Search Results (1,142)

With the widespread application of artificial intelligence in real estate price prediction, model explainability has become a critical factor influencing its acceptability and trustworthiness. The Shapley value, as a classic cooperative game theory method, quantifies the average marginal contribution of each feature, ensuring global fairness in the explanation allocation. However, its focus on average fairness lacks robustness under data perturbations, model changes, and adversarial attacks. To address this limitation, this paper proposes a hybrid explainability framework that integrates the Shapley value and Least Core attribution. The framework leverages the Least Core theory by formulating a linear programming problem to minimize the maximum dissatisfaction of feature subsets, providing bottom-line fairness. Furthermore, the attributions from the Shapley value and Least Core are combined through a weighted fusion approach, where the weight acts as a tunable hyperparameter to balance the global fairness and worst-case robustness. The proposed framework is seamlessly integrated into mainstream machine learning models such as XGBoost. Empirical evaluations on real-world real estate rental data demonstrate that this hybrid attribution method not only preserves the global fairness of the Shapley value but also significantly enhances the explanation consistency and trustworthiness under various data perturbations. This study provides a new perspective for robust explainable AI in high-risk decision-making scenarios and holds promising potential for practical applications. Full article

A data set on Stark broadening parameters defining the Lorentzian line profile (spectral line widths and shifts) for 31 multiplets of four-times-charged nitrogen ion (N V), with lines broadened by impacts with electrons (e), protons (p), He II ions, $\alpha$ particles (He III), and B III, B IV, B V, and B VI ions, is given. The above-mentioned data have been calculated within the frame of the semiclassical perturbation theory, for temperatures from 50,000 K to 1,000,000 K, and densities of perturbers from 10¹⁵ cm⁻³ up to 10²¹ cm⁻³. These data are, first of all, of interest for diagnostics and modeling of laser-driven plasma in experiments and investigations of proton–boron fusion, especially when the target is boron nitride (BN). Data on Stark broadening by collisions with e, p, He II ions, and $\alpha$ particles are useful for the investigation of stellar plasma, in particular for white dwarf atmospheres and subphotospheric layer modeling. Full article

Miller’s rule originated as an empirical relation between the nonlinear and linear optical coefficients of materials. It is now accepted as a useful tool for guiding experiments and computational materials discovery, but its theoretical foundation had long been limited to a derivation for the classical Lorentz model with a weak anharmonic perturbation. Recently, we developed a mathematical framework which enabled us to prove that Miller’s rule is equally valid for quantum anharmonic oscillators, despite different dynamics due to zero-point fluctuations and further quantum-mechanical effects. However, our previous derivation applied only to one-dimensional oscillators and to the special case of second- and third-harmonic generation in a monochromatic electric field. Here we extend the proof to three-dimensional quantum anharmonic oscillators and also treat all orders of the nonlinear response to an arbitrary multi-frequency field. This makes the results applicable to a much larger range of physical systems and nonlinear optical processes. The obtained generalized Miller formulae rigorously express all tensor elements of the frequency-dependent nonlinear susceptibilities in terms of the linear susceptibility and thus allow a computationally inexpensive quantitative prediction of arbitrary parametric frequency-mixing processes from a small initial dataset. Full article

Mine water hazards represent one of the principal threats to safe coal mine operations; therefore, accurately predicting mine water inflow is critical for drainage system design and water hazard mitigation. Because mine water inflow is governed by the combined influence of multiple hydrogeological factors and thus exhibits pronounced non-linear characteristics, conventional approaches are inadequate in terms of forecasting accuracy and medium- to long-term predictive capability. To address this issue, this study proposes a Chaos-Autoformer-based method for predicting mine water inflow. First, the univariate inflow series is mapped into an m-dimensional phase space by means of phase-space reconstruction from chaos theory, thereby fully preserving its non-linear features; the reconstructed vectors are then used to train and forecast inflow with an improved Chaos-Autoformer model. On top of the original Autoformer architecture, the proposed model incorporates a Chaos-Attention mechanism and a Lyap-Dropout scheme, which enhance sensitivity to small perturbations in initial conditions and complex non-linear propagation paths while improving stability in long-horizon forecasting. In addition, the loss function integrates the maximum Lyapunov exponent error and earth mode decomposition (EMD) indices so as to jointly evaluate dynamical consistency and predictive performance. An empirical analysis based on monitoring data from the Liangshuijing Coal Mine for 2022–2025 demonstrates that the trained model delivers high accuracy and stable performance. Ablation experiments further confirm the significant contribution of the chaos-aware components: when these modules are removed, forecasting accuracy declines to only 76.5%. Using the trained model to predict mine water inflow for the period from June 2024 to June 2025 yields a root mean square error (RMSE) of 30.73 m³/h and a coefficient of determination (R²) of 0.895 against observed data, indicating excellent fitting and predictive capability for medium- to long-term tasks. Extending the forecast to July 2025–November 2027 reveals a pronounced annual cyclical pattern in future mine water inflow, with markedly higher inflow in summer than in winter and an overall slowly declining trend. These findings show that the Chaos-Autoformer can achieve high-precision medium- and long-term predictions of mine water inflow, thereby providing technical support for proactive deployment and refined management of mine water hazard prevention. Full article

