Distribution Theory Research Articles

Estimating the Sampling Distribution of Posterior Decision Summaries in Bayesian Clinical Trials.

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate conditioning on a given set of parameters. These operating characteristics are commonly obtained via simulation studies. The utility of Bayesian measures, such as "assurance," that incorporate uncertainty about model parameters in estimating the probabilities of various decisions in trials has been demonstrated. However, the computational burden remains an obstacle toward wider use of such criteria. In this article, we propose methodology which utilizes large sample theory of the posterior distribution to define parametric models for the sampling distribution of the posterior summaries used for decision making. The parameters of these models are estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward the assessment of conditional and marginal operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based. It enables formal incorporation of uncertainty about the trial assumptions via a design prior and significantly reduces the computational burden for the design of Bayesian trials ingeneral.

Study of gluon GPDs in exclusive J/ψ production in electron-proton scattering

Exclusive photoproduction of heavy J/ψ meson is performed within the handbag factorization method. The general parton distributions (GPDs) for gluons, which are an essential ingredient here, are constructed using double distribution (DD) representation. The calculated cross section for few sets of gluon GPDs Hg describe fine J/ψ production experimental data from HERA to LHC energies. Based on this approach we estimate J/ψ spin asymmetries determined by Eg and H˜g. The GPDs factorization approach can be employed to analyze heavy vector meson production in electron-proton scattering. Investigations of this reactions at future electron-ion colliders in USA and China can give essential information on gluon GPDs. Published by the American Physical Society 2024

An Integrated Multi-Model Framework Utilizing Convolutional Neural Networks Coupled with Feature Extraction for Identification of 4mC Sites in DNA Sequences

N4-methylcytosine (4mC) is a chemical modification that occurs on one of the four nucleotide bases in DNA and plays a vital role in DNA expression, repair, and replication. It also actively participates in the regulation of cell differentiation and gene expression. Consequently, it is important to comprehend the role of 4mC in the epigenetic regulation for revealing the complications of the gene expression and their associated governing cellular operations. However, the inherent resource requirements and time constraints of the experimental procedure, present challenges to the cellular culture process. While data-driven methodologies present promising solutions to mitigate the demand for extensive experimental efforts, their performance relies on the suitability and existence of high-quality data. This study presents a multi-model framework that integrates convolutional neural network (CNN) with the distributed k-mer and embedding feature extraction techniques to enhance the identification of 4mC sites in DNA sequences. The integration of k-mers ensures the effective representation of the local sequence patterns, while the utilization of embedding enables a more holistic encoding by considering the broader context and semantics of the sequence data. Following the initial step, the obtained distributed representation of the DNA sequence seamlessly enters the CNN, triggering a crucial convolution operation wherein a set of adaptable filters systematically convolves across the sequence to detect vital local patterns. The proposed integrated multi-model framework was applied to six publicly available datasets and evaluated against the cutting-edge 4mCPred, 4mCCNN, iDNA4mC, Meta-4mCpred, DeepTorrent, 4mCPred-SVM, and DMKL-HFIS methods. The evaluation was based on accuracy, specificity, sensitivity, and Matthews Correlation Coefficient. The results demonstrated that the proposed multi-model framework outperformed the state-of-the-art methods, as well as one-hot encoding and the hybrid of one-hot & TNC features, in accurately identifying 4mC sites.

A Multi-Scale Model for Predicting Physically Short Crack and Long Crack Behavior in Metals

The fatigue behavior of metal specimens is influenced by defects, material properties, and loading. This study aims to establish a multi-scale fatigue crack growth model that describes physically short crack (PSC) and long crack (LC) behavior. The model allows the calculation of crack growth rates for uniaxial loading at different stress ratios based on the material properties and specimen geometry. Furthermore, the model integrates the Gaussian distribution theory to consider material heterogeneity and the experimental measurement errors that cause fatigue scatter. The crack growth rate and fatigue life of metal specimens with different notch geometry were predicted. The curves generated by the multi-scale model were mainly consistent with the test data from the published literature at the PSC and LC stages.

