Mixture Of Distributions Research Articles

Inpainting of damaged temple murals using edge- and line-guided diffusion patch GAN

Mural paintings are vital cultural expressions, enriching our lives by beautifying spaces, conveying messages, telling stories, and evoking emotions. Ancient temple murals degrade over time due to natural aging, physical damage, etc. Preserving these cultural treasures is challenging. Image inpainting is often used for digital restoration, but existing methods typically overlook naturally degraded areas, using randomly generated binary masks or small, narrow regions for repair. This study proposes a novel architecture to reconstruct large areas of naturally degraded murals, maintaining intrinsic details, avoiding color bias, and preserving artistic excellence. The architecture integrates generative adversarial networks (GANs) and the diffusion model, including a whole structure formation network (WSFN), a semantic color network (SCN), and a diffusion mixture distribution (DIMD) discriminator. The WSFN uses the original image, a line drawing, and an edge map to capture mural details, which are then texturally inpainted in the SCN using gated convolution for enhanced results. Special attention is given to globally extending the receptive field for large-area inpainting. The model is evaluated using custom-degraded mural images collected from Tamil Nadu temples. Quantitative analysis showed superior results than state-of-the-art methods, with SSIM, MSE, PSNR, and LPIPS values of 0.8853, 0.0021, 29.8826, and 0.0426, respectively.

Interfacial and mass transport phenomena in the tri-ethylene glycol-methane system at process conditions of natural gas dehydration

AbstractUnderstanding the phase and interphase behavior at equilibrium and during the mass transfer between two adjacent fluid phases is relevant for optimizing and designing efficient separation processes. This study experimentally investigates the interfacial and transport behavior of systems comprising tri-ethylene glycol (TEG) and methane (CH4) under conditions relevant to the gas dehydration process. A comprehensive review of the interfacial tension (IFT) and diffusivity of systems involving non-polar and polar compounds at elevated pressures was studied. However, a research gap exists, particularly concerning the interfacial tension of systems involving TEG, TEG + water, and different types of gases as well as the diffusivity of CH4 in TEG. To address this gap, this study presents new data on mixture densities, interfacial tension, and drop volumes of TEG and TEG + water in CH4 and CH4 + CO2 mixtures at temperatures ranging from 20 to 50 °C and pressures up to 250 bar using the oscillating U-tube and pendant drop methods, respectively. Additionally, time-dependent fluid mixture densities and TEG droplet volumetric expansion, coupled with an analytical approach for the binary diffusion were applied to determine the CH4 solubility and diffusivity in TEG. The results show that IFT and drop volume of TEG and TEG + water in CH4 and CH4 + CO2 mixtures decrease with increasing pressure. The presence of water increases the IFT of TEG-CH4 up to $$\sim$$ ∼ 5mN/m, while CO2 reduces it by $$\sim$$ ∼ 2mN/m. Interestingly, the IFT and drop volume of TEG-CH4 show no significant change at elevated pressures when temperatures rise from 20 to 50 °C. IFT remains relatively constant over time at moderate pressures but decreases by $$\sim$$ ∼ 3mN/m at an elevated pressure of 150 bar, suggesting methane solubilization into TEG to have a significant influence which is confirmed by TEG drop volume expansion. The diffusivity of CH4 in TEG at 150 bar and 50 °C is determined to be in the range of 10–10 m2/s, which is in agreement with the diffusivity of CH4 in liquids of similar viscosity, i.e. according correlations may be applied as good engineering practice. To the best of our knowledge, there is no such comprehensive work on the properties of fluid mixtures relevant in gas dehydration processes published up to date.

