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Symmetry, Volume 18, Issue 8 (August 2026) – 165 articles

Cover Story (view full-size image): What new forms of matter could emerge from the heaviest quarks produced at the LHC? All-bottom tetraquarks, built from two bottom quarks and two bottom antiquarks, are among the most elusive exotic particles predicted by QCD and remain experimentally unconfirmed. This work explores how such states could be produced and identified during the forthcoming high-luminosity phase of the LHC, the next major upgrade of the collider. Using the TQ4Q2.0 fragmentation framework and precision high-energy methods, we connect heavy-quark dynamics, multiquark formation, and collider observables to highlight promising discovery channels. Future measurements may reveal whether all-bottom tetraquarks exist and open a new window onto how the strong force assembles matter beyond conventional hadrons. View this paper
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21 pages, 2775 KB  
Article
Type-III Shubnikov Point Groups for Guided-Wave Stimulated Brillouin Scattering: Conjugate Symmetry and Selection Rules
by Xue-Yuan Xing, Xiao-Xing Su and Guo-Shuang Shui
Symmetry 2026, 18(8), 1408; https://doi.org/10.3390/sym18081408 - 21 Aug 2026
Viewed by 327
Abstract
In guided-wave stimulated Brillouin scattering (SBS), the opto-mechanical coupling strength is determined by the spatial overlap of optical and elastic fields, fundamentally constrained by symmetry. Conventional analyses based on ordinary point groups assume that fields share the waveguide’s symmetry, which is valid for [...] Read more.
In guided-wave stimulated Brillouin scattering (SBS), the opto-mechanical coupling strength is determined by the spatial overlap of optical and elastic fields, fundamentally constrained by symmetry. Conventional analyses based on ordinary point groups assume that fields share the waveguide’s symmetry, which is valid for standing-wave modes with zero longitudinal wavenumber. However, in waveguides with longitudinal-axis-reversing operations, such operations flip the wavenumber sign for traveling-wave modes, making the conventional framework insufficient—a limitation not addressed before. Here, we introduce the type-III Shubnikov (magnetic) point groups, combining time reversal with axis-reversing spatial operations, and establish a co-representation theory for such traveling-wave modes. We prove that these modes obey a conjugate symmetry derived from the antiunitary elements of the magnetic point group. From this, we derive a general selection rule for backward SBS: if the waveguide possesses only one nontrivial axis-reversing operation (and no other independent symmetry), the conjugate symmetry allows the coupling to be nonzero. Numerical validations on single-crystal lithium niobate, fused silica, and single-crystal silicon waveguides of a trapezoidal cross-section confirm the predicted conjugate symmetry and show that materials with lower intrinsic symmetry more favorably realize such symmetry-enabled backward SBS. This work represents a systematic introduction of magnetic group theory to nonmagnetic waveguides, offering new insights for material selection and coupling control in guided-wave SBS. Full article
(This article belongs to the Section C: Physics)
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48 pages, 588 KB  
Article
Tame Symmetric Algebras of Period Four with Small Gabriel Quivers
by Karin Erdmann, Alicja Jaworska-Pastuszak and Adam Skowyrski
Symmetry 2026, 18(8), 1407; https://doi.org/10.3390/sym18081407 - 21 Aug 2026
Viewed by 197
Abstract
The tame symmetric algebras of period four, TSP4 algebras for short, form an important class of algebras, with interesting connections to various branches of modern algebra. The study of this class has been recently developed in two major directions. The first embraces new [...] Read more.
The tame symmetric algebras of period four, TSP4 algebras for short, form an important class of algebras, with interesting connections to various branches of modern algebra. The study of this class has been recently developed in two major directions. The first embraces new classes of examples of TSP4 algebras, such as virtual mutations and generalized weighted surface algebras, both extending the known class of weighted surface algebras. The second provides new classifications of TSP4 algebras (based on known results for 2-regular case), which handle algebras for which Gabriel quivers satisfy more general properties; the classification in biregular case is known (the biserial case is a current work in progress). An ongoing project sheds a new light on the combinatorics of such algebras, introducing a useful new tool for their classification called periodicity shadows. In this paper, we address the problem of classifying TSP4 algebras from another perspective: we provide a classification of all TSP4 algebras with not-too-big Gabriel quivers, i.e., having at most 5 vertices, but without restrictions on their structure, which differentiates it from previous classifications. The result is based on the application of the concept of the periodicity shadow, which allows all possible Gabriel quivers of such algebras to be computed (for small number of vertices) as well as on recent results concerning iterated mutations of algebras with periodic simple modules. The main result shows that TSP4 algebras with at most 5 vertices are generalized weighted surface algebras, confirming a general conjecture in this case. Full article
(This article belongs to the Section B: Mathematics)
14 pages, 271 KB  
Article
Phragmén–Lindelöf Alternative Results for the Thermoelasticity of Type III on an Exterior Region in ℝ3
by Jincheng Shi
Symmetry 2026, 18(8), 1406; https://doi.org/10.3390/sym18081406 - 21 Aug 2026
Viewed by 263
Abstract
This paper investigates the spatial asymptotic behaviour of solutions to a coupled thermoelastic system of Green–Naghdi Type III in an exterior domain of R3. The system couples elastodynamics with a second-order heat conduction law and contains indefinite cross-coupling terms between mechanical [...] Read more.
This paper investigates the spatial asymptotic behaviour of solutions to a coupled thermoelastic system of Green–Naghdi Type III in an exterior domain of R3. The system couples elastodynamics with a second-order heat conduction law and contains indefinite cross-coupling terms between mechanical and thermal variables. By constructing a weighted energy functional and deriving a first-order differential inequality in the radial direction, we establish a Phragmén–Lindelöf alternative: for each fixed time, the total energy either grows exponentially or decays exponentially as r, with an explicit decay rate that depends on the material coefficients and a free parameter ω. This dichotomy itself reveals a fundamental symmetry in the spatial behaviour—growth versus decay—which is intimately linked to the radial symmetry of the exterior geometry and the inherent structure of the coupled system. The result provides a complete characterization of spatial stability for this thermoelastic model in unbounded exterior domains. Full article
(This article belongs to the Section B: Mathematics)
25 pages, 2355 KB  
Article
Physics-Informed Neural Networks Versus Differential Transform Method for Reduced Second-Order ODEs in Membrane Shell Theory
by Rafał Brociek, Mariusz Pleszczyński and Oliwier Wójcik
Symmetry 2026, 18(8), 1405; https://doi.org/10.3390/sym18081405 - 21 Aug 2026
Viewed by 223
Abstract
This paper presents a comparative study of two approaches for solving second-order ordinary differential equations arising from the membrane theory of shells of revolution. The considered equations originate from the rotational symmetry of shell structures, which enables the reduction of the governing partial [...] Read more.
