Probability Distribution Research Articles

Comparative Diagnostic Efficacy of Abbreviated and Full Protocol Breast MRI: A Systematic Review and a Meta-Analysis.

This meta-analysis aims to compare the efficacy, limitations, and clinical implications of Abbreviated Breast MRI (AB-MRI) and Full Protocol MRI (FP-MRI). It focuses on diagnostic accuracy across various populations and settings, extending the scope of prior meta-analyses by including studies conducted after 2019 in both screening and diagnostic contexts. We conducted a systematic review (from 11/2019 to 12/2022). A bivariate model was used to calculate the summary estimates of sensitivity and specificity. Random effect models were used to calculate summary AUC and probability distributions for negative and positive predictive values were obtained. Subgroup analyses were conducted to investigate the differences between the AB-MRI and FP-MRI in terms of sensitivity, specificity, and AUC. The search across multiple databases yielded 11 eligible studies, including one prospective and ten retrospective studies. Statistical analysis revealed a significant difference in sensitivity between FP-MRI (95%) and AB-MRI (86%, p = 0.005), but not in specificity (p = 0.50). AB-MRI demonstrated a shorter acquisition time, suggesting potential for increased patient throughput. However, challenges remain in detecting small lesions and non-mass enhancements, with some studies suggesting the inclusion of additional sequences such as DWI with ADC mapping to enhance diagnostic performance. While FP-MRI remains the gold standard in breast cancer detection, AB-MRI presents as a viable, quicker alternative, especially useful in high-risk screening scenarios. Its lower sensitivity compared to FP-MRI, however, limits its utility as a standalone diagnostic tool. Future research should focus on optimizing AB-MRI protocols and investigating patient-specific factors to refine breast cancer screening and diagnostic strategies.

Managing Resources for Shared Micromobility: Approximate Optimality in Large-Scale Systems

We consider the problem of managing resources in shared micromobility systems (bike sharing and scooter sharing). An important task in managing such systems is periodic repositioning/recharging/sourcing of units to avoid stockouts or excess inventory at nodes with unbalanced flows. We consider a discrete-time model; each period begins with an initial inventory at each node in the network, and then, customers (demand) materialize at the nodes. Each customer picks up a unit at the origin node and drops it off at a randomly sampled destination node with an origin-specific probability distribution. We model the above network inventory management problem as an infinite horizon discrete-time discounted Markov decision process (MDP) and prove the asymptotic optimality of a novel mean-field approximation to the original MDP as the number of stations becomes large. To compute an approximately optimal policy for the mean-field dynamics, we provide an algorithm with a running time that is logarithmic in the desired optimality gap. Lastly, we compare the performance of our mean field-based policy with state-of-the-art heuristics via numerical experiments, including experiments using Austin scooter-sharing data. This paper was accepted by Jeannette Song, operations management. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.02023 .

On The Modeling of Biomedical Data Sets with a New Generalized Exponentiated Exponential Distribution

Introduction: Many experts in the field of distribution theory have focused on extending probability distributions utilizing extended families of continuous distributions to improve the modeling adaptability of the conventional probability distributions. Methods: This research employed a continuous family of probability distributions as introduced in the literature using the T-X methodology. Through this, some of statistical and mathematical properties of the model were derived and studied Results: This study had introduced a brand-new, five-parameter generalized exponentiated exponential distribution, which is a continuous probability distribution. With the aid of the quantile function, moments, moment generating function, survival function, hazard function, mean, and median, among other mathematical and statistical aspects, the new distribution's shape was deduced and researched. It was also possible to derive the probability density function for the minimum and maximum order statistics for this distribution. The method of maximum likelihood estimate was used to produce a conventional estimation of the unknown parameters. A simulation study was carried out to assess the efficiency and consistency of the estimation method used. To evaluate the fit and adaptability of the new model, it was applied to four real-world datasets in the field of medicine. Conclusion: The analysis's findings demonstrated that the new model performs better than its counterparts and offers a better fit than the Topp-Leone exponentiated exponential, Topp-Leone Kumaraswamy exponential, exponentiated exponential, and exponential distributions.

