidating the roles of symmetry and asymmetry within these networks. By highlighting their strengths, limitations, and potential applications, we delve into methods for network reconstruction, topological analysis with an emphasis on symmetry detection, and the examination of network dynamics, which together reveal the nuanced balance between stable, symmetrical configurations and the dynamic, asymmetrical shifts that underpin biological functionality. This review equips researchers with a multifaceted toolbox designed to navigate and decipher biological networks’ intricate, balanced landscape, thereby advancing our understanding and manipulation of complex biological systems. Through this detailed exploration, we aim to foster significant advancements in biological network analysis, paving the way for novel therapeutic interventions and a deeper comprehension of the molecular underpinnings of life.

Event related potentials (ERP) reveal a robust response to visual symmetry in unattended visual regions

Visual symmetry at fixation generates a bilateral Event Related Potential (ERP) called the Sustained Posterior Negativity (SPN). Symmetry presented in the left visual hemifield generates a contralateral SPN over the right hemisphere and vice versa. The current study examined whether the contralateral SPN is modulated by the focus of spatial attention. On each trial there were two dot patterns, one to the left of fixation, and one to the right of fixation. A central arrow cue pointed to one of the patterns and participants discriminated its regularity (symmetry or random). We compared contralateral SPN amplitude generated by symmetry at attended and unattended spatial locations. While the response to attended symmetry was slightly enhanced, the response to unattended symmetry was still substantial. Although visual symmetry detection is a computational challenge, we conclude that the brain processes visual symmetry in unattended parts of the visual field.

Scattering spectra models for physics.

Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a pointwise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multiscale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to fourth order. The scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.

Data-driven Lie point symmetry detection for continuous dynamical systems

Symmetry detection, the task of discovering the underlying symmetries of a given dataset, has been gaining popularity in the machine learning community, particularly in science and engineering applications. Most previous works focus on detecting ‘canonical’ symmetries such as translation, scaling, and rotation, and cast the task as a modeling problem involving complex inductive biases and architecture design of neural networks. We challenge these assumptions and propose that instead of constructing biases, we can learn to detect symmetries from raw data without prior knowledge. The approach presented in this paper provides a flexible way to scale up the detection procedure to non-canonical symmetries, and has the potential to detect both known and unknown symmetries alike. Concretely, we focus on predicting the generators of Lie point symmetries of partial differential equations, more specifically, evolutionary equations for ease of data generation. Our results demonstrate that well-established neural network architectures are capable of recognizing symmetry generators, even in unseen dynamical systems. These findings have the potential to make non-canonical symmetries more accessible to applications, including model selection, sparse identification, and data interpretability.

Mirror Symmetry Coils for Foreign Object Detection and Location with Wireless Power Transmission

Background: Wireless power transmission technology effectively avoids safety issues caused by accidental contact, wire aging, and friction. However, due to the presence of foreign objects, other severe accidents such as fire hazard can occur, and the charging system can be interfered with and even damaged by the foreign objects. background: As a new charging technology, the wireless power transmission (WPT) technology has shown some favorable application prospects on safety, reliability, and convenience. Method: Therefore, this paper proposes (MSD) mirror symmetry detection coils to detect and locate foreign objects. First, we conduct theoretical analysis and derive formulas to validate our proposed method. Next, we employ ANSYS Maxwell to simulate the (WPT) wireless power transmission system, considering various sizes and materials of foreign objects and comparing them to a system without foreign objects. Result: Furthermore, we conducted experiments using mirror symmetrical detection coils to detect and locate foreign objects, providing additional verification for our proposed method. Conclusion: The simulation and experimental results show that the proposed method of mirror symmetry detection coils can effectively identify and locate the foreign objects.

Detecting affine equivalences between certain types of parametric curves, in any dimension

<abstract><p>Two curves are affinely equivalent if there exists an affine mapping transforming one of them onto the other. Thus, detecting affine equivalence comprises, as important particular cases, similarity, congruence and symmetry detection. In this paper we generalized previous results by the authors to provide an algorithm for computing the affine equivalences between two parametric curves of certain types, in any dimension. In more detail, the algorithm is valid for rational curves, and for parametric curves with nonrational but meromorphic components, it admits an also meromorphic, and in fact rational, inverse. Unlike other algorithms already known for rational curves, the algorithm completely avoids polynomial system solving, and instead uses bivariate factoring as a fundamental tool. The algorithm has been implemented in the computer algebra system ${\mathtt{Maple}}$ and can be freely downloaded and used.</p></abstract>

Detection of quasicrystalline symmetries in electron diffraction data

Detection of quasicrystalline symmetries in electron diffraction data

Impaired face symmetry detection under alcohol, but no 'beer goggles' effect.

