Search Results (2,988)

This paper develops a general framework for Tsallis entropy (TsE) and cumulative residual Tsallis entropy (CRTsE) for concomitants of generalized order statistics under the Cambanis family of bivariate distributions. Explicit closed-form expressions and alternative representations for TsE and its cumulative residual counterparts, including a unique formulation of the alternative CRTsE, are derived. Various structural properties are established, including symmetry relations between low- and high-rank concomitants, as well as connections with classical submodels such as order statistics and record values. A nonparametric estimator for the CRTsE is proposed; its mean, variance, and consistency properties are investigated analytically and through extensive Monte Carlo simulations. The theoretical framework is further illustrated through two application domains: reliability assessment of real bivariate system data, and histogram-based image segmentation via a rank-sensitive Tsallis-thresholding scheme. The proposed methodology constitutes a flexible, dependence-aware generalization of classical Shannon-based entropy measures and is particularly advantageous for systems exhibiting nonlinear dependence, tail sensitivity, or non-extensive behavior. Full article

The growing demand for compact and high-performance motors in industrial robotic joints has intensified interest in axial flux permanent magnet motors (AFPMs), which inherently offer high torque density and a thin form factor compared with conventional radial flux permanent magnet motors (RFPMs). Among various AFPM structures, printed circuit board (PCB) Stator motors have gained significant attention due to their slotless configuration, reduced cogging torque, low vibration and acoustic noise, and enhanced geometric thinness enabled by PCB-etched conductors. This study proposes a conductor arrangement strategy that mitigates back-EMF imbalance in concentrated-winding single-rotor PCB AFPM for robotic joints. Several conductor configurations are analyzed and compared through electromagnetic finite-element evaluation, and an optimized arrangement is identified that effectively improves phase EMF symmetry while maintaining structural thinness. The results provide design guidelines for high-performance PCB AFPMs suitable for next-generation robotic actuators. Full article

This paper develops a two-variable truncated-exponential-based Hahn–Appell polynomial family of order r in quantum q-calculus, generated by $\mathcal{A}\left(t\right){(1-\eta t^r)}^{-1}{e}_q^{wt}\left(\zeta t\right)$, where $\mathcal{A}\left(t\right)$ is a normalized determining function and $e_q^{wt}$ denotes the Hahn-type q-exponential. From this relation, we derive connections with the underlying Hahn–Appell basis, the finite expansion induced by the truncation factor, the Hahn lowering property, operational resolvents, step-r recurrences, determinant formulas, and Hahn-factorial representations. We also obtain origin values, normalized monicity, parameter-connection and parameter-differentiation identities, quasi-monomial operators, and the associated Hahn-grid difference equation. Limiting and special cases recover known q-truncated-exponential and classical truncated-exponential Appell constructions. For the unit-Appell specialization $\mathcal{A}\left(t\right)=1$, numerical computations for $q=1/2$, $r=2$, $\eta =1$, and $w=1$ provide explicit polynomials, zero tables, diagnostics, and plots that illustrate parameter sensitivity, Hahn-grid deformation, conjugate symmetry of non-real zeros, origin zeros in odd degrees, and the observed layered rightward spread of zero clouds. Full article

Background: Normalized strength outcomes and limb symmetry indices (LSIs) are widely used but poorly characterized across testing conditions, and it is unclear if these vary by sex. This study aimed, first, to investigate sex-related differences in normalized knee flexor strength and LSI values across multiple strength-testing conditions in healthy recreational athletes, and, second, to descriptively examine associations among strength outcomes obtained under different testing conditions within female and male participants. Methods: In this cross-sectional study, 52 healthy, recreationally active adults (26 females and 26 males) underwent bilateral knee flexor strength testing using three force plate-based isometric assessments, one static dynamometer-based isometric assessment, and three isokinetic dynamometer-based assessments. Differences were analyzed with a mixed analysis of variance (ANOVA), and associations were assessed using Pearson correlations. Results: Males showed higher normalized knee flexor strength than females across all testing conditions (main effect of sex: p < 0.001; partial η² = 0.334–0.371), with the magnitude of these sex-related differences varying across testing conditions (sex-by-testing condition interaction: p < 0.001; partial η² = 0.215–0.230). LSI values did not differ by sex (p = 0.896) and remained consistent across testing conditions (p = 0.385). Correlations were generally stronger within force plate-based and isokinetic dynamometer-based assessments (r = 0.528–0.922) than between different testing conditions. Conclusions: Sex-related differences were observed for normalized knee flexor strength but not for LSI values. Strength outcomes obtained under different testing conditions should not be considered directly interchangeable. Full article

