Search Results (100)

This paper explores coherent upper conditional previsions, a class of nonlinear functionals that generalize expectations while preserving consistency properties. The study focuses on their integral representation using the countably additive Möbius transform, which is possible if coherent upper previsions are defined with respect to a monotone set function of bounded variation. In this work, we prove that an integral representation with respect to a countably additive measure is also possible, on the Borel $\sigma$-algebra, even when the coherent upper prevision is defined by the Choquet integral with respect to a Hausdorff measure, which is not of bounded variation. It occurs since Hausdorff outer measures are metric measures, and therefore every Borel set is measurable with respect to them. Furthermore, when the conditioning event has a Hausdorff measure in its own Hausdorff dimension equal to zero or infinity, coherent conditional probability is defined via the countably additive Möbius transform of a monotone set function of bounded variation. The paper demonstrates the continuity of coherent conditional previsions induced by Hausdorff measures. Full article

With the deepening of degradation, the stability and reliability of the degrading system usually becomes poor, which may lead to random jumps occurring in the degradation path. A non-homogeneous jump diffusion process model is introduced to more accurately capture this type of degradation. In this paper, the proposed degradation model is translated into a state–space model, and then the Monte Carlo simulation of the state dynamic model based on particle filtering is employed for predicting the degradation evolution and estimating the remaining useful life (RUL). In addition, a general model identification approach is presented based on maximization likelihood estimation (MLE), and an iterative model identification approach is provided based on the expectation maximization (EM) algorithm. Finally, the practical value and effectiveness of the proposed method are validated using real-world degradation data from temperature sensors on a blast furnace wall. The results demonstrate that our approach provides a more accurate and robust RUL estimation compared to CNN and LSTM methods, offering a significant contribution to enhancing predictive maintenance strategies and operational safety for systems with complex, non-monotonic degradation patterns. Full article

In his foundational work on classical and quantum electrodynamics, Stueckelberg introduced an external evolution parameter, $\tau$, in order to overcome difficulties associated with the problem of time in relativity. Stueckelberg particle trajectories are described by the evolution of spacetime events under the monotonic advance of $\tau$, the basis for the Feynman–Stueckelberg interpretation of particle–antiparticle interactions. An event is a solution to $\tau$-parameterized equations of motion, which, under simple conditions, including the elimination of pair processes, can be reparameterized by the proper time of motion. The $4+1$ formalism in general relativity (GR) extends this framework to provide field equations for a $\tau$-dependent local metric ${\gamma }_{\mu \nu }(x,\tau )$ induced by these Stueckelberg trajectories, leading to $\tau$-parameterized geodesic equations in an evolving spacetime. As in standard GR, the linearized theory for weak fields leads to a wave equation for the local metric induced by a given matter source. While previous attempts to solve the wave equation have produced a metric with the expected features, the resulting geodesic equations for a test particle lead to unreasonable trajectories. In this paper, we discuss the difficulties associated with the wave equation and set up the more general ADM-like $4+1$ evolution equations, providing an initial value problem for the metric induced by a given source. As in the familiar $3+1$ formalism, the metric can be found as a perturbation to an exact solution for the metric induced by a known source. Here, we propose a metric, ansatz, with certain expected properties; obtain the source that induces this metric; and use them as the initial conditions in an initial value problem for a general metric posed as a perturbation to the ansatz. We show that the ansatz metric, its associated source, and the geodesic equations for a test particle behave as required for such a model, recovering Newtonian gravitation in the nonrelativistic limit. We then pose the initial value problem to obtain more general solutions as perturbations of the ansatz. Full article

One of the key expectations of AI product manufacturers for their products is the ability to scale to larger markets, especially across legal systems, with fewer prototypes and lower adaptation costs. This paper focuses on the increasingly dynamic legal compliance challenges faced by designers of AI products in achieving this goal. Based on non-monotonic reasoning, we design an automated reasoning tool to help them better understand the legal implications of their designs in a transnational context and, ultimately, adjust the design of AI products more flexibly. This tool supports the quantitative representation of the strength of legal significance to help designers better understand the reasons for their decisions from their own perspective. To illustrate this functionality, a case study on traffic regulations across the UK, France, and Japan demonstrates the system’s ability to resolve legal conflicts—such as driving-side mandates and speed radar detector prohibitions—through quantitative evaluation. Full article

