Search Results (2,028)

This paper investigates the decomposition of the $\lambda$-fold complete 3-uniform hypergraph $\lambda K_{\nu }^{\left(3\right)}$ into 4-cycles, denoted as $S_{\lambda }(3,{\mathrm{\Gamma }}_{5,1},v)$. Using the ${\mathrm{\Gamma }}_{5,1}$-structure as a model, we develop recursive construction techniques that exploit symmetric properties and provide explicit designs for small orders. These recursive frameworks enable the systematic generation of large-order hypergraph designs from smaller building blocks, illustrating the symmetric inheritance of structural properties. We establish that the necessary conditions for such a decomposition are also sufficient: an $S_{\lambda }(3,{\mathrm{\Gamma }}_{5,1},v)$ exists if and only if $24\mid \lambda v(v-1)(v-2),2\mid \lambda (v-1)(v-2),\mathrm{and}v\ge 5.$ This result highlights the deep interplay between combinatorial design theory and symmetry in hypergraph decompositions. Full article

In this paper, the use of nilpotent Lie algebras as the basis for homomorphic encryption based on additive operations is explored. The $g$-setting is set up over $g{l}_n\left({\mathbb{Z}}_q\right)$) and the group $G=exp\left(g\right)$, and it is noted that the exponential and logarithm series are truncated by nilpotency in a natural way. From this, an additive symmetric conjugation scheme is constructed: given a message element $M$ and a central randomizer $U\in z\left(g\right),$ we encrypt $=Kexp\left(M+U\right)K^{-1}$ and decrypt to $M=log\left(K^{-1}CK\right)-U$. The scheme is additive in nature, with the security defined in the IND-CPA model. Integrity is ensured using an encrypt-then-MAC construction. These properties together provide both confidentiality and robustness while preserving the homomorphic functionality. The scheme realizes additive homomorphism through a truncated BCH-sum, so it is suitable for ciphertext summations. We implemented a prototype and took reproducible measurements (Python 3.11/NumPy) of the series $\{{10,10}^2,{10}^3,{10}^4,{10}^5\}$ over 10 iterations, reporting the medians and 95% confidence intervals. The graphs exhibit that the latency per operation remains constant at fixed values, and the total time scales approximately linearly with the batch size; we also report the throughput, peak memory usage, $\mid C\mid /\mid M\mid$ expansion rate, and achievable aggregation depth. The applications are federated reporting, IoT telemetry, and privacy-preserving aggregations in DBMS; the limitations include its additive nature (lacking general multiplicative homomorphism), IND-CPA (but not CCA), and side-channel resistance requirements. We place our approach in contrast to the standard FHE building blocks BFV/BGV/CKKS nd the emerging NIST PQC standards (FIPS 203/204/205), as a well-established security model with future engineering optimizations. Full article

A novel category of convex functions, termed multiplicatively trigonometric convex functions, are introduced in this paper. We explore their algebraic characteristics and establish connections between such functions and other forms of convex functions. We even show that these functions are symmetric with respect to their components. Furthermore, we prove the Hermite–Hadamard inequality for the mentioned category of functions. In addition, we present new structures of the Hermite–Hadamard inequality within the framework of multiplicative integrals. By broadening these inequalities, the purpose is to reveal some properties and relations that help the advancement of more robust mathematical techniques. Full article

Road-surface distress poses a serious threat to traffic safety and imposes a growing burden on urban maintenance budgets. While modern detectors based on convolutional networks and Vision Transformers achieve strong frame-level performance, they often overlook an essential property of road environments—structural symmetry within road networks and damage patterns. We present Graph-MambaRoadDet (GMRD), a symmetry-aware and lightweight framework that integrates dynamic graph reasoning with state–space modeling for accurate, topology-informed, and real-time road damage detection. Specifically, GMRD employs an EfficientViM-T1 backbone and two DefMamba blocks, whose deformable scanning paths capture sub-pixel crack patterns while preserving geometric symmetry. A superpixel-based graph is constructed by projecting image regions onto OpenStreetMap road segments, encoding both spatial structure and symmetric topological layout. We introduce a Graph-Generating State–Space Model (GG-SSM) that synthesizes sparse sample-specific adjacency in $\mathcal{O}\left(M\right)$ time, further refined by a fusion module that combines detector self-attention with prior symmetry constraints. A consistency loss promotes smooth predictions across symmetric or adjacent segments. The full INT8 model contains only 1.8 M parameters and 1.5 GFLOPs, sustaining 45 FPS at 7 W on a Jetson Orin Nano—eight times lighter and 1.7× faster than YOLOv8-s. On RDD2022, TD-RD, and RoadBench-100K, GMRD surpasses strong baselines by up to +6.1 mAP_50:95 and, on the new RoadGraph-RDD benchmark, achieves +5.3 G-mAP and +0.05 consistency gain. Qualitative results demonstrate robustness under shadows, reflections, back-lighting, and occlusion. By explicitly modeling spatial and topological symmetry, GMRD offers a principled solution for city-scale road infrastructure monitoring under real-time and edge-computing constraints. Full article

