Mixture Of Distributions Research Articles

Shear zones in granular mixtures of hard and soft particles with high and low friction.

Granular materials show inhomogeneous flows characterized by strain localization. When strain is localized in a sheared granular material, rigid regions of a nearly undeformed state are separated by shear bands, where the material yields and flows. The characteristics of the shear bands are determined by the geometry of the system, the micromechanical material properties, and the kinematics at the particle level. For a split-bottom shear cell, recent experimental work has shown that mixtures of hard, frictional and soft, nearly frictionless particles exhibit wider shear zones than samples with only one of the two components. To explain this finding, we investigate the shear zone properties and the stress response of granular mixtures using discrete element simulations. We show that both interparticle friction and elastic modulus determine the shear-band properties and packing density of granular mixtures of various mixing ratios, but their stress response depends strongly on the interparticle friction. Our study provides a fundamental understanding of the micromechanics of shear band formation in granular mixtures.

Very short-term probabilistic and scenario-based forecasting of solar irradiance using Markov-chain mixture distribution modeling

This study investigates probabilistic and scenario-based forecasting of solar irradiance with Markov-chain mixture (MCM) distribution modeling, Persistence Ensemble (PeEn) and Climatology. Forecasts from MCM models with uniform and empirical emission distribution settings, respectively, are compared with PeEn and Climatology in terms of probabilistic forecasting performance. The MCM model is also extended with scenario generation capabilities and compared to scenario generation of the Climatology by means of Monte Carlo sampling. Forecasts were made on minute resolution normalized solar irradiance, i.e. the clear-sky index, from National Renewable Energy Laboratory and Swedish Meteorological and Hydrological Institute for two climatic regions: Oahu, Hawaii, USA and Norrköping, Sweden, respectively. Results show that the MCM models are neither necessarily the most reliable, nor the sharpest in terms of Prediction Normalized Average Width (PINAW), but they are the most accurate in terms of Continuous Ranked Probability Score (CRPS). MCM models with uniform and empirical emission distribution settings perform similar in the tested probabilistic forecasting metrics. In terms of scenario forecasting, MCM models with N=30 perform similar in probability distribution goodness-of-fit and autocorrelation Mean Absolute Error (MAE) and superior to N=2 and N=10 number of states. Mathematically, forecasts from the MCM model with empirical distribution setting are shown to correspond to PeEn and Climatology forecasts given special settings of the MCM model. Based on the conclusions, the suggestion is to use the MCM scenario forecast generator with uniform emission distribution setting as benchmark for scenario forecasts of very short-term solar irradiance.

Virtual Classification: Modulating Domain-Specific Knowledge for Multidomain Crowd Counting.

Multidomain crowd counting aims to learn a general model for multiple diverse datasets. However, deep networks prefer modeling distributions of the dominant domains instead of all domains, which is known as domain bias. In this study, we propose a simple-yet-effective modulating domain-specific knowledge network (MDKNet) to handle the domain bias issue in multidomain crowd counting. MDKNet is achieved by employing the idea of "modulating", enabling deep network balancing and modeling different distributions of diverse datasets with little bias. Specifically, we propose an instance-specific batch normalization (IsBN) module, which serves as a base modulator to refine the information flow to be adaptive to domain distributions. To precisely modulating the domain-specific information, the domain-guided virtual classifier (DVC) is then introduced to learn a domain-separable latent space. This space is employed as an input guidance for the IsBN modulator, such that the mixture distributions of multiple datasets can be well treated. Extensive experiments performed on popular benchmarks, including Shanghai-tech A/B, QNRF, and NWPU validate the superiority of MDKNet in tackling multidomain crowd counting and the effectiveness for multidomain learning. Code is available at https://github.com/csguomy/MDKNet.

Effect of Erosion on Surface Roughness and Hydromechanical Characteristics of Abrasive-Jet Machining

The article contains the fundamental results of the experimental and numerical investigations for pneumo-abrasive unit nozzles with different geometries. The research was purposed by the pressing need to develop an inexpensive and effective working nozzle design of the air-abrasive unit which can be applied for surface processing before some technological processes are performed, as well as for surface coating, descaling after thermal treatment, processing of hollow holes of the crankshafts, smoothing of the inner surfaces of the narrow channels between the impeller blades after electric discharge machining for ultrahigh-pressure combination compressors. Several designs were considered, ranging from the simplest to those with a complicated inner channel geometry. The impact of the nozzle material and challenging inner surface application on its characteristics has also been studied. The research was done using the application of modern CFD complexes for numerical modeling of the air-abrasive mixture discharge from the working nozzle of the pneumo-abrasive unit. In addition, physical experimentation was provided. The methods applied in the research allow for profound, systematic research of spraying units operating on the air-abrasive mixture within a wide range of geometrical and mode parameters. The novelty of the gained results lies in the development of the mathematical model of the pneumo-abrasive nozzle operating process, the working out of a cheaper nozzle design, getting information about air-abrasive mixture distribution along the nozzle length, giving practical recommendations for calculation and designing a working nozzle for the jet-abrasive unit.