A procedure for Bayesian nonparametric regression is described that automatically adjusts the degree of smoothing as the curvature of the underlying function changes. Relative to previous work adopting a similar approach that either employs a single global smoothing parameter or assumes that the smoothing process follows a random walk, the model considered here permits adaptive smoothing and imposes stationarity in the autoregressive smoothing process. An efficient Markov Chain Monte Carlo (MCMC) scheme for model estimation is fully described for this stationary case, and the performance of the method is illustrated in several generated data experiments. An application is also provided, analyzing the relationship between behavioral problems in students and academic achievement. Point estimates from the nonparametric methods suggest (a) expected achievement declines monotonically with a behavioral problems index (BPI) score and (b) the rate of decline is relatively flat at the left tail of the BPI distribution and then becomes sharply more negative. Full article

China’s unique economic growth target system exerts significant economic growth pressure (EGP) on local officials, leading to notable economic and environmental consequences for urban land use. Consequently, this system is theoretically expected to have a significant impact on urban land green utilization efficiency (ULGUE). This study investigates the invisible institutional factors that shape ULGUE within China’s distinct economic growth target system. The results indicate an inverted U-shaped relationship between EGP and ULGUE, and this nonlinear relationship is statistically significant in central, western, and northeastern cities but not in eastern cities. EGP influences ULGUE in a non-monotonic manner by affecting land marketization, green technology innovation, and industrial structure upgrading. Furthermore, environmental regulation and financial technology investment moderate the relationship between EGP and ULGUE. Heterogeneity analysis reveals that the inverted U-shaped relationship is more pronounced in resource-dependent cities and cities with stringent target constraints. This study contributes empirical evidence on the interaction between EGP and ULGUE while offering both theoretical insights and practical implications. Full article

Natural gas hydrates (shortened as hydrates) are expected to be a prospective alternative to traditional fossil energies. The main strategy of exploring hydrates is achieved by dissociating solid hydrates into gas and water with the depressurization method. However, we have little knowledge on the changes in heat and energy, which are implicit essences compared with explicit temperature. Thus, this study for the first time investigates the evolutionary patterns of heat and energy during hydrate dissociation, by fully coupled thermal–hydraulic–mechanical–chemical modelling. A novel numerical technique (physics-based constrained conditions) is proposed to guarantee the stability and precision of the numerical computation. The classic Masuda’s experiment is used as a case study. Results show that the cumulative conduction heat tends to increase first and then decrease during the dissociation of hydrate, while the cumulative advection heat has the tendency to increase monotonically. External heat sources increase the energy, while phase change has a reduction effect on the change in energy. The role of conduction heat is minor, but the contribution of advection heat is considerable for the change in energy. Additionally, two implications are given for lab-scale experiments and in situ engineering from the perspective of energy. Our findings provide new insights into the mechanism of hydrate dissociation and are beneficial to the real-world engineering of hydrate exploration in terms of cost evaluation. Full article

Among the most investigated hypotheses for a radiobiological explanation of the mechanism behind the FLASH effect in ultra-high dose rate radiotherapy, intertrack recombination between particle tracks arriving at a close spatiotemporal distance has been suggested. In the present work, we examine these conditions for different beam qualities and energies, defining the limits of both space and time where a non-negligible chemical effect is expected. To this purpose the TRAX-CHEM chemical track structure Monte Carlo code has been extended to handle several particle tracks at the same time, separated by pre-defined spatial and temporal distances. We analyzed the yields of different radicals as compared to the non-interacting track conditions and we evaluated the difference. We find a negligible role of intertrack for spatial distances larger than 1 $\mu$m, while for temporal distances up to $\mu$s, a non-negligible interaction is observed especially at higher LET. In addition, we emphasize the non-monotonic behavior of some relative yield as a function of the time separation, in particular of ${\mathrm{H}}_2{\mathrm{O}}_2$, due to the onset of a different reaction involving solvated electrons besides well-known $\mathrm{O}{\mathrm{H}}^{·}$ recombination. Full article

