Search Results (520)

Achieving robust environmental responsiveness in early stage architectural spatial layout design remains a critical challenge under the imperatives of global carbon neutrality and climate-adaptive building practice. Conventional parametric design and multi-objective optimization approaches suffer from computational inefficiency, inadequate constraint satisfaction, and opaque generative logic when operating in high-dimensional design spaces. This paper presents a mathematically rigorous, climate-responsive spatial layout generation framework that unifies category theory with conditional diffusion modeling. The proposed method formalizes site-specific environmental parameter systems and architectural spatial topologies as two small categories, and establishes structure-preserving environment-to-space mappings via covariant functors; natural transformations are further introduced to characterize morphological transitions across distinct design strategies. A conditional diffusion model (CDM) serves as the generative engine, producing candidate spatial topological configurations subject to environmental parameter conditioning. A three-stage categorical constraint screening mechanism—constructed from groupoid structures and pullback limits—enforces simultaneous compliance with functional adjacency requirements, topological coherence, and multi-criteria environmental performance targets. Extensive experiments across three climatically contrasting sites (Hangzhou, Qingdao, and Lijiang) demonstrate that the framework substantially enhances environmental response performance while preserving spatial topological rationality, achieving competitive generation efficiency and constraint satisfaction relative to conventional parametric optimization baselines. These findings establish that categorical structures can serve as interpretable, mathematically consistent constraint engines within AI-driven generative design pipelines, offering a principled computational paradigm for climate-responsive architectural layout synthesis. Full article

The Gielis superformula is a powerful parametric tool that generates an infinite variety of natural and organic curves and surfaces through a compact set of parameters. However, classical differential geometry has lacked a unified framework for analyzing their curvature, torsion, and intrinsic geometric properties. This study addresses this gap by developing a novel superelliptic geometric framework that integrates the superformula with the differential geometry of curves and surfaces. We define the superelliptic inner and cross products, the star derivative, and the superelliptic Frenet frame to extend Euclidean and Riemannian interpretations of curvature and torsion to a more flexible parametric structure. The framework provides a uniform geometric characterization of all Gielis curves and surfaces in an intrinsic sense with respect to the proposed superelliptic metric, rather than relying on their classical Euclidean parametric representations; singular cases (e.g., $n_1<2$), which correspond to non-smooth or corner-like behavior in the Euclidean setting due to degeneracies in the radial function $r\left(t\right)$, are regularized within this framework, since the induced metric maps such Gielis-type curves to intrinsically circular geometries with constant superelliptic curvature. This unifies the entire family under a common, robust foundation while preserving orthonormality and differentiability. This superelliptic approach offers a consistent and computationally tractable model that bridges mathematical abstraction with real-world morphology, with the superformula serving as a representative example of the framework’s broad generality for diverse geometric structures. The proposed theoretical framework is further supported by computational visualization, and all figures and numerical illustrations presented in this study were generated using MATLAB R2024a, ensuring a consistent implementation of the proposed superelliptic model. Full article

The mathematical characterization of non-stationary signals remains a significant challenge, particularly when impulsive components are obscured by high-dimensional noise and structural coupling. This paper proposes an application-driven mathematical methodology for a learnable discrete wavelet transform (LDWT) that combines classical multi-resolution analysis with task-optimized data-driven adaptivity. Rather than introducing entirely new foundational theory, our approach strategically relaxes constraints from orthogonal wavelet theory within the non-perfect reconstruction filter bank framework, enabling controlled spectral decomposition optimized for supervised fault diagnosis. We introduce a specialized regularization term based on the half-band property to ensure spectral complementarity and minimize cross-band correlation, while a Jacobian-based stabilization approach is formulated to ensure the convergence of filter coefficients during optimization. The proposed algorithmic architecture, LDBRFnet, features a dual-branch encoder system designed to capture the mathematical synergy between sub-band-level global statistics and time-domain local morphology. This dual-view representation effectively mitigates feature leakage and overconfidence in classification. Theoretical analysis and numerical experiments demonstrate that the learned filters satisfy the frequency-shift property and maintain robust spectral partitioning even under low signal-to-noise ratios. Validation on complex vibration datasets confirms that the framework achieves superior diagnostic accuracy (over 95.5%) and computational efficiency, reducing model parameters by 96.7% compared to state-of-the-art baselines. This work provides a generalizable mathematical approach for adaptive signal decomposition and robust pattern recognition in interdisciplinary applications. Full article

