Search Results (250)

We construct and analyze a family of support-defined Brauer-type configurations canonically associated with the Boolean geometry underlying the Grassmann algebra. The construction is governed by an x-support map on monomial labels, which identifies the vertex set with the Boolean lattice $\mathcal{P}\left(\right[n\left]\right)$. This identification yields a Boolean support quiver isomorphic to the directed Hasse diagram of $\mathcal{P}\left(\right[n\left]\right)$, equivalently, to an oriented hypercube. We then equip the family with a canonical cyclic ordering at each vertex and obtain a genuine connected reduced Brauer configuration in the standard sense, together with its associated Brauer configuration algebra and its standard Brauer quiver. A ghost-variable mechanism is introduced to obtain a connected realization without altering any support-controlled invariants. We prove that polygon membership, valencies, multiplicities, Boolean stratification, and the support quiver are invariant under support-preserving ghost relabelings. We also give an explicit description of the standard Brauer quiver and show that it is different from the Boolean support quiver. On the algebraic side, we derive closed formulas for the center dimension, the algebra dimension, and the normalization constant of the induced weighted distribution. On the probabilistic side, we distinguish the vertex entropy from the layer entropy, establish an exact decomposition of the former by Hamming layers, and show that the layer distribution is asymptotically concentrated on the middle layers, while extremal vertices and any fixed maximal path contribute a negligible fraction of the total weight. As a consequence, the layer entropy satisfies a logarithmic asymptotic law. We also investigate geometric consequences of the Boolean model transported through the support identification. Coordinate projections produce a rigidity phenomenon for antipodal pairs, providing a combinatorial analogue of Greenberger–Horne–Zeilinger (GHZ)-type fragility, whereas the first Boolean layer exhibits a persistence property analogous to W-type robustness. Together, these results exhibit a concrete bridge between Grassmann combinatorics, Brauer configuration theory, hypercube geometry, and entropy asymptotics. Full article

The rise of generative artificial intelligence (GenAI) is creating new opportunities for assessment design in universities, particularly in subjects that emphasize analytical and creative skills. This paper introduces the Educator–GenAI Partnership Model, an iterative five-stage model that helps educators create assessments that foster higher-order thinking (HOT). The model is grounded in constructive alignment and Bloom’s taxonomy, with a central emphasis on preserving human oversight to ensure educators retain control over assessment validity, academic integrity, and the ethical use of AI. The model maps out the unique strengths and responsibilities of both educators and GenAI, showing how each plays a distinct role in the assessment design process. It illustrates how GenAI can support the rapid generation of assessment tasks and marking rubrics, while positioning educators as critical decision-makers who only review, adapt, and iteratively refine AI-generated outputs to ensure alignment with higher-order learning outcomes. Overall, this paper presents a structured and practical model for utilizing GenAI responsibly in assessment design, thereby strengthening academic rigor while enhancing efficiency for educators. Full article

Unmanned Aerial Vehicles (UAVs) are complex nonlinear systems characterized by high dimensionality. They are prone to aerodynamic effects, structural dynamics, actuation constraints, and networked interactions, requiring advanced mathematical models and precise control. Their governing equations involve nonlinear rigid-body dynamics coupled with fluid and elasticity models, while modern architectures introduce redundancy that creates constrained mappings between generalized forces and actuator inputs. Coordinated UAV teams add another layer of mathematical structure through graph-based interaction models that determine consensus, formation keeping, and distributed stability. These characteristics give rise to several interconnected challenges. High-fidelity aerodynamic and aeroelastic solvers provide accurate results; however, these are computationally intensive, motivating the development of reduced-order models and data-driven approximations that preserve dominant physical behavior. Methods for quantifying uncertainty support robustness assessments by characterizing the effects of parametric variation and model form error. At the actuation level, control allocation problems rely on constrained linear algebra, convex optimization, and dynamic formulations to ensure feasible and stable realization of command forces and moments. In multi-agent systems, the spectral properties of adjacency and Laplacian matrices govern convergence and cooperative behavior. This article reviews the state of the art in these areas, highlights the mathematical foundations that relate them, and provides a coherent perspective on the methods that enable reliable modeling and control of modern UAV systems. Full article