The present paper investigates a new tool for analyzing stability/convergence properties and robustness against matched perturbations of a class of nonlinear systems. We start with a scalar system, where it is shown that the state can be regulated or stabilized to a prescribed time using time-varying functions. The proof is based on Lyapunov theory. We developed a robust terminal-integral sliding mode controller that guarantees convergence of the system states to a desired equilibrium within a user-defined time, irrespective of initial conditions and under bounded disturbances. The method was extended to a class of second-order nonlinear systems, achieving both fixed-time (prescribed-time) convergence and robustness. Theoretical properties were established via Lyapunov-based analysis, and numerical simulations confirmed the effectiveness of the proposed methods in terms of robustness and convergence. Full article

The Lorentz-breaking theory not only modifies the geometric structure of curved spacetime but also significantly alters the quantum dynamics of bosonic and fermionic fields in black hole spacetime, leading to observable physical effects on Hawking temperature and Bekenstein–Hawking entropy. This study establishes the first systematic theoretical framework for entropy modifications of charged accelerating Anti-de Sitter black holes, incorporating gauge-invariant corrections derived from Lorentz-violating quantum field equations in curved spacetime. The obtained analytical expression coherently integrates semi-classical approximations with higher-order quantum perturbative contributions. Furthermore, the methodologies employed and the resultant conclusions are subjected to rigorous analysis, establishing their physical significance for advancing fundamental investigations into black hole entropy. Full article

The rapid growth of e-commerce has created substantial environmental impacts, driving the need for advanced optimization models to enhance supply chain sustainability. As consumer preferences shift toward environmental responsibility, organizations must adopt robust quantitative methods to reduce ecological footprints while ensuring operational efficiency. This study develops a novel hybrid multi-criteria decision-making (MCDM) model to evaluate and prioritize green suppliers under uncertainty, integrating the rough-Dombi best–worst method (BWM) and an improved Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The proposed model addresses two key challenges: (1) inconsistency in expert judgments through rough set theory and Dombi aggregation operators and (2) ranking instability via an enhanced TOPSIS formulation that mitigates rank reversal. Mathematically, the rough-Dombi BWM leverages interval-valued rough numbers to model subjective expert preferences, while the Dombi operator ensures flexible and precise weight aggregation. The modified TOPSIS incorporates a dynamic distance metric to strengthen ranking robustness. A case study of five e-commerce suppliers validates the model’s effectiveness, with results identifying cost, green competitiveness, and external environmental management as the dominant evaluation dimensions. Key indicators—such as product price, pollution control, and green design—are rigorously prioritized using the proposed framework. Theoretical contributions include (1) a new rough-Dombi fusion for criteria weighting under uncertainty and (2) a stabilized TOPSIS variant with reduced sensitivity to data perturbations. Practically, the model provides e-commerce enterprises with a computationally efficient tool for sustainable supplier selection, enhancing resource allocation and green innovation. This study advances the intersection of uncertainty modeling, operational research, and sustainability analytics, offering scalable methodologies for mathematical decision-making in supply chain contexts. Full article

This paper investigates distributed optimization problems for multi-agent systems with parametric uncertainties over unbalanced directed communication networks. To settle this class of optimization problems, a continuous-time algorithm is proposed by integrating adaptive control techniques with an output feedback tracking protocol. By systematically employing Lyapunov stability theory, perturbed system analysis, and input-to-state stability theory, we rigorously establish the asymptotic convergence property of the proposed algorithm. A numerical simulation further demonstrates the effectiveness of the algorithm in computing the global optimal solution. Full article

