Leak detection in pipelines transporting gas-liquid multiphase flow remains a challenging task due to complex and inherently unsteady flow behavior, particularly under intermittent regimes such as plug flow. Conventional leak detection techniques, which are well established for single-phase flow, often suffer from reduced sensitivity and false alarms when applied to multiphase systems. Motivated by these limitations, the present study investigates leakage characteristics in a horizontal pipeline conveying gas-liquid plug flow under underwater conditions. A three-dimensional transient numerical model based on the Volume of Fluid (VOF) approach is developed to simulate various leakage scenarios, including different discharge sizes and gas-liquid superficial velocities. The numerical results are validated against experimental data obtained from a dedicated multiphase flow loop. Time-series pressure signals are analyzed using statistical metrics, probability density functions, and continuous wavelet transform techniques to assess their effectiveness in identifying leakage occurrence. Furthermore, a non-dimensional analysis is employed to develop a nomograph for estimating gas release velocity from underwater leaks. The results demonstrate that leakage significantly alters pressure fluctuation characteristics and gas void fraction distribution, with detectability strongly influenced by flow conditions and discharge size. The proposed nomograph predicts gas release velocity with reasonable agreement relative to experimental measurements, highlighting its potential applicability for subsea leak assessment and process safety analysis in multiphase pipeline systems.

Collagen fibrils provide mechanical integrity to the extracellular matrix in a variety of biological tissues. In biomedical research, quantification of fibril diameters is essential to describe remodeling of the matrix that can occur during development, disease, and healing. However, current statistical methods to analyze differences in the distribution of fibril diameters have significant limitations. This study evaluated a rigorous alternative method, Statistical nonParametric Mapping (SnPM), to compare fibril diameter distributions. Randomly generated simulated datasets and experimental datasets of fibril diameter distributions were analyzed using both conventional tests and SnPM. Results from each method were compared. Conventional statistical tests to compare fibril diameter distributions demonstrated limitations. Comparison of average diameters detected overall shifts in distributions but not more nuanced changes, while analysis of binned relative frequencies showed dependency on the choice of bin width and location. In contrast, comparison of kernel density estimated probability density functions using SnPM both detected differences between groups and located those differences to specific ranges of fibril diameters. Comparative analysis of groups of fibril diameter distributions using SnPM overcomes the limitations of current techniques and provides a reliable and rigorous technique for these data. Other potential applications for SnPM in biomedical research abound, extending to other distributional or multidimensional data.

The eigenvalue probability density function of the Gaussian unitary ensemble permits a q q -extension related to the discrete q q -Hermite weight and corresponding q q -orthogonal polynomials. A combinatorial counting method is used to specify a positive sum formula for the spectral moments of this model. The leading two terms of the scaled 1 / N 2 1/N^2 genus-type expansion of the moments are evaluated explicitly in terms of the incomplete beta function. Knowledge of these functional forms allows for the smoothed leading eigenvalue density and its first correction to be determined analytically.

Nyström-aware approximations for matrix-based Rényi's entropy.

Noncontact ultrasonic materials identification based on improved frequency responses.

In this paper, the surge characteristics of a centrifugal compressor are investigated under various operating conditions through experimental analysis. The stable operational range of the centrifugal compressor at low flow rates is predominantly constrained by the presence of unstable phenomena such as stall and surge. The aerodynamic features spanning from the stall stage (preceding surge occurrence) to the surge stage (following surge occurrence) are comprehensively documented within the experimental framework. The power spectrum density (PSD) of mass flow rate and pressure is utilized to elucidate the fluid dynamics within the centrifugal compressor at deep surge condition (5° valve opening), moderate surge condition (12°), and mild surge condition (15°), respectively. Subsequently, a thorough comparison is conducted between the time-domain and frequency-domain distributions of pressure fluctuations during the transitional zone between the stall and surge stages. The evolution trend of mass flow rate and pressure are compared at deep, moderate, and mild surge conditions, and the transition zone between the stall stage and the surge stage, which could be detected in advance and contribute to prevent surge, is pointed out. The utilization of probability density function (PDF) distribution is implemented to deeply explore a detailed examination of pressure fluctuation disparities between the stall and surge stages, elucidating the impact of surge-induced fluctuations on flow stability within the centrifugal compressor. The characteristics of shaft vibration are deeply explored. The above comparison can provide a profound insight into understanding the physical mechanism of centrifugal compressor at surge conditions.