A finite mixture distribution to model genetic architecture of image‐based oat grain morphology

AbstractThe multi‐floral oat (Avena sativa L.) inflorescence influences grain size and shape distributions, affecting the physical attributes of grain quality such as plumpness, size, and uniformity. While the grain size and shape distribution has been characterized as multi‐modal, very little is known about the genetic determinants of those distributions and their properties. The goal of this study was to model grain size and shape distribution using a finite mixture distribution approach and propose new distributional traits (i.e., emerging distributional traits) to characterize genotypes. We evaluated 47 oat genotypes in four highly replicated field experiments. Grains of three panicles per plot were individually threshed and scanned. Grain area, length, width, and roundness were obtained from each grain‐based image, while emerging distributional traits were evaluated using a finite mixture distribution approach. Finally, grain size distributions from hand‐threshed panicles (representing the full biological distribution) were compared with the grain size distributions of grains harvested with a combine harvester representing commercial harvest where small grains may be blown out. The heritability of all grain traits was high (0.89–0.94), and trait distributions differed among genotypes. Grain area and length show bi‐ and trimodal distributions, while grain width and roundness are uni‐ and bimodal. Although the full biological distribution of grains differed from the combine‐harvested grains, their genetic correlations were high, suggesting the combine‐harvested distributions can be used as a proxy for full biological distributions. This study proposes a straightforward methodological approach to model grain attributes that can aid in quality evaluations for genetic studies, breeding decisions, and industry characterization.

Comprehensive Application of Mixture Density Network Model and Action Feature Screening Strategy in the Choreography of Different Dance Styles

Comprehensive Application of Mixture Density Network Model and Action Feature Screening Strategy in the Choreography of Different Dance Styles

Probing Electrostatic and Hydrophobic Associative Interactions in Cells.

Weak nonspecific interactions between biomacromolecules determine the cytoplasmic organization. Despite their importance, it is challenging to determine these interactions in the intracellular dense and heterogeneous mixture of biomacromolecules. Here, we develop a method to indicate electrostatic and hydrophobic associative interactions and map these interactions. The method relies on a genetically encoded probe containing a sensing peptide and a circularly permuted green fluorescent protein that provides a ratiometric readout. Inside bacterial and mammalian cells, we see that the cytoplasmic components interact strongly with cationic and hydrophobic probes but not with neutral hydrophilic probes, which remain inert. The Escherichia coli cytoplasm interacts strongly with highly negatively charged hydrophilic probes, but the HEK293T cytoplasm does not. These associative interactions are modulated by ATP depletion. Hence, the nonspecific associative interaction profile in cells is condition- and species-dependent.

Probabilistic reliability model of electrical motors in submersible well pumping units used in the uranium mining by in-situ leaching

Relevance. A submersible electric motor is the most vulnerable component of an electric centrifugal pumping unit used in in-situ leaching uranium mining. The accuracy of calculating the need for new electric motors directly affects the profitability of the uranium production. Aim. Development of a probabilistic reliability model for a submersible electric motor that provides the calculation of its failure probability for the upcoming period of time and allows estimating with sufficient accuracy the number of motors required to replace the failed ones. Methods. Statistical methods, survival analysis, statistical hypothesis testing. Results and conclusions. The authors conducted a study of three probabilistic reliability models for electric motors of submersible well pumping units used in in-situ leaching uranium mining. As a result of the study, the maximum likelihood estimates of model parameters were determined for each model; the adequacy of the models under study was checked based on nonparametric goodness-of-fit tests. Despite the fact that the test results did not allow excluding any of the considered models, a model based on a mixture of two Weibull distributions was selected as a probabilistic reliability model demonstrating higher consistency with real data, compared to the other models. At the same time, the analysis of the components of the mixture distribution indicated the presence of a group of electric motors with an uncharacteristically low time-to-failure value compared to the average value calculated for the entire set of equipment under study, and made it possible to estimate the share of such motors, which amounted to 8% of the total population. Possible reasons explaining such heterogeneity of data, according to the authors, are hidden manufacturing defects or more severe operating conditions in which some submersible electric motors operate.

