Search Results (335)

Strict minimum message length (SMML) is an information-theoretic coding principle that represents a continuous statistical model by a finite set of assertions and a partition of the sample space. We show that the SMML objective decomposes into assertion entropy and conditional cross-entropy, balancing the cost of identifying an assertion against the cost of encoding data under the assigned model. For any fixed partition, the optimal codepoint for each cell is the model distribution that minimises Kullback–Leibler (KL) divergence from the data distribution restricted to that cell. Using the local Fisher–Rao geometry of regular parametric models, we show that, under a high-resolution LAN-scale regime, SMML partitions are asymptotically the pullback, through the maximum-likelihood estimator, of weighted Fisher–Rao Voronoi tessellations in parameter space, with assertion probabilities appearing as additive weights. For regular canonical exponential families, SMML codepoints satisfy a moment-matching condition and admit an interpretation as KL/Bregman centroids, while exact SMML cells are pullbacks of convex polyhedra in sufficient-statistic space. Together, these results show that SMML induces a natural information-geometric quantisation linking entropy-based coding, KL projection, and divergence-based Voronoi geometry. Full article

The mechanical response of cellular structures is governed not only by relative density and average cell geometry but also by the spatial arrangement of cells. However, the manner in which arrangement-dependent effects evolve with increasing cell number has not been systematically clarified. In this study, the compressive behavior of closed-cell structures with varying cell numbers was investigated using finite element analysis under dynamically equilibrated compression conditions while maintaining constant relative density and identical material parameters. Cellular models were generated using hierarchical Poisson disk sampling combined with Voronoi tessellation. The number of cells was increased through three distinct approaches: mirror replication of a reference structure, enlargement of the overall specimen size, and refinement of cell size under fixed external dimensions. To characterize arrangement-dependent effects, two distinct features of the compressive response were introduced: averaging, defined as a reduction in variability across responses from different initial cell arrangements, and smoothing, defined as the suppression of abrupt stress fluctuations within an individual response. Quantitative metrics were employed to evaluate both effects. Averaging was observed in plate-type models compressed in the z-direction and in fixed-size models, whereas mirror-connected models retained strong arrangement dependence despite large cell numbers. Smoothing occurred predominantly in plate-type models compressed in the z-direction and was strongly correlated with the number of cell layers aligned along the compression direction rather than with total cell number alone. The simulations were conducted in a dynamically equilibrated regime in which internal stress equilibrium was achieved during deformation. These results demonstrate that compressive behavior is governed not only by cell number but also by structural arrangement and directional cell-layer alignment, providing mechanistic insight into the transition from arrangement-dependent variability to stable macroscopic response under dynamic compression. Full article

This study examines graphs that demonstrate Gallai’s property, particularly those in which for every prescribed set S of vertices with $\left|S\right|=j$ there exists a longest path or cycle that avoids that set. Such graphs are naturally fault-tolerant in the structural sense: if some vertices fail, there can still exist longest routes that bypass the failed vertices. Our main purpose is to construct explicit Gallai-type graphs that admit embeddings into a rigorously defined three-dimensional geometric adjacency structure derived from an icosahedral–tetrahedral polyhedral cell complex. We show that similar graphs may be found in three-dimensional structures obtained from a periodic polyhedral packing (cell complex) built from tetrahedral and icosahedral cells. Importantly, we do not claim a face-to-face tessellation of ${\mathbb{R}}^3$ by congruent regular icosahedra and tetrahedra; instead, we define a specific periodic cell complex ${\mathcal{IT}}^3$ and work in its associated adjacency graph $\Gamma \left({\mathcal{IT}}^3\right)$. These geometric constructions expand lattice-based findings to a three-dimensional adjacency setting and provide new embeddings for Gallai-type graphs. Connections to AI systems are mentioned at the conceptual level. Full article