The result of accelerated development and technological progress is manifested through numerous changes in the labor market, primarily concerning the competencies of future employees. Many of those competencies have symmetrical character. The determinants that may influence the development of specific competencies are variable and dynamic, yet they share the characteristic of transcending temporal and spatial boundaries. In this paper we propose the use of a combination of Principal Component Analysis (PCA) and Fuzzy Analytic Hierarchy Process (FAHP) to rank 21st-century competencies that are developed independently of the formal educational process. Ability to organize and plan, appreciation of diversity and multiculturalism, and ability to solve problems appeared to be the highest-ranked competencies. The development of key competencies is symmetrical to the skills for the labor market. Also, the development of key competencies is symmetrical to the right selection of the quality of media content. The paper proves that the development of key competencies is symmetrical to the level of education of both parents. One of the key findings is that participants with higher levels of media literacy express more readiness for the contemporary labor market. Moreover, the family, particularly parents, exerts a highly significant positive influence on the development of 21st-century competencies. Parents with higher levels of education, in particular, provide a stimulating environment for learning, foster critical thinking, and encourage the exploration of diverse domains of knowledge. Full article

This study investigates the structural behavior of composite double-web steel beams filled with different types of concrete made from a combination of recycled concrete aggregates and normal aggregates. The research includes both experimental and numerical analyses. Seven specimens were tested under symmetrical two-point loading, all having identical geometric properties: a span length of 1100 mm, flange plates 120 mm wide and 6 mm thick, and web plates 3 mm thick and 188 mm deep. The specimens were divided into two groups, with a control beam without concrete infill. Group one included beams filled with normal concrete in different locations (middle region, two sides, and fully filled), while group two mirrored the same fill locations but used recycled concrete instead. The experimental results showed that using normal concrete improved the ultimate load by 10.19% to 55.30%, with the fully filled beam achieving a maximum increase in ductility of about 568% and a stiffness improvement ranging from 2.6% to 39% compared to the control beam. Beams filled with recycled concrete showed increases in ultimate load from 9.52% to 42.03%, ductility improvements of up to 380%, and stiffness enhancements between 4.5% and 8.03%. Numerical modeling using ABAQUS (2021) showed excellent agreement with the experimental results, with differences in ultimate load and maximum deflection averaging 5.5% and 7.9%, respectively. Full article

This work presents a comprehensive study of weakly B-symmetric warped product manifolds ${\left(WBS\right)}_n$, a natural extension of several classical curvature-restricted geometries including B-flat, B-parallel, and B-recurrent manifolds. We begin by formulating the fundamental properties of the B-tensor $B(X,Y)=aS(X,Y)+brg(X,Y)$, where S is the Ricci tensor, r the scalar curvature, and $a,b$ are smooth non-vanishing functions. The warped product structure is then exploited to obtain explicit curvature identities for base and fiber manifolds under various geometric constraints. Detailed characterizations are established for Einstein conditions, Codazzi-type tensors, cyclic parallel tensors, and the behavior of geodesic vector fields. The weakly B-symmetric condition is analyzed through all possible projections of vector fields, leading to sharp criteria describing the interaction between the warping function and curvature. Several applications are discussed in the context of Lorentzian geometry, including perfect fluid and generalized Robertson–Walker spacetimes in general relativity. These results not only unify different curvature-restricted frameworks but also reveal new geometric and physical implications of warped product manifolds endowed with weak B-symmetry. Full article

In this paper, we aim to investigate a type of lattice-valued fuzzy metric within the framework of L-topology. Firstly, we present a comprehensive construction theorem for this type of metric, utilizing the concept of L-quasi metric. Secondly, we provide an equivalent characterization through the use of C-nbd clusters, which are formed from all $B_r$: one of four types of basic spheres defined herein. Thirdly, recognizing that these four types of basic spheres serve as essential tools for characterizing various metrics, we meticulously examine the relationships among them and outline a series of topological properties associated with these metrics, which include their opening and closing characteristics, symmetrical property, and more. Finally, in addressing the corresponding symmetry problem between two types of basic spheres, namely $B_r\left(a\right)$ and $Q_r\left(a\right)$, we introduce a novel fuzzy p-metric and demonstrate tht the L-real line $\mathbf{R}\left(L\right)$ satisfies this fuzzy p-metric. Full article

