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Multiconfigurational Dynamical Symmetry Description of 40Ca Spectrum -
Revisiting Ramanujan’s Master Theorem -
Analysis of the Fluid Flow for Liquid Steel at the Drain System of Tundishes Using Different Stopper Rod Configurations -
Substitution Driven Local Symmetry Effect in Halogen–π Complexes of Alkenes and Alkynes: A Quantum Chemical Study -
Analytical Description of Strain-Controlled Transport Anisotropy in Graphene
Journal Description
Symmetry
Symmetry
is an international, peer-reviewed, open access journal covering research on symmetry/asymmetry phenomena wherever they occur in all aspects of natural sciences, and is published monthly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within SCIE (Web of Science), Scopus, CAPlus / SciFinder, Inspec, Astrophysics Data System, and other databases.
- Journal Rank: JCR - Q2 (Multidisciplinary Sciences) / CiteScore - Q1 (General Mathematics )
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.3 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2026).
- Recognition of Reviewers: Reviewers whose reports are timely and of high quality receive an APC discount voucher for a future publication in an MDPI journal. Become a reviewer.
- Journal Cluster of Mathematics and Its Applications: AppliedMath, Axioms, Computation, Fractal and Fractional, Geometry, International Journal of Topology, Logics, Mathematics and Symmetry.
Impact Factor:
2.2 (2025);
5-Year Impact Factor:
2.1 (2025)
Latest Articles
Consistency Conditions for Astrons
Symmetry 2026, 18(10), 1649; https://doi.org/10.3390/sym18101649 - 30 Sep 2026
Abstract
We reassess the consistency conditions for a hypothetical population of primordial, electrically charged compact objects, here called astrons. This paper formulates astrons not as a completed model, but as a set of quantitative consistency tests for a primordial large-charge compact-object scenario. The fiducial
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We reassess the consistency conditions for a hypothetical population of primordial, electrically charged compact objects, here called astrons. This paper formulates astrons not as a completed model, but as a set of quantitative consistency tests for a primordial large-charge compact-object scenario. The fiducial phenomenological parameters, , , and megaparsec-scale separations, are treated as a benchmark to be tested rather than as an established outcome of the model. We show explicitly that ordinary accretion-driven charge separation produces charges only of order – for this mass, leaving an 18–21 order-of-magnitude gap relative to the fiducial branch. Thus the large-charge branch, if it exists, must arise from a primordial charge-concentration mechanism not supplied by the minimal capture model. Likewise, the failure of linear Debye–Hückel screening in the enormous electrostatic potential of an astron does not demonstrate charge survival; it identifies a nonlinear neutralization and kinetic-transport problem. Finally, a cosmologically relevant abundance of compact objects requires mean separations of several megaparsecs and must satisfy discreteness, Poisson-power, clustering, and dynamical constraints. The homogeneous Coulomb interaction energy scales as , so it cannot by itself act as a late-time cosmological constant. Moreover, the Lorentz force acts directly only on charged astrons, not on the no-net-charge population of galaxies, photons and neutral dark matter. Any viable cosmological implementation must therefore derive a metric-level or domain-averaged acceleration shared by the neutral cosmic flow, rather than merely a pairwise repulsion among charged sources.
Full article
(This article belongs to the Topic Dark Matter, Dark Energy and Cosmological Anisotropy)
Open AccessArticle
Green Twist to Solvent Extraction and Separation of Metallic Species with Asymmetric Elfin Chelating Ligands
by
Maria Atanassova, Lama Mzek, Rositsa Kukeva, Stanislava Todorova and Vanya Kurteva
Symmetry 2026, 18(10), 1648; https://doi.org/10.3390/sym18101648 - 30 Sep 2026
Abstract
This competitive solvent extraction study of various metal species (27) in the periodic table was conducted by using a series of asymmetric ligands, tested for the first time, composed of N-heterocyclic receptors with variable ring size and a β-dicarbonyl fragment with the aim
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This competitive solvent extraction study of various metal species (27) in the periodic table was conducted by using a series of asymmetric ligands, tested for the first time, composed of N-heterocyclic receptors with variable ring size and a β-dicarbonyl fragment with the aim of providing a snapshot of their efficacy. We evaluated the effect of heteroatoms in the substituent on solvent extraction performance and the selectivity of this type of chelating extractant with equivalent binding sites but an unsymmetric backbone due to differing coordination environments. The influence of the chemical nature of the organic liquid phase on the solvent extraction process was also discussed: ionic liquids ([C1Cnim+][Tf2N−]) or typical organic diluents. Fe3+ can be extracted with all ligands only in IL medium (100%). The separation factors (SFs) between adjacent metals of 4f-series and iron towards other s-, p, d- and f-block metal ions have been assessed from a circular economy perspective: to extend the product lifecycle and regenerate natural resources. The SF values (Fe/Lns) were below ca. 6 for CHCl3, while the SFs for adjacent 4f-series ions were generally close to 1.1, with higher selectivity observed for selected ion pairs. In addition, the competitive solvent extraction process of 12 refractory metals as well as 8 platinum group metals was investigated with the synthesized ligands. The diluent n-heptane (a structurally symmetric alkane) outperformed isooctane (an asymmetric branched alkane) and chloroform (a polar asymmetric solvent) for refractory metal recovery with a maximum efficiency (100%). Furthermore, EPR, Raman and DTA-TG-MS spectroscopy analyses were used to study the extracted d- and f-chelate complexes in the ionic liquid media: Gd3+, Cu2+ and Fe3+.