Non-invasive, real-time biomass estimation is critical for smart aquaculture, yet high computational latency and the cost of specialized optical sensors remain significant bottlenecks. This study proposes an ultra-low-cost, edge-deployable stereo-vision framework utilizing a dual-webcam architecture synchronized with a lightweight YOLOv11n-pose model. To address the spatial uncertainties in non-rigid fish locomotion, we integrated advanced spatial loss functions to achieve precise anatomical keypoint extraction. These coordinates are processed through a three-point Bézier curve interpolation and a mathematically derived Dynamic Shape Factor (K) to correct for optical refraction and morphological variations. As a proof-of-concept, the proposed system was validated on a live multi-species cohort (N = 10), achieving a Mean Absolute Percentage Error (MAPE) of 8.64% and an R² of 0.92 under strict Leave-One-Out Cross-Validation (LOOCV), drastically outperforming traditional naive volumetric baselines (MAPE > 54%). Requiring only 6.7 GFLOPs and 5.5 MB of memory, the model achieves 111.6 FPS. These results demonstrate the feasibility of highly efficient, cost-effective AI solutions for precision aquaculture while clearly defining the validity boundaries and statistical constraints for future large-scale deployment. Full article

This paper investigates co-continuous structures in immiscible polymer blends through three-dimensional (3D) computational calculations based on a multiphase phase-field equation for fluid flow. The mathematical model describes phase separation with the Cahn–Hilliard (CH) equation and fluid motion with the incompressible Navier–Stokes (NS) equations. Both polymers are treated as Newtonian viscous fluids, and the model includes surface tension, viscosity, and volume fraction effects. A semi-implicit finite difference method (FDM) solves the CH equation, and a projection method maintains the incompressibility of the flow field. Multigrid techniques solve the nonlinear systems efficiently. In addition, a connectivity-based detection algorithm determines whether a phase forms a connected structure that reaches all boundaries of the numerical domain. The numerical results show that the morphology changes from a droplet–matrix structure to a co-continuous structure as the volume fraction increases. The interfacial area per unit volume reaches a local maximum near the transition between these two regimes. Full article

Three-dimensional seed phenotyping requires imaging systems capable of achieving micron-level resolution across a centimeter-level field of view (FOV), a goal constrained by the resolution–FOV trade-off in conventional light field architectures. This paper presents a hardware–software co-optimized framework that integrates a reconfigurable optical system with computational imaging pipelines to address this limitation. At the hardware level, we develop a tunable-focus lens module that enables flexible adjustment of the effective focal length, combined with a custom-designed microlens array (MLA). A mathematical model is established to analyze the interdependencies among FOV, lateral resolution, depth of field (DOF), and system configuration, guiding the design of individual optical components. On the computational side, we propose a hybrid aberration correction strategy: first, a co-calibration of lens and MLA aberrations based on line-feature detection; second, a conditional generative adversarial network (cGAN) with attention-guided residual learning to enhance sub-aperture images, achieving a PSNR of 34.63 dB and an SSIM of 0.9570 on seed datasets. Experimentally, the system achieves a resolution of 6.2 lp/mm at MTF50 over a 2–3 cm FOV, representing a 307% improvement over the initial configuration (1.52 lp/mm). The reconstruction pipeline combines epipolar plane image (EPI) analysis with multi-view consistency constraints to generate dense 3D point clouds at a density of approximately 1.5 × 10⁴ points/cm² while preserving spectral and textural features. Validation on bitter melon and rice seeds demonstrates accurate 3D reconstruction and accurate extraction of morphological parameters across a large area. By integrating optical and computational design, this work establishes a reconfigurable imaging framework that overcomes the resolution–FOV limitations of conventional light field systems. The proposed architecture is also applicable to robotic vision and biomedical imaging. Full article