Statistical Distribution Theory and Fractional Calculus

This is an overview paper. This paper is an attempt to show that fractional calculus can be reached through statistical distribution theory. This paper brings together results on fractional integrals and fractional derivatives of the first and second kinds in the real and complex domains in the scalar, vector, and matrix-variate cases, and shows that all these results can be reached through statistical distribution theory. It is shown that the whole area of fractional integrals can be reached through distributions of products and ratios in the scalar variable case and distributions of symmetric products and symmetric ratios in the matrix-variate cases. While summarizing the materials, the real domain results are also listed side by side with the complex domain results so that a comparative study is possible. Fractional integrals and derivatives in the real domain mean that the parameters involved could be real or complex with appropriate conditions, the arbitrary function is real-valued, and the variables involved are all real. These in the complex domain mean that the parameters could be real or complex and the arbitrary function is still real-valued but the variables involved are in the complex domain. Fully complex domain means the variables as well as the arbitrary function are in the complex domain. Most of the materials on fractional integrals and fractional derivatives involving a single matrix or a number of matrices in the real or complex domain are of this author. Slight modifications of the results, compared with the published works in various papers, are there in various sections. In the paragraph on notations, the lemmas that are taken from this author’s own book on Jacobians are common with published works and hence the similarity index with this author’s works will be high. Section Matrix-Variate Joint Distributions and Fractional Integrals in Many Matrix-Variate Cases material on a statistical approach to Kiryakova’s multi-index fractional integral and its extension to the real scalar case of second kind integrals as well as extensions of first and second kind integrals to real and complex matrix-variate cases are believed to be new. Matrix differential operators are introduced in Section Fractional Derivatives and, with the help of these operators, fractional derivatives are constructed from the corresponding fractional integrals. These operators are applicable in a large variety of functions. Applicability is shown through identities created from scale transformed gamma random variables. Some concluding remarks are given and some open problems are pointed out in Section Concluding Remarks.

A Method for Analyzing Transverse Stress in Link Slabs of Simply Supported Steel–Concrete Composite Bridges

The cracking of link slabs in jointless bridges presents significant challenges due to the complexity of their stress conditions. This study focused on analyzing the transverse stresses in link slabs of jointless steel–concrete composite bridges. Utilizing linear elasticity theory and partial differential equations of plates, the deflection and stress distribution functions for the link slabs were determined. The validity of these analytical solutions was confirmed through comparisons with finite element models and load tests. Results from both the load tests and the finite element model indicate that the upper face of the girder end link slabs experiences maximum tensile stresses in both transverse and longitudinal directions. The stress values obtained from the analytical method align well with these results, showing that the total stress, when considering transverse stresses, reaches 107% of the longitudinal stresses alone. Furthermore, a 40% reduction in longitudinal girder spacing or a 50% increase in girder end length can lead to link slab stresses of 128% and 145% of the longitudinal stresses, respectively. This finding suggests that even loads lower than those designed based solely on longitudinal stresses can result in cracking. Therefore, it is recommended that transverse stresses be considered in the design of link slabs for jointless bridges. Relying solely on conventional longitudinal stress analyses may underestimate actual stress conditions and contribute to the formation of cracks.

Theoretical research on load distribution of composite pre-tightened teeth connections embedded with soft layers

Abstract It has been proved by experiments that the soft layers can effectively adjust the load distribution ratio of composite pre-tightened tooth connection, but theoretical research on the composite pre-tightened tooth connection embedded with soft layers has not been carried out. Therefore, in this work, the load distribution theory of composite pre-tightened tooth connection embedded with soft layers is studied by spring stiffness method. First, based on deformation compatibility condition, the theoretical calculation formula of load distribution ratio of each tooth is derived by spring stiffness method. Then, load distribution ratio is obtained by experiments, and the theoretical calculation results are verified. Finally, through the derived formula, the load distribution ratio of the composite pre-tightened tooth connection embedded with soft layers is parameterized. Research shows that (1) The theoretical value is in good agreement with the experimental value, and the maximum error of calculation result of the load distribution of the joint is 8%; (2) Under the action of soft layers, each tooth of two-teeth and three-teeth joints are damaged at the same time, the ultimate bearing capacity is increased by 29.0 and 21.6%, respectively, compared with the traditional two-teeth and three-teeth joints; (3) The elastic modulus and thickness of soft layers have a significant impact on the load distribution ratio of each tooth.

A Biogeographical Debate at the Origins of Limnology in Switzerland and Italy: The Issue over Pelagic Fauna Between Pietro Pavesi and François-Alphonse Forel.