Accurate estimation of forest above-ground biomass (AGB) is essential for quantifying forest carbon stocks and supporting regional carbon accounting. However, regional AGB mapping requires the integration of field observations with satellite data, and the associated scale transformation often causes the loss of spatial detail and reduced estimation consistency. To address this issue, this study proposes a forest canopy height-constrained area-to-area regression kriging (CCAM) method for upscaling UAV-derived AGB and generating a high-precision wall-to-wall AGB map for artificial forests in the sandy lands of northwest Liaoning Province, China. The framework integrates RFE-SVM-based feature selection, XGBoost-based UAV-AGB modeling, and CHM-constrained residual correction within a Regression-then-Kriging (R-K) strategy, while also evaluating the effects of moving-window size, scale transition, and the order of regression and kriging on upscaling performance. The results showed that the reconstructed UAV-AGB model achieved the highest accuracy, with R² = 0.91 and rRMSE = 0.12, providing a reliable 0.1 m AGB baseline for subsequent upscaling. Among the tested moving-window sizes, the $7\times 7$ window was identified as optimal. Under this setting, CCAM achieved R² = 0.81 and rRMSE = 0.08, substantially outperforming direct GF-2-based estimation (R² = 0.49, rRMSE = 0.24). The final 2 m regional AGB map further attained a validation accuracy of R² = 0.79 and rRMSE = 0.18. These results demonstrate that CCAM can effectively preserve fine-scale UAV-derived biomass information during scale transformation and provide a reliable pathway for linking UAV and satellite observations in regional forest AGB mapping. Full article

Reducing traction energy in urban rail systems while preserving safety, punctuality, and passenger comfort remains challenging. Additionally, route-level tram studies that train deep reinforcement learning (DRL) policies using Operational Train Monitoring Recorder (OTMR) logs and benchmark them across multiple objectives remain limited. This study develops and evaluates a Human-Assisted Deep Reinforcement Learning (HADRL) framework for multi-objective tram control in an OTMR-grounded simulation. Two HADRL agents were trained using a human-assistance action mapping: a standard Proximal Policy Optimisation (PPO) baseline and a recurrent, history-augmented PPO. Their performance was compared against that of four human drivers using indices for speed-limit compliance, schedule deviation, traction energy, jerk-based comfort, and stopping accuracy. These performance measures were aggregated using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with both equal and entropy-derived weights. Both HADRL agents reproduce the characteristic accelerate–coast–brake driving pattern, reduce traction energy relative to all human baselines, and achieve near-complete speed-limit compliance, all while remaining within the specified schedule-deviation and comfort thresholds. TOPSIS yields identical rankings under both weighting schemes, with Multi-Objective Tram Operation Non-Stationary Proximal Policy Optimisation (MOTO-NSPPO, a recurrent, history-augmented PPO) ranked first and PPO second. Full article

The derivations presented in this paper suggest an intimate relationship between geometry and the electroweak sector at the Planck scale. A Lorentz-invariant maximally symmetric stochastically perturbed spacetime transformed to spherical coordinates reveals an emergent Schwarzschild metric, entirely a statistical structure of stochastic spacetime. Similarly, the transition from a maximally symmetric universe with a complex $SU\left(2\right)$ scalar doublet $\varphi$, comprising four independent real scalar fields with a zero vacuum expectation value (VEV), to spherical coordinates at the Planck scale reveals the spontaneously broken electroweak (EW) sector. Working in the unitarity gauge, the resulting EW potential can be simultaneously mapped in space at the Planck scale and across the EW sector. In space, the resulting EW potential includes a deep well within the Schwarzschild sphere and a shallow well just outside corresponding to an accretion disk. The same potential mapped in the EW space provides an entire family of possible sombrero hat potentials with fourth-order coupling specific to a point in space. At the minimum points of the potential in space, inside the Schwarzschild sphere and at the accretion disk, the $\lambda$ corresponding to the Standard Model (SM) fourth-order coupling is instead derived as $\frac{\lambda }{5}$. The factor of $\frac{1}{5}$ is a simple consequence of the conservation of the EW VEV and the fact that the SM formulation of the EW potential does not account for situations where the perturbations in $\varphi$ dominate. A more general formulation of the EW potential restores the SM quartic coupling and preserves $\lambda$ in space. An emergent Higgs field inside the Schwarzschild black hole is found to directly relate to the stochastic spacetime fields normalized by the Schwarzschild radius. The corresponding Higgs vacuum has both a ground and excited state and the possibility of both positive and negative vacuum entropy. Finally, the scalar-field VEV degeneracy in EW space of the metastable Higgs vacuum appears instead differentiated in space with possible probability, tunneling, and entropy implications. Full article

Laser powder bed fusion (LPBF) is susceptible to defects arising from melt pool instabilities, spatter, heat accumulation, and powder spreading anomalies. In situ infrared (IR) monitoring can detect these issues; however, it typically generates large volumes of data that are costly to store and analyze. This work proposes a projection-based framework that directly maps in situ thermal measurements onto a three-dimensional (3D) voxelized part geometry, substantially reducing storage requirements while preserving spatial fidelity. In addition, several IR derived features are incorporated into a practical workflow for defect detection and process model calibration, including laser scan order, local pre-deposition temperature, maximum pre-scan temperature, and spatter generation and landing locations. For completeness, commonly used metrics such as interpass temperature, heat intensity, cooling rate, and relative melt pool area are extracted within the same unified processing pipeline. All features are computed using a consistent, reproducible Python-based implementation to streamline integration into routine monitoring and analysis tasks. Multiple parts are fabricated, monitored, and characterized to evaluate the proposed framework, demonstrating that the extracted features reliably identify process anomalies and correlate with observed defects. Full article

