Probability Distribution Function Research Articles

A novel approach for rapid quantification and length distribution of microfibers released during domestic laundry.

A novel approach for rapid quantification and length distribution of microfibers released during domestic laundry.

A NEW MODELING FRAMEWORK FOR PROBABILISTIC LANDSLIDE TSUNAMI HAZARD ANALYSES

Landslide tsunamis, although even less frequent than coseismic tsunamis, can be particularly damaging for the nearest coast and coastal communities, because: (i) for large slide volumes, shallow submergence, and large vertical displacement, they can be made of steeper, more locally damaging and narrowly focused waves; (ii) they are typically triggered in relatively shallower, sediment rich, nearshore areas (e.g., continental shelf break and slope), hence at a short propagation distance from shore, allowing less time for advance warning when detected; and (iii) they may not even be detected at all before they impact the shore. An additional difficulty in assessing landslide tsunami hazard is the large variety of parameters that significantly influence wave generation (some mentioned earlier), which requires considering a large number of scenarios, and running corresponding simulations, to properly quantify coastal hazard. The latter is best tackled in a probabilistic Monte Carlo simulation (MCS) framework, in which random scenarios are defined on the basis of relevant probability distribu- tion functions (PDFs) for each salient parameter. Such Probabilistic Tsunami Hazard Analyses (PTHA), which are increasingly routinely performed for coseismic tsunamis, are still quite rare for landslide tsunamis (e.g., Grilli et al 2009; Grezio et al 2012; Cecioni et al., 2023) as they face practical difficulties for: (i) properly assessing salient landslide parameters and quantifying their PDFs; (ii) acquiring relevant site-specific data on bottom/sub- bottom sediment properties and triggering mechanisms (e.g., seismicity); and (iii) developing a physically meaningful, but sufficiently efficient, numerical model for tsunami generation and propagation.

The trimer paradox: The effect of stiff constraints on equilibrium distributions in overdamped dynamics.

We reconsider the classical problem of a freely joined chain of Brownian particles connected by elastic springs and study its conformational probability distribution function in the overdamped regime in the limit of infinite stiffness of constraints. We show that the well-known solution by Fixman [Proc. Natl. Acad. Sci. U. S. A. 71, 3050 (1974)] is missing a shape-related term, later alluded to but not computed by Helfand [J. Chem. Phys 71, 5000 (1979)]. In our approach, the shape term, also termed zero-point energy, arises explicitly from a careful treatment of the distributional limit. We present a computationally feasible method for the calculation of the shape term and demonstrate its validity in a couple of examples.

Numerical Simulation of Mixing Enhancement in a Single Screw Extruder by Different Internal Baffles

AbstractThe metering section of an industrial‐scale single screw extruder is modeled, and two kinds of discontinuous baffles, three rows of plate baffles, and two types of plow‐shaped baffles, arranged in staggered or parallel ways, are proposed to improve the distributive and dispersive mixing. Considering the narrow gap between the screw and barrel, the finite element method along with the mesh superposition technique is applied to solve fully 3D isothermal flow fields where the fluid is assumed to obey the Carreau constitutive model. The computation codes are successfully developed to achieve particle tracking using the fourth‐order Runge–Kutta scheme. Distributive mixing is evaluated in terms of the evolution of tracer particles and Poincaré sections. Dispersive mixing is then examined in terms of shear rates, mixing index, distribution probability function of mixing index, and its integral function for particles tracking with time. For the same pressure drop and the same screw rotating speed, when compared to the conventional single screw, the numerical simulation results showed that the screw with staggered plow‐shaped baffles achieved better distributive mixing with the output nearly unchanged while three rows of plate baffles significantly enhanced both distributive and dispersive mixing at the cost of output reduction by 13.2%.

Towards the Real-World Analysis of Lumbar Spine Standing Posture in Individuals with Low Back Pain: A Cross-Sectional Observational Study.

