Distribution Theory Research Articles

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.

Interactive multi-agent convolutional broad learning system for EEG emotion recognition

Electroencephalogram (EEG) emotion recognition is gaining significance in intelligent human–computer interaction. Multi-agent learning can capture more complete and reliable features, compensating for the lack of a single agent’s knowledge. However, previous EEG emotion recognition only focused on a single agent. Therefore, to extract effective features from high-dimensional EEG data, a novel interactive multi-agent (IMA) learning framework is proposed, and introduced into convolutional broad learning system (CNNBLS), then the interactive multi-agent convolutional broad learning system (IMA-CNNBLS) is proposed for EEG emotion recognition. It can effectively model high-dimensional EEG data, automatically extract EEG features related to emotions through convolutional neural network (CNN), and then extend the above features to a vast space to quickly extract generalized features through broad learning system (BLS), consider a CNNBLS as an agent, and multi-agent interact in the IMA part. As the theoretical basis of IMA-CNNBLS, the consistency is mathematically proved through the stationary distribution theory of Markov processes. To demonstrate the superiority of our proposed model, sufficient experiments are conducted on the DEAP, DREAMER and SEED datasets. The experimental results show the model can effectively improve the EEG emotion recognition accuracy, the best recognition performance is achieved on all datasets. In addition, our proposed model also shows the multi-agent interaction significantly affects EEG emotion recognition.

A novel asymmetric extension of power XLindley distribution: properties, inference and applications to engineering data

It is impossible to overstate the importance of using trigonometric functions appropriately in distribution theory. The main contribution of the research is to construct a flexible trigonometric extension of the power XLindley distribution. More specifically, we build an innovative two-parameter lifetime distribution known as the sine power XLindley distribution (SPXLD) using characteristics from the sine-generated family of distributions. As the main motivational fact, it provides an attractive alternative to the power Lindley, power XLindley, weighted Lindley, and extended power Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic and platkurtic nature. In contrast to the increasing, decreasing, and reversed-j-shaped hazard rate function, the density exhibits asymmetric shapes with varying peakedness levels. Several significant characteristics are illustrated, including moments, the quantile function, the probability density function in series representation, the stress-strength reliability, and incomplete moments. To analyze the behavior of the suggested distribution, sixteen estimation techniques are applied, such as the maximum likelihood, percentiles, some methods of minimum distances, some methods based on minimum and maximum spacing distances, and the Kolmogorov method. After that, an extensive simulation study and the examination of two survival real datasets are used to show the viability, usefulness, and adaptability of the SPXLD. Relevant goodness of fit criteria demonstrates that the SPXLD fits several current distributions.

Standard Errors for Two-Way Clustering with Serially Correlated Time Effects

Abstract We propose improved standard errors and an asymptotic theory for two-way clustered panels. Our theory allow for arbitrary serial dependence in the common time effects, which is excluded by existing two-way methods. Our asymptotic distribution theory is the first which allows for this level of inter-dependence. Under weak conditions, we demonstrate that OLS is asymptotically normal, our proposed variance estimator is consistent, and t-ratios are asymptotically standard normal. The results extend to two-way fixed-effect models; we argue that two-way clustering is still necessary even if two-way fixed effects are included. Simulation and empirical illustration are provided.

An ultrafast optical sensor for simultaneous detection of NH3 temperature and concentration based on ultraviolet absorption spectral redshift combined with spectral reconstruction

As a renewable and carbon-free fuel with high energy density, ammonia (NH3) is a promising alternative to fossil fuels. Real-time detection of its temperature and concentration is significant in improving NH3 combustion efficiency. In this paper, we report an optical sensor, which enables simultaneous measurement of temperature and concentration of NH3. The key idea is to acquire the temperature of NH3 through absorption spectral redshift, and determine its concentration by building three-dimensional field map combined with spectral reconstruction. Firstly, we explain the generation mechanism of temperature-induced redshift in ultraviolet differential absorption spectrum based on energy level distribution theory. The relationship between spectral redshift and temperature is then established using spectral autocorrelation algorithm. Secondly, a spectral reconstruction method based on absorbed intensity mapping wavelength is proposed to ensure real-time detection of NH3. Finally, a three-dimensional field map between temperature, reconstruction slope, and concentration is constructed to achieve the detection. Results indicated that the mean relative error in temperature measurement was 1.04% and the mean absolute error in concentration detection was 0.26mg/m3 in air. Additionally, the NH3 sensor enabled long-term detection with a detection limit of 15.50μg/m2, demonstrating its potential to broaden the application of NH3 as a fuel.

