Search Results (88)

In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum systems and decision-making processes under partial, noisy, or ambiguous information. Our formalism generalizes the Born rule within a multi-valued logic structure, linking Positive Operator-Valued Measures (POVMs) with data-driven plausibility estimators, agent-based credibility priors, and fuzzy-theoretic possibility functions. We develop a hybrid classical–quantum inference engine that computes a vectorial aggregation of the quadruples, enhancing robustness and semantic expressivity in contexts where classical probability fails to capture non-Kolmogorovian phenomena such as entanglement, contextuality, or decoherence. The approach is validated through three real-world application domains—quantum cybersecurity, quantum AI, and financial computing—where the proposed model outperforms standard probabilistic reasoning in terms of accuracy, resilience to noise, interpretability, and decision stability. Comparative analysis against QBism, Dempster–Shafer, and fuzzy quantum logic further demonstrates the uniqueness of architecture in both operational semantics and practical outcomes. This contribution lays the groundwork for a new theory of epistemic quantum computing capable of modelling and acting under uncertainty beyond traditional paradigms. Full article

To address the issue of uncertainty in renewable energy and its impact on the safe and stable operation of power systems, this paper proposes a transient stability constrained optimal power flow (TSCOPF) calculation method that takes into account the uncertainty of wind power and load. First, a non-parametric kernel density estimation method is used to construct the probability density function of wind power, while the load uncertainty model is based on a normal distribution. Second, a TSCOPF model incorporating the critical clearing time (CCT) evaluation metric is constructed, and corresponding probabilistic constraints are established using opportunity constraint theory, thereby establishing a TSCOPF model that accounts for wind power and load uncertainties; then, a semi-invariant probabilistic flow calculation method based on de-randomized Halton sequences is used to convert opportunity constraints into deterministic constraints, and the improved sooty tern optimization algorithm (ISTOA) is employed for solution. Finally, the superiority and effectiveness of the proposed method are validated through simulation analysis of case studies. Full article

Conventional risk assessment frameworks usually define risk as a function of vulnerabilities and threats, but they frequently lack a single quantitative model that incorporates the unique features of each element. In order to close this gap, this paper creates a flexible, open, and theoretically sound risk assessment formula that is still reliable even in the absence of complete vulnerability data. This is particularly important for financial institutions operating in emerging markets, where regulators rarely provide centralized vulnerability assessments and where Basel-type frameworks are only partially implemented. The contribution of the paper is a practically verified Bayesian network model that integrates threat likelihoods, vulnerability likelihoods, and their impacts within a probabilistic structure. Using 500 stratified Monte Carlo scenarios calibrated to real fintech and banking institutions operating under EU and national supervision, we demonstrate that excluding vulnerability impact from the model does not significantly reduce the predictive performance. These findings advance the theory of risk assessment, simplify practical implementation, and enhance the scalability of risk modeling for both traditional banks and fintech institutions in emerging economies. Full article

This study presents and evaluates three sampling strategies to characterize electricity demand in regions of Colombia with limited metering infrastructure. These areas lack Advanced Metering Infrastructure (AMI), relying instead on traditional monthly consumption records. The objective of the research is to obtain user samples that are representative of the original population and logistically efficient, in order to support energy planning and decision-making. The analysis draws on five years of historical data from 2020 to 2024. It includes monthly energy consumption, geographic coordinates, customer classification, and population type, covering over 500,000 users across four subregions of operation determined by the region grid operator: North, South, Center, and East. The proposed methodologies are based on Shannon entropy, consumption-based probabilistic sampling, and Kullback–Leibler divergence minimization. Each method is assessed for its ability to capture demand variability, ensure representativeness, and optimize field deployment. Representativeness is evaluated by comparing the differences in class proportions between the sample and the original population, complemented by the Pearson correlation coefficient between their distributions. Results indicate that entropy-based sampling excels in logistical simplicity and preserves categorical diversity, while KL divergence offers the best statistical fit to population characteristics. The findings demonstrate how combining information theory and statistical optimization enables flexible, scalable sampling solutions for demand characterization in under-instrumented electricity grids. Full article

In this work, we propose a definition of the random fractional Riemann–Liouville integral operator, where the order of integration is given by a random variable. Within the framework of random operator theory, we study this integral with a random kernel and establish results on the measurability of the random Riemann–Liouville integral operator, which we show to be a random endomorphism of $L^1[a,b]$. Additionally, we derive the semigroup property for these operators as a probabilistic version of the constant-order Riemann–Liouville integral. To illustrate the behavior of this operator, we present two examples involving different random variables acting on specific functions. The sample trajectories and estimated probability density functions of the resulting random integrals are then explored via Monte Carlo simulation. Full article

In today’s dynamic and highly uncertain environment, organizations, particularly in the aviation sector, face increasing challenges that demand resilient, flexible, and data-driven change management decisions. Responding to the growing need for structured approaches to managing complex uncertainties—geopolitical tensions, economic volatility, social shifts, rapid technological advancements, environmental pressures and regulatory changes—this research proposes a theoretical change management model for aviation service providers, such as airports. Integrating three analytical approaches, the model offers a robust, multi-method approach for supporting sustainable transformation under uncertainty. Normative analysis using Bayesian decision theory identifies influential external environmental factors, capturing probabilistic relationships, and revealing causal links under uncertainty. Prescriptive planning through scenario theory explores alternative future pathways and helps to identify possible predictions, offer descriptive evaluation employing fuzzy comprehensive evaluation, and assess decision quality under vagueness and complexity. The proposed four-stage model—observation, analysis, evaluation, and response—offers a methodology for continuous external environment monitoring, scenario development, and data-driven, proactive change management decision-making, including the impact assessment of change and development. The proposed model contributes to the theoretical advancement of the change management research area under uncertainty and offers practical guidance for aviation organizations (airports) facing a volatile external environment. This framework strengthens aviation organizations’ ability to anticipate, evaluate, and adapt to multifaceted external changes, supporting operational flexibility and adaptability and contributing to the sustainable development of aviation services. Supporting aviation organizations with tools to proactively manage systemic uncertainty, this research directly supports the integration of sustainability principles, such as resilience and adaptability, for long-term value creation through change management decision-making. Full article

Accurate extraction of representative operating conditions is crucial for optimizing systems in renewable energy applications. This study proposes a novel framework that combines the Parzen window estimation method, ideal for nonparametric modeling of wind, solar, and load datasets, with a game theory-based time scale selection mechanism. The novelty of this work lies in integrating probabilistic density modeling with multi-indicator evaluation to derive realistic operational profiles. We first validate the superiority of the Parzen window approach over traditional Weibull and Beta distributions in estimating wind and solar probability density functions. In addition, we analyze the influence of key meteorological parameters such as wind direction, temperature, and solar irradiance on energy production. Using three evaluation metrics, the main result shows that a 3-day representative time scale offers optimal accuracy when determined through game theory methods. Validation with real-world data from Inner Mongolia confirms the robustness of the proposed method, yielding low errors in wind, solar, and load profiles. This study contributes a novel 3-day typical profile extraction method validated on real meteorological data, providing a data-driven foundation for optimizing energy storage systems under renewable uncertainty. This framework supports energy sustainability by ensuring realistic modeling under renewable intermittency. Full article

The entanglement entropy of a random tensor network (RTN) is studied using tools from free probability theory. Random tensor networks are simple toy models that help in understanding the entanglement behavior of a boundary region in the anti-de Sitter/conformal field theory (AdS/CFT) context. These can be regarded as specific probabilistic models for tensors with particular geometry dictated by a graph (or network) structure. First, we introduce a model of RTN obtained by contracting maximally entangled states (corresponding to the edges of the graph) on the tensor product of Gaussian tensors (corresponding to the vertices of the graph). The entanglement spectrum of the resulting random state is analyzed along a given bipartition of the local Hilbert spaces. The limiting eigenvalue distribution of the reduced density operator of the RTN state is provided in the limit of large local dimension. This limiting value is described through a maximum flow optimization problem in a new graph corresponding to the geometry of the RTN and the given bipartition. In the case of series-parallel graphs, an explicit formula for the limiting eigenvalue distribution is provided using classical and free multiplicative convolutions. The physical implications of these results are discussed, allowing the analysis to move beyond the semiclassical regime without any cut assumption, specifically in terms of finite corrections to the average entanglement entropy of the RTN. Full article

The water–energy nexus (WEN) is of great significance due to the strong interdependence between the energy and water sectors. Nevertheless, water leakage in water distribution networks (WDNs), which is often ignored in existing WEN operation models, causes notable water and energy losses. In this research, a cooperative operation model for WEN considering WDN water leakage is put forward. A hybrid stochastic–information gap decision theory (IGDT) method was tailored in this study to properly manage the probabilistic uncertainties associated with renewable generation, electrical and water demand in the WEN, and water leakage with limited information to enhance the robustness of the operation strategies of the WEN under complex operational conditions. The proposed model and method were validated on a modified IEEE 33-bus system integrated with a 15-node commercial WDN. The co-optimization model reduced the operational cost by 23.01% compared to the independent operation model. When considering water leakage, the joint optimization resolved the water supply shortage issue caused by ignoring leakage and reduced the water purchase volume by 94.44 cubic meters through coordinated optimization. These quantitative results strongly demonstrate the effectiveness of the proposed framework. Full article

General aviation trajectory prediction plays a crucial role in enhancing safety and operational efficiency at non-towered airports. However, current research faces multiple challenges including variable weather conditions, complex aircraft interactions, and flight pattern constraints specified by general aviation regulations. This paper proposes a deep learning method based on stochastic processes aimed at addressing uncertainty issues in general aviation trajectory prediction. First, we design a probabilistic encoder–decoder structure enabling the model to output trajectory distributions rather than single paths, with regularization terms based on Lyapunov stability theory to ensure predicted trajectories maintain stable convergence while satisfying flight patterns. Second, we develop a multi-layer attention mechanism that accounts for weather factors, enhancing the model’s responsiveness to environmental changes. Validation using the TrajAir dataset from Pittsburgh-Butler Regional Airport (KBTP) not only advances deep learning applications in general aviation but also provides new insights for solving trajectory prediction problems. Full article

The failure mode and effect analysis (FMEA) method, which estimates the risk levels of systems or components solely based on the multiplication of simple risk rating indices, faces several limitations. These include the risk of inaccurate risk level judgment and the potential for misjudgments due to human factors, both of which pose significant threats to the safe operation of aircraft. Therefore, a Probabilistic Language based on a cumulative prospect theory (Probabilistic Language, PL) risk assessment strategy was proposed, combining the technique for order preference with similarity to an ideal solution (TOPSIS). The probabilistic language term value and probability value were fused in the method through the cumulative prospect theory, and a new PL measure function was introduced. The comprehensive weights of evaluation strategies were determined by calculating the relevant weights of various indicators through the subjective expert weight and objective entropy weight synthesis. So, a weighted decision matrix was constructed to determine the ranking order close to the ideal scheme. Finally, the risk level of each failure mode was ranked according to its close degree to the ideal situation. Through case validation, the consistency of risk ranking was improved by 23.95% compared to the traditional FMEA method. The rationality of weight allocation was increased by 18.2%. Robustness was also enhanced to some extent. Compared with the traditional FMEA method, the proposed method has better rationality, application, and effectiveness. It can provide technical support for formulating a new generation of airworthiness documents for the risk level assessment of civil aircraft and its subsystem components. Full article

Addressing the critical challenges of sealing integrity and operational optimization in aquifer gas storage (AGS), this study focuses on a block within the Qianjiang Basin to systematically investigate geological modeling and injection–production strategies. Utilizing 3D seismic interpretation, drilling, and logging data, a stochastic geological modeling approach was employed to construct a high-resolution 3D reservoir model, elucidating the distribution of reservoir properties and trap configurations. Numerical simulations optimized the gas storage parameters, yielding an injection rate of 160 MMSCF/day (40 MMSCF/well/day) over 6-month-long hot seasons and a production rate of 175 MMSCF/day during 5-month-long cold seasons. Interval theory was innovatively applied to assess fault stability under parameter uncertainty, determining a maximum safe operating pressure of 23.5 MPa—12.3% lower than conventional deterministic results. The non-probabilistic reliability analysis of caprock integrity showed a maximum 11.1% deviation from Monte Carlo simulations, validating the method’s robustness. These findings establish a quantitative framework for site selection, sealing system evaluation, and operational parameter design in AGS projects, offering critical insights to ensure safe and efficient gas storage operations. This work bridges theoretical modeling with practical engineering applications, providing actionable guidelines for large-scale AGS deployment. Full article