Prolonged periods of standing are linked to low back pain (LBP). Evaluating lumbar spine biomechanics in real-world contexts can provide novel insights into these links. This study aimed to determine if standing behaviour can be quantified, in individuals with LBP, in real-world environments. A three-stage design was used, (i) Verification of a bespoke algorithm characterising lumbar standing behaviour, (ii) Day-long assessment of standing behaviours of individuals with posture-related low back discomfort, and (iii) Case study application to individuals with clinical LBP. Analysis of standing posture across time included variability, fidgeting, and amplitude probability distribution function analysis. The study demonstrated that accelerometers are a valid method for extracting standing posture from everyday activity data. There was a wide variety of postures throughout the day in people with posture-related low back discomfort and people with clinical LBP. Frequency profiles ranged from slightly flexed to slightly extended postures, with skewed bell-shaped distributions common. Postural variability ranged from 3.4° to 7.7°, and fidgeting from 1.0° to 3.0°. This work presents a validated accelerometer-based method to capture, identify, and quantify real-world lumbar standing postures. The distinct characteristics of people with low back discomfort or pain highlight the importance of individualised approaches.

Effective Long-Time Diffusivity of Particles of Arbitrary Shape in an External Orienting Field

Abstract Pertaining to the motion of a rigid particle in a flow, several distinct “centers” of the rigid particle can be identified, including the geometric center (centroid), center of mass, hydrodynamic center, and center of diffusion. In this work, we elucidate the relevance of these centers in Brownian motion and diffusion. Starting from the microscopic stochastic equations of motions, we systematically derive the coarse-grained Fokker–Planck equations that govern the evolution of the probability distribution function (PDF) in phase space and in configurational space. For consistency with the equilibrium statistical mechanics, we determine the unknown Brownian forces and torques. Next, we analyze the Fokker–Planck equation for the PDF in the position and orientation space. Through a multiscale analysis, we find the unit cell problem for defining the effective long-time translational diffusivity of a particle of arbitrary shape in an external orienting field. We also show some fundamental properties of the effective long-time translational diffusivity, including rigorous variational bounds for effective long-time diffusivity and invariance of effective diffusivity with respect to change of reference or tracking points. Exact results are obtained in the absence of an orienting field and in the presence of a strong orienting field. These fundamental results hold significant potential for applications in biophysics, colloidal science, and micro-swimmers design.

3D CMZ. II. Hierarchical Structure Analysis of the Central Molecular Zone

Abstract The Central Molecular Zone (CMZ) is the way station at the heart of our Milky Way Galaxy, connecting gas flowing in from Galactic scales with the central nucleus. Key open questions remain about its 3D structure, star formation properties, and role in regulating this gas inflow. In this work, we identify a hierarchy of discrete structures in the CMZ using column density maps from Paper I (C. Battersby et al.) We calculate the physical (N(H2), T dust, mass, radius) and kinematic (HNCO, HCN, and HC3N moments) properties of each structure as well as their bolometric luminosities and star formation rates. We compare these properties with regions in the Milky Way disk and external galaxies. Despite the fact that the CMZ overall is well below the Gao-Solomon dense gas star formation relation (and in modest agreement with the Schmidt–Kennicutt relation), individual structures on the scale of molecular clouds generally follow these star formation relations and agree well with other Milky Way and extragalactic regions. We find that individual CMZ structures require a large external pressure (P e /k B > 107−9 K cm−3) to be considered bound; however, simple estimates suggest that most CMZ molecular-cloud-sized structures are consistent with being in pressure-bounded virial equilibrium. We perform power-law fits to the column density probability distribution functions of the inner 100 pc, SgrB2, and the outer 100 pc of the CMZ as well as several individual molecular cloud structures and find generally steeper power-law slopes (−9 < α < −2) compared with the literature (−6 < α < −1).

