Symmetry doi: 10.3390/sym18111910

Authors: Yingjie Wang Kevin Kabera Njuguna Jong-Dar Yau

Railway culverts and their transition zones constitute mechanically heterogeneous systems in which abrupt variations in structural and geotechnical stiffness disrupt the symmetry of train–track–soil–structure interaction (TTSSI). The resulting stiffness asymmetry alters load transfer within the TTSSI system and contributes to dynamic amplification, differential settlement, vibration concentration, and progressive track deterioration. Although substantial research has been conducted on railway transition zones, a systematic synthesis from a symmetry-oriented perspective remains lacking. This review critically examines studies published between 2000 and 2026 on railway culvert dynamics, transition-zone design, TTSSI mechanisms, numerical modeling, field monitoring, international design standards, and emerging digital-twin technologies. Particular attention is given to the influence of stiffness asymmetry on load-transfer mechanisms, vibration propagation, soil–structure interaction, and long-term infrastructure performance. Numerical approaches ranging from simplified analytical formulations to fully coupled three-dimensional TTSSI models are assessed alongside experimental evidence and field observations. The review demonstrates that the dynamic behavior of railway transition zones is fundamentally governed by stiffness discontinuities that break the mechanical symmetry between embankments and buried structures. Despite significant advances in vehicle–track interaction modeling and digital monitoring, important challenges remain in nonlinear soil behavior, hydro-mechanical coupling, resilience quantification, and long-term field validation. To address these limitations, a system-oriented digital-twin framework is proposed that integrates sensing, data assimilation, physics-based simulation, and predictive maintenance. The framework provides a pathway toward resilient, intelligent, and data-driven management of railway culvert transition zones while identifying key priorities for future research.

Symmetry doi: 10.3390/sym18111909

Authors: Shayea Aldossari Sami H. Saif

Let R=GR(p2,m) where q=pm and p≠3. We classify and enumerate the λ-constacyclic codes of length 3ps over R, derive their Euclidean dual codes, and characterize the self-dual and self-orthogonal subfamilies. The classification is based on the symmetries of the constacyclic shift, the cube class of λ, and the factorization of x3ps−λ. Explicit constituent descriptions for cube and noncube multipliers are obtained from that of prime-power ideals. The characteristic-p2 carry differentiates chain-ring constituents from cyclic algebras over unramified Galois-ring extensions. The reciprocal symmetries pair the dual codes, and the quadratic part is endowed with Galois-twisted cyclic duality. We also enumerate self-orthogonal cyclic codes via affine systems with explicit ranks and solvability conditions. These results give generators, cardinalities, and enumeration formulas in all multiplier cases; the only count not obtained in closed form is the number of nested pairs of ideals in the split involutory case.

Symmetry doi: 10.3390/sym18111908

Authors: Dianqiang Li Anquan Liu Xinyue Miao Yuanyuan Wei

This paper investigates the bipartite output feedback tracking control problem for stochastic nonlinear heterogeneous leader-following multi-agent systems under signed communication graphs, where multiplicative measurement noise exists in information transmission and the state of each agent is unmeasurable. First, based on the structural balance property of signed graphs, the followers’ state observers and distributed leader state observers are constructed. By the certainty equivalence principle and nonlinear output regulation theory, we propose distributed bipartite output-feedback control laws. Sufficient conditions relying on graph connectivity, noise intensity and Lipschitz constants of nonlinear terms are derived to guarantee mean-square bounded bipartite output tracking. It is shown that mean-square bipartite output tracking can be achieved if the additive diffusion noises of followers vanish. Finally, numerical simulations are provided to verify the effectiveness of the proposed distributed control laws.

Symmetry doi: 10.3390/sym18111907

Authors: Henrry Revollo Maria T. Veliz Sergio Curilef

In this article, we introduce a viewpoint based on structural correlations described by the pair distribution function, yielding an effective interaction coefficient that influences the critical response and conveys interacting-particle potentials to the critical and transport properties. We use ab initio model data and fit it with a Lennard-Jones (L-J) potential with Gaussian corrections. We evaluate seven ab initio-based models (CCSD(T), Dunning basis sets) for neon and argon to assess basis-set sensitivity. According to the CCSD(T) models, the critical temperature is estimated to be between 31.8 K and 55.1 K for neon and between 124.8 K and 179.7 K for argon. Molecular dynamics simulations describe argon, while neon is not fully described because quantum effects are neglected in these calculations.

Symmetry doi: 10.3390/sym18111906

Authors: Bin Shi Yongkang Pi Haonan Yang Jingke Yan Bingyan Chen Tong Yang

Accurate crack segmentation is important for intelligent infrastructure inspection and has potential applications in railway infrastructure monitoring. However, cracks usually exhibit thin, elongated, irregular, and spatially asymmetric morphologies, while weak boundaries and complex surface textures further increase segmentation difficulty. To address these challenges, this paper proposes HLGCrack, a lightweight hierarchical CNN-Mamba-attention network for efficient crack segmentation. The network adopts a stage-wise representation strategy in which shallow asymmetric convolution and large-kernel modeling enhance directional edge responses and local crack structures, while deeper visual state-space and local–global attention modules capture long-range dependencies and contextual information. A Lightweight Progressive Fusion decoder progressively aggregates multi-level features to recover fine crack boundaries with low computational cost, and BCE, Dice, and clDice losses are jointly employed to improve region overlap and structural continuity. HLGCrack is evaluated on CamCrack789 and four additional public pavement and structural crack datasets covering diverse crack morphologies, surface textures, and interference conditions. On CamCrack789, it achieves Dice and IoU scores of 0.860 and 0.755, respectively, with only 3.53 M parameters and 4.03 G FLOPs. The results demonstrate its effectiveness and robustness for general crack segmentation and provide a basis for subsequent adaptation to railway-specific inspection scenarios.

Symmetry doi: 10.3390/sym18111905

Authors: Piotr Jastrzȩbski Adam Lecko

This paper continues our earlier work, in which the differential evolution algorithm was applied to coefficient problems in Geometric Function Theory, and the sharp 1/8 bound of the fourth Hankel determinant detH4,1(f) was identified numerically in the class S* of starlike functions, i.e., of analytic univalent functions f in the unit disk D normalized by f(0)=0 and f′(0)=1, for which f(D) is starlike with respect to the origin. Here, the approach is extended to the fifth and sixth Hankel determinants detH5,1(f) and detH6,1(f). Using finite-dimensional reduction in the extremal problem provided by the Hummel–Sakaguchi theorem on support points of the Carathéodory class, we perform a fully documented and reproducible differential evolution search. In all independent runs, the values found agree, to within 10−14, with 16/625 and 1/243, respectively, and all maximizers found coincide, up to rotation, with the q-fold symmetric Koebe function fq(z)=z(1−zq)−2/q, q=5,6. We prove that |detHq,1(fq)|=(2/q)q−1 for every q∈N so that these values are attained in S*. Combining the numerical computations with the known sharp bounds for q≤3, we conjecture that |detHq,1(f)|≤(2/q)q−1 for all f∈S* and q=4,5,6, with equality for fq and its rotations. In the whole class S*, these upper bounds are supported by numerical computations but are not proved; they are stated explicitly as conjectures. We also show that the pattern does not extend to all orders: For every q≥10, the function fq−1 satisfies |detHq,1(fq−1)|=2q−2(q−3)/(q−1)q>(2/q)q−1 so that fq is not extremal for q≥10 and the general inequality |detHq,1(f)|≤(2/q)q−1, q∈N, is false.

Symmetry doi: 10.3390/sym18111904

Authors: Antonino Del Popolo

We test whether a genuinely two-degree-of-freedom Extended Cuscuton can raise the late-time Hubble constant by transiently modifying the pre-recombination expansion history without spoiling the cosmic microwave background (CMB). Using CLASS 3.4.0, we first show that a two-window expansion history can match H0=72kms−1Mpc−1 and the acoustic angle at the background level but already leaves several-percent TT/EE residuals. We then reconstruct this target within the luminal Extended-Cuscuton subclass (v4=MPl2/2, transient v3(ϕ)), implementing the nondynamical scalar sector as a radiation-inclusive algebraic D=0 constraint rather than as an extra evolution equation, and we show analytically that the original, minimal Cuscuton could never have supplied the required transient in the first place. For a single recombination-centered braiding window, the perturbation sector amplifies rather than compensates for the background mismatch, to a combined TT/EE screening residual of ∼100% (vs. ∼8% background-only) for both signs of the braiding amplitude. Widening this window, or replacing it with two windows aligned to the background target’s own bumps, brings the residual down to ∼81% in the best completed case—still far from the background-only value—before the scan is stopped by a pole in the algebraically solved perturbation coefficients, traced to one super-horizon mode and shown not to be an integrator artifact; cases beyond this point remain unresolved rather than excluded. We conclude that the transient Extended-Cuscuton constructions tested here, minimal and extended alike, do not provide a viable resolution of the Hubble tension.

Symmetry doi: 10.3390/sym18111903

Authors: Chao Xi Long Chen Chan Wang

Hyperspectral image classification (HSI) faces substantial class-membership uncertainty in mixed-pixel and spectrally confused scenes. The existing Mamba-based methods can model long-range spatial–spectral dependencies with linear complexity, but they usually rely on deterministic feature propagation and do not explicitly represent graded pixel membership during the forward pass. To address this limitation, this paper proposes Fuzzy-MambaHSI, a novel hyperspectral classification framework that embeds learnable fuzzy neural networks into a full-image dense-prediction Mamba backbone. The framework contains three key designs: (1) a fuzzy token perturbation module, which applies soft rule-weighted additive perturbations to tokens at the input of the spatial scan; (2) a fuzzy spatial–spectral fusion module, which replaces global scalar fusion with pixel-wise fuzzy neural network inference; and (3) a training stabilization strategy composed of linear warm-up and rule-center diversity regularization. Experiments with the same settings show that Fuzzy-MambaHSI improves the MambaHSI baseline by 0.96 and 2.92 % in overall accuracy on Pavia University and WHU-Hi-HanChuan, respectively, and yields lower variance in the agricultural scene with stronger spectral confusion. A rule activation analysis shows that different spatial fuzzy rules focus more strongly on homogeneous regions and high-frequency boundary regions, revealing observable differences in pixel membership during the forward pass.

Symmetry doi: 10.3390/sym18111902

Authors: Chenjie Zhou Xinyun Wu Mao Luo Caiquan Xiong Yuanzhi Ke

The Minimum Hitting Set (MinHS) problem is a classic NP-hard problem in combinatorial optimization, widely applied across fields such as artificial intelligence diagnosis, bioinformatics, and network monitoring. This paper proposes a local search algorithm with Dual-evaluation mode, named DemHS (Dual-evaluation mode search algorithm), tailored for large-scale hitting set instances. The evaluation employs two types of functions: strong and weak. Strong evaluation accurately calculates the exchange gain by introducing a cross-correction term within the local neighborhood defined by an inserted vertex; meanwhile, weak evaluation quickly estimates the gain through global random sampling to broaden the search scope. These two functions synergistically guide the search process. Furthermore, we introduce an age strategy to break ties and enhance the diversity of the search path. When no improvements are made for extended iterations, a large-scale random perturbation is executed to help the algorithm escape local stagnation. Comparative experiments were conducted using 200 public hitting set instances (100 metaheuristic and 100 exact cases) from PACE-2025. The results show that, in the metaheuristic case group, DemHS improves the record on 62 instances and in the precise case group, DemHS obtains optimal solutions across all tested instances. The ablation studies demonstrate a significant positive gain from the dual-evaluation neighborhood structure on optimization results.

Symmetry doi: 10.3390/sym18111900

Authors: Shujian Li Yonghui Huang Menglai Wang Bingqian Sun Changtao Wei Jiantao Pang

Blasting in open-pit mines can disturb permanent underground structures. This study examines an underground water sump in medium–hard dolomite at Kunyang Phosphate Mine. A detailed three-dimensional model was built in ANSYS Workbench. The Drucker–Prager (D-P) yield criterion was used. Measured acceleration time histories were applied throughout the model in three directions. Six cases were identified by representative peak vibration velocities of 6.4–27.1 cm/s. Transient dynamic analyses examined stress, displacement, vibration velocity and local safety reserve. High stresses occurred at junctions of the roof and walls, bottom corners and sump–shaft connections. The peak equivalent stress increased almost linearly from 8.08 to 12.90 MPa. The maximum principal stress showed local tension and compression. Its tensile peak increased from 0.72 to 3.56 MPa. This was below the static tensile reference of 9.44 MPa for intact laboratory specimens. The minimum principal stress was mainly compressive. The peak compressive stress in the deep surrounding rock reached −15.10 MPa. Positive displacement peaks increased from 0.69 to 2.51 mm. Negative peaks changed from −0.80 to −2.71 mm. These values describe transient model responses. Positive velocity peaks increased from 6.36 to 26.74 cm/s. Cases P2–P6 exceeded the project control reference of 8.5 cm/s. The local indicator FS was greater than one for the extracted states at all nine monitoring locations. At high vibration levels, FS was about 1.25 at the arch baseline and the middle of the bottom side wall. These locations had relatively low reserves. The results provide a quantitative basis for blast parameter optimisation and vibration control for the water sump.

Symmetry doi: 10.3390/sym18111901

Authors: Leonardo Domenichelli Giada Sagnella Federica Sinibaldi Almerinda Di Venere Luisa Di Paola

Phosphofructokinase-1 (PFK1) is a key regulatory enzyme of glycolysis, controlling the irreversible conversion of fructose-6-phosphate to fructose-1,6-bisphosphate. Its activity is finely tuned by allosteric effectors such as ATP, ADP, and fructose-2,6-bisphosphate. In this study, starting from recently resolved cryo-EM structures of the human liver isoform of PFK1 in both its active (R) and inactive (T) states, we analyze the residue-level interactions adopting a network-based approach (Protein Contact Network). We demonstrate that the two states exhibit distinct inter-subunit communication patterns, participation coefficients, betweenness centrality and symmetry. These features suggest a reorganization of inter-subunit communication between the R and T states, characterized by a transition from localized, bottleneck-dominated communication in the T state to a more distributed and symmetric network in the R state. Our findings offer new insight into the structural logic underlying allosteric control in homo-tetrameric metabolic enzymes.

Symmetry doi: 10.3390/sym18111899

Authors: Min-Hee Lee Kyuseok Kim Youngjin Lee

Sleep quality is associated with brain development and cognition; however, its relationship with hemispheric cortical organization during late adolescence and early adulthood remains unclear. We examined the associations among subjective sleep quality, cortical thickness asymmetry, and fluid cognition in 100 participants using cross-sectional data from the Human Connectome Project–Development (aged 19.98 ± 1.15 years; 53% female). Sleep quality was assessed using the Pittsburgh Sleep Quality Index (PSQI) and cortical thickness lateralization indices (LIs) calculated for 34 homologous cortical regions. Regression models were adjusted for age, sex, body mass index, handedness score, education level, and global mean LI, with false discovery rate (FDR) correction. Poor sleepers had lower LIs in the entorhinal, medial orbitofrontal, parahippocampal, and insular cortices and the frontal and temporal poles (all FDR-corrected p < 0.05). Higher PSQI scores were associated with lower LIs in the entorhinal cortex, temporal pole, and insula (all FDR-corrected p < 0.05). No LI–fluid cognition associations were maintained after FDR correction. In a post hoc exploratory mediation analysis, a significant indirect effect on the entorhinal LI (β [95% confidence interval] = −0.705 [−0.873, −0.411], p = 0.006) was observed. These findings suggest that subjective sleep quality is associated with region-specific differences in cortical thickness asymmetry.

Symmetry doi: 10.3390/sym18111897

Authors: Xiaojie Hu Shujing Dong Xiaoping Huang Xuelai Li Lulu Sun Yuhang Yang

Transmission windows between resonance gaps restrict the useful bandwidth of open duct phononic crystals. We numerically compare two prescribed locations for an equal porous volume: compact blocks at the cavity roofs and an insert in an independent inter-cavity bridge. In the lossless-air-wall two-dimensional pressure-acoustic model, bridge placement increases the five-cell continuous 10 dB attenuation span from 0.51 to 0.67 kHz, a 32% increase relative to this cavity-top baseline. Matched 0.25 Hz scans give window minimum transmission losses of 0.61 and 15 dB, respectively. Direct constitutive integration at 1150 Hz gives porous dissipation fractions of 0.016 and 0.42 of incident power. Mesh and frequency refinement quantify numerical sensitivity. Separate three-dimensional wall-loss calculations give an 8.5 dB placement benefit at 1150 Hz and lower rejection at adjacent sampled frequencies; they do not establish a continuous three-dimensional bandwidth. Two-dimensional hydraulic screening predicts pressure drops of 0.033–0.17 Pa at mean velocities of 0.10–0.50 m s−1. The comparison identifies a geometry-specific effect of dissipation placement under a fixed material budget. Insert characterization, mounting effects and experimental performance remain to be established.