From falcons spotting prey to humans recognizing faces, the ability to rapidly process visual information depends on a foveated retinal organization that provides high-acuity central vision while preserving low-resolution peripheral vision. This organization is conserved along early visual pathways, yet remains under-explored in machine learning. Here, we examine the impact of embedding a foveated retinotopic transformation as a preprocessing layer on convolutional neural networks (CNNs) for image classification. By applying a log-polar mapping to off-the-shelf models and retraining them, we achieve comparable accuracy while improving robustness to scale and rotation. We demonstrate that this architecture is highly sensitive to shifts in the fixation point and that this sensitivity provides an effective proxy for defining saliency maps that facilitate object localization. Our results demonstrate that foveated retinotopy encodes prior geometric knowledge, providing a solution for visual searches and a meaningful classification robustness and localization trade-off. These findings provides a proof of concept in order to connect principles of biological vision with artificial networks, suggesting new, robust and efficient approaches for computer vision systems. Full article

We propose a reformulated notion of Levitin–Polyak (abbreviated as LP) well posedness for fuzzy optimization problems formulated in the fuzzy order-preserving (FOP) setting, where minimizing sequences are governed by a total ordering defined on fuzzy intervals. Under this formulation, we present verifiable sufficient conditions that guarantee LP well-posed behavior. These conditions are derived using ranking mechanisms that maintain interval order relations and ensure solution comparability. One central contribution is an equivalence-based theoretical characterization of LP well posedness obtained through an examination of the topological properties of the approximate solution mapping, particularly its closed-graph structure and upper semicontinuity. In addition, convergence of approximating solution sequences is investigated under the upper Hausdorff metric, leading to stability results for the associated solution sets. The established criteria provide a comprehensive framework for analyzing the convergence performance of algorithms designed for fuzzy optimization environments. Full article

We propose Distribution-Preserving Latent Steganography via Conditional Optimal Transport (DPL-COT), a coverless image steganography framework for latent diffusion models. Unlike classical cover-modifying schemes, DPL-COT embeds a bitstream directly into the initialization noise latent ${\mathbf{z}}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ without model retraining. Our primary objective is high recoverability and a low bit error rate (BER) under deterministic inversion, which is inherently imperfect due to numerical discretization and VAE nonlinearity. To maximize decoding stability, we restrict embedding to the natural tails of the latent prior by selecting the largest-magnitude coordinates, thereby increasing the sign decision margin against inversion drift. To preserve distributional stealth, per-bit target values are analytically derived from truncated Gaussians matching the marginal distribution of the selected coordinates. Conditional 1D optimal transport is applied independently for each bit class, mapping every coordinate to its target value while preserving rank order. We generate 5000 stego images using a pretrained diffusion model and demonstrate a favorable capacity–reliability trade-off (e.g., 4916 bits/image with 0.473% mean BER) and strong robustness to JPEG compression (sub-1% mean BER at $Q=60$). Compared with LDStega, a recent LDM-based scheme reporting 99.28% clean-channel accuracy, DPL-COT achieves 99.53% at a comparable operating point and sustains above-99% accuracy under all tested JPEG quality factors. Latent-space tests further confirm negligible cover–stego distribution shift (mean ${\mathrm{KS}}_2<0.003$, mean $W_1<0.003$), a property not formally addressed by prior methods. Full article

We present a geodesic dynamics framework for discrete-time state evolution on the unit sphere $S^{N-1}$ that maintains exact unit-norm constraints through Riemannian exponential mapping. Given an input sequence and an initial state, the method constructs trajectories by projecting inputs to tangent spaces and updating states along geodesics, incorporating temporal memory via approximate parallel transport of velocity directions. Unlike traditional approaches requiring post hoc normalization of linear updates, the geodesic formulation preserves $\parallel {\mathbf{x}}_t\parallel =1$ to machine precision while eliminating explicit $N\times N$ transition matrices in favor of $D\times N$ input embeddings when the intrinsic input dimension D is much smaller than the ambient dimension N. The update corresponds to a first-order exponential integrator on the sphere. We establish local Lipschitz continuity of the exponential map on positively curved manifolds with careful treatment of basepoint dependence, derive perturbation bounds showing linear-to-exponential growth transitions via Grönwall-type estimates, and we prove third-order asymptotic equivalence with normalized linear systems under appropriate scaling. Numerical experiments on synthetic data validate exact norm preservation over extended time horizons, confirm theoretical perturbation growth predictions, and demonstrate the effectiveness of the temporal memory mechanism in reducing long-horizon prediction errors. The framework provides a principled geometric approach for applications requiring exact directional or compositional constraints. Full article