High-Resolution Coastal Wind Energy Assessments Based on Copula Models and Meteorological Data

Abstract Accurate wind energy assessment (WEA) is essential to reduce the risk of wind project investment. In this paper, the overall framework and detailed process of wind resource assessment are presented for the first time, and the effectiveness of this method is validated by combining meteorological data with copula models. The average hourly wind speed and direction in Wenchang, Hainan Province, from 2016 to 2017 are used to study the joint probability distribution function (JPDF). However, the marginal probability density function (MPDF) of wind direction and wind speed is established and compared by parametric and nonparametric methods. The comparison results reveal that nonparametric kernel density estimation (KDE) performs better than parametric distributions in fitting wind speed empirical distribution but worse in wind direction empirical distribution. The copula function is subsequently utilized to construct JPDF. Six individual and comprehensive goodness-of-fit (GoF) metrics are employed to discern the ideal model out of all the potential models. The evaluation results show that the optimal model varies from year to year, and the Gumbel and Ali–Mikhail–Haq (AMH) copula models can best reproduce the 2-yr empirical distribution of wind speed and wind direction, respectively. Compared with the WEA method based on wind speed, the efficacy of the copula method is confirmed. The study simplifies the WEA procedure and realizes the systematic evaluation of available wind resources, which is of great significance for the further study of direction-related WEA in other regions.

Evaluation of Future Water Supply Capacity Based on Multipurpose Dam Operation Methods in Seomjin River Watershed

This study assessed the water-supply capacity of the Seomjin River Basin, focusing on dam operation methods and supply priorities. Water scarcity characteristics were analyzed using reliability, resilience, and vulnerability metrics, and probability distribution functions were applied to gain a comprehensive understanding of water shortage patterns. Comparing firm and deficit supply operation methods, firm supply was found to ensure consistent water distribution across regions, but showed limited resilience during droughts. In contrast, a supply deficit increased flexibility in water delivery, enhancing reliability and resilience in certain areas despite leading to imbalances across regions depending on the capacity of the hydraulic structures. This study suggests that a hybrid approach can effectively address these disparities, emphasizing the importance of adaptive region-specific strategies in future water resource policymaking.

A joint learning approach for automated diagnosis of keratinocyte carcinoma using optical attenuation coefficients

Keratinocyte carcinoma, such as Actinic Keratosis (AK) and Basal Cell Carcinoma (BCC), share similar clinical presentations but differ significantly in prognosis and treatment, highlighting the importance of effective screening. Optical coherence tomography (OCT) shows promise for diagnosing AK and BCC using signal intensity and skin layer thickness, but variability due to skin characteristics and system settings underscores the need for a standardized diagnostic method. Here, we propose an automated diagnostic method using the optical attenuation coefficient (OAC) and a joint learning strategy to classify AK, BCC, and normal skin. OAC images extracted from OCT data revealed notable disparities between normal and cancerous tissues. By incorporating probability distribution function (PDF) information alongside OAC images, the model achieved an accuracy of over 80% and approaching 100% by utilizing 3D OAC data to enhance robustness. This approach highlights the potential of OAC-based analysis for automated, intelligent diagnosis of early-stage non-melanoma skin cancers.

Evolution of Massive Red Galaxies in Clusters from z = 1.0 to z = 0.3

Abstract A critical issue in studying the evolution of galaxy clusters is to find ways that enable meaningful comparisons of clusters observed at different redshifts, as well as in various stages of their growth. Studies in the past have typically suffered from uncertainties in cluster mass estimates due to the scatter between cluster observables and mass. Here we propose a novel and general approach that uses the probability distribution function of an observable–cluster mass relation, together with dark matter halo merger trees extracted from numerical simulations, such that one can trace the evolution in a self-contained fashion, for clusters chosen to lie in a specified range in mass and redshift. This method, when applied to clusters of different mass ranges, further allows one to examine the evolution of various observable-cluster mass scaling relations. We illustrate the potential of this method by studying the stellar mass content of red cluster member galaxies, as well as the growth of brightest cluster galaxies, from z = 1.0 to z = 0.3, using a large optically detected cluster sample from the Subaru Hyper Suprime-Cam Survey, finding good agreement with previous studies.