Comments on Nobuo Okishio’s review of Piero Sraffa’s Production of commodities by means of commodities (1960)

AbstractIn this note we scrutinize and comment on Nobuo Okishio’s review of Piero Sraffa’s Production of Commodities by Means of Commodities. We limit ourselves only to observations by Okishio which we consider debatable. These concern in particular his treatment of wages in the price equations, his interpretation of Sraffa’s Standard commodity and his criticism of the marginalist theory of value and distribution.

Reconstruction of ionospheric VTEC using empirical orthogonal function and its performance during extreme geomagnetic storm

This paper demonstrates that the spatial distribution of the ionospheric TEC over the Indian region can be reconstructed with appreciable accuracy using minimal numbers of empirical orthogonal functions as a basis. These basis functions were derived using the Singular Value Decomposition of a matrix composed of pragmatic vertical Total Electron Content (VTEC) values collected across varied ionospheric conditions and measured over the region of interest. The reconstruction was achieved by linearly combining the appropriately chosen significant bases with corresponding weight factors. The reconstruction accuracy of the algorithm was found to be better than 4 TECU (TECU = 1016 electrons/m2) for more than 99.9 % of the time when tested over the complete year of 2016 with only eight basis vectors. The containment factor, defined here, indicates the goodness of the chosen bases in representing the arbitrary VTEC distributions and is found to remain typically high, aiding in improved algorithm performance. The performance, however, was found to be sensitive to the seasons and geomagnetic conditions. Deteriorated performance was observed when tested for the St. Patrick's Day storm data. The deterioration was attributed to the structural alteration of the ionospheric plasma density and the presence of atypical modes during the storm. The results ascertain the prospect of a faithful representation of the spatial distribution of the ionospheric VTEC using limited parametric variables, which may find utility in navigation, radar, and various other applications.

Waiting time representation of discrete distributions

We discuss a representation of any probability distribution on the set of non-negative integers as a waiting time distribution in a sequence of independent Bernoulli trials. Several associated results are derived and illustrated by examples. Multivariate extensions are briefly treated as well.

Hollow microspheres of layered double hydroxides through surfactant-free method enhanced heavy metals removal from soil

A three-dimensional MgAl layered double hydroxides hollow microsphere (HMS-LDH) is fabricated by surfactant-free method. The microstructure and the formation mechanism of HMS-LDH are investigated by XRD (X-ray diffraction), SEM (Scanning Electron Microscope), EDS (Energy dispersive Spectrometer) and XPS (X-ray photoelectron spectrometer). The morphology of LDHs could be varied by changing the ratio of metal cations to urea. The adsorption properties of HMS-LDH for heavy metals from soil are investigated. The results of experiments demonstrates that the adsorption kinetics of Cu(Ⅱ), Pb(Ⅱ), As(Ⅴ), Cr(Ⅵ) are in good agreement with the pseudo-second-order kinetic and intraparticle diffusion model. The adsorption isotherm data of Cu(Ⅱ)/Pb(Ⅱ) is accordance with the Langmuir-Freundlich model, while the equilibrium adsorption of As(Ⅴ)/Cr(Ⅵ) follow the Generalized-Langmuir isotherm model well. Site energy distribution theory denotes the hollow microsphere structure increases the adsorption sites of heavy metals, which is conducive to the adsorption process. The different mechanisms of precipitation for Cu(Ⅱ)/Pb(Ⅱ) removal and interlayer adsorption for As(Ⅴ)/Cr(Ⅵ) removal are proposed. The effects of coexisting cations and column leaching experiments on the performance evaluation are also investigated, which indicate most the ions have no effect on the adsorption of Cu (Ⅱ)/Pb(Ⅱ) and As(Ⅴ)/Cr(Ⅵ). This work proposes a simple approach to prepare LDHs hollow microspheres and demonstrates their excellent properties for the remediation of heavy metal polluted soil.