This paper presents a comparative study of two approaches for solving second-order ordinary differential equations arising from the membrane theory of shells of revolution. The considered equations originate from the rotational symmetry of shell structures, which enables the reduction of the governing partial differential equations to a sequence of ordinary differential equations corresponding to individual circumferential harmonics. The study compares the classical Differential Transform Method (DTM) with Physics-Informed Neural Networks (PINNs). Both initial value and boundary value problems are investigated, including benchmark examples with known analytical solutions and a systematic analysis of the influence of PINN architecture on the solution accuracy. For the PINN approach, the effects of the number of collocation points, hidden layers, and neurons per layer on the approximation error and training time are examined. The results demonstrate that DTM provides an efficient framework for constructing analytical solutions of initial value problems with minimal computational cost. However, its application to boundary value problems requires the introduction of additional auxiliary parameters and the solution of supplementary nonlinear equations, considerably increasing the analytical complexity of the procedure. In contrast, PINNs achieve high accuracy for both initial and boundary value problems while naturally incorporating boundary conditions through the loss function. The presented results demonstrate how the exploitation of geometric symmetry, combined with modern scientific machine learning techniques, provides an effective computational framework for solving differential equations arising in shell mechanics. Full article
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25 pages, 2018 KB  
Article
Harnessing Symmetry in Stiffness Matrix Formulation for Tensegrity Structures with Equal Cable Length via Linear Stiffness Theory
by Yingyu Zhao, Ani Luo and Heping Liu
Symmetry 2026, 18(8), 1404; https://doi.org/10.3390/sym18081404 - 20 Aug 2026
Viewed by 373
Abstract
Tensegrity structures, due to their lightweight and self-equilibrating characteristics, have found extensive applications across various engineering fields. The introduction of equal cable length as an additional geometric constraint enables a high degree of geometric symmetry, resulting in uniform internal force distribution and predictable [...] Read more.
Tensegrity structures, due to their lightweight and self-equilibrating characteristics, have found extensive applications across various engineering fields. The introduction of equal cable length as an additional geometric constraint enables a high degree of geometric symmetry, resulting in uniform internal force distribution and predictable mechanical responses. However, existing stiffness matrix assembly methods predominantly rely on conventional node-element topological connectivity matrices confined to classical one-to-one force-displacement systems, struggling to exploit the geometric regularities inherent in equal-length constraints and highly symmetric configurations. To address this, the paper proposes a stiffness matrix modeling method tailored for equal-cable-length tensegrity structures within the linear stiffness framework. A generalized connectivity matrix is introduced to unify the topological description of struts and cables while integrating displacement compatibility, internal equilibrium, and geometric constraints into a cohesive algebraic system. Leveraging symmetry properties and member categorization by loading type, the method embeds equal-length and symmetry grouping information directly into assembly, significantly reducing independent variables and construction complexity. A finite element model is established for numerical implementation, and experiments on a three-bar tensegrity structure validate the theoretical model, with minor deviations confirming its reliability. Full article
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30 pages, 404 KB  
Article
New Identities and Operational Formulas for Leonardo-Type Polynomial Bases
by Amr Kamel Amin, Naher Mohammed A. Alsafri, Mohammed Atef Abdallah and Waleed Mohamed Abd-Elhameed
Symmetry 2026, 18(8), 1403; https://doi.org/10.3390/sym18081403 - 20 Aug 2026
Viewed by 217
Abstract
This paper investigates a class of Leonardo polynomials defined by a nonhomogeneous recurrence relation, whose algebraic structure differs significantly from that of classical Fibonacci-type polynomial families. First, we develop a new connection formula expressing Leonardo polynomials in terms of Fibonacci polynomials, and then [...] Read more.
This paper investigates a class of Leonardo polynomials defined by a nonhomogeneous recurrence relation, whose algebraic structure differs significantly from that of classical Fibonacci-type polynomial families. First, we develop a new connection formula expressing Leonardo polynomials in terms of Fibonacci polynomials, and then we derive the corresponding inverse connection formula. These two identities are subsequently employed to develop an explicit power-form representation of the Leonardo polynomials together with its corresponding monomial inversion formula. Building upon these fundamental representations, the paper derives new derivative and connection formulas involving generalized Fibonacci and generalized Lucas polynomial families in terms of the Leonardo basis. Several consequences for the classical Fibonacci and Lucas polynomials are also established. Furthermore, new product identities involving Leonardo polynomials are developed. The derived representations also reveal parity-dependent symmetry patterns in the Leonardo polynomial coefficients and clarify how these patterns are inherited from the associated Fibonacci- and Lucas-type bases. Many of the resulting coefficients are expressed in terms of terminating hypergeometric functions, yielding compact representations that are expected to be useful in approximation theory and operational methods for differential equations. Full article
25 pages, 561 KB  
Article
Traceable Symmetry-Aware Image Processing for Two-Dimensional Morphological Diagnostics in Product Concept Design: A Four-Alternative Smart-Speaker Study
by Xinman Wang, Wenjie Liu and Lingwan Huang
Symmetry 2026, 18(8), 1402; https://doi.org/10.3390/sym18081402 - 20 Aug 2026
Viewed by 290
Abstract
Product concept images combine symmetry, closure, balance, and repeated components. Existing shape analysis and computational aesthetic methods can quantify these properties; however, when evidence is reduced to global descriptors or aggregate scores, image-layer provenance and sensitivity to rasterization or heuristic settings may be [...] Read more.
Product concept images combine symmetry, closure, balance, and repeated components. Existing shape analysis and computational aesthetic methods can quantify these properties; however, when evidence is reduced to global descriptors or aggregate scores, image-layer provenance and sensitivity to rasterization or heuristic settings may be obscured. This paper presents a traceable image-processing pipeline based on scenario framing, alternative specification, geometry-informed computation, evidence synthesis, and design embodiment (SAGE-D), evaluated on four controlled smart-speaker alternatives using separate body, light-band, and aperture masks. Seven dimensionless descriptors measure silhouette reflection, centroid balance, light-band closure, aperture regularity and gradient, component-scale retention, and contour compactness. Resolution resampling, one-pixel morphology, parameter perturbation, and synthetic controls assess sensitivity. At 512×512 pixels, A, B, and R showed exact bilateral silhouette consistency; B and R showed complete light-band occupancy; and C and R showed strong downward aperture-radius gradients. Conventional same-mask measures gave concordant geometric readings, while leave-one-gate-out analysis showed that screening depended mainly on predefined closed-ring and linear-gradient requirements. Only R passed all six case gates. SAGE-D is used here as an auditable organization of layer-specific measurements and bounded screening rules, not as a superior descriptor set. The conclusions are limited to the supplied two-dimensional (2D) representations and do not establish population-level generalizability, preference, or engineering performance. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Computer-Aided Industrial Design: 2nd Edition)
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32 pages, 19591 KB  
Article
Thermal Buoyancy as a Wake Controller: Coupled Wake Dynamics and Heat Transfer in Mixed Convection
by Visakh Sasankan, Ajith Kumar Sasidharanpillai and Petha Sethuraman Vignesh Ram
Symmetry 2026, 18(8), 1401; https://doi.org/10.3390/sym18081401 - 20 Aug 2026
Viewed by 186
Abstract
The dominance and impact of pronounced thermal buoyancy effects on the thermal and hydrodynamic properties of a horizontally heated cylinder of circular configuration immersed in a vertically ascending laminar flow stream have been numerically investigated. The dynamics are determined by numerically solving the [...] Read more.