Symmetry doi: 10.3390/sym18111898

Authors: Danni Chen Baixin Gao Libang Wu

The Human Learning Optimization (HLO) algorithm is a binary metaheuristic algorithm that simulates human random learning, individual learning, and social learning processes. Owing to its simple structure and low computational cost, HLO has been widely applied to continuous optimization and machine-learning hyperparameter tuning. However, when applied to continuous optimization, the original HLO suffers from three major limitations: the Hamming cliff phenomenon associated with standard binary encoding, the limited source of knowledge for social learning, and an almost fixed learning probability. To address these issues, this study proposes a Gray-code and successful-memory human learning optimization algorithm based on a pretrained language model, termed LGSM-HLO. Specifically, the Pre-trained Language Model-Inspired Strategy (PLMS) treats elite encodings as a knowledge corpus and extracts shared encoding patterns through weighted pretraining, masked reconstruction, and online fine-tuning. The Gray-code Coarse-to-Fine Semantic Learning strategy (GCFSL) employs Gray coding to improve encoding-neighborhood consistency and dynamically adjusts the learning granularity throughout the evolutionary process. The Successful-History Differential Teacher Strategy (SHDTS) integrates historical successful parameters, high-quality individuals, and population differential information to construct personalized social teachers, while providing a Cauchy-based escape mechanism for stagnated individuals. Experiments on the CEC2017 (30-dimensional) and CEC2022 (10- and 20-dimensional) benchmark suites show that LGSM-HLO achieves superior mean performance and standard deviation on most functions compared with nine competitive algorithms. The Wilcoxon rank-sum test and Friedman rank test further confirm its overall superiority. Moreover, none of the three proposed strategies introduces additional objective-function evaluations, and the proposed algorithm retains the same dominant asymptotic computational complexity as the original HLO. Furthermore, an LGSM-HLO-RF model is developed by employing LGSM-HLO for joint hyperparameter optimization of a random forest. In the three-class prediction of higher-education student achievement, LGSM-HLO-RF outperforms the comparison algorithms in terms of Accuracy, Macro-F1, and Macro-Recall, demonstrating the strong transferability of LGSM-HLO from benchmark optimization to practical educational data-mining tasks.

Symmetry doi: 10.3390/sym18111896

Authors: Zhiqiang Li Yu Wu Mengji Shi Henghui Liu Shuting Xu

We formulate fixed-route replenishment scheduling for plant protection unmanned aerial vehicles (UAVs), jointly selecting replenishment timing, operation type, and station to minimize additional replenishment time. Resource resets invalidate the monotone-depletion premise of standard resource-constrained shortest-path methods; the two resources deplete asymmetrically (endurance throughout, pesticide only when spraying), and because joint or serial replenishments share a detour while the pesticide-type consistency constraint forces refills at type switches, the battery- and pesticide-side decisions cannot be separated. We develop event-graph dynamic programming (EGDP), which discretizes replenishment timings into event points and encodes the five replenishment types as arcs, reducing the joint decision to a shortest path solved by label-setting search with dominance and redundancy pruning. On 20 instances with four fields, EGDP’s total working times matched those of a same-grid mixed-integer linear programming (MILP) model within 10−6 min in 19 cases; in the remaining case, the MILP failed to prove optimality and was 0.07% worse, while EGDP was about 3069 times faster. Across 100 instances spanning five scales, EGDP reduced additional replenishment time by 10.9% relative to a greedy baseline; on 20 instances with six fields, the 0.5 min grid produced a mean deviation of 0.72% from the finest 0.05 min grid, with a runtime of 0.66 s, supporting pre-flight planning.

Symmetry doi: 10.3390/sym18111895

Authors: Dazhi Zhao Zherui Liu Li Chen

Large-scale urban traffic signal optimization presents substantial challenges arising from high-dimensional decision spaces, expensive microscopic simulations, and competing mobility and environmental objectives. This study formulates large-scale traffic signal timing as a high-dimensional bi-objective black-box optimization problem, in which average waiting time and total CO2 emissions are minimized simultaneously, thereby ensuring a symmetric and preference-neutral treatment of the two conflicting objectives without imposing predefined preference weights. To address the computational challenges, a Pareto–Hypervolume Guided Trust-Region Bayesian Optimization (PHV-TuRBO) method is proposed. The framework integrates Pareto-guided center selection, exploiting front sparsity and surrogate uncertainty, with hypervolume-driven trust-region adaptation to balance exploration and exploitation under limited simulation budgets. Experiments on 100-dimensional DTLZ1 and DTLZ2 benchmarks demonstrate superior convergence and Pareto-front approximation compared with NSGA-II, ParEGO, qEHVI-MOBO, and MORBO. Further validation on a large-scale Beijing traffic network involving 456 continuous decision variables and a budget of 5000 simulator evaluations demonstrates the effectiveness of PHV-TuRBO in identifying diverse efficiency–emission trade-offs. Representative Pareto-optimal solutions achieve substantial improvements in waiting time, travel time, queue length, stop frequency, mean speed, and CO2 emissions relative to the original signal plan. These results establish PHV-TuRBO as a sample-efficient approach to high-dimensional, multi-objective traffic signal optimization for sustainable urban mobility.

Symmetry doi: 10.3390/sym18111894

Authors: Ahad Hamoud Alotaibi Muhammad Waseem Asghar

In this paper, we introduce a new adaptive double-inertial viscosity algorithm to solve a variational inequality and split common fixed point problem in Hilbert spaces. In our proposed method, we combine two inertial terms with a projected variational inequalities with a self-adaptive step size, an averaged demicontractive mapping and a viscosity approximation. This combination allows the algorithm to use information from previous iterates in each step. Under suitable assumptions on mappings used and sequences of the parameters, we prove the proposed sequence converges strongly to a solution of the considered problem. Several numerical examples are presented to study the convergence behavior of the proposed method. The numerical results show that the proposed algorithm converges faster for different initial points and performs better than the comparable existing algorithm in the tested cases. As an application, the proposed method is used for image restoration. The restoration quality is evaluated using PSNR, SSIM, and MSE, together with CPU time and the number of iterations. The proposed method gives the highest PSNR and SSIM values and the lowest MSE for all considered images. The visual results also show that the proposed method can remove degradation while preserving important image structures. The proposed algorithm is also assessed through a numerical example, and its performance is compared graphically with several existing methods from the literature. These results show that the proposed algorithm is effective both for the theoretical problem and for the considered image-restoration application.

Symmetry doi: 10.3390/sym18111893

Authors: Muhammad Saeed Ahmad Muhammad Waseem Asghar Farkhanda Yasmin Saima Nazeer Rehana Ashraf

Graph-based encryption proposals often combine a message-dependent graph representation with matrix transformations and then assess security through key-space size, operation counts, entropy, or visual complexity. Those indicators can be useful implementation diagnostics, but they do not rule out algebraic leakage. This paper gives a structural cryptanalysis of a subdivision-star construction whose ciphertext has the form C=PTAPK over a finite field. We first prove a generic kernel-transport theorem: if a message matrix is masked on the left and right by invertible matrices, its rank and nullity are preserved and its left nullspace is merely transported by the left mask. For the subdivision-star family, A has rank 2m in dimension 2m+1, so every ciphertext exposes a one-dimensional, plaintext-dependent left nullspace. We derive that null vector explicitly and introduce a complete signature for its scale-and-permutation orbit. For the explicitly defined challenge over F101, this yields a chosen-message distinguisher that separates “AAAA” and “BBBB” with success probability one for every admissible permutation and invertible right key. Because the source construction lacks a complete key-generation specification, this is an IND-CPA-style experiment rather than an IND-CPA theorem for a fully specified conventional cipher. An explicitly reconstructed “RAIN” numerical instance is checked exactly over F101, and seeded regression tests recover the predicted signature in all 200 randomized trials. The available materials do not identify an independently verifiable earlier publication for that instance. We also correct the computational accounting, quantify the quadratic ciphertext expansion, explain why entropy and raw key counts are nondiagnostic, and give a practical audit checklist for graph- and matrix-based cipher proposals. The case study shows why an invertible right mask combined with a secret left permutation may leave a plaintext-dependent nullspace orbit visible in public ciphertexts.

Symmetry doi: 10.3390/sym18111892

Authors: Vesselin G. Gueorguiev

A recent 2026 paper by Courbin and Maeder demonstrated that the Hubble tension can be resolved within the Scale-Invariant Vacuum (SIV) paradigm, but they did not demonstrate that the CMB spectra would be correctly reproduced. In this paper, an equivalent but physically different idea using time Reparameterization-Invariant Scaling Symmetry (RISS) is utilized to build a model that resolves the Hubble tension without introducing new particles or fields. Here, the Hubble tension is recognized to be caused by the difference in the unit of time during the decoupling and the current era since the corresponding gravitational potentials are different. This is justified by considering the SIV-like scaling factor using the Newtonian gauge to define λ=N/N0=(1+2Φ)/N0, where N is the lapse function as related to the evolving gravitational potential Φ and N0 is its current value. Then, by introducing specific λ(a), a new gauge-independent background reformulation is achieved since now λ depends on the expansion scale factor a, which can be viewed as a specific time parametrization for the evolution of the Universe. The key is an epoch-dependent re-scaling of the Hubble function Hnew=ξ(a)−1Hstd(a). Finally, after adjustments to the main cosmology parameters, one can reproduce the original LCDM CMB spectrum within less than a few percent of the individual ClTT values. The values of the new H0 parameter are consistently between H0=70 and 75 km/s/Mpc depending on the adopted model. However, for the RISS/SIV-motivated w=−2/3 extension of the LCDM model, that is, adding 1/a substance, my preliminary MCMC calculations result in H0=72±3 km/s/Mpc, Ωm=0.27, but very high ΩΛ=0.95 and a cosmological fluid with negative energy density Ωw=−0.23.

Symmetry doi: 10.3390/sym18111891

Authors: Long Zhao Shuaihua Ye Xiaoning Zhang Huibin Liu Hao Zeng Limin Wu Haibo Fang

Radial soil displacement during pile installation and pressuremeter testing is commonly interpreted using cylindrical cavity expansion theory. However, conventional plane strain solutions neglect vertical deformation and may be inadequate for unsaturated ground subjected to approximately constant overburden stress. This study develops a semi-analytical elastoplastic solution for cylindrical cavity expansion under constant total vertical stress. An unsaturated modified Cam-Clay model and a soil-water retention relationship are incorporated within a skeleton stress framework, while vertical deformation is explicitly considered in radial equilibrium. Coupled first-order governing equations are established for undrained and constant-suction drained conditions. The formulation agrees with an existing saturated drained solution in the limiting case. For the initial stress states examined, increasing overconsolidation ratio is associated with higher cavity pressure at a given expansion ratio but a smaller expansion ratio at which the cavity wall reaches the critical state. For normally consolidated soil, the corresponding ratios are 1.203 (undrained) and 1.375 (constant-suction drained). Under undrained conditions, changes in suction and saturation cause the vertical skeleton stress to evolve despite constant total vertical stress. The proposed framework provides a theoretical basis for evaluating cavity-induced soil disturbance and stress redistribution relevant to foundation construction in unsaturated ground.

Symmetry doi: 10.3390/sym18111888

Authors: Yanji Jiang Hongwei Zhou Hao Dong Haiyang Zhang Zhongbin Luo

Traffic flow forecasting estimates future vehicle counts at monitored road locations from historical observations. A central challenge is determining how strongly forecasts should respond when recent observations depart from recurring traffic patterns. We propose LaCoCast, which combines a periodic reference with lag-aware cross-sensor corroboration to regulate local forecast corrections. The reference encodes temporal translation symmetry by assigning the same baseline flow level to matching phases across cycles, while a local forecaster predicts deviations from this reference. Earlier neighbor observations reconstruct recent target deviations, providing evidence for evaluating their agreement with observed target behavior. A correction gate combines this agreement with evidence availability, neighbor coverage, and local context to adjust the residual candidate’s contribution at each forecast horizon. Experiments on PEMS03, PEMS04, PEMS07, and PEMS08 yielded mean absolute errors 0.38–6.13% below the lowest published baseline values included in the comparison for each dataset. Ablation and evidence perturbation experiments further support the use of temporally matched neighbor observations to regulate residual contributions, connecting a periodic structural reference with adaptive traffic flow forecasting.

Symmetry doi: 10.3390/sym18111890

Authors: Chenchen Bai Wenyang Deng Siming Wu Zelin Liu

Forecast errors in significant wave height and dominant wave period can propagate differently to wave energy converter (WEC) power, depending on error direction and the device response. Hourly records from NDBC Station 46014 (2019–2020) were used for direct 1, 3, and 6 h forecasts from 24 h histories. Valid wind-direction observations recorded as 360° (north) were retained during preprocessing. Persistence, raw-input GRU, and forecast-origin CEEMDAN-GRU were compared. Paired forecasts were converted to power using a published Pontoon WEC power matrix on shared valid timestamps. Finite-change analysis separated height, period, and joint power-error contributions. A sign-reversal index compared equal-magnitude positive and negative forecast errors at each observed sea state. CEEMDAN-GRU produced mapped-power RMSEs of 83.22, 98.15, and 115.65 kW; its differences from raw-input GRU were small, with calendar-block confidence intervals including zero. The period–direction mean absolute asymmetry index exceeded the height–direction index by 0.194, 0.180, and 0.164 on jointly valid samples, with all 95% confidence intervals above zero. This ordering persisted under grid-normalized perturbations and two alternative interpolation methods. The results concern forecast-error propagation through the published matrix at one buoy station, without measured electrical-output validation.

Symmetry doi: 10.3390/sym18111889

Authors: Christian Akrong Hesse Emmanuel Dodzi Kpeglo Dominic Buer Boyetey Saralees Nadarajah Evans Tee

This study evaluates the finite-sample performance of maximum likelihood estimation (MLE) and Bayesian maximum a posteriori (MAP) estimation for Exponential and Weibull lifetime distributions under Type-II right censoring. Data were simulated from both distributions, with each life-testing experiment ending after a specified number of failures among n units. Estimator performance was assessed using bias, mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE) under alternative prior specifications, including calibrated, weakly informative and deliberately misspecified priors. The results indicate that the relative performance of MAP and MLE depends on the quality of prior information and the degree of censoring. For the Weibull distribution, estimation performance also differed between the shape and scale parameters. An illustrative application to ball-bearing fatigue-life observations using their original right-censoring information further demonstrates posterior-mode estimation, prior sensitivity and Markov Chain Monte Carlo (MCMC) based uncertainty quantification. In summary, the location of the MAP estimate within the region of greatest posterior concentration is consistent with direct numerical maximisation of the joint posterior density.

Symmetry doi: 10.3390/sym18111887

Authors: Yang Liu Jichao Huang Jing Dong Xia Zhang

We compared the effects of anthocyanin loading on the tensile properties and color response of chitosan/sodium alginate (CS/SA) composite films and used molecular dynamics simulations to examine local contacts between a representative pigment and the polysaccharide matrix. Among the six formulations containing 0–5 mL of extract, the 2 mL group had the highest recorded tensile strength (9.57 MPa) and extension at break (3.77 mm), 45.66% and 95.34% above the 0 mL group, respectively. In models M0–M5, which represented relative pigment counts, M2 had the highest short range peaks in the CS–SA and anthocyanin–matrix radial distribution functions (1.547 and 3.875, respectively) and the highest target hydrogen bond count per pigment molecule (2.49 ± 0.31) over the analysis window. M4 had the highest component binding energy per pigment molecule (486.39 ± 5.69 kcal mol−1), giving a different ranking from the tensile measurements. In the chicken packaging test at 4 °C, the 2 mL group showed the largest color difference at every measured time point from 48 to 120 h, reaching 31.1 at 120 h. Among the formulations tested, the 2 mL group combined the highest recorded tensile values with the largest color differences in the middle and late stages of storage.

Symmetry doi: 10.3390/sym18111886

Authors: Emilio Gómez-Déniz Yolanda M. Gómez Diego I. Gallardo Héctor W. Gómez Osvaldo Venegas

This paper introduces a new two-parameter discrete distribution obtained by mixing the geometric distribution with a particular case of the Log-Gamma distribution; equivalently, it is a geometric distribution whose success probability is driven by a gamma latent variable. The proposed model is unimodal, presents a zero vertex, and accommodates over-dispersion, which are features commonly observed in automobile insurance-claim data. For α<1, it is shown to be more dispersed and to have more zeros than the geometric distribution with the same mean. Closed-form expressions are derived for several actuarial quantities and reliability measures, including the failure rate, mean residual life, Value at Risk (VaR), through the Lambert W function, and Tail Value at Risk (TVaR). In addition, the geometric distribution is obtained as a limiting case of the proposed model when α<1. We study parameter estimation using a zero-proportion and mean estimator, maximum-likelihood estimation, and an ECME algorithm. The practical performance of the proposed model is illustrated through a Monte Carlo study that explicitly accounts for boundary solutions, and through three automobile insurance datasets, where it is compared with the Poisson and negative binomial distributions using asymptotic and parametric bootstrap goodness-of-fit tests. The proposed model performs as well as the negative binomial distribution in two classical datasets, whereas for a portfolio of 100,000 policies it attains the smallest AIC but, like the negative binomial model, it is rejected by the goodness-of-fit tests.