Heatwaves risk assessment for Australia using variants of the Cox model

Abstract We investigated the influence of key factors on the hazards associated with the occurrence of temporal clustering of heatwaves using variants of the Cox regression model. The use of survival analysis as a statistical framework to infer characteristics of probability distribution functions is a powerful method for modelling the full distribution of climate variables rather than confining the analysis to simple statistical parameters like mean and variance. This approach allows for the assessment of the probability of extremes that are more informative than central tendency measures and constitutes the core of probabilistic risk assessments. Variants of the Cox model account for non-stationary patterns resulting from external influences such as climate change for situations where events do not depend on the observed time from last occurrence, nor on the number of events previously observed. We apply this concept to the onset of heatwaves to assess their effect by location and time. We use observed maximum daily temperatures across 28 urban and rural areas in Australia for the period 1956–2022, along with monthly observations for the Oceanic Niño Index (ONI) sea surface temperature anomalies and the Indian Ocean Dipole (IOD) sea surface temperature index as climate covariates to estimate the probability of heatwave occurrence over time after an initial time reference. We find that location (urban/rural) and climate covariates derived from ONI and IOD are significant indicators of heatwave hazards, while epoch (pre-1980/post-1980) exhibited only a moderate difference. Despite the urban heat island effect, urban locations are less prone to extremes in heatwave frequency than rural locations.

Development of a database on multivariate soil properties for collapsible loess in Xi’an, China

Several global or regional databases for various types of soils have been developed due to their importance in engineering design and analysis. However, a database is not yet available for collapsible loess in which severe geohazards often occur. In this study, a comprehensive loess database with twelve soil parameters is compiled by collecting results of field and laboratory tests on collapsible loess from the city of Xi’an, China. Basic statistics, marginal probability distribution functions (PDFs), and a correlation matrix for loess parameters are estimated from the database. To the best of the authors’ knowledge, this is the first collapsible loess database at a municipal level. In addition, existing databases often lack sufficiently complete multivariate measurement data for a proper estimation of statistical correlations among multiple soil properties. In this study, this incomplete multivariate measurement data problem is tackled by Bayesian methods (i.e., Bayesian Gaussian mixture model and Bayesian compressive sampling (BCS) with Karhunen–Loève (KL) expansion, BCS-KL), which are illustrated and validated using the incomplete and complete subsets of the loess database, respectively. Both the Bayesian Gaussian mixture model and BCS-KL are non-parametric, and they offer a flexible way of modeling marginal PDFs and a correlation matrix from incomplete measurements in a realistic manner.

Determining Clinically Meaningful Improvement in Children and Adolescents with Tourette Syndrome Receiving Pharmacotherapy.

Introduction: Accurate assessment of treatment outcomes in patients with Tourette syndrome (TS) is essential for evidence-based clinical care. This report determined the minimal clinically important difference (MCID) on the Yale Global Tic Severity Scale (YGTSS) Total Tic Score (YGTSS-TTS) and YGTSS Impairment Scale (YGTSS-I), using the Clinical Global Impression of TS Severity (CGI-TS-S) and Improvement (CGI-TS-I) as anchors, in pediatric patients with TS receiving pharmacotherapy. Materials and Methods: Analyses used data from two clinical trials of ecopipam (a randomized controlled trial and its open-label extension). Receiver operating characteristic (ROC) analysis determined the percentage reduction in YGTSS scores that distinguished patients with improvement from those with no change or worsening on the CGI-TS-S and CGI-TS-I. Spearman's correlation, empirical cumulative distribution function, and probability distribution function analyses examined relationships between YGTSS-TTS and CGI-TS-S or CGI-TS-I. Results: Overall, 133 patients (75.2% male; mean [SD] age, 12.7 [2.8]) were included; 63.2% had improvement on the CGI-TS-S, and 78.2% showed improvement on the CGI-TS-I. Percentage reduction in YGTSS scores that distinguished improvement from no change or worsening on the CGI-TS-S and CGI-TS-I ranged from 18.6%-33.3% (area under the ROC curve range, 0.71-0.81). Improvement on the YGTSS-TTS was correlated with posttreatment CGI-TS-S (r = -0.65; p < 0.001) and CGI-TS-I (r = -0.61; p < 0.001) scores. The MCID for YGTSS-TTS was achieved by 67% and 62% of patients with improvement on the CGI-TS-S and CGI-TS-I, respectively. Conclusions: This analysis is the first to determine the MCID for YGTSS in a pediatric population with TS receiving pharmacotherapy. Whether using CGI-TS-S or CGI-TS-I as the anchor, a 25% reduction in YGTSS scores was a generally appropriate minimum threshold to define clinically meaningful improvement in this population. Findings offer an objective threshold for classifying clinically meaningful improvement in children and adolescents receiving pharmacotherapy for TS in clinical practice.