The dominance and impact of pronounced thermal buoyancy effects on the thermal and hydrodynamic properties of a horizontally heated cylinder of circular configuration immersed in a vertically ascending laminar flow stream have been numerically investigated. The dynamics are determined by numerically solving the standard energy and two-dimensional laminar Navier–Stokes equations and by incorporating buoyancy through the Boussinesq approximation in the mixed-convection co-flow configuration. The Reynolds number (Re) is varied within the range of 80Re160, while the Prandtl number (Pr) is maintained constant at 0.71. The thermal buoyancy effect of the co-flow configuration is assessed by altering the Richardson number (0Ri1). The code is validated against and compared against several numerical and experimental results, and its strong prediction capabilities are confirmed. This study examines significantly observed von Kármán vortices and their disappearance at above a threshold Richardson number, which has been identified as the critical Richardson number. This study provides a detailed explanation of a new phenomenon, termed ‘vortex switching’, which arises from the interaction between inertia–buoyancy interactions. The study showcases representative patterns of vorticity, streamlines, and isotherms while also plotting the average Nusselt numbers against the Ri for various Re. Furthermore, it offers a correlation for the changes in wake width, recirculation bubble length, and vortex switching length, which are essential for optimizing design and enhancing thermal efficiency. Lastly, the thermal characteristics provide deeper insights into the impact of thermal buoyancy on wake dynamics and heat transfer. Full article
(This article belongs to the Special Issue Symmetries and Asymmetries in Fluid Dynamics)
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19 pages, 8195 KB  
Article
Mechanisms of Σ3 Grain Boundary Formation in Laser Powder Bed Fusion-Produced AlSi10Mg Alloy Processed by Twist ECAP
by Przemysław Snopiński
Symmetry 2026, 18(8), 1400; https://doi.org/10.3390/sym18081400 - 19 Aug 2026
Viewed by 270
Abstract
Grain boundaries affect the mechanical and functional properties of crystalline materials by influencing interfacial energy, mobility, segregation, and the accumulation of damage. Among the grain boundaries in the grain boundary network, coincidence site lattice boundaries form a particular type of special grain boundary [...] Read more.
Grain boundaries affect the mechanical and functional properties of crystalline materials by influencing interfacial energy, mobility, segregation, and the accumulation of damage. Among the grain boundaries in the grain boundary network, coincidence site lattice boundaries form a particular type of special grain boundary that is characterized by a higher degree of lattice-site coincidence. The present study examined the mechanisms involved in the formation of grain boundaries in a laser-powder-bed-fused AlSi10Mg alloy which had been subjected to two-pass twist equal-channel angular pressing (twist-ECAP). The microstructural evolution, deformation texture, and local orientation gradients were investigated using electron backscatter diffraction (EBSD). Moreover, atomistic simulations were carried out in order to assess the effect of geometrically necessary boundary (GNB)-like dislocation walls on the retention of planar faults. The EBSD results indicated that twist-ECAP considerably refined the microstructure and produced a strong fiber texture. Most of the Σ3 grain boundary segments detected were found in areas dominated by the ⟨110⟩||ED component, showing that their appearance is strongly dependent on the texture. Also, the atomistic modelling showed that the presence of a GNB-like wall led to the retention of planar-fault configurations and thus resulted in the highest number of atomic environments related to faults and extended dislocation-line lengths. These results show that the formation of Σ3 grain boundary segments in severely deformed LPBF AlSi10Mg is a coupled process which is mainly controlled by macroscopic texture selection and is locally assisted by deformation-boundary evolution. Full article
(This article belongs to the Section F: Engineering and Materials)
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21 pages, 2479 KB  
Article
Attribute Control Charts for the Compound Weibull and Compound Exponential–Gamma Distribution Under Truncated Life Tests
by Ayten Yiğiter, Nazan Danacıoğlu and Canan Hamurkaroğlu
Symmetry 2026, 18(8), 1399; https://doi.org/10.3390/sym18081399 - 19 Aug 2026
Viewed by 277
Abstract
This study presents the development of an attribute control chart for monitoring the number of failures in a truncated life test under a single sampling plan, where the product lifetime follows either the Compound Weibull (CW) distribution or its special case, the Compound [...] Read more.
This study presents the development of an attribute control chart for monitoring the number of failures in a truncated life test under a single sampling plan, where the product lifetime follows either the Compound Weibull (CW) distribution or its special case, the Compound Exponential–Gamma (CEG) distribution. The control chart constants were determined for various parameter settings through an iterative design procedure. Specifically, the chart parameters were obtained for different quality levels and specified in-control Average Run Length (ARL0) values. Furthermore, the performance of the proposed control charts was evaluated in terms of the out-of-control Average Run Length (ARL1), Standard Deviation of Run Length (SDRL), Expected Average Run Length (EARL), and Extra Quadratic Loss (EQL) under various process shift levels. Numerical tables were provided for different combinations of the shape parameters, sample sizes, target ARL0 values, and shift parameters. Finally, a simulation study was conducted to demonstrate the effectiveness of the proposed control charts in monitoring defective items. Overall, the results demonstrate that the proposed attribute control chart is applicable to processes in which product lifetimes follow the CW and CEG distributions and provides an effective tool for monitoring process shifts. The study demonstrates how the np chart’s performance is affected under different scenarios regarding CW and CEG distributions. It was observed that the chart exhibits high performance by enabling early detection during significant process shifts. In cases of minor process changes, the chart was found to be sensitive under the CW distribution assumption. Full article
(This article belongs to the Section B: Mathematics)
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21 pages, 914 KB  
Article
MSATE-Net: A Multi-Scale Attention-Enhanced Bidirectional Temporal Network for Stock Index Forecasting
by Taoyin Wang, Yiyuan Cheng, Zihao Tang, Yahui Shan and Hao Wang
Symmetry 2026, 18(8), 1398; https://doi.org/10.3390/sym18081398 - 19 Aug 2026
Viewed by 287
Abstract
This study proposes MSATE-Net for next-day stock index forecasting. The model combines parallel one-dimensional convolutions with receptive fields of 3, 7, and 15 trading days, a bidirectional LSTM operating entirely inside a historical lookback window, sample-dependent temporal attention, and a residual regularized prediction [...] Read more.
This study proposes MSATE-Net for next-day stock index forecasting. The model combines parallel one-dimensional convolutions with receptive fields of 3, 7, and 15 trading days, a bidirectional LSTM operating entirely inside a historical lookback window, sample-dependent temporal attention, and a residual regularized prediction head. Here, “bidirectional” denotes paired processing of the same observed window; it does not assert time-reversal invariance of financial prices or access to observations after the forecast origin. The globally learned attention temperature controls overall selectivity and is not described as a regime-specific adaptive parameter. Experiments use S&P 500, CSI 300, and Nikkei 225 data; persistence and drift benchmarks; recent forecasting architectures; five-seed uncertainty estimates; expanding-window tests; return and directional metrics; and Diebold–Mariano comparisons. The revised evidence supports lower price-level errors, while directional and significance results are mixed across markets. Because a separate model is fitted in each market, the findings establish cross-market consistency rather than transfer learning. Full article
(This article belongs to the Section A: Computer Science)
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20 pages, 1822 KB  
Article
Adaptive Prescribed-Time Tracking Control for Output-Constrained Hydraulic Servo Systems with Time-Varying Parameters
by Mengjie Wang, Kou Du, Ximing Cai, Shuai Li, Qian Qin, Yayun Zhang, Jinjie Gan, Lianhua Wang, Peiguo Zhang, Pengfei Li, Jianyong Yao and Xiaowei Yang
Symmetry 2026, 18(8), 1397; https://doi.org/10.3390/sym18081397 - 19 Aug 2026
Viewed by 175
Abstract
This paper proposes an adaptive prescribed-time tracking control strategy based on the dynamic surface technique for hydraulic servo systems subject to time-varying parameters, external disturbances, and output constraints. First, a state-constrained transformation function is introduced to convert the strict output constraint condition into [...] Read more.
