Factorization Model Research Articles

Source identification and migration fate of heavy metals of soil-groundwater system in a thousand-year cultivation region.

Pollution of farmland by heavy metals threatens food security and human health. In addition, heavy metals in soil could infiltrate into groundwater to influence the water quality and safety of drinking water. However, the relationship between heavy metal pollution in soil and groundwater is still not clear. In this study, we investigated the soil and groundwater in the Guanzhong Plain region, which is a significant grain production base in China, and determined the spatial distributions, ecological risk, sources, and migration fates of heavy metals (As, Cd, Cr, Cu, Ni, Pb, and Zn). The results showed that the mean values (0-20cm) in the soil were 19.57mgkg-1 for As, 0.71mgkg-1 for Cd, 69.65mgkg-1 for Cr, 21.97mgkg-1 for Cu, 28.67mgkg-1 for Ni, 17.54mgkg-1 for Pb, and 73.77mgkg-1 for Zn, and the corresponding mean values in groundwater were 1.2, 0.04, 4.69, 0.15, 0.07, 0.3, and 3.6μg L-1, respectively. The mean values for As, Cd, Cr, Pb, and Zn in soil exceeded the background values, and the mean values for As, Cd and Pb exceeded those in groundwater. Positive matrix factorization models identified five sources (fertilizers and organic fertilizers, natural sources, pesticides and herbicides, industrial activities, and sedimentation caused by transportation) for heavy metal pollution in soil and four sources (industry activity, atmospheric sedimentation caused by transportation, natural sources, and agriculture) for heavy metal pollution in groundwater. The soil particle composition and soil organic carbon content were important factors that affected the vertical distribution of heavy metals in the soil. The migration modes (convection and diffusion) were not found for all heavy metals. These results help to understand the relationships between heavy metals in soil and groundwater in farmland ecosystems regionally.

Characteristics and Source Apportionment of Volatile Organic Compounds in a Coastal Industrial Area: A Case Study in the Yangtze River Delta of China.

In recent years, the coastal area in East China has experienced elevated volatile organic compounds (VOCs) levels during specific periods. VOCs have become one of the major atmospheric pollutants in these areas. In this study, 64 compounds including alkanes, alkenes, halohydrocarbons, aromatics, and oxygenated VOCs (OVOCs) were obtained by the TO-15 method through a 12-month campaign in industrial, urban and suburban areas in the Yangtze River Delta of China. The overall trends of total VOC (TVOC) concentrations at eight sampling sites were as follows: winter > autumn > spring > summer. The proportion of VOC categories was various at industrial sites, while OVOCs and halohydrocarbons had high proportions at urban sites and suburban sites, respectively. Coating, vehicle emission, petrochemical source, industrial source, and gasoline volatilization were identified as the major VOC emission sources by the positive matrix factorization model. Petrochemical and coating sources were the prime VOC sources at industrial sites. Aromatics contributed the most ozone formation potential at industrial sites, while OVOCs provided the main contributions at both urban and suburban sites during four seasons. According to the health risk assessment, a high probability of non-carcinogenic risk existed at three industrial sites. Special attention should be given to certain VOCs, such as acrolein and 1,2-dibromoethane in industrial areas.

Evaluation of groundwater quality with multi-source pollution based on source identification and health risks