Evaluating fatigue and electromechanical degradation in REBCO CC tapes at cryogenic temperature using optical fiber sensors

Abstract Preliminary demonstrations show Rayleigh scattering-based optical frequency-domain reflectometry distributed optical fiber sensors (DOFSs) effectively detect and locate fatigue damage in rare-earth barium copper oxide (REBCO) coated conductor (CC) tape by reconstructing time-series macro-strain data. While significant degradation of critical current ( I c ) may occur prior to mechanical failures when these tapes are subjected to cyclic stresses or strains. To address this issue, a comprehensive study was conducted on the degradation mechanism and critical current level of REBCO CC tapes under cyclic fatigue loading. A new method has been developed to estimate fatigue damage on I c degradation by reconstructing time-series macro-strain data using DOFSs. The damage variable was introduced to quantitatively characterize impact on I c degradation of REBCO CC tape under cyclic fatigue loading. Additionally, the fatigued specimens were analyzed using scanning electron microscopy for microstructural changes, aiming to verify the feasibility of the method and elucidate the mechanism behind I c degradation. Experimental results demonstrate that the introduced damage variable exhibits consistency with the I c degradation, which has been further adapted to evaluate I c degradation of REBCO CC tapes in combination with Weibull probability distribution function. This provides a reliable and real-time measurement methodology for I c degradation assessments in REBCO CC tapes under actual operating conditions, facilitating to provide critical reference values for optimizing designs and ensure the stable and safe operation of superconducting structures.

Monotonicity of the RG flow in an emergent dual holography of a worldsheet nonlinear σ model

Based on the renormalization group (RG) flow of worldsheet bosonic string theory, we construct an effective holographic dual description of the target space theory identifying the RG scale with the emergent extra dimension. This results in an effective dilaton-gravity-gauge theory, analogous to the low-energy description of bosonic M theory. We argue that this holographic dual effective field theory is nonperturbative in the α′ expansion, where a class of string quantum fluctuations are resummed to all orders. To investigate the monotonicity of the RG flow of the target space metric in the emergent spacetime, we consider entropy production along the RG flow. We construct a microscopic entropy functional based on the probability distribution function of the holographic dual effective field theory, regarded as Gibbs- or Shannon-type entropy. Given that the Ricci flow represents the 1-loop RG flow equation of the target space metric for the 2D nonlinear sigma model, and motivated by Perelman’s proof of the monotonicity of Ricci flow, we propose a Perelman’s entropy functional for the holographic dual effective field theory. This entropy functional is also nonperturbative in the α′ expansion, and thus, generalizes the 1-loop result to the all-loop order. Furthermore, utilizing the equivalence between the Hamilton-Jacobi equation and the local RG equation, we suggest that the RG flow of holographic Perelman’s entropy functional is the Weyl anomaly. This eventually reaffirms the monotonicity of RG flow for the emergent target spacetime but in a nonperturbative way. Interestingly, we find that the microscopic entropy production rate can be determined by integrating the rate of change of the holographic Perelman’s entropy functional over all possible metric configurations along the flow. Published by the American Physical Society 2025

DeepDISC-photoz: Deep Learning-Based Photometric Redshift Estimation for Rubin LSST

Photometric redshifts will be a key data product for the Rubin Observatory Legacy Survey of Space and Time (LSST) as well as for future ground and space-based surveys. The need for photometric redshifts, or photo-zs, arises from sparse spectroscopic coverage of observed galaxies. LSST is expected to observe billions of objects, making it crucial to have a photo-z estimator that is accurate and efficient. To that end, we present DeepDISC photo-z, a photo-z estimator that is an extension of the DeepDISC framework. The base DeepDISC network simultaneously detects, segments, and classifies objects in multi-band coadded images. We introduce photo-z capabilities to DeepDISC by adding a redshift estimation Region of Interest head, which produces a photo-z probability distribution function for each detected object. On simulated LSST images, DeepDISC photo-z outperforms traditional catalog-based estimators, in both point estimate and probabilistic metrics. We validate DeepDISC by examining dependencies on systematics including galactic extinction, blending and PSF effects. We also examine the impact of the data quality and the size of the training set and model. We find that the biggest factor in DeepDISC photo-z quality is the signal-to-noise of the imaging data, and see a reduction in photo-z scatter approximately proportional to the image data signal-to-noise. Our code is fully public and integrated in the RAIL photo-z package for ease of use and comparison to other codes at https://github.com/LSSTDESC/rail_deepdisc