This paper proposes an adaptive prescribed-time tracking control strategy based on the dynamic surface technique for hydraulic servo systems subject to time-varying parameters, external disturbances, and output constraints. First, a state-constrained transformation function is introduced to convert the strict output constraint condition into an error boundedness problem. Meanwhile, the dynamic surface control (DSC) technique is employed to effectively avoid the “explosion of complexity” inherent in traditional backstepping design. Second, to tackle complex uncertainties, prescribed-time-driven adaptive update and disturbance estimation laws are separately formulated for precise parameter learning and active disturbance feedforward compensation. Furthermore, a smooth nonlinear robust term is specifically integrated to suppress the residual errors induced by parameter adaptation. Based on the transformed system, a novel control framework integrating error constraints, adaptive parameter estimation, and prescribed-time performance is developed. Rigorous Lyapunov stability analysis proves that the proposed controller not only strictly prevents the system output from violating the constraint boundaries throughout the entire operation, but also ensures that the tracking error converges rapidly and smoothly to a small bounded region near the origin within a time that can be independently predetermined by the designer. Finally, the effectiveness and superiority of the proposed control strategy are fully validated through simulations. Full article
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22 pages, 2359 KB  
Article
Tidal Deformability in Neutron Stars from an Ab Initio Point of View
by Francesca Sammarruca and Prabin Thapa
Symmetry 2026, 18(8), 1396; https://doi.org/10.3390/sym18081396 - 19 Aug 2026
Viewed by 194
Abstract
We present results for the tidal deformability of neutron stars, the tidal Love number k2, and the effective deformability of a binary system. The equation of state for cold β-stable neutron matter is based upon high-precision two-neutron forces and includes [...] Read more.
We present results for the tidal deformability of neutron stars, the tidal Love number k2, and the effective deformability of a binary system. The equation of state for cold β-stable neutron matter is based upon high-precision two-neutron forces and includes the chiral three-neutron forces required at each order. Although we show results at both the third (N2LO) and fourth (N3LO) orders of the chiral expansion, we emphasize that only the results at N2LO can be considered truly ab initio. This is because of standing problems with regularizing three-nucleon forces at N3LO and higher orders and maintaining chiral symmetry. Thus, the results at N3LO are for illustration purposes only. We review and motivate our choices for the high-density continuation of the microscopic equation of state. We discuss our predictions and observe that they are well within multimessenger constraints. In contrast, stiff equations of state that yield radii larger than about 13 km are ruled out by GW170817 constraints. One of the main contributions from this work is the finding that tidal properties are insensitive to the high-density continuation of the equation of state, suggesting that future tidal measurements can provide robust constraints on the equation of state in the medium-density region, where the predictions from chiral effective field theory are most reliable. Full article
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10 pages, 1428 KB  
Article
Research on Dual-Comb Ranging Technology Based on Si3N4 Microcomb
by Yang Xie, Ruizhi Yi, Ziyue Zhang, Ziyang Chen, Zhongyuan Fu, Ce Yang, Jianjie Yin and Lin Xiao
Symmetry 2026, 18(8), 1395; https://doi.org/10.3390/sym18081395 - 19 Aug 2026
Viewed by 280
Abstract
To promote the transition of microresonator dual-comb ranging (DCR) technology from the laboratory to practical applications, we have developed a DCR system based on two self-developed, self-starting silicon nitride (Si3N4) microcombs with repetition-rate-locking. By integrating servo-control circuits and employing [...] Read more.
To promote the transition of microresonator dual-comb ranging (DCR) technology from the laboratory to practical applications, we have developed a DCR system based on two self-developed, self-starting silicon nitride (Si3N4) microcombs with repetition-rate-locking. By integrating servo-control circuits and employing an all-polarization-maintaining fiber design, we have achieved long-term stable operation of the system. To validate the system’s performance parameters, we conducted two verification experiments at the National Institute of Metrology, China (NIM): a comparison against the indoor national long-base comparator and a repeatability test at an outdoor field baseline. Over the indoor test range of 0–60 m, measurement results showed deviations within 6 μm when compared against the indoor national long-base comparator. At the outdoor field baseline location of 618 m, with a signal acquisition duration of 1 ms per measurement, the ranging standard deviation was 2.38 μm. During outdoor ranging experiments, the system operated continuously for over 4 h without the need for specialized thermal insulation or vibration isolation measures. These results demonstrate the exceptional measurement accuracy and stability of the microresonator DCR system. Full article
(This article belongs to the Section C: Physics)
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25 pages, 4772 KB  
Article
Physics-Informed Neural Networks for Non-Recurrent Traffic Congestion Detection: A Case Study on the Seoul Ring Expressway
by Woohun Jeon, Joyoung Lee, Jinguk Kim and Md Tufajjal Hossain
Symmetry 2026, 18(8), 1394; https://doi.org/10.3390/sym18081394 - 19 Aug 2026
Viewed by 257
Abstract
Non-recurrent congestion (NRC), caused by unforeseen events such as crashes, lane closures, and adverse weather, accounts for approximately half of all delays on urban freeways, yet it remains difficult to distinguish from routine congestion at recurrent bottlenecks. This study proposes an NRC detection [...] Read more.
Non-recurrent congestion (NRC), caused by unforeseen events such as crashes, lane closures, and adverse weather, accounts for approximately half of all delays on urban freeways, yet it remains difficult to distinguish from routine congestion at recurrent bottlenecks. This study proposes an NRC detection framework based on a Physics-Informed Neural Network (PINN) that embeds the Lighthill–Whitham–Richards (LWR) conservation law into the learning process to construct a physically consistent baseline of normal traffic states. The traffic flow physics is represented by a two-regime fundamental diagram combining the Greenshields model for free-flow conditions and the Underwood model for congested conditions, and the network is trained by minimizing a composite loss that adaptively balances the data fitting error against the LWR residual. NRC is then detected when the observed density exceeds the PINN-estimated baseline density beyond a tolerance threshold of 150%. The framework was evaluated on a 12 km segment of the Seoul Ring Expressway in Korea using six months of 15 min data collected from seventeen sensor stations. The results show that the proposed model reliably isolates NRC events from recurrent peak-period congestion. From the perspective of symmetry, the framework interprets recurrent traffic as a temporally symmetric background state governed by a conservation law, and non-recurrent congestion as a local breaking of this symmetry, which the physics-constrained residual is designed to expose. The key contribution of this study is a theoretically grounded, label-free anomaly detection approach that couples machine learning with traffic flow theory, offering traffic management centers an automated and interpretable tool for incident detection and response. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Intelligent Transportation System)
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31 pages, 5925 KB  
Article
Feedforward–Feedback Symmetry for Risk Control: A Hybrid Framework Coupling Genetic Algorithms with RAG-Enhanced Large Language Models
by Ke He, Xuefeng Xia and Changfeng Wang
Symmetry 2026, 18(8), 1393; https://doi.org/10.3390/sym18081393 - 18 Aug 2026
Viewed by 241
Abstract
Petroleum engineering projects face complex risk environments. Existing risk control systems often only provide overall risk safety thresholds. They lack effective quantitative interval estimation methods. Moreover, translating quantitative analysis findings into actionable on-site management instructions remains challenging. Symmetry serves as a core analytical [...] Read more.