Symmetry doi: 10.3390/sym18111885

Authors: Selin Kaptan İbrahim Özkol

Functionally graded porous (FGP) metal-foam beams offer advantages for lightweight structures, but thermal loading can alter their vibration response and stability. This study develops a framework based on the Generalized Differential Quadrature Method (GDQM) to investigate the effects of through-thickness porosity symmetry and asymmetry on the broadband dynamic response, thermal stability, and parameter sensitivity of FGP Timoshenko beams. The formulation incorporates temperature-dependent material properties, thermally induced compressive axial force, symmetric and asymmetric porosity distributions, three temperature profiles, and different boundary conditions. The governing equations are derived using Timoshenko beam theory and solved using GDQM. Validation against analytical and published benchmark solutions precedes parametric and normalized sensitivity analyses. Under the investigated thermal loading conditions, increasing temperature shifts the resonance characteristics toward lower frequencies and reduces the thermal stability margins. Uniform temperature distributions produce the strongest thermo-mechanical effects, whereas linear and nonlinear profiles yield similar broadband responses. Asymmetric porosity produces greater sensitivity and lower stability margins than symmetric porosity, demonstrating the influence of material symmetry on the thermoelastic dynamic behavior. Stronger boundary constraints enhance stability. Sensitivity analyses identify elastic modulus, temperature rise, and porosity coefficient as key parameters controlling the broadband response. Increasing structural damping suppresses resonance amplitudes and normalized temperature-rise sensitivity without significantly changing the resonance frequencies. The proposed framework supports stability-aware assessment and design of lightweight porous beams operating in thermal environments.

Symmetry doi: 10.3390/sym18111884

Authors: Shiwei Du Li Zhang Guan Wang Ikromjon Rakhmonov Usmonovich Nurbek Nurullo ugli Kurbonov Teng Yue

Rain erosion changes the surface profile and dielectric interfaces of wind turbine blade protection coatings, introducing geometry-dependent bias into surface charge reconstruction. A constrained inversion method combines a finite library of erosion profiles with continuous radial charge parameterization in a three-dimensional laminate model. Candidate-specific responses and variable projection jointly estimate geometry and charge, while the square specimen’s D4 symmetry reduces the computational domain to one eighth. Continuous-source finite-element potentials provide the numerical observations. With matched generating and inverse discretizations, median global errors over 24 inputs are 0.172% and 1.039% at single-reading noise standard deviations of 0.003 and 0.1 V, respectively. At 0.003 V, 21 inputs have global errors at or below 20%; three broad-charge realizations reach 65.69–70.01%. Across six out-of-library cases, candidate selection reduces the median pit-interior error from 10.264% to 4.821%, while the median pit-edge error increases. Joint ±10% permittivity shifts give global errors of 9.660% and 8.027% in one representative case. Representative finite-aperture simulations and controlled mesh refinement further reveal the sensitivity of fine-scale recovery. The method relates the estimated charge distribution to erosion geometry, providing a numerical approach to local electrical characterization of damaged coatings.

Symmetry doi: 10.3390/sym18111883

Authors: Xuezhang Mao Dongqi Han Jucheng Wang Jian Xue Tongtong Liang

Multi-hop knowledge graph question answering (KGQA) faces practical deployment hurdles: large language models suffer from high computational overhead and hallucination risks, while graph-based methods rely on entity-centric subgraphs that adapt poorly to dynamic graphs. To address these issues, we propose SymPath, a lightweight symmetric path retrieval method that decouples neural semantic retrieval from symbolic graph execution. Leveraging architectural symmetry, SymPath employs a parameter-shared 22-million-parameter dual-tower encoder that maps natural-language questions and candidate relation paths into a unified, symmetric semantic space, eliminating the parameter redundancy and representation drift of asymmetric encoders. A multi-grained alignment mechanism combines global mean pooling with token-level MaxSim to accurately discriminate multi-hop paths, which are then executed symbolically without free-form generation. Consequently, the model adapts to updated graphs without retraining. Under the gold topic entity protocol, experiments on WebQSP and ComplexWebQuestions show that SymPath achieves 67.8% and 60.6% F1, respectively, and reaches 61.7% Hits@1 under random entity sampling, outperforming a 110-million-parameter baseline. Furthermore, SymPath requires only ∼1 GB GPU memory and achieves low per-batch latency (300 ms on GPU; 530 ms on CPU). These results demonstrate a competitive accuracy–efficiency trade-off for resource-constrained KGQA.

Symmetry doi: 10.3390/sym18111881

Authors: Mengxing Wang Ming Tang Pengbo Wang Lichao Wu Chong Xiao

Side-channel analysis (SCA), particularly deep learning-based SCA (DLSCA), threatens cryptographic implementations by automatically exploiting complex and nonlinear leakage and weakening countermeasures such as masking. Existing countermeasures against DLSCA mainly suppress, decorrelate, or obscure exploitable leakage. This work introduces Spoofing-based Mitigation (SPM), a leakage-shaping approach designed to mislead key-recovery attacks by biasing their key hypotheses. SPM introduces a controllable offset into AES intermediate-value computations and compensates for it to preserve the correct ciphertext, while shaping the relationship between measured leakage and the intermediate-value labels used for profiling. We implement SPM at the first-round S-box output and evaluate it at first-round and last-round attack points on an XMEGA128D4 microcontroller using a ChipWhisperer platform. Under the evaluated identity-label settings, the induced key’s rank rapidly reaches zero across seven CNN-based DLSCA models, two MLP-based models, and a template attack, while the correct key remains unrecovered. These results provide experimental evidence that leakage shaping can misdirect the evaluated key-recovery attacks. The collected dataset is publicly available to support reproducible research.

Symmetry doi: 10.3390/sym18111882

Authors: Pengxiang Li Huafang Li Jinshuai Zhao Pinpin Liu

Internal fractures in engineering rock masses generate intense local stress concentrations that trigger catastrophic instability. Understanding how structural symmetry governs stress redistribution and damage evolution is crucial for geotechnical stability prediction. To elucidate these mechanisms, uniaxial compression tests were performed on rock specimens containing prefabricated symmetrical V-shaped flaws with included angles of 30°, 70° and 110°. Acoustic emission (AE) monitoring and digital image correlation (DIC) were simultaneously employed to track transient microcracking and surface strain localization. Furthermore, a grain-based model (GBM) within a discrete-element framework was developed to capture polycrystalline heterogeneity and mesoscopic fracturing. The macro- and mesoscopic analyses demonstrate that although the flaw geometry is initially symmetrical, local stress concentration at the flaw tips induces stress symmetry breaking, ultimately triggering asymmetric microcrack initiation and progressive strain localization. Smaller included angles amplify this stress asymmetry, leading to crack initiation at lower stress thresholds and earlier AE activation. By capturing grain-scale failure modes, the GBM uncovers the mechanical transition from initial geometrical symmetry to asymmetric failure evolution. These findings elucidate the nonlinear mesoscopic damage mechanisms of rocks containing complex flaws and provide a solid theoretical basis for instability evaluation in geotechnical engineering.

Symmetry doi: 10.3390/sym18111880

Authors: Herminia Gavilán Luis Benites Claudio Ruff Escobar Alexis Matheu Pérez

Institutional accreditation is a high-stakes decision under uncertainty: Chilean universities commit strategic resources years before knowing which indicators will weigh the most in the National Accreditation Commission’s judgment. We characterize the accreditation status of 48 Chilean universities from financial, academic and management indicators reported to the Higher Education Information System (SIES) for 2017–2021 (240 institution-year observations). Three symmetry structures organize the analysis: scale invariance (indicators normalized per student or per academic), the symmetric correlation matrix under hierarchical clustering, and a permutation-symmetric specification that variable selection deliberately breaks. A stable core of predictors, admission selectivity, the net financial result per student, and students per doctoral full-time-equivalent, survives four robustness checks: ordered logit re-estimation, institution-clustered errors, a 2000-replication institution-level bootstrap, and leave-one-institution-out cross-validation (out-of-sample cross-validated coefficient of determination, Q2, near 0.71). Research output per academic, decisive in M2, falls outside that battery and is not claimed as verified. First-year retention is significant under clustered errors but clears neither the ordinal re-estimation (p = 0.614) nor the 95% sign stability threshold (88.2%) and is reported as suggestive rather than stable. The institutional-type intercept is absorbed once research intensity enters, but interaction tests reject slope symmetry between CRUCH (the Chilean Council of Rectors) and private universities: the association structure is partially, not fully, symmetric. We discuss implications for strategic planning and Goodhart risks.

Symmetry doi: 10.3390/sym18111879

Authors: Can Xu Yaqin Huang Haike Lei Jie Yang

Survival prediction from longitudinal clinical records is challenged by heterogeneous feature availability, irregular observation intervals, and imbalanced event distributions with heavy censoring. These interacting feature, temporal, and event asymmetries are only partly addressed by approaches that reduce histories to fixed covariates, place observations on regular grids, or optimize a single survival objective. We propose CliTsSurv, an integrated framework that learns separate representations of longitudinal and static inputs, encodes actual elapsed time at multiple scales, and combines latent-space augmentation with a multi-task objective comprising negative log-likelihood, ranking loss, and Brier loss. We evaluated CliTsSurv on a retrospective breast cancer cohort of 7509 patients with 92,820 longitudinal records and up to 171 months of follow-up. Across 20 repeated experiments using random patient-level splits and independent model initializations, CliTsSurv-Transformer achieved an IPCW C-index of 0.970, a Harrell C-index of 0.965, and an integrated Brier score of 0.032, outperforming the strongest baseline under the common evaluation protocol. Ablation and sensitivity analyses examined the contributions and limitations of the representation learning, temporal encoding, and augmentation components and identified elapsed-time encoding as the largest contributor. These findings support coordinated modeling of feature, temporal, and event asymmetries for survival prediction from irregular clinical records.

Symmetry doi: 10.3390/sym18111878

Authors: Oqlah Al-Refai Jamal Salah Mohammed Ali Khalifa Al-Shaqsi Hameed Ur Rehman Ahmad Al Azab

For n≥3, we study the subclass Cn of univalent functions f with a2=…=an=0 in which the whole allowance of the Al-Refai–Darus criterion is assigned to the nth derivative of z/f. The map f↦(z/f)(n) is a bijection of Cn onto a closed ball of H∞, which turns extremal problems into problems for bounded analytic functions. We prove sharp growth, distortion, covering-radius and coefficient bounds with the (n+j)-fold symmetric extremal functions z/(1+czn+j); the exact region of (an+1,an+2), whose boundary is attained by Möbius parameters written in closed form; an exact radius for dilations of products f1f2/z, sharp both for Aksentev’s inequality and for univalence. The vanishing of a2,…,an does not by itself imply n-fold symmetry; the n-fold symmetric members of Cn correspond exactly to g(zn) with g in the same ball, which provides the exact region of (an+1,a2n+1). For the larger class defined by a2=0 and the criterion, we obtain sharp bounds as well. The comparison with n-fold symmetric univalent functions records a gap; it is not a sharpening of known results.

Symmetry doi: 10.3390/sym18111877

Authors: Ziyang Zheng

Retrieval-augmented generation (RAG) across independent data providers requires local data custody, verifiable evidence handling, and fair compensation for contributed knowledge. We present BC-MultiRAG, a permissioned framework in which providers retrieve locally and release only candidate passages and metadata. Each provider commits to a canonical, domain-separated Merkle root and signs the candidate count, root, task, timestamp, and software version. The shared service verifies these commitments before cross-encoder reranking and generation. Contributions are estimated with Shapley values over a bounded teacher-forced support score. Validity and audited service reliability adjust settlement, while providers with identical node contexts share one credit group. A smart contract enforces budget conservation and records evaluator and settlement state. We evaluate a three-provider deployment on MultiHop-RAG, HotpotQA, and Natural Questions. Provenance verification changed retrieval and answer quality only slightly. The protocol rejected the specified tampering and replay tests at a measured confirmation cost. In a controlled settlement simulation, contribution-weighted payment improved participation and high-quality evidence and reduced allocation disparity relative to a shuffled-contribution placebo. Claims of semantic citation correctness and performance across naturally separate institutional collections remain outside the present evidence.

Symmetry doi: 10.3390/sym18111876

Authors: Momchil Naydenov

Fermions with a small effective charge, qeff≪1, arise from kinetic mixing between an unbroken (or nearly unbroken) dark U(1)′ and electromagnetism, or from a genuinely fractional charge. Millicharged particles (mCPs) inherit the Pauli-exclusion constraints on fermionic dark matter (DM) in galaxies, while adding a long-range plasma phenomenology absent for neutral candidates. This review connects three strands: (i) the symmetry structure, cosmology and astrophysical bounds of millicharged fermions, comparing kinetic-mixing and fractional-charge realizations; (ii) the role of mCPs in galactic halo formation and dynamics, and when they fit the Ruffini–Argüelles–Rueda (RAR) self-gravitating core–halo model; and (iii) experimental techniques for detecting mCPs trapped on Earth, arriving from the galactic halo, or emitted by the Sun. We show that a collisionless halo of keV–MeV millicharged fermions requires α′≲7×10−13–2×10−10, depending on mass and velocity, orders of magnitude below the coupling needed for thermal freeze-out via χχ¯→A′A′ in the Milky Way and dwarf galaxies. A RAR halo made of the mCP itself thus needs non-thermal production, a charge-symmetric plasma and very small dark coupling, whereas a sub-dominant mCP component can be added without changing the halo. We close with open theoretical and experimental challenges and a summary of the allowed mCP parameter space.

Symmetry doi: 10.3390/sym18111875

Authors: Zhuo Han Fei Wen

A k-I-total coloring φ of a graph G is a mapping from the elements in V(G)∪E(G) to k colors such that no two adjacent vertices as well as edges receive same color in G, and moreover, if Cφ(u)≠Cφ(v) for any uv∈E(G), where Cφ(u) denotes the set of colors assigned to u and its incident edges under φ, then φ is termed k-adjacent vertex distinguishing I-total coloring of G, and the smallest positive integer k is called adjacent vertex distinguishing I-total chromatic number, denoted by χati(G) for short. Let Δ(G) and mad(G) be the maximum degree and the maximum average degree of G, respectively. In this paper, we employ the discharging method to prove that χati(G)≤max{7,Δ(G)+1} for any graph G with mad(G)<4.

Symmetry doi: 10.3390/sym18111874

Authors: Qing Li Yongjian Chen Wenhao Ding Sheng Lv Rui Hu Lei Zhong Fei Li

Gamma dose rate meters are used in environmental radiation monitoring and radiation safety assessment. Conventional global G(E) functions can concentrate dose conversion errors at low energies. A segmented G(E) compensation method based on the multi-segment least-squares method (MSLSM) was developed for a compact CsI(Tl)–silicon photomultiplier (SiPM) meter, with separate functions for 20–200 keV and 200 keV < E ≤ 2000 keV. Full-spectrum fitting mean absolute percentage error (MAPE) decreased from 10.36% to 5.83%, a relative reduction of 43.73%, while low-energy MAPE decreased from 22.32% to 11.42%. For simulated nuclide spectra, the 241Am relative deviation decreased from 9.17% to 1.83%; results for 137Cs, 60Co, and most mixtures were comparable to or slightly better than those of the conventional global least-squares method (LSM). After correction, the maximum absolute relative deviations between the prototype meter and the commercial SAM945 instrument were approximately 7.5% for 137Cs and 14.91% for 60Co. Segmented G(E) modeling thus improves the regional error distribution and dose rate fitting accuracy over a wide energy range for the detector studied.

Symmetry doi: 10.3390/sym18111873

Authors: Kasamsuk Ungchittrakool Somyot Plubtieng

We propose a Halpern-Inertial Three-Operator Splitting Algorithm with Moving Point Projection (HI-TOS-MPP) for solving monotone inclusion problems involving the sum of two maximally monotone operators and one cocoercive operator in real Hilbert spaces. The framework incorporates adaptive Polyak-type inertial extrapolation into the Davis–Yin splitting scheme, employs a Halpern anchor to ensure strong convergence, and applies a moving point projection (MPP) onto dynamically generated half-spaces enclosing the solution set. Under mild and verifiable conditions on the parameters, we prove the strong convergence of the iterate sequence without imposing compactness assumptions. To assess practical performance, we apply the algorithm to image inpainting under severe micro-scratch degradation, which is formulated via dual-directional matrix and tensor nuclear norm regularizations. Numerical experiments on four benchmark images (two grayscale and two color RGB) damaged by four distinct scratch patterns (straight lines, curved hairline cracks, cross-hatching, and random dashes) show that HI-TOS-MPP consistently outperforms both the classical Davis–Yin three-operator splitting method (Davis–Yin TOS) and the Halpern three-operator splitting method (Halpern-TOS), achieving SNR gains of up to 14.31 dB along with marked improvements in SSIM. Furthermore, comparative benchmarks against the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) on the composite objective demonstrate that our two-operator variant achieves a 2.10× wall-clock speedup to target quality thresholds, while the three-operator HI-TOS-MPP attains the highest overall reconstruction fidelity (22.04 dB). The moderate per-iteration resolvent overhead is justified by the algorithm’s capability to decouple non-separable multi-operator and tensor inclusions where FISTA cannot be applied directly.