Spatiotemporal prediction of gas extraction-induced seismicity is a key challenge in regional seismic risk management, hindered by heterogeneous spatial coupling among reservoir blocks and extreme class imbalance in seismicity records. This study proposes a multi-task spatiotemporal forecasting framework based on a dual-encoder architecture combining a Graph Attention Network (GAT) with a Long Short-Term Memory (LSTM) network. The monitoring network is represented as a graph with node-level features including monthly production, reservoir pressure, compaction, and historical seismicity. A Voronoi tessellation strategy maps continuous epicentral coordinates to discrete graph nodes. The GAT encodes heterogeneous spatial interactions via adaptive attention, while a two-layer LSTM extracts multiscale temporal dependencies. Event detection and magnitude classification are treated as parallel tasks, jointly optimized using focal loss and focal-adjusted weighted cross-entropy to mitigate class imbalance. A Seismic Risk Index (SRI) integrates event occurrence and magnitude class probabilities into a continuous risk estimate. Validated on the KNMI seismic catalog and Groningen production data, the model achieves an event Probability of Detection (POD) of 0.677 and a magnitude classification macro average recall (MAvA) of 0.548 under an event rate of 0.07%. Compared with a pure LSTM baseline, the GAT improves POD by 2.1% and MAvA by 7.9%. The time-averaged risk field exhibits spatial heterogeneity broadly consistent with observed seismicity patterns, indicating the potential of this framework for fine-grained spatiotemporal risk assessment of extraction-induced seismicity. Full article

One of the main tasks in the field of directional statistics is to build goodness-of-fit tests for uniformity on circles, spheres or more abstract manifolds. We discuss a goodness-of-fit test for uniformity on a distance-regular graph. Our main tool is the pseudo-inverse of the combinatorial Laplacian, for which we give explicit expressions in terms of the intersection array of the graph. Such a test can be used as a test for uniformity of data from the circle or the sphere, grouped on the tiles of a regular tessellation associated with some finite group of isometries. We describe the cases of Platonic graphs and provide examples based on real circular and spherical data, vectorial or axial. Full article

Subsurface rolling contact fatigue (RCF) failure is one of the primary failure modes in properly installed and lubricated rolling bearings. Its actual service life often exhibits significant scatter, posing a formidable challenge to the reliable life prediction and operational safety of bearings. This study establishes a macro-meso-coupled rolling contact fatigue model that accounts for crystalline anisotropy and grain topological structures. This model utilizes Voronoi tessellations and random Euler angles to construct a polycrystalline mesoscopic model, which is subsequently integrated with a macroscopic Hertzian contact finite element analysis to simulate the roller bearing loading cycles and determine the localized stress responses within the material. The results indicate that variations in macroscopic structural and operating parameters primarily affect the overall stress level of the subsurface RCF failure. The relative fatigue life of the bearing exhibits an exceptionally high sensitivity to changes in macroscopic and operating parameters. Specifically, an increase in radial load leads to an exponential decrease in relative life, with the Weibull slope ranging between 1.001 and 1.129, which is broadly consistent with the classical Lundberg–Palmgren experimental value of 1.125. Conversely, the heterogeneity of the mesoscopic crystalline structure strongly influences the statistical variance of localized extreme stresses. The scatter in bearing fatigue life demonstrates a much more pronounced sensitivity to mesostructural alterations; as the grain size increases from 10 μm to 40 μm, the Weibull slope drops from 1.041 to 0.784. This study provides an analytical basis for the reliable life prediction of rolling bearings. Full article