This article explores the early biogeographical debates that shaped the beginning of limnology, focusing on the differences of opinion concerning the origins of pelagic fauna between two pioneering scientists: Pietro Pavesi and François-Alphonse Forel. The study examines how Pavesi's hypothesis of a marine origin for pelagic fauna contrasts with Forel's theory of passive distribution, situating their arguments within a broader Darwinian framework. The first part of the paper provides a historical overview of Italian limnology, highlighting Pavesi's contributions and interpreting Forel's writings to underscore the significance of discovering pelagic fauna in conceptualizing lakes as microcosms. The second part compares Pavesi's and Forel's hypotheses, emphasizing their impact on the scientific understanding of freshwater ecosystems. The importance of this discovery, in both historical and scientific contexts, lies in recognizing the presence of plankton in lakes as a crucial element for the mature formulation of ecological concepts, such as the ecosystem.

Likelihood Ratio Test For The Multivariate Normal Generalized Variance

An interesting measure of variability in multivariate populations is the determinant of the covariance matrix Σp×p, denoted as |Σ|, commonly referred to as generalized variance. This measure succinctly captures the dispersion of a multivariate population into a single value, while accounting for inter-variable dependencies. Consequently, it finds applications across various domains concerned with assessing dispersion within multivariate populations of interest. In this study, we introduce a likelihood ratio test for the generalized variance of multivariate normal distributions, accompanied by a theoretical exposition on the distribution theory of sample generalized variances. We propose both the Likelihood Ratio Test (LRT) and the Bartlett-Corrected Likelihood Ratio Test (BCLRT) for assessing the hypothesis that the generalized variance equals a parameter η, where η ∈ R. The development of these tests is purely theoretical. Our recommendation is to employ the BCLRT test primarily in scenarios where p = 2, particularly when n > 30. As for the LRT test, we suggest its application in cases where p = 2 or p = 3, provided that n > 30, and for p = 5 when n > 50.

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.

THE ‘MATERIAL EXPENSES’ APPROACH TO THE THEORY OF VALUE AND DISTRIBUTION IN THE WEALTH OF NATIONS

The paper discusses the influence of physiocratic ideas on Adam Smith’s approach to the theory of value and distribution in The Wealth of Nations (WN). It is shown that Smith attempted to elaborate on the contributions of the Physiocrats by adopting elements of two different approaches to the theory of value and distribution which he found in their writings: A material-based approach and a labor-based one. While tentatively proposing a labor theory of value, Smith also retained elements of the material expenses approach which he had inherited from his precursors. The paper specifically draws attention to some tensions and inconsistencies that arise from the simultaneous presence of the two different approaches to the theory of value and distribution in the WN.

ADAM SMITH’S THEORY OF VALUE AND THE FALLING RATE OF PROFIT: UNCOMMON CONCEPTIONS AND COMMON MISCONCEPTIONS

Smith’s theory of value and distribution, which emphasizes labor time as the determinant of prices, has been widely misunderstood. Ricardo misinterpreted it as relevant only to primitive societies, while Marx inaccurately aligned it with his own labor theory of value. In reality, Smith’s perspective oscillates between a labor-based and a labor-commanded approach to relative prices, intended for modern economies. Neoclassical economists further distorted Smith’s views by incorporating utility theory. Moreover, while Smith is often linked to the theory of a falling rate of profit due to competition, he actually attributed it to rising capital intensity. Contrary to the belief that Smith was a staunch advocate of free markets, he supported reasonable government intervention.

Circular vs One-Way Production Processes: Two Different Views on Production and Income Distribution

ABSTRACT This paper examines two distinct representations of production processes: circular production, where commodities function as both inputs and outputs, and one-way production, which starts with factors of production and ends with finished goods. These frameworks offer different views on profits. In circular systems, profits arise from surplus production, while in one-way systems, they appear to emerge from price differences between final goods and inputs. Using Sraffa’s price equations, we analyse the properties of both systems. We demonstrate that while one-way systems seem to allow for profit increases by raising prices, this is an illusion as it ultimately reduces real wages, the true source of profits. Additionally, we show that one-way systems become circular when real wages are fixed. Finally, the paper discusses how this distinction is important in understanding the shift from Walras’ general equilibrium theory to neo-Walrasian formulations. This study highlights the importance of circularity in the functioning of capitalist economies and its implications for the theory of distribution.