A UUV Cluster Route-Planning Method for Dynamic Target Search

Aiming to address the problem of regional dynamic target search under weak communication conditions, this paper proposes a UUV cluster search method based on cumulative probability optimization. First, by estimating the probability distribution of the initial target location, an initial probability map is established. Then, based on the Bayesian model and Markov decision model, the target probability distribution is periodically updated, and based on the cumulative detection probability optimal principle of the UUV cluster, the UUV cluster is guided to search the region with high detection probability preferentially. Finally, we implement the simulation experiment and compare with the random search method. The results verify that the proposed method has higher search efficiency in the cases of without prior information and with prior information.

Preprocessing and postprocessing analysis for hot-mix asphalt dynamic modulus experimental data

Dynamic modulus (|E*|) measurements of hot-mix asphalt (HMA) mixtures are critical for understanding material behavior but present significant challenges due to the complex testing procedures and precision required. While substantial efforts have focused on developing predictive models for |E*|, the critical role of experimental data preprocessing has been largely overlooked in the existing literature. This study addresses this gap by proposing a novel, comprehensive framework for both preprocessing and post-processing of dynamic modulus data. Leveraging the well-established ASU |E*| database and the NCHRP 1–40D Witczak prediction model as benchmarks, we introduce advanced empirical techniques, including probability distribution analysis, scatter and box plots, correlation coefficients, and mutual information metrics, to refine data quality and enhance the interpretability of predictive models. Our approach reveals new insights into the interaction of various input factors and |E*| values, leading to improved model robustness and reliability. The post-processing techniques further substantiate the predictive power of the Witczak model, yielding significant enhancements in accuracy and reliability. This research pioneers a standardized data preparation methodology that sets a new precedent in asphalt material engineering, offering a robust foundation for future |E*| modeling and analysis.

Investigating the Impact of Random Field Element Size on Soil Slope Reliability Analysis

The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/De) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/De on the distribution of safety factors (Fs) and failure probability (PF), with overestimation observed at smaller H/De ratios. When H/De exceeds 10 for Example 1 and 15 for Example 2, the Fs distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/De and remains basically unchanged when H/De exceeds 10 and 15, respectively. Consequently, a recommended H/De ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.

The Safety Assessment of Civil Ships against Capsizing Based on the Probability Analysis of Multiple Threshold-crossings of Stochastic Sea Waves

Abstract This paper investigates the impact of threshold-crossing events on ship capsizing through a probabilistic model that predicts random wave heights. Utilizing statistical data from wave height observations, this paper proposes that random waves can be approximated and modeled using the Wiener process, employing autocorrelation function identification and probabilistic statistical verification methods. The threshold-crossing duration of a random wave is just the period of the wave exceeds a given threshold, which can reflect the frequency property of the stochastic sea waves. And the probability distribution of the period can theoretically be determined using the derived probability density function for the time interval between any two adjacent crossings of the Wiener process and a threshold. Based on the above theories, the capsizing probabilities of a civil ship sailing in different wave areas are analyzed under different safety thresholds considering certain ratios of the ship's intrinsic period and wave period. The research results can provide a reference for the anti-overturning design of the ships under the action of random waves.

Operational reliability and non-deterministic resilience estimation of active distribution network incorporating effect of real-time dynamic hosting capacity