A two-stage optimization model for relief distribution to disaster survivors under two-fold uncertainty

Disasters are unforeseen occurrences requiring extensive transport deployment to support and relieve victims. Sometimes, this transportation is not feasible directly from some supply points to some destination points. Due to this tragedy, it is unclear precisely what is available at supply points, what is needed at destinations, how much transportation capacity there is, and what the routes are like. In this study, we investigate a two-stage multi-item fixed charge four-dimensional transportation problem using the concept of big data theory under the two-fold uncertainties. Here, the model’s parameters such as unit transportation costs, availabilities of items at the suppliers, fixed charges, capacities of conveyances, and demands of the items at the retailers are considered type-2 zigzag uncertain variables. Using big data theory and based on uncertain programming theory, two novel uncertain models are developed such as chance-constrained programming and expected value programming model. These two uncertain models transformed into the deterministic form via uncertainty inverse distribution theory. A critical value based reduction method with three categories (i.e., expected value, pessimistic value, and optimistic value) is applied to reduce the type-2 zigzag uncertain variable to the type-1 zigzag uncertain variable. The genetic algorithm and particle swarm optimization techniques have been proposed to find the optimal solution for the two deterministic models. The efficiency of our proposed approach is demonstrated with a real-life numerical example.

A General and Efficient Fault Diagnosis Approach Using Hyperdimensional Computing Enhanced by Local Feature Extraction

Abstract Ensuring the safe and reliable operation of industrial equipment is of great importance, and accordingly, machine fault diagnosis has attracted considerable attention. Recently, various deep learning-based fault diagnosis models have been widely developed due to the powerful ability of feature learning and nonlinear modeling of deep learning models, and these methods heavily rely on large amounts of data and high memory and resources. However, it is difficult to obtain enough data in practical applications, thus leading to the unsatisfactory performance of deep learning-based models and high cost. In this paper, we propose a new and efficient fault diagnosis approach based on Hyperdimensional computing (HDC), which can learn high-dimensional, random, and holographic distributed representations of input features. It has the advantages of single training, low training cost, and does not require a large amount of data. Therefore, we apply HDC to the field of few-shot fault diagnosis for the first time, and propose a simple and efficient approach for few-shot fault diagnosis based on hyperdimensional computing with local feature extraction(L-HDC). Instead of using original data, the model firstly extracts the local features of original data by hand-designed features, and then carries out HDC-encoding, training, and test classification. Through the comparison of various models and the analysis of various data, the effectiveness of our proposed model is verified. In the case of few-shot learning, the recognition accuracy is as high as 90\% and the training time of ordinary HDC model is 5-10 times that of L-HDC model, which is superior to other models.

Quantitative spectral micro-CT of a CA4+ loaded osteochondral sample with a tabletop system

Micro-computed tomography (μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT) is the gold standard for nondestructive 3D imaging of biomedical samples in the centimeter scale, but it has limited effectiveness in revealing intricate soft tissue details due to the limited attenuation contrast. Radiopaque contrast agents that accumulate in the structures of interest are employed to enhance their visibility. However, the increased attenuation provided by the contrast agents does not guarantee discrimination among tissues. This issue can be solved by spectral μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT (Sμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT) systems employing small-pixel chromatic photon-counting detectors. These detectors, combined with material decomposition algorithms, allow the generation of high-resolution material-specific 3D maps. This work aims to demonstrate the potential of photon-counting X-ray Sμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT on osteochondral samples loaded with a cationic iodinated contrast agent (CA4+) at a spatial resolution below 50 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}m, and to compare the results against a conventional μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT system. An osteochondral sample extracted from a bovine stifle joint was loaded with CA4+ and imaged with a novel multimodal X-ray imaging system, featuring a 62 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}m pixel CdTe spectral detector (Pixirad1-PixieIII). After material decomposition, quantitative 3D density maps of iodine and hydroxyapatite were reconstructed. The same sample was also scanned with a commercial μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}CT scanner with matched spectrum and exposure time. SCTμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document} images at a (measured) spatial resolution comparable with the commercial scanner (∼\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sim$$\\end{document}45 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu$$\\end{document}m) were obtained. Spectral images allowed for a fully automatic segmentation of cartilage and subchondral bone. The unambiguous discrimination between iodine and hydroxyapatite revealed a more realistic representation of proteoglycan distribution compared to conventional imaging.

