Search Results (139)

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

Magnetoplasmadynamic thrusters (MPDTs) are becoming increasingly viable as electric propulsion (EP) technology for space missions, yet their complex plasma behaviour, intricate thrust-generation process, and nonlinear multi-physics thrust–field interactions prove difficult for conventional modelling approaches, including empirical techniques. Traditional empirical modelling shortcomings include failure to predict accurately across wide operational regimes. This paper introduces a physically interpretable, artificial intelligence (AI)-powered thrust model for Applied-Field Magnetoplasmadynamic Thrusters (AF-MPDTs), developed using symbolic regression (SR) to address the gap between data-driven prediction and physics-based understanding. The proposed method, an alternative to traditional black box AI methods, incorporates physics-aware composite-term operators, ensuring that the resulting analytical expressions are bounded by known physical behaviours while retaining the flexibility to discover previously overlooked nonlinear couplings. A comprehensive dataset of AF-MPDTs undergoes rigorous preprocessing to ensure dimensional consistency and noise robustness. The SR model then evolves candidate equations, balancing predictive accuracy with interpretability through Tree-Structured Parzen Estimator (TPE) optimisation. The results, closed-form surrogate correlations with 95.98% of accuracy as goodness of fit, root mean square error of 0.0199, mean absolute error of 0.0143, and mean absolute percentage error reduction of 28.91% against the benchmark model in the literature. A post-discovery protocol for numerical robustness and physical consistency is implemented, with Shapley Additive Explanations (SHAP) providing insight into the influence of each composite-term in the developed correlation, followed by a numerical robustness and physical consistency validation using a Monte Carlo (MC) envelope. A StabilityScore is calculated for all developed correlations, enabling explicit accuracy–complexity–stability comparisons. In doing so, we demonstrated that SR can systematically recover known physical relationships—such as the scaling of thrust with discharge current and applied magnetic field—while proposing interpretable higher-order corrections that improve fit quality. The resulting SR-based thrust models not only achieve competitive accuracy relative to state-of-the-art numerical and empirical methods but also offer more explainable and interpretable results capable of revealing compact formulations that capture essential acceleration mechanisms with transparency. Overall, this paper, using SR, advances explainable AI (XAI) methodologies capable of generating trustworthy, analytically transparent models for next-generation electric propulsion systems. Full article

We propose the Bivariate Poisson–X–Exponential Distribution (BPXED), a flexible bivariate count model obtained by compounding Poisson variables with a shared X–Exponential latent mixing distribution. The model extends the Poisson–X–Exponential (PXED) distribution and includes several bivariate Poisson-type models as special or limiting cases. Closed-form expressions are derived for the joint probability mass function, probability generating function, moments, and covariance structure, showing that dependence arises from shared latent heterogeneity and is restricted to positive correlation. Parameter estimation is developed using maximum likelihood, regression-based, and Bayesian approaches, and a Monte Carlo simulation study demonstrates a good finite-sample performance. Applications to soccer scores, reliability failures, and correlated photon counts illustrate improved goodness-of-fit over classical and recent competing models. Overall, BPXED provides an analytically tractable and interpretable framework for modeling positively dependent and overdispersed bivariate count data. Full article