Symmetry doi: 10.3390/sym18111872

Authors: Watcharaporn Cholamjiak Papatsara Inkrong Papinwich Paimsang Mohammad Farid

In this paper, we propose a two-step inertial Mann-type forward–backward–forward method with a self-adaptive step-size strategy for solving variational inclusion problems in real Hilbert spaces. The proposed method modifies two inertial terms to exploit information from previous iterates, while the self-adaptive step-size rule avoids the need for prior knowledge of the Lipschitz constant of the underlying operator. Under suitable conditions on the operators and control parameters, we establish the weak convergence of the generated sequence to a solution of the variational inclusion problem. The proposed method is then applied to train ELM classifiers in a two-stage breast ultrasound classification framework using the BUSI dataset. Stage 1 distinguishes normal images from lesion-containing images, while Stage 2 classifies lesions as benign or malignant using predicted mask regions of interest. Numerical results and comparisons with other optimization methods and standard machine learning classifiers demonstrate the applicability and classification performance of the proposed method.

Symmetry doi: 10.3390/sym18111871

Authors: Ioannis Dachis Evangelos P. Hadjigeorgiou Konstantinos G. Beltsios

Programmable metamaterials are designed to tailor mechanical properties and stable configurations through the selection of geometric and material parameters. Here, a two-dimensional auxetic unit is combined with a bistable unit to create a three-dimensional metamaterial mechanism with tunable bistable behaviour. The rotating-triangle architecture of the auxetic unit has a Poisson’s ratio of −1, while the second stable state is governed by the geometry and relative bond stiffnesses of the two units. Bistability occurs when ka/kb<1.25, where ka and kb are the bond stiffnesses of the auxetic and bistable units, respectively. The design parameters determine the second stable state and, in turn, the mechanism’s effective properties. The symmetry of the base cell enables its periodic repetition to form a three-dimensional metamaterial lattice.

Symmetry doi: 10.3390/sym18111870

Authors: Abdelhamid Taieb Zaidi

We develop a direct Hilbert–Schmidt analysis of classical and sequential conformable fractional boundary value problems. For the classical problem of order γ∈(1,2], factorizing the Green kernel before squaring preserves a cancellation lost in termwise estimates. This yields H1=(b−a)2γ/(3γ(4γ2−1)), which is finite for every γ>1 and shows that the apparent singularity at γ=3/2 is removable. Combined with a uniform kernel estimate and Rus’s two-metric fixed-point theorem, this extends the uniqueness criterion to the full range γ∈(1,2], for solutions that need not be twice differentiable at the left endpoint. This sufficient criterion is proved to be strictly less restrictive than the Banach contraction criterion throughout that interval. For the sequential problem with δ∈(1/2,1], we prove the analogous uniqueness theorem with error estimates. For the sequential kernel, we obtain a compact closed form of the squared Hilbert–Schmidt norm, show that the kernel is square-integrable exactly when δ>1/4, and determine the crossover order δ*=(65−5)/8 between the Hilbert–Schmidt and Banach-type bounds. Numerical comparisons quantify the improvement in the admissible Lipschitz constant, and a nonlinear example with γ=1.25, validated by node refinement, residuals and an independent reference solution, exhibits a regime where the Banach condition fails while the full-range criterion guarantees uniqueness.

Symmetry doi: 10.3390/sym18111869

Authors: Raghu Kulkarni

The Selection–Stitch Model (SSM) treats the vacuum as a face-centered-cubic (FCC) lattice whose ⟨110⟩ bonds carry a stabilizer code but no propagating electromagnetic field. We construct its electromagnetic sector by asking where a compact U(1) gauge field can live without sharing the code’s variables, comparing the Gaussian spectrum of the compact U(1) Hamiltonian on three candidate complexes. With triangular plaquettes, the ⟨110⟩ network supports a two-polarization photon, but only on the code’s bonds. On the code complex, whose two-cells are the octahedral checks, four zero-frequency flat bands appear, with harmonic dimension equal to the code’s logical count, 2L3+2. The ⟨100⟩ links joining FCC nodes to octahedral voids form a simple cubic lattice that shares no bond with the code and has the Maxwell count: this is the proposed sector. Gauge invariance keeps its photon massless even when the two site types differ, and centrosymmetry removes the leading strain coupling. Matter hopping along a ⟨110⟩ bond passes through an octahedral void, coupling minimally to the gauge links. In four dimensions, the cubic lattice is a slice of D4*, whose point group W(F4) makes the Euclidean photon isotropic through quartic order. With qubits instead of a gauge field, the same links form the three-dimensional toric code.

Symmetry doi: 10.3390/sym18111868

Authors: Lu Jin Ying Jin Yunfeng Hou

Financial fragility is a forward-looking indicator that characterizes the potential financial deterioration risks of economic entities under adverse shocks. Household financial fragility assessment is often subject to epistemic uncertainty induced by limited information and subjective expert judgement, which cannot be properly captured by classical probabilistic frameworks. This paper develops an uncertain logistic regression framework for household financial fragility modeling rooted in uncertainty theory. We first construct two measurement indicators, namely financial margin and liquidity capacity, to quantify household financial fragility. Then we derive the uncertain maximum likelihood estimator and design a numerical algorithm to implement parameter estimation. Using micro household data from the China Family Panel Studies (CFPS), we carry out empirical analysis for rural labor-transfer households. The empirical results show that the proposed uncertain logistic regression model delivers stable and economically interpretable estimates under epistemic uncertainty with unstable event frequencies. Compared with classical probabilistic logistic regression, the uncertain framework exhibits better applicability for such small-sample scenarios dominated by cognitive uncertainty.

Symmetry doi: 10.3390/sym18111867

Authors: He Yuan Yutong Yin Xiaokui Li Lili Ma

In this paper, we study the structure of nonlinear mixed bi-skew Jordan and bi-skew Lie-type higher derivations on *-algebras. Using mathematical induction, we establish that every nonlinear mixed bi-skew Jordan and bi-skew Lie n-higher derivation on *-algebras is an additive higher *-derivation. Furthermore, this conclusion is applied to prime *-algebras, factor von Neumann algebras, and standard operator algebras, with the corresponding corollaries derived accordingly.

Symmetry doi: 10.3390/sym18111866

Authors: Zhao Yang Dai Luo Liu Duan Wang

Identifying influential spreaders requires structural measures that capture local connectivityand a node’s position in the wider network. We propose structure and core enhanced centrality(SCEC), a ranking heuristic combining degree, clustering, coreness, and multi-orderneighbor information. The degree–clustering and first- and second-order degree–corenessterms form an SCC score, and SCEC aggregates the SCC values of immediate neighbors.We evaluate the method on eight empirical networks against archived sequential-updatesusceptible–infected–recovered (SIR) influence estimates at five transmission probabilitiesfrom 0.8 to 1.2 times a degree-moment threshold. Across the 40 network–transmissionsettings, SCEC had a mean Kendall correlation of 0.798 and a mean top-20% Jaccard similarityof 0.729, compared with 0.776 and 0.684 for NCC, the strongest principal baseline bythese averages. The performance varied by network and transmission setting. Ablationsindicate a larger contribution from final neighbor aggregation than from the clustering term,whose incremental benefit is limited in these data. Weight and selection-budget analysescharacterize the sensitivity within the tested settings.

Symmetry doi: 10.3390/sym18111865

Authors: Soundar Rajan Somasundaram Baskar Babujee Jayapal

Cordial labeling is a well-established graph labeling scheme with rich combinatorial properties and significant applications in graph theory. In this paper, we investigate the existence of cordial labelings for the mycielskian of trees, cycles, complete bipartite graphs Km,n, and bull graph. We present explicit vertex labelings that satisfy the cordiality conditions and show how the mycielskian transformation affects the labeling behavior of the underlying graph. These results extend the current understanding of cordial labeling under graph transformations and yield new classes of mycielskian graph that admit cordial labeling.

Symmetry doi: 10.3390/sym18111863

Authors: Hongjiang Li Weiping Jin Mengping Gao Junxiang Cheng Chengpeng Ma Zhan Gan

Accurate estimation of system harmonic impedance is an important prerequisite for apportioning harmonic responsibilities and achieving harmonic mitigation. To address the susceptibility of harmonic impedance estimation to background harmonic fluctuations, a system harmonic impedance estimation method based on improved Complex Independent Component Analysis (CICA) is proposed. First, based on the intrinsic characteristics of system harmonic impedance, an impedance constraint model is introduced to constrain the separation matrix. Then, a constraint violation degree indicator is constructed to adaptively update the penalty coefficient and Lagrange multiplier during the iteration process, and these are embedded into the update direction of the traditional fixed-point iteration. Finally, the separation matrix is solved through adaptive constraint strength fixed-point iterative updating, and the equivalent system harmonic impedance is determined according to the corresponding relationship among the elements in the impedance matrix. The method is tested on a photovoltaic grid-connected simulation system with background fluctuation levels from k = 0.1 to k = 1.0 and on 7th-harmonic measurements from an urban distribution network in Yunnan Province (1322 phasor sets); in both cases the constraints keep the estimated impedance physically realizable and suppress the non-physical solutions produced by unconstrained separation.

Symmetry doi: 10.3390/sym18111864

Authors: Rahaf Marzouq Alharbi Kholood Mohammad Alsager

Decision-making in sustainable supply chains requires mathematical frameworks capable of handling uncertainty, parameterization, and relationships among alternatives. This paper proposes a Picture Fuzzy Soft Rough Graph with VIKOR (PFSRG-VIKOR) framework for multi-criteria group decision-making by integrating picture fuzzy sets, soft sets, rough approximations, graph structures, and VIKOR compromise ranking. The framework combines these five components while accounting for group utility and individual regret. Fundamental mathematical properties are established, and a decision-making algorithm is developed. The framework is applied to an illustrative sustainable supplier selection problem involving ten suppliers evaluated against economic, environmental, and social criteria. The supplier evaluations are hypothetical and are used solely to demonstrate the proposed methodology. The country names serve only as illustrative identifiers and do not represent actual assessments of the manufacturing capabilities of the countries concerned. Under the specified settings, A6 (Taiwan) attains the lowest compromise index (Q=0.0000), followed by A7 (Vietnam), with Q=0.2504. Comparison with the SAW benchmark yields a Kendall rank correlation coefficient of τ=0.6889. A comparative analysis of ten existing methods indicates that, among the methods examined, the proposed framework uniquely integrates all five components. Sensitivity analysis shows that A6 retains the highest ranking across the tested VIKOR balancing and graph influence parameter settings and in nine of the ten criterion-weight scenarios. The preferred alternative changes when greater emphasis is placed on the economic criterion. These findings illustrate the behavior of the proposed framework using hypothetical evaluations and demonstrate its potential applicability to sustainable supplier selection and decision-making problems in energy, healthcare, and smart city planning.

Symmetry doi: 10.3390/sym18111862

Authors: Shi-Hao Chen Qing-Wen Wang

We derive the necessary and sufficient conditions for the solvability of a system of dual quaternion matrix equations (AX, XC, EXF) = (B, D, G) as well as their general solution expressions by means of the Moore–Penrose inverse and rank equalities. Then, the main conclusions of this paper are verified via a numerical example, and the applications of such equation systems to image encryption and decryption are investigated.

Symmetry doi: 10.3390/sym18111861

Authors: Hank Chen Florian Girelli

In this paper, we explore the algebraic and geometric structures that arise from a procedure we dub “gauging the gauge”, which involves the promotion of a certain global, coordinate independent symmetry to a local one. By gauging the global 1-form shift symmetry in a gauge theory, we demonstrate that the structure of a Lie algebra crossed-module and its associated 2-gauge theory arises. Moreover, performing this procedure once again on a 2-gauge theory generates a 3-gauge theory, based on Lie algebra 2-crossed-modules. As such, we show that the physical procedure of “gauging the gauge” can be understood mathematically as a categorification. Applications of such higher-gauge structures are considered, including general relativity, high-energy physics and condensed matter theory. Of particular interest is the mechanism of anomaly resolution, in which one introduces a higher-gauge structure to absorb curvature defects. This mechanism has been shown to allow one to consistently gauge an anomalous background symmetry in QFT.

Symmetry doi: 10.3390/sym18111860

Authors: Xinyu Qiu Jingchao Liu Pengli Xu Chenghao Lu Yu Fu

Scene text image super-resolution must preserve character identity and glyph geometry, including approximate symmetry where present and asymmetric details that distinguish characters. Erroneous optical character recognition (OCR) priors can distort characters during generative reconstruction. We combine constrained large language model (LLM) correction and Mamba-based visual sequence modeling in a conditional residual diffusion method. The LLM proposes replacements within OCR candidate and edit constraints; deterministic validation rejects invalid suggestions and retains the original transcription. Corrected text, position, and low-resolution structural priors are fused by sample-level reliability gating and injected through cross-attention. A bottleneck Mamba block models horizontal visual dependencies. Under separately trained TextZoom and Real-CE protocols, the method achieves peak signal-to-noise ratios of 25.06 and 24.38 dB and exact-match accuracies of 83.4% and 50.2%, respectively. Five-seed paired ablations show that constrained OCR correction improves full-model reconstruction by 0.07 dB in PSNR and 0.6 percentage points in exact-match accuracy on both TextZoom and Real-CE, with the corresponding 95% confidence intervals excluding zero. Compared with the tested lightweight Transformer, Mamba reduces reconstruction latency by 7.82 ms with comparable quality. Independent recognition evaluation supports improved readability. The results support constrained correction and complementary visual conditioning.

Symmetry doi: 10.3390/sym18111859

Authors: Tao Zhou Wenxiang Xu Yichen Zhou Yi Wang Cheng Wang

During symmetrical faults in photovoltaic (PV)-integrated distribution networks, induction motor (IM) deceleration elevates reactive-power demand and delays post-fault voltage recovery, whereas conventional voltage-driven support can withdraw prematurely upon initial voltage rebound. To resolve this mismatch, this paper proposes a coordinated transient voltage support (CTVS) strategy that explicitly incorporates IM electromechanical dynamics. A coupled differential-algebraic equation (DAE) model integrating third-order IM dynamics, distributed PV (DPV) DC-link dynamics, and network power balance is formulated, from which a trajectory-local closed-loop Q–V sensitivity is derived to characterize location-dependent support effectiveness. The CTVS controller coordinates critical-bus voltage magnitude, voltage-decrease rate, and rotor slip through fixed spatial participation coefficients under local converter current limits and DC-link voltage feedback. Case studies on a modified IEEE 33-bus feeder under Bus-32 three-phase faults demonstrate that, for the representative 140 ms fault, CTVS suppresses post-fault secondary voltage depression and reduces the sustained recovery delay to 23.85 ms, compared with 342.30 ms for local low-voltage ride-through and 390.85 ms for adaptive Q–V droop control. Matched ablations identify slip-conditioned support persistence as the principal contributor to sustained voltage recovery, whereas the fixed spatial coefficients provide a local allocation advantage under unsaturated conditions rather than a separate large-disturbance recovery benefit under the tested conditions.

Symmetry doi: 10.3390/sym18111858

Authors: Qi-Liang Xie Qiu-Rui Wu Zi-Jun Li Fang-Chao Han Yu Zhuge Zhan-Wei Liu

Hadron resonances are intrinsically dynamical states whose observable properties are governed by the interplay between quark-model configurations and hadronic channels. Hamiltonian effective field theory provides a practical framework for connecting hadron dynamics with experimental observables and lattice QCD results. In this review, we outline the infinite- and finite-volume formulations of Hamiltonian effective field theory and survey its applications to light-hadron spectroscopy and resonance structure. By constraining the same Hamiltonian framework with experimental scattering data and lattice QCD spectra, Hamiltonian effective field theory can help distinguish among scenarios that describe the available scattering data comparably well. We further discuss the model uncertainties associated with the interpretation of resonance structure. We also review recent extensions of the Hamiltonian framework developed to address more complicated dynamical settings.