Objective.We propose a new formulation for ideal observers (IOs) that incorporate stochastic object models (SOMs) for data acquisition optimization.Approach. A data acquisition system is considered as a (possibly nonlinear) discrete-to-discrete mapping from a finite-dimensional object space,x∈Rnd, to a finite-dimensional measurement space,y∈Rm. For binary tasks, the two underlying SOMs,H0andH1, are specified by two probability density functions (PDFs)p0(x),p1(x). This leads to the notion of intrinsic likelihood ratio (LR)ΛI(x)=p1(x)/p0(x)and intrinsic class separability (ICS), the latter quantifies the population separability that is independent of data acquisition. With respect to ICS, the IO employs the 'extrinsic' LRΛ(y)=pr(y|H1)/pr(y|H0)of the data and quantifies the extrinsic class separability (ECS). The difference between ICS and ECS measures the efficiency of data acquisition. We show that the extrinsic LRΛ(y)is the expectation of the intrinsic LRΛI(x), where the expectation is with respect to the posterior PDFpr(x|y,H0)underH0.Main results. We use two examples, one to clarify the new IO and the second to demonstrate its potential for real world applications. Specifically, we apply the new IO to spectral optimization in dual-energy CT projection domain material decomposition (pMD), for which SOMs are used to describe variability of basis material line integrals. The performance rank orders obtained by IO agree with physics predictions.Significance.The main computation in the new IO involves sampling from the posterior PDFpr(x|y,H0), which are similar to (fully) Bayesian reconstruction. Thus our IO computation is amenable to standard techniques already familiar to CT researchers. The example of dual-energy pMD serves as a prototype for other spectral optimization problems, e.g., for photon counting CT or multi-energy CT with multi-layer detectors.

This study introduces the Novel Alpha Power Gumbel-X (NAPG-X) family of distributions, developed through the T-X transformation with a logarithmic generalizer. The NAPG-Exponential (NAPGEX) distribution is studied as a sub-model, with key mathematical properties derived, including the probability density function, cumulative distribution function, moments, moment generating function, Rényi entropy, and order statistics. The hazard rate function exhibits versatile shapes including increasing-decreasing, reversed-J, and L-shaped, making it suitable for diverse reliability applications. Ten classical estimation methods are evaluated through extensive Monte Carlo simulations across varying sample sizes and three parameter combinations. Results demonstrate that maximum likelihood and Anderson-Darling consistently provide superior performance with minimal bias, mean relative errors and root mean square errors. Furthermore, the practical applicability of the NAPGEX distribution is validated using three real-life datasets. Comprehensive comparisons using various performance measures reveal that the NAPGEX significantly outperforms competing models. These findings establish the NAPG-X family as a flexible and powerful tool for modeling asymmetric, positively skewed lifetime datasets across several scientific disciplines.

. The Gram-Charlier expansion provides a flexible and effective framework for analyzing complex data distributions. Recognizing the skewness and heavy-tailed characteristics commonly observed in financial and other real-world datasets, this study constructs a novel asymmetric distribution derived from the logistic distribution, designed to capture both heavy tails and central peaks. We first demonstrate that the probability density function of the logistic distribution can serve as a weight function, providing a solid mathematical foundation for constructing new distributions. The Newton-Raphson algorithm is then employed to obtain maximum likelihood estimates of the distribution parameters, with numerical simulations verifying the feasibility and accuracy of these estimates. Empirical analysis of daily log-returns for four representative financial assets, the CSI 300 Index, S & P 500 Index, German DAX Index, and Gold Futures, demonstrates that the logistic expansion distribution significantly outperforms the normal distribution, effectively modeling both asymmetry and extreme observations. These results highlight the distribution’s potential as a robust tool for modeling complex financial data, assessing tail risk, and supporting statistical inference in contexts where conventional distributions fail to capture skewness and kurtosis adequately.