Active distribution networks are increasingly recognized essential for achieving sustainable development goals. Traditionally, hosting capacity was considered as a static measure for planning distributed energy resources integration. This work introduces the concept of dynamic hosting capacity, which recurrently re-evaluates hosting capacity in response to erratic modern grid conditions. The introduction of dynamic hosting capacity facilitated testing variations of power injection from minimum to 100 %, sustaining power system governing parameter limits. This embarked the need of operational reliability assessment and enhancing situational awareness for optimum power injection and balance. To achieve operational reliability analysis based on dynamic hosting capacity, hybrid probability distribution function-based Monte Carlo simulation is proposed. This resulted in 85–90 %. improvisation of solar photovoltaic generation and load alignment, as this methodology provides comprehensive and accurate assessment of system performance under diverse uncertainties. The framework's validation includes projection of time-varying operational reliability indices, over time independent reliability indices i.e., dynamic loss of load probability, dynamic loss of load expectation, dynamic loss of load duration, dynamic loss of load frequency, dynamic grid margin, and dynamic grid dependency. This resulted in 30 % improvement in assessment of grid margin, facilitating reliable uncertainty handling competence. Additionally, expectation maximization algorithm is proposed to evaluate non-deterministic resilience due to ambiguities associated with solar photovoltaic distributed energy resources. The non-deterministic resilience assessment testified 80 % bounce-back rate, demonstrating better adaptability and robustness. The entire analysis is conducted in MATLAB, validated using Typhoon Hardware-in-Loop real-time platform, and compared with existing literatures to demonstrate its effectiveness.

Multi-objective simulated annealing-based quantum circuit cutting for distributed quantum computation

In the current noisy intermediate-scale quantum (NISQ) era, the number of qubits and the depth of quantum circuits in a quantum computer are limited because of complex operation among increasing number of qubits, low-fidelity quantum gates under noise, and short coherence time of physical qubits. However, with distributed quantum computation (DQC) in which multiple small-scale quantum computers cooperate, large-scale quantum circuits can be implemented. In DQC, it is a key step to decompose large-scale quantum circuits into several small-scale subcircuits equivalently. In this paper, we propose a quantum circuit cutting scheme for the circuits consisting of only single-qubit gates and two-qubit gates. In the scheme, the number of non-local gates and the rounds of subcircuits operation are minimized by using the multi-objective simulated annealing (MOSA) algorithm to cluster the gates and to choose the cutting positions whilst using non-local gates. A reconstruction process is also proposed to calculate the probability distribution of output states of the original circuit. As an example, the 7-qubit circuit of Shor algorithm factoring 15 is used to verify the algorithm. Five cutting schemes are recommended, which can be selected according to practical requirements. Compared with the results of the mixing integer programming (MIP) algorithm, the number of execution rounds is efficiently reduced by slightly increasing the number of nonlocal gates.

Research on Evaluation Method of Natural Gas Hydrate Resources Based on Probability Distribution Model

Natural gas hydrate, as a highly efficient and clean energy source, has garnered significant attention from both developed and energy-deficient nations. However, to achieve industrial application, several technical challenges must be addressed, including resource exploration, spatial positioning, resource assessment, economic production evaluation, and climate change impact assessment. Currently, our exploration and evaluation system for gas hydrate resources remains immature. This study aims to determine the probability distribution of effective thickness, porosity, and saturation of natural gas hydrate resource parameters in the study area and their variations. Utilizing probability statistics theory, we calculated specific values for all gas hydrate resource parameters from open-source data of 14 exploration well locations, determined their probability distributions, and conducted distribution detection to identify specific distributions. Data analysis was performed using linear graphs and bar charts to summarize patterns. Subsequently, by applying the mathematical formula Q = A×Z×∅×S×E, we categorized natural gas hydrate resource parameters, calculated gas hydrate resources at each effective depth, determined the probability distribution of each obtained data point, and ultimately solved for the total natural gas hydrate resources, yielding a final solution of 31875763695.08.