Full article
(This article belongs to the Section D: Chemistry: Symmetry/Asymmetry)
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Open AccessArticle
Protodetect: Prototype Compactness and Inference Calibration for Few-Shot Out-of-Distribution Detection
by
Zexia Huang, Haoyu Jiang, Jinsong Hu, Xu Gu and Xiaoliang Chen
Symmetry 2026, 18(10), 1647; https://doi.org/10.3390/sym18101647 - 30 Sep 2026
Abstract
Detecting out-of-distribution (OOD) samples from limited labeled data is important for reliable recognition under semantic novelty. Existing few-shot approaches use synthetic or auxiliary unknowns, model only in-distribution (ID) data, or rely on large pretrained vision–language models. This paper presents Protodetect, a metric-learning framework
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Detecting out-of-distribution (OOD) samples from limited labeled data is important for reliable recognition under semantic novelty. Existing few-shot approaches use synthetic or auxiliary unknowns, model only in-distribution (ID) data, or rely on large pretrained vision–language models. This paper presents Protodetect, a metric-learning framework for the conventional episodic, prototype-based setting. Model weights are optimized using ID episodes only, while held-out OOD samples during meta-validation are used to select inference hyperparameters. Protodetect combines the prototypical classification objective with a prototype-anchored triplet loss to encourage compact within-class representations and separation between known classes. At inference, temperature scaling and gradient-based input preprocessing are applied to the prototype-distance scores. Experiments on miniImageNet and tieredImageNet evaluate both closed-set accuracy and OOD AUROC. Across three independent training seeds, Protodetect obtains a mean AUROC of 81.13% under the reported 5-way 5-shot miniImageNet protocol, 1.28 percentage points above the strongest evaluated baseline. On tieredImageNet, the corresponding mean AUROCs are 75.74% and 83.65% in the 1-shot and 5-shot settings, respectively. These results establish Protodetect as an effective incremental approach under the evaluated episodic protocols.
Full article
(This article belongs to the Section A1: Artificial Intelligence with Applications)
Open AccessArticle
Toward Classroom Evaluation Indicator-System Construction for Generative AI-Enabled Teaching: High-Dimensional Indicator Selection via Generative Rebalancing and Asymmetric Heuristic Optimization
by
Xinyuan Zhang
Symmetry 2026, 18(10), 1646; https://doi.org/10.3390/sym18101646 - 30 Sep 2026
Abstract
Generative AI-enabled teaching increasingly requires evaluation mechanisms that can process large candidate indicator sets without being dominated by uneven category frequencies or redundant variables. Existing filter methods are computationally inexpensive but mainly measure marginal relevance, whereas wrapper optimizers can capture feature interactions at
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Generative AI-enabled teaching increasingly requires evaluation mechanisms that can process large candidate indicator sets without being dominated by uneven category frequencies or redundant variables. Existing filter methods are computationally inexpensive but mainly measure marginal relevance, whereas wrapper optimizers can capture feature interactions at the cost of a rapidly expanding combinatorial search space. Standard PSO can additionally be sensitive to random initialization and fixed or weakly adaptive search controls, which may reduce diversity or promote premature convergence. To address this computational trade-off, this study combines a conditional generative adversarial network (CGAN) for class-conditioned rebalancing, a two-stage Pearson correlation coefficient and improved particle swarm optimization (PCC–IPSO) procedure for indicator/feature selection, and a parallel-pooling one-dimensional convolutional neural network with a bidirectional gated recurrent unit (1D-CNN–BiGRU) for downstream validation. IPSO uses Logistic–Sine chaotic initialization, nonlinear inertia control, asymmetric cognitive/social learning-factor schedules, and adaptive t-distribution mutation. Because no classroom dataset is introduced, the computational mechanism is examined on the five-class NSL-KDD benchmark as a high-dimensional, strongly imbalanced test bed. PCC reduces the 41 benchmark variables to 31, and the archived IPSO output contains 16 selected variables. The retained experimental record reports 99.06% aggregate accuracy for the integrated benchmark pipeline and favorable single-run convergence behavior on several optimization functions. However, the archived record does not preserve an independently verifiable final split identifier, repeated-seed statistics, synthetic-sample distance metrics, or computational-cost measurements; therefore these results are reported as recorded benchmark outcomes rather than as statistically validated superiority or official-KDDTest+ performance. Within these limits, the study illustrates how generative rebalancing and deliberately asymmetric heuristic search can be combined for reduced indicator selection under distribution asymmetry.