Symmetry doi: 10.3390/sym18111857

Authors: Jiaqian Ji Jiake Li Huixiao Zhou Lifeng Yang Shaopeng Zhou

Video anomaly detection is critical for information security in IoT-based intelligent surveillance, where heterogeneous sensors continuously measure the physical environment and anomalies manifest as deviations from learned normal behavior. Existing methods, however, still struggle to jointly model long-range spatio-temporal dependencies and to fuse heterogeneous multimodal measurements. Deploying such detectors on resource-constrained edge devices remains a further practical barrier. To address these challenges, we propose E-STG-DiffNet, an edge–cloud collaborative multimodal spatio-temporal graph diffusion network that formulates secure IoT surveillance as a network measurement problem. The system employs a Video Swin Transformer to extract multi-scale visual features with linear complexity. A dynamic adaptive spatio-temporal graph convolutional network (ST-GCN) with trainable node embeddings then fuses the heterogeneous sensor measurements in non-Euclidean space, and a masked latent diffusion model (MLDM) combines masked context reconstruction with stochastic denoising for anomaly scoring. A confidence-aware edge–cloud collaborative inference mechanism, supported by knowledge distillation, enables low-latency deployment. On UCSD Ped2, CUHK Avenue, and ShanghaiTech, E-STG-DiffNet reaches frame-level micro-AUC scores of 98.1%, 90.4%, and 78.3%, respectively, competitive with the strongest recent methods on these benchmarks. All results are averaged over three random seeds. Ablation studies confirm that each core component contributes to the overall performance. In the efficiency analysis, the system sustains 26.3 FPS with a mean end-to-end latency of 43 ms (99th percentile: 88 ms), while only about 10% of frames are offloaded to the cloud as compressed latents, about 0.03% of the raw-video uplink traffic. Because the public benchmarks used in our experiments do not contain real non-visual sensor streams, the temperature, vibration, and acoustic modalities are simulated following an established protocol. The reported results therefore primarily validate the video anomaly detection capability of the framework, and validation on real multimodal sensor networks is left to future work.

Symmetry doi: 10.3390/sym18111856

Authors: Žiga Donik Srečko Glodež Janez Kramberger Tadeusz Łagoda Jernej Klemenc

In this study, the mechanical behavior of continuous-fiber-reinforced rubber composites is investigated experimentally and numerically. Uniaxial tensile tests were performed on the rubber matrix, individual reinforcement fibers, and composite laminates with different fiber orientations and layer configurations. The experimental results were used to calibrate and validate a finite element model developed in ANSYS MAPDL (release 2026 R1), in which the rubber matrix was described using an incompressible Mooney–Rivlin hyperelastic formulation, while the reinforcement was represented by embedded discrete elements with a linear-elastic or a nonlinear elastic cord model. The composite simulations capture the main influence of fiber orientation and laminate structure on the global stress–strain response. The 0∘/90∘ configurations exhibit higher stiffness because fibers aligned with the loading direction transfer load directly, whereas the 45∘/−45∘ configurations show a more compliant response governed by matrix deformation and fiber reorientation. At higher deformation levels, the measured softening was not captured by the model. These differences may be attributed to damage mechanisms such as matrix degradation and fiber–matrix debonding, which are not included in the current formulation. The proposed modeling approach provides a basis for assessing the global mechanical response of such composites and for future extensions that include interfacial damage and fatigue.

Symmetry doi: 10.3390/sym18111855

Authors: Dacheng Shan Shishun Zhu Changchun Cheng Wei Liu Yuxuan Yang Yan Li Cen Chen

Advanced persistent threats are complex, stealthy, and long-lasting attacks that can seriously compromise networked systems. System logs provide critical information for APT detection, and provenance graph analysis is commonly used for log anomaly detection. However, existing graph-based methods build provenance graphs from a single perspective, lacking adequate integration of structural and semantic information among entities. To address this issue, we propose a log anomaly detection method based on dual graph modeling and mutual knowledge distillation. The structural branch captures event interactions among entities, while the semantic branch captures associations implied by node text attributes. Relational graph convolution is applied for representation learning in both views. During training, a mutual knowledge distillation framework enables the two branches to serve as teachers and students for each other, facilitating bidirectional knowledge transfer. A reliability estimator based on noise-perturbation invariance assigns higher weights to samples with more trustworthy teacher outputs. Experiments on three public datasets demonstrate that the proposed method achieves statistically significant improvements in Recall on Wget and Cadets, and in Precision on StreamSpot, while maintaining F1-scores comparable to MAGIC across several datasets. Threshold-independent ROC-AUC evaluation further shows that the observed advantages on Wget and Cadets are also reflected in anomaly ranking performance rather than being solely attributable to threshold selection. Ablation experiments validate the contributions of dual-graph modeling, mutual distillation, and the reliability estimation mechanism.

Symmetry doi: 10.3390/sym18111854

Authors: Linjing Tang Yiyang Zhou Xin Fu Song-Zhi Su

Music offers a stringent test of embodied intelligence because performance couples precise timing, morphology-dependent sound production, action-conditioned perception and interpersonal coordination. We conducted a systematic mapping survey with a piano-priority mechanism sample. Source screening retained 12,175 version-merged records, thematic screening retained 1944 and task-context screening advanced 831. Abstract and selected-method assessment advanced 241 technically relevant records, from which 96 research papers were selected for full-text coding. We propose three operational tests, a five-axis taxonomy and a separate L0–L4 ladder. The 96 independent full-text coder pairs yielded linear-weighted Cohen’s κ=0.939 for sensorimotor closure and κ=0.958 for embodiment level. Among 62 physical musical papers, 20 reported task-level acoustic feedback, 18 numerical system/component delay and 38 hardware limitation, failure or recovery; none of nine socially interactive physical papers separately quantified both influence directions. These are descriptive reporting frequencies in a purposive piano-priority sample and do not estimate field-wide prevalence. Forty-eight contextual references support definitions and transfer interpretation outside core denominators. The symmetry-aware synthesis separates geometric invariance/equivariance from directional partner influence and morphology-dependent action constraints. It supplies falsifiable propositions and proposed tests, rather than symmetry-coded prevalence results or new robot experiments.

Symmetry doi: 10.3390/sym18111853

Authors: Lirong Huang Hua Zhang

AI technology is widely used in contemporary supply chain management; however, its asymmetric effects on upstream and downstream supply chain concentration risks remain underexplored. Based on information asymmetry theories, this study empirically examines the relationships between corporate AI technology and asymmetric supply chain concentration risks. Specifically, Python 3.8.10-based word frequency analysis is used to measure corporate AI technology levels, and the Ordinary Least Squares (OLS) regression technique is applied to analyze panel data from Chinese listed firms from 2013 to 2025. The results reveal a significant asymmetric effect: AI reduces upstream supplier concentration risk but increases downstream customer concentration risk. This divergent pattern breaks the symmetry of risk distribution between upstream and downstream supply chain partners. As a result, AI adoption lowers firms’ total supply chain management risk. Further analysis shows how information asymmetry critically moderates these effects. Among firms facing greater information asymmetry, AI strongly mitigates upstream supplier and overall supply chain management risk. Nevertheless, its moderating effect on downstream customer concentration risk is not significant. This conditional asymmetry demonstrates that AI’s risk impacts are not fixed but depend on the symmetric state of information exchange in supply chains. As such, this study clarifies AI’s asymmetric governance role in supply chains and reveals the broken symmetry in upstream and downstream risk evolution driven by AI. It defines conditions for AI-enabled risk optimization and enriches information asymmetry theories by explaining how information imbalance reshapes the symmetric properties of supply chain risk. The findings offer practical guidance for firms to tailor AI strategies and balance upstream and downstream risk management.

Symmetry doi: 10.3390/sym18111852

Authors: Yaohui Wang Zhibin Wang Jiehan Xu Xiaoyi Zhou Yajun Lu Hao Wang Chen Du Qi Zhang

For targeted backdoor attacks against power load time-series classification models, attackers can exploit covert temporal triggers to misclassify genuine high-load states as low-load states, leading to issues such as underestimation of load risks and failure of alarms. Since trigger effects may vary across different network modules, existing methods, such as pruning, fine-tuning, and unlearning, typically apply a one-size-fits-all approach, making it difficult to balance backdoor suppression with the accurate identification of normal loads. To the best of our knowledge, this paper is the first to systematically investigate backdoor defense in this scenario, focusing primarily on local time-domain triggers and verifying the method’s applicability under frequency-domain attack conditions. To this end, we propose PRISM-TS, a proxy-trigger-guided personalized backdoor defense method. This method utilizes independent proxy triggers to assess module backdoor sensitivity and jointly selects high-risk modules under clean accuracy constraints. Differentiated cleansing strategies are applied to different modules: high-risk modules are replaced with corresponding modules from the clean reference model, while the remaining modules undergo weighted averaging between the clean and backdoor models. In random time-domain attack experiments on the AEP dataset, PRISM-TS reduced the attack success rate to 4.60% while maintaining a clean accuracy of 96.04% and a high-load retention rate of 85.20%. Frequency-domain extension experiments further demonstrate that this method offers effective defense capabilities. However, in three independent experiments on LSTM models, the module search failed to find any combinations that satisfied the clean accuracy constraint, indicating that the method’s applicability to other architectures remains limited.

Symmetry doi: 10.3390/sym18111851

Authors: Yanhua Cai Yuhao Mai Fanqi Meng Hanlong Chen Xiaolong Wang Zhuoli Zhao Xiangang Peng Yutong Wen Weixin Xie

Regional meteorological information does not fully resolve local microclimatic variability, while moving clouds over varied terrain cause dynamic spatial heterogeneity in distributed photovoltaic (PV) power output. This study performs retrospective evaluation adopting observed future period meteorology as known inputs. This study proposes an implicit neural motion field (INMF) for multi-step conditional prediction of distributed PV power under limited local meteorological sensing. Learnable site coordinates, site embeddings, and radial basis function interpolation map discrete site states onto a regular latent grid. A neural ordinary differential equation evolves this field through a wind-modulated Fourier layer, in which wind speed conditions spectral amplitudes and wind direction conditions spectral phases. An auxiliary irradiance-consistency term regularizes the temporal relationship between predicted outputs and irradiance. The model is evaluated on 20 rooftop PV sites in Hong Kong using observed target-period meteorology. Joint wind modulation reduces RMSE by 8.9–18.5% across the four evaluated step horizons. In the ablation experiments, phase modulation and the irradiance-consistency term yield reductions in aggregated-series RMSE. The latent coordinates represent learned intersite relationships, and the evolving field provides a representation of PV dynamics under the specified meteorological conditions.

Symmetry doi: 10.3390/sym18111850

Authors: Xingxing Li Xiaochen Liu Qunli Wang Zhengchao Wei Ming Linghu Xin Liu Haoran Sun

Transparent objects produce incomplete RGB-D measurements, degrading scene geometry and downstream pose-candidate generation. We designed TransGeo6D, a lightweight two-stage framework linking transparent-object depth completion to six-degree-of-freedom pose-candidate generation. Lite-DCNet combines explicit depth-validity and gradient cues with learned RGB-D features through geometry-aware gating and convolutional gated recurrent refinement. Lite-GSNet integrates a Ghost-based sparse backbone with channel- and point-wise candidate attention. Candidate-point pooling yields permutation-invariant channel descriptors, while twofold rotational symmetry identifies equivalent orientations of the ideal parallel-jaw representation. These properties support feature aggregation and the interpretation of candidate-pose consistency. On the scene-exclusive TransCG test set, Lite-DCNet has 0.308 million parameters and achieves a mean absolute depth error of 10.26 mm. Lite-GSNet has 2.3953 million parameters and reaches 15.19 frames per second in module-level profiling. With Lite-GSNet frozen on 30 scene-disjoint TransCG test scenes, Lite-DCNet achieves translation and rotation drifts of 57.95 mm and 39.77°, respectively, with a PCR@30/30 of 27.40% and a GT-CF@50 of 33.62%, the highest rates among the three compared learned depth front ends. Controlled regional perturbations reveal spatially nonuniform sensitivity to comparable depth disturbances, linking depth recovery to candidate stability under the parallel-jaw orientation equivalence.

Symmetry doi: 10.3390/sym18111849

Authors: Zhong-Mei Gao

Offline reinforcement learning aims to learn effective policies from fixed datasets without further interaction with the environment. However, limited behavior-policy coverage can lead to value-estimation errors and unreliable policy improvement, particularly when multiple critics provide conflicting update directions. To address these challenges, we propose Probability-Ratio-Constrained Q-Learning (PCR-QL), which integrates behavior-density modeling, conservative ensemble-based Q-learning, and probability-ratio-regularized policy extraction to control distributional shift. Building on this framework, we further introduce Consensus-Gated PCR-QL (CG-PCR-QL), which evaluates critic-specific actor gradients using shared states and policy noise and adaptively attenuates the ensemble-mean policy-improvement direction according to the weakest critic-gradient agreement. Theoretically, we establish results connecting ratio-constrained Bellman approximation, behavior-density estimation errors, policy-feasibility repair, and multi-critic gradient geometry, together with conditional guarantees for completed optimizer updates. Experiments on eleven Datasets for Deep Data-Driven Reinforcement Learning (D4RL) benchmark tasks compare nine policy-extraction rules across ten matched runs. CG-PCR-QL achieves a mean performance improvement of +6.32 (95% CI [5.14, 7.50]) over PCR-QL and a pooled interquartile-mean (IQM) improvement of +7.19 [5.63, 8.69]. Furthermore, an analysis of 2400 paired Adam-update events shows an increase of +13.0 [11.1, 14.9] percentage points in the frequency of simultaneous improvement across all critics. Additional ablations and diagnostics examine the effects of gradient consensus, behavior-density estimation, parameter sensitivity, and computational cost. These results highlight the effectiveness of integrating probability-ratio constraints with critic-gradient consensus for more reliable policy improvement in offline reinforcement learning.

Symmetry doi: 10.3390/sym18111848

Authors: Nguyen Minh Tuan Paiwan Wongsasinchai Chaiyod Kamthorncharoen Sekson Sirisubtawee Chukiat Saksurakan

This paper introduces a new sixth-order (2+1)-dimensional generalized Calogero–Bogoyavl enskii–Schiff (S2GCBS) equation and provides exact analytical solutions by using Physics-Informed Neural Network simulation (PINNs). By applying an appropriate traveling wave transformation, the governing nonlinear partial differential equation is reduced to an ordinary differential equation. A systematic solution procedure is then employed to derive several classes of exact solutions. As a result, different types of wave structures are obtained, including hyperbolic function solutions (soliton solutions), trigonometric function solutions (periodic wave solutions), and rational solutions. In particular, the obtained results contain bright soliton solutions, dark soliton solutions, singular soliton solutions, and periodic wave solutions expressed in compact analytical forms. These solutions reveal the rich dynamical behavior of the gCBS model and demonstrate the effectiveness of the proposed method in constructing exact solutions for nonlinear evolution equations arising in mathematical physics. The physical characteristics of the obtained solutions are illustrated through several graphical representations.

Symmetry doi: 10.3390/sym18111847

Authors: Zhaofeng Wang Yuqi Pang Shuai Zhang Mengtao Lao Zekun Xue

This study focuses on the single-objective day-ahead economic dispatch of grid-connected microgrids. It proposes an asymmetric GE-RTH-SH framework that integrates gradient-guided elite search (GE), Red-Tailed Hawk Optimization (RTH), and SHADE-lite adaptive differential search (SH). Based on the three-stage search mechanism of RTH (high-altitude circling, low-altitude circling, and dive hunting), GE local fine search and SH adaptive differential search based on successful history are introduced to improve local optimization accuracy and parameter adaptability and alleviate search stagnation. An aggregated microgrid model with a 24 h scheduling cycle and a 1 h time resolution is constructed to coordinate wind power, photovoltaic power, micro gas turbines, fuel cells, energy storage, and power exchange with the grid. The model is implemented in Python, aiming to minimize operation and maintenance costs, fuel costs, and net grid transaction costs, while satisfying power balance, equipment output, ramping, energy storage state of charge (SOC), and grid power exchange constraints. With a budget of 30,000 function evaluations per run, the average cost of 50 independent runs is CNY 5295.06, the standard deviation is 10.01, the best cost is CNY 5269.11, and the average renewable energy supply ratio is 62.55%. Through benchmark-function and ablation experiments, the search effects of the GE and SH modules are analyzed, and the optimization performance, economic performance, and repeatability of the complete algorithm are evaluated through comparisons with other algorithms in the microgrid case and four moderate disturbance scenarios. The results show that the proposed method can provide a feasible optimization scheme for coordinated power allocation and economic operation of grid-connected microgrids.