Urban heritage structures are most commonly understood as memorial artifacts, tourism assets, or redevelopment resources. While this common view acknowledges cultural and economic value, it overlooks a deeper function of heritage within the long evolution of human settlements. This paper advances a counter thesis: in addition to its historic contingencies and power relationships—which are real, but only part of the picture—urban heritage embodies valuable but often hidden intelligence that is highly relevant to contemporary urban challenges. Specifically, heritage environments encode useful structured information about spatial configurations that have gained adaptive value over time in a process known as stigmergy. Drawing on complexity science, network theory, the mathematics of symmetry, and theories of extended cognition, the paper argues that enduring urban forms persist not only for symbolic or historical reasons, but because they embed structural properties conducive to resilience, legibility, social interaction, climatic adaptation, and human well-being. Recurring characteristics include fine-grained network connectivity, fractal scaling hierarchies, organized symmetry, articulated thresholds, and biophilic integration. Evidence from environmental psychology, public health, and urban morphology suggests that such properties correlate with reduced stress, increased walkability, stronger social capital, and improved ecological performance. The paper proposes a methodological framework—what we call the Adaptive Patterns Model—for identifying, evaluating, and translating this embedded intelligence into contemporary regeneration practice. The Model is presented as a four-phase, conceptually synthesized framework—integrating insights from complexity science and stigmergy, urban morphological analysis, and pattern-language methodology—comprising documentation, pattern extraction, encoding, and performance correlation. It concludes by challenging a still-prevalent assumption that contemporary conditions invalidate accumulated spatial knowledge. Instead, urban heritage is understood as adaptive capital within an ongoing evolutionary process, offering a structurally grounded foundation for resilient urban transformation. Full article

This study proposes a morphological convolutional neural network (MCNN) architecture that integrates morphological operations with CNN layers for facial expression recognition (FER). Conventional CNN-based FER models primarily rely on appearance features and may be sensitive to illumination and demographic variations. This work investigates whether morphological structural representations provide complementary information to convolutional features. A multi-source and multi-ethnic FER dataset was constructed by combining CK+, JAFFE, KDEF, TFEID, and a newly collected Indonesian Facial Expression dataset, resulting in 3684 images from 326 subjects across seven expression classes. Subject-independent data splitting with 10-fold cross-validation was applied to ensure reliable evaluation. Experimental results show that the proposed MCNN1 model achieves an average accuracy of 88.16%, while the best MCNN2 variant achieves 88.7%, demonstrating competitive performance compared to MobileNetV2 (88.27%), VGG19 (87.58%), and the morphological baseline MNN (50.73%). The proposed model also demonstrates improved computational efficiency, achieving lower inference latency (21%) and reduced GPU memory usage (64%) compared to baseline models. These results indicate that integrating morphological representations into convolutional architectures provides a modest but consistent improvement in FER performance while enhancing generalization and efficiency under heterogeneous data conditions. Full article

Geological environment evaluation for urban underground space (UGEE) is a critical foundation for optimizing the utilization of urban underground space (UUS) and mitigating exploitation risks. With recent advancements in 3D geological modeling technology, 3D UGEE has emerged as a transformative approach, offering innovative perspectives and technical solutions for rational 3D spatial development and geological risk reduction in subsurface engineering. A core component of the 3D UGEE workflow is the integration of diverse 3D spatial analysis methods, which enable comprehensive extraction of evaluation indices from multidimensional datasets—forming the essential basis for scientifically informed development planning. Focusing on quantitative 3D UGEE, this study systematically investigates the implementation of 3D spatial analysis methods across four key stages: (1) geological condition analysis, (2) evaluation information extraction, (3) 3D comprehensive evaluation, and (4) result analysis. Specifically, five core methodologies are highlighted: (1) 3D spatial statistical analysis, (2) 3D mathematical morphological analysis, (3) 3D surface morphology analysis, (4) 3D spatial distance field analysis, and (5) 3D spatial interpolation analysis. To improve the reliability and objectivity of 3D comprehensive evaluation results, we integrate game theory-based combination weighting with an improved TOPSIS model, which balances the subjectivity of expert judgment and the objectivity of data characteristics while adapting to the 3D block unit data structure, effectively avoiding the bias of single weighting or evaluation models. To validate these techniques, a case study in Hangzhou, Zhejiang Province, is conducted, demonstrating their practical effectiveness in evaluating UUS resources. The findings underscore that advanced 3D spatial analysis methods significantly enhance decision-making precision in UUS planning and risk management, providing a replicable framework for sustainable subsurface development. Full article