Petroleum engineering projects face complex risk environments. Existing risk control systems often only provide overall risk safety thresholds. They lack effective quantitative interval estimation methods. Moreover, translating quantitative analysis findings into actionable on-site management instructions remains challenging. Symmetry serves as a core analytical perspective for cutting-edge research in control theory and system engineering. Feedforward and feedback controls are functionally complementary and sequentially cascaded, featuring intrinsic complementary symmetry. From the perspective of feedforward–feedback symmetry, this study constructs a GA-LLM hybrid framework combining genetic algorithm (GA) and large language models (LLMs) to address the above shortcomings. This framework is jointly composed of four collaboratively functioning modules, comprising the risk status input module, GA feedforward control module, retrieval-augmented generation (RAG) knowledge retrieval module, and the LLM feedback control strategy-generation module. In this framework, the GA serves as the feedforward controller, which computes the joint inscribed control box for each risk factor offline based on the risk relationship model established by the Back Propagation (BP) neural network. The RAG-enhanced LLM serves as the feedback controller, dynamically generating structured risk control instructions based on deviations. Case validation results demonstrate that the BP neural network achieved excellent performance with an R2 of 0.99575 under leave-one-out cross-validation. The GA successfully solved the joint control box for the 14 risk factors, achieving a 100% joint constraint satisfaction rate for any combination within the box. The RAG retrieval module achieved a Recall@5 of 0.8933, MRR@5 of 0.7367, nDCG@5 of 0.7505, and Success@5 of 1.000. Ablation experiments show that the RAG-LLM scheme outperformed both the LLM without RAG scheme and the rule-based template scheme across four dimensions, with an inter-rater reliability ICC(2,1) of 0.719, reaching a moderate reliability level. This study integrates the quantitative optimization capability of GA with the semantic generation capability of LLM, enabling the transformation from the joint control box to executable management instructions. It not only provides a practical tool for petroleum engineering risk management but also offers new insights for the design of intelligent control systems from the perspective of feedforward–feedback symmetry. Full article
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32 pages, 4733 KB  
Article
Symmetry Patterns and Machine Learning Prediction of Urban Pollutant Dispersion
by Muhammad Zawad Mahmud, Md. Mamun Molla, Md Farhad Hasan and Most. Nasrin Akhter
Symmetry 2026, 18(8), 1392; https://doi.org/10.3390/sym18081392 - 18 Aug 2026
Viewed by 252
Abstract
Urban pollutant dispersion is governed by highly nonlinear interactions between flow structures, turbulence characteristics, and scalar transport processes, making accurate prediction computationally demanding. The present study investigates pollutant dispersion behaviour within an idealised urban configuration using a combined computational fluid dynamics (CFD) and [...] Read more.
Urban pollutant dispersion is governed by highly nonlinear interactions between flow structures, turbulence characteristics, and scalar transport processes, making accurate prediction computationally demanding. The present study investigates pollutant dispersion behaviour within an idealised urban configuration using a combined computational fluid dynamics (CFD) and surrogate machine learning. Reynolds-averaged Navier–Stokes simulations were performed to analyse the effects of Reynolds number, Schmidt number, turbulence kinetic energy, concentration transport, velocity distribution, and injection ratio on flow symmetry and pollutant redistribution. The numerical results showed that variations in Reynolds number and injection ratio modified the spatial organisation and relative symmetry of the computed vorticity and concentration fields, together with the corresponding centreline concentration, velocity, and turbulent kinetic energy responses. To complement the CFD analysis, an Extreme Gradient Boosting (XGBoost) model was trained to predict concentration, velocity, and turbulence kinetic energy using CFD-generated datasets. Feature importance analysis further revealed physically meaningful relationships among the governing transport variables, with Reynolds number dominating velocity and turbulence kinetic energy behaviour, while concentration transport remained strongly influenced by injection ratio. Full article
(This article belongs to the Special Issue Symmetry in Thermal Fluid Sciences and Energy Applications)
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24 pages, 7078 KB  
Article
A Symmetry-Aware GGA-XGB Model for Lithology Prediction Under Complex Geological Conditions
by Yang Huang, Yu Yan, Yihang Zhao and Ling Wang
Symmetry 2026, 18(8), 1391; https://doi.org/10.3390/sym18081391 - 18 Aug 2026
Viewed by 265
Abstract
Lithology prediction is a fundamental component of geological exploration and hydrocarbon reservoir characterization, playing a critical role in improving subsurface structural interpretation and enhancing resource prediction accuracy. However, well log data are typically characterized by high dimensionality, strong nonlinearity, severe class imbalance, and [...] Read more.
Lithology prediction is a fundamental component of geological exploration and hydrocarbon reservoir characterization, playing a critical role in improving subsurface structural interpretation and enhancing resource prediction accuracy. However, well log data are typically characterized by high dimensionality, strong nonlinearity, severe class imbalance, and asymmetric geological feature distributions, which significantly restrict the predictive accuracy and generalization capability of conventional machine learning methods. To address these challenges, this study proposes a symmetry-aware lithology classification framework based on a Hybrid Grey Wolf Optimizer–Genetic Algorithm optimized Extreme Gradient Boosting (GGA-XGB) model. The proposed framework establishes a symmetric collaborative optimization mechanism by integrating the global exploration capability of the Grey Wolf Optimizer (GWO) with the local exploitation ability of the Genetic Algorithm (GA), thereby achieving a balanced optimization strategy between exploration and exploitation. Specifically, GWO first performs coarse-grained global hyperparameter optimization of XGBoost to improve search efficiency and optimization stability, while GA subsequently refines the parameter space to further enhance local optimization accuracy. Experimental results on a multi-class well logging dataset demonstrate that the proposed method achieves outstanding classification performance, with precision, recall, and F1-score all reaching 0.9862. Compared with several conventional machine learning methods, the proposed GGA-XGB framework exhibits superior predictive accuracy. The symmetry-aware optimization strategy provides an effective solution for intelligent lithology prediction under complex geological conditions and offers both theoretical insights into symmetry-aware optimization mechanisms and practical value for intelligent geoscience and hydrocarbon exploration. Full article
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32 pages, 664 KB  
Article
Local Stability and Hopf Bifurcation in a Three-Dimensional Photocatalytic Microplastic Reactor Model with Adaptive Gain
by Sultan Selçuk Sütlü
Symmetry 2026, 18(8), 1390; https://doi.org/10.3390/sym18081390 - 18 Aug 2026
Viewed by 293
Abstract
Adaptive feedback can destabilize a loop that would be stable under any fixed gain, so the speed at which the gain adapts is itself a design parameter. We study this effect in a minimal three-dimensional model motivated by the photocatalytic degradation of microplastics: [...] Read more.
Adaptive feedback can destabilize a loop that would be stable under any fixed gain, so the speed at which the gain adapts is itself a design parameter. We study this effect in a minimal three-dimensional model motivated by the photocatalytic degradation of microplastics: a pollutant concentration is driven toward a setpoint by an ultraviolet (UV) actuator whose gain adapts online. The model has a single bilinear nonlinearity, so the local analysis can be carried out in closed form. Under an explicit feasibility condition, the system has a unique positive equilibrium. The Routh–Hurwitz criterion shows that this equilibrium is locally asymptotically stable below an explicit critical adaptation speed κc and unstable above it. At κ=κc, a purely imaginary eigenvalue pair crosses the imaginary axis transversally, and a Hopf bifurcation occurs, with an explicit onset frequency. The first Lyapunov coefficient is computed in closed form; it separates a supercritical onset, for well-damped actuators, from a subcritical onset with hysteresis, for weakly damped actuators. Numerical experiments confirm the predicted limit cycle and the classification. All the stability results established here are local. Full article
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23 pages, 8896 KB  
Article
Cluster Resource Load Prediction Method Based on Temporal-Feature Attention and Dynamic Stacking
by Qiaoyan Zhang, Kaijun Wu and Chenshuai Bai
Symmetry 2026, 18(8), 1389; https://doi.org/10.3390/sym18081389 - 18 Aug 2026
Viewed by 234
Abstract
Accurate prediction of computing-resource workloads is important for capacity planning, overload warning, and intelligent system management. Large-scale computing systems exhibit complex temporal fluctuations, sudden variations, and multi-resource coupling characteristics, making accurate workload prediction challenging. To address these challenges, this paper proposes a Hybrid [...] Read more.
