You are currently viewing a new version of our website. To view the old version click .

Symmetry

Symmetry is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences, and is published monthly online by MDPI.

Quartile Ranking JCR - Q2 (Multidisciplinary Sciences)

All Articles (16,495)

Infrared and visible image fusion-based object detection is critical for robust environmental perception under adverse conditions, yet existing methods still suffer from insufficient modeling of modality discrepancies and limited adaptivity in their fusion mechanisms. This work proposes an asymmetric spatial–frequency fusion network, AsyFusionNet. The network adopts an asymmetric dual-branch backbone that extends the RGB branch to P5 while truncating the infrared branch at P4, thereby better aligning with the physical characteristics of the two modalities, enhancing feature complementarity, and enabling fine-grained modeling of modality differences. On top of this backbone, a local–global attention fusion (LGAF) module is introduced to model local and global attention in parallel and reorganize them through lightweight convolutions, achieving joint spatial–channel selective enhancement. Modality-specific feature enhancement is further realized via a hierarchical attention module (HAM) in the RGB branch, which employs dynamic kernel selection to emphasize multi-level texture details, and a fourier spatial spectral modulation (FS2M) module in the infrared branch, which more effectively captures global thermal radiation patterns. Extensive experiments on the M3FD and VEDAI datasets demonstrate that AsyFusionNet attains 86.3% and 54.1%mAP50, respectively, surpassing the baseline by 8.8 and 6.4 points (approximately 11.4% and 13.4% relative gains) while maintaining real-time inference speed.

17 December 2025

Comparison of feature-level fusion strategies for one stage detectors: (a) traditional feature-level fusion; (b) the asymmetric feature-level fusion proposed in this paper.

On a New Extension of the t-Transformation of Probability Measures

  • Abdulmajeed Albarrak,
  • Raouf Fakhfakh and
  • Ghadah Alomani

This paper establishes a comprehensive analytical framework for a new transformation of probability measures, denoted by , which unifies the classical t- and Ta-transformations in free probability. We derive the functional equation characterizing through the Cauchy–Stieltjes transform and explicitly show how it specializes to known deformations when a=0 or t=1. Within the setting of Cauchy-Stieltjes kernel families, we prove structural symmetry and invariance properties of the transformation, demonstrating in particular that both the free Meixner family and the free analog of the Letac-Mora class remain invariant under . Furthermore, we obtain several new limiting theorems that uncover symmetric relationships among fundamental free distributions, including the semicircular, Marchenko–Pastur, and free binomial laws.

17 December 2025

BiHom–Lie Brackets and the Toda Equation

  • Botong Gai,
  • Chuanzhong Li and
  • Jiacheng Sun
  • + 2 authors

We introduce a BiHom-type skew-symmetric bracket on general linear Lie algebra built from two commuting inner automorphisms α=Adψ and β=Adϕ, with and integers i,j. We prove that is a BiHom–Lie algebra, and we study the Lax equation obtained by replacing the commutator in the finite nonperiodic Toda lattice by this bracket. For the symmetric choice ϕ=ψ with , the deformed flow is equivariant under conjugation and becomes gauge-equivalent, via , to a Toda-type Lax equation with a conjugated triangular projection. In particular, scalar deformations amount to a constant rescaling of time. On embedded 2×2 blocks, we derive explicit trigonometric and hyperbolic formulae that make symmetry constraints (e.g., tracelessness) transparent. In the asymmetric hyperbolic case, we exhibit a trace obstruction showing that the right-hand side is generically not a commutator, which amounts to symmetry breaking of the isospectral property. We further extend the construction to the weakly coupled Toda lattice with an indefinite metric and provide explicit 2×2 solutions via an inverse-scattering calculation, clarifying and correcting certain formulas in the literature. The classical Toda dynamics are recovered at special parameter values.

17 December 2025

The neural mechanisms of auditory and visual processing are not only a core research focus in cognitive neuroscience but also hold critical importance for the development of brain–computer interfaces, neurological disease diagnosis, and human–computer interaction technologies. However, EEG-based studies on classifying auditory and visual brain activities largely overlook the in-depth utilization of spatial distribution patterns and frequency-specific characteristics inherent in such activities. This paper proposes an analytical framework that constructs symmetrical spatio-temporal–frequency feature association vectors to represent brain activities by computing EEG microstates across multiple frequency bands and brain functional connectivity networks. Then we construct an Adaptive Tensor Fusion Network (ATFN) that leverages feature association vectors to recognize brain activities related to auditory, visual, and audiovisual processing. The ATFN includes a feature fusion and selection module based on differential feature enhancement, a feature encoding module enhanced with attention mechanisms, and a classifier based on a multilayer perceptron to achieve the efficient recognition of audiovisual brain activities. The feature association vectors are then processed by the Adaptive Tensor Fusion Network (ATFN) to efficiently recognize different types of audiovisual brain activities. The results show that the classification accuracy for auditory, visual, and audiovisual brain activity reaches 96.97% using the ATFN, demonstrating that the proposed symmetric spatio-temporal–frequency feature association vectors effectively characterize visual, auditory, and audiovisual brain activities. The symmetrical spatio-temporal–frequency feature association vectors establish a computable mapping that captures the intrinsic correlations among temporal, spatial, and frequency features, offering a more interpretable method to represent brain activities. The proposed ATFN provides an effective recognition framework for brain activity, with a potential application for brain–computer interfaces and neurological disease diagnosis.

17 December 2025

News & Conferences

Issues

Open for Submission

Editor's Choice

Get Alerted

Add your email address to receive forthcoming issues of this journal.

XFacebookLinkedIn
Symmetry - ISSN 2073-8994