To accurately quantify the intrinsic absorption efficiency of bamboo leaves to the solar spectrum, we measured the reflectance and transmittance of leaves from 55 bamboo species cultivated at the same site, and developed a mathematical model to calculate the annual cumulative photon absorption of photosynthetically active radiation (PAR) per leaf. The results showed the following: (1) Bamboo leaf optical properties exhibited high instrumental and spatial measurement consistency, with transmittance not significantly fluctuating with changes in incident light intensity or quality. (2) Bamboo leaves exhibited significant spectral selective absorption characteristics, with stronger absorption of blue and red light and weaker absorption of green light; Phyllostachys vivax had the highest mean absorptance per unit area, while Chimonobambusa tumidinoda had the lowest. (3) The annual photon absorption per unit leaf area ranged from 1.83 × 10⁵ to 9.86 × 10⁵ μmol, with Phyllostachys iridescens being the lowest and Chimonobambusa marmorea the highest. The annual photon absorption per single leaf ranged from 1.84 × 10⁶ to 5.13 × 10⁷ μmol, with Indocalamus decorus achieving the highest total absorption due to its largest leaf area (114.9 cm²), while Bambusa multiplex var. riviereorum was the lowest. (4) All tested bamboo species showed consistent seasonal dynamics in photon absorption, with the highest in summer and lowest in winter. Although unit-area absorptance reflects the intrinsic light interception efficiency, leaf morphology has a substantial influence (explaining 99.56% of the variance) in determining total light acquisition per leaf. Full article

The optimal deployment of Low-Power Wide-Area Networks (LPWANs) such as LoRaWAN in complex urban environments remains an NP-Hard Set Covering Problem. Traditional network planning often relies on 2D mathematical grids that ignore physical RF barriers, leading to topographic shadowing and single points of failure. This research proposes the Native 3D Memetic Spatially Aware Genetic Algorithm (3D-M-SAGA), an optimization framework that operates over a Morphological Digital Twin. By fusing OpenStreetMap (OSM) vector topologies with NASA SRTM elevation data and autonomous urban clutter classification, the framework evaluates physical constraints—including ITU-R knife-edge diffraction and dielectric absorption—directly within the evolutionary loop. To counteract the epistatic variance inherent to standard genetic algorithms, the 3D-M-SAGA integrates a vectorized memetic “Smart Repair” operator driven by heuristic attraction and repulsion forces. Formulated as a multi-objective optimization problem balancing Capital Expenditure (CAPEX) and topological Quality of Service (QoS) through K-coverage, the framework is evaluated using a 36-scenario parametric grid search and a 50-iteration Monte Carlo benchmark. Results show that the 3D-M-SAGA tightly bounds stochastic CAPEX variance ($\sigma =\pm 0.51$ gateways) while reducing single-point-of-failure network fragility ($K=1$) by up to 20%, guaranteeing fault tolerance ($K\ge 2$) without over-provisioning civic infrastructure. Full article

Soybean meal (SBM) is a foundational protein source, but its industrial application is constrained by a complex matrix of anti-nutritional factors (ANFs). This review provides a critical synthesis of the biochemical transition from raw SBM to fermented SBM (FSBM), focusing on the synergistic mechanisms of fungal and bacterial co-fermentation. We identify that the efficacy of FSBM is primarily driven by the microbial proteolysis of glycinin into low-molecular-weight bioactive peptides (<1000 Da). These peptides serve as the primary drivers for improved intestinal morphology (increased villus height) and the modulation of the gut microbiota, providing a mechanistic basis for reported probiotic effects. Furthermore, we establish that the 5–10% improvement in the feed conversion ratio (FCR) documented for swines mathematically offsets the processing premium of fermentation. However, critical gaps remain in the standardization of solid-state fermentation (SSF) protocols, specifically regarding the selection of fungal (Aspergillus) and bacterial (Bacillus or Lactobacillus) strains, whose distinct metabolic pathways significantly diversify the functional profile of the resulting FSBM. Full article