Conventional contact-based monitoring of heart rate (HR) presents challenges such as patient discomfort, skin irritation, and poor long-term adherence, motivating the development of contactless, video-based sensing systems. This study proposes a robust hybrid framework combining advanced signal processing with machine learning to enhance HR estimation accuracy from facial video. The methodology integrates a two-stage geometric stabilization pipeline with dense facial tessellation to mitigate motion. Eulerian Video Magnification (EVM) amplifies subtle color variations, followed by chrominance-based Region of Interest (ROI) filtering. Signal recovery utilizes a sliding-window Principal Component Analysis (PCA) for local coherence, followed by Second-Order Blind Identification (SOBI), with a Light Gradient Boosting Machine (LightGBM) classifier employed to automatically identify physiological sources. Validated on the challenging COHFACE dataset, the approach achieves a Mean Absolute Error (MAE) of 1.50 bpm, a Root Mean Square Error (RMSE) of 3.07 bpm, and a Pearson Correlation Coefficient (PCC) of 0.97 on the test set. The method demonstrates robustness across diverse lighting conditions, outperforming traditional algorithms and achieving parity with state-of-the-art deep learning models, while offering an interpretable solution for contactless health monitoring. Full article

Despite the growing use of tessellated and patterned façades in contemporary architecture, their thermal performance, particularly in cooling-dominated educational buildings, remains insufficiently quantified, with existing studies largely prioritizing daylighting or aesthetic outcomes over energy-driven thermal behavior. This study aims to systematically evaluate how different tessellated façade geometries and perforation ratios influence thermal performance and cooling demand in a Mediterranean climate, and to identify an optimal façade configuration that balances multiple thermal objectives. Three tessellation typologies—nature-inspired (Voronoi), Islamic geometric, and folded origami-based patterns—were parametrically generated and applied as external shading screens to an educational building. Annual thermal simulations were conducted using Climate Studio to assess four performance metrics: solar heat gain, energy use intensity, hours of overheating derived from operative temperature, and peak cooling demand. A post-simulation, data-driven, multi-objective, decision-support approach was applied using Compromise Programming to systematically evaluate and rank discrete façade alternatives based on multiple thermal performance criteria. Results indicate that all tessellated façades reduce solar heat gain and peak cooling demand relative to the unshaded baseline, with performance strongly dependent on both geometry and perforation ratio. Lower perforation ratios (20%) consistently outperform more open configurations, while Voronoi-based façades achieve the most balanced overall thermal performance across all evaluated criteria and emerging as the top-ranked solution. The study’s novelty lies in its comparative, cooling-focused evaluation of fundamentally different tessellation logics using transparent, decision-oriented optimization rather than subjective comfort indices or computationally intensive evolutionary algorithms. Beyond its specific findings, the research provides a transferable methodological framework for integrating geometry-informed façade design into early-stage decision-making, supporting climate-responsive and energy-efficient educational architecture in Mediterranean and similar climates. Full article

The magnetic properties of materials similar to Nd-Fe-B permanent magnets are highly sensitive to microstructure. Using Hybrid Monte Carlo micromagnetics simulations, we systematically investigate how grain boundary (GB) and grain crystallographic orientation affect coercivity (H_c) and remanence (M_r). A polycrystalline model with independently adjustable microstructural parameters is constructed via Voronoi tessellation. Our results show that increasing GB width from 2 nm to 10 nm reduces Hc by 32% and M_r by 16%. Grain boundary acts as both a nucleation site and pinning center: a wider GB facilitates reverse domain nucleation, especially at the triple junctions. However, domain wall propagation is underpinned by GB during the propagation process. For a thick GB, H_c decreases with increasing GB saturation magnetization (M_s′), because the thick weakly magnetic layer weakens exchange coupling between adjacent grains, shifting the reversal behavior from collective switching to more localized nucleation. Increasing the average easy-axis tilt angle reduces H_c, as the misalignment lowers the effective anisotropy component along the applied field direction, facilitating magnetization reversal. These findings confirm the importance of GB and texture control in optimizing the magnetic performance of Nd-Fe-B permanent magnets, offering references for experimental investigations. Full article