Accurate prediction of computing-resource workloads is important for capacity planning, overload warning, and intelligent system management. Large-scale computing systems exhibit complex temporal fluctuations, sudden variations, and multi-resource coupling characteristics, making accurate workload prediction challenging. To address these challenges, this paper proposes a Hybrid Temporal-Feature Attention enhanced Multi-task Stacking model (HTAM-Stack) for multivariate cluster workload forecasting. First, a Temporal-Feature Hybrid Attention (TFHA) module is designed to jointly capture temporal dependencies and cross-resource feature interactions, enabling adaptive extraction of critical temporal patterns and important resource characteristics. Second, a Multi-Task Learning (MTL) framework is introduced to simultaneously predict CPU and Memory workloads by exploiting the correlations among heterogeneous resource variables. Furthermore, a Dynamic Stacking (DS) mechanism is developed to adaptively adjust the contributions of heterogeneous base learners through a weight generation network, and a Residual Corrector (RC) is incorporated to further enhance prediction robustness. Extensive experiments conducted on two widely used public cluster workload datasets, including Google Cluster Trace and Alibaba Cluster Trace, demonstrate that HTAM-Stack achieves competitive prediction performance under complex and dynamic workload conditions. The proposed model achieves MAE values of 0.0012 and 0.0010, RMSE values of 0.0031 and 0.0027, MAPE values of 0.20% and 0.16%, and R2 values of 0.9715 and 0.9782 on the two datasets, respectively. Moreover, HTAM-Stack requires only 3.20 ms inference time with 8.60 M parameters, achieving a favorable balance between prediction accuracy and computational efficiency. The results validate the general effectiveness of the proposed framework on public cluster workload benchmarks rather than its direct applicability to railway IT systems. Because no representative railway workload dataset was available, railway IT is discussed only as a potential application context that requires domain-specific validation. Full article
(This article belongs to the Section A: Computer Science)
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11 pages, 831 KB  
Article
Selective Reorganization of Reactive Gait Control: Interpreting Repeated Gait Perturbations Within the Framework of Locomotor Symmetry
by Rafał Borkowski and Michalina Błażkiewicz
Symmetry 2026, 18(8), 1388; https://doi.org/10.3390/sym18081388 - 18 Aug 2026
Viewed by 244
Abstract
Maintaining stability during walking requires rapid reactive adjustments to unexpected perturbations. Although repeated perturbations are known to induce locomotor adaptations, it remains unclear whether these changes reflect a generalized habituation of the locomotor system or selective modifications of specific biomechanical mechanisms. The aim [...] Read more.
Maintaining stability during walking requires rapid reactive adjustments to unexpected perturbations. Although repeated perturbations are known to induce locomotor adaptations, it remains unclear whether these changes reflect a generalized habituation of the locomotor system or selective modifications of specific biomechanical mechanisms. The aim of this study was to investigate changes in lower-limb kinematics, joint torques, and ground reaction force amplitudes during five consecutive treadmill-induced perturbations applied during the pre-swing phase of gait. Twenty-one healthy young women walked on an instrumented split-belt treadmill while five unilateral perturbations were applied to the left belt. For each perturbation, amplitudes of ankle, knee, and hip joint angles, joint torques, and ground reaction force components were calculated. Differences across perturbations were evaluated using Friedman repeated-measures analysis of variance followed by Bonferroni-corrected Wilcoxon tests. Significant effects of perturbation number were observed for hip joint angle amplitude, ankle joint torque amplitude, and anterior–posterior ground reaction force amplitude, whereas a weaker overall effect was detected for vertical ground reaction force amplitude. Hip angle amplitude decreased during later perturbations, whereas ankle torque and anterior–posterior ground reaction force amplitudes increased. No significant changes were found for knee and ankle joint angles, hip and knee joint torques, or mediolateral ground reaction force amplitude. These findings are consistent with the concept of locomotor symmetry as a theoretical framework for interpreting adaptive locomotor responses rather than as a directly measured outcome. Full article
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24 pages, 3596 KB  
Article
A Collaborative Multi-Compression Acceleration Mechanism for Neural Networks in Keyword Spotting
by Junbang Jiang, Rui Pu, Jin Li and Man Zhu
Symmetry 2026, 18(8), 1387; https://doi.org/10.3390/sym18081387 - 18 Aug 2026
Viewed by 255
Abstract
To address the large model size, high computational cost, and limited deployment resources of keyword spotting models on edge platforms, this study proposes a collaborative multi-compression framework for lightweight deployment. Built on LiteKWS-Net, an attention-enhanced 2-D convolutional backbone, the framework combines adaptive importance-aware [...] Read more.
To address the large model size, high computational cost, and limited deployment resources of keyword spotting models on edge platforms, this study proposes a collaborative multi-compression framework for lightweight deployment. Built on LiteKWS-Net, an attention-enhanced 2-D convolutional backbone, the framework combines adaptive importance-aware structured pruning, mixed-precision quantization, and quantization-aware multi-stage knowledge distillation. The retrained teacher reaches 97.90% (mean, 100,813 parameters, 0.385 MiB). MPDQ reaches 95.53 ± 1.16% at 8.27× theoretical weight compression. AIASP reaches 97.59% at a 30% target and 43.9% realized sparsity. The final joint model reaches 96.82% and, under ideal packed sparse mixed-precision storage, has a 51.55× theoretical weight-compression factor relative to the FP32 teacher; sparse-index overhead is excluded. On a Jetson Nano, the TensorRT FP16 network-body benchmark reports 2.86 ms latency and 0.69 mJ per inference. Full article
(This article belongs to the Section A: Computer Science)
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38 pages, 706 KB  
Article
Prompt Sensitivity Under Semantic Perturbations in CLIP-Family Models for Zero-Shot Classroom Behavior Analysis
by Yan Ma, Lizhuo Zhang and Xinjie Wu
Symmetry 2026, 18(8), 1386; https://doi.org/10.3390/sym18081386 - 17 Aug 2026
Viewed by 245
Abstract
Vision–language foundation models such as CLIP are increasingly used for zero-shot behavior recognition, yet their robustness to prompt variations remains poorly understood. This paper investigates prompt sensitivity as a critical robustness concern in CLIP-family models for zero-shot classroom behavior analysis, treating prompt wording [...] Read more.
Vision–language foundation models such as CLIP are increasingly used for zero-shot behavior recognition, yet their robustness to prompt variations remains poorly understood. This paper investigates prompt sensitivity as a critical robustness concern in CLIP-family models for zero-shot classroom behavior analysis, treating prompt wording as a controlled semantic perturbation. Five representative vision–language models (CLIP/OpenAI, OpenCLIP/LAION, SigLIP2, EVA02-CLIP, and DFN-CLIP) are evaluated on three public classroom behavior benchmarks under a strict symmetric protocol. We compare four generic prompt strategies with a training-free Class-Aware Prompt Ensemble (CAPE). Results show that minor prompt changes can cause catastrophic performance degradation. On SigLIP2, an alternative wording of CAPE reduces Hit@1 on TeacherBehavior from 85.5% to 31.4%, a 54.1 percentage-point drop that exceeds the differences between model backbones. Across all five models, action-oriented prompts improve Hit@1 by up to 54 percentage points compared with label-only prompts. We further demonstrate that the apparent superiority of zero-shot CLIP over supervised linear probes largely arises from metric asymmetry. While zero-shot methods achieve higher Hit@1, they consistently underperform linear probes in multi-label evaluation (Sample-F1: 60–66% vs. 88–90%; Macro-F1: 49–60% vs. 68–78%). Bootstrap confidence intervals and paired-bootstrap significance tests further show that several reported performance differences are not statistically significant. These findings reveal prompt sensitivity as a fundamental deployment risk for vision–language foundation models in domain-specific behavior analysis. Prompt variations involving only a few words can silently undermine recognition performance while remaining hidden by conventional evaluation metrics. We therefore recommend that future benchmark studies report prompt configurations, multi-label F1 scores, and uncertainty estimates alongside headline Hit@1 to provide a more complete and reliable assessment of model capability. Full article
(This article belongs to the Special Issue Applications Based on Symmetry in Adversarial Machine Learning)
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136 pages, 1305 KB  
Article
Statistical Learning Theory for Inverse-Probability-Weighted Conditional U-Statistics via Delta Sequences Under Functional Missing-at-Random Models
by Salim Bouzebda
Symmetry 2026, 18(8), 1385; https://doi.org/10.3390/sym18081385 - 17 Aug 2026
Viewed by 196
Abstract
This paper develops a unified asymptotic theory for inverse-probability-weighted conditional U-statistics of arbitrary fixed order in the presence of missing-at-random responses and infinite-dimensional functional covariates. The target is a conditional higher-order functional generated by a measurable response kernel and evaluated locally on a [...] Read more.
