Probability Distribution Research Articles

Simulation of adaptive immune receptors and repertoires with complex immune information to guide the development and benchmarking of AIRR machine learning.

Machine learning (ML) has shown great potential in the adaptive immune receptor repertoire (AIRR) field. However, there is a lack of large-scale ground-truth experimental AIRR data suitable for AIRR-ML-based disease diagnostics and therapeutics discovery. Simulated ground-truth AIRR data are required to complement the development and benchmarking of robust and interpretable AIRR-ML methods where experimental data is currently inaccessible or insufficient. The challenge for simulated data to be useful is incorporating key features observed in experimental repertoires. These features, such as antigen or disease-associated immune information, cause AIRR-ML problems to be challenging. Here, we introduce LIgO, a software suite, which simulates AIRR data for the development and benchmarking of AIRR-ML methods. LIgO incorporates different types of immune information both on the receptor and the repertoire level and preserves native-like generation probability distribution. Additionally, LIgO assists users in determining the computational feasibility of their simulations. We show two examples where LIgO supports the development and validation of AIRR-ML methods: (i) how individuals carrying out-of-distribution immune information impacts receptor-level prediction performance and (ii) how immune information co-occurring in the same AIRs impacts the performance of conventional receptor-level encoding and repertoire-level classification approaches. LIgO guides the advancement and assessment of interpretable AIRR-ML methods.

Best fitting probability distributions of monthly rainfall extremes in Nasiriyah city, southern Iraq

Best fitting probability distributions of monthly rainfall extremes in Nasiriyah city, southern Iraq

Metropolis-Hastings Algorithms based on a Zero-inflated Poisson Model

The Metropolis-Hastings algorithm is a well-proven Markov Chain Monte Carlo (MCMC) technique for generating sequences of random samples from probability distributions difficult to sample directly. In this article, we develop two versions of the Metropolis-Hastings algorithm Independent Metropolis and Random-Walk Metropolis and integrate them with a zero-inflated Poisson model to calculate the percentage of children among widowed women in Manchester, 2021. The excess of zeros in the data are estimated using a zero-inflated Poisson distribution. So we calculate both Metropolis-Hastings algorithms for estimation of the parameters of the model such as the Poisson rate parameter and the zero-inflation parameter. Using these algorithms we have shown that the zero-inflated Poisson model estimates are quite consistent with observed data and hence useful for modelling count data with excess zeros. These observations indicate that Independent Metropolis and Random-Walk Metropolis methods both fit the model parameters correctly, with Random-Walk Metropolis resulting in stable convergence.

Assessment of environmental impacts of heavy metal pollution in rice in Nanning, China

Nowadays rice has become one of the world’s staple foods. Rice in southern China is also a staple food for everyone, however, with the development of China’s industrialization model, many industrial areas may be contaminated by heavy metals, leading to contamination of the agricultural areas. With the development of recent years, Nanning has become a heavily industrial development area, and rice is also a favourite staple food. Therefore, it is a matter of concern to detect whether heavy metals contaminate rice in Nanning due to environmental factors. Five administrative villages were selected from 12 districts, and 20% of the natural villages were randomly selected for soil and water sample taking using probability distribution points and making the number of samples in each village evenly distributed. The single gene index pollution method and Nemerow composite pollution index method was used to evaluate whether heavy metals polluted the crops. Rice was evaluated through the national standard of Food Safety and Food Contaminant Limits. The survey shows that the heavy metal pollution of rice is moderate, especially cadmium pollution is more serious, but the risk of environmental factors in the Nanning area has a small impact on the overall safety and quality of rice, which is still within the controllable range. The total exceedance rate of heavy metals in the surveyed local rice was 20.95%, and the exceedance rate of paddy rice was 33.33%. The exceedance rates of lead, cadmium, inorganic arsenic, and total mercury in rice were 2.23%, 17.88%, 0.56%, and 0.84% respectively. Cadmium was identified as the primary heavy metal contaminant in local rice, with the highest detected concentration reaching 1.23 mg/kg, which is 6.15 times above the limit set by national health standards. This study shows that the concentration of heavy metals in the environment of Nanning Province is low, and the risk caused by environmental factors has relatively little impact on the safety and quality of rice. However, since the pollution of heavy metals will continue to enrich the food chain with time, long-term use will also cause harm to the human body. Therefore, it is necessary to raise the attention of local governments in rice-producing areas to food safety, and then take effective measures to improve local heavy metal detection technology, improve crop quality, and protect people’s food safety.