Planar linkage mechanisms remain a cornerstone of motion generation and trajectory control, yet the geometric tools that desRcribe their instantaneous behavior, namely centrodes and Bresse’s circles, have been developed almost exclusively for mechanisms with entirely revolute joints, where a sliding pair fundamentally alters the velocity and acceleration fields and disrupts the symmetries on which classical curvature theory relies. This paper presents a comprehensive higher-order kinematic analysis of a planar six-link, single-degree-of-freedom mechanism in which a slider-crank stage and a rocker stage are coupled through a shared prismatic joint that acts simultaneously as output and input. Using vector algebra and a matrix-based loop-closure formulation, the position, velocity, and acceleration analyses are derived in closed form, yielding angular velocity ratios, the instantaneous centers of rotation and acceleration of both coupler links, and their inflection and stationarity circles. The analysis reveals a distinctive geometric constraint on the slider-side coupler’s instantaneous center, a decoupling of the curvature loci of the two couplers, and degenerate configurations, linked to coupler instantaneous-stop and rocker dead-point conditions, that arise at joint-invariant crank angles. Implemented as a computational algorithm and demonstrated on a carton flap-closing mechanism and cross-validated against independent multibody simulation, the framework confirms favorable transmission and dead-point clearance behavior, extending curvature-theory tools to linkages containing sliding pairs. Full article

This paper establishes new criteria for the constancy of real-valued functions defined on general Banach spaces and on exterior domains in ${\mathbb{R}}^n$. The main analytical tool is a complement to Ekeland’s variational principle, while several auxiliary lemmas based on convex analysis play a crucial role in extending the argument to the non-convex framework of exterior domains. The obtained results establish constancy criteria under suitable growth assumptions at infinity, both in general Banach spaces and in the Euclidean setting. A key aspect of the analysis is the distinction between the whole-space and exterior-domain frameworks, showing that stronger asymptotic assumptions are required in the latter case. To illustrate the applicability of the general framework, we present an application to differentiable functions satisfying suitable symmetry-type assumptions on their derivatives. Full article

Starting from the circular aperture diffraction experiment, this paper decomposes the intrinsic interactions underlying wave–particle duality and proposes a specific interaction force: the velocity-perpendicular interaction force. We derive the characterization formula of this force and show that it can induce the phenomenon of circular aperture diffraction of light, with the theoretical results being highly consistent with those calculated by the Huygens–Fresnel principle. The direction of this force is perpendicular to the relative velocity, originating from the coupling effect between the wave nature of light and the particle nature of the circular aperture structure, and it satisfies a modified inverse square law of distance related to the relative velocity. When photons pass through different positions of the circular aperture, the symmetry effect generates a net interaction time. The product of the main component of this force, the net interaction time, and the radius of the circular aperture constitutes a modulation quantity (a ratio of the Planck’s constant), which exerts an on–off modulation effect on the interaction force, thereby inducing the emergence of annular diffraction fringes. This study provides a novel physical interpretation for the circular aperture diffraction of light from the perspective of interaction forces and clarifies the possible existence form of wave–matter interaction forces. This force formula is expected to effectively describe the behavior of microscopic particles, just like the Schrödinger equation, while providing a brand-new perspective on interactions. It holds great application prospects in fields such as single-photon manipulation and quantum precision measurement. Full article

Power grids are complex networks; their dynamics have strong nonlinearity due to the symmetry breaking in their topological structure. Synchronization stability, which is essential for secure and reliable operation, is the focus of this study. In this paper, the effects of phase shift on dynamics and stability in symmetry-breaking power networks are investigated. To clarify the influence of phase shift parameters, power networks of different sizes and topological structures are systematically analyzed, including a two-node power network, the Nepal power network, and the UK power network. The results show that phase shift significantly changes the collective dynamical behaviors of power networks, leading to transitions from frequency synchronization to complete synchronization or desynchronization under different parameter conditions. Moreover, the stability region shrinks as the phase shift increases. The stability transition region is further found to be strongly related to network size, topological structure, and the spatial distribution of generators and consumers in the power network. The results indicate that the stronger the symmetry-breaking in a power network, the more significant the impact of the phase shift parameter on the dynamics and stability. The results of the basin stability analysis for the power system provide quantitative support for this result and reveal the mechanism of power system instability under the effect of phase shift parameters. These findings provide a deeper understanding of the effect of phase shift on the dynamics of symmetry-breaking power networks and offer new insights into synchronization stability and structural design in complex power systems. Full article