A Novel inverse-Wishart-Student’s t mixture distribution based Variational Bayesian Kalman Filter

A Novel inverse-Wishart-Student’s t mixture distribution based Variational Bayesian Kalman Filter

OTFS Detection Based on Gaussian Mixture Distribution: A Generalized Message Passing Approach

OTFS Detection Based on Gaussian Mixture Distribution: A Generalized Message Passing Approach

A biomechanics-based study of stroke technique in student tennis players

Abstract Studying the hitting technique of student tennis players is of great significance in improving the technical and tactical level of student tennis and promoting the popularization and scientificization of tennis. Since the performance of tennis hitting action recognition depends on the representation of the action, this study utilizes the Gaussian mixture distribution as a statistical distribution of human action data to provide a more accurate description of tennis hitting action. This paper presents the LM skeletal point coordinate fitting method to enhance the structure of the Gaussian mixture distribution-based Hidden Markov Model to capture the act of hitting the ball. In the end, the biomechanical properties of the tennis hitting technique were examined by analyzing the motion images of forehand and backhand hitting techniques of college tennis players. The mean values of the angle between the racket surface and the ground during the forehand stroke and the topspin stroke were 82.96° and 35.95°, respectively, and the speed of the grip point and wrist joint was faster than that of the flat stroke during the topspin stroke. The angles and velocities of the knee, hip, and ankle joints of the lower limbs were faster than those of the open backhand stroke in the closed backhand stroke. The angle and speed are smaller than that of the open backhand stroke, while the angle of the shoulder and elbow joints is larger than that of the open backhand stroke. The tennis action recognition model and algorithm designed in this paper can effectively acquire and analyze the technical characteristics of tennis hitting.

Recursive copula-augmented space-correlated temporal very-short term spatiotemporal probabilistic forecasting of the clear-sky index

This study introduces a recursive model framework for augmenting separate temporal probabilistic forecasts of multiple correlated time-series with a copula correlation model. The model is applied to the Markov-chain mixture distribution (MCM) model to spatiotemporally forecast minute resolution normalized solar irradiance, c.f. the clear-sky index, derived from radiometer array measurements of Global Horizontal Irradiance (GHI) for 18 geographically adjacent stations at Oahu, Hawaii, USA. The results are evaluated by univariate and multivariate probabilistic forecast metrics in comparison with forecasts from purely temporal MCM, Climatology and the spatiotemporal Multivariate Persistence Ensemble (MuPEn) benchmark. Results show that the Climatology and the MuPEn forecasts are most reliable, while superiority in sharpness, based on Prediction Interval Normalized Average Width (PINAW), depends on forecast horizon. In terms of accuracy, measured with the univariate measure Continuous Ranked Probability Score (CRPS), the MCM model (with and without copula) forecasts are most accurate for the first two steps ahead forecasts, while the Climatology and MuPEn both have superior score for longer horizons. In terms of multivariate scores, the accuracy estimate Energy Score results for the forecasts are similar to the CRPS, while the Variogram Score, which takes into consideration the correlational structure of the multivariate time-series, is significantly improved by the copula-augmented MCM model compared to the univariate MCM model. The MuPEn model generated the lowest Variogram Score among all models. Tests with fewer stations and swapped training and test data gave similar model-to-model relative dynamics with variations in magnitude.