Cluster Head (CH) selection is a crucial process in clustered Wireless Sensor Networks (WSNs) because it directly affects energy balance and network lifetime. However, CH selection is an NP-hard optimization problem, and many metaheuristic-based methods suffer from limited search diversity and premature convergence, leading to uneven energy dissipation. This paper formulates CH selection as a multi-criteria energy-aware optimization problem and proposes an Enhanced Secretary Bird Optimization Algorithm (ESBOA). The proposed ESBOA improves the original Secretary Bird Optimization Algorithm by integrating logistic chaotic map-based population initialization to enhance early-stage exploration and an iterative local search mechanism to strengthen solution refinement in later iterations. A multi-criteria fitness function considering residual energy, distance to the base station, and node degree explicitly guides the optimization toward energy-efficient clustering. The proposed method is implemented in a Python 3.11.9-based simulation framework using a first-order radio energy model and evaluated against standard SBOA, Crested Porcupine Optimization (CPO), and Dung Beetle Optimization (DBO). Simulation results demonstrate that ESBOA preserves more alive nodes, maintains higher residual energy, delivers more cumulative packets to the base station, and extends network lifetime, achieving approximately 3–13% improvement in last node death (LND) compared with the standard SBOA. Full article

Genetic sequences play a central role in biological and medical research, and mathematics provides powerful means for their representation and analysis. Conventional approaches, such as the fuzzy polynucleotide space ${[0, 1]}^{12}$, model codons as 12-dimensional vectors, but this comes at the cost of high dimensionality. In this study, we introduce two new models, Vector-Fuzzy-I and Vector-Fuzzy-II, that map codons and genetic sequences into the 4-dimensional Euclidean space ℝ⁴ using vector algebra and fuzzy set theory. In the first model, sequence structure is represented by successive vector addition, while in the second, it is represented by positional frequencies normalized by nucleotide locations. These low-dimensional representations are unique, preserve sequence order, and allow effective measurement of similarity and difference via Euclidean metrics. Compared with the fuzzy polynucleotide space, the proposed models achieve dimensionality reduction while enhancing the resolution of sequence differentiation. Our approach offers new mathematical perspectives for sequence analysis in theoretical biology. Full article

An integrated nonlinear dynamic model was developed to investigate resonance in a four-cylinder engine mounted on a viscoelastic foundation. A coupled lumped-parameter formulation captures vertical and torsional responses under unbalanced inertial forces, combustion torque, and stochastic base excitation. Time-domain simulations show that at low rotational speeds the vertical displacement reaches transient amplitudes before converging to periodic oscillations, whereas higher excitation speeds reduce steady-state amplitudes. Torsional motion exhibits initial angles near 0.05 rad that decay below 0.01 rad in steady state, with further reduction at higher speeds. Frequency-domain analysis indicates that vibration energy is concentrated in engine-order harmonics between approximately 8 and 50 Hz, while components above 60 Hz are strongly attenuated, yielding a dynamic range exceeding 50 dB. Finite element modal analysis identifies the first four structural modes between 18 Hz and 666 Hz, revealing an increasingly dominant overall translational mode and a localized directional behavior at higher frequencies. A high-dimensional kernel density spectrogram integrates modal and spectral features to map resonance regions. Results indicate that increasing rotational excitation enhances inertial stiffening, systematically reduces displacement amplitudes, and preserves bounded periodic dynamics without instability. Full article

This paper presents a minimally intrusive experimental methodology for identifying and modeling power losses in the electric powertrain of a battery electric vehicle, including the inverter, electric motor and speed reducer. Measurements are performed on a roller test bench equipped with an eddy current brake, using two complementary approaches to determine the mechanical power at the wheel: (i) a direct measurement based on an onboard rotary torque sensor integrated into a driveshaft; (ii) an indirect estimation derived from brake power measurements corrected for bench losses and tire longitudinal slip. The two approaches are systematically compared in order to quantify the accuracy loss associated with brake-based measurements and to identify the operating conditions under which they can reliably substitute direct torque measurements. The experimental results show that brake-based estimations provide acceptable accuracy at moderate–high torque levels, while significant deviations occur at low torque. Based on the experimental dataset, an overall power loss model is identified using a polynomial function of motor torque and speed. Two fitting strategies are investigated: an unconstrained least-squares approach, allowing all coefficients to vary freely, and a constrained formulation enforcing physically admissible (non-negative) loss terms; while the unconstrained method slightly improves the numerical fit, it may lead to non-physical coefficients and invalid efficiency predictions. In contrast, the constrained approach preserves physical interpretability and ensures consistent loss and efficiency maps. Finally, a step-by-step practical guide is provided to facilitate the implementation of the proposed methodology for powertrain loss identification on electric vehicles without extensive mechanical disassembly. Full article