Symmetry doi: 10.3390/sym18111846

Authors: Lingxiao Liu Fei Wang Chenglei Han Jian Song Li Zhou Yingke Gao

Soft-error detection in resource-constrained out-of-order processors requires balancing reliability against the cost of redundant execution. This paper proposes an independent dual-trajectory mechanism that preserves separate data-dependence chains while sharing physical backend resources, with error checking at selected architectural-event boundaries. Evaluation on SPECint2006 shows that redundant execution costs 18.3% geometric-mean IPC, versus 5.5% for a SHREC-like checker, along with higher protection-logic area. A 2400-injection campaign achieves an 86.4% conditional detection rate and a 78.5% reduction in adjudicated silent data corruption (SDC) relative to a detection-disabled baseline. A targeted ablation further demonstrates the benefit of independent value propagation, increasing detection from 8.7% to 84.3% compared with shared-source execution. These results quantify the reliability benefits of logical independence and its associated performance and hardware costs within a fixed-capacity out-of-order backend.

Symmetry doi: 10.3390/sym18111845

Authors: Zhiqiang Niu Ziyi Qiao Anran Li Fangtong Jiao Ziyue Li Yuyan (Annie) Pan

Strategic drone-delivery planning couples field locations with drone assignments and customer allocations under field capacity, cumulative payload, and round-trip energy constraints. We formulate this problem as a mixed-integer linear program and derive a Lagrangian primal heuristic with capacity-aware recovery and facility-exchange search. We show that the Lagrangian dual equals the linear-programming relaxation of the original model. For divisible demand, integer drone counts yield an exact reformulation that removes interchangeable drone labels; type-specific allocation flows extend the result to heterogeneous fleets. Experiments on 45 synthetic instances assess feasible solution quality against independent bounds. A same-machine comparison shows that the count formulation solves all 15 instances with 30 customers to optimality, while the Lagrangian heuristic has a mean objective excess of 0.72%. The count formulation also supplies incumbents and bounds for all 60- and 100-customer instances. Resource experiments distinguish changes in optimal planning cost from variation in heuristic solutions: payload tightening leaves the optimum unchanged over the tested ample fleet range, whereas a restrictive battery budget increases cost in a designated random-layout instance. The computational results favor the compact formulation for the tested divisible-demand model and identify the conditions under which the Lagrangian search improves feasible plans.

Symmetry doi: 10.3390/sym18111844

Authors: Jintao Wu Yang Hong Xin Wang

With the growing demand for community-based eldercare services, bathing safety, caregiving assistance, and facility compatibility in bathing-support spaces have become important issues in age-friendly product design. However, in the design of bathing chairs for community eldercare settings, the alignment of requirements from multiple user groups with design elements from a symmetry perspective remains insufficiently explored. This study investigated six community eldercare service facilities in Hefei, Anhui Province, and developed an integrated research framework integrating multi-stakeholder needs analysis, weight assessment, design-scheme development, and performance validation. User needs were collected through semi-structured interviews, field observations, and questionnaire surveys, and were consolidated into 24 need dimensions using the affinity diagram method. Core needs were then screened using the FKANO model. An evaluation index system comprising six criterion-level dimensions and 19 indicator-level criteria was then established. Integrated weights were calculated using the precedence chart method and the CRITIC method, and the QFD House of Quality was then used to translate the key needs into design elements. The results indicate that bathing-chair design for community-based assisted-bathing settings should prioritize stable support, sit-to-stand assistance, compact storage, lateral access for caregivers, and lockable rotation. Three alternative design schemes were developed based on these results. The TOPSIS evaluation showed that Scheme C achieved the highest relative closeness coefficient of 0.608 and was therefore selected as the preferred alternative. JACK digital human simulation was then used to evaluate its human–product fit and assess the ergonomic suitability of the design. This study provides an integrated design decision-making framework for translating multi-stakeholder needs into specific design elements, thereby offering a systematic methodological basis for bathing-chair design in community eldercare spaces.

Symmetry doi: 10.3390/sym18111843

Authors: Yifei Li Shouliang Li Aiwei Jiang Fuqiang Yu

Medical lesion segmentation remains challenging due to ambiguous boundaries, heterogeneous appearances, and the limited ability of visual features alone to capture clinically meaningful semantics. Existing vision-language segmentation methods have demonstrated the value of textual guidance, but they often rely on fixed or shared textual representations across different decoder stages, despite the fact that visual features progressively evolve from coarse semantic representations to finer spatial details. To address this stage-wise representation mismatch, we propose SAF-Net, a stage-aware vision-language segmentation framework that couples stage-specific semantic allocation with frequency-refined progressive decoding. Specifically, Adaptive Hierarchical Text Allocation (AHTA) retains the hidden representations from all layers of a frozen medical language encoder and learns independent layer-mixing distributions for different text-guided decoder stages, enabling stage-specific semantic guidance without manually predefined layer-to-stage correspondence. Meanwhile, Frequency-Gated Spatial-aware Channel Attention (FGSCA) refines the incoming decoder features through complementary frequency-aware spatial-channel modeling before cross-modal interaction. By coordinating hierarchical textual semantics with frequency-aware visual refinement across progressive decoding stages, SAF-Net allows the representations participating in multimodal interaction to better adapt to the changing requirements of hierarchical decoding. Extensive experiments on QaTa-COV19 and MosMedData+ demonstrate the effectiveness and competitiveness of the proposed framework.

Symmetry doi: 10.3390/sym18111842

Authors: José R. García-Martínez

An accurate fit to a finite response record may leave both stable and non-Hurwitz models compatible with the observations. Spectral Possibilistic Identification (SPI) measures the additional observation loss required to admit a non-Hurwitz model within a prescribed parameter family and identifies strictly stable possibility cuts. For a cyclic Jordan family of dimension n, explicit response bounds and the spectrum yield the sharp misfit–spectral exponent 1/(2n). The minimum non-Hurwitz loss occurs at the stability boundary and scales as Θ(β2n) as nominal damping decreases. A mass–spring–damper realization illustrates the theory, while nonlinear cart–pole simulations examine observation duration, outputs, and excitation. For the original six-second cart–pole experiment, the local quadratic approximation underestimates the full-loss margin by 82.13%. Lohner-type validated integration encloses the ideal-data margin in [0.93777,0.93778]. Exact spectral profiling has the same optimization target as SPI; changing the output direction can reverse the quadratic approximation error. The margin can help assess whether an allowed fitting-loss increase excludes non-Hurwitz alternatives or whether further observations are needed. Its interpretation depends on the model family, residual normalization, and experiment. The sharp law concerns the specified defective scalar family; the nonlinear certificate establishes local Jacobian stability for the ideal-data benchmark, not global stability or a noisy-data guarantee.

Symmetry doi: 10.3390/sym18111841

Authors: Razvan Bocu Maksim Iavich

Autonomous vehicles, which can drive themselves, represent a novel approach to traffic optimization in crowded urban environments. The behaviour of these vehicles is influenced by environmental data, which determine their driving decisions. Consequently, this paper reports an autonomous driving solution, which comprises the specification and implementation of a comprehensive autonomous vehicle driving model. The traffic data are gathered using a multi-sensor information fusion approach, then encrypted and transmitted to the central backend using the public 4G or 5G mobile data network through a symmetric communication channel. The algorithmic model relies on an optimized deep neural network that retains only the necessary features. Validation and training-loss monitoring indicate that the model does not exhibit a diverging train/validation gap. The solution includes advanced 3D object detection primitives. The model was experimentally evaluated using 200 prototype cars supplied by the partner car manufacturer, which supported this research with relevant real-world experimental data. The outcomes of the experimental evaluation process indicate that the system detects relevant road objects in real time, with a detection rate (recall at IoU 0.5) of 98.92%. This figure characterizes the class-correct detection rate only; it does not by itself constitute a safety assessment of the driving system.

Symmetry doi: 10.3390/sym18111840

Authors: Junwei Huang Wujie Chao Liyu Dai Jinke Wang Xinyi Lin Liye Zhang Yuhong Wang Jianquan Liao

Finite-level nearest-level modulation (NLM) couples modular multilevel converter (MMC) internal dynamics to a discontinuous arm-voltage execution error. Building on an established proportional reduced-order quasi-resonant (P-ROQR) circulating-current regulator and a Fourier-based NLM error-correction concept, this study investigates the interaction between harmonic pre-distortion and circulating-current control under discrete NLM execution. A unified energy/error model and an exact threshold-crossing representation show that sub-level pre-distortion can affect the converter only when an integer insertion command changes. However, threshold opportunity alone does not guarantee closed-loop improvement. A causal cycle-wise quantization-error shaping (QES) layer is therefore combined with a threshold-aware efficacy supervisor that rejects candidate shaping actions when they do not alter the discrete actuator or are predicted to increase the circulating-current response. During large operating-point changes, the QES path is temporarily blocked and is reactivated after coefficient reacquisition and smooth recovery. The fixed QES implementation is first examined in mean-arm and individual-submodule models, where its performance is shown to depend strongly on numerical and model fidelity. In the individual-submodule model, fixed QES reduces the selected high-order component but increases the total circulating-current rms and peak. In the ten-submodule-per-arm model, supervised QES reduces circulating-current rms relative to both fixed QES and the P-ROQR baseline, although its steady-state current peak and switching-transition count remain above the baseline values. During the tested power step, transient blocking keeps the peak circulating-current deviation close to the P-ROQR result while reducing the additional excursion introduced by fixed QES. These results support the use of local prediction to screen candidate shaping actions within the investigated simulation conditions; performance in larger MMC systems and hardware implementations remains to be established.

Symmetry doi: 10.3390/sym18111839

Authors: Dawei Wang Shuaijun Zhou Min Liu Wentao Gui Zixuan Hu Da Liu Zhenfei Guo

To address the strong contact nonlinearity associated with explicit thread modeling and the high computational cost of long-term wear simulations during the cyclic operation of symmetric high-repeatability precision locators, an experimentally calibrated equivalent axial displacement method is proposed. Material parameters and the evolution of clamping force were obtained through tensile tests of T8A carbon tool steel, ball-on-flat reciprocating wear tests, and a 2000-cycle clamping test. The measured clamping force under a reference tightening torque of 3.5 N·m was then used to calibrate the equivalent axial displacement in a thread-free finite element model. On this basis, the Archard wear model was incorporated to investigate load transfer and wear evolution across multiple contact interfaces. The results show that the equivalent model can satisfactorily reproduce the overall evolution trend of the experimentally measured clamping force while preserving the principal load-transfer paths. The wear distribution is jointly governed by local contact pressure and relative sliding, with the inner wall of the locator-body bore identified as the primary wear-sensitive region. Cyclic wear continuously modifies the contact geometry, contact stiffness, and load distribution, resulting in a stagewise evolution of the clamping force. This experimentally calibrated thread-free model connects calculated local wear evolution with the measured global clamping response under the tested condition, providing an engineering basis for evaluating wear-sensitive contacts in precision locators.

Symmetry doi: 10.3390/sym18111837

Authors: Mingzheng Wang Houqing Wang Yanchang Yao Jiayue Qian Yongxin Li

Offset boosting enables spatial regulation of chaotic attractors, yet interactions among jointly regulated states and their computational value remain insufficiently explored. To connect correlated state regulation with intelligent search, this study develops a competitive offset regulation mechanism in a four-dimensional chaotic system. Numerical analysis reveals symmetric chaotic evolution, continuous attractor translation, and infinitely many homogeneous coexisting attractors. Competitive–compensatory interactions between the regulated states further enable coupling-dependent waveform overlap and separation. The principal dynamical behaviors are reproduced on an STM32H750 microcontroller, verifying the feasibility of digital implementation. To exploit the differentiated state information, single-state driving, fixed dual-state fusion, and adaptive regulation strategies are introduced to reconstruct the escaping-energy perturbation in Harris Hawks Optimization while preserving its original position-update mechanism. Comparative experiments and ablation studies demonstrate improved path quality and search stability in complex grid environments, particularly those containing narrow passages and multiple local optima. These findings connect competitive offset regulation with chaos-driven optimization and demonstrate the value of coordinated chaotic-state utilization for constrained path search.

Symmetry doi: 10.3390/sym18111838

Authors: Phassarapon Puengpapat Saowanit Sukparungsee Yupaporn Areepong

Statistical process monitoring for autocorrelated processes with exogenous variables requires control chart methods that can account for both temporal dependence and the distributional characteristics of the process. This study develops an explicit analytical expression for the average run length (ARL) of the Double Homogeneously Weighted Moving Average (DHWMA) control chart for moving average processes with exogenous variables, denoted by MAX(q,r), with exponential white noise. The proposed framework considers both symmetric two-sided control limits and asymmetric one-sided control limits to examine process shifts under different monitoring directions. The asymmetric exponential innovation structure further provides a setting for evaluating the proposed methodology beyond the conventional symmetric distributional assumption. The accuracy of the proposed explicit formulation is evaluated against the Numerical Integral Equation (NIE) method for several MAX(q,r) processes. The results show that the explicit formulation produces ARL values in close agreement with those obtained from the NIE method while substantially reducing the computational time. The DHWMA control chart is subsequently compared with the Homogeneously Weighted Moving Average (HWMA) and cumulative sum (CUSUM) control charts in terms of ARL, standard deviation of run length (SDRL), and median run length (MRL). The simulation results show that the DHWMA chart generally provides lower out-of-control run-length measures than the competing methods. A real-data application using weekly financial data further supports the simulation findings, with the DHWMA chart showing faster detection of process shifts. Overall, the proposed explicit formulation provides an efficient approach for ARL evaluation, while the DHWMA chart demonstrates favorable monitoring performance for MAX(q,r) processes under both symmetric and asymmetric control limit settings.

Symmetry doi: 10.3390/sym18111836

Authors: Zhiyan Zhong Bei Zhang Hongxin Wang

Printed circuit board (PCB) defect detection remains challenging because micro-scale defects often exhibit weak contrast and are easily suppressed by conventional downsampling and balanced multi-scale detection heads. To address these limitations, this paper proposes YOLO-SAM, a lightweight YOLOv8n-based detector with an asymmetric prediction topology for industrial visual inspection. YOLO-SAM integrates an Efficient Channel Attention (ECA)-based C2f_Attention block to enhance defect-aware feature responses, replaces strided downsampling with space-to-depth convolution (SPD-Conv) to preserve fine-grained spatial information, and introduces a high-resolution 160×160 prediction branch while pruning the coarse 20×20 head. MPDIoU loss is further adopted to improve corner-aware bounding box regression. Experiments on the PKU PCB benchmark show that YOLO-SAM achieves 94.68% mAP@0.5 and 92.42% F1-Score with only 1.50 M parameters, improving mAP@0.5 over YOLOv8n by 5.50 percentage points while reducing the parameter count by approximately 50%. Additional evaluations on the DeepPCB and magnetic tile datasets achieve 99.22% and 98.20% mAP@0.5, respectively, indicating that the proposed asymmetric lightweight architecture is effective for heterogeneous industrial defect inspection tasks.

Symmetry doi: 10.3390/sym18111835

Authors: Noha M. Seyam Hamada F. El-Mekawy

In this article, the magneto-thermoelastic response of an isotropic homogeneous half-space within several Green–Lindsay (GL) models is examined in relation to initial stress and operator expansion factors. Through a unifying operator-expansion framework, various stages of thermal relaxation are described by simple, refined, and exponential GL theories as well as classical thermoelasticity theory. The effects of the magnetic field and initial stress are taken into account in the governing coupled equations, and the normal mode approach is used to explain the resulting boundary-value problem. To investigate the impact of the initial stress factor and operator expansion order, numerical outcomes are provided for the temperature, displacement, and stress distributions. The projected thermoelastic responses of the classical, simple, refined, and exponential GL models varied significantly.

Symmetry doi: 10.3390/sym18111834

Authors: Nattan Roberto Caetano

Symmetry is a fundamental notion in thermal fluid sciences and energy applications [...]

Symmetry doi: 10.3390/sym18111833

Authors: Zhikang Niu Meng Chen

Carbon allowance-price forecasting is a multiscale sequence-regression problem: persistent price-level movements coexist with short-term disturbances and associations with observable financial, energy, and environmental indicators. This study evaluates a CEEMDAN–LSTM pipeline in which sample entropy reduces nine intrinsic mode functions (IMFs) to five additive component targets, partial autocorrelation selects component-specific histories, and Spearman coefficients screen CSI 300, the CZCE thermal coal index, and Wuhan AQI as candidate covariates. The component predictors use a common LSTM transition structure with different input configurations. A Harris hawks optimizer incorporating Tent-map exploration and crossover–greedy updates (CRTHHO) searches for the hidden-neuron count and learning rate. On the reported Hubei carbon-market sample of 2009 aligned observations, the updated final-model comparison records MAE = 0.49394, RMSE = 0.88785, and MAPE = 0.01194, versus 0.73014, 1.13677, and 0.01988 for the untuned configuration. These correspond to observed relative error reductions of 32.35%, 21.90%, and 39.94%. The study characterizes the interface between multiscale inputs and recurrent prediction rather than proposing new CEEMDAN or LSTM theory. Results are conditional on the documented evaluation procedure; the available record does not establish complete isolation of test data during every preprocessing and tuning stage. The forecasts concern allowance prices and do not constitute a direct valuation of carbon derivatives.