Probabilistic streamflow models play a pivotal role in quantifying hydrological uncertainty and form the backbone of modern risk management strategies for flood and drought forecasting, water allocation planning, and the design of resilient infrastructure. Unlike deterministic approaches that yield single-point estimates, these models provide a spectrum of possible outcomes, enabling a more realistic assessment of extreme events and supporting informed, sustainable water resource decisions. By explicitly accounting for natural variability and uncertainty, probabilistic models promote transparent, robust, and equitable risk evaluations, helping decision-makers balance economic costs, societal benefits, and environmental protection for long-term sustainability. In this study, we introduce the bounded half-logistic distribution (BHLD), a novel heavy-tailed probability model constructed using the T–Y method for distribution generation, where T denotes a transformer distribution and Y represents a baseline generator. Although the BHLD is conceptually related to the Pareto and log-logistic families, it offers several distinctive advantages for streamflow modeling, including a flexible hazard rate that can be unimodal or monotonically decreasing, a finite lower bound, and closed-form expressions for key risk measures such as Value at Risk (VaR) and Tail Value at Risk (TVaR). The proposed distribution is defined on a lower-bounded domain, allowing it to realistically capture physical constraints inherent in flood processes, while a log-logistic-based tail structure provides the flexibility needed to model extreme hydrological events. Moreover, the BHLD is analytically characterized through a governing differential equation and further examined via its characteristic function and the maximum entropy principle, ensuring stable and efficient parameter estimation. It integrates a half-logistic generator with a log-logistic baseline, yielding a power-law tail decay governed by the parameter $\beta$, which is particularly effective for representing extreme flows. Fundamental properties, including the hazard rate function, moments, and entropy measures, are derived in closed form, and model parameters are estimated using the maximum likelihood method. Applied to four real streamflow data sets, the BHLD demonstrates superior performance over nine competing distributions in goodness-of-fit analyses, with notable improvements in tail representation. The model facilitates accurate computation of hydrological risk metrics such as VaR, TVaR, and tail variance, uncovering pronounced temporal variations in flood risk and establishing the BHLD as a powerful and reliable tool for streamflow modeling under changing environmental conditions. Full article

As heritage museums shift toward more experience-oriented development, fragmented layouts and discontinuous visitor flows can reduce both spatial efficiency and the coherence of on-site experience. This study proposes an immersive experience-centred evaluation framework for exhibition layout in heritage museums, intended to translate experience goals into practical and diagnosable criteria for spatial optimization. An indicator system was refined through two rounds of Delphi consultation with an interdisciplinary expert panel, resulting in a hierarchical framework comprising five dimensions and multiple indicators. To support intervention prioritization in design and operations, weights were derived using the Group Analytic Hierarchy Process (GAHP), with Aggregation of Individual Judgments (AIJs) and consistency checks applied to control group judgement quality. A CV–entropy procedure was further used to support prioritization at the third-indicator level. Importance–Performance Analysis (IPA) was then employed to convert “importance–fit” assessments into an actionable sequence of optimization priorities. The results indicate that narrative and scene design carries the greatest weight (0.2877), followed by circulation and spatial organization (0.2281), sensory experience and atmosphere (0.1981), authenticity and sense of place (0.1644), and interactivity and participation (0.1217), suggesting that a “narrative–circulation–atmosphere” chain forms the core support for immersive layout design. A feasibility application using the Yinxu Museum demonstrates the framework’s value for benchmarking and diagnosis, helping decision-makers enhance visitor experience while respecting conservation constraints and more precisely target spatial investment priorities. Full article

The Mixed-Conduction Model for oxide films is used to quantitatively interpret in situ electrochemical and ex situ surface analytical results on the corrosion of AISI 316L (an internal reactor material) and Alloy 690 (a steam generator tube material) in small modular reactor primary coolant with the addition of soluble Zn. The model parameters of alloy oxidation and corrosion release are estimated with the time of exposure up to 168 h and anodic polarization potential (up to −0.25 V vs. standard hydrogen electrode) using fitting of the transfer function to experimental impedance spectra. Model parameters of individual alloy constituents are estimated by fitting of the model equations to the atomic fraction profiles of respective elements in the formed oxide obtained by Glow-Discharge Optical Emission Spectroscopy (GDOES). Conclusions on the effect of Zn addition on film growth and cation release processes in boron-free SMR coolant are drawn and future research directions are outlined. Full article