The growing demand for low-frequency, broadband vibration and noise suppression technologies in next-generation mechanical equipment has become increasingly urgent. Effective negative mass locally resonant structures represent one of the most paradigmatic classes of acoustic metamaterials. Their unique elastic wave bandgaps enable efficient suppression of low-frequency vibrations, while inherent nonlinear effects provide significant potential for the design and tunability of these bandgaps. To achieve ultra-low-frequency and ultra-broadband vibration attenuation, this study employs Duffing oscillators exhibiting negative-stiffness characteristics as structural elements, establishing a bistable nonlinear acoustic-metamaterial mechanical model. Subsequently, based on the effective negative mass local resonance theory, the perturbation solution for the dispersion curves is derived using the perturbation method. Finally, the effects of mass ratio, stiffness ratio, and nonlinear term on the starting and cutoff frequencies of the bandgap are analyzed, and key geometric parameters influencing the design of ultra-low vibration reduction bandgaps are comprehensively investigated. Subsequently, the influence of external excitation amplitude and the nonlinear term on bandgap formation is analyzed using numerical computation methods. Finally, effective positive mass, negative mass, and zero-mass phenomena within distinct frequency ranges of the bandgap and passband are examined to validate the theoretically derived results. The findings demonstrate that, compared to a positive-stiffness system, the bandgap of the bistable nonlinear acoustic metamaterial incorporating negative-stiffness Duffing oscillators shifts to higher frequencies and widens by a factor of $\sqrt{2}$. The external excitation amplitude F changes the bandgap starting frequency and cutoff frequency. As F increases, the starting frequency rises while the cutoff frequency decreases, resulting in a narrowing of the bandgap width. Within the frequency range bounded by the bandgap starting frequency and cutoff frequency, the region between the resonance frequency and cutoff frequency corresponds to an effective negative mass state, whereas the region between the bandgap starting frequency and resonance frequency exhibits an effective positive mass state. Critically, the bandgap encompasses both effective positive mass and negative mass regions, wherein vibration propagation is suppressed. Concurrently, a zero-mass state emerges within this structure, with its frequency precisely coinciding with the bandgap cutoff frequency. This study provides a theoretical foundation and practical guidelines for designing nonlinear acoustic metamaterials targeting ultra-low-frequency and ultra-broadband vibration and noise mitigation. Full article

An asymptotic stability velocity tracking controller is designed to enable the autonomous maneuvering flight of unmanned helicopters. Firstly, taking the UH-60A without pilots as the research object, a high-efficient rotor aerodynamic modeling is developed, which incorporates a free-wake vortex method with the flap response of blades. The consummate flight dynamic model is complemented by wind tunnel-validated fuselage/tail rotor load regressions. Secondly, a linear state–space equation is derived via the small perturbation linearization method based on the flight dynamic model within the body coordinate system. A decoupled model is formulated based on the linear state–space equation by employing the implicit model approach. Subsequently, a system of ordinary differential equations is constructed, which is related to the deviation between actual velocity and its expected value, along with higher-order derivatives of this discrepancy. The I&I (immersion and invariance) theory is then employed to facilitate the design of a non-cascade control loop. Finally, the response of desired velocity in longitudinal channel is simulated with step signal to compare the control effect with a PID (proportional–integral–derivative) controller. By adjusting the coefficients, the response progress of the PID controller is similar to the effect of adaptive controller with I&I theory. However, there is no obvious overshoot in the process with I&I adaptive controller, and the average response amplitude accounts for 16.69% of the random white noise, which is 7.38% of the oscillation level under the PID controller. The parameter tuning complexity when employing I&I theory is significantly lower than that of the PID controller, which is evaluated by mathematical derivations and simulations. Meanwhile, the sidestep and pirouette maneuvers are simulated and analyzed to examine the controller in accordance with the performance criteria outlined in the ADS-33E-REF standards. The simulation results demonstrate that the speed expectation-oriented asymptotic stability control can achieve a fast response. Both sidestep and pirouette maneuvers can satisfy the desired performance requirements stipulated by ADS-33E-REF. Full article

We develop a general framework for response theory in Markovian diffusion processes governed by Fokker–Planck equations. Our formalism, based on the notion of the dissipation function, is capable of handling dynamics that are driven by an external perturbation arbitrarily far from a given reference process. Using the analytically solvable Brownian oscillator model, we derive exact response formulae for both overdamped and underdamped dynamics of harmonically bound Brownian particles. We also demonstrate that for certain observables and under suitable time scaling, the operations of model reduction and response formula extraction commute, which highlights a relevant symmetry of the adopted mathematical formalism. Notably, the time reversal invariance symmetry, which is manifested as detailed balance in stochastic processes and is often required in statistical mechanics, is not necessary in our response framework. Full article