Graph neural networks (GNNs) have shown great advantages in collaborative filtering recommender systems due to their capacity to model user–item relationships through information propagation. However, traditional GNN-based recommenders often fail to distinguish nodes with the same local structure, leading to identical representations after propagation. Some studies address this issue by introducing positional encoding. However, most existing positional encoding approaches break the permutation and orthogonal symmetries of graph representations and degrade generalization ability. To address this limitation, we propose EPCF (equivariant positional collaborative filtering), a novel GNN model for collaborative filtering that introduces an equivariant propagation mechanism for Laplacian positional features. The proposed mechanism preserves equivariance of positional features under orthogonal transformations while maintaining the permutation equivariance inherent to graphs, which can improve generalization. The equivariant positional features are further leveraged to guide node embedding propagation. Our experiments on real-world datasets show that EPCF achieves better average performance than the evaluated baselines, achieving average improvements of 7.01% in Recall@20 and 1.17% in area under the curve (AUC) over the strongest baselines. Furthermore, integrating EPCF as a plug-in mechanism into five different GNN backbone models achieves improvements of 23.13% in Recall@20 and 2.14% in AUC across five datasets, demonstrating its generalization capability. Full article

In maritime navigation, vessel dynamics and open-water environments often exhibit inherent symmetries, whereas control objectives, particularly collision avoidance and COLREGs compliance, are strictly asymmetric, specifying unique responsibilities (e.g., give-way versus stand-on) and distinct desired trajectories. This paper proposes a runtime-assured, dual-envelope predictive safety-control framework for autonomous surface vehicles (ASVs) that directly addresses the symmetry and asymmetry in complex encounters. To manage asymmetric semantic objectives, a large language model (LLM) serves as a semantic-governance module, generating structured COLREGs labels (encounter type, vessel responsibility, and maneuver tendency). These semantic outputs are strictly validated before entering the control stack. In parallel, to break the dangerous symmetry of collision risks, vessel-motion prediction and uncertainty inflation construct a physical safety envelope. A deterministic MPC-CBF safety filter then computes admissible control commands, balancing the symmetric homogeneous tracking dynamics with asymmetric collision-avoidance constraints. A runtime assurance monitor supervises semantic validity and solver latency, preventing unsafe decisions. Simulation results demonstrate that the proposed intelligent decision-making and control scheme significantly improves rule-aware collision avoidance while reducing excessive conservatism, providing a profound perspective for viewing maritime safety through symmetric and asymmetric control theory. Full article

This work presents a comprehensive review of axion physics through the generative lens of a novel theoretical framework: Real-Now-Front (RNF) cosmology. Moving beyond the standard treatment of the axion as a fundamental particle in a pre-existing spacetime, we systematically reinterpret it as a specific collective excitation, a “twist” mode, arising from the alignment dynamics of the more fundamental Chronon field, from which spacetime itself emerges. Within this paradigm, the axion’s mass, its couplings to photons and matter, and the symmetry-breaking scale $f_a$ are not independent parameters but are derived from the microscopic stiffness and correlation length of the Chronon field, governed by the Temporal Coherence Principle. We re-examine the entire axion landscape, including benchmark models (KSVZ, DFSZ, ALPs) and the full spectrum of experimental constraints from terrestrial haloscopes, helioscopes, and astrophysical environments, translating them into probes of Chronon alignment dynamics. Furthermore,this generative framework yields unique, testable predictions, such as emergent bimetric effects and primordial black hole seeds from closed domain walls, providing independent avenues for falsification. By synthesizing established knowledge with this foundational new perspective, the review aims to establish a unified basis for the next generation of axion searches, positioning them as direct tests of the microscopic architecture of emergent spacetime, leveraginga multi-decade, multi-messenger observational campaign. Full article