Comparing Summed Probability Distributions of Shoreline and Radiocarbon Dates from the Mesolithic Skagerrak Coast of Norway

By developing a new methodology for handling and assessing a large number of shoreline dated sites, this paper compares the summed probability distribution of radiocarbon dates and shoreline dates along the Skagerrak coast of south-eastern Norway. Both measures have previously been compared to elucidate demographic developments in Fennoscandia, but these have not been based on probabilistic methods for shoreline dating. The findings indicate a largely diverging development of the two data sets through the Mesolithic. The number of shoreline dated sites undergoes some process of overall decrease through the period, while the radiocarbon data is characterised by a lacking signal in the earliest parts of the period and then undergoes a logistic growth that quickly plateaus and remains stable for the remainder of the period. The precise nature of this discrepancy will necessitate further substantiation and the method of shoreline dating itself still requires further testing and assessment. Having noted this, we still tentatively suggest that while the number of shoreline dated sites is not devoid of influence from a demographic signal, this measure could be more heavily influenced by mobility patterns. Conversely, we also suggest that the lacking radiocarbon data from the earliest part of the Mesolithic is in part the result of mobility patterns, but that the radiocarbon data could be reflecting population dynamics more directly.

Bayesian-Based Standard Values of Effective Friction Angle for Clayey Strata

In this study, a methodology using probabilistic distribution techniques to determine the parameters of the soil’s effective internal friction angle (φ’) was proposed. The method was grounded in quantitative survey information extracted from geotechnical reports. Extensive equivalent samples were estimated using Markov chain Monte Carlo (MCMC) simulations and probability density functions (PDFs). The effective internal friction angle (φ’) of silty clay layers was probabilistically characterized using the plasticity index (PI), in situ static cone penetration test (qc), and standard penetration test (NSPT). A systematic quantitative analysis integrated prior information from different sources was systematically integrated with sampling data. By establishing a Bayesian framework that incorporated the regression relationship and uncertainties associated with the effective internal friction angle (φ’), the model ensured balance and symmetry in the treatment of prior information and observed data. The model was then transformed into equivalent sample values based on three models, reflecting the symmetrical consideration of different data sources. Further considerations involved correcting the three different analysis methods. A comparison of equivalent sample values with the mean values of the sampling data, along with the parameter optimization updates, was performed by combining the three models. Using three sets of sampling data, a linear relationship model for the new soil parameters was derived. The analysis results demonstrated that the proposed method could obtain equivalent samples for the effective internal friction angle.

Volcano‑tectonic seismicity and related hazard: a component of the multi‑hazard assessment in the highly exposed region of Mt. Etna (Italy)

In this study, seismic hazard, a component of the multi‑hazard assessment studied in the framework of the PANACEA project, was performed following the probabilistic approach (PSHA) based on historical macroseismic data. This approach uses intensity site observations to compute the seismic history for each investigated locality. Site seismic histories completeness are improved the integrating observed intensities with “virtual” values calculated according to attenuation laws, starting from the earthquake parameters (epicentre and epicentral intensity). The probability distribution of the expected intensities at a given site is calculated for exposure times of 10, 30 and 50 years. Results are given as reference intensity and peak ground acceleration for a chosen exceeding probability. In order to obtain hazard also in terms of expected peak ground acceleration (PGA) a relation between macroseismic intensity and ground acceleration calibrated for Mt. Etna was also developed. A PGA value was predicted for each intensity site observation using a specific ground motion model for Mt. Etna shallow events, assuming a soil class A. We tested the performance of the obtained relationship through synthetic and observed PGAs associated with the most energetic seismic event instrumentally recorded at Etna. Finally, the probability distribution for PGA at the site for a given exposure time results from the combination of the corresponding seismic hazard curve for the macroseismic intensity and the specific local intensity‑PGA relationship.