Full article
(This article belongs to the Special Issue Application of Symmetry/Asymmetry and Machine Learning)
Open AccessArticle
Symmetry-Preserving Clustering and Coordinated Control for Voltage Fluctuation Mitigation and Stability Enhancement in Active Distribution Networks with SoC Balancing of Battery Energy Storage
by
Mingjun He, Xiankui Wen, Siyu Ren, Jinsong Yu, Ke Zhou and Xinyu You
Symmetry 2026, 18(10), 1645; https://doi.org/10.3390/sym18101645 - 30 Sep 2026
Abstract
High penetration of distributed renewable generation in active distribution networks frequently leads to severe voltage fluctuations and challenges system voltage stability, as the inherent power-flow symmetry is disrupted by stochastic and bidirectional power injections. To address these issues, this paper proposes a symmetry-preserving
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High penetration of distributed renewable generation in active distribution networks frequently leads to severe voltage fluctuations and challenges system voltage stability, as the inherent power-flow symmetry is disrupted by stochastic and bidirectional power injections. To address these issues, this paper proposes a symmetry-preserving coordinated control strategy that integrates topology-constrained clustering with state-of-charge (SoC) balancing of battery energy storage systems to actively mitigate voltage fluctuations and enhance operational stability. First, an agglomerative hierarchical clustering algorithm that explicitly enforces physical line connectivity is employed to partition the distribution network into multiple structurally symmetric autonomous control zones. Within each zone, the SoC of distributed storage units is balanced and aggregated into a virtual battery model, thus maintaining energy-level symmetry and reducing the risk of uneven charging/discharging that would otherwise exacerbate voltage deviations. A model predictive control-based rolling optimization framework is then developed to coordinate photovoltaic inverters and energy storage systems across the zones, explicitly targeting the suppression of voltage fluctuations and the maintenance of short-term voltage stability under varying operating conditions. The proposed method is validated on a modified IEEE 34-bus test feeder with high renewable penetration. Simulation results demonstrate that the strategy effectively limits voltage fluctuation magnitudes, keeps nodal voltages within the required bounds, improves the SoC balance among the storage units, and maintains the nodal voltages within the required bounds across all evaluated coordination strategies.
Full article
(This article belongs to the Special Issue Symmetry and Distributed Power System)
Open AccessArticle
TriSAIL: A Source-Sensitive Audit Protocol for Symmetric and Asymmetric Transfer in Hidden-State Safety Probes
by
Guorui Chen, Yifan Xia, Xinliang Ma and Zhijiang Li
Symmetry 2026, 18(10), 1644; https://doi.org/10.3390/sym18101644 - 30 Sep 2026
Abstract
Hidden-state probes are widely used to study safety-related behavior in language and multimodal models, yet their results can change with the data sources, behavior labels, extracted layer, and probe family. We introduce TriSAIL, an evaluation protocol that records these choices and tests how
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Hidden-state probes are widely used to study safety-related behavior in language and multimodal models, yet their results can change with the data sources, behavior labels, extracted layer, and probe family. We introduce TriSAIL, an evaluation protocol that records these choices and tests how they affect the resulting claim. TriSAIL uses three response-derived states—benign, non-refusal jailbreak, and borderline/refusal—and assigns train, validation, and test data by source. We extract hidden states from the final input position in the first generation forward pass, before a generated token is returned. The operating layer is selected using validation data only. We evaluate the protocol on five text-only LLMs and six MLLMs with logistic, kNN, and SVM probes. The LLM results vary substantially across held-out attack families, probe families, and source assignments. The MLLM probes achieve high label separability, while source-ID decoding, prediction–source association, and residualization tests show strong source alignment in the same representations. Because the main MLLM matrix couples sources and labels, these results describe source-sensitive separability. Source-transfer conclusions use source-held-out columns; mixed accuracy is a descriptive overall summary. TriSAIL reports these results with probe sensitivity and source diagnostics so that each score is interpreted under the conditions that produced it.
Full article
(This article belongs to the Special Issue Studies of Symmetry and Asymmetry in Cryptography)
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Open AccessArticle
Symmetry Stability Index: Real-Time Formation Monitoring for Robotic Platoons Based on Turn-Induced Lateral Dispersion
by
Aarón Hernández-Escobar and Alfredo Santana-Díaz
Symmetry 2026, 18(10), 1643; https://doi.org/10.3390/sym18101643 - 30 Sep 2026
Abstract
Robotic platoons must maintain geometric formation integrity while navigating complex environments, yet existing performance metrics primarily evaluate tracking accuracy or inter-vehicle spacing without directly quantifying the evolution of formation symmetry. This paper presents a real-time symmetry monitoring framework based on the proposed Turn-Induced
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Robotic platoons must maintain geometric formation integrity while navigating complex environments, yet existing performance metrics primarily evaluate tracking accuracy or inter-vehicle spacing without directly quantifying the evolution of formation symmetry. This paper presents a real-time symmetry monitoring framework based on the proposed Turn-Induced Lateral Dispersion (TILD) metric and the Symmetry Stability Index (SSI), a normalized indicator that continuously evaluates geometric symmetry degradation during platoon operation. The methodology estimates the lateral geometric error of each follower, accumulates it through the TILD metric, and transforms the resulting dispersion into the bounded SSI. Using predefined thresholds, the framework classifies platoon operation into NORMAL, DEGRADED, and CRITICAL states, enabling continuous online supervision without modifying the underlying controller. The framework was implemented in a ROS 2 and Gazebo environment and validated with a robotic platoon navigating representative BARN benchmark worlds of increasing geometric complexity. The results reveal a consistent inverse relationship between accumulated lateral dispersion and symmetry stability, allowing progressive formation degradation to be quantitatively characterized across operating conditions. The framework thus offers a lightweight, interpretable, and continuously operating symmetry assessment that complements conventional platoon metrics, establishing a foundation for future symmetry-aware supervisory, diagnostic, and cooperative recovery control strategies.