Dimension reduction for constructing high-dimensional response distributions by accounting for unimportant and important variables

Probability distributions of responses have been widely used in structural analysis and design because of their complete statistical information. In practice, the dimensionality of input variables could easily reach hundreds or thousands, making it computationally expensive to obtain accurate distributions. In this paper, a generalized most probable point (MPP) method is developed to effectively build the response distributions of high-dimensional problems. First, a global index based on one-iteration MPPs is presented for dimension reduction, which is to divide the input variables into important and unimportant variables. After fixing the unimportant variables at their one-iteration MPP components, the MPP components of the important variables are obtained by performing the inverse first-order reliability method (FORM) in the reduced space. Predictive models of the all MPP components are then established to quickly estimate the MPPs of other cumulative distribution function (CDF) values. To accurately calculate CDF points of limit state functions with different shapes, a comprehensive uncertainty analysis method that accommodates the contributions of the important and unimportant variables is proposed by multiple combinations of FORM, second-order reliability method, and second-order saddlepoint approximation. Finally, the response distributions are generated based on Gaussian mixture distribution and all CDF points. The effectiveness of the proposed method is verified by a mathematical example and two engineering cases.

Research on Quality Evaluation of Smart Education Schools Based on Fuzzy Clustering Algorithm and Strategies for Future Development

Abstract The burgeoning field of wisdom education has led to a disparity in the quality of educational institutions, thereby necessitating enhancements to the existing school quality evaluation systems. This study refines the traditional fuzzy C-mean clustering algorithm by incorporating a Gaussian mixture distribution and information entropy regularization. It then employs this enhanced algorithm to construct a quality evaluation system for smart education schools. The improved fuzzy C-mean clustering algorithm demonstrated in this paper significantly outperforms the standard C-means used at SCU and the K-means algorithm in terms of Mean Absolute Error (MAE) and Total Hit Rate (THR). Specifically, the optimized algorithm decreased the MAE to 0.572 from 0.619, a reduction of 16.01% compared to the K-means algorithm. It increased the THR to 0.158 from 0.147, marking an improvement of 17.04% over the Kmeans algorithm. Furthermore, the refined clustering algorithm achieved an impressive accuracy of 95.71%. Analysis through this clustering approach reveals that the developed quality evaluation system accurately reflects the operational level of smart education within schools. The establishment of such a system is anticipated to significantly guide the future progression of smart education and aid in the foundational development of smart education schools.

Temporal Mixture Density Networks for Enhanced Investment Modeling

Temporal Mixture Density Networks for Enhanced Investment Modeling

XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting Considering High Volatility

XRMDN: An Extended Recurrent Mixture Density Network for Short-Term Probabilistic Rider Demand Forecasting Considering High Volatility

Neural networks for evaluating induced fission product yields

Fission product yields (FPYs) play a crucial role in various aspects of nuclear science and technology, including nuclear structure and reactions. However, the inherent constraints of traditional computational methods used in theoretical models, and lack of experimental access to key observables pose challenges in obtaining accurate and comprehensive fission data. Neural Networks (NNs) present a promising solution to address these challenges by effectively modeling and acquiring energy-dependent fission yields. Mixture Density Networks (MDNs) enable learning from available data, predicting unknowns, and quantifying uncertainties simultaneously. Our study demonstrates the effectiveness of MDNs in evaluating fission product yields, particularly in scenarios where experimental data are incomplete. Machine learning algorithms like Gaussian Process Regression (GPR) can capture the distribution of single-fission yields and generate high-quality samples. These samples serve as valuable inputs for MDN networks. This study introduces an MDN approach for evaluating energy-dependent fission mass yields. The results of MDN evaluations indicate satisfactory accuracy in determining both the distribution positions and energy dependencies of FPYs.

Ensemble of Pruned Bagged Mixture Density Networks for Improved Water Quality Retrieval Using Sentinel-2 and Landsat-8 Remote Sensing Data

Ensemble of Pruned Bagged Mixture Density Networks for Improved Water Quality Retrieval Using Sentinel-2 and Landsat-8 Remote Sensing Data

Adversarial Mixture Density Network and Uncertainty-Based Joint Learning for 360$^\circ$ Monocular Depth Estimation

Adversarial Mixture Density Network and Uncertainty-Based Joint Learning for 360$^\circ$ Monocular Depth Estimation

Fuzzy Synchronization Likelihood Graph in Deep Neural Networks for Human Motion Time Series Analysis.