This paper develops a unified asymptotic theory for inverse-probability-weighted conditional U-statistics of arbitrary fixed order in the presence of missing-at-random responses and infinite-dimensional functional covariates. The target is a conditional higher-order functional generated by a measurable response kernel and evaluated locally on a separable Banach space. Localization is formulated through delta sequences, providing a common framework for kernel, partition, regressogram, orthogonal series, and related smoothing procedures without recourse to finite-dimensional density arguments. For bounded kernels, we establish uniform almost-complete convergence over pseudo-compact functional domains and obtain a sharp decomposition into deterministic localization bias and stochastic fluctuation. The latter is governed by the localized-kernel variance, the envelope of the delta sequence, the metric complexity of the indexing domain, and the small-ball concentration of the functional covariate. Unbounded kernels are treated under explicit weighted moment, truncation, and summability conditions. The feasible theory quantifies the additional perturbation induced by estimating the propensity score and identifies conditions under which this first-stage uncertainty is asymptotically negligible. Pointwise distributional theory is derived through a denominator linearization combined with the Hoeffding decomposition of the centered localized kernel. The Gaussian limit is driven by the first projection, while the higher-order canonical components are shown to be negligible under explicit local-mass, moment, and noncancellation assumptions. This yields oracle-equivalent feasible inference, a consistent first-projection variance estimator, and asymptotically valid studentized confidence intervals. A finite-grid adaptive comparison principle is also developed for data-driven resolution selection. The scope of the theory is illustrated through conditional rank functionals, discrimination with incomplete labels, metric-learning criteria, and functional prediction. Synthetic and semi-synthetic studies based on functional classification, phoneme log-periodograms, and growth trajectories document the finite-sample interaction between covariate-dependent label observation, local information loss, propensity estimation, and inverse-weighting variance. Full article
(This article belongs to the Section B: Mathematics)
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22 pages, 5385 KB  
Article
Comparative Study on Seismic Performance Between Improved Joint with Steel-Strand-Embedded Anchorage and SCOPE Joint
by Suguo Wang, Yulin Chen, Binghui Fan, Yongjie Xu and I Cheang
Symmetry 2026, 18(8), 1384; https://doi.org/10.3390/sym18081384 - 17 Aug 2026
Viewed by 232
Abstract
The structure comprising precast prestressed concrete components (SCOPE joint) is widely used in prefabricated buildings. For this type of joint, insufficient anchorage of U-shaped reinforcing bars can lead to premature core failure. To address this, finite element models of SCOPE joints are developed [...] Read more.
The structure comprising precast prestressed concrete components (SCOPE joint) is widely used in prefabricated buildings. For this type of joint, insufficient anchorage of U-shaped reinforcing bars can lead to premature core failure. To address this, finite element models of SCOPE joints are developed in ABAQUS for parametric and mechanical analysis of U-shaped bars, and an improved joint with steel-strand-embedded anchorage is proposed. Comparisons of seismic performance and frame performance are conducted. The results indicate that in the conventional SCOPE joint, the strain of the U-shaped reinforcing bars concentrates within 100–150 mm outside the column, and the anchorage effect of the vertical segments is not mobilized; the yield penetration phenomenon further aggravates bond failure. In the improved joint, steel strands are anchored into the core and lapped in opposite directions, leading to a superior failure mechanism and plastic hinge formation sequence, enhanced capacity and ductility, and better conforming to the strong-joint–weak-component principle. This research offers a theoretical basis and detailing reference for seismic optimization of the SCOPE system. Full article
(This article belongs to the Special Issue Symmetry and Finite Element Method in Civil Engineering, 2nd Edition)
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25 pages, 4658 KB  
Article
CCFC: Bridging Federated Clustering and Contrastive Learning
by Jing Liu, Jie Yan and Zhong-Yuan Zhang
Symmetry 2026, 18(8), 1383; https://doi.org/10.3390/sym18081383 - 17 Aug 2026
Viewed by 181
Abstract
Federated clustering, an essential extension of centralized clustering for federated scenarios, enables multiple data-holding clients to collaboratively group data while keeping their data locally. In centralized scenarios, clustering driven by representation learning has made significant advancements in handling high-dimensional complex data. However, the [...] Read more.
Federated clustering, an essential extension of centralized clustering for federated scenarios, enables multiple data-holding clients to collaboratively group data while keeping their data locally. In centralized scenarios, clustering driven by representation learning has made significant advancements in handling high-dimensional complex data. However, the combination of federated clustering and representation learning remains underexplored. To bridge this gap, we first tailor a cluster-contrastive model for learning clustering-friendly representations. Then, we harness this model as the foundation for proposing a new federated clustering method, named cluster-contrastive federated clustering (CCFC). Benefiting from representation learning, the clustering performance of CCFC even doublesthat of the best baseline methods in some cases. Compared to the most related baseline, the benefit results in substantial NMI score improvements of up to 0.41 on the most conspicuous case. Moreover, CCFC also shows superior performance in handling device failures from a practical viewpoint. Full article
(This article belongs to the Section A: Computer Science)
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32 pages, 6635 KB  
Article
Design of a Risk Assessment Model for Grassroots Agricultural Product Quality and Safety Based on Bayesian Networks and Evidential Reasoning
by Yijia Qiu and Yuheng Li
Symmetry 2026, 18(8), 1382; https://doi.org/10.3390/sym18081382 - 17 Aug 2026
Viewed by 214
Abstract
The quality and safety supervision of agricultural products at the grassroots level has long faced the triple superposition dilemma of small-sample sampling, multi-source evidence conflict, and risk chain evolution. Although existing data-driven models have considerable accuracy, they are difficult to leverage for intervention [...] Read more.