Probabilistic Prediction and Assessment of Train-Induced Vibrations Based on Mixture Density Model

This study presents a probabilistic prediction method for train-induced vibrations by combining a deep neural network (DNN) with the mixture density model in a cascade fashion, referred to as the DNN-RMDN model in this paper. A benchmark example is conducted to demonstrate and evaluate the prediction performance of the DNN-RMDN model. Subsequently, the model is applied to a case study to investigate and compare the uncertainties of train-induced vibrations in the throat area and testing line area of a metro depot. After training, the model is capable of accurately predicting the probability density function (PDF) of train-induced vibrations at different distances from the track and at different frequencies. Utilizing the predicted PDF, probabilistic assessments can be performed to ascertain the likelihood of surpassing predefined limits. By employing a mixture density model instead of a single Gaussian distribution, the DNN-RMDN model achieves more accurate prediction of the PDF for train-induced vibrations. The proposed probabilistic assessment framework can effectively assist in vibration screening during the planning phase and in selecting and designing vibration mitigation measures of appropriate levels.

Characterisation of fibre distribution uniformity in steel fibre-reinforced concrete under microwave-induced heating during casting

Traditional active microwave thermography (AMT) tests for hardened steel fibre-reinforced concrete (SFRC). The surface temperature of SFRC derived from AMT cannot fully characterise the distribution of steel fibres in the SFRC. This study proposes a microwave-induced heating method combined with temperature sensors (MI-TS) to estimate the fibre dispersion of an SFRC mixture during casting. The principles and testing process are discussed, and a numerical model is developed to evaluate the temperature distribution of the SFRC mixture following microwave exposure. Through MI-TS and numerical models, the temperature in the SFRC mixture with uniform fibre distribution, fibre clustering and fibre sinking is investigated, and the results are compared with those obtained by AMT and destruction technology to evaluate the feasibility of the proposed method. The results show that in the same specimen, the temperature difference between areas with similar fibre content falls in a very narrow range (e.g., 3.5–4.5 °C for a 100 × 100 × 100 mm specimen exposed to 600 W of microwave irradiation for 180 s). When the fibre content in a given area is more than 0.5 vol%, a large temperature difference forms between this and other areas. When the equivalent fibre content of the specimen is ignored, the temperature difference between the two areas is directly proportional to the difference in fibre content. Therefore, the area that shows differences in fibre clustering and fibre content can be easily determined found based on the temperature difference derived from MI-TS.

Partial stochastic resetting with refractory periods

Abstract The effect of refractory periods in partial resetting processes is studied. Under Poissonian partial resets, a state variable jumps to a value closer to the origin by a fixed fraction at constant rate, $x\to a x$. Following each reset, a stationary refractory period of arbitrary duration takes place. We derive an exact closed-form expression for the propagator in Fourier-Laplace space, which shows rich dynamical features such as connections not only to other resetting schemes but also to intermittent motion. For diffusive processes, we use the propagator to derive exact expressions for time dependent moments of $x$ at all orders. At late times the system reaches a non-equilibrium steady state which takes the form of a mixture distribution that splits the system into two subpopulations; trajectories that at any given time in the stationary regime find themselves in the freely evolving phase, and those that are in the refractory phase. In contrast to conventional resetting, partial resets give rise to non-trivial steady states even for the refractory subpopulation. Moments and cumulants associated with the steady state density are studied, and we show that a universal optimum for the kurtosis can be found as a function of mean refractory time, determined solely by the strength of the resetting and the mean inter-reset time. The presented results could be of relevance to growth-collapse processes with periods of inactivity following a collapse.

A Robust and Efficient Cubature Kalman filter based on the Variation Bayesian Method and Its Application in Target Tracking

Abstract This paper proposes a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix (MNCM). This paper studies situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse-Gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart mixture distribution (GSTIW) is used to model the one-step prediction distribution. Modeling generates a large number of unknown parameters. Therefore, this article adopts the statistical linearization method to linearize the observation function and then estimates the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm's efficiency. Finally, using the variational Bayesian (VB) method, a novel and efficient robust cubature Kalman filter based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.