J-PLUS: Bayesian object classification with a strum of BANNJOS

With its 12 optical filters, the Javalambre-Photometric Local Universe Survey (J-PLUS) provides an unprecedented multicolor view of the local Universe. The third data release (DR3) covers 3,192 deg$^2$ and contains 47.4 million objects. However, the classification algorithms currently implemented in the J-PLUS pipeline are deterministic and based solely on the morphology of the sources. Our goal is to classify the sources identified in the J-PLUS DR3 images as stars, quasi-stellar objects (QSOs), or galaxies. For this task, we present a machine learning pipeline that utilizes Bayesian neural networks to provide the full probability distribution function (PDF) of the classification. has been trained on photometric, astrometric, and morphological data from J-PLUS DR3 DR3, and using over 1.2 million objects with spectroscopic classification from DR18 DR9, the Early Data Release, and DR3. Results were validated on a test set of about $1.4 10^5$ objects and cross-checked against theoretical model predictions. outperforms all previous classifiers in terms of accuracy, precision, and completeness across the entire magnitude range. It delivers over $95<!PCT!>$ accuracy for objects brighter than $r = 21.5$ mag and $ 90<!PCT!>$ accuracy for those up to $r = 22$ mag, where J-PLUS completeness is $ 25<!PCT!>$. is also the first object classifier to provide the full PDF of the classification, enabling precise object selection for high purity or completeness, and for identifying objects with complex features, such as active galactic nuclei with resolved host galaxies. effectively classified J-PLUS sources into around 20 million galaxies, one million QSOs, and 26 million stars, with full PDFs for each, which allow for later refinement of the sample. The upcoming J-PAS survey, with its 56 color bands, will further enhance 's ability to detail the nature of each source.

Clinical Impact of 3- versus 5-Minute Delay and 30- versus 60-Second Intervals on Unattended Automated Office Blood Pressure Measurements.

Guidelines advise automated office blood pressure (AOBP) with an initial 5-minute delay and multiple measurements at least 60 seconds apart. Recent studies suggest that AOBP may be accurate with shorter delays or intervals, but evidence in clinical settings is limited. Patients referred to one hypertension (HTN) center underwent 24-hour ambulatory blood pressure monitoring (ABPM) and one of four non-randomized, unattended AOBP protocols: a 3- or 5-minute delay with a 30 or 60-second interval, i.e., 3min/30sec/30sec, 3/60/60, 5/30/30 and 5/60/60 protocols. HTN was defined as systolic blood pressure ≥140 or diastolic blood pressure ≥90 mmHg. We compared differences in mean blood pressure and HTN classification between average AOBP and awake-time ABPM by t-tests and Fisher's exact test. Among 212 participants (mean 58.9 years, 61% women, 25% Black), there was substantial overlap in the probability distributions of awake-time ABPM and each of the three AOBP measures. Systolic blood pressure means were similar between the 5/60/60 and 3/30/30 protocols and 5/30/30 and 3/60/60 protocols. The 5/30/30 was associated with a higher proportion of systolic HTN, while the 3/60/60 protocol was associated with a higher proportion of diastolic HTN. There were no significant differences in systolic or diastolic HTN between 5/60/60 and 3/30/30 protocols with respect to awake-time ABPM. In this quality improvement study, the shortest AOBP protocol did not differ significantly from the longest protocol. The time savings of shorter protocols may improve AOBP adoption in clinical practice without meaningfully compromising accuracy.

Discrete dynamics in the set of quantum measurements

Abstract A quantum measurement, often referred to as positive operator-valued measurement, is a set of positive operators P j = P j † ⩾ 0 summing to identity, ∑ j P j = 𝟙 . This can be seen as a generalization of a probability distribution of positive real numbers summing to unity, whose evolution is given by a stochastic matrix. We describe transformations in the set of quantum measurements by blockwise stochastic matrices, composed of positive blocks that sum columnwise to identity, and the notion of sequential product of matrices. We show that such transformations correspond to a sequence of quantum measurements. Imposing additionally the dual condition that the sum of blocks in each row is equal to identity we arrive at blockwise bistochastic matrices (also called quantum magic squares). Analyzing their dynamical properties, we formulate a quantum analog of the Ostrowski description of the classical Birkhoff polytope and introduce the notion of majorization between quantum measurements. Our framework provides a dynamical characterization of the set of blockwise bistochastic matrices and establishes a resource theory in the set of quantum measurements.

