Search Results (132)

The Kolmogorov–Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single-variable functions. Subsequent simplifications of this representation involve expressing these functions as parameterized sums of a smaller number of unique monotonic functions. Kolmogorov–Arnold Networks (KANs) have been recently proposed as an alternative to multilayer perceptrons. KANs feature learnable nonlinear activations applied directly to input values, modeled as weighted sums of basis spline functions. This approach replaces the linear transformations and sigmoidal post-activations used in traditional perceptrons. In this work, we propose a novel KAN variant by replacing both the inner and outer functions in the Kolmogorov–Arnold representation with weighted sinusoidal functions of learnable frequencies. We particularly fix the phases of the sinusoidal activations to linearly spaced constant values and provide a proof of their theoretical validity. We also conduct numerical experiments to evaluate its performance on a range of multivariable functions, comparing it with fixed-frequency Fourier transform methods, basis spline KANs (B-SplineKANs), and multilayer perceptrons (MLPs). We show that it outperforms the fixed-frequency Fourier transform B-SplineKAN and achieves comparable performance to MLP. Full article

Conventional wildfire assessment products emphasize regional-scale ignition likelihood and potential spread derived from fuels and weather. While useful for broad planning, they do not directly support boundary-aware, scenario-specific decision-making for localized threats to communities in the Wildland–Urban Interface (WUI). This limitation constrains the ability of fire managers to effectively prioritize mitigation efforts and response strategies for ignition events that may lead to severe local impacts. This paper introduces WUI-BTI—a scenario-based, simulation-driven boundary-threat index for the Wildland–Urban Interface that quantifies consequences conditional on an ignition under standardized meteorology, rather than estimating risk. WUI-BTI evaluates ignition locations—referred to as Fire Amplification Sites (FAS)—based on their potential to compromise the defined boundary of a community. For each ignition location, a high-resolution fire spread simulation is conducted. The resulting fire perimeter dynamics are analyzed to extract three key metrics: (1) the minimum distance of fire approach to the community boundary ($D_{min}$) for non-breaching fires; and for breaching fires, (2) the time required for the fire to reach the boundary ($T_p$), and (3) the total length of the community boundary affected by the fire ($L_c$). These raw outputs are mapped through monotone, sigmoid-based transformations to yield a single, interpretable score: breaching fires are scored by the product of an inverse-time urgency term and an extent term, whereas non-breaching fires are scored by proximity alone. The result is a continuous boundary-threat surface that ranks ignition sites by their potential to rapidly and substantially compromise a community boundary. By converting complex simulation outputs into scenario-specific, boundary-aware intelligence, WUI-BTI provides a transparent, quantitative basis for prioritizing fuel treatments, pre-positioning suppression resources, and guiding protective strategies in the WUI for fire managers, land use planners, and emergency response agencies. The framework complements regional hazard layers (e.g., severity classifications) by resolving fine-scale, consequence-focused priorities for specific communities. Full article

In cold and arid regions, the mechanical properties and influencing mechanisms of the root–soil interface during the thawing stage remain poorly understood. This study focuses on Alhagi sparsifolia root–clayey sand composites to investigate the effects of temperature (−10 °C to 25 °C), initial soil water content (4–12%), and naturally varying root diameter (4.50–5.05 mm) on root pullout behaviour, and integrates endoscopic macro-observation, environmental scanning electron microscopy (ESEM), soil water migration tests, and nuclear magnetic resonance (NMR) techniques to reveal the dominant influencing mechanisms. Key findings reveal the following: (1) An increase in soil water content from 4% to 12%, and a temperature rise from −10 °C to 25 °C led to a maximum reduction in the average peak pullout force (F_T) of roots exceeding 95%. (2) There is a non-monotonic relationship between root diameter and pull-out force, which can be attributed to two distinct failure modes: a newly observed failure mode known as root bark peeling, occurring under high soil moisture conditions (≥8%), and a commonly observed failure mode referred to as partial soil detachment, occurring under low soil moisture conditions (≤6%). (3) The coupling effects of temperature and water content reveal that the increase in temperature predominantly contributes to strength loss (>63%) during the ice–water phase transition (−10 °C to 0 °C), while soil water content primarily influences root pullout behaviour in the liquid water stage (5 °C to 25 °C). (4) As the temperature rises, in soils with low water content (4–6%), the reinforcing effect of roots appears to stabilize at −1 °C, whereas in soils with high water content (8–12%), stabilization occurs only beyond 5 °C. These findings enhance the understanding of root–soil interactions in thawing environments and provide a theoretical basis for soil bioengineering techniques aimed at slope stabilization in cold and arid regions. Full article