Groundwater is a crucial water supply source in Chengdu City, western China, a region experiencing significant water scarcity. The sources of inorganic pollutants in groundwater and their potential health risks are of great concern. In this study, based on 156 groundwater samples collected in 2021 in the study area were analyzed for hydrochemical characterization and controlling factors. The Positive Matrix Factorization (PMF) model was used for contaminant source analysis, and Monte Carlo Simulation (MCS) combined with the Health Risk Evaluation Model (HREM) was used to quantify the health risks. The results indicate that the groundwater in the study area is predominantly of the Ca·Na-SO4·HCO3, Ca·Na-HCO3·SO4 and Ca-HCO3·SO4 types, mainly influenced by the combination of evaporation-concentration-crystallization and rock leaching-weathering. K+, Na+, and Cl− mainly originate from the weathering and dissolution of potassium feldspar and rock salt, while Ca2+, Mg2+, HCO3−, and SO42− primarily come from the weathering and dissolution of sulfate minerals. The main sources of groundwater pollution and their contributions are as follows: domestic pollution (25.6 %), dissolution-filtration-evaporation-concentration action (22.8 %), hydrogeochemical evolution (15.8 %), water-rock interactions (12.8 %), primary geologic context (12.1 %), and agricultural non-point source pollution (11.0 %). Cl− and As are the primary contributors to non-carcinogenic and carcinogenic risks, respectively. Non-carcinogenic risks are below USEPA standards, while the average carcinogenic risk for arsenic exceeded the maximum acceptable risk level thresholds by 23 and 109 times for adults and children, respectively. Non-carcinogenic and carcinogenic health risks were mainly influenced by pollutant concentrations. The primary geological background and domestic pollution contributed the most to the non-carcinogenic risk for adults (50.3 %) and children (77.1 %), and 38.2 % and 10.3 %, respectively. This study highlights the necessity of establishing a comprehensive groundwater pollution monitoring system, enhancing industrial waste management practices, and raising public awareness to mitigate contamination and ensure the sustainable use of groundwater resources in Chengdu City.

Impact of vehicles at the roadside of expressway in urban area: Simultaneous measurement of particle size distribution and positive matrix factorization

This study conducted real-time monitoring of size-resolved particle concentrations ranging from 9 nm to 10 μm simultaneously at four sites on the park ground and the roof of a five-story apartment buildings in the upwind and downwind areas of the Olympic Expressway next to apartment complex areas of Seoul, Korea. Using a positive matrix factorization model for source apportionment, eight factors were resolved at each monitoring site: four exhaust emissions of vehicles, one non-exhaust emission of vehicle, two regional sources, and one unknown source. After categorizing monitoring data into three cases by wind conditions, impact and contribution of each vehicle-related source on the local road to the roadside pollution was quantified and characterized by subtracting the urban background concentrations. Throughout the measurement period, the contribution of vehicle-related sources to the particle number concentration at each monitoring site ranged from 61 % to 69 %, while that to the particle mass concentration ranged from 39 % to 87 %. During periods of steady traffic flow and wind blowing from the road to three downwind sites at speeds exceeding >0.5 m/s during working hours, the particle number concentrations at the downwind sites were 2.2–2.5 times higher than the average levels. Among vehicle-related sources, gasoline vehicles with multiple injections or high-emitting diesel vehicles showed the highest contribution to particle number concentrations at all sites. As wind speed increased, the number concentrations of particles from vehicle exhaust and non-exhaust emissions decreased and increased, respectively, probably due to enhanced dilution and transport, respectively. In addition, particle number concentrations showed a parabolic curve-like trend with traffic volumes increasing to approximately 10,000 vehicles/h, and then decreasing for both vehicle exhaust and non-exhaust emissions. These results can be utilized in numerical modeling studies and in establishing traffic-related environmental policies to reduce seasonal and temporal particle exposure near the roadsides.

Source apportionment of PM2.5 and PM10 pollutants near an urban roadside site using positive matrix factorization

This paper presents results from a comprehensive study of source apportionment of particulate matter (PM) of size PM2.5 and PM10 near a busy highway in Sharjah, United Arab Emirates. Source apportionment was carried out using US Environmental Protection Agency (EPA) Positive Matrix Factorization model. Furthermore, backward trajectory analysis and Potential Source Contribution Function were used to assess air mass transport pathways and identify potential source regions, respectively. The results revealed six major sources for PM2.5, including traffic, sea salt, fugitive dust, secondary aerosols, heavy oil combustion and mineral dust. For PM10, four major sources were identified, including secondary aerosols, traffic, sea salt and mineral dust. Traffic emissions were found to be significant contributors to both PM2.5 and PM10 pollution, along with natural sources like sea salt and mineral dust. Backward trajectory analysis indicated the influence of different wind regimes on air mass transport, with contributions from regions like Arabian Gulf, Arabian Sea, Oman and Iran. