Search Results (90)

Count outcomes are commonly analyzed using Poisson regression, but empirical data often exhibit overdispersion, excess ties, heaping, or other departures from the Poisson distribution. This paper evaluates a rank-Poisson transformation, denoted poisrank, designed to map observed counts onto Poisson quantiles before fitting a Poisson regression model. Our goal is to test whether a rank-Poisson transformation offers a useful general-purpose strategy when count data do not satisfy Poisson assumptions. Using an empirical example and a Monte Carlo simulation study with Poisson, overdispersed, rounded, and gapped count distributions, we compared Poisson regression on raw counts, Poisson regression after the poisrank transformation, quasi-Poisson regression, and additional comparison approaches. Although the transformation made the marginal distribution more similar to a Poisson distribution, it generally did not outperform standard alternatives for inference. In particular, quasi-Poisson regression more consistently maintained appropriate rejection rates with overdispersion whereas poisrank tended to be conservative and often reduced power. These findings suggest that the rank-Poisson transformation is better understood as an exploratory robustness device than as a preferred replacement for established count-data methods. Full article

Uncertainty quantification (UQ) is essential for the robust and competitive design of climate-friendly transportation systems, such as aircraft and space launch systems. However, supporting software applications for UQ are fragmented across numerous open-source libraries, often require in-depth knowledge of the mathematics underlying UQ, and commercial solutions often involve licensing costs. This can make it difficult for design experts to take uncertainties into account. To address this issue, we propose a modular, web-based framework that will guide practitioners through the most common UQ processes, such as statistical sampling, propagation through design workflows, and statistical analysis of the results. Adopting a modern client-server architecture, a backend service, called uqFramework, wraps relevant software libraries for each of the aforementioned steps. The current version focuses on probabilistic approaches, enabling the generation of Design-of-Experiment (DOE) inputs via Quasi-Monte Carlo, Latin Hypercube, and Low Discrepancy Sequence sampling methods. Furthermore, it enables the parallel execution of design and analysis workflows via DLR’s Remote Component Environment (RCE) or Python scripts. Finally, uqFramework performs global sensitivity analyses using Sobol, FAST, or Morris techniques. An interactive front-end application called uqStudio connects to uqFramework through a Representational State Transfer (REST) interface. It guides users through the UQ process via an intuitive, step-by-step interface. Interactive visualizations enable detailed exploration of each step. The framework’s capabilities are illustrated through two examples, the Ishigami function and a multidisciplinary UAV design study, verifying its precision, adaptability, and user-friendliness. We demonstrate that uqStudio enables researchers to conduct integrated UQ studies covering uncertainty specification, propagation, and sensitivity analysis without the difficulty of installing and properly using fragmented libraries. Future work includes extending visualization capabilities and integrating surrogate-modeling capabilities to enable faster workflow execution. Full article

Distributed beamforming in UAV swarms requires fast and accurate carrier-phase alignment under sparse connectivity and propagation-induced phase bias. This paper proposes a physics-aware decentralized synchronization framework for quasi-static UAV swarm beamforming by integrating momentum-accelerated Metropolis–Hastings consensus with position-aided phase pre-compensation. To preserve phase evolution on the circular manifold, a sinusoidal coupling law is adopted, while the momentum term improves convergence in sparse random geometric graphs. A propagation model is further established to characterize how geometric separation and ranging uncertainty translate into residual phase error and coherent power loss. Under small-signal conditions, local stability is analyzed, and Monte Carlo simulations are conducted to evaluate convergence, synchronization accuracy, robustness, and beam-focusing performance. Results show that, at 2.4 GHz with low-centimeter ranging uncertainty, the proposed method achieves sub-wavelength synchronization accuracy while providing an effective balance among convergence speed, accuracy, and complexity. Compared with standard Metropolis–Hastings, fixed-weight, and other accelerated consensus methods, the proposed scheme converges faster over most sparse topologies. Although its steady-state accuracy is slightly lower than that of filter-based predictive methods such as KF-DFPC in some cases, those schemes incur higher implementation and computational overhead. Therefore, from the perspectives of decentralized realization and practical deployment, the proposed method is more suitable for lightweight phase synchronization in distributed UAV swarms. Full article

To address the issues of safety risk analysis and conflict assessment for integrated flight of manned aircraft and fixed-wing unmanned aerial vehicles (UAVs) in low-altitude mixed-operation airspace, this study enhances the foundational Event model. By incorporating UAV characteristics such as geometric features and aerodynamic mechanisms, alongside design dimensions and onboard performance metrics, an improved collision risk model is developed—the Enhanced Event-Based Framework for Multidimensional Geometry and Quasi-Monte Carlo Analysis of Flight Performance (EMGF-M). This enhancement rectifies the limitations of the basic model regarding parameter coverage and scenario adaptability, thereby improving the reliability and validity of the computational results. Experimental results demonstrate that, in accordance with the target safety level for airspace conflicts set by the International Civil Aviation Organization (ICAO), the application of the improved Event collision model yields quantifiable assessments of safety risks and safe separation distances for integrated operations in low-altitude mixed-use airspace. Utilizing these computational results for integrated flight procedure design at a general airport in Southwest China, the study shows that the air traffic flow in the low-altitude mixed-operation airspace increased from 9.2 to 20.9 operations per hour. The practical significance of this method lies in its guidance for accurately assessing safety risks in mixed airspace operations and for determining quantifiable separation minima for integrated flight trajectory planning. Full article

We study a parsimonious constrained two-component Gaussian mixture with symmetric locations $\pm \lambda$ and unequal weights controlled by $\alpha \in [-1,1]$; we refer to this family as the asymmetric bimodal normal. The constraint eliminates label switching and yields an identifiable parametrization for $\lambda >0$, while noting the boundary degeneracy at $\lambda =0$ where $\alpha$ is not identifiable. We derive closed-form analytical expressions for the density and distribution functions, an equivalent constructive representation (useful for simulation and interpretation), explicit moment formulas, and conditions distinguishing unimodality from bimodality. For inference, we develop maximum likelihood estimation with observed information standard errors and provide numerically stable fits via a block-coordinate quasi-Newton routine using method of moments initial values. A Monte Carlo simulation study across representative parameter settings evaluates bias and root mean squared error, and examines the behavior of Hessian-based standard error estimates, highlighting regimes where the observed information becomes ill-conditioned under weak separation. Empirical analyses, chemical calibration deviations from the National Institute of Standards and Technology and a regression example with asymmetric errors, show competitive or superior fit and interpretability relative to skewed normal alternatives, asymmetric Laplace models, and unconstrained Gaussian mixtures, with consistent advantages under model comparison using the Akaike information criterion and the Bayesian information criterion. Full article

This computational study investigates the optical properties of a sixth-order Fibonacci quasi-periodic photonic crystal cavity designed for the infiltration of near-infrared colloidal quantum dots (QDs, e.g., InAs/ZnSe or PbS) and fully compatible with plasma-enhanced chemical vapor deposition (PECVD) using porous silicon layers. Using the transfer matrix method (TMM), we simulate transmission (T), reflection, absorption, electric field distributions and Purcell factors (F) for both TE and TM polarizations, incorporating the wavelength-dependent absorption of porous silicon. A multi-objective figure-of-merit is defined to simultaneously maximize transmission ($T>95\%$ at 800 nm) and the one-dimensional Purcell factor. The optimized structure ($P_H=0416$) yields a quality factor $Q\approx 4300$, a 1D Purcell factor $F_{1D}\approx 3.6$ and a realistic 3D Purcell enhancement estimated between 4 and 8 (under lateral confinement assumptions). This conservative estimate, derived via the effective index method to account for 3D effects, aligns with the detailed discussion within the article and is lower than the ideal upper bound of the 1D model. The integrated emission enhancement is approximately 3.0-fold. Monte Carlo simulations demonstrate remarkable robustness to fabrication tolerances ($\pm 10$ nm thickness variations result in a <5% reduction in transmission), highlighting the structure’s scalability for PECVD-based processing. Comparison with periodic Bragg structures reveals superior angular stability and disorder tolerance in the Fibonacci design, positioning it as a promising platform for robust QD-based light sources and integrated refractive index sensors. Full article

The high proportion of renewable energy connected to the grid poses new challenges to the safe and economic operation of active distribution networks (ADNs). However, most of the existing research focuses on single-objective optimization or ignores the influence of the uncertainty of renewable energy output and the demand response mechanism, and lacks verification of the scalability of models in large-scale systems. For an active distribution network system with distributed wind power and photovoltaic access, this paper establishes a multi-objective day-ahead optimal dispatching model that takes into account economy, reliability, and safety. The research adopts a scenario-based method and chance-constrained programming (CCP) to handle the uncertainty of wind and solar output. It combines the quasi-Monte Carlo (QMC) method and Kantorovich distance to achieve scenario generation and reduction, and introduces price-based and incentivized demand response mechanisms to form four combined optimization models. The multi-objective optimization solution was carried out based on the multi-objective evolutionary algorithm based on decomposition (MOEA/D), verifying the effectiveness of the proposed method in terms of operation cost, load shedding expectation, and node voltage limit control. The case study is based on the improved IEEE 30-node and 200-node 49-generator systems. The results indicate that this method can effectively balance multiple objectives such as operation costs, load shedding expectations, and node voltage limit; can significantly enhance the renewable energy consumption capacity of active distribution networks; and can provide an effective solution for the optimal dispatching of active distribution networks with a high proportion of renewable energy. Full article

Accurate conjugate heat transfer (CHT) analysis is critical to the thermal management of hypersonic vehicles operating in rarefied environments, where non-equilibrium gas dynamics dominate. While numerous sophisticated CHT solvers exist for continuum flows, they are physically invalidated by rarefaction effects. This paper presents a novel partitioned coupling framework that bridges this methodological gap by utilizing the preCICE library to non-intrusively integrate the Direct Simulation Monte Carlo (DSMC) method, implemented in SPARTA, with the finite element method (FEM) via FEniCS for high-fidelity simulations of rarefied hypersonic CHT. The robustness and accuracy of this approach are validated through three test cases: a quasi-1D flat plate benchmark confirms the fundamental coupling mechanism against a reference finite difference solution; a 2D flat-nosed cylinder demonstrates the capability of the framework to handle highly non-uniform heat flux distributions and resolve the ensuing transient thermal response within the solid; finally, a standard cylinder case confirms the compatibility with curved geometries and its stability and accuracy in long-duration simulations. This work establishes a validated and accessible pathway for high-fidelity aerothermal analysis in rarefied gas dynamics, effectively decoupling the complexities of multi-physics implementation from the focus on fundamental physics. Full article

We forecast short time series iteratively using a model based on stochastic differential equations. The recorded process is assumed to be consistent with an $\alpha$-stable Lévy motion. The generalized moments method provides the values of the scaling exponent and the parameter $\alpha$, which determine the form of the stochastic term at each iteration. Seven weekly recorded economic time series—the DAX, CAC, FTSE100, MIB, AEX, IBEX, and STOXX600—were examined for the period from 2020 to 2025. The parameter $\alpha$ is always 2 for the four of them, FTSE100, AEX, IBEX, and STOXX600, indicating quasi-Gaussian processes. For FTSE100, IBEX, and STOXX600, the processes are anti-persistent (H < 0.5).The rest of the examined markets show characteristics of uncorrelated processes whose values are drawn from either a log-normal or a log-Lévy distribution. Further, all processes are multifractal, as the non-zero value of the mean intermittency indicates. The model’s forecasts, with the time horizon always one-step-ahead, are compared to the forecasts of a properly chosen ARIMA model combined with Monte Carlo simulations. The low values of the absolute percentage error indicate that both models function well. The model’s outcomes are further compared to ARIMA forecasts by using the Diebold–Mariano test, which yields a better forecast ability for the proposed model since it has less average loss. The ability and accuracy of the model to forecast even small time series is further supported by the low value of the absolute percentage error; the value of 4 serves as an upper limit for the majority of the forecasts. Full article

In this paper, we develop a fast numerical algorithm, termed MDI-LR, for the efficient implementation of quasi-Monte Carlo lattice rules in computing d-dimensional integrals of a given function. The algorithm is based on converting the underlying lattice rule into a tensor-product form through an affine transformation, and further improving computational efficiency by incorporating a multilevel dimension iteration (MDI) strategy. This approach computes the function evaluations at the integration points collectively and iterates along each transformed coordinate direction, allowing substantial reuse of computations. As a result, the algorithm avoids the need to explicitly store integration points or compute function values at those points independently. Extensive numerical experiments are conducted to evaluate the performance of MDI-LR and compare it with the straightforward implementation of quasi-Monte Carlo lattice rules. The results demonstrate that MDI-LR achieves a computational complexity of order $O\left(N^2{d}^3\right)$ or better, where N denotes the number of points in each transformed coordinate direction. Thus, MDI-LR effectively mitigates the curse of dimensionality and revitalizes the use of QMC lattice rules for high dimensional integration. Full article

Accurate and efficient estimation of Sobol’ sensitivity indices is a cornerstone of variance-based global sensitivity analysis, providing critical insights into how uncertainties in input parameters affect model outputs. This is particularly important for large-scale environmental, engineering, and financial models, where understanding parameter influence is essential for improving model reliability, guiding calibration, and supporting informed decision-making. However, computing Sobol’ indices requires evaluating high-dimensional integrals, presenting significant numerical and computational challenges. In this study, we present a comparative analysis of two of the best available Quasi-Monte Carlo (QMC) techniques: polynomial lattice rules (PLRs) and modified Sobol’ sequences. The performance of both approaches is systematically assessed in terms of performance and accuracy. Extensive numerical experiments demonstrate that the proposed PLR-based framework achieves superior precision for several sensitivity measures, while modified Sobol’ sequences remain competitive for lower-dimensional indices. Our results show that IPLR-α3 outperforms traditional QMC methods in estimating both dominant and weak sensitivity indices, offering a robust framework for high-dimensional models. These findings provide practical guidelines for selecting optimal QMC strategies, contributing to more reliable sensitivity analysis and enhancing the predictive power of complex computational models. Full article

As high-energy-consumption underground public space, subway stations are responsible for a particularly significant proportion of air-conditioning energy use, especially during the cooling season, making the investigation of cooling-load characteristics highly important. However, the determination of independent influencing factors in different situations has not yet reached a consensus, and the role of interaction effects is lacking, which hinders the development of energy-saving strategies. For this purpose, this study proposes a sensitivity analysis framework based on 10 typical influencing factors from thermal parameters, meteorological parameters, internal heat disturbances, and indoor environmental setpoints. An input set was generated by integrating equal-step parameter discretization and Saltelli quasi-MonteCarlo sampling. A database containing 11,264 samples was constructed through an EnergyPlus–Python co-simulation method. Based on the Sobol global sensitivity analysis, the key influencing factors of subway station cooling load were identified and quantified, and the impact of these 10 factors was systematically analyzed. Results show that occupant density (S_i^T = 0.5605) and fresh air volume (S_i^T = 0.4546) are the dominant factors, contributing more than 50% of the load variance. In contrast, the characteristics of an underground structure significantly weaken the influence of the building-envelope heat transfer coefficient (S_i^T = 0.1482) and soil temperature (S_i^T = 0.0884). Furthermore, five groups of strong interaction effects were identified in this study, including occupant density–fresh air volume (S_ij = 0.1094), revealing a nonlinear load response mechanism driven by multi-parameter coupling. This research provides a theoretical foundation and quantitative tool for the refined design and optimized dynamic coupled operation of underground transportation hubs. Full article

This study presents a novel framework for uncertainty propagation in power-law, Bingham, and Casson fluids through rectangular ducts under stochastic viscosity (Case I) and pressure gradient conditions (Case II). Using the computationally efficient Stochastic Finite Difference Method with Homogeneous Chaos (SFDHC), validated via comparison with quasi-Monte Carlo simulations, we demonstrate significantly lower computational costs across varying Coefficients of Variation (COVs). For viscosity uncertainty (Case I), results show a 0.54–2.8% increase in mean maximum velocity with standard deviations reaching 75.3–82.5% of the COV, where the power-law model exhibits the greatest sensitivity (velocity variations spanning 71.2–177.3% of the mean at COV = 20%). Pressure gradient uncertainty (Case II) preserves mean velocities but produces narrower and symmetric distributions. We systematically evaluate the effects of aspect ratio, yield stress, and flow behavior index on the stochastic velocity response of each fluid. Moreover, our analysis pioneers a performance hierarchy: Herschel–Bulkley fluids show the highest mean and standard deviation of maximum velocity, followed by power-law, Robertson–Stiff, Bingham, and Casson models. A key finding is the extreme fluctuation of the Robertson–Stiff model, which exhibits the most drastic deviations, reaching up to 177% of the average velocity. The significance of fluid-specific stochastic analysis in duct system design is underscored by these results. This is especially critical for non-Newtonian flows, where system performance and reliability are greatly impacted by uncertainties in viscosity and pressure gradient, which reflect actual operational variations. Full article

This paper proposes a novel transport quasi-Monte Carlo framework that combines randomized quasi-Monte Carlo sampling with a neural autoregressive flow architecture for efficient sampling and integration over complex, high-dimensional distributions. The method constructs a sequence of invertible transport maps to approximate the target density by decomposing it into a series of lower-dimensional marginals. Each sub-model leverages normalizing flows parameterized via monotonic beta-averaging transformations and is optimized using forward Kullback–Leibler (KL) divergence. To enhance computational efficiency, a hidden-variable mechanism that transfers optimized parameters between sub-models is adopted. Numerical experiments on a banana-shaped distribution demonstrate that this new approach outperforms standard Monte Carlo-based normalizing flows in both sampling accuracy and integral estimation. Further, the model is applied to A-share stock return data and shows reliable predictive performance in semiannual return forecasts, while accurately capturing covariance structures across assets. The results highlight the potential of transport quasi-Monte Carlo (TQMC) in financial modeling and other high-dimensional inference tasks. Full article

Bi-phasic (with a local minimum) response of fluorescence to scattering when probed by a single fiber (SF) was first observed in 2003. Subsequent experiments and Monte Carlo studies have shown the bi-phasic turning of SF fluorescence to occur at a dimensionless reduced scattering of ~1 and vary with absorption. The bi-phase of SF fluorescence received semi-empirical explanations; however, better understandings of the bi-phase and its dependence on absorption are necessary. This work demonstrates a quasi-analytical projection of a bi-phasic pattern comparable to that of SF fluorescence via photon-transport analyses of fluorescence in a center-illuminated-area-detection (CIAD) geometry. This model-approach is principled upon scaling of the diffuse fluorescence between CIAD and a SF of the same size of collection, which expands the scaling of diffuse reflectance between CIAD and a SF discovered for steady-state and time-domain cases. Analytical fluorescence for CIAD is then developed via radial-integration of radially resolved fluorescence. The radiance of excitation is decomposed to surface, collimated, and diffusive portions to account for the surface, near the point-of-entry, and diffuse portion of fluorescence associated with a centered illumination. Radiative or diffuse transport methods are then used to quasi-analytically deduce fluorescence excited by the three portions of radiance. The resulting model of fluorescence for CIAD, while limiting to iso-transport properties at the excitation and emission wavelengths, is compared against the semi-empirical model for SF, revealing bi-phasic turning [0.5~2.6] at various geometric sizes [0.2, 0.4, 0.6, 0.8, 1.0 mm] and a change of three orders of magnitude in the absorption of the background medium. This model projects a strong reduction in fluorescence versus strong absorption at high scattering, which differs from the semi-empirical SF model’s projection of a saturating pattern unresponsive to further increases in the absorption. This framework of modeling fluorescence may be useful to project frequency-domain and lifetime pattens of fluorescence in an SF and CIAD. Full article