This study introduces an innovative approach to Horadam sequences. The aim of this paper is to investigate the Tricomplex Horadam sequence and its properties. It begins with the tricomplex ring $\mathbb{T}$ and key results related to Horadam-type sequences. The Tricomplex Horadam sequence is then defined, with a discussion of its properties, the Binet formula, and the generating function in vector form. Next, several fundamental identities, including the Tagiuri–Vajda and d’Ocagne identities, are examined, along with their implications and examples from previous Tricomplex Horadam-type sequences. Finally, the sum of terms associated with the Tricomplex Horadam sequence is presented. The research problem consists in determining properties symmetrical or analogous to the Horadam-type sequence for the Tricomplex Horadam sequence. Full article

The concept of a genome signature broadly refers to characteristic patterns in DNA sequences that enable the identification and comparison of species or individuals, often without requiring sequence alignment. Such signatures have applications ranging from forensic identification of individuals to cancer genomics. In comparative genomics and evolutionary biology, genome signatures typically rely on statistical properties of DNA that are species-specific and carry phylogenetic information reflecting evolutionary relationships. We propose a novel genome signature based on the compositional structure of DNA, defined by the distributions of strong/weak, purine/pyrimidine, and keto/amino ratios across DNA segments identified through entropic segmentation. We observe that these ratio distributions are similar among closely related species but differ markedly between distant ones. To quantify these differences, we employ the Jensen–Shannon distance—a symmetric and robust measure of distributional dissimilarity—to define a genome-to-genome distance metric, termed Segment Compositional Distance ($\mathcal{D}$). Our results demonstrate a clear correlation between $\mathcal{D}$ and species divergence times, and also that this metric captures a strong phylogenetic signal. Our method employs a genome-wide approach rather than tracking specific mutations; thus, $\mathcal{D}$ offers a coarse-grained perspective on genome compositional evolution, contributing to the ongoing discussion surrounding the molecular clock hypothesis. Full article

The resource theory of coherence addresses the extent to which quantum properties are present in a given quantum system. While coherence has been extensively studied for individual quantum states, measures of coherence for ensembles of quantum states remain an area of active research. The entanglement-based approach to ensemble coherence—arising from the measurement–ensemble duality principle and the Born rule—connects the ensemble coherence with both the entanglement resource and the measurement’s uncertainty. This paper presents two methods for generating ensemble coherence from a fixed amount of entanglement between two qubit systems. The first method involves applying a von Neumann measurement to one part of a non-maximally entangled bipartite state, resulting in a pair of non-orthogonal states whose coherence can equal the initial entanglement. The second method considers a class of symmetric observables capable of generating ensembles used in quantum key distribution (QKD) protocols such as B92, BB84, and three-state QKD. As a result, this work contributes to understanding how much ensemble coherence can be obtained from a given amount of entanglement. Full article

Photodynamic inactivation and antimicrobial photodynamic therapy (PDI/APDT) based on the toxic properties of reactive oxygen species (ROS), which are generated by a number of photoexcited dyes, are promising for preventing and treating infections, especially those associated with drug-resistant pathogens. The negatively charged bacterial cell surface attracts polycationic photosensitizers, which contribute to the vulnerability of the bacterial plasma membrane to ROS. The integrity of the plasma membrane is critical for the viability of the bacterial cell. Polycationic phthalocyanines are regarded as promising photosensitizers due to their high quantum yields of ROS generation (mainly singlet oxygen), high extinction coefficients in the far-red spectral range, and low dark toxicity. For application in PDI/APDT, the wide range of possibilities of modifying the chemical structure of phthalocyanines is particularly valuable, especially by introducing various peripheral and non-peripheral substituents into the benzene rings. Depending on the type and location of such substituents, it is possible to obtain photosensitizers with different photophysical properties, photochemical activity, solubility in an aqueous medium, biocompatibility, and tropism for certain structures of photoinactivation targets. In this study, we tested novel water-soluble Zn (II) phthalocyanines bearing four 4-((diethylmethylammonium)methyl)phenoxy substituents with symmetric and asymmetric charge distributions for photodynamic antibacterial activity and compared them with those of water-soluble octacationic zinc octakis(cholinyl)phthalocyanine. The obtained results allow us to conclude that the studied tetracationic aryloxy-substituted Zn(II) phthalocyanines effectively bind to the oppositely charged cell wall of the Gram-negative bacteria E. coli. This finding is supported by data on bacteria’s zeta potential neutralization in the presence of phthalocyanine derivatives and fluorescence microscopy images of stained bacterial cells. Asymmetric substitution influences the aggregation and fluorescent characteristics but has little effect on the ability of the studied tetracationic phthalocyanines to sensitize the bioluminescent E. coli K12 TG1 strain. Both symmetric and asymmetric aryloxy-substituted phthalocyanines are no less effective in PDI than the water-soluble zinc octakis(cholinyl)phthalocyanine, a photosensitizer with proven antibacterial activity, and have significant potential for further studies as antibacterial photosensitizers. Full article