As indoor robots are expected to operate in increasingly complex environments, the need for rich and scalable semantic representations has become critical. While semantic mapping is a standard tool, existing representations often fall at two extremes: dense voxel-based maps that are computationally expensive to query, or schematic graphs that lack geometric detail. This trade-off limits the scalability of semantic maps in real-world tasks. We propose an object-aware semantic mapping framework that models key static objects using probability density functions (PDFs). Objects like beds, fridges or desks are detected via 3D point cloud processing and encoded as 2D probabilistic occupancy distributions. This formulation provides a compact, robust representation that preserves semantic identity and geometric shape, while handling noise and partial views. The map is structured around rooms and their contents, enabling global relocalization and semantically informed path planning. Using Differential Evolution and Kullback-Leibler divergence, our method achieves robust relocalization without prior pose. Its object-centric, probabilistic nature also supports functional scene understanding for context-aware navigation. We validate our approach on a benchmark dataset and in a real apartment, showing improved performance over traditional methods in ambiguous or cluttered scenes, and demonstrating the advantages of a unified representation for multiple robotic behaviors.

Based on the test for equality of quantiles originally introduced by Kosorok (1999), we propose new power formulas for the comparison of one quantile between two treatment groups, as well as for the comparison of a collection of quantiles. Under the null hypothesis of equality of quantiles, the test statistic follows asymptotically a normal distribution in the univariate case and a with degrees of freedom in the multivariate case, with the number of quantiles compared. The variance of the test statistic depends on the estimation of the probability density function of the distribution of failure times at the quantile being tested. In order to apply the test on real data, we propose to estimate this quantity using a resampling-based method, as an alternative to Kosorok's original kernel density estimator. The whole procedure provides a practical tool for designing and analyzing data arising from clinical trials using quantiles of survival as an endpoint. Simulation studies are performed to show the appropriateness of the power formulas. We illustrate the proposed test in a phase III randomized clinical trial where the proportional hazards assumption between treatment arms does not hold.

This study addresses the challenge of anticipatory resource allocation in field-deployed communication networks under dynamic unmanned aerial vehicle jamming. In such scenarios, energy supply is severely constrained. It cannot be replenished in real time, necessitating a one-time resource pre-allocation that must remain effective throughout the mission. To overcome these limitations, we propose a novel optimization framework consisting of four integrated components: (1) independent threat assessment via trajectory-coverage spatial mapping using digital elevation models and ray-tracing algorithms, (2) evidence-theoretic fusion of heterogeneous information sources—including objective intelligence data and subjective expert knowledge, (3) jamming distribution modeling through dedicated probability transformation algorithms for fixed-interval and continuous random jamming modes, and (4) decoupled resource-confidence optimization solved via convex programming. By employing evidence discount factors and Dempster’s combination rule, the framework quantifies reliability disparities. It integrates multiple heterogeneous sources and uses theoretically derived, forward-computable models—combining Binomial distributions, piecewise cubic Hermite interpolation, and uniform distribution assumptions—to efficiently convert threat basic probability assignments into jamming duration probability density functions. Extensive Monte Carlo simulations demonstrate significant improvement in mission assurance metrics, with consistent performance under diverse uncertainties. The approach is also validated in cross-domain applications using Bohai rescue data, confirming its utility in resource-limited, highly uncertain environments.