Full article
(This article belongs to the Special Issue Symmetry Applications in Robotics: Current Advances)
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Open AccessArticle
Coordinate-Exchange Symmetry and Generator-Dependent Optimization in Two-Dimensional Fractional Random Walks with Resetting
by
Yunzhi Zhu, Sen Zhang and Saisai Hou
Symmetry 2026, 18(10), 1642; https://doi.org/10.3390/sym18101642 - 30 Sep 2026
Abstract
Does square-lattice symmetry determine the search parameters selected by a fractional random walk with resetting? We compare a walk that updates one coordinate per movement with a walk generated by a fractional power of the full square-torus Laplacian. Both have the same lattice
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Does square-lattice symmetry determine the search parameters selected by a fractional random walk with resetting? We compare a walk that updates one coordinate per movement with a walk generated by a fractional power of the full square-torus Laplacian. Both have the same lattice symmetry and nearest-neighbor limit. For the coordinate-updated walk, we prove that coordinate exchange maps the complete first-passage distribution to that of the parameter-swapped target problem. This identity pairs asymmetric local minima and separates the Hessian at a symmetric stationary point into even and odd sectors. For the full-torus walk, we derive the probability of simultaneous two-coordinate motion and relate it exactly to the ratio of the two lazy-chain spectral gaps. Matched searches on a 31-by-31 torus resolve one equal-index candidate for the coordinate-updated walk and two for the full-torus walk at axial target distances 3–5. One-sided derivatives support the reported boundary candidates as constrained solutions, not estimates of an unconstrained optimal index. A fixed-relative-geometry comparison at side lengths 31, 62, and 93 shows that these candidates remain sensitive to lattice resolution and the index cutoff. Thus exchange symmetry constrains relations among search problems, while the generator, encounter rule, and reset timing determine the candidates recovered in a specified finite system.
Full article
(This article belongs to the Section C: Physics)
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Open AccessArticle
The Investigation of Fault Behaviors and Locations in Hybrid Multiterminal HVDC System Integrated with Renewable Energy Sources
by
Olumoroti Ikotun, Evans Eshiemogie Ojo and Musasa Kabeya
Symmetry 2026, 18(10), 1641; https://doi.org/10.3390/sym18101641 - 30 Sep 2026
Abstract
The study of hybrid multiterminal high-voltage direct current (HVDC) systems revealed different outcomes regarding their performance under fault conditions. Previous research showed that under the fault conditions, the high-voltage direct current (HVDC) voltage experienced a drop to zero, accompanied by a reverse overshoot.
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The study of hybrid multiterminal high-voltage direct current (HVDC) systems revealed different outcomes regarding their performance under fault conditions. Previous research showed that under the fault conditions, the high-voltage direct current (HVDC) voltage experienced a drop to zero, accompanied by a reverse overshoot. In this paper, a model that integrates hybrid multiterminal line commutated converters (LCCs) and a voltage source converter (VSC) with an HVDC network is presented. The model has been mathematically formulated and implemented using Matlab/Simulink (R2018b) software to examine its fault behaviors and locations, particularly on the DC line to ground fault, line to line fault, and single line to ground fault across various fault resistance levels. The system consists of a wind energy conversion system, a photovoltaic array, protection scheme, LCC rectifier station, VSC inverter station, inverter control, AC filters, a distributed parameter transmission line for the HVDC transmission line, a three-phase inductor-capacitor (LC) filter, and a three-phase transformer. The findings indicated that during the scenario of an 8 ohms of resistance under a single line to ground fault, phase A of the inverter AC grid voltage decreased from its operational level. Meanwhile, the voltage across the DC line increased, accompanied by a rise in DC line current. Additionally, calculations of the fault location were determined to be 1.1561 km from the point of reference. This study contributes to the understanding of fault dynamics in HVDC systems, providing essential insights that enhance operational reliability and efficiency in power transmission networks.
Full article
(This article belongs to the Section F: Engineering and Materials)
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Open AccessArticle
Distributed Assembly Permutation Flowshop Scheduling with Capacity-Triggered Batch Transportation and Dedicated Closed-Loop Vehicles
by
Jingcao Cai, Junkui Han, Deming Lei, Lei Wang, Yingjie Wang, Duohao Geng, Shuai Yang, Mengrui Luo, Chang Liu, Xiangqiang Zhong, Qi Hao, Chuang An and Chao Huang
Symmetry 2026, 18(10), 1640; https://doi.org/10.3390/sym18101640 - 30 Sep 2026
Abstract
This paper investigates a distributed assembly permutation flowshop scheduling problem with first-in-first-out (FIFO) batch transportation triggered by vehicle capacity and heterogeneous dedicated vehicles operating in closed loops. Components are processed at multiple factories and transported in batches to a central assembly station, where
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This paper investigates a distributed assembly permutation flowshop scheduling problem with first-in-first-out (FIFO) batch transportation triggered by vehicle capacity and heterogeneous dedicated vehicles operating in closed loops. Components are processed at multiple factories and transported in batches to a central assembly station, where a product can be assembled only after all of its required components have arrived. The objective is to minimize the makespan. Factory assignment and sequencing within each factory determine processing completion times and, through the prescribed transportation rules, affect batch departures, vehicle return times, component arrivals, product readiness, and assembly timing. To address these coupled temporal effects, a Timing Propagation Cooperative Population-Based Iterated Greedy algorithm (TPCPIG) is proposed. It combines multisource population construction guided by temporal features, hierarchical joint reinsertion of factory assignment and sequencing, and bilateral cross-factory cooperative reconstruction; all candidate solutions are evaluated by a unified schedule decoder. Computational experiments on 120 test instances show that TPCPIG achieves an overall average relative percentage deviation of 0.906%, compared with 3.006–8.607% for the four comparison algorithms, and obtains the lowest mean makespan for all tested job sizes from onward. Further ablation experiments and analyses of search behavior clarify the respective roles of the three proposed mechanisms in population construction, evaluation effort, and adjustment across factories.