Symmetry doi: 10.3390/sym18111832

Authors: Jingqi He Hao Yang Xiangyang Xu

Crack images and their annotation labels constitute a critical foundation for intelligent crack detection, yet manual annotation is time-consuming and labor-intensive with high costs. Existing generative methods face difficulties in simultaneously generating well-matched high-quality images and labels, resulting in insufficient reliability. Therefore, a two-stage crack data generation framework is proposed. The data are manually divided according to crack type, and category-specific mask-generation models are trained accordingly. The generated masks are then converted by E-Pix2Pix into realistic crack images with diverse backgrounds, alleviating class imbalance and data scarcity. First, to tackle discontinuous and noisy masks produced by the traditional Deep Convolutional Generative Adversarial Network (DCGAN), CA-DCGAN is constructed for category mask generation with the existing long-range modeling ConvAttn module. By suppressing image noise via enhanced structural similarity, it enables category-specific label production and addresses data imbalance at the source. Compared to DCGAN baseline, FID decreased by 42.38% and SSIM increased by 2.10%. Second, E-Pix2Pix is constructed for mask-to-image translation using the existing low-light-enhancing EBlock module to generate realistic images with stochastic backgrounds. This approach mitigates edge-feature obscuration in low-contrast environments, enhancing synthesis quality while effectively addressing data scarcity. Compared to Pix2Pix baseline, LPIPS decreased by 46.86% and FID decreased by 42.95%. To validate the authenticity and practical utility of the generated data, synthetic samples were merged with Crack500 to create three augmented datasets. Evaluations on six mainstream models show improved IoU, Dice, and F1, confirming category-based synthesis as a robust solution for data-scarce crack segmentation.

Symmetry doi: 10.3390/sym18111831

Authors: Liang Hua Zhen Zhang Bowen Wang Yun Cheng Yinlong Yuan

Overhead ground wires exhibit a regularly repeated stranded configuration, providing a symmetry-related perspective on their local structural organization. Local damage disrupts this regularity, introducing deviations in strand continuity, contour organization, or surface morphology. These damage-associated structural deviations provide important cues for distinguishing different damage types. Reliable recognition is challenging because different damage types may present similar local appearances, while motion blur, haze, illumination variation, and other imaging degradations can further obscure damage-related cues. To improve recognition robustness under variable imaging conditions, this paper proposes a method based on physical-structure evidence learning. Here, physical-structure evidence refers to a structure-related representation learned under hierarchical supervision and structural constraints, rather than an independently validated damage-localization map. The structural differences among dispersed broken strands, non-dispersed broken strands, and conductor wear are represented through two hierarchical states: broken-strand presence and conditional spatial dispersion. A shared broken-strand evidence field is constructed from shallow visual features to encode localized damage-associated structural evidence, and the Broken-Strand Evidence Dispersion Index (BEDI) is introduced to characterize its spatial distribution. Physical-structure constraints and local evidence intervention are further incorporated to encourage structure-related representations. A two-stage training strategy is then employed, consisting of structural-evidence learning on clean samples followed by environment-adaptation training while preserving the learned structural representation. Experiments on a constructed overhead ground wire dataset show that the resulting CBEF-Env model achieves a Clean Acc of 93.18%, a Clean F1 of 93.37%, an OOD Avg of 92.79%, and an OOD Worst of 91.91%. Compared with the ResNet18 baseline, these metrics are improved by 2.76, 2.82, 2.71, and 3.10 percentage points, respectively. Compared with AugMix, RIDG, and RDM, the OOD Avg is improved by 1.96, 3.00, and 2.91 percentage points, while the OOD Worst is improved by 2.05, 3.38, and 3.74 percentage points, respectively. These results indicate improved robustness across the controlled synthetic degradations evaluated in this study, providing a basis for further validation on independently acquired field data.

Symmetry doi: 10.3390/sym18111830

Authors: Maryam H. Aljadani Ashraf M. Zenkour

This paper examines the influence of the empirical material coefficient on the propagation of plane waves in a one-dimensional isotropic thermoelastic lamina with temperature-dependent material properties. Lamé’s parameters and thermal conductivity are considered to vary linearly with reference temperature, and the analysis is performed within the exponential formulation of Lord and Shulman’s generalized thermoelastic theory, which includes a single thermal relaxation time to guarantee a finite speed of thermal waves. The coupled governing equations are converted to the Laplace domain to allow analytical treatment, and the resulting expressions are numerically inverted to attain solutions in the physical domain. We derive explicit formulae for the temperature, displacement, expansion, and thermal stress fields. To highlight the impacts of the temperature-dependent properties, the numerical results are shown graphically. Comparisons with the standard Lord–Shulman model and classical coupled theory are presented to highlight the differences in wave behavior and thermoelastic response.

Symmetry doi: 10.3390/sym18111829

Authors: Zian Li Lihua Wang Ji Li Yang Kou Chaoran Yang Pengtao Wu

An active symmetry support control method based on model predictive control and incorporating transient synchronization security boundaries is developed for a grid-following (GFL)/grid-gorming (GFM) hybrid renewable-energy station comprising GFL wind energy and GFM energy storage. The control objective is to suppress disturbance-induced departures from the dynamic balance between generation-side support and grid/load demand, which are referred to here as power asymmetry rather than phase-domain three-phase imbalance, and to restore a power-symmetric operating state through coordinated active- and reactive-power support. Reduced-order transient synchronization models are established separately for the GFL phase-locked loop and the GFM virtual synchronous generator without explicitly constructing a transient coupling model between the two converter types. For the GFM converter, damping energy is incorporated into the fault-stage transient-energy balance. The resulting transient-energy functions and critical-energy criteria are used to determine the synchronization-stability boundaries, which are then mapped into dynamically updated P-Q feasible regions. A frequency–voltage prediction model combining a system frequency-response model and a point-of-common-coupling voltage-sensitivity model is then established. The GFL/GFM transient-energy constraints, dynamic P-Q security regions, power-regulation capability limits, and command-direction constraints are embedded in the receding-horizon optimization to coordinate active- and reactive-power support while preserving transient synchronization security. Local linearization of the transient-energy constraints and second-order-cone reformulation of the dynamic P-Q regions are adopted to improve online computational efficiency. Simulation results show that, compared with MPC without transient synchronization security boundaries, the proposed strategy limits power-angle excursions, enhances active- and reactive-power support, and mitigates frequency and voltage deviations. A sensitivity analysis is further conducted to examine how uncertainties in grid impedance, inertia, damping, and filter inductance affect the calculated critical energies and P-Q security regions. The results highlight the distinct effects of these parameters on the critical-energy thresholds and dynamic energy margins.

Symmetry doi: 10.3390/sym18111828

Authors: Jingqi Luo

This study addresses existing gaps in collaborative-warranty research for mission-cycle systems, especially the risk–responsibility asymmetry between manufacturers and heterogeneous users. Major drawbacks in prior models include neglected user-usage heterogeneity, static assumptions regarding manufacturers’ repair capabilities, and inadequate post-threshold compensation mechanisms. This paper proposes a dual-threshold collaborative warranty incorporating usage and repair heterogeneity (DTCW-URH) to mitigate such asymmetry. Under this framework, dual thresholds categorize users into light-type and heavy-type groups. A repair-learning mechanism is embedded, enabling manufacturers to improve repair efficiency using pre-threshold repair data. Furthermore, a dual-layer compensation framework is established, covering one-time failure compensation and two-stage downtime-loss compensation for delayed repairs, to re-balance the asymmetric loss-bearing responsibilities of both parties. Guided by reliability and probability theory, pre-threshold and post-threshold cost and period metrics are derived, and multiple limit warranty models are developed via parameter constraints. A profit-oriented pricing model is constructed by combining user segmentation, Softmax-derived purchase-selection probabilities, and the Cobb–Douglas function. Numerical analyses verify the validity of the proposed framework. This research offers a targeted warranty-phase reliability-management solution for mission-cycle systems, balancing costs and risks for both manufacturers and users.

Symmetry doi: 10.3390/sym18111827

Authors: Xiaoliang Liu Zetang Wang Chunhua Gao Yuanzheng Li

Deep-buried tunnels excavated in soft-hard interbedded rock masses under high in-situ stresses frequently suffer from severe asymmetric squeezing. To elucidate the multi-scale controlling mechanism of the bedding dip angle (β), a finite–discrete element method (FDEM) model was developed on the Abaqus platform using the Muzhailing Tunnel as an engineering prototype. The model couples the Mohr–Coulomb criterion for rock matrix plasticization with zero-thickness cohesive elements for interface debonding and shear slip. Following specimen-scale validation against multi-orientation uniaxial compression tests (average peak strength error of 4.67%) and a qualitative consistency check against field failure patterns, the model was employed to investigate the evolution of surrounding-rock deformation, interface damage, and matrix plastic zones across β=0–90∘. Results demonstrate that maximum radial convergence responds non-monotonically to the bedding dip, peaking at β=45∘ (74.47 mm), which is approximately 52% larger than the minimum at β=60∘ (48.97 mm), defining a prominent deformation amplification window within 40–50∘. An asymmetry index (AI) quantifies the pronounced bias induced by inclined strata, reaching a maximum of 0.153 at 75∘. Dominant deformation zones migrate systematically along the perimeter governed by the geometric tangency between bedding planes and the excavation profile; uniquely, intense interlayer shear slip at 30∘ shifts the peak convergence anomaly to the right sidewall. Crucially, macroscopic convergence, interface damage, and matrix plasticization evolve asynchronously, where modest radial convergence may mask substantial subsurface interlayer slip. The asymmetric instability is fundamentally a progressive, cross-scale process driven by the synergy between discontinuous interface slip and continuous matrix shear yielding, providing theoretical guidelines for non-symmetric support design in deep stratified ground.

Symmetry doi: 10.3390/sym18111826

Authors: Mohd Raiz Mohammad Farid Nadeem Rao

In this study, we introduce a Chlodowsky-type generalization of the linear positive Agratini operators and investigate their fundamental approximation properties. We derive exact algebraic expressions for the moments and central moments of the proposed operators. Furthermore, we establish the rate of convergence and obtain quantitative estimates of the degree of approximation using the classical modulus of continuity on expanding intervals. We also investigate the local approximation properties for Lipschitz classes and establish a standard Voronovskaya-type asymptotic theorem. Additionally, we construct a bivariate extension of the newly introduced operators and investigate its weighted convergence properties and rates of convergence. Finally, we present numerical evaluations and graphical illustrations to support the theoretical convergence results.

Symmetry doi: 10.3390/sym18111825

Authors: Qiang Han Bingbing Li Liang Wang Jingjing Gao Fengxiang Wang

Exploring the dynamic evolution of carbon storage plays a crucial role in maintaining ecological stability in river basins. This paper takes the Huai River Basin as the research object and uses the PLUS model to predict land use changes under different development scenarios in the future. Based on the predicted results and meteorological, ecological and other data, the InVEST model was coupled to analyze the spatiotemporal changes of carbon storage under different scenarios in the future. The driving mechanism of carbon stock evolution within the watershed was ultimately analyzed using the GeoDetector model. The results show that (1) the land use pattern of the basin remained generally stable from 2000 to 2023, with cropland as the dominant land use type, impervious surfaces continuously expanding, and the areas of cropland, forestland, and grassland generally decreasing; (2) carbon storage in the basin generally showed a slowly declining trend, exhibiting a spatial pattern of high in the south and low in the north and high in the west and low in the east; (3) natural factors such as the DEM and slope have the greatest impact on the spatial distribution of carbon storage, the interactions among multiple factors are significantly enhanced, and the influence of socio-economic factors has gradually strengthened; and (4) by 2030, carbon storage increases under all scenarios, with the largest increase under the ecological protection scenario and the smallest under the economic development scenario. The results can provide a scientific basis for land use optimization, carbon sink enhancement, and ecological protection under the dual-carbon goals.

Symmetry doi: 10.3390/sym18111824

Authors: David Sanchez-Hernandez Guillermo Urriolagoitia-Sosa Gerardo Reyes-Ruiz Beatriz Romero-Angeles Jacobo Martinez-Reyes Julian Patiño-Ortiz Miguel Patiño-Ortíz Israel Alvarado-Martínez Flavio Arturo Dominguez-Pacheco Claudia Hernández-Aguilar Jonatan Mireles-Hernandez Candy Esmeralda Hernandez-Bravo Francisco Chávez-Gutiérrez Ana Paulina Castellanos-Santibáñez Jonathan Rodolfo Guereca-Ibarra Luis Itzcoatl Lugo-Chacón Fernando Rene Esquivel-Patiño Jorge Alberto Gomez-Niebla

Oblique inflow breaks the nominal rotational periodicity of a geometrically symmetric propeller by introducing an azimuth-dependent velocity component across the rotor disk. This study develops a transparent reduced order blade element/momentum framework to examine the resulting once-per-revolution aerodynamic loading of a representative two-bladed small UAV propeller. The formulation combines blade element aerodynamics, momentum-based induction, Fourier decomposition, and advancing–retreating blade diagnostics over moderate oblique inflow conditions. Particular attention is given to distinguishing quantities that arise directly from the assumed harmonic structure from quantities that provide independent aerodynamic information. A first-order analytical expansion shows that, for small in-plane velocity, the normalized first-harmonic loading scales approximately with the in-plane velocity ratio and therefore with J sin(α), consistent with the numerical model. The analysis additionally reports the absolute first-harmonic load amplitude, spanwise development of the asymmetry, cross-plane hub load components, circulation imbalance, and sensitivity to aerodynamic model assumptions. Published axial and non-axial propeller data are used to establish the range over which the reduced order trends can be interpreted. The results indicate that advance ratio and inflow angle govern the modeled cyclic asymmetry, whereas quantitative magnitudes remain sensitive to sectional aerodynamic assumptions and induced flow representation. The framework is therefore intended as a computationally inexpensive screening and interpretation tool for oblique inflow symmetry breaking rather than as a substitute for phase-resolved CFD or experimental measurements.

Symmetry doi: 10.3390/sym18111823

Authors: Yihong Gu Jingyun Li Hong Ouyang Xiaokang Du Bin Wang

This paper develops a geometrically nonlinear coupled finite element model for high-speed rotating AFG beams using the complete Green–Lagrange strain tensor. The model extends the complete Green–Lagrange formulation, previously used for homogeneous rotating beams, to AFG beams and retains all higher-order axial nonlinear terms. Instead of directly adding a density-dependent centrifugal stiffening term, it solves the steady-state axial deformation from dynamic equilibrium and uses it as an intermediate variable carrying the joint distribution of E(x) and ρ(x), so that both properties enter the geometric stiffening terms. The gyroscopic coupling matrix G is fully retained. Numerical results show that (i) under the present Green–Lagrange formulation, the model predicts a monotonic stiffening trend consistent with complete stiffening in the limiting case at high rotational speeds, whereas the conventional centrifugal-force model can exhibit nonphysical softening under the fully coupled formulation; (ii) the coupled model captures frequency veering and mode exchange; and (iii) the steady-state tip deformation and first bending frequency show opposite trends with k. These results provide a reference for gradient design of rotating AFG beams within the considered parameter range.

Symmetry doi: 10.3390/sym18111822

Authors: Zannatul Ferdous Tulona Joan G. Lynam Mohammad Tarikuzzaman Rajinder K. Bhasin Sven E. Eklund

At present, many secondary agricultural residues are landfilled or burned in the open field, leading to the loss of the valuable nutrients they contain. The valorization of agricultural biomass provides a promising route for resource recovery and circular bioeconomy development, allowing for symmetry in their reuse. Hydrothermal carbonization (HTC) offers a sustainable method for converting agricultural waste to both solid and liquid carbon-containing products. Since the liquid product is highly dilute, it is a challenge to apply it at large scales. In this work, a low-energy separation process, direct contact membrane distillation (DCMD), has been used to concentrate the liquid product from HTC of rice husks while recovering water from it. The effect of feed temperature on DCMD performance in terms of water recovery percentage and concentration factors for the fermentable sugars xylose and glucose was investigated at feed temperatures of 50 °C, 65 °C, and 80 °C. DCMD conducted at a feed temperature of 80 °C yielded the highest value for average water flux at 3.4 L/m2·h. DCMD at 80 °C also showed the highest water recovery (56.9%) compared to the lower temperatures, and concentrated xylose and glucose by 2.06 and 3.20 times, respectively3. Incremental flux measurements revealed evidence of limiting mechanisms, such as temperature and concentration polarization, with prolonged operation time. The results from this study thus establish an integrated HTC–DCMD system for efficient water recovery and the concentration of HTC liquor, thereby enhancing its potential for commercial use.