Abstract The increasing popularity of motorcycles has led to a growing concern for their better performance. They are exposed to random vibrations from engine loads and road irregularities, affecting both ride comfort and motorcycle handling. This paper presents a study on the use of electrorheological elastomers (EREs) as tunable engine mounts to improve motorcycles performance. First, a six DoF model is provided for a motorcycle system equipped with ERE engine mounts. The eigenvalue problem is then solved to identify the natural frequencies of the system. Both engine excitation and road irregularities are modeled as random signals, allowing for a realistic assessment of the problem. Ride comfort is evaluated using frequency-weighted acceleration, to address the body’s sensitivity to various excitation frequencies. Moreover, the evaluation of the road holding index is performed by calculation of the tire-road interacting forces. To reflect real-world conditions, three missions (off-road, urban, and highway) are defined using a Beta probability density function to capture variations in speed and road quality. Numerical random vibration analysis is performed for each mission. A cost function is then introduced to provide a balance between these two indices, and the optimization is carried out via the genetic algorithm. Results show that optimized ERE engine mounts significantly improve both ride comfort and road holding. On this basis, the main contributions of this paper are introducing and parametrically identifying tunable ERE-based engine mounts within a coupled motorcycle-engine-rider random-vibration model, and developing a frequency-domain random-vibration and optimization framework that simultaneously accounts for road and engine excitations while tuning mount properties for ride comfort and road holding. These findings highlight the potential of tunable ERE mounts, combined with systematic optimization, in advancing motorcycle vibration attenuation.

Abstract In this article, we introduce a new form of compound distribution by combining Gamma and Laplace components. This new distribution is specifically designed to address the limitations of traditional models when dealing with skewed and heavy tailed data. Its flexible parameters enable precise control over tail heaviness and data concentration, making it adaptable to assorted data behavior common in finance, insurance, and engineering. Additionally its balanced decay mechanism ensures symmetrical treatment of extreme values, enhancing accuracy in modeling risks and uncertainties, ultimately supporting more robust decision-making in high-stakes environments. A detailed analysis of the unique structural properties of this newly proposed model is carried out, including probability density function (PDF), cumulative distribution function(CDF), survival function, hazard function, moments, parameter estimation, tail behavior analysis, ordered statistics, and risk measures.

Conventional indicators of battery health, such as capacity and energy, are difficult to measure directly and are therefore often estimated. This article proposes assessing lithium-ion battery health using the statistical properties of the voltage across the battery terminals, a measurement already available in battery management systems. The evolution of the voltage probability density function during the cycle is assessed using Kullback-Leibler divergence (KLD) as a health indicator. It is studied for two battery chemistries (Lithium iron Phosphate (LFP) and Nickel Manganese Cobalt (NMC)). The batteries are subjected to cycles with a dynamic current profile derived from globally harmonised test cycles for light vehicles (WLTC). Spearman's correlation coefficients, above 86% for NMC cells and 74% for LFP cells, also indicate that this new health indicator is strongly correlated with conventional measurements of battery health (capacity or energy). The analysis also shows that the divergence not only closely follows the degradation trend even at high noise levels (SNR = 10 dB) but is also insensitive to noise levels higher than 30 dB.

Abstract The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here, we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by H I and young stellar objects data. We find that the N-PDFs of Cygnus-X and four subregions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

Surface-enhanced Raman spectroscopy (SERS) possesses molecular specificity and single-molecule sensitivity. Yet, intensity-based SERS assays are vulnerable to nontarget analyte-induced intensity fluctuations, while frequency-shift-based SERS assays are constrained by the instrument's spectral resolution, limiting the translational quantitative applications of SERS. Herein, we introduce a stochastic colloidal plasmon-enhanced spectral sampling (SCOPE) strategy for spectral super-resolution SERS spectroscopy. Through large-scale stochastic spectral sampling in a chemically homogeneous, spectrally dynamic colloidal solution containing plasmonic nanoparticles and analyte molecules, we obtain an empirical approximation of the probability density function of the sample's spectral response. This enables accurate estimation of the true peak center with subresolution precision through Gaussian histogram fitting. Building on SCOPE, we develop a spectrally super-resolved colloidal SERS immunoassay for multiplexed detection of a panel of protein biomarkers spanning endocrine, cardiovascular, and hemostatic conditions. We believe this study paves the way for spectrally super-resolved spectroscopic applications in a variety of analytical domains.