The cycling stability and widespread practical implementation of aqueous zinc ion batteries (AZIBs) are impeded by dendrite growth and the hydrogen evolution reaction (HER). Herein, theaflavins, a low-cost organic bio-compounds and a major component of tea, were innovatively introduced as an electrolyte additive for AZIBs to address these challenges. When added into the electrolyte, theaflavins, with their strong de-solvation capability, facilitated the more uniform and stable diffusion of zinc ions, effectively suppressing dendrite formation and HER. This, in turn, significantly enhanced the coulombic efficiency (>95% in Zn/Cu system) and the stability of the zinc deposition/stripping process in Zn/Zn system. The Zn/Zn symmetric battery system stably cycled for approximately 3000 h at current densities of 1 mA/cm². Compared with H₂O molecules, theaflavins exhibited a narrower LUMO and HOMO gap and higher adsorption energy on zinc surfaces. These properties enabled theaflavins to be preferentially adsorbed onto zinc anode surfaces, forming a protective layer that minimized direct contact between water molecules and the zinc surface. This layer also promoted the electron transfer associated with zinc ions, thereby greatly enhancing interfacial stability and significantly mitigating HER. When 10 mmol/L of theaflavins was present in the electrolyte, the system exhibited lower impedance activation energy, a smoother zinc ion deposition process, reduced corrosion current, and higher HER overpotential. Furthermore, incorporating theaflavins into the electrolyte enhanced the vanadium redox reaction and accelerated zinc ion diffusion, thereby significantly improving battery performance. This work explores the design of a cost-effective electrolyte additive, providing essential insights for the progress of practical AZIBs. Full article

Financial markets exhibit fundamental asymmetries in temporal causality, where policy interventions create asymmetric transmission patterns that traditional symmetric modeling approaches fail to capture. This work introduces a mathematical framework that exploits the inherent symmetries of transformer architectures while preserving essential asymmetric temporal relationships in financial causal inference. We develop CausalFormer, a symmetry-aware neural architecture that maintains the permutation equivariance properties of self-attention mechanisms while enforcing strict temporal asymmetry constraints for causal discovery. The framework incorporates three mathematically principled components: (1) a symmetric attention matrix construction with asymmetric temporal masking that preserves the mathematical elegance of transformer operations while ensuring causal consistency, (2) a multi-scale convolution module with symmetric kernel initialization but asymmetric temporal receptive fields that captures policy transmission effects across heterogeneous time horizons, and (3) enhanced Nelson–Siegel decomposition that maintains the symmetric factor structure while modeling the evolution dynamics of asymmetric factors. Our mathematical formulation establishes the formal symmetry properties of the attention mechanism under temporal transformations while proving asymmetric convergence behaviors in policy transmission scenarios. The integration of symmetric optimization landscapes with asymmetric causal constraints enables simultaneous achievement of mathematical elegance and economic interpretability. Comprehensive experiments on monetary policy datasets demonstrate that the symmetry-aware design achieves a 15.3% improvement in the accuracy of causal effect estimations and a 12.7% enhancement in the predictive performance compared to those for existing methods while maintaining 91.2% causal consistency scores. The framework successfully identifies asymmetric policy transmission mechanisms, revealing that monetary tightening exhibits 40% faster propagation than easing policies, establishing new mathematical insights into the temporal asymmetries in financial systems. This work demonstrates how principled exploitation of architectural symmetries combined with domain-specific asymmetric constraints opens up new directions for mathematically rigorous yet economically interpretable deep learning in financial econometrics, with broad applications spanning computational finance, economic forecasting, and policy analysis. Full article

For active control of impulsive noise, the conventional filtered-x least mean square (FxLMS) algorithm has poor noise reduction performance. To address this issue, this paper designs a robust cost function by embedding the cost function of the FxLMS algorithm into the framework of the adjustable Softsign function, thereby designing a robust Softsign-FxLMS (SFxLMS) algorithm for ANC systems. Furthermore, the parameter λ of the SFxLMS algorithm significantly influences its robustness and convergence speed. Therefore, a variable λ-parameter SFxLMS (VSFxLMS) algorithm is designed to improve the performance of the ANC system. Simulation studies indicate that the proposed SFxLMS algorithm and VSFxLMS algorithm exhibit stronger robustness, faster convergence rates, and better tracking performance compared to several robust FxLMS algorithms. Moreover, the symmetric properties of the proposed Softsign function contribute to balanced error suppression in both positive and negative directions, enhancing the robustness and stability of the ANC system under asymmetric impulsive noise conditions. Full article