Reflectance by yellow to red carotenoid-based plumages in birds with ultraviolet-sensitive (UVS) color vision typically shifts to redder (longer) wavelengths as carotenoid consumption (Diet_c) increases. This apparent asymmetric red-shift response implies an overall bias against conceivable shifts to bluer (shorter) wavelengths. However, recent studies among species of Piciformes–Coraciiformes (e.g., woodpeckers, barbets, toucans, bee-eaters, and allies) with violet-sensitive (VS) color vision discovered two kinds of blue shifts between the same plumage and dietary traits. Compared to UVS absolute red shifts (positive slopes at higher Diet_c), VS express absolute (negative slopes at higher Diet_c for yellow and orange plumages) or relative (zero slope for red plumages) blue shifts. These contrasting patterns for different color vision systems suggest that generalized symmetry concepts of opposite (plumage shift) patterns that maintain invariant (Diet_c, perception) processes can be abstracted from physical to biological systems, with positive versus negative responses formalized as “antisymmetries” and relative responses formalized as “broken symmetries”. A subset of VS “true woodpecker” (Picinae) species with known yellow and red plumage-carotenoid chemistries demonstrated similar blue shifts for the main reflectance bands and their independence from phylogeny, sex, and specimen collection year, thus providing key chemical details to further test generalized plumage symmetries. Juxtapositions were facilitated because both yellow and red plumages in true woodpeckers contained comparatively blue- and red-shifted carotenoid types. Despite this parallel, each plumage deployed chemical variations in radically different ways. Yellow plumage contained only chemically defined yellow carotenoids, including intrinsically more red-shifted natives (i.e., hydroxy-xanthophylls) widespread among birds through their diets, and intrinsically more blue-shifted picofulvins (i.e., 7,8-di- and tetra-hydro-carotenoids) probably characteristic of and metabolized by VS birds. Higher absolute and relative (to natives) picofulvin concentrations were significant predictors of absolute blue shifts in yellow plumage reflectance, and were significantly predicted by higher Diet_c. Transitivity implied Diet_c ⟶ native ⟶ picofulvin ⟶ reflectance, such that picofulvins caused absolute blue shifts at higher Diet_c, and natives caused absolute red shifts at lower Diet_c. Moreover, opposite trends for picofulvin and native concentrations in feathers were consistent with the proposed endogenous synthesis of picofulvins from natives. Yellow plumages comprised mainly of picofulvins at very low (from very low Diet_c from ants and termites) or high (from very high Diet_c from fruits) concentrations were especially distinctive for some of these and other interrelationships, suggesting some heterogeneity in yellow pigmentation strategies from dietary idiosyncrasies. Red plumages contained only relatively low concentrations of yellow dietary natives (hydroxy-xanthophylls), but varied widely in the concentration of metabolites of comparatively intermediate (4-oxo-keto-carotenoids) or extreme (4,4′-oxo-keto-carotenoids) redness. However, different red chemistries lacked any corresponding significant relationships with variations in reflectance or Diet_c. Variations in reflectance based on chemical compositions were more visible to humans for yellow than red plumage types, setting minimum salience levels for the more discriminating diurnal avian color visions. Therefore, VS yellow plumage chemistries that emphasize deposition of easily obtained (cheaper) dietary natives at low Diet_c, and of more deliberately synthesized (costly) picofulvin metabolites at higher Diet_c were consistent with several forms of honest signaling in UVS from resource limitations based on Diet_c, including through potential costs and benefits and their trade-offs. Conversely, the diverse chemical compositions and costs of red plumages of similar physical reflectance properties, and evidence that intrinsically orange carotenoids intermediate between red and yellow ones were actively excluded from plumage, suggested that true woodpecker reds were under selection for a convergent appearance. In light of true woodpecker biology, sensory bias, and social and aposematic mimicry are likely mechanisms promoting resemblance. These results extend to the chemical level earlier interpretations of opposite shift patterns as antisymmetries of invariant processes and relative shift patterns as broken symmetries of altered processes for VS vis-à-vis UVS carotenoid-based systems. Full article