Exploring the New Exponentiated Inverse Weibull Distribution: Properties, Estimation, and Analysis via Classical and Bayesian Approaches

The “New Exponentiated Inverse Weibull” (NEIW) distribution is a novel probability distribution with versatile applications in reliability engineering, survival analysis, and related fields. This study explores the properties of the NEIW distribution, including moments, hazard function behavior, and reliability measures, through rigorous theoretical analysis and simulation studies. Additionally, maximum likelihood estimators (MLEs) for NEIW parameters are investigated via simulation studies to evaluate their performance under various scenarios. Empirical analysis using real-world data sets demonstrates the applicability of the NEIW model in capturing the underlying data structure and extracting meaningful insights. Parameter estimation and analysis are conducted using classical and Bayesian approaches, showcasing the robustness and flexibility of the NEIW distribution. The latest Bayesian analysis software STAN is used to perform the Bayesian analysis using Hamiltonian Monte Carlo (HMC) under No-U-Turn Sampler (NUTS). Overall, this research contributes to the advancement of statistical modeling and analysis by providing a comprehensive framework for utilizing the NEIW distribution in practice, with implications for diverse fields and potential for further exploration and innovation.

Gaussian Process Regression with Soft Equality Constraints

This study introduces a novel Gaussian process (GP) regression framework that probabilistically enforces physical constraints, with a particular focus on equality conditions. The GP model is trained using the quantum-inspired Hamiltonian Monte Carlo (QHMC) algorithm, which efficiently samples from a wide range of distributions by allowing a particle’s mass matrix to vary according to a probability distribution. By integrating QHMC into the GP regression with probabilistic handling of the constraints, this approach balances the computational cost and accuracy in the resulting GP model, as the probabilistic nature of the method contributes to shorter execution times compared with existing GP-based approaches. Additionally, we introduce an adaptive learning algorithm to optimize the selection of constraint locations to further enhance the flexibility of the method. We demonstrate the effectiveness and robustness of our algorithm on synthetic examples, including 2-dimensional and 10-dimensional GP models under noisy conditions, as well as a practical application involving the reconstruction of a sparsely observed steady-state heat transport problem. The proposed approach reduces the posterior variance in the resulting model, achieving stable and accurate sampling results across all test cases while maintaining computational efficiency.

Maximally entangled gluons for any x

Individual quarks and gluons at small x inside an unpolarized hadron can be regarded as Bell states in which qubits in the spin and orbital angular momentum spaces are maximally entangled. Using the machinery of quantum information science, we generalize this observation to all values 0<x<1 and describe gluons (but not quarks) as maximally entangled states between a qubit and a qudit. We introduce the conditional probability distribution P(lz|sz) of a gluon’s orbital angular momentum lz given its helicity sz. Restricting to the three states lz=0,±1, which constitute a qutrit, we explicitly compute P as a function of x. Published by the American Physical Society 2025

Pharmacology Students' Perception of the Use of Animals Prior to Laboratory Practice

Aims: Technological development in computing and biochemistry has allowed the development of teaching tools that are useful in the teaching-learning process. In this descriptive-inferential work, the perception of Pharmaceutical Biological Chemistry (QFB) degree regarding the use of animals in their laboratory practices was evaluated, taking as a reference the practice of testing drugs with hypoglycemic effect. Study Design: The design of the study was descriptive inferential. Place and Duration of Study: The study was realized in FES Zaragoza, UNAM, with Biology Pharmaceutical Chemist student careers between february to may in 2024. Methodology: In this work, an evaluation instrument was designed and developed and that was validated by expert criteria and that was applied to 132 students prior to carrying out the practice in the laboratory. The applied evaluation instrument contained 3 questions aimed at knowing this perception of the students. Results: The results present a binomial distribution probability greater than 0.99 in favor of reducing or replacing research animals with computer simulators. Conclusion: The students consider that is possible to replacement or to reduce the animal research in teaching laboratory.