Achieving reliable and real-time inverse kinematics (IK) for 6-degree-of-freedom (6-DoF) spherical-wrist manipulators remains a significant challenge. Analytical formulations often struggle with complex geometries and modeling errors, and standard numerical solvers (e.g., Levenberg–Marquardt) can stall near singularities or converge slowly. Purely data-driven approaches may require large networks and struggle with extrapolation. In this paper, we propose a low-latency, polynomial-based IK solution for spherical-wrist robots. The method leverages spherical coordinates and low-degree polynomial fits for the first three (positional) joints, coupled with a closed-form analytical solver for the final three (wrist) joints. An iterative partial-derivative refinement adjusts the polynomial-based angle estimates using spherical-coordinate errors, ensuring near-zero final error without requiring a full Jacobian matrix. The method systematically enumerates up to eight valid IK solutions per target pose. Our experiments against Levenberg–Marquardt, damped least-squares, and an fmincon baseline show an approximate 8.1× speedup over fmincon while retaining higher accuracy and multi-branch coverage. Future extensions include enhancing robustness through uncertainty propagation, adapting the approach to non-spherical wrists, and developing criteria-based automatic solution-branch selection. Full article

We propose an uncertainty propagation framework based on phase space that treats the error distribution as the marginal of a Wigner quasi-probability distribution and defines an effective uncertainty constant quantifying the minimal resolvable phase-space cell. Recognizing that observational updates systematically reduce uncertainty, we adopt a generalized Koopman–von Neumann equation grounded in operator dynamical modeling to propagate the density operator corresponding to the error distribution. The scaling parameter $\kappa$ quantifies the reduction in uncertainty following each filter update. Although the potential is presently retained only to second order—so that both propagation and update preserve Gaussian form and permit direct Kalman recursion—the framework itself lays the analytical foundation for a future treatment of non-Gaussian features. Validated on 1215 orbits (semi-major axis: 9600 km to 42,164 km), the method shows that within a 3 min fit/10 min forecast window, observational noise contributes 350 m while unmodeled dynamics adds only 0.6 m. Kruskal–Wallis rank-sum tests and the accompanying scatter-plot trend rank the semi-major axis as the dominant sensitive parameter. The proposed model outperforms Chebyshev and high-fidelity propagators in real time, offering a physically interpretable route for short-arc orbit prediction. Full article

The built environment, serving as the core spatial vehicle for human production and daily activities, constitutes a vital foundation for achieving sustainable urban development and high-quality renewal. However, amidst rapid urbanisation, certain areas continue to grapple with issues such as ageing infrastructure, inefficient land use, and imbalanced spatial structures, hindering the establishment of sustainable urban forms. Consequently, identifying the evolutionary characteristics and influencing mechanisms of the built environment from the perspective of spatial heterogeneity holds critical significance for advancing refined governance and sustainable planning. Taking Kwun Tong District in Hong Kong as a case study, this research constructs an Adaptive-Entropy Multi-Scale Geographically Weighted Regression (MGWR) analytical framework. This systematically reveals the spatial distribution patterns of built environment elements and their multi-scale spatial heterogeneity characteristics. The findings indicate the following: (1) The built environment exhibits significant spatial differentiation and clustering structures across different scales, reflecting complex spatial processes driven by multiple interacting factors (2) Compared with the OLS model at a 1000 m scale and the GWR model at a 500 m scale, the Adaptive-Entropy MGWR model at a 100 m scale demonstrated superior fitting accuracy and explanatory power. It more effectively captured local structural variations and scale effects, thereby offering greater guidance value for sustainable planning. Building upon these findings, this study further proposes pathway recommendations for urban renewal and built environment optimisation in Kwun Tong District, offering an analytical approach and technical framework that may serve as a reference for sustainable development in high-density cities. Full article

We present an analytical model for the lethargic neutron spectrum (${\varphi }_u\left(E\right)$, i.e., per unit of $u=ln\left(E\right)$), which is specifically suited to nuclear fusion environments. The spectrum is represented as the sum of three components: (i) a stretched Maxwellian thermal component, (ii) a windowed power-law epithermal plateau and (iii) a log-normal high-energy peak. While being simple and concise, this model allows for accurate fitting to experimental data or transport calculation results, as well as easy extrapolation for different operating conditions. We present the physical basis of the model and provide guidelines for adjusting it. We also demonstrate how it can accurately reproduce neutron spectra from experiments or Monte Carlo simulations that are representative of various nuclear fusion environments. Finally, we use this model to estimate the soft-error rate (SER) for circuits operating in fusion environments, considering, in addition, analytical forms for the single-event neutron cross-section of the circuit in the thermal and high-energy domains to derive analytical or semi-analytical expressions of the SER. Full article