Background: Evidence on powered wearable exoskeleton gait training in patients with chronic hypoxic-ischemic encephalopathy (HIE) is virtually absent, and existing studies have focused on macroscopic functional outcomes while neglecting joint-level neuromuscular force-generation characteristics such as rate of force development (RFD). Objective: To examine the effects of a six-week powered exoskeleton gait training program on isometric hip strength and RFD, sit-to-stand (STS) performance, frontal-plane hip strength, and center-of-pressure (CoP) dynamics in a patient with chronic HIE-induced quadriparesis. Methods: A case report with pre- and post-intervention evaluation was conducted. A 47-year-old male with chronic HIE-induced quadriparesis (onset 2017) completed 18 sessions (three per week, six weeks) of powered lower-limb exoskeleton gait training. Outcomes included isometric hip peak force and RFD (DynaMo, Vald Performance), STS peak force and body mass-normalized RFD (ForceDecks, Vald Performance), frontal-plane hip strength (ForceFrame, Vald Performance), and CoP path length and mean velocity. Results: Hip extension peak force increased by 247–256% bilaterally, and hip extension RFD increased by 174–188%, whereas hip flexion peak force showed minimal change (+3.3–5.2%). Body mass-normalized STS RFD increased by 250% (10 to 35 N·s⁻¹·kg⁻¹), representing the largest relative gain. Hip abduction strength increased by 27.1–36.8% with improved bilateral symmetry; hip adduction imbalance reversed from right to left dominance. CoP path length and mean velocity each decreased by 3.7%. Conclusions: Six weeks of powered exoskeleton gait training selectively enhanced time-dependent neuromuscular output—particularly RFD—beyond maximal strength gains, with meaningful improvements in functional weight acceptance during STS. These findings support exoskeleton-based training as a promising rehabilitation strategy for patients with chronic CNS injury. Full article

Industrial defect image generation is an effective way to alleviate data scarcity and class imbalance in visual inspection. In industrial images, defects usually appear as local asymmetric perturbations on globally regular background structures, which makes defect synthesis dependent on both background consistency and local anomaly fidelity. Existing generative methods still face difficulties when only limited anomalous samples are available, especially in representing fine-grained discrepancies among defect categories, coordinating global and local branches across diffusion stages, and constraining small defect regions and their boundary transitions. To address these issues, this paper develops a symmetry-aware multi-constraint diffusion framework based on the dual-branch architecture of DualAnoDiff. The framework treats multi-class industrial defect generation as a joint optimization problem involving class-conditioned discrepancy representation, diffusion-stage-aware branch coordination, and saliency-guided regional supervision. First, Class-Conditioned Shared-Basis LoRA (CSB-LoRA) models category-specific defect characteristics by combining cross-class shared low-rank bases with class-dependent coefficients, allowing common structural priors and class-specific asymmetric patterns to be represented simultaneously. Second, Temporal Dual-branch Attention Modulation (TDAM) adjusts branch interaction, background information injection, and residual feature fusion according to the denoising stage, so that the generation process can gradually shift from global structure restoration to local defect refinement. Third, Saliency-Guided Reconstruction Loss (SGRL) applies stronger spatial constraints to defect regions and boundary neighborhoods, improving local detail preservation and defect-background continuity. Experiments on the MVTec AD dataset show that the proposed method improves both generation quality and perceptual diversity compared with DualAnoDiff. The average IS increases from 1.93 to 2.07, and IC-LPIPS increases from 0.38 to 0.41. When the generated samples are used for downstream defect segmentation, AP-P improves from 84.5% to 85.7%, and F1-P improves from 78.8% to 79.3%. These results indicate that the generated samples can serve as useful synthetic training data for few-shot and class-imbalanced industrial inspection. Full article

Overexertion, usually caused by manual material handling (MMH), often leads to work-related musculoskeletal disorders (WMSDs). These can be prevented during MMH tasks by redesigning them to include sufficient rest periods. Task characteristics play an important role in the redesign of the job. This study evaluated the effect of five task characteristics—weight, duration, frequency, distance, and angle of symmetry—at two levels on the maximum voluntary contraction recovery rate (Muscle Voluntary Contraction Recovery Time (MVCRT), defined as the time required for the muscle to recover to 80% of the initial Maximum Voluntary Contraction (MVC) value) of the muscles and developed a work-rest interval model based on these task characteristics. The results show that the weight and duration had a significant effect on MVCRT, increasing it by 32% and 21%, respectively. The interaction between frequency and distance also significantly impacted MVCRT. A simplified mathematical model was developed and validated by comparing a set of the model-generated data with experimental data. The simplified regression model demonstrated moderate predictive capability with an R² value of 0.52. The ANOVA shows no significant difference between the data. The study’s results and mathematical models can be used during task design to reduce WMSDs. Because approximately 48% of the variability in MVCRT remained unexplained, direct application of the model to establish worker-specific work-rest intervals may result in underestimation or overestimation of recovery requirements. Therefore, the model should be interpreted as a preliminary estimation framework. Full article