Full article
(This article belongs to the Special Issue Meta-Heuristics for Manufacturing Systems Optimization, 4th Edition)
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Open AccessArticle
Changes in Elastic Bounce Mechanics Across a Competitive Cross-Country Season
by
Marcus Marek Tortorella and Monique Mokha
Symmetry 2026, 18(10), 1639; https://doi.org/10.3390/sym18101639 - 30 Sep 2026
Abstract
The spring–mass model (SMM) provides a whole-body representation of elastic behavior during running. Effective contact time (tce), effective aerial time (tae), rebound asymmetry (REB), vertical stiffness (kvert), and step frequency (SF) describe complementary temporal
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The spring–mass model (SMM) provides a whole-body representation of elastic behavior during running. Effective contact time (tce), effective aerial time (tae), rebound asymmetry (REB), vertical stiffness (kvert), and step frequency (SF) describe complementary temporal and mechanical features of elastic bouncing, yet little is known whether these characteristics change across a competitive distance-running season. Therefore, this study examined pre- to post-season changes in SMM-derived elastic bounce characteristics in university runners tested at the same within-runner velocity. Twelve university runners from the same team completed a six-minute treadmill run with synchronized motion capture before and after a seven-week season. Bilateral kinematics and kinetics were collected and elasticity variables computed. No significant changes were observed in elastic bounce characteristics. SF increased by 1.65 steps/min (p = 0.409, d = 0.25), but not significantly. kvert showed small decreases (left: p = 0.374, d = 0.28; right: p = 0.613, d = 0.16). REB remained unchanged (left: p = 0.904, d = 0.04; right: p = 0.871, d = 0.05). The competitive season had little influence on group-level elastic bounce characteristics tested at a given running velocity, although individual responses varied.
Full article
(This article belongs to the Special Issue Symmetry and Biomechanics in Sport, Tactical Performance and Physical Expression)
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Open AccessArticle
Structure of Nonlinear Maps Preserving A*B − ξBA onto an Arbitrary ∗-Algebra
by
Sanaa Ahmed Bajri and Bilal Ahmad Wani
Symmetry 2026, 18(10), 1638; https://doi.org/10.3390/sym18101638 - 29 Sep 2026
Abstract
We show that every bijection between complex ∗-algebras satisfying , for a fixed , is additive as soon as its domain is a prime unital ∗-algebra with a nontrivial projection, with nothing assumed about its codomain at all. In the additivity theorems for products built from the involution that we have been able to trace, the codomain carries a hypothesis of the same kind as the domain. But the equation does not merely tolerate an unrestricted codomain: for , surjectivity of alone is already enough to give it a unit and a centre, and once is bijective it becomes semilinear over that centre, a phenomenon we call range rigidity. This already rules out a surjection onto for noncompact X, and, for an infinite dimensional Hilbert space H, onto or a Schatten class. A second, independent argument then extends the exclusion of to every , and reaches the operator ideals on an infinite dimensional H as well at the classical parameter . Through a conjugate-linear equivalence with the classical products , the same machinery yields a new proof of the known classification of such maps between factor von Neumann algebras, which is due to Dai and Lu, for every other than . At , the classification is the one of Li, Lu and Fang, and it is quoted here rather than reproved.
Full article
(This article belongs to the Section B: Mathematics)
Open AccessArticle
Hierarchical Detection and D-S Evidence Fusion-Based Insulation Diagnosis of Oil-Immersed Current Transformers
by
Qingchuan Zhang, Guanghu Xu, Zhongqiang Zhan, Gang Chen, Bei Dong and Yingbin Shi
Symmetry 2026, 18(10), 1637; https://doi.org/10.3390/sym18101637 - 29 Sep 2026
Abstract
Partial discharge monitoring of oil-immersed current transformers (CTs) is susceptible to electromagnetic interference, and single-parameter detection is biased due to incomplete information. To further improve the safety of the oil-immersed CT, an insulation diagnosis method combining hierarchical detection with Dempster–Shafer evidence (D-S) theory
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Partial discharge monitoring of oil-immersed current transformers (CTs) is susceptible to electromagnetic interference, and single-parameter detection is biased due to incomplete information. To further improve the safety of the oil-immersed CT, an insulation diagnosis method combining hierarchical detection with Dempster–Shafer evidence (D-S) theory is proposed in this paper. A three-step diagnostic framework is constructed. At the first step, the liquid level is monitored since it changes with the gas generated by partial discharge. If an abnormality is identified in the first-step screening, features of partial discharge and oil chromatography are synchronously collected at the second step. At the third stage, the basic probability assignment (BPA) of evidence is constructed by adopting the Sigmoid membership function. Two types of diagnostic results, including normal state and discharge fault, are output through D-S evidence theory fusion. The unique contribution of this work lies in using simple oil level monitoring as a trigger for high-precision partial discharge (PD) and dissolved gas analysis (DGA) detection, which significantly reduces the diagnostic cost. Furthermore, by fusing the two evidence sources with D-S theory, the diagnostic reliability for oil-immersed CTs is improved. To verify the proposed method, tests are performed on a 110 kV oil-immersed CT. It is demonstrated that the rise in oil level is observable. Partial discharge signals are often mistaken for false pulses, while oil chromatography data has excellent anti-electromagnetic interference performance and can stably reflect the cumulative deterioration state of insulation. Restricting false partial discharge signals by oil chromatography data can reduce the misjudgment tendency caused by noise. After D-S evidence fusion, the fault confidence level is increased from 0.68 to 0.83, and the diagnostic uncertainty is reduced from 0.13 to 0.02, which effectively alleviates the ambiguity caused by the single partial discharge detection method. A cost analysis, compared with the PD and DGA fully installation scheme, further shows that the proposed scheme has significant cost advantage because the practical failure rate is far below the break-even value of 98.44%. The scheme proposed in this paper significantly improves the online insulation assessment accuracy for high-voltage current transformers via the hierarchical monitoring framework.