The quality and safety supervision of agricultural products at the grassroots level has long faced the triple superposition dilemma of small-sample sampling, multi-source evidence conflict, and risk chain evolution. Although existing data-driven models have considerable accuracy, they are difficult to leverage for intervention decisions, and the simple serial connection of traditional Bayesian networks and evidence theory cannot respond to dynamic scenarios. Aiming at this research gap, this paper constructs a dynamic risk assessment model, CIBE-DR, that deeply couples Bayesian networks with evidential reasoning. It contains three core innovations. First, the structure learning method of the causally identifiable Bayesian network embeds a graded do-calculus identifiability score covering both back-door and front-door criteria into the BDeu scoring function and combines this reward with an expert-prior divergence penalty that breaks Markov equivalence so as to realize the transition from relevance modeling to intervention decision modeling. Second, the conflict-aware adaptive evidence synthesis rule orthogonally decomposes multi-source conflict into an epistemic component and an ontological component, which are modeled respectively by Tsallis belief entropy and abductive inference over a discrete twenty-seven-point heterogeneity hypothesis space and are then fused under a reparameterized Dempster–Yager interpolation in which the two endpoints recover the two named rules under a single consistent interpretation. Third, the bidirectional closed-loop coupling mechanism between BN and ER realizes the mutual calibration between the conditional probability table and the evidence credibility prior under a Lyapunov monotone descent argument with the explicit Lipschitz bound Lθ ≤ 0.028 < 1, endowing the model with time-varying self-correction ability. Based on experiments on 156,847 sampling samples from counties and townships in East China, Central China, and Southwest China from 2021 to 2024, the proposed method achieved the best value in six of the seven evaluation indicators, with a minority recall of 0.864 ± 0.014, an intervention effect estimation error of 0.063 ± 0.005, and a dynamic response delay of 2.8 ± 0.3 days, significantly ahead of eleven mainstream baselines under the McNemar test on classification (p < 0.001) and the Wilcoxon signed-rank test on intervention-effect estimation (p < 0.001). The only indicator on which CIBE-DR does not lead is overall accuracy, which is 0.002 lower than that of Transformer; this difference does not reach statistical significance under the McNemar test (p = 0.32) and does not weaken the value of grassroots supervision in the strong-imbalance scenario where the positive rate is only 1.04%. The robustness advantage of the model is particularly prominent in the scenarios of sparse data, adversarial perturbation, and prior-graph incompleteness, and the intervention-effect estimates were additionally validated against two post-2022 policy interventions with absolute deviations of 1.4 and 1.2 percentage points respectively. These results verify the product gain and grassroots deployability of the three mechanisms. Full article
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21 pages, 2437 KB  
Article
Class-Wise Reliability Fusion of Multimodal Driver Responses for Weather-Condition Classification
by Yi Tian, Jianping Hu, Wen Dong, Binhe Yang, Jialin Hu, Yuting Liu and Yu Ding
Symmetry 2026, 18(8), 1381; https://doi.org/10.3390/sym18081381 - 17 Aug 2026
Viewed by 254
Abstract
Multimodal classification often suffers from recognition reliability that is asymmetric across data sources and classes, and its evaluation is frequently complicated by information leakage from overlapping sampling windows. This paper proposes a class-wise-optimized reliability fusion model (CORF), using the classification of multimodal driver [...] Read more.
Multimodal classification often suffers from recognition reliability that is asymmetric across data sources and classes, and its evaluation is frequently complicated by information leakage from overlapping sampling windows. This paper proposes a class-wise-optimized reliability fusion model (CORF), using the classification of multimodal driver responses under four controlled weather conditions as a validation case. Electroencephalogram, electrocardiogram, and vehicle signals were recorded for 30 participants, and two leakage-free protocols were adopted: leave-one-subject-out (LOSO) cross-validation and a purged temporal-block cross-validation, with all preprocessing, probability calibration, and weight estimation refitted inside every fold. Under LOSO, CORF achieved an accuracy of 0.356 (chance = 0.25) and a 0.630 macro-average area under the curve (AUC), whereas the originally used random overlapping-window split inflated accuracy to 0.92; the fused adverse-class probability discriminated adverse- from clear-weather windows with an AUC of 0.73. The fusion retains a symmetric reliability-weighting structure across classes, and its moderate symmetry-breaking difficulty emphasis significantly improved the most challenging adverse-weather class over equal-weight fusion (snow F1 +9.8 percentage points, Holm-corrected p < 0.001) at a small, statistically non-significant overall accuracy cost. CORF therefore provides a probability-calibrated, interpretable mechanism for controlling class-specific performance tradeoffs, highlighting the necessity of leakage-free validation in multimodal physiological classification. Full article
(This article belongs to the Special Issue Symmetry or Asymmetry in Machine Learning)
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27 pages, 423 KB  
Article
Likelihood and Bayesian Inference for Two Lomax Populations Under Balanced Joint Adaptive Progressive Type-II Censoring with an Exponential Ridge
by Zeyu Zou, Ge Fang, Yinuo Dong and Wenhao Gui
Symmetry 2026, 18(8), 1380; https://doi.org/10.3390/sym18081380 - 16 Aug 2026
Viewed by 198
Abstract
Balanced joint adaptive progressive Type-II censoring (B-JAPC) is developed for two independent Lomax populations with a common shape parameter and population-specific scale parameters. Classical and Bayesian inference methods are constructed for the model parameters, survival functions, and hazard rates. To address the exponential [...] Read more.
Balanced joint adaptive progressive Type-II censoring (B-JAPC) is developed for two independent Lomax populations with a common shape parameter and population-specific scale parameters. Classical and Bayesian inference methods are constructed for the model parameters, survival functions, and hazard rates. To address the exponential scale–shape ridge where standard maximum likelihood estimates often fail to converge, a constrained maximum likelihood estimator (CMLE) with parametric bootstrap confidence intervals is established. A partially conjugate Bayesian framework under a Beta–Gamma prior is also implemented via a Metropolis-within-Gibbs algorithm. Monte Carlo simulations demonstrate that the proposed adaptive design substantially reduces the mean test duration compared to non-adaptive schemes while maintaining high inferential accuracy. The methodology is successfully applied to randomized cloud-seeding rainfall data, confirming its practical utility and quantifying the sensitivity of lifetime inference to shape regularization. Full article
(This article belongs to the Topic Statistics and Data Science)
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33 pages, 888 KB  
Article
EC-MHS: Equivalence-Based Compression for Minimal Hitting Set Enumeration in Model-Based Diagnosis
by Shisong Lu, Jianzhong Tang, Chengcheng Xia, Zhenhui Li and Yabo Liu
Symmetry 2026, 18(8), 1379; https://doi.org/10.3390/sym18081379 - 16 Aug 2026
Viewed by 211
Abstract
Enumerating all inclusion-minimal hitting sets is a fundamental combinatorial task that arises in areas such as model-based diagnosis, hypergraph dualization, and data mining. In conflict-driven model-based diagnosis, exact enumeration becomes a computational bottleneck when both the component set and the diagnosis family are [...] Read more.
Enumerating all inclusion-minimal hitting sets is a fundamental combinatorial task that arises in areas such as model-based diagnosis, hypergraph dualization, and data mining. In conflict-driven model-based diagnosis, exact enumeration becomes a computational bottleneck when both the component set and the diagnosis family are large. Existing exact methods mainly exploit conflict reuse or conflict-family structure, while component equivalence has rarely been integrated into search, output representation, and partition maintenance as a unified mechanism. This paper presents EC-MHS, an equivalence-aware framework for minimal hitting set enumeration in diagnosis. It combines Static Twin Compression (STC), which exploits coverage-signature symmetry among components to reduce the representative search space before enumeration, Dynamic Twin Compression (DTC) to merge candidates whose residual-state symmetry renders them interchangeable during search, a Compact Diagnosis Family Representation (CDFR) for exact weight-based aggregation and lossless class-wise expansion at the STC level, and iSTC to maintain the static partition under monotonic conflict addition. Experiments on ISCAS-85 benchmark circuits show that static equivalence appears in at least 96% of the dataset instances and that STC reduces the number of search candidates by 69–87% before search. On redundancy-rich benchmark instances, DTC reduces runtime by up to 75%, and iSTC maintains the STC partition 24 times faster than a full rebuild. Full article
(This article belongs to the Section A: Computer Science)
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