High-Dimensional Expected Shortfall Regression

Expected shortfall is defined as the average over the tail below (or above) a certain quantile of a probability distribution. Expected shortfall regression provides powerful tools for learning the relationship between a response variable and a set of covariates while exploring the heterogeneous effects of the covariates. In the health disparity research, for example, the lower/upper tail of the conditional distribution of a health-related outcome, given high-dimensional covariates, is often of importance. Under sparse models, we propose the lasso-penalized expected shortfall regression and establish non-asymptotic error bounds, depending explicitly on the sample size, dimension, and sparsity, for the proposed estimator. To perform statistical inference on a covariate of interest, we propose a debiased estimator and establish its asymptotic normality, from which asymptotically valid tests can be constructed. We illustrate the finite sample performance of the proposed method through numerical studies and a data application on health disparity.

Probabilistic model for ultimate displacement of reinforced concrete columns with flexural failure

AbstractIn order to describe the probabilistic characteristics of the ultimate displacement, a probabilistic model for ultimate displacement of reinforced concrete columns with flexural failure was proposed based on the Bayesian theory and the Markov Chain Monte Carlo (MCMC) method. An analytical model for probabilistic ultimate displacement was established first according to the plane cross‐section assumption and the equivalent plastic hinge theory. Then probabilistic model parameters were determined based on the Bayesian theory and the MCMC method. Finally, the proposed model was verified by comparison with 252 sets of experimental data and existing ultimate displacement models. Comparisons show that the proposed model not only provides reasonable prediction accuracy but also describes the probability distribution of ultimate displacement realistically. Furthermore, the proposed model is useful for the validation of the accuracy and applicability of available deterministic ultimate displacement models, which provide probabilistic validation methods based on the confidence interval and probability density function.

Uncovering dissipation from coarse observables: A case study of a random walk with unobserved internal states.

Inferring underlying microscopic dynamics from low-dimensional experimental signals is a central problem in physics, chemistry, and biology. As a trade-off between molecular complexity and the low-dimensional nature of experimental data, mesoscopic descriptions such as the Markovian master equation are commonly used. The states in such descriptions usually include multiple microscopic states, and the ensuing coarse-grained dynamics are generally non-Markovian. It is frequently assumed that such dynamics can nevertheless be described as a Markov process because of the timescale separation between slow transitions from one observed coarse state to another and the fast interconversion within such states. Here, we use a simple model of a molecular motor with unobserved internal states to highlight that (1) dissipation estimated from the observed coarse dynamics may significantly underestimate microscopic dissipation even in the presence of timescale separation and even when mesoscopic states do not contain dissipative cycles and (2) timescale separation is not necessarily required for the Markov approximation to give the exact entropy production, provided that certain constraints on the microscopic rates are satisfied. When the Markov approximation is inadequate, we discuss whether including memory effects can improve the estimate. Surprisingly, when we do so in a "model-free" way by computing the Kullback-Leibler divergence between the observed probability distributions of forward trajectories and their time reverses, this leads to poorer estimates of entropy production. Finally, we argue that alternative approaches, such as hidden Markov models, may uncover the dissipative nature of the microscopic dynamics even when the observed coarse trajectories are completely time-reversible.

A Bayesian Interpretation of CABANA and Other Randomized Controlled Trials for Catheter Ablation in Patients With Atrial Fibrillation.