The 'beer goggles' phenomenon describes sexual attraction to individuals when alcohol intoxicated whom we would not desire when sober. One possible explanation of the effect is that alcohol impairs the detection of facial asymmetry, thus lowering the drinker's threshold for physical attraction. We therefore tested the hypotheses that higher breath alcohol drinkers would award more generous ratings of attractiveness to asymmetrical faces, and be poorer at discriminating bilateral facial asymmetry than less intoxicated counterparts. Ninety-nine male and female bar patrons rated 18 individual faces for attractiveness and symmetry. Each type of rating was given twice, once per face with an enhanced asymmetry and once again for each face in its natural form. Participants then judged which of two same-face versions (one normal, the other perfectly symmetrised) was more attractive and, in the final task, more symmetrical. Alcohol had no influence on attractiveness judgements but higher blood alcohol concentrations were associated with higher symmetry ratings. Furthermore, as predicted, heavily intoxicated individuals were less able to distinguish natural from perfectly symmetrised face versions than more sober drinkers. Findings therefore suggest alcohol impairs face asymmetry detection, but it seems that this perceptual distortion does not contribute to the 'beer goggles' phenomenon.

A symmetry-aware alignment method for photogrammetric 3D models

Despite the rapid development of crowd-sourced photogrammetric reconstruction, a huge database of 3D models is still given in arbitrary scale, position, and orientation. To alleviate the issue, model alignment methods have been proposed to identify good viewpoints for 3D models. This work introduces a symmetry-aware alignment method for photogrammetric 3D models. Our key idea is to associate the best orientation with global symmetry and place objects in a way they commonly appear in our surroundings. Compared to the previous alignment methods that only infer upright orientation, we also determine frontal orientation. The proposed method works in four steps. First, we compute symmetry features using point global symmetry descriptors (PGSD). Second, a set of reflective symmetry planes are generated by feature aggregation. Third, we extract global symmetry and the principal axis based on a subset of symmetry planes with smaller detection errors. Finally, upright and frontal orientations are determined by the principal axis and information entropy successively. We evaluated the proposed method on synthetic and real photogrammetric datasets. Experiments show that the proposed PGSD has achieved higher efficiency and accuracy than curvature, FPFH, and deep learning-based frameworks. Our method outperforms the existing symmetry detection and upright orientation methods, where the average recall of main symmetry plane is 71.13%, and 78.50% of the models are well-aligned.

Vertical Symmetry Is Special to Infants; Vertical Symmetry in Upright Human Faces More So

Symmetry has long been viewed as a feature of objects that facilitates ease of perception. Three experiments investigated 4- to 5-month-old infants’ detection and processing of vertical symmetry, oblique symmetry, and asymmetry in novel patterns and faces. In Experiment 1, infants showed the fewest shifts in visual fixations to vertical symmetry in patterns and faces, supporting the view that vertical symmetry is processed more efficiently than oblique symmetry or asymmetry. In Experiment 2, stimulus presentation disallowed more than a single visual fixation, and infants looked longer at a face that is vertically symmetrical compared to obliquely symmetrical or asymmetrical, and they looked equally to patterns regardless of symmetry. In Experiment 3, where pattern exposures were prolonged and inverted faces viewed, infants discriminated vertical symmetry in patterns but lost the advantage with vertical symmetry in faces. Thus, symmetry in patterns requires more processing time from infants, and inverting the face costs infants the normal perceptual advantage of symmetry, even though components of the face remain symmetrical. These findings suggest that infants are prepared to exploit symmetry in their everyday perceptual worlds.

Learning-Based Intrinsic Reflectional Symmetry Detection.

Reflectional symmetry is a ubiquitous pattern in nature. Previous works usually solve this problem by voting or sampling, suffering from high computational cost and randomness. In this article, we propose a learning-based approach to intrinsic reflectional symmetry detection. Instead of directly finding symmetric point pairs, we parametrize this self-isometry using a functional map matrix, which can be easily computed given the signs of Laplacian eigenfunctions under the symmetric mapping. Therefore, we manually label the eigenfunction signs for a variety of shapes and train a novel neural network to predict the sign of each eigenfunction under symmetry. Our network aims at learning the global property of functions and consequently converts the problem defined on the manifold to the functional domain. By disentangling the prediction of the matrix into separated bases, our method generalizes well to new shapes and is invariant under perturbation of eigenfunctions. Through extensive experiments, we demonstrate the robustness of our method in challenging cases, including different topology and incomplete shapes with holes. By avoiding random sampling, our learning-based algorithm is over 20 times faster than state-of-the-art methods, and meanwhile, is more robust, achieving higher correspondence accuracy in commonly used metrics.

Symmetry Detection in Autistic Adults Benefits from Local Processing in a Contour Integration Task.