Multi-Modal Pose Representations for 6-DOF Object Tracking

Pose estimation methods for robotics should return a distribution of poses rather than just a single pose estimate. Motivated by this, in this work we investigate multi-modal pose representations for reliable 6-DoF object tracking. A neural network architecture for simultaneous object segmentation and estimation of fiducial points of the object on RGB images is proposed. Given a priori probability distribution of object poses a particle filter is employed to estimate the posterior probability distribution of object poses. An advanced observation model relying on matching the projected 3D model with the segmented object and a distance transform-based object representation is used to weight samples representing the probability distribution. Afterwards, the object pose determined by the PnP algorithm is included in the probability distribution via replacing a particle with the smallest weight. Next, a k-means++ algorithm is executed to determine modes in a multi-modal probability distribution. A multi-swarm particle swarm optimization is then executed to determine the finest modes in the probability distribution. A subset of particles for final pose optimization is found in a multi-criteria analysis using the TOPSIS algorithm. They are verified using conflicting criteria that are determined on the basis of object keypoints, segmented object, and the distance transform. On the challenging YCB-Video dataset it outperforms recent algorithms for both object pose estimation and object pose tracking.

LLM-enhanced Composed Image Retrieval: An Intent Uncertainty-aware Linguistic-Visual Dual Channel Matching Model

Composed image retrieval (CoIR) involves a multi-modal query of the reference image and modification text describing the desired changes, allowing users to express image retrieval intents flexibly and effectively. The key of CoIR lies in how to properly reason the search intent from the multi-modal query. Existing work either aligns the composite embedding of the multi-modal query and the target image embedding in the visual domain through late-fusion or converts all images into text descriptions and leverage large language models (LLM) for text semantic reasoning. However, this single-modality reasoning approach fails to comprehensively and interpretably capture the users’ ambiguous and uncertain intents in the multi-modal queries, incurring the inconsistency between retrieved results and ground truth. Besides, the expensive manually-annotated datasets limit the further performance improvement of CoIR. To this end, this paper proposes an LLM-enhanced Intent Uncertainty-aware Linguistic-Visual Dual Channel Matching Model (IUDC), which combines the strengths of multi-modal late-fusion and LLMs for composed image retrieval. We first construct an LLM-based triplet augmentation strategy to generate more synthetic training triplets. Based on this, the core of IUDC consists of two matching channels: the semantic matching channel is responsible for intent reasoning on the aspect-level attributes extracted by an LLM, and the visual matching channel accounts for the fine-grained visual matching between multi-modal fusion embedding and target images. Considering the intent uncertainty presented in the multi-modal queries, we introduce Probability Distribution Encoder (PDE) to project the intents as probabilistic distributions in the two matching channels. Consequently, a mutually enhanced module is designed to share knowledge between the visual and semantic representations for better representation learning. Finally, the matching scores of two channels are added to retrieve the target image. Extensive experiments conducted on two real datasets demonstrate the effectiveness and superiority of our model. Notably, with the help of the proposed LLM-based triplet augmentation strategy, our model achieves a new record of state-of-the-art performance among all datasets.

The Two Component Generalized Finite Erlang Mixture and its Properties and Special Cases

This research proposes the construction of a two-component generalized finite Erlang mixture with four parameters. Three distinct cases of this mixture are presented, differing in their mixing weights and corresponding component probability (Erlang) distributions. Special cases of these mixtures, including the one-, two-, and three-parameter finite Erlang mixtures, have also been derived. The statistical properties examined for these mixtures include the distribution function, survival function, hazard function, moment generating function, raw and central moments, mean, variance, coeffcient of skewness, coeffcient of kurtosis, and order statistics. Parameter estimation for the finite Erlang mixtures was conducted using both the method of moments and maximum likelihood estimation. Furthermore, the 4-parameter mixed Erlang distributions were applied to a real dataset on the relief times of patients receiving an analgesic, to evaluate their goodness of fit. The results demonstrate the potential of these mixtures to provide robust modeling for empirical data, suggesting their applicability in various statistical and practical contexts.

Does Positron Attachment Take Place in Water Solution?