Full article
(This article belongs to the Special Issue Advanced Technologies in Electrical and Electronic Engineering, 4th Edition)
Open AccessReview
Asymmetry in Heat Transfer and Phase Change Materials: A Review of Modeling, Simulation, and Applications in Energy Systems
by
Javier Martínez-Gómez, Mario Cando-Cevallos, Paúl Dávila and Juan Francisco Nicolalde
Symmetry 2026, 18(10), 1636; https://doi.org/10.3390/sym18101636 - 29 Sep 2026
Abstract
Asymmetric heat transfer is an intrinsic and defining feature of phase change material (PCM) systems, arising from the nonlinear coupling between conduction, buoyancy-driven convection, interfacial motion, and geometric or operational non-uniformities. This review synthesizes the physical, numerical, and application-specific mechanisms through which asymmetry
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Asymmetric heat transfer is an intrinsic and defining feature of phase change material (PCM) systems, arising from the nonlinear coupling between conduction, buoyancy-driven convection, interfacial motion, and geometric or operational non-uniformities. This review synthesizes the physical, numerical, and application-specific mechanisms through which asymmetry emerges and shapes the thermal behavior of PCM-based energy systems. We first examine the fundamental origins of asymmetry, highlighting how natural convection, material heterogeneity, and spatially uneven boundary conditions distort temperature fields and melt front evolution even in nominally symmetric enclosures. We then provide a comprehensive assessment of state-of-the-art modeling approaches—including full-domain CFD, advanced interface tracking methods, stability and bifurcation analysis, and reduced-order modeling—emphasizing their capacity to resolve asymmetric flow structures and capture the complex dynamics governing phase transition. Experimental observations from optical, infrared, and flow visualization techniques further validate the prevalence of asymmetric patterns and underscore the need for high-resolution multi-field datasets. Building upon these foundations, the review analyzes the implications of asymmetry across key energy applications such as thermal energy storage, building envelopes, solar receivers, electronics cooling, transportation systems, and industrial heat exchangers. We also provide a literature review on the importance of using multicriteria evaluation as a key tool in the design of multidimensional symmetric and asymmetric PCM systems. In this context, we address and analyze the performance criteria, evaluation metrics, case studies, and optimization strategies to be considered in the design of these systems. Finally, we identify critical research gaps—including multiphysics coupling, uncertainty quantification, CFD–machine learning integration, and the exploration of emerging asymmetric applications—and outline pathways toward next-generation PCM-based technologies that not only accommodate asymmetry but strategically exploit it for enhanced thermal performance.
Full article
(This article belongs to the Special Issue Advances in Fluid Dynamics and Energy Systems: Applications of Symmetry and Asymmetry)
Open AccessArticle
Set Stabilization of Probabilistic Boolean Control Networks via Self-Triggered Control
by
Xinling Li, Lei Deng and Huixin Kan
Symmetry 2026, 18(10), 1635; https://doi.org/10.3390/sym18101635 - 29 Sep 2026
Abstract
This paper addresses the set stabilization problem of probabilistic Boolean control networks (PBCNs) via a self-triggered control strategy. Firstly, the algebraic representation of the considered PBCNs is established by employing the semi-tensor product (STP) of matrices. Secondly, Lyapunov functions (LFs) are introduced for
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This paper addresses the set stabilization problem of probabilistic Boolean control networks (PBCNs) via a self-triggered control strategy. Firstly, the algebraic representation of the considered PBCNs is established by employing the semi-tensor product (STP) of matrices. Secondly, Lyapunov functions (LFs) are introduced for the set stabilization analysis, and a constructive algorithm for deriving such LFs is provided. On this basis, a necessary and sufficient condition in terms of the LF is obtained to determine whether a PBCN can achieve stabilization to a prescribed target set with probability one. Furthermore, a design method for self-triggered controls (STCs) is developed. Finally, the Escherichia coli lactose operon is presented as an example to validate the theoretical results of this paper.