Catheter ablation improves symptoms and quality of life in atrial fibrillation patients, but its effect on adverse cardiovascular outcomes and mortality remains uncertain. Bayesian analysis of randomized controlled trials offers a deeper understanding of treatment effects beyond conventional p-value thresholds. We conducted a post hoc Bayesian reanalysis of CABANA and four similar trials to estimate catheter ablation's effect on cardiovascular and survival outcomes. Using publicly available, trial-level data, we fitted ordinal Bayesian regression models to assess the impact of catheter ablation on the primary composite outcome-comprising all-cause mortality, stroke with disability, serious bleeding, and cardiac arrest-as well as mortality alone. We considered two sets of prior distributions: (1) a noninformative prior, where all effect sizes are equally probable and inference is primarily based on trial data, and (2) a treatment effect distribution derived from four trials using a random effects model. In this analysis, refined probability distributions for treatment effects were obtained by integrating data from CABANA with diverse priors through Bayes' theorem, offering a novel, nuanced probabilistic understanding of the potential impact of ablation compared with medical therapy on cardiovascular outcomes and all-cause mortality. In contrast to CABANA's original frequentist estimates, which were inconclusive, Bayesian analyses indicated probabilities of 82.6% and 81.1% that ablation is superior in reducing adverse cardiovascular outcomes and mortality, respectively. Incorporating results from four other similar trials increased the probability of improved effects on mortality to 86.0%. Bayesian analysis augmented the interpretation of previously inconclusive findings, suggesting a clinically relevant probability of benefit from catheter ablation compared to medical therapy in a broad population with atrial fibrillation.

Relaxation dynamics of a mixed ferrimagnetic Ising system with random anisotropy

The relaxation dynamics of a mixed spin-1/2 and spin-1 ferrimagnetic Ising system with random anisotropy has been investigated using Onsager’s theory of irreversible thermodynamics. The magnetic Gibbs energy production, arising due to irreversible processes, is computed using the equilibrium mean-field Gibbs energy, based on the variational principle and the Gibbs–Bogoliubov inequality. In the framework of linear response theory, the time derivatives of the sublattice magnetizations are treated as fluxes conjugate to their corresponding generalized forces. Two relaxation times are computed, and their dependence on temperature and crystal field variances is examined near phase transition points for four distinct topologies, each corresponding to different phase diagrams. These phase diagrams emerge from random anisotropy drawn from a bimodal probability distribution: P(Δi)=12δ(Δi-Δ(1+α))+δ(Δi-Δ(1-α)). One of the relaxation times, denoted as τ1, increases rapidly and diverges near the critical and tricritical points separating the ferrimagnetic and paramagnetic phases. For α≥0, critical slowing down, characterized by the divergence of τ1, is observed near the isolated ordered critical points between the ferrimagnetic and disorder-induced ferrimagnetic phases. Finally, the variance of the relaxation times is analyzed across regions of crystal field and temperature, as well as the values of α at which re-entrant phenomena occur, due to the competing interactions in the random system.

Robust stochastic optimisation strategies for locoregional hyperthermia treatment planning using polynomial chaos expansion

Objective.Conventional temperature optimization in hyperthermia treatment planning aims to maximize tumour temperature (e.g.T90; the temperature reached in at least 90% of the tumour) while enforcing hard constraints on normal tissue temperature (max(Ttissue) ⩽45 °C). This method generally incorrectly assumes that tissue/perfusion properties are known, typically relying on average values from the literature. To enhance the reliability of temperature optimization in clinical applications, we developed new robust optimization strategies to reduce the impact of tissue/perfusion property uncertainties.Approach.Within the software package Plan2Heat, temperature calculations during optimization apply efficient superposition of precomputed distributions, represented by a temperature matrix (T-matrix). We extended this method using stochastic polynomial chaos expansion models to compute an averageT-matrix (Tavg) and a covariance matrixCto account for uncertainties in tissue/perfusion properties. Three new strategies were implemented usingTavgandCduring optimization: (1)Tavg90 maximization, hard constraint on max(Ttissue), (2)Tavg90 maximization, hard constraint on max(Ttissue) variation, and (3) combinedTavg90 maximization and variation minimization, hard constraint on max(Ttissue). Conventional and new optimization strategies were tested in a cervical cancer patient. 100 test cases were generated, randomly sampling tissue-property probability distributions. TumourT90 and hot spots (max(Ttissue) >45 °C) were evaluated for each sample.Main Results.Conventional optimization had 28 samples without hot spots, with a medianT90 of 39.7 °C. For strategies (1), (2) and (3), the number of samples without hot spots was increased to 33, 41 and 36, respectively. MedianT90 was reduced lightly, by ∼0.1 °C-0.3 °C, for strategies (1-3). Tissue volumes exceeding 45 °C and variation in max(Ttissue) were less for the novel strategies.Significance.Optimization strategies that account for tissue-property uncertainties demonstrated fewer, and reduced in volume, normal tissue hot spots, with only a marginal reduction in tumourT90. This implies a potential clinical utility in reducing the need for, or the impact of, device setting adjustments during hyperthermia treatment.