We performed a computational study of positron attachment to hydrated amino acids, namely glycine, alanine, and proline in the zwitterionic form. We combined the sequential quantum mechanics/molecular mechanics (s-QM/MM) method with various levels of any particle molecular orbital (APMO) calculations. Consistent with previous studies, our calculations indicate the formation of energetically stable states for the isolated and microsolvated amino acids, in which the positron localizes around the carboxylate group. However, for the larger clusters, composed of 7 to 40 water molecules, hydrogen bonding between the solute and solvent molecules disfavors positron attachment to the amino acids, giving rise to surface states in which the positron is located around the water-vacuum interface. The analysis of positron binding energies, positronic orbitals, radial probability distributions, and annihilation rates consistently pointed out the change from positron-solute to positron-solvent states. Even with the inclusion of an electrostatic embedding around the aggregates, the positrons did not localize around the solute. Positron attachment to molecules in the gas phase is a well-established fact. The existence of hydrated positronic molecules could also be expected from the analogy with transient anion states, which are believed to participate in radiation damage. Our results indicate that positron attachment to hydrated biomolecules, even to zwitterions with negatively charged carboxylated groups, would not take place. For the larger clusters, in which positron-water interactions are favored, the calculations indicate an unexpectedly large contribution of the core orbitals to the annihilation rates, between 15 and 20%. Finally, we explored correlations between positron binding energies (PBEs) and dipole moments, as well as annihilation rates and PBEs, consistent with previous studies for smaller clusters.

Improving electric vehicle charging forecasting: A hybrid deep learning approach for probabilistic predictions

AbstractElectric vehicles (EVs) have gained significant attention recently. Despite their advantages, challenges in the power grid, such as providing necessary information for optimal operation, persist. High‐precision forecasting techniques are essential to address the nonlinear and complex behavior of EV charging. A hybrid structure based on deep learning, called LSTLNet, has been proposed. LSTLNet combines convolutional neural networks (CNN), gated recurrent neural networks (GRU), attention mechanisms (AM), and automatic regression (AR) models. This combination improves the deterministic forecasting model and addresses the weaknesses of CNN and GRU. Deterministic prediction, which determines only one point of consumption charge, is prone to error. Therefore, probabilistic forecasting, represented as a probability distribution function (PDF) containing comprehensive statistical information, is preferred. A smooth band limit maximum likelihood (SBLM) estimator is used to indirectly predict the PDF from the data. Comparative results with conventional shallow and deep methods for similar time series forecasting demonstrate the superiority of the proposed method for both deterministic and probabilistic forecasting.

A machine learning-based probabilistic wind speed prediction model with multi-resolution data, quantile regression and bound estimation

Wind speed prediction can be important for management of long-span cross-sea bridges, and probabilistic prediction models are needed to take uncertainty of future wind speed into consideration. However, there are two shortcomings of existing models. One is the lack of supplementary input of detailed fluctuations of wind speed, and the other is that fixed quantiles are usually selected when the predicted probability distribution is converted into a confidence interval. To this end, we propose a novel machine learning-based probabilistic model with multi-resolution data, quantile regression and bound estimation. The proposed model is composed of the distribution prediction part and the interval prediction part. In the distribution prediction part, we employ multi-resolution data as input, which can complement details of fluctuations of wind speed to reduce uncertainty. The interval prediction part employs the lower upper bound estimation method to postprocess predicted quantiles and output a superior interval than selecting fixed quantiles. The proposed model is validated on the monitoring wind speed data of two long-span cross-sea bridges, where the superiority of the distribution part and the effectiveness of the interval part are demonstrated.

Bivariate Pareto–Feller Distribution Based on Appell Hypergeometric Function

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate distribution based on the Appell hypergeometric function with marginal Pareto–Feller distributions obtained from two independent gamma random variables. The proposed distribution has the beta prime marginal distributions as special case, which were obtained using a Kibble-type bivariate gamma distribution, and the stochastic representation was obtained by the quotient of a scale mixture of two gamma random variables. This result can be viewed as a generalization of the standard bivariate beta I (or inverted bivariate beta distribution). Moreover, the obtained bivariate density is based on two confluent hypergeometric functions. Then, we derive the probability distribution function, the cumulative distribution function, the moment-generating function, the characteristic function, the approximated differential entropy, and the approximated mutual information index. Based on numerical examples, the exact and approximated expressions are shown.