Habitat suitability and representation of the potential distribution of the lowland tapir (Tapirus terrestris) within land cover types and protected areas of eastern Colombia

Habitat suitability and representation of the potential distribution of the lowland tapir (Tapirus terrestris) within land cover types and protected areas of eastern Colombia

Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo.

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations, we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We further demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics in covariance.

Accretion of SiO2/doped-Si cuboid for terahertz absorber and impedance matching

This paper presents an ultra-broadband polarization-insensitive terahertz absorber that consists of a doped Si substrate and a triple-layer of doped Si covered with a SiO2 anti-reflective coating. The finite element method is used to investigate the absorption of the absorber. The absorber exhibits high absorption rates of over 95 % between frequencies of 0.9 THz and 9.2 THz, with a center frequency of 5.05 THz and a relative bandwidth ratio of 164 %. Moreover, it exhibits outstanding wide-angle absorption properties, achieving over 90 % absorption at angles of incidence ranging from 0 to 55° and frequencies spanning from 1.1 to 10 THz. Furthermore, the underlying mechanisms behind broadband absorption and high absorption rates are studied by analyzing the electric field distribution and impedance matching theory. Additionally, this absorber showcases excellent fabrication tolerance. Therefore, the proposed terahertz absorber featuring doped silicon triple-layer stacked arrays has significant potential in applications such as sensing, stealth technology, and biomedicine.

Similarity searching for wafer bin maps by measuring shape, location, and size similarities of defect patterns

A wafer bin map (WBM) is a visual representation of the spatial distribution of defective chips on a wafer. WBMs showing specific defect patterns are usually a result of process-assignable causes; thus, it is important to identify them to eliminate assignable causes. With advances in semiconductor manufacturing technology, identifying new defect patterns, and diagnosing their causes have become critical. However, most existing methods for WBM analysis use a supervised learning approach, which only detects previously known defect patterns. The similarity-search approach is a suitable alternative for defining new defect patterns. The proposed method uses an unsupervised approach to search for similar WBMs by measuring the similarities of three spatial features of defect patterns–shape, location, and size–which are useful for defining new defect patterns and diagnosing their causes. These three similarities are achieved using tensor voting and the mountain function for shape similarity, Euclidean distance for location similarity, and a combination of defect count and average radius for size similarity. The overall similarity was assessed using the weighted average of the three similarities. The weights are determined by quantifying the uncertainty of each similarity based on information entropy theory to better distinguish between similar patterns. The experimental results demonstrate the effectiveness of the proposed method compared to existing methods and highlight its capability to identify and describe the spatial features of defect patterns.

Impact of cloud properties and aerosols on the spatial distribution of Indian summer monsoon rainfall: A case study

Quantitative seasonal Indian summer monsoon (ISM) rainfall forecasting has been a challenge for the climate models as it is sensitive to cloud properties, which are modulated by large-scale dynamics. Proper understanding of the role of dynamics, aerosols, and cloud microphysical processes is important for the precipitation calculation in dynamical models. The all-India averaged seasonal ISM rainfall (ISMR) from June to September had been normal or above normal, however there were large spatial variations. Some meteorological subdivisions, the majority of which lie in the Gangetic Plains, received deficient seasonal rainfall during recent years 2022 and 2010. The quantitative seasonal prediction of the spatial distribution of ISMR from global coupled models (GCMs) has also shown a hard time for accurate spatial rainfall distribution. Four monsoon years (2022, 2021, 2011, and 2010) are considered, in which the country as a whole (all India land points) was ‘above normal’ or ‘normal’. However, in two specific years (2022 and 2010), some subdivisions received deficient rainfall (17% and 15% of the total area). We have used several datasets from the ground, and satellite observations, along with reanalysis products and computed climatology and anomalies for monsoon years of 2022 and 2010. The low-level wind and vertical velocity along with cloud microphysics played a pivotal role in the heterogeneous distribution of ISMR during 2022 and 2010 as compared to years 2021 and 2011. Here, we have demonstrated that the spatial heterogeneity of the positive and negative precipitation anomalies was consistent with cloud properties. Aerosols might have an impact on the cloud microphysical processes and modulate cloud properties and rainfall over different regions due to the availability of water vapor. Therefore, the inclusion of aerosol indirect effects in climate models is crucial for better interactions among dynamics, aerosol, and cloud microphysics. Proper representation of cloud droplet size distribution and microphysical conversion rates might be helpful for quantitative seasonal ISMR forecasting at a smaller spatial scale.