Research on extreme value estimations and dynamic coefficients of wheel load for high-speed railway based on generalized Pareto distribution theory

The design value of wheel load is one of the key design parameters for high-speed railway ballastless track structure, which essentially belongs to the extreme estimation of wheel load. Based on the generalized Pareto distribution theory, this article carries on the research on the extreme value estimations of wheel load excited by whole wavelength range irregularity, which provides a basis for the design of ballastless track structure. When using automatic threshold selection method, sample declustering can improve the independence between data. The shape parameter screening method is proposed for the extreme value estimations of wheel load, and the corresponding sample size and shape parameter range for each cluster are determined. A reasonable sample size is determined, and the mean of the extreme estimations of wheel load is used as the final extreme estimation of wheel load. The dynamic coefficients that match the design life of the ballastless track structure are obtained.

A Three-Dimensional Modeling Approach for Carbon Nanotubes Filled Polymers Utilizing the Modified Nearest Neighbor Algorithm.

Carbon nanotubes (CNTs) are extensively utilized in the fabrication of high-performance composites due to their exceptional mechanical, electrical, and thermal characteristics. To investigate the mechanical properties of CNTs filled polymers accurately and effectively, a 3D modeling approach that incorporates the microstructural attributes of CNTs was introduced. Initially, a representative volume element model was constructed utilizing the modified nearest neighbor algorithm. During the modeling phase, a corresponding interference judgment method was suggested, taking into account the potential positional relationships among the CNTs. Subsequently, stress-strain curves of the model under various loading conditions were derived through finite element analysis employing the volume averaging technique. To validate the efficacy of the modeling approach, the stress within a CNT/epoxy resin composite with varying volume fractions under different axial strains was computed. The resulting stress-strain curves were in good agreement with experimental data from the existing literature. Hence, the modeling method proposed in this study provides a more precise representation of the random distribution of CNTs in the matrix. Furthermore, it is applicable to a broader range of aspect ratios, thereby enabling the CNT simulation model to more closely align with real-world models.

Borel control and efficient numerical techniques to solve the Allen–Cahn equation governed by temporal multiplicative noise

In this manuscript, we investigate a stochastic version of the Allen–Cahn equation, which is a nonlinear partial differential equation from mathematical physics. The stochastic model considers temporal multiplicative noise in the form of the derivative of the standard Wiener process. The existence and the uniqueness of solutions for this stochastic model is established rigorously using the theory of distributions. As a corollary from these analytical results, some a priori optimal estimates for the solutions of this model are constructed. In this work, we develop reliable numerical schemes which possess similar features as those of the solutions for the analytical model. Moreover, we establish mathematically the von Neumann stability and the consistency for the schemes proposed in this paper. Both the analytical and numerical results derived in this work are computationally verified through some simulations.

3D Geological Modeling and Metallogenic Prediction of Kamust Sandstone-Type Uranium Deposit in the Eastern Junggar Basin, NW China

Sandstone-type uranium deposits hold significant value and promise within China’s uranium resource portfolio, with the majority of these deposits found at the junctions of basins and mountains within Mesozoic and Cenozoic basins. The Kamust uranium mining area, located in the eastern part of the Junggar Basin, represents a significant recent discovery. Prior research on this deposit has been confined to two-dimensional analyses, which pose limitations for a comprehensive understanding of the deposit’s three-dimensional characteristics. To address the issue of uranium resource reserve expansion, this study employs 3D geological modeling and visualization techniques, guided by uranium deposit models and mineral prediction methods. First, a 3D model database of the Kamust uranium deposit was constructed, comprising drill holes, uranium ore bodies, ore-controlling structures, interlayer oxidation zones, and provenance areas. This model enables a transparent and visual representation of the spatial distribution of favorable mineralization horizons, structures, stratigraphy, and other predictive elements in the mining area. Second, based on the three-dimensional geological model, a mineral prediction model was established by summarizing the regional mineralization mechanisms, ore-controlling factors, and exploration indicators. Combined with big-data technology, this approach facilitated the quantitative analysis and extraction of ore-controlling factors, providing data support for the three-dimensional quantitative prediction of deep mineralization in the Kamust uranium deposit. Finally, using three-dimensional weights of evidence and three-dimensional information-quantity methods, comprehensive information analysis and quantitative prediction of deep mineralization were conducted. One prospective area was quantitatively delineated, located east of the Kalasay monocline, which has been well-validated in geological understanding. The research indicates that the area east of the Kalasay monocline in the Kamust mining district has significant exploration potential.