Thermal oxidative aging failure of high-temperature vulcanized silicone rubber (HTV) in high-voltage insulators is the core hidden danger of power grid security. In this study, terahertz time domain spectroscopy (THz-TDS) and attenuated total reflection infrared spectroscopy (ATR-FTIR) were combined to reveal the quantitative structure–activity relationship between dielectric response and chemical group evolution of HTV during accelerated aging at 200 °C for 80 days. In this study, HTV flat samples were made in the laboratory, and the dielectric spectrum of HTV in the range of 0.1 THz to 0.4 THz was extracted by a terahertz time–domain spectrum platform. ATR-FTIR was used to analyze the functional group change trend of HTV during aging, and the three-stage evolution of the dielectric real part (0.16 THz), the dynamics of the carbonyl group, the monotonic rise of the dielectric imaginary part (0.17 THz), and the linear response of silicon-oxygen bond breaking were obtained by combining the double Debye relaxation theory. Finally, three aging stages of HTV were characterized by dielectric loss angle data. The model can warn about the critical point of early oxidation and main chain fracture and identify the risk of insulation failure in advance compared with traditional methods. This study provides a multi-scale physical basis for nondestructive life assessment in a silicon rubber insulator. Full article

Cascading link failures continue to imperil power grids, transport networks, and cyber-physical systems, yet the relationship between a network’s robustness at the moment of attack and its subsequent resiliency remains poorly understood. We introduce a dynamic framework in which connectivity-based cascades and distributed self-healing act concurrently within each time-step. Failure is triggered when a node’s active-neighbor ratio falls below a threshold $\phi$; healing activates once the global fraction of inactive nodes exceeds trigger $T$ and is limited by budget $B$. Two real data sets—a 332-node U.S. airport graph and a 1133-node university e-mail graph—serve as testbeds. For each graph we sweep the parameter quartet ($\phi ,\hspace{0.17em}B,\hspace{0.17em}T,attackmode$) and record (i) immediate robustness $R$, (ii) 90% recovery time T₉₀, and (iii) cumulative average damage. Results show that targeted hub removal is up to three times more damaging than random failure, but that prompt healing with $B\ge 0.12$ can halve T₉₀. Scatter-plot analysis reveals a non-monotonic correlation: high-$R$ states recover quickly only when $B$ and $T$ are favorable, whereas low-$R$ states can rebound rapidly under ample budgets. A multiplicative fit $T_{90}\propto B^{-\beta }g\left(T\right)h\left(R\right)$ (with $\beta \approx 1$) captures these interactions. The findings demonstrate that structural hardening alone cannot guarantee fast recovery; resource-aware, early-triggered self-healing is the decisive factor. The proposed model and data-driven insights provide a quantitative basis for designing infrastructure that is both robust to failure and resilient in restoration. Full article

Accurate spatial interpolation of environmental data requires utilizing flexible models that can capture complex spatial patterns. In this paper, we present two improved dual kriging (DK) models comprising a nonlinear trend function that combines Gaussian radial basis functions with a first-order polynomial. The proposed model, DK–RBFP, and its extension, DK–RBFPGA, which includes k-means clustering and a genetic algorithm for parameter optimization, respectively, exhibit enhanced performance in capturing spatial variation. The complete monotonicity of the covariance function and the strict positive definiteness of the coefficient matrix provide theoretical support for the uniqueness of the DK solution. When applied to datasets of PM_2.5 concentrations for northern Thailand, both models perform better than the conventional DK model using a second-order polynomial trend (DK–POLY), as evidenced by accuracy metrics including the mean absolute percentage error (MAPE), the mean squared error (MSE), and the root mean square error (RMSE). The outcomes indicate that integrating nonlinear trend components with data-driven optimization significantly enhances accuracy and flexibility in environmental spatial predictions. Full article

Electronic devices (EDs) exhibit complex failure patterns throughout their lifetime, with failure modes (FaM) can be monotonic, non-monotonic, or a combination of both. This complexity is increased by using advanced semiconductors and flexible electronics, which introduce variability in degradation mechanisms. Although multiple reliability models exist, many lack flexibility or practical applicability in this context. This work proposes a novel competing risk (CR) model that combines the Fréchet and Chen distributions, called Fréchet-Chen Competitive Risk (FCCR). This model allows for modeling the minimum time to failure between two relevant FaMs. Its key mathematical properties and applicability to real-life scenarios are analyzed. Parameter estimation is performed using maximum likelihood (MLE) and Bayesian inference (BEM) using Hamiltonian Monte Carlo (HMC), which provides a robust basis for analysis. Two case studies with real-life ED data validate the model, demonstrating its superior fit and predictive capability compared to classical models. Furthermore, the effect of FCCR parameters on system behavior is explored, highlighting its usefulness in accurately modeling complex failure patterns in EDs. Full article