Abstract The probability density function of drops is difficult to model. Current approaches make assumptions that are often problematic, as they allow negative values for the mean of the distribution. While the statistical goodness of fit of those models might be reasonable for precipitation radar estimation, the situation is unsatisfactory if a fully consistent physical modeling of precipitation across scales is desired. This is the case of weather and climate models. This paper discusses a model that satisfies mathematical and physical consistency. The model can be seamlessly integrated into the parameterizations of the microphysics of precipitation and is tested on an extensive disdrometer data set. Comparison with existing models shows that the new method has substantial practical and theoretical advantages. The research has implications in elucidating the role of clouds in the climate sensitivity of climate models.

The rising global energy demand, along with the growth of electric power transmission and distribution systems, has intensified the need to incorporate renewable energy sources to foster sustainable development. However, achieving optimal operation within such systems poses significant challenges due to the stochastic nature of renewable energy generation. As a result, the optimal power flow (OPF) problem becomes increasingly complex when addressing the inherent uncertainty of renewable inputs. This study presents a new approach to addressing the OPF problem through the implementation of a hybrid Weighted Mean of Vectors Optimization Algorithm (INFO) based on artificial rabbits optimization (ARO) called ARINFO technique. The proposed ARINFO algorithm aims to reach an exploration-exploitation balance to improve search efficiency. To effectively manage the uncertainty associated with renewable energy output, modifications are implemented on standard test systems: in the IEEE 30-bus system (consisting of 30 buses, 6 thermal generators, and 41 branches), three thermal units are substituted with two wind turbines and one solar photovoltaic (PV) generator; a similar modification is made to the IEEE 57-bus system (which includes 57 buses, 7 thermal generators, and 80 branches) and large scale test system (IEEE 118-bus system). The stochastic characteristics of wind and solar power are modeled using Weibull and lognormal distributions, respectively. Their impact on the OPF problem is examined by incorporating reserve and penalty costs for overestimating and underestimating power output. Load demand variability is also assessed through standard probability density functions (PDF) to capture its uncertainty. Furthermore, operational constraints of thermal generators, such as ramp rate limits, are considered. The performance of the ARINFO algorithm is rigorously evaluated through 23 benchmark functions and the CEC-2022 test suite, with its effectiveness compared against nine established optimization methods. The results demonstrate that ARINFO achieved 1st rank overall on both the CEC-2017 and CEC-2022 test suites. When applied to the modified IEEE 30-bus system, ARINFO achieved a minimum generation cost of 781.1538 $/h, reduced emissions to 0.0922140 t/h, and minimized power losses to 1.734974 MW. For the larger IEEE 57-bus system, it attained a total cost of 20193.270 $/h, confirming its scalability and superior performance in managing the OPF problem under uncertainty in both generation and demand scenarios.

Wind-solar power generation is inherently uncertain. These uncertainties bring considerable difficulties to the assessment of hosting capacity. To tackle these difficulties, it is essential to create typical scenarios that can precisely capture the statistical traits and interrelationships of wind-solar power. In this research, we systematically integrate various scenario generation techniques, resulting in the creation of a holistic framework grounded in kernel density estimation (KDE) and Copula functions. Our proposed approach represents the stochastic nature of wind-solar power output by constructing their respective probability density functions (PDFs). It comprehensively depicts the potential spatiotemporal complementarity between wind-solar power by utilizing Copula functions and establishing a joint probability distribution model. Through Monte Carlo simulation, we generated a large number of wind-solar output scenarios. Subsequently, we employed the K-means clustering algorithm to reduce the number of scenarios. The findings reveal that the integrated framework, which combines KDE and Copula theory, achieves higher fitting accuracy for the marginal distributions and correlation structures of wind-solar power generation. As a result, the generated scenarios are more representative and reliable, offering strong support for photovoltaic (PV) hosting capacity analysis (HCA) and the formulation of typical plans. We validate the proposed method using historical wind-solar data from several representative regions in China, such as Inner Mongolia, northern Hebei, the Beijing–Tianjin–Hebei region, and Hubei Province. This validation demonstrates the method’s applicability under various geographical and climatic conditions.