Grokhovskyite, CuCrS₂, was observed in small sulfide inclusions (up to 50–80 µm) in Ni-rich iron (kamacite) of the Uakit iron meteorite (IIAB) in the Republic of Buryatia, Russia. The grain sizes of this mineral are usually less than 5 μm, and the biggest detected crystals are 10 × 5 μm in size. It is commonly associated with daubréelite, troilite, schreibersite, and, sometimes, with carlsbergite and uakitite. Within inclusions, the mineral forms elongated splintered crystals, or, rarely, needle-shaped grains in daubréelite. The grokhovskyite-containing associations in the Uakit meteorite seem to form due to high-temperature (>1000 °C) separation of Fe-Cr sulfide liquid, which is locally enriched in Cu, from Fe-Ni metal melt. Physical and optical properties of grokhovskyite are quite similar to those of synthetic CuCrS₂: yellow–brown and non-transparent phase with metallic luster; Mohs hardness ≈ 4; gray to light gray color with yellow tint in reflected light; weak to medium bireflectance, anisotropy, and pleochroism; density (calc.) = 4.559 g/cm³. Grokhovskyite is structurally related to the Cr-containing disulfide minerals with general formula Me⁺CrS₂ (where Me⁺ = Na, Cu, Ag), including caswellsilverite, NaCrS₂; schöllhornite, Na_0.3CrS₂·H₂O; and cronusite, Ca_0.2CrS₂·2H₂O. Structural data were obtained for one grokhovskyite crystal using the EBSD technique. Fitting of the EBSD patterns for a synthetic α-CuCrS₂ model (trigonal R3m; a = 3.4794(8) Å; c = 18.702(4) Å; V = 196.08(10) ų; Z = 3) resulted in the parameter MAD = 0.57–1.16° (good fit). Analytical data for grokhovskyite (n = 36, in wt.%) are as follows: Cu—32.97; Cr—27.65; Fe—3.69; Ni—0.16; S—35.71; Na, Zn, V, Mn, and Co—below detection limit (<0.005 wt.%). The empirical formula is (Cu_0.930Cr_0.952Fe_0.118Ni_0.005)_2.005S_1.995; however, different concentrations of Fe are indicated in two individual grains of grokhovskyite (0.09–0.17 apfu). Such variations may be explained by Fe incorporation in the grokhovskyite structure according to the scheme ^IVCu⁺ + ^VICr³⁺ → ^IVFe²⁺ + ^VIFe²⁺. The three main bands (near 110, 250, and 310 cm⁻¹), which are common of synthetic CuCrS₂, were observed in the Raman spectra of grokhovskyite. Full article

Over recent decades, planners in the U.S. have increasingly adopted mixed-use projects to reduce automobile dependency and strengthen local community identity, although results remain inconsistent across cities. Urban health and fitness outcomes are shaped by complex interactions between the built environment, socioeconomic factors, and demographic characteristics. This study introduces a Health and Fitness Index (HFI) for 28,758 U.S. ZIP codes, derived from normalized measures of walkability, healthcare facility density, and carbon emissions, to assess spatial disparities in health-supportive environments. Using four modeling approaches—lasso regression, multiple linear regression, decision trees, and k-nearest neighbor classifiers—we evaluated the predictive importance of 15 urban and socioeconomic variables. Multiple linear regression produced the strongest generalization performance (R² = 0.60, RMSE = 0.04). Key positive predictors included occupied housing units, business density, land-use mix, household income, and racial diversity, while income inequality and population density were negatively associated with health outcomes. This study evaluates five statistical formulations (Metropolis Hybrid Models) that incorporate different combinations of walkability, land-use mix, environmental variables, and socioeconomic indicators to test whether relationships between urban form and socioeconomic conditions remain consistent under different variable combinations. In cross-sectional multivariate regression, although mixed-use development in high-density areas is strongly associated with healthcare facilities, these areas tend to serve younger and more racially diverse populations. Decision tree feature importance rankings and clustering profiles highlight structural inequalities across regions, suggesting that enhancing business diversity, land-use integration, and income equity could significantly improve health-supportive urban design. This research provides a data-driven framework for urban planners to identify underserved neighborhoods and develop targeted interventions that promote walkability, accessibility to health infrastructure, and sustainability. It contributes to the growing literature on urban health analytics, integrating machine learning, spatial clustering, and multidimensional urban indicators to advance equitable and resilient city planning. Full article