Full article
(This article belongs to the Section B: Mathematics)
Open AccessArticle
Symmetry-Breaking Powder Concentration and Temperature Distributions in the Weld Zone of a Geometrically Symmetric A-Type Mold During Metal Powder Injection Molding
by
Po-Yu Yen and Chao-Ming Lin
Symmetry 2026, 18(10), 1634; https://doi.org/10.3390/sym18101634 - 29 Sep 2026
Abstract
A-type mold flow analyses were performed to examine the effects of the feedstock flow behavior on the powder particle distribution in the weld zone following the forward collision of two flow fronts during metal powder injection molding. Although the A-type mold cavity and
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A-type mold flow analyses were performed to examine the effects of the feedstock flow behavior on the powder particle distribution in the weld zone following the forward collision of two flow fronts during metal powder injection molding. Although the A-type mold cavity and the two converging feedstock flow paths are geometrically symmetric about the central weld plane, the present numerical results indicate that the coupled shear-heating and viscosity variation during flow-front collision break this symmetry, resulting in an asymmetric powder concentration and temperature field at the weld zone. This local departure from mirror symmetry was quantified using a proposed Mirror Asymmetry Index (MAI). The complex rheological characteristics of the weld zone result in a separation of the particles and the binder, which leads to changes in the powder concentration distribution. Such predicted concentration non-uniformity may be relevant to local density variation after de-binding and sintering; however, the present study does not simulate sintering or experimentally measure density or mechanical properties. Thus, to enhance the powder concentration in the weld zone and ensure a uniform distribution of the particles, mold flow analysis simulations, combined with the Taguchi experimental method, were performed to identify the optimal material and processing parameters for the metal powder injection molding process. The results indicate that regions of the weld zone with higher shear rates exhibit lower powder concentrations. In addition, local stagnation occurs at the intersection of the two flow fronts, which causes radial flow and phase-separation effects in the weld zone. Among the four factors examined (melt temperature, mold temperature, particle diameter, and injection flow rate), particle diameter was found to exert the dominant effect on weld-plane powder concentration, while the injection flow rate had the least influence. The optimal material and processing conditions (a melt temperature of 220 °C, a mold temperature of 60 °C, a particle diameter of 5 micron, and a filling rate of 10 cm3/s) improved the powder concentration in the weld zone and achieved a more uniform distribution, raising the mean particle concentration by 63.3% and reducing its standard deviation by 74.2% relative to the default settings. These findings show that geometric symmetry alone does not necessarily guarantee perfectly mirror-symmetric predicted process fields under the numerical assumptions used here. Physical confirmation of the predicted asymmetry remains necessary.
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(This article belongs to the Section F: Engineering and Materials)
Open AccessArticle
Short-Term Power Load Forecasting Model Based on an Adaptive Multi-Strategy Gold Rush Optimizer for Optimizing an Dilated BiGRU
by
Xiyuan Li and Yangjian Yang
Symmetry 2026, 18(10), 1633; https://doi.org/10.3390/sym18101633 - 29 Sep 2026
Abstract
Short-term power load forecasting plays a crucial role in the operation scheduling, energy management, and security assessment of smart grids, as its accuracy directly affects the economic efficiency and reliability of power systems. However, power load series are characterized by strong nonlinearity, non-stationarity,
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Short-term power load forecasting plays a crucial role in the operation scheduling, energy management, and security assessment of smart grids, as its accuracy directly affects the economic efficiency and reliability of power systems. However, power load series are characterized by strong nonlinearity, non-stationarity, and multi-scale temporal dependencies, which make it difficult for traditional forecasting models to achieve both high accuracy and strong generalization under complex load scenarios. In recent years, deep learning models have demonstrated promising performance in load forecasting; nevertheless, their effectiveness is highly dependent on hyperparameter configurations. Manual hyperparameter tuning is not only time-consuming but also prone to premature convergence to suboptimal solutions. To overcome these challenges, this study develops an AMS-GRO-based short-term power load forecasting framework. By improving the original Gold Rush Optimizer (GRO), three adaptive strategies are integrated into the proposed optimizer, namely the current-to-pbest/1 mutation strategy, adaptive elite-guided search strategy, and success-rate-based adaptive strategy selection mechanism. These improvements jointly enhance the global exploration capability, local exploitation ability, and strategy adaptability of the optimizer. Subsequently, the proposed AMS-GRO is employed to perform global hyperparameter optimization for a Dilated BiGRU-Attention model, forming the AMS-GRO–Dilated BiGRU forecasting framework. Key hyperparameters, including the learning rate, number of hidden units, attention dimension, and regularization coefficient, are adaptively optimized. Extensive numerical experiments were conducted on the 30-dimensional CEC2017 suite and the 10- and 20-dimensional CEC2022 suites using 30 independent runs. According to the Friedman test, AMS-GRO achieved mean ranks of 1.37, 1.33, and 1.25, respectively, ranking first in all three experimental settings. In the short-term power load forecasting experiment, AMS-GRO–Dilated BiGRU achieved an MAE of 21.09, MAPE of 0.0177, MSE of 791.10, and R2 of 0.9746. Compared with the unoptimized Dilated BiGRU model, these results correspond to reductions of 13.0%, 13.7%, and 21.5% in MAE, MAPE, and MSE, respectively, together with a 0.70-percentage-point improvement in R2. From a symmetry perspective, the proposed framework balances global exploration and local exploitation through adaptive strategy selection, while the Dilated BiGRU exploits bidirectional temporal symmetry to capture multi-scale load patterns. These results demonstrate that the proposed framework provides competitive optimization performance and improves forecasting accuracy on the investigated load dataset.