Variable interactivity is crucial in biological multivariate time series analysis. This research suggests using graph structures to represent such interactions for more explainable decision-making processes. However, measuring the variable interaction in a graph is an open problem with no unique solution. Existing graph construction methods are either computationally costly, require extensive training, or disregard the inherent data nonlinearities and nonstationarity. We propose using the Fuzzy Synchronization Likelihood (FSL) criterion to address these challenges in constructing a graph and examining the qualitative similarity and dependency among variables. We propose applying this strategy to automated rehabilitation exercise evaluations based on human joint motion data. This multivariate time series application benefits from FSL-constructed graphs by offering further insight into the kinematics of joint interactions. Finally, we extend the convolutional layer in the Deep Mixture Density Neural Network (DMDN) to process the FSL-constructed graph, extracting practical information regarding task-based variable dependencies. An ablation study shows that the proposed FSL Graph-based Deep Neural Network (FSLGDN) outperforms its competitive approaches that use linear correlations and human anatomy for graph construction. Results also indicate that task-based consideration of joint motion data interactions is more beneficial than anatomy. Furthermore, the inherent nonstationarity of motion data leads to the extraction of more information than its linear correlation counterpart. Finally, while the proposed approach ranks competitively with a DMDN, the proposed approach's graph construction and representation of feature dependencies are more intuitive, leading to more explainable decision-making processes.

Galaxy 3D shape recovery using mixture density network

Abstract Since the turn of the century, astronomers have been exploiting the rich information afforded by combining stellar kinematic maps and imaging in an attempt to recover the intrinsic, three-dimensional (3D) shape of a galaxy. A common intrinsic shape recovery method relies on an expected monotonic relationship between the intrinsic misalignment of the kinematic and morphological axes and the triaxiality parameter. Recent studies have, however, cast doubt about underlying assumptions relating shape and intrinsic kinematic misalignment. In this work, we aim to recover the 3D shape of individual galaxies using their projected stellar kinematic and flux distributions using a supervised machine learning approach with mixture density network (MDN). Using a mock dataset of the EAGLE hydrodynamical cosmological simulation, we train the MDN model for a carefully selected set of common kinematic and photometric parameters. Compared to previous methods, we demonstrate potential improvements achieved with the MDN model to retrieve the 3D galaxy shape along with the uncertainties, especially for prolate and triaxial systems. We make specific recommendations for recovering galaxy intrinsic shapes relevant for current and future integral field spectroscopic galaxy surveys.

Transfer Learning-Assisted Inverse Modeling in Nanophotonics Based on Mixture Density Networks

Transfer Learning-Assisted Inverse Modeling in Nanophotonics Based on Mixture Density Networks

Deep Drug Synergy Prediction Network Using Modified Triangular Mutation-Based Differential Evolution.

Drug combination therapy is crucial in cancer treatment, but accurately predicting drug synergy remains a challenge due to the complexity of drug combinations. Machine learning and deep learning models have shown promise in drug combination prediction, but they suffer from issues such as gradient vanishing, overfitting, and parameter tuning. To address these problems, the deep drug synergy prediction network, named as EDNet is proposed that leverages a modified triangular mutation-based differential evolution algorithm. This algorithm evolves the initial connection weights and architecture-related attributes of the deep bidirectional mixture density network, improving its performance and addressing the aforementioned issues. EDNet automatically extracts relevant features and provides conditional probability distributions of output attributes. The performance of EDNet is evaluated over two well-known drug synergy datasets, NCI-ALMANAC and deep-synergy. The results demonstrate that EDNet outperforms the competing models. EDNet facilitates efficient drug interactions, enhancing the overall effectiveness of drug combinations for improved cancer treatment outcomes.

A generalized Budan-Fourier approach to generalized Gaussian and exponential mixtures

<p>In the literature, finite mixture models were described as linear combinations of probability distribution functions having the form $ f(x) = \Lambda \sum\limits_{i = 1}^n w_i f_i(x) $, $ x \in \mathbb{R} $, where $ w_i $ were positive weights, $ \Lambda $ was a suitable normalising constant, and $ f_i(x) $ were given probability density functions. The fact that $ f(x) $ is a probability density function followed naturally in this setting. Our question was: <italic>if we removed the sign condition on the coefficients $ w_i $, how could we ensure that the resulting function was a probability density function?</italic></p><p>The solution that we proposed employed an algorithm which allowed us to determine all zero-crossings of the function $ f(x) $. Consequently, we determined, for any specified set of weights, whether the resulting function possesses <italic>no</italic> such zero-crossings, thus confirming its status as a probability density function.</p><p>In this paper, we constructed such an algorithm which was based on the definition of a suitable sequence of functions and that we called a <italic>generalized Budan-Fourier sequence</italic>; furthermore, we offered theoretical insights into the functioning of the algorithm and illustrated its efficacy through various examples and applications. Special emphasis was placed on generalized Gaussian mixture densities.</p>