Probabilities of the Third Type: Statistical Relational Learning and Reasoning with Relative Frequencies

Dependencies on the relative frequency of a state in the domain are common when modelling probabilistic dependencies on relational data. For instance, the likelihood of a school closure during an epidemic might depend on the proportion of infected pupils exceeding a threshold. Often, rather than depending on discrete thresholds, dependencies are continuous: for instance, the likelihood of any one mosquito bite transmitting an illness depends on the proportion of carrier mosquitoes. Current approaches usually only consider probabilities over possible worlds rather than over domain elements themselves. An exception are the recently introduced Lifted Bayesian Networks for Conditional Probability Logic, which express discrete dependencies on probabilistic data. We introduce functional lifted Bayesian networks, a formalism that explicitly incorporates continuous dependencies on relative frequencies into statistical relational artificial intelligence. and compare and contrast them with ifted Bayesian Networks for Conditional Probability Logic. Incorporating relative frequencies is not only beneficial to modelling; it also provides a more rigorous approach to learning problems where training and test or application domains have different sizes. To this end, we provide a representation of the asymptotic probability distributions induced by functional lifted Bayesian networks on domains of increasing sizes. Since that representation has well-understood scaling behaviour across domain sizes, it can be used to estimate parameters for a large domain consistently from randomly sampled subpopulations. Furthermore, we show that in parametric families of FLBN, convergence is uniform in the parameters, which ensures a meaningful dependence of the asymptotic probabilities on the parameters of the model.

Estimation of cement paste stiffness and UHPC elastic modulus through measured phase-property upscaling

The elastic stiffness of bulk concrete materials results from the complex interaction of aggregates, voids, and hydrated cement (which can have multiple hardened phases at multiple length scales). Given the complexities associated with understanding the arrangement of these particles within bulk concrete volumes, estimations for elastic modulus often rely on empirical correlations with unit weight and compressive strength. Such estimations are inherently scale-dependent and fail to capture variability in mix designs, particularly the variability found in specialty concrete mixes. To develop a scale-independent method for estimating elastic modulus from mix-design volume fraction information, this study explores a novel bottom-up approach using cement paste phase stiffness values determined through micro-mechanical experimentation and randomized Monte-Carlo spring arrangement simulations. Statistical representations of cement paste phase stiffness distributions and bulk volume fraction data are combined to provide estimations for elastic stiffness in both the composite cement paste and bulk concrete containing fine aggregate and fibers. Resulting a priori estimations of UHPC cement paste stiffness from the micro-mechanical upscaling simulations were within 4% of measured values (based on mix-design and void volume fraction information alone) for a selected sample of mix proportions. When applied to the two UHPC mixes containing fibers and fine aggregate, upscaling simulations consistently overpredicted the measured elastic modulus, likely due to the aggregate-cement interfacial transition zone (ITZ) properties that were not captured in the micro-mechanical testing.

Investigating the closure stress and crack initiation stress in fractured rocks using the student t distribution and Monte Carlo simulation method.

Traditional method of determining closure and initiation stress of fractured rocks by analyzing the stress-strain curve has problems such as strong subjectivity and large errors. This study utilized the rock closure stress values and onset stress values determined by three traditional methods, namely, axial strain method, fracture volume method and empirical value taking method, as the base database. The Student t distribution theory was used to obtain a confidence interval based on its overall distribution of values and to achieve a combination of the advantages of multiple methods. Within confidence interval, the Monte Carlo stochastic simulation was used to determine the convergence interval of the second stage to further improve the accuracy. Finally, mean value of the randomly sampled values after reaching the convergence stage was taken as the probability value of rock closure and crack initiation stress. The results showed that the 3 traditional methods for calculating rock closure and initiation stresses are significantly different. In contrast, the proposed method biases more towards multi-numerical distribution intervals and also considers the preference effects of different calculation methods. In addition, this method does not show any extreme values that deviate from the confidence intervals, and it has strong accuracy and stability compared to other methods.