Universality laws for Gaussian mixtures in generalized linear models*

Abstract Let ( x i , y i ) i = 1 , … , n denote independent samples from a general mixture distribution ∑ c ∈ C ρ c P c x , and consider the hypothesis class of generalized linear models y ^ = F ( Θ ⊤ x ) . In this study, we investigate the asymptotic joint statistics of a family of generalized linear estimators ( Θ 1 , … , Θ M ) obtained either from (a) minimizing an empirical risk R ^ n ( Θ ; X , y ) or (b) sampling from the associated Gibbs measure exp ⁡ ( − β n R ^ n ( Θ ; X , y ) ) . Our main contribution is to characterize under which conditions the asymptotic joint statistics of this family depends (in a weak sense) only on the means and covariances of the class conditional features distribution P c x . In particular, this allows us to prove the universality of different quantities of interest, such as the training and generalization errors, redeeming a recent line of work in high-dimensional statistics working under the Gaussian mixture hypothesis. Finally, we discuss the applications of our results in different machine learning tasks of interest, such as ensembling and uncertainty quantification.

Efficient training of energy-based models using Jarzynski equality**This article is an updated version of: Carbone D, Hua M, Coste S and Vanden-Eijnden E 2023 Efficient training of energy-based models using Jarzynski equality Advances in Neural Information Processing Systems vol 36, ed A Oh, T Naumann, A Globerson, K Saenko, M Hardt and S Levine (Curran Associates, Inc.) pp 52583–614.

Abstract Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is well measured by the cross-entropy (CE) of the model distribution relative to the data distribution. Using the CE as the objective for training is, however, challenging because the computation of its gradient with respect to the model parameters requires sampling of the model distribution. Here, we show how the results for nonequilibrium thermodynamics based on the Jarzynski equality together with tools from sequential Monte Carlo sampling can be used to perform this computation efficiently and avoid the uncontrolled approximations made using the standard contrastive divergence algorithm. Specifically, we introduce a modification of the unadjusted Langevin algorithm (ULA), in which each walker acquires a weight that enables the estimation of the gradient of the CE at any step during gradient descent, thereby bypassing sampling biases induced by slow mixing of the ULA. We illustrate these results with numerical experiments on Gaussian mixture distributions as well as the MNIST and CIFAR-10 datasets. We show that the proposed approach outperforms methods based on the contrastive divergence algorithm in all the considered situations.

A comparative study of different deep learning methods for time-series probabilistic residential load power forecasting

The widespread adoption of nonlinear power electronic devices in residential settings has significantly increased the stochasticity and uncertainty of power systems. The original load power data, characterized by numerous irregular, random, and probabilistic components, adversely impacts the predictive performance of deep learning techniques, particularly neural networks. To address this challenge, this paper proposes a time-series probabilistic load power prediction technique based on the mature neural network point prediction technique, i.e., decomposing the load power data into deterministic and stochastic components. The deterministic component is predicted using deep learning neural network technology, the stochastic component is fitted with Gaussian mixture distribution model and the parameters are fitted using great expectation algorithm, after which the stochastic component prediction data is obtained using the stochastic component generation method. Using a mature neural network point prediction technique, the study evaluates six different deep learning methods to forecast residential load power. By comparing the prediction errors of these methods, the optimal model is identified, leading to a substantial improvement in prediction accuracy.