Sandwich structures are increasingly employed in high-performance applications due to their excellent strength-to-weight ratio. However, their mechanical reliability often depends on the structural core, which remains susceptible to failure under shear and flexural loads. Additive manufacturing (AM) enables the design and fabrication of complex, bio-inspired core architectures, such as those derived from Voronoi tessellations, which can potentially enhance energy absorption and mechanical performance. This study investigates the mechanical behavior of PLA-based cellular cores, produced via Fused Filament Fabrication (FFF), under quasi-static and intermediate strain rates (up to 33 s⁻¹). Two infill geometries were compared: a standard cubic pattern and an open Voronoi-based structure inspired by biological morphologies. The results demonstrate strain-rate sensitivity in both configurations, characterized by increased stiffness and peak stress at higher loading rates. While the Voronoi structure exhibited lower maximum strength compared to the cubic pattern, it demonstrated a more gradual post-peak softening, indicating potentially superior energy dissipation capabilities. These findings support the potential of bio-inspired, additively manufactured structures in energy-absorbing applications. Full article

Heterogeneity at the grain scale strongly influences hydraulic fracturing in crystalline rock; however, systematic studies quantifying its impacts on the evolution of injection pressure and crack propagation remain limited. To address this gap, we employ a hydro-mechanical phase-field model incorporating Voronoi-based microstructures to systematically quantify the effects of grain-scale heterogeneity on hydraulic fracturing. Two numerical experimental programs are designed to examine the effects of (i) mean grain size and (ii) mineral distribution under different axial stresses. The simulations reveal a close coupling between injection pressure and crack-length evolution, and both responses are strongly governed by grain-scale heterogeneity. When the fracture enters weak minerals, it advances rapidly and pressure drops; when it encounters on strong minerals, growth slows or arrests and pressure builds until a threshold triggers the next advance. Moreover, peak pressure statistics further indicate that mineral distribution dominates the response scatter, while axial stress plays a secondary role. Specifically, the mean peak pressures at 0 and 10 MPa are similar (about 14.31 and 14.21 MPa), whereas rearranging minerals within the same Voronoi tessellation changes peak pressure by more than 4 MPa. Higher peaks occur when strong minerals lie ahead of the initial crack tip, increasing resistance to initiation and early growth. Finally, the stress state modulates fracture trajectories: under low axial stress, fractures preferentially follow mineral boundaries, whereas higher axial stress strengthens macroscopic stress guidance and shifts the path toward a direction closer to being perpendicular to the maximum principal stress. This trend is consistent with energy minimization, since interface detouring under high axial stress incurs a larger elastic free energy penalty. Full article

Grain-scale heterogeneity strongly influences hydraulic fracture initiation and trajectory in crystalline rocks, yet its contributions to non-planar growth and the interaction of multiple nearby cracks remain insufficiently quantified. To address this gap, we perform numerical experiments on a model containing two parallel pre-existing cracks using a hydro-mechanical phase-field framework, systematically quantifying how mineral distribution and axial compression govern non-planar hydraulic fracture growth and inter-fracture competition. The results demonstrate that mineral distribution is the primary driver of fracture complexity. Even within the same Voronoi tessellation, redistributing minerals alone yields markedly different trajectories, deflections, branching patterns, and final morphologies. Furthermore, non-planar growth follows a stepwise, energy-threshold-driven mechanism. When cracks penetrate strong grains or undergo large-angle deflections, propagation is impeded, and injection pressure builds up. Once a critical energy threshold is reached, accumulated energy is rapidly released along the path of minimum incremental energy, manifested as abrupt pressure drops and rapid crack advance. Additionally, the two nearby fractures exhibit strong mechanical competition. Despite negligible hydraulic interference in low-permeability granite, early growth of one fracture redistributes stresses and suppresses the driving force of the other, resulting in asymmetric development. Finally, axial compression primarily governs the overall propagation orientation and influences local failure modes but has a limited effect on peak pressure relative to mineral distribution. Full article