Computer modeling of the synthesis of styrene–butadiene rubber: Influence of the feed of a chain transfer agent on the characteristics of the product

Objectives. To develop mathematical approaches and algorithms for analyzing the influence of various methods for feeding a chain transfer agent to a cascade of reactors, taking into account the choice of feed points on the characteristics of the final product of copolymerization using computer modeling.Methods. The processes of synthesis of copolymers were mathematically modeled using a statistical approach (Monte Carlo method). The developed algorithm is based on calculating the probabilities of elementary reactions in the process under study. In the case of continuous production of the copolymer in a cascade of reactors, it must be taken into account that the residence time of each particle of the reaction mixture in the reactor is subject to a probability distribution. The algorithm models the formation of copolymer macromolecules at the particle level, permitting the average molecular characteristics of the copolymer to be calculated and its microstructure to be studied based on modeling results.Results. The dependencies of the intrinsic viscosity on the reactor number and conversion were constructed by means of mathematical modeling. The calculation results showed satisfactory agreement with the experimental data obtained in production. The dependencies of the molecular weight distribution of the copolymer, the weight-average molecular weight, and the microheterogeneity index on the reactor number were constructed for various methods of feed of the chain transfer agent, i.e., to two and/or three points of the reactor cascade. The modeling and calculation results confirmed the influence of the method of adding the chain transfer agent to the cascade reactors on the molecular characteristics of the copolymer.Conclusions. The analysis of the structure of the molecular units of the styrene–butadiene copolymer showed a decrease in the weightaverage molecular weight of the final product and an increase in its stiffness in the case of the three-point feed of the chain transfer agent.

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 article 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 CoIR. 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.

Robust discrimination between closely related species of salmon based on DNA fragments.

Closely related species of Salmonidae, including Pacific and Atlantic salmon, can be distinguished from one another based on nucleotide sequences from the cytochrome c oxidase sub-unit 1 mitochondrial gene (COI), using ensembles of fragments aligned to genetic barcodes that serve as digital proxies for the relevant species. This is accomplished by exploiting both the nucleotide sequences and their quality scores recorded in a FASTQ file obtained via Next Generation (NextGen) Sequencing of mitochondrial DNA extracted from Coho salmon caught with hook and line in the Gulf of Alaska. The alignment is done using MUSCLE (Muscle 5.2) (Edgar in Nat Commun 13:6968, 2022), applied to multiple versions of each fragment perturbed according to the nucleobase identification error probabilities underlying the quality scores. The Damerau-Levenshtein distance was used to determine the genetic barcode of the candidate species that is closest to each aligned, perturbed fragment. The "votes" that the sampled fragments cast for the different candidate species are then pooled and converted into identification probabilities, using weights determined by the entropy of the fragment-specific identification probability distributions. This novel approach to quantify the uncertainty associated with measurements made using NextGen Sequencing can be applied to discriminate closely related species, hence to value-assignment for reference materials supporting determinations of the authenticity of seafood, for example, NIST Reference Materials 8256 and 8257 (Coho salmon) (Ellisor et al., 2021).