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(This article belongs to the Special Issue Symmetry in Optimization: From Algorithmic Design to Applications)
Open AccessArticle
RECAP-RL: Symmetry-Guided Retention Shaping and Mirrored Credit Assignment for Personalized Instrumental-Practice Recommendation
by
Yanlu Li, Zhaoen Qu and Zhuodong Liu
Symmetry 2026, 18(10), 1632; https://doi.org/10.3390/sym18101632 - 29 Sep 2026
Abstract
Personalized instrumental-practice planning requires selecting and ordering exercises, allocating duration and difficulty, and accounting for prerequisites, fatigue, spacing, and forgetting across multiple sessions. This paper presents RECAP-RL, a symmetry-guided reinforcement-learning framework that post-trains a structured large language model (LLM) policy to generate budget-feasible,
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Personalized instrumental-practice planning requires selecting and ordering exercises, allocating duration and difficulty, and accounting for prerequisites, fatigue, spacing, and forgetting across multiple sessions. This paper presents RECAP-RL, a symmetry-guided reinforcement-learning framework that post-trains a structured large language model (LLM) policy to generate budget-feasible, teacher-editable practice plans optimized for delayed retention. Symmetry enters at two levels. At the objective level, retention-anchored dense analytic reward shaping (RADAR) re-expresses terminal retention-adjusted learning gain (RALG) as telescoping differences in a retention potential based on the learner’s projected retained mastery; this re-expression preserves core-objective policy ordering and yields an action-independent retention-state baseline whose variance effect is characterized analytically. At the intervention level, matched-intervention replay with residualized order-graph rewards (MIRROR) pairs each exercise with an equal-duration null-practice twin under a common continuation; exchanging the twins reverses the signed retained and prerequisite-unlock contrast, and zero-mean residualization preserves the mean exercise-block advantage when credit is assigned to exercise-token blocks. We instantiate the framework for piano practice in a mechanistic environment with 72 skills and 520 exercises. Against eleven comparison planners on held-out and structurally shifted learner families, RECAP-RL reaches a RALG of , exceeding the strongest observable-state model-based planner by 0.034 and terminal-reward group-relative policy optimization by 0.027, while reducing mean cross-family degradation from 26.6% to 18.8% and improving prerequisite repair and spacing alignment. These simulation results support symmetry-guided reward and credit design for delayed educational planning; longitudinal human studies remain necessary to establish educational effectiveness.
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(This article belongs to the Special Issue Symmetry in Artificial Intelligence and Machine Learning: Current Advances)
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Open AccessArticle
Optimization of Flocculation–Settlement and Continuous Gravity Discharge for Unclassified Sulfide Ore Tailings in a Deep Mine Vertical Sand Tank
by
Jie Chen, Dengpan Qiao, Jun Wang, Yongming Li, Shanshan Zhou and Tianyu Yang
Symmetry 2026, 18(10), 1631; https://doi.org/10.3390/sym18101631 - 29 Sep 2026
Abstract
The continuous thickening and high-concentration discharge of fine unclassified sulfide ore tailings remain a critical challenge for deep-mine cemented paste backfill systems, yet a systematic optimization framework integrating flocculation chemistry, hydrodynamic simulation, and continuous discharge control has been lacking. This study fills this
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The continuous thickening and high-concentration discharge of fine unclassified sulfide ore tailings remain a critical challenge for deep-mine cemented paste backfill systems, yet a systematic optimization framework integrating flocculation chemistry, hydrodynamic simulation, and continuous discharge control has been lacking. This study fills this gap by combining experimental flocculation–settlement tests, response surface methodology (RSM), CFD-PBM-KTGF numerical simulations, and industrial-scale validation for a vertical sand tank operating at over 1000 m depth. A non-ionic polyacrylamide with an optimized molecular weight was selected, achieving a settling velocity approximately five times that of natural sedimentation. Response surface methodology (RSM) analysis revealed that slurry solids concentration, flocculant solution concentration, and flocculant dosage were all significant individual factors affecting the solid flux, whereas none of their pairwise interactions were statistically significant. The optimized parameters achieved a target solid flux that meets the mine’s backfill capacity requirements. CFD-PBM simulations revealed that floc growth occurs predominantly in the mid-depth zone and established a stable sand bed height of 12 m for continuous discharge. A 34 h industrial trial validated the optimized conditions, maintaining average underflow and overflow concentrations well within industrial specifications while achieving a stable dynamic mass balance. This work provides a comprehensive, experimentally validated framework for optimizing tailings thickening and continuous gravity discharge, offering both theoretical guidance and practical reference for deep-mine backfill operations.
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(This article belongs to the Special Issue Asymmetry and Nonlinearity in Geotechnical, Soil and Rock Engineering: Modelling, Mechanisms and Applications)
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Open AccessArticle
Covarying Coupling Constants and Tired Light-like Hypotheses from the Covarying-Bi-Scalar Theory
by
Rodrigo R. Cuzinatto, Rajendra P. Gupta and Pedro J. Pompeia
Symmetry 2026, 18(10), 1630; https://doi.org/10.3390/sym18101630 - 29 Sep 2026
Abstract
This paper presents an attempt to provide a scalar-tensor theoretical foundation for the Covarying Coupling Constants plus Tired Light-like (CCC+TL) phenomenological framework. This is done in the context of the Covarying-Bi-Scalar Theory (CBST) in which the gravitational coupling G and the speed of
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This paper presents an attempt to provide a scalar-tensor theoretical foundation for the Covarying Coupling Constants plus Tired Light-like (CCC+TL) phenomenological framework. This is done in the context of the Covarying-Bi-Scalar Theory (CBST) in which the gravitational coupling G and the speed of light c vary simultaneously while respecting a constraint of the type . This constraint is a global stable critical point of their dynamical evolution in the early universe. In a previous work, it was shown that the varying couplings give rise to a screening mechanism in the Jordan frame, dubbed the c-meleon mechanism. Here, we reconstruct the potential for the c-meleon field , thereby explaining the CCC hypothesis used by one of the authors with phenomenological success. The TL-like behavior of the field is obtained from the spatial dependence of the perturbation of on top of an FLRW background. This work is a step towards a fundamental justification for CCC+TL based on a scalar-tensor theory for modified gravity in the context of our CBST framework.
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(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2026)
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