Porous tubular structures are of significant interest in engineering due to their exceptional potential for lightweight design, energy absorption, and multifunctional integration. Inspired by the unique net architecture of natural luffa sponges, this study introduces a novel design approach for such structure, namely bio-inspired Voronoi Tube (BVT). This design employs Voronoi tessellation patterns, parametrically controlled through the spatial distribution of seed points and integrates iterative optimization algorithms, to achieve precise coordinated regulation over the randomness and continuity of the resulting spatial network, closely mimicking the biological paradigm. Then, specimens are fabricated via additive manufacturing and then quasi-statically compressed axially, followed by systematic mechanical testing of the base material. The experimental results are analyzed to reveal the BVT structure’s mechanical responses and simultaneously validate finite-element simulation model. Subsequently, a systematic numerical analysis is performed to further understand the deformation mechanisms of the BVT structure and the influence of key geometric parameters. The results indicate that the iteratively optimized BVT structure successfully replicates the characteristic energy absorption behavior of the natural luffa sponge, confirming the effectiveness of the bio-inspired design. A rise in diameter from 0.6 mm to 1.0 mm results in a 78.32% increase in the specific energy absorption (SEA). Under identical mass conditions, tailored adjustments to the geometry can enhance the SEA by up to 34.57%. Full article

We investigate the application of soft-cell tessellations—a recently discovered class of curved-boundary space-filling shapes—to finite element mesh generation. Using Gmsh and scikit-fem, we compare the solution accuracy for Poisson equation benchmarks on curved domains. The results demonstrate that soft-cell meshes achieve optimal $O\left(h^2\right)$ convergence rates in $L^2$, matching conventional elements. More significantly, we identify a fundamental limitation: coarse polygon boundaries introduce systematic boundary condition (BC) error (∼3%) that does not decrease with mesh refinement. We prove analytically that the BC error scales as $O(1/n^2)$ for n-point polygon boundaries, explaining why doubling boundary points reduces the error by $4\times$. Fine spline boundaries reduce this error by 96%, with the interior solution error reduced by 97.5%. For complex organic shapes, the improvement reaches 56–80%. We establish a connection between the soft-cell softness measure $\sigma$ and FEM accuracy: a higher softness yields a lower BC error. Comparison with Isogeometric Analysis reveals that while IGA achieves exact geometry (${10}^{-16}$ error), fine spline FEM boundaries reduce the geometric error by 5–6 orders of magnitude versus coarse polygons. These results establish that the boundary representation quality fundamentally limits the FEM accuracy on curved domains, making soft-cell representations particularly valuable. Full article

Segmenting CAD models into developable surface patches is a fundamental problem in geometric modeling and manufacturing-oriented applications. Existing approaches often rely on discrete Gaussian curvature estimation or Gauss map analysis; however, their performance on CAD meshes is frequently hindered by numerical instability, sensitivity to mesh tessellation, and complex parameter tuning. In this work, we propose a simple and robust method for developable surface segmentation based on a sparse normal discontinuity prior. Our key observation is that industrial CAD models are typically composed of large developable regions separated by a sparse set of sharp creases and edges. Consequently, segmentation boundaries correspond to sparse discontinuities in the surface normal field rather than continuous variations in curvature. Based on this perspective, we formulate developable surface segmentation as the detection of sparse normal jump discontinuities. In the discrete setting of triangle meshes, this formulation naturally leads to a dihedral angle-based approach that avoids explicit curvature estimation and admits an efficient graph-based solution. The proposed algorithm consists of face normal computation, dihedral angle-based boundary detection, and connected component extraction on a thresholded face adjacency graph. The method requires only a single geometrically interpretable parameter and naturally aligns segmentation boundaries with sharp features commonly found in CAD models. Experimental results on a diverse set of industrial CAD meshes, including standard benchmarks widely used in related research, demonstrate that the proposed approach achieves robust and accurate segmentation, as validated by both visual coherence and quantitative developability metrics. Full article