Income is often viewed as the main determinant of life insurance demand. However, in the last two decades, the world’s life insurance penetration has continued to decrease even as income grows. This study investigates the relationship between income and life insurance demand using panel data from forty-one countries from 2013 to 2022, along with education and life expectancy as control variables. The study finds a non-monotonic relationship between income and life insurance penetration and between education and life insurance penetration, while life expectancy shows a monotonic relationship with life insurance penetration. This study provides significant policy implications for insurers to predict life insurance demand and suggests that non-high-income countries emphasize the improvement of their life insurance sector development. Full article

Background: To investigate the behavior of spiking neural networks (SNNs), the sensitivity of input perturbation serves as an effective metric for assessing the influence on the network output. However, existing methods fall short in evaluating the sensitivity of SNNs featuring biologically plausible leaky integrate-and-fire (LIF) neurons due to the intricate neuronal dynamics during the feedforward process. Methods: This paper first defines the sensitivity of a temporal-coded spiking neuron (SN) as the deviation between the perturbed and unperturbed output under a given input perturbation with respect to overall inputs. Then, the sensitivity algorithm of an entire SNN is derived iteratively from the sensitivity of each individual neuron. Instead of using the actual firing time, the desired firing time is employed to derive a more precise analytical expression of the sensitivity. Moreover, the expectation of the membrane potential difference is utilized to quantify the magnitude of the input deviation. Results/Conclusions: The theoretical results achieved with the proposed algorithm are in reasonable agreement with the simulation results obtained with extensive input data. The sensitivity also varies monotonically with changes in other parameters, except for the number of time steps, providing valuable insights for choosing appropriate values to construct the network. Nevertheless, the sensitivity exhibits a piecewise decreasing tendency with respect to the number of time steps, with the length and starting point of each piece contingent upon the specific parameter values of the neuron. Full article

Polydopamine has the capacity to adhere to a large variety of materials and this property offers the possibility to bind nanoparticles to solid surfaces. In this work, magnetite nanoparticles were deposited on gold substrates coated with polydopamine films. The aim of this work was to investigate the effects of the composition and morphology of the PDA layers on the sticking of magnetite nanoparticles. The polydopamine coating of gold surfaces was achieved by the oxidation of alkaline solutions of dopamine with various reaction times. The length of the reaction time to form PDA was expected to influence the composition and surface roughness of the PDA films. Magnetite nanoparticles were deposited on these polydopamine films by immersing the samples in aqueous dispersions of nanoparticles. The morphology at the nanometric scale and the composition of the surfaces before and after the deposition of magnetite nanoparticles were investigated by means of AFM and XPS. We found that the amount of magnetite nanoparticles on the surface did not vary monotonically with the reaction time of PDA formation, but it was at the minimum after 20 min of reaction. This behavior may be attributed to changes in the chemical composition of the coating layer with reaction time. Full article

To investigate the mechanical properties and microstructure evolution of P92 steel during long-term service, the operated P92 main steam pipes from the first ultra-supercritical units in China were sectioned into samples representing various service durations and stresses (0# (as-received state, 1# (82,000 h, 67.3 MPa), 2# (85,000 h, 78.0 MPa), and 3# (100,000 h, 80.3 MPa)). Thereafter, a comprehensive assessment of their mechanical properties, including tensile strength, impact, hardness, and creep resistance, as well as a detailed microstructure analysis, was carried out. The effect of stress on the aging of material properties during operation is discussed. The results show that the circumferential stress caused by the increase in the internal steam pressure can significantly promote the creep life consumption of P92 steel, resulting in the degradation of mechanical properties and the expedited aging of the microstructure. The R_p0.2 and R_m of the P92 main steam pipe at room temperature and 605 °C decreased with the service time increase, reflecting the influence of stress in operation, which is expected to be used for the residual life evaluation of P92 steel. The relationship between the impact absorption energy (FATT50), Brinell hardness, and the operating time of P92 operating pipes is non-monotonic, indicating that these parameters are not sensitive indicators of material aging due to stress. The evaluation of performance degradation in P92 operating pipes due to stress-induced aging is not reliably discernible through optical metallography alone. To achieve a thorough assessment, the use of transmission electron microscopy (TEM) is essential. Full article