This study investigates the cooperative transport of a cable-suspended payload by two multirotor unmanned aerial vehicles (UAVs). A compact nonlinear control law that allows to simultaneously (i) track a slow reference trajectory, (ii) hold a prescribed inter-vehicle geometry, and (iii) actively damp load swing is developed. The model treats the two aerial robots and the payload as three point masses connected by linear-elastic cables, and the controller is obtained through a Newton–Euler formulation. A singular-perturbation analysis shows that, under modest gain–separation conditions, the closed-loop system is locally exponentially stable: fast dynamics govern formation holding and swing suppression, while slow dynamics takes into account trajectory tracking. Validation is performed in a realistic simulation scenario that includes six-degree-of-freedom rigid-body vehicles, Blade-Element theory rotor models, and sensor noise. Compared to an off-the-shelf, baseline controller, the proposed method significantly improves flying qualities while minimizing hazardous payload oscillations. Owing to its limited parameter set and the absence of heavy optimization, the approach is easy to tune and well suited for real-time implementation on resource-limited UAVs. Full article

Natural gas plays a critical role in integrated energy systems. In this context, the present study proposes an optimization model for the electricity–gas coupling system, grounded in the theory of interdependent networks. By integrating network topology parameters with real-time operational metrics, the model substantially enhances system robustness and adaptability. To quantify nodal vulnerability and importance, the study introduces two novel evaluation indicators: the Electric Potential–Closeness Fusion Indicator (EPFI) for power networks and the Pressure Difference–Closeness Comprehensive Indicator (PDCI) for natural gas systems. Leveraging these indicators, three coupling paradigms—assortative, disassortative, and random—are systematically constructed and analyzed. System resilience is assessed through simulation experiments incorporating three attack strategies: degree-based, betweenness centrality-based, and random node removal. Evaluation metrics include network efficiency and the variation in the size of the largest connected subgraph under different coupling configurations. The proposed framework is validated using a hybrid case study that combines the IEEE 118-node electricity network with a 20-node Belgian natural gas system, operating under a unidirectional gas-to-electricity energy flow model. Results confirm that the disassortative coupling configuration, based on EPFI and PDCI indicators, exhibits superior resistance to network perturbations, thereby affirming the effectiveness of the model in improving the robustness of integrated energy systems. Full article

We investigate pseudo-complex General Relativity (pcGR)—a coordinate-extended formulation of General Relativity (GR)—within the framework of Hořava-Lifshitz gravity, a regularized theory featuring anisotropic scaling. The pcGR framework bridges GR with modified gravitational theories through the introduction of a minimal length scale. Focusing on Schwarzschild black holes, we derive the Wheeler-deWitt equation, obtaining a quantized description of pcGR. Using perturbative methods and semi-classical approximations, we analyze the solutions of the equations and their physical implications. A key finding is the avoidance of the central singularity due to nonlinear interaction terms in the Hořava-Lifshitz action. Notably, extrinsic curvature (kinetic energy) contributions prove essential for singularity resolution, even in standard GR. Furthermore, the theory offers new perspectives on dark energy, proposing an alternative mechanism for its accumulation. Full article

In addressing the challenges of low path tracking accuracy and poor robustness during tractor autonomous operation, this paper proposes a path tracking control method for tractors that integrates prescribed performance with sliding mode control (SMC). A key feature of this control method is its inherent immunity to system parameter perturbations and external disturbances, while ensuring path tracking errors are constrained within a predefined range. First, the tractor is simplified into a two-wheeled vehicle model, and a path tracking error model is established based on the reference operation trajectory. By defining a prescribed performance function, the constrained tracking control problem is transformed into an unconstrained stability control problem, guaranteeing the boundedness of tracking errors. Then, by incorporating SMC theory, a prescribed performance sliding mode path tracking controller is designed to achieve robust path tracking and error constraint for the tractor. Finally, both simulation and field experiments are conducted to validate the method. The results demonstrate that compared with the traditional SMC method, the proposed method effectively mitigates the impact of complex farmland conditions, reducing path tracking errors while enforcing strict error constraints. Field experiment data shows the proposed method achieves an average absolute error of 0.02435 m and a standard deviation of 0.02795 m, confirming its effectiveness and superiority. This research lays a foundation for the intelligent development of agricultural machinery. Full article