Evaluation for coarse aggregate distribution of asphalt mixtures based on the two-dimensional digital image analysis

Meso-structure is one of the major sources of macro-performance in asphalt mixtures. The research on aggregate distribution state is of great significance for the further improvement of asphalt mixture macro-performance. However, the variations of research methods among prior works hamper the deduction of the holistic potential and promising directions of coarse aggregate distribution analysis from current research findings. This work comprehensively verified the quantifying ability of aggregate distribution state indices and their correlation with rutting performance under an advanced digital image processing technique and a wide range of asphalt mixture types, and aims to provide a reference of the holistic potential and promising directions of coarse aggregate distribution analysis for subsequent research. To this end, eleven typical asphalt mixtures’ aggregate distribution state and rutting performance were measured, quantified, and correlated. The results show that Kpe nears or more than 0.56 can be the sign of coarse aggregates effectively interlocked while it nears or less than 0.26 is the opposite; Uarea nears or less than 2 % can be the sign of reaching a coarse aggregate distribution equilibrium; Δorien approaches 6.21 can be the sign of reaching a coarse aggregate orientation equilibrium; mixtures with a nominal maximum aggregate size of 10 mm are disabled in gathering contact chains. Moreover, these coarse aggregate distribution state quantifying indices proposed in existing research can indeed describe the meso-structural features of asphalt mixtures to a certain extent. However, these indices fail to capture the underlying meso-structural features relating to rutting performance and lead to limited applicability. Furthermore, the poor performance of these coarse aggregate distribution state quantifying indices in the global fitting mainly comes from their incompatibility with changes in nominal maximum aggregate size.

Visual object detection model integrating deep active learning

The perception of surrounding objects by vehicle autonomous driving is an important means to ensure traffic safety. Object detection models based on deep learning are widely used, but they require a large amount of labeled data for training. This paper proposes an active visual object detection model that uses Gaussian mixture distribution to estimate the uncertainty of unlabeled images, reducing the dependence of model training on labeled data. First, a mixed density network is used as the detection head, and the image features extracted by the deep neural network are used as input to estimate the probability distribution of the classification and positioning of the target prediction box. Secondly, the classification score value of the target prediction box is mapped to the probability space, and the classification uncertainty of the target is calculated using the edge uncertainty; the positioning uncertainty of the target is measured using the prediction box positioning variance. Finally, the most unstable samples are selected for labeling. Compared with other typical active learning sampling strategies on the VOC dataset, the proposed method achieves the best performance, and the 54%data annotation amount can reach the performance of YOLOX supervised learning 98.8%, saving nearly 45% of the data annotation amount.

Stochastic Model for Novel Mixture Distribution with Properties and Its Application

Medical research is the one of the most important applications of statistical analysis. A great deal of occasions, specific statistical considerations are needed for cancer research in order to determine the model that best fits the survival data. In this paper, the proposed a new two parameter continuous distribution. It is called a new mixture distribution (NMD). Some statistical properties of the distribution are derived such as, the moments, moments generating function, reliability analysis. Also, the distribution of order statistics is presented and entropies are derived. The application of the maximum likelihood estimate technique to the performance of traditional parameter estimation. Two authentic data sets describing cancer patients' survival are used to empirically demonstrate the potential importance and usability of the proposed distribution. Comparing the new mixture distribution to some other competing distribution, the analysis's results demonstrated that it performed quite well.

Determination of Compressed Liquid Densities for CO2 + n-Decane Using a Vibrating Tube Densimeter

Understanding the density of CO2 + n-decane is crucial for designing and operating CO2 capture, transport, and storage. The safety and effectiveness of CO2 burial is directly affected by the density of CO2 + n-decane mixtures. The liquid densities of CO2(1) + n-decane(2) mixtures with mole fractions of CO2 x1 = 0, 0.2032, 0.4434, 0.7589, and 0.8947 were measured using a vibrating tube densimeter. The combined expanded uncertainties of density with a level of confidence of 0.95 are estimated to be 0.6 kg·m−3. A total of 221 compressed liquid densities of CO2(1) + n-decane(2) mixtures along the five isotherms between T = (283 and 363) K with pressures up to 100 MPa were presented. The densities of mixtures were correlated by the modified Tait equation, resulting in absolute average deviations between the experimental and calculated values of 0.028%, 0.013%, 0.017%, 0.044%, and 0.042%. In addition, the isothermal compressibility, isobaric thermal expansivity, and excess molar volume were derived from the modified Tait equation.