Failure of a safety-critical system during mission execution can result in significant financial losses. Implementing mission abort policies is an effective strategy to mitigate the system failure risk. This research delves into systems that are subject to cumulative shock degradation, considering uncertainties in shock damage. To account for the varied degradation parameters, we employ a dynamic Bayesian learning method using real-time sensor data for accurate degradation estimation. Our primary focus is on modeling the mission abort policy with an integrated parameter learning approach within the framework of a finite-horizon Markov decision process. The key objective is to minimize the expected costs related to routine inspections, system failures, and mission disruptions. Through an examination of the structural aspects of the value function, we establish the presence and monotonicity of optimal mission abort thresholds, thereby shaping the optimal policy into a controlled limit strategy. Additionally, we delve into the relationship between optimal thresholds and cost parameters to discern their behavior patterns. Through a series of numerical experiments, we showcase the superior performance of the optimal policy in mitigating losses compared with traditional heuristic methods. Full article

There is much interest in the topic of partial information decomposition, both in developing new algorithms and in developing applications. An algorithm, based on standard results from information geometry, was recently proposed by Niu and Quinn (2019). They considered the case of three scalar random variables from an exponential family, including both discrete distributions and a trivariate Gaussian distribution. The purpose of this article is to extend their work to the general case of multivariate Gaussian systems having vector inputs and a vector output. By making use of standard results from information geometry, explicit expressions are derived for the components of the partial information decomposition for this system. These expressions depend on a real-valued parameter which is determined by performing a simple constrained convex optimisation. Furthermore, it is proved that the theoretical properties of non-negativity, self-redundancy, symmetry and monotonicity, which were proposed by Williams and Beer (2010), are valid for the decomposition $I_{\mathrm{ig}}$ derived herein. Application of these results to real and simulated data show that the $I_{\mathrm{ig}}$ algorithm does produce the results expected when clear expectations are available, although in some scenarios, it can overestimate the level of the synergy and shared information components of the decomposition, and correspondingly underestimate the levels of unique information. Comparisons of the $I_{\mathrm{ig}}$ and $I_{\mathrm{dep}}$ (Kay and Ince, 2018) methods show that they can both produce very similar results, but interesting differences are provided. The same may be said about comparisons between the $I_{\mathrm{ig}}$ and $I_{\mathrm{mmi}}$ (Barrett, 2015) methods. Full article

Timely forecasting of aboveground vegetation biomass is crucial for effective management and ensuring food security. However, research on predicting aboveground biomass remains scarce. Artificial intelligence (AI) methods could bridge this research gap and provide early warning to planners and stakeholders. This study evaluates the effectiveness of deep learning (DL) algorithms in predicting aboveground vegetation biomass with limited-size data. It employs an iterative forecasting procedure for four target horizons, comparing the performance of DL models—multi-layer perceptron (MLP), long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), and CNN-LSTM—against the traditional seasonal autoregressive integrated moving average (SARIMA) model, serving as a benchmark. Five limited-size vegetation biomass time series from Kenyan grasslands with values at 15-day intervals over a 20-year period were chosen for this purpose. Comparing the outcomes of these models revealed significant differences (p < 0.05); however, none of the models proved superior among the five time series and the four horizons evaluated. The SARIMA, CNN, and CNN-LSTM models performed best, with the statistical model slightly outperforming the other two. Additionally, the accuracy of all five models varied significantly according to the prediction horizon (p < 0.05). As expected, the accuracy of the models decreased as the prediction horizon increased, although this relationship was not strictly monotonic. Finally, this study indicated that, in limited-size aboveground vegetation biomass time series, there is no guarantee that deep learning methods will outperform traditional statistical methods. Full article