Since the monotonicity of the best approximant is crucial to establish partial ordering methods, in this paper, we, respectively, characterize the best approximants in Banach function spaces and Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$, in which we especially focus on the monotonicity characterizations. We first study monotonicity characterizations of the metric projection operator onto sublattices in general Banach function spaces by the property $H_g$. The sufficient and necessary conditions for monotonicity of the metric projection onto cones and sublattices are then, respectively, established in ${\mathrm{\Gamma }}_{p,w}$. The Lorentz spaces ${\mathrm{\Gamma }}_{p,w}$ are also shown to be reflexive under the condition $R{B}_p$, which is the basis for the existence of the best approximant. As applications, by establishing the partial ordering methods based on the obtained monotonicity characterizations, the solvability and approximation theorems for best proximity points are deduced without imposing any contractive and compact conditions in ${\mathrm{\Gamma }}_{p,w}$. Our results extend and improve many previous results in the field of the approximation and partial ordering theory. Full article

This paper proposes an improved wave function asperity elastic–plastic model. A cosine function that could better fit the geometric morphology was selected to construct the asperity, the elastic phase was controlled by the Hertz contact theory, the elastoplastic transition phase was corrected by the hyperbolic tangent function, and the fully plastic phase was improved by the projected area theory. The model broke through the limitations of the spherical assumption and was able to capture the stress concentration and plastic flow phenomena. The results show that the contact pressure in the elastic phase was 22% higher than that of the spherical shape, the plastic strain in the elastoplastic phase was 52% lower than that of the spherical shape, and the fully plastic phase reduced the contact area error by 20%. The improved hyperbolic tangent function eliminated the unphysical oscillation phenomenon in the elastoplastic phase and ensured the continuity and monotonicity of the contact variables, with an error of <5% from the finite element analysis. Meanwhile, extending the proposed model, we developed a rough surface contact model, and it was verified that the wavy asperity could better match the mechanical properties of the real rough surface and exhibited progressive stiffness reduction during the plastic flow process. The model in this paper can provide a theoretical basis for predicting stress distribution, plastic evolution, and multi-scale mechanical behavior in the connection interface. Full article

The traditional approach that separates remaining useful life prediction from maintenance strategy design often fails to support efficient decision-making. Effective maintenance requires a comprehensive consideration of prediction accuracy, cost control, and equipment safety. To address this issue, this paper proposes a multi-objective maintenance optimization method based on stochastic modeling. First, a multi-sensor data fusion technique is developed, which maps multidimensional degradation signals into a composite degradation state indicator using evaluation metrics such as monotonicity, tendency, and robustness. Then, a linear Wiener process model is established to characterize the degradation trajectory of equipment, and a closed-form analytical solution of its reliability function is derived. On this basis, a multi-objective optimization model is constructed, aiming to maximize equipment safety and minimize maintenance cost. The proposed method is validated using the NASA aircraft engine degradation dataset. The experimental results demonstrate that, while ensuring system reliability, the proposed approach significantly reduces maintenance costs compared to traditional periodic maintenance strategies, confirming its effectiveness and practical value. Full article

To explore the influence of mine roof on the damage and failure of sandstone surrounding rock under different pressure rates, mechanical experiments with different strain rates were carried out on sandstone rock samples. The strength, deformation, failure, energy and damage characteristics of rock samples with different strain rates were also discussed. The research results show that with the increases in the strain rate, peak stress, and elastic modulus show a monotonically increasing trend, while the peak strain decreases in the reverse direction. At a low strain rate, the proportion of the mass fraction of complete rock blocks in the rock sample is relatively high, and the shape integrity is good, while rock samples with a high strain rate retain more small-sized fragmented rock blocks. This indicates that under high-rate loading, the bifurcation phenomenon of secondary cracks is obvious. The rock samples undergo a failure form dominated by small-sized fragments, with severe damage to the rock samples and significant fractal characteristics of the fragments. At the initial stage of loading, the primary fractures close, and the rock samples mainly dissipate energy in the forms of frictional slip and mineral fragmentation. In the middle stage of loading, the residual fractures are compacted, and the dissipative strain energy keeps increasing continuously. In the later stage of loading, secondary cracks accelerate their expansion, and elastic strain energy is released sharply, eventually leading to brittle failure of the rock sample. Under a low strain rate, secondary cracks slowly expand along the clay–quartz interface and cause intergranular failure of the rock sample. However, a high strain rate inhibits the stress relaxation of the clay, forces the energy to transfer to the quartz crystal, promotes the penetration of secondary cracks through the quartz crystal, and triggers transgranular failure. A constitutive model based on energy damage was further constructed, which can accurately characterize the nonlinear hardening characteristics and strength-deformation laws of rock samples with different strain rates. The evolution process of its energy damage can be divided into the unchanged stage, the slow growth stage, and the accelerated growth stage. The characteristics of this stage reveal the sudden change mechanism from the dissipation of elastic strain energy of rock samples to the unstable propagation of secondary cracks, clarify the cumulative influence of strain rate on damage, and provide a theoretical basis for the dynamic assessment of surrounding rock damage and disaster early warning when the mine roof comes under pressure. Full article