Effects of Diesel Pre-Injection Time on Combustion Process and Emission Characteristics of Diesel/Methanol Dual Fuel Engine

ABSTRACT The traditional diesel engine not only causes the reduction of nonrenewable energy but also aggravates environmental pollution. The utilization of renewable fuels in engine can not only effectively reduce the dependence on oil sources but also effectively reduce emissions. As a renewable oxygen-containing fuel with low production cost and widely sourced, methanol holds vast potential for application in engine. The dual-fuel combustion of diesel and methanol has emerged as an important research issue in the internal combustion engine industry. This paper conducted a study on the combustion and emission characteristics of the diesel/methanol dual fuel based on the optical engine test platform and 3D numerical simulation software. The results show that the change in cylinder pressure is relatively small and the heat release rate increases with the advance of diesel pre-injection time. The pre-injection time of diesel mainly affects the mixture distribution of pre-injection diesel, and the mixture is more evenly mixed with the advance of the pre-injection time. The degree of premixed combustion becomes higher, premixed combustion will lead to more rapid combustion, so the peak heat release rate shows an increasing trend. The pre-injection time of diesel is advanced, resulting in a leaner mixture in the early stage, and the fuel is not easy to burn, so CA10 and CA50 are delayed. The soot formation decreases as the mixture becomes more uniform, and the number of pixels of KL factor in each range also decreases. The average temperature in the cylinder is reduced and the NOX shows a decreasing trend with the advance of the pre-injection time. The change in CO generation is relatively small with the advance of pre-injection time.

Particle tracking-aided digital volume correlation for clay–sand soil mixtures

In this study, a novel, interdisciplinary method is introduced that merges fundamental geomechanics with computer vision to develop an advanced hybrid feature-aided digital volume correlation (DVC) technique. This technique is specifically engineered to measure and compute the full-field strain distribution in fine-grained soil mixtures. A clay–sand mixture specimen composed of quartz sand particles and kaolinite was created. Its mechanical properties and deformation behaviour were then tested using a mini-triaxial apparatus, combined with micro-focus X-ray computed tomography (μCT). The CT slices underwent image processing for denoising, segmentation of distinct phases, reconstruction of sand particles and feature extraction within the soil specimen. The proposed approach incorporated a two-step particle tracking method, which initially uses particle volume and surface area features to establish a preliminary matching list for a reference particle and then use the iterative closest point method for precise target particle matching. The soil specimen's initial displacement field was then mapped onto the DVC method's grid, and further refined through sub-voxel registration by way of a three-dimensional inverse compositional Gauss–Newton algorithm. The proposed method's effectiveness and efficiency were validated by accurately calculating the displacement and strain fields of the soil mixture sample, and comparing the results with those from a traditional DVC method. Given the soil's compositional and microstructural characteristics, these image-matching techniques can be integrated to create a versatile, efficient, and robust DVC system, suitable for a variety of soil mixture types.

Probabilistic surrogate modeling of damage equivalent loads on onshore and offshore wind turbines using mixture density networks

Abstract. The use of load surrogates in offshore wind turbine site assessment has gained attention as a way to speed up the lengthy and costly siting process. We propose a novel probabilistic approach using mixture density networks to map 10 min average site conditions to the corresponding load statistics. The probabilistic framework allows for the modeling of the uncertainty in the loads as a response to the stochastic inflow conditions. We train the data-driven model on the OpenFAST simulations of the IEA 10 MW reference wind turbine (IEA-10MW-RWT) and compare the predictions to the widely used Gaussian process regression. We show that mixture density networks can recover the accurate mean response in all load channels with values for the coefficient of determination (R2) greater than 0.95 on the test dataset. Mixture density networks completely outperform Gaussian process regression in predicting the quantiles, showing an excellent agreement with the reference. We compare onshore and offshore sites for training to conclude the need for a more extensive training dataset in offshore cases due to the larger feature space and more noise in the data.