Atomic Structure Simulation and Properties’ Prediction using Machine Learning on Neodymium Oxide Nanoparticles Zinc Tellurite Glasses Aided by FTIR and TEM Analysis

The optical, structural, and physical characteristics of zinc tellurite glasses doped with neodymium oxide nanoparticles, which are produced by the melt-quenching method, were examined in this work. The amorphous character of the glasses was verified by XRD analysis. Using the Pair Distribution Function (PDF) and Monte Carlo simulations and visualisation for precise molecule distribution representation, an intuitive Python interface was created to emphasize these features. The density increased with increasing Nd2O3 concentrations, from 5346 to 5606 kg/cm2. Density data was used to infer the molar volume. The best projected density was achieved by the Gradient Boosting Regressor model, with a R2 of 0.9988 and an RMSE of 0.0032; the best predicted molar volume was achieved by linear regression, with a R2 of 1 and an RMSE of 2.67e-15. These models successfully represent the correlations between dopant concentration and glass properties, advancing our knowledge of the optical properties for further glass technology research.

Convection-permitting climate model representation of severe convective wind gusts and future changes in southeastern Australia

Abstract. Previous research has suggested that the frequency and intensity of surface hazards associated with thunderstorms and convection, such as severe convective winds (SCWs), could potentially change in a future climate due to global warming. However, because of the small spatial scales associated with SCWs, they are unresolved in global climate models, and future climate projections are uncertain. Here, we evaluate the representation of SCW events in a convection-permitting climate model (Bureau of Meteorology Atmospheric Regional Projections for Australia, BARPAC-M) run over southeastern Australia for the months of December–February. We also assess changes in SCW event frequency in a projected future climate for the year 2050 and compare this with an approach based on identifying large-scale environments favourable for SCWs from a regional parent model (BARPA-R). This is done for three different types of SCW events that have been identified in this region, based on clustering of the large-scale environment. Results show that BARPAC-M representation of the extreme daily maximum wind gust distribution is improved relative to the gust distribution simulated by the regional parent model. This is due to the high spatial resolution of BARPAC-M output, as well as partly resolving strong and short-lived gusts associated with convection. However, BARPAC-M significantly overestimates the frequency of simulated SCW events, particularly in environments having steep low-level temperature lapse rates. A future decrease in SCW frequency under conditions with steep lapse rates is projected by BARPAC-M, along with less frequent favourable large-scale environments. In contrast, an increase in SCW frequency is projected under conditions of high surface moisture, with more frequent favourable large-scale environments. Therefore, overall changes in SCWs for this region remain uncertain, due to different responses between event types, combined with historical model biases.

Multivariate Scalar on Multidimensional Distribution Regression With Application to Modeling the Association Between Physical Activity and Cognitive Functions

ABSTRACTWe develop a new method for multivariate scalar on multidimensional distribution regression. Traditional approaches typically analyze isolated univariate scalar outcomes or consider unidimensional distributional representations as predictors. However, these approaches are suboptimal because (i) they fail to utilize the dependence between the distributional predictors and (ii) neglect the correlation structure of the response. To overcome these limitations, we propose a multivariate distributional analysis framework that harnesses the power of multivariate density functions and multitask learning. We develop a computationally efficient semiparametric estimation method for modeling the effect of the latent joint density on the multivariate response of interest. Additionally, we introduce a new conformal prediction algorithm for quantifying the uncertainty of our multivariate predictions based on subject characteristics and individualized distributional predictors, providing valuable insights into the conditional distribution of the response. We validate the effectiveness of our proposed method through comprehensive numerical simulations, clearly demonstrating its superior performance compared to traditional methods. The application of the proposed method is demonstrated on triaxial accelerometer data from the National Health and Nutrition Examination Survey 2011–2014 for modeling the association between cognitive scores across various domains and distributional representation of physical activity among the older adult population. Our results highlight the advantages of the proposed approach, emphasizing the significance of incorporating multidimensional distributional information in the triaxial accelerometer data.