Symmetry studies in autism are inconclusive possibly due to different types of stimuli used which depend on either local or global cues. Therefore, this study compared symmetry detection between 20 autistic and 18 non-autistic adults matched on age, IQ, gender and handedness, using contour integration tasks containing open and closed contours that rely more on local or global processing respectively. Results showed that the autistic group performed equally well with both stimuli and outperformed the non-autistic group only for the open contours, possibly due to a different strategy used in detecting symmetry. However, there were no group differences for the closed contour. Results explain discrepant findings in previous symmetry studies suggesting that symmetry tasks that favour a local strategy may be advantageous for autistic individuals. Implications of the findings towards understanding visual sensory issues in this group are discussed.

Reflection Symmetry Detection in Earth Observation Data.

The paper presents a new algorithm for reflection symmetry detection, which is specialized to detect maximal symmetric patterns in an Earth observation (EO) dataset. First, we stress the particularities that make symmetry detection in EO data different from detection in other geometric sets. The EO data acquisition cannot provide exact pairs of symmetric elements and, therefore, the approximate symmetry must be addressed, which is accomplished by voxelization. Besides this, the EO data symmetric patterns in the top view usually contain the most useful information for further processing and, thus, it suffices to detect symmetries with vertical symmetry planes. The algorithm first extracts the so-called interesting voxels and then finds symmetric pairs of line segments, separately for each horizontal voxel slice. The results with the same symmetry plane are then merged, first in individual slices and then through all the slices. The detected maximal symmetric patterns represent the so-called partial symmetries, which can be further processed to identify global and local symmetries. LiDAR datasets of six urban and natural attractions in Slovenia of different scales and in different voxel resolutions were analyzed in this paper, demonstrating high detection speed and quality of solutions.

High-resolution X-ray diffraction to probe quantum dot asymmetry

The symmetry of nanostructures forming an active part of optoelectronic devices severely impacts their properties. It is crucial for the design of polarization-insensitive semiconductor optical amplifiers or sources of entangled photon pairs. We show how quantum dot symmetry can be measured, including atomic force microscopy and polarization-resolved spectroscopy. We discuss the drawbacks of the typical approaches for nanostructure symmetry detection and propose a way to determine quantum dot geometrical aspect ratio based on high-resolution X-ray diffraction. The offered method provides a non-destructive insight into crystal lattice disturbances reflecting in-plane quantum dot geometrical aspect ratio.

Multiple Axes of Visual Symmetry: Detection and Aesthetic Preference

Little is known about the detection of and preference for multiple simultaneous parallel axes of symmetry. Neuroscientists have suggested that the detection of symmetry occurs in extrastriate brain areas with large receptive fields. Such large receptive fields may potentially hinder the simultaneous detection of more than one axis of symmetry. In contrast, psychophysicists have found that symmetry detection occurs within small spatial windows, allowing for the concurrent detection of multiple axes of symmetry. Using psychophysical and computational methods, we aim to test whether multiple axes of symmetry can be detected in parallel and to understand the role of multiple axes of symmetry on aesthetic valence. Experiment 1 provides evidence that multiple axes of symmetry cannot be detected simultaneously. However, with relatively long temporal integration, people can detect them. Experiment 2 suggests that multiple axes of symmetry tend to increase preference. However, the preference for symmetry is not universal because, although most people prefer symmetry, others prefer complex images without axes of symmetry. We present and test a computational model that explains the results of these experiments.

Dual-polarization quantum-enhanced stimulated Raman scattering microscopy

In this paper, we propose an approach for implementing quantum-enhanced stimulated Raman scattering (QESRS) microscopy using a dual-polarization scheme. This approach has advantages for high-power operation and enables ultrasensitive Raman detection of molecular vibrational mode symmetry. To demonstrate the feasibility and effectiveness of our technique, we present both the theoretical framework and experimental results of dual-polarization QESRS. Our technique resulted in a noticeable reduction of noise on both parallel and orthogonal QESRS spectra as well as on the depolarization ratio spectra. These results validate the potential of our approach for achieving high-speed QESRS imaging with sub-shot-noise sensitivity.

Symmetry Detection and Breaking in Linear Cost-Optimal Numeric Planning

One of the main challenges of domain-independent numeric planning is the complexity of the search problem. The exploitation of structural symmetries in a search problem can constitute an effective method of pruning search branches that may lead to exponential improvements in performance. For over a decade, symmetry breaking techniques have been successfully used within both optimal and satisficing classical planning. In this work, we show that symmetry detection methods applied in classical planning with some effort can be modified to detect symmetries in linear numeric planning. The detected symmetry group, thereafter, can be used almost directly in the A*-based symmetry breaking algorithms such as DKS and Orbit Space Search. We empirically validate that symmetry pruning can yield a substantial reduction in the search effort, even if algorithms are equipped with a strong heuristic, such as LM-cut.

Hamiltonian neural networks with automatic symmetry detection.

Recently, Hamiltonian neural networks (HNNs) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows us to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.