Symmetry doi: 10.3390/sym18111821

Authors: Xiaohui Cheng Min Duan Yanjun Wang Yun Deng Qiu Lu

Soil visible–near-infrared (Vis-NIR) spectroscopy enables rapid, high-throughput estimation of soil physicochemical properties, but complex deep learning models can increase computational cost and reproducibility burden. This study developed a lightweight full-spectrum embedding multilayer perceptron (LSE-MLP) for simultaneous prediction of soil pH, organic carbon (OC), and total nitrogen (N). LSE-MLP maps 4200-dimensional spectra into a compact, learnable representation and uses residual MLP modules for subsequent nonlinear regression. Using the LUCAS2009 dataset, LSE-MLP was compared with PLSR, SVR-RBF, 1D-CNN, ResNet-1D, and Transformer-1D under a POINT_ID-grouped cross-validation framework. Model performance was assessed using internal split sensitivity analysis, ablation experiments, multi-random-seed analysis, and an independent blind test set. On this test set, LSE-MLP achieved R2 values of 0.9437, 0.9519, and 0.9363 for pH, OC, and N, respectively. Its computational efficiency was primarily reflected in low floating-point operations (FLOPs) and fast batch CPU inference, rather than the smallest parameter count or model storage footprint. Supplementary experiments indicated that band compression reduced input dimensionality with limited performance loss, whereas direct transfer of frozen LUCAS-trained models to KSSL and AUT showed substantial performance degradation associated with spectral and target-distribution differences. Overall, LSE-MLP provides a practical and computationally efficient option for soil property prediction using Vis-NIR spectroscopy under the evaluated conditions, while reliable cross-dataset transfer requires further investigation.

Symmetry doi: 10.3390/sym18111820

Authors: Amir M. Alramady Sirajah A. Alsharif Sherif S. Nafee

We present a systematic, experiment-only parameterization of the radiative neutron capture cross section σn, γ(E) for thirteen actinides of importance to reactor physics, fuel-cycle modeling and transmutation (232Th, 233U, 235U, 238U, 237Np, 239Pu, 240Pu, 241Pu, 242Pu, 241Am, 243Am, 244Cm and 246Cm). A total of 90,299 EXFOR points were reduced to a per-isotope tabular form and analyzed in three regimes whose boundaries follow standard nuclear-data conventions: thermal (E < 0.5 eV), resonance (split into RRR, 0.5 eV–1 keV and URR, 1–100 keV) and fast (0.1–1.0 MeV). In every regime, an empirical and a semi-empirical description are fitted to the same data under a common point-uncertainty model; the effect of dataset-wide normalization offsets is assessed separately by refits with per-dataset log-normalization parameters. Models are compared by reduced χ2, AIC/BIC and—in the URR—by dataset-level hold-out validation, and every derived quantity carries both a delta-method uncertainty and a dataset-level resampling 95% interval. In the thermal region the bound-level-plus-first-resonance form recovers first-resonance energies for 239Pu, 241Pu, 237Np, 241Am and 243Am to more than 3% from cross-section data alone; in the URR the Porter–Thomas-corrected statistical model is preferred on AIC for 7 of 12 nuclides, with fission competition included for the four fissile targets, but on dataset-level hold-out for only 3 of 5; and in the fast region the closed-form black-nucleus statistical model used here fails for 232Th, 238U and 237Np, whereas a default TALYS calculation reproduces the energy dependence for 232Th and 238U after a single normalization, attributing the failure to the approximations of the closed-form model rather than to statistical-model theory. Dataset-level resampling intervals are up to eighty times wider than delta-method uncertainties, demonstrating that inter-experiment discrepancy—not counting statistics—dominates the uncertainty of the pooled actinide capture record.

Symmetry doi: 10.3390/sym18111819

Authors: Yitong Zhang Bobin Yao

Stereo foundation models provide strong cross-domain generalization but remain computationally expensive for real-time and resource-constrained deployment. We propose BRD-Stereo, a bilateral reliability distillation framework that transfers foundation-model stereo knowledge to a lightweight BANet-style student. BRD-Stereo treats reciprocal left–right correspondence after geometric warping as an exchange symmetry and uses localized symmetry violations from occlusion or mismatching to reduce teacher reliability. BRD-Stereo models the spatial reliability of teacher supervision and aligns different forms of teacher knowledge with the student’s detail/smooth aggregation structure. The detail branch receives boundary- and gradient-aware supervision, while the smooth branch is guided by low-frequency disparity consistency and local plane regularization. Reliability cues from left–right consistency, image disparity edge agreement, local regularity, occlusion-aware validity, and available teacher confidence weight the pseudo-label objectives. Sliced score distribution distillation transfers a locally softened disparity target around the teacher prediction without requiring full teacher cost volume supervision. Experiments on Scene Flow, KITTI, ETH3D, and Middlebury show consistent gains over plain pseudo-label distillation, with the largest improvements concentrated in boundary, occlusion, weak-texture, and large-disparity regions while preserving BANet-scale inference efficiency.

Symmetry doi: 10.3390/sym18111818

Authors: Igor Kabashkin

Wireless sensing improves the flexibility of condition monitoring but introduces additional uncertainty from sensor faults, packet loss, and communication degradation, which can resemble genuine physical degradation. This study proposes a symmetry-aware framework for resilient monitoring of homologous paired technical systems, defined as pairs of functionally similar components operating under comparable conditions. The framework is based on conditional cross-component symmetry: paired components are not assumed to produce identical measurements, but their normalized multivariate states are expected to retain a statistically consistent healthy relationship once operating conditions and component-specific differences are accounted for. Departures from this relationship support discrimination between physical degradation and sensor- or communication-related anomalies, while the homologous component simultaneously serves as an external source of analytical redundancy for reconstructing unavailable measurements. A twin-engine aircraft configuration is used as a representative pre-deployment case study for prospective wireless engine-health monitoring. Because the real engines are not equipped with the full wireless sensing architecture investigated here, the quantitative evaluation uses a reproducible synthetic paired-engine environment grounded in real operating and maintenance context. Robustness is examined across independent data generations and under controlled nonlinear model-form mismatch. Within this synthetic setting, the results indicate that cross-component information complements conventional local analytical redundancy, particularly for exhaust gas temperature (EGT) reconstruction as local observability deteriorates, while its benefit decreases when the homologous-component information path itself degrades. The study therefore proposes extending symmetry from a diagnostic property to a potential information resource for resilient wireless sensing and provides a basis for subsequent validation with synchronized operational data.

Symmetry doi: 10.3390/sym18111815

Authors: Yikun Cao Xianmeng Zhao

The Graduate Student Evolutionary Algorithm (GSEA) provides a simple population-based optimization framework, but its performance may be limited by unreliable mentor selection, insufficient adaptation of learning behavior, and inadequate utilization of historical search information. From the perspective of symmetry-related search coordination, maintaining an appropriate balance between exploration and exploitation while accommodating the asymmetric contributions of different individuals and search experiences is essential for effective optimization. To address these challenges, this study proposes an Improved Graduate Student Evolutionary Algorithm, termed IGSEA, for global optimization and grid-connected microgrid scheduling. Three complementary mechanisms are incorporated into the original framework. First, a mental-resilience-based adaptive learning regulation strategy adjusts individual search behavior according to relative fitness and stagnation information, facilitating a dynamic balance between global exploration and local exploitation. Second, a collective value-guided mentor–peer collaboration strategy integrates the global best solution, rank-weighted elite information, population consensus, and peer differences to construct more reliable search guidance while coordinating individual and collective information. Third, a practice–reflection-based knowledge feedback strategy employs asymmetric feedback from successful and unsuccessful search movements, retaining beneficial directions and using unsuccessful updates to generate corrective information. Through these mechanisms, IGSEA seeks to coordinate competing search requirements without imposing artificial symmetry on the optimization landscape. The proposed algorithm is evaluated on the CEC2017 benchmark suite under 10-, 30-, 50-, and 100-dimensional settings. Numerical results, convergence curves, boxplots, Friedman rankings, and Wilcoxon signed-rank tests demonstrate its competitive solution accuracy and robustness. IGSEA obtains Friedman mean ranks of 1.47, 1.33, 1.43, and 1.87 under the four dimensional settings, respectively. Furthermore, IGSEA is applied to day-ahead scheduling of a grid-connected microgrid comprising renewable energy sources, dispatchable generators, battery energy storage, and utility-grid interaction. It achieves a best scheduling cost of 1275.65 and an average cost of 1393.56, reducing the average cost by 9.42% compared with CBSO and 19.15% compared with the original GSEA. These results indicate that IGSEA provides a competitive optimization approach by coordinating adaptive search regulation, collective guidance, and asymmetric knowledge feedback in numerical and constrained engineering optimization problems.

Symmetry doi: 10.3390/sym18111817

Authors: Angelina Osetrova Sándor Frey Oleg Titov Alexey Melnikov Panna Gelle

According to astrometric very long baseline interferometry (VLBI) observations accurate to sub-milliarcsecond levels, the radio quasar 1524−136 (J1526−1351) exhibited an exceptionally large shift, more than 0.1″, between the 1990s and 2010s. This luminous quasar is known for its extended (∼0.4″), highly asymmetric and non-collinear jet structure. Here we analyse historical VLBI astrometric and imaging data, as well as Gaia optical astrometric information, to find the cause of the sudden apparent change in the position. At the X band (∼8.4 GHz frequency), where radio positions are conventionally measured, the core region brightened substantially relative to the hotspot at the end of the northern jet. As a result, the brightness peak shifted from the hotspot to the core, causing the VLBI position to shift accordingly. Similar changes could affect the astrometric positions of other radio sources. A better understanding of the astrophysical reasons behind them is important for maintaining the stability of the VLBI-based celestial reference frame.

Symmetry doi: 10.3390/sym18111816

Authors: Meir Shimon

The Past Hypothesis posits that the Universe began in a state of exceptionally low entropy, matter being near thermal equilibrium while the gravitational degrees of freedom were unusually ordered, and the Weyl Curvature Hypothesis identifies the latter condition with a very small early-time Weyl curvature. Here, an origin for it is proposed within Weyl-invariant (WI) gravity, whose conformalized Einstein–Hilbert (EH) sector of Lagrangian density is supplemented with a quadratic curvature term, −αCμνρσCμνρσ, where Cμνρσ is the Weyl curvature tensor. In the Einstein gauge, the reduced action separates into terms that distinguish one spatial shape from another and terms that do not, the latter canceling from any comparison of configurations. The sign of the Weyl coupling, α>0, is fixed by the spectrum of the theory; α<0 renders the massive spin-2 mode tachyonic. With the sign so fixed, and with the gravitational path integral continued to the Euclidean regime, the Weyl sector of the action is non-negative and vanishes only on conformally flat geometries, so configurations of large Weyl curvature are exponentially suppressed whatever the character of that curvature. The resulting preference for low-Weyl initial configurations is one possible realization of the Weyl Curvature Hypothesis, in which the content of the Past Hypothesis resides as the matter sector is observationally inferred to have been near thermal equilibrium. Its connection to small initial shear is conditional, since conformally flat geometries can in principle be sheared. The quantitative estimates discussed here illustrate the weighting within certain families of configurations. The proposal addresses the low-Weyl gravitational initial conditions relevant to inflation, without—however—requiring an inflationary epoch.

Symmetry doi: 10.3390/sym18111814

Authors: Yunsheng Xu Xinru Li Chen Zhang Ziyi Tang Xingchen Xiang Yunfei Lu Tianping Deng Bo Xu

The increasing deployment of Unmanned Aerial Vehicle (UAV) swarms in Internet of Things (IoT) systems enables large-scale cooperative data collection. However, cooperative data collection by UAV swarms remains difficult due to sparse rewards, redundant exploration, inefficient coordination, and the need to refine discrete policy proposals before environment execution. To address these limitations, this paper studies cooperative UAV target collection in randomized simulated environments with observable target and obstacle locations and proposes a Full Spatial Coverage Memory Multi-Agent Proximal Policy Optimization (FSCM-MAPPO), a cooperative data collection algorithm integrating global perception grid with dynamic shared memory, a dense reward shaping mechanism, and a neuro-physical hybrid action controller. Specifically, a global perception grid with dynamic shared memory provides explicit spatial memory and coverage awareness, in which the global coverage information is complementary to each UAV’s local observation, thereby alleviating reward sparsity and redundant search. A neuro-physical hybrid action controller refines policy outputs through local geometric screening, velocity-based intent refinement, and discrete action selection. In an enhanced Multi-Agent Particle Environment with dynamic energy constraints, FSCM-MAPPO attains 71.80±9.73% full-task success and 95.77±1.67% target collection across five independent seeds under deterministic action selection, outperforming the tested MARL baselines. Ablations further show that coverage memory improves visitation and reduces repeated visits, while dense shaping and hybrid control aid task completion. Furthermore, fixed-policy comparisons reveal that hybrid control reduces accumulated contact exposure but increases contact-entry events, indicating a trade-off between task completion and contact behavior.

Symmetry doi: 10.3390/sym18111813

Authors: Raghu Kulkarni

In the Selection–Stitch Model, the vacuum is a face-centered-cubic lattice carrying a stabilizer code, and matter is a node trapped in a tetrahedral void; a predecessor construction closes the bond algebra of vacuum and matter into the algebra f4, with color a factor of the fixed subalgebra of a triality twist and electric charge quantized in thirds. This paper is an algebraic result with a physical interpretation, and the two are kept separate throughout. The two tetrahedral void orientations are exact inversion partners in the static crystal, so orientation is not a label there; but on a chronological defect worldline, the pairing relaxes from P to PT, and doubling every matter weight by the now-physical orientation label—with the three glue classes at 120° in a new plane—assembles the 72-root system of E6, verified by reflection closure, rank, and Cartan determinant, the charge-based competitor failing. The orientation flip is an automorphism folding e6 back to f4; trinification follows from the root system, and the 27’s color-singlet block is a lepton-family-structured sector whose fold is the predecessor’s octet plus one singlet. The same geometry selects a charge direction: among Cartan charges commuting with color, those odd under the extended inversion and even under the orientation flip, which every hop performs, form one line, unique up to sign, spanned by Q, on which the 27 carries the Standard Model charges, integer unit included; of eighteen operators with that spectrum, only ±Q passes. Reading Q as the physical electric charge rests on identifications of the two operations that are argued, not proved. No gauge dynamics is constructed; a table maps each claim to its type, status, source, and falsifier, and the open frontier is the chiral projection.

Symmetry doi: 10.3390/sym18111812

Authors: Yang Yu Tianxiang Long Minjia Huang

Urban nighttime vitality and daytime surface heat are often examined separately, leaving unclear how their relationship varies across spatial supports and stages of urban change. This study examines music-cultural nighttime vitality across 4593 fixed 500 m grids in Changsha, China, from 2013 to 2024. We integrated a 2025 music-cultural point-of-interest inventory, annual VIIRS nighttime radiance, warm-season Landsat land surface temperature, and built-environment data. The 2025 music-cultural representativeness index served as a fixed present-day functional reference, while annual radiance captured temporal variation in nighttime activity. Same-grid and neighborhood analyses were used to evaluate spatial scale dependence, and stage-specific relative-change analysis assessed temporal asymmetry. High-MCNVI grids consistently showed greater high-heat prevalence than low-MCNVI grids, with same-grid overlap exceeding spatially constrained null expectations. Bivariate LISA identified recurring high-vitality–high-neighboring-heat clusters, while site and neighborhood thermal levels remained closely aligned. Under the primary 2018 stage division, the dominant relative-change regime reversed from negative-decoupling dominance in 2013–2018 to decoupling dominance in 2018–2024, with the directional contrast shifting from −47.95 to 55.63 percentage points. Panel and XGBoost–SHAP analyses further showed that vegetation and built-up intensity were more consistently associated with DSHBI and contributed more to prediction than function-specific nighttime vitality. These results distinguish spatial scale dependence from temporal asymmetry and provide a function-specific framework for examining the thermal context of urban nighttime culture.

Symmetry doi: 10.3390/sym18111811

Authors: Iqbal Ahmad Ahmad Almutlg

Julia and Mandelbrot sets are fundamental objects in fractal geometry and complex dynamical systems. Their generation commonly relies on escape-time algorithms combined with iterative schemes. While previous studies have mainly considered generalized rational functions, this work introduces a novel fractal-generation framework based on the Das–Debata iteration. An escape criterion is established for the proposed scheme by incorporating complex generalized rational functions and different orders of their application within the iterative method. Several numerical examples of Julia and Mandelbrot sets are presented to illustrate the resulting fractal structures and the effects of varying iteration parameters on their size and shape. In addition, the average escape time (AET) and non-escaping area index (NAI) are employed to quantitatively analyze the dependence of the generated fractals on the iteration parameters. The numerical results reveal a nonlinear dependence of these measures on the selected parameters for both function orders. The proposed framework provides a flexible approach for generating and analyzing diverse fractal structures.We believe that the insights gained from this study will inspire and motivate researchers and enthusiasts with a deep interest in fractal geometry.