Performance evaluation of wireless node positioning over α − η − μ fading channel

Abstract The increasing demand for diverse services, ubiquitous coverage, and device-oriented point-to-point communications necessitates a focus on user mobility in characterizing the wireless channel environment. This study addresses the random waypoint mobility (RWP) model, where users follow a zigzag path between waypoints, causing significant fluctuations in perceived signal power. Recognizing the critical role of mobility-driven channel modelling in optimizing network infrastructure, this paper evaluates user mobility in non-linear and non-line-of-sight (NLOS) scenarios, leveraging the α-η-μ fading distribution. We derive a closed-form expression for the probability distribution function (PDF) by integrating the RWP mobility model with the α-η-μ fading channel. The study explores path loss exponent variations under different node positioning dimensions (1D, 2D, and 3D). The novel RWP-modelled α-η-μ composite fading channel PDF is then used to quantify performance metrics, including outage performance and bit error rate (BER) in communication systems, particularly in the context of evolving to 5 G networks. Additionally, this work considers dynamic node mobility in various distributions such as one-sided Gaussian, exponential, Nakagami-m (with its discrete version Chi), Rayleigh, and Weibull. The obtained results from the derived expressions are rigorously validated through Monte Carlo simulations.

Modeling and Performance Analysis of Task Offloading of Heterogeneous Mobile Edge Computing Networks

Mobile edge computing architecture (MEC) can provide users with low latency services by integrating computing, storage and processing capabilities near users and data sources. As such, there has been intense interest in this topic, especially in single-server and homogeneous multi-server scenarios. The impact of network heterogeneity and load fluctuations is ignored, and the performance evaluation system relies too much on statistical mean indicators, ignoring the impact of real-time indicators. In this paper, we propose a new heterogeneous edge computing network architecture composed of multi-core servers with varying transmission power, computing capabilities and waiting queue length. Since it is necessary to evaluate and analyze the service performance of MEC to guarantee Quality of Service (QoS), we design some indicators by solving the probability distribution function of response time, such as average task offloading delay, immediate service probability and blocking probability. By analyzing the impact of bias factors and network parameters associated with MEC servers on network performance, we provide insights for MEC design, deployment and optimization.

Optimal Probability Distribution Function and Plotting Position for Annual Maximum Flood in Mahanadi River System, India

In the present work, optimum probability distribution function and plotting position of annual maximum flood series data obtained for Mahanadi River system has been analysed. For the analysis, 25 to 45 years of data obtained from Nineteen gauging stations of Mahanadi river system have been considered. Different commonly used probability distribution functions have been tested for their applicability at all the nineteen gauging stations individually. They are Generalised Extreme Value (GEV), Generalised Pareto (GP), Log-Pearson III (LP III), Normal, Log normal (LN), Log-Logistic (LL), Log-Logistic 3P(LL-3P), Log normal 3P(LN-3P), Pareto (P) and Gumbel max method. A comparison of the results obtained using these distributions has been done with the Weibull, Hazen &amp; California plotting positions. From the results, the Generalised Pareto (GP) probability distribution provided best results followed by GEV and Log Pearson Type III. The goodness of fit tests namely Kolmogorov-Smirov (KS), Anderson-Darling (AD), and Chi squared (CS) tests has been done to assess the best performing probability distribution. The annual maximum flow observed are compared well with the predicted annual maximum flow for the return period of 5, 10, 20, 25, 30, 35 and 45 years. The results obtained are promising and can be used for design and development of water resources projects in Mahanadi river system.