This study establishes a novel mathematical framework for stochastic maintenance optimization in production systems by integrating Markov decision processes (MDPs) with convex programming theory. We develop a Z-transformation-based dual-space decomposition method to reconstruct MDPs into a solvable linear programming form, resolving the inherent instability of traditional models caused by uncertain initial conditions and non-stationary state transitions. The proposed approach introduces three mathematical innovations: (i) a spectral clustering mechanism that reduces state-space dimensionality while preserving Markovian properties, (ii) a Lagrangian dual formulation with adaptive penalty functions to handle operational constraints, and (iii) a warm start algorithm accelerating convergence in high-dimensional convex optimization. Theoretical analysis proves that the derived policy achieves stability in probabilistic transitions through martingale convergence arguments, demonstrating structural invariance to initial distributions. Experimental validations on production processes reveal that our model reduces long-term maintenance costs by 36.17% compared to Monte Carlo simulations (1500 vs. 2350 average cost) and improves computational efficiency by 14.29% over Q-learning methods. Sensitivity analyses confirm robustness across Weibull-distributed failure regimes (shape parameter $\beta \in$ [1.2, 4.8]) and varying resource constraints. Full article

The vigorous development of urban air mobility (UAM) is reshaping the urban travel landscape, but it also poses severe challenges to the safe and efficient operation of dense and complex airspace. Potential conflicts between flight plans have become a core bottleneck restricting its development. Traditional flight plan adjustment and management methods often rely on deterministic trajectory predictions, ignoring the inherent temporal uncertainties in actual operations, which may lead to the underestimation of potential risks. Meanwhile, existing global optimization strategies often face issues of inefficiency and overly broad adjustment scopes when dealing with large-scale plan conflicts. To address these challenges, this study proposes an innovative flight plan conflict management framework. First, by introducing a probabilistic model of flight time errors, a new conflict detection mechanism based on confidence intervals is constructed, significantly enhancing the ability to foresee non-obvious conflict risks. Furthermore, based on complex network theory, the framework accurately identifies a small number of “critical flight plans” that play a core role in the conflict network, revealing their key impact on chain reactions of conflicts. On this basis, a phased optimization strategy is adopted, prioritizing the adjustment of spatiotemporal parameters (departure time and speed) for these critical plans to systematically resolve most conflicts. Subsequently, only fine-tuning the speeds of non-critical plans is required to address remaining local conflicts, thereby minimizing interference with the overall operational order. Simulation results demonstrate that this framework not only significantly improves the comprehensiveness of conflict detection but also effectively reduces the total number of conflicts. Additionally, the proposed phased artificial lemming algorithm (ALA) outperforms traditional optimization algorithms in terms of solution quality. This work provides an important theoretical foundation and a practically valuable solution for developing robust and efficient UAM dynamic scheduling systems, holding promise to support the safe and orderly operation of large-scale urban air traffic in the future. Full article

In the framework of quasi-Hermitian quantum mechanics, the eligible operators of observables may be non-Hermitian, $A_j\ne A_j^{†}$, $j=1,2,\dots ,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\mathsf{\Theta }\ne I$, guaranteeing the quasi-Hermiticity $A_j^{†}\mathsf{\Theta }=\mathsf{\Theta }{A}_j$. The task is easy at $K=1$ because there are many eligible metrics $\mathsf{\Theta }=\mathsf{\Theta }\left(A_1\right)$. In our paper, the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric, $\mathsf{\Theta }=\mathsf{\Theta }(A_1,A_2)$, are presented and discussed. Full article