This study presents a comprehensive investigation of exact fractional wave solutions and bifurcation analysis for the (3 + 1)-dimensional extended shallow water wave (3D-eSWW) equation with $\beta$-derivative, which models nonlinear wave phenomena in fluid dynamics and coastal engineering. Leveraging the flexibility of the fractional derivative, the model provides a more generalized and adaptable framework for describing shallow water wave propagation. The Modified Extended Direct Algebraic Method (MEDAM) is systematically employed to derive a broad spectrum of novel exact analytical solutions. These include the following: dark solitary waves, singular solitons, singular periodic waves, periodic solutions expressed via trigonometric and Jacobi elliptic functions, polynomial solutions, hyperbolic wave patterns, combined dark–singular structures, combined hyperbolic–linear waves, and exponential-type wave profiles. Each solution family is presented with explicit parameter constraints that ensure both mathematical consistency and physical relevance, thereby offering a robust classification of wave regimes under diverse conditions. A thorough bifurcation analysis is conducted on the reduced dynamical system to examine parametric dependence and stability transitions. Critical bifurcation thresholds are identified, and distinct solution branches are mapped in the parameter space spanned by wave numbers, nonlinear coefficients, external forcing, and the fractional order $\beta$. The analysis reveals how solution dynamics undergo qualitative transitions—such as the emergence of solitary waves from periodic patterns or the appearance of singular structures—driven by the interplay of nonlinearity, dispersion, and fractional-order effects. These insights are crucial for understanding wave stability, predictability, and the onset of extreme events in shallow water contexts. Graphical representations of selected solutions validate the analytical results and illustrate the influence of $\beta$ on wave morphology, propagation, and stability. The simulations demonstrate that varying the fractional order can significantly alter wave profiles, highlighting the role of fractional calculus in capturing complex real-world behaviors. This work demonstrates the efficacy of the MEDAM technique in handling high-dimensional fractional nonlinear PDEs and provides a systematic framework for predicting and classifying wave regimes in real-world shallow water environments. The findings not only enrich the solution inventory of the 3D-eSWW equation but also advance the analytical toolkit for studying complex spatio-temporal dynamics in fractional mathematical physics and fluid mechanics. Ultimately, this research contributes to the development of more accurate models for coastal protection, tsunami forecasting, and marine engineering applications. Full article

Variational Mode Decomposition (VMD) is a powerful formalism for the time-scale analysis of vibration signals from rotating machinery. However, its performance is often compromised by complex parameter configuration, where subjective manual tuning leads to mode mixing or information loss. In this study, we present a physics-guided framework that generalizes VMD optimization across diverse operating conditions. We utilized a meta-dataset combining three distinct sources (CWRU, HUST, UO) to validate the approach. Through a shaft-normalized segmentation strategy and K-Means++ clustering, we identified six distinct signal archetypes based on spectral morphology. Central to this framework is the Energy-Dispersion Index (EDI), a novel physically interpretable metric designed to differentiate between structured fault transients and stochastic noise. Extensive validation via a full-factorial Design of Experiments (8640 trials) confirmed the statistical superiority of EDI over benchmarks like kurtosis and envelope entropy, yielding an 8.3% improvement in modal fidelity. Furthermore, a rigorous ablation study demonstrated that the proposed archetype-based parameterization is highly efficient. This strategy achieved a $392\times$ speedup over online optimization while maintaining statistically equivalent diagnostic accuracy. Additionally, by generalizing parameters from high-quality archetype representatives, the framework reduced spectral leakage (Orthogonality Index) by 51.4% compared to instance-wise optimization. The resulting framework provides a mathematically rigorous, real-time solution for automated vibration signal decomposition. Full article

Background/Objectives: Clonazepam (CLZ), a BCS Class II drug, presents significant oral delivery challenges due to its low aqueous solubility. This study explores the systematic development of solid self-emulsifying drug delivery systems (S-SEDDS) using Quality by Design (QbD). The primary objective was to evaluate and compare advanced mathematical optimization frameworks, specifically Derringer’s Desirability Function (D) and Weighted Goal Programming (WGP), to identify a robust formulation that enhances drug solubilization while ensuring superior processability and flowability. Methods: Liquid SEDDS were solidified by adsorption onto a porous matrix (Aerosil^® 200/Lactose). A multi-objective optimization was conducted to define a robust Design Space (DS), comparing D against WGP. The trade-offs between competing Critical Quality Attributes (CQAs), specifically powder flowability (angle of repose, AR), blending efficiency (BE), and CLZ recovery (CR), were evaluated. Characterization included morphology from Environmental Scanning Electron Microscopy (ESEM), droplet size analysis, and pH-dependent dissolution studies. Results: D provided a highly robust baseline, yielding constant optimal coordinates (F2, F3 = +1; F4 = 0) across all sensitivity levels, with a predicted AR of 40.46°, BE of 0.12 and CR of 90.0%. However, WGP successfully refined this solution by allowing a more flexible weighting of goals, achieving a more favorable compromise with an AR of 38.96°, a BE of 0.11, and a CR of 90.23%. The optimized system maintained nanometric droplet sizes (<200 nm) and showed a controlled, pH-independent release profile, reaching 80% drug solubilization at 6 h. Conclusions: Integrating WGP into the QbD framework offers a more versatile and precise optimization than the traditional D for complex pharmaceutical systems. This approach ensures the production of high-quality S-SEDDS, bridging the gap between mathematical modeling and the stringent requirements of industrial solid dosage manufacturing. Full article