We utilize the moving planes technique to prove the radial symmetry along with the monotonic characteristics of solutions for a system of parabolic Laplacian equations. In this system, the solutions of the two equations are interdependent, with the solution of one equation depending on the function of the other. By use of the maximal regularity theory that has been established for fractional parabolic equations, we ensure the solvability of these systems. Our initial step is to formulate a narrow region principle within a parabolic cylinder. This principle serves as a theoretical basis for implementing the moving planes method. Following this, we focus our attention on parabolic systems with fractional Laplacian equations and deduce that the solutions are radial symmetric and monotonic when restricted to the unit ball. Full article

The rheological behavior of firefighting foam is the basis for analyzing foam flow and foam spreading. This experimental study investigates the complex rheological behavior of rapidly aging firefighting foams, specifically focusing on alcohol-resistant aqueous film-forming foam. The primary objective is to characterize the time-dependent viscoelasticity, yielding, and viscous flow of firefighting foam under controlled shear conditions, addressing the significant challenge posed by its rapid structural evolution (drainage and coarsening) during measurement. Using a cylindrical Couette rheometer, conductivity measurements for the liquid fraction, and microscopy for the bubble size analysis, the study quantifies how foam aging impacts key rheological parameters. The results show that the creep and relaxation response of the firefighting foam in the linear viscoelastic region conforms to the Burgers model. The firefighting foam shows ductile yielding and significant shear thinning, and its flow curve under slow shear can be well represented by the Herschel–Bulkley model. Foam drainage and coarsening have competitive effects on the rheology of the firefighting foam, which results in monotonic and nonmonotonic variations in the rheological response in the linear and nonlinear viscoelastic regions, respectively. The work reveals that established empirical relationships between rheology, liquid fraction, and bubble size for general aqueous foams are inadequate for firefighting foams, highlighting the need for foam-specific constitutive models. Full article

We introduce a quantum integrated-information measure $\Phi$ for multipartite states within the Relational Quantum Dynamics (RQD) framework. $\Phi \left(\rho \right)$ is defined as the minimum quantum Jensen–Shannon distance between an n-partite density operator $\rho$ and any product state over a bipartition of its subsystems. We prove that its square root induces a genuine metric on state space and that $\Phi$ is monotonic under all completely positive trace-preserving maps. Restricting the search to bipartitions yields a unique optimal split and a unique closest product state. From this geometric picture, we derive a canonical entanglement witness directly tied to $\Phi$ and construct an integration dendrogram that reveals the full hierarchical correlation structure of $\rho$. We further show that there always exists an “optimal observer”—a channel or basis—that preserves $\Phi$ better than any alternative. Finally, we propose a quantum Markov blanket theorem: the boundary of the optimal bipartition isolates subsystems most effectively. Our framework unites categorical enrichment, convex-geometric methods, and operational tools, forging a concrete bridge between integrated information theory and quantum information science. Full article

To investigate the impact of sand-laden flow on energy loss in Francis turbines, this study integrates entropy generation theory with numerical simulations conducted using ANSYS CFX. The mixture multiphase flow model and the SST k-ω turbulence model are employed to simulate the solid–liquid two-phase flow throughout the entire flow passage of the turbine at the Gengda Hydropower Station (Minjiang River Basin section, 103°17′ E and 31°06′ N). The energy loss characteristics under different off-design conditions are analyzed on the basis of the average sediment concentration during the flood season (2.9 kg/m³) and a median particle diameter of 0.058 mm. The results indicate that indirect entropy generation and wall entropy generation are the primary contributors to total energy loss, while direct entropy generation accounts for less than 1%. As the guide vane opening increases, the proportion of wall entropy generation initially rises and then decreases, while the total indirect entropy generation exhibits a non-monotonic trend dominated by the flow pattern in the draft tube. Entropy generation on the runner walls increases steadily with larger openings, whereas entropy generation on the draft tube walls first decreases and then increases. The variation in entropy generation on the guide vanes remains relatively small. These findings provide technical support for the optimal design and operation of turbines in sediment-rich rivers. Full article