We have developed mold matrices that can be employed to distinguish between enantiomers (D- and L-glucose) and structural isomers (n- and iso-stearic acid) in matrix-assisted laser desorption/ionization mass spectrometry. Utilizing a temperature-responsive polymer, a molecular structure recognition film was created around metal or semiconductor particles, such as silver (Ag) or cadmium telluride (CdTe), forming the core. Molecules that fit the template structure were selectively ionized. To elucidate the properties of the mold matrix, the relationship between molecular recognition rate and peak intensity of analyte ion was investigated by varying polymer film thickness around the core. The relationship between molecular recognition rate and hydrophobicity of the template molecule was also examined. It was found that increasing the amount of polymer forming the molecular recognition film improved the molecular recognition rate. However, the peak intensity of the analyte ion decreased. It was also found that using highly hydrophobic molecules as template molecules resulted in high molecular recognition rates. In addition, a water-splitting photocatalyst was synthesized and utilized to fabricate the mold matrix. It was applicable to both positive and negative ion generation while recognizing the molecular structure of the analyte. Full article

This study investigates the effects of socioeconomic characteristics, density, built environment, and urban spatial structure on vehicle miles traveled (VMT) across 461 urbanized areas in the United States. Using multiple regression models, we compare the explanatory power of conventional variables with those representing the spatial distribution of major urban elements, such as population, employment, land use, and travel demand to city centers. The results show that population-weighted distance to the city center and the contiguity of high-intensity land use significantly influence vehicle travel, with greater distances from city centers and more fragmented land use leading to higher VMT. Models incorporating urban spatial structure variables exhibit improved explanatory power and better fit than those including only socioeconomic, density, and built environment variables. These findings demonstrate that urban spatial structure captures key aspects of vehicle travel behavior that are overlooked by traditional measures. Policy implications include the promotion of compact, mixed-use development, infill and brownfield redevelopment, and urban growth boundaries to reduce vehicle dependence. The study highlights the importance of spatial planning in managing urban travel demand and offers a refined analytical framework for examining the interplay between urban form and mobility. Full article

In this work, a quantitative analysis of Li in natural brines was carried out by laser-induced breakdown spectroscopy (LIBS) assisted by the τ–algorithm for detailed analysis of the experimental line shapes (τLIBS). Brine samples were collected from different salars located in the Puna plateau (Northwest Argentina) and analyzed by LIBS in the form of solid pressed pellets. The emission intensities of Li I, H_α, and Mg I–II lines were measured and spatially integrated along the line of sight with temporal resolution by using a high-spectral-resolution spectrometer equipped with an intensified charge-coupled device (iCCD) detector. The plasma was characterized through the determination of the electron density and the temperature. The τ–algorithm calculated the optical thicknesses of the Li I lines to generate synthetic intensity profiles that were subsequently fitted to the experimental spectra. By applying the developed τLIBS approach, valuable spectroscopic insight was recovered about the physical processes occurring in the plasma, such as self-absorption. The analytical process involved an univariate external calibration process using the resonant Li I line at 6707.7 Å measured from a series of Li standard samples. Self-absorption effects were evaluated and subsequently compensated. The final LIBS results, with an enhanced accuracy of 15%, were validated by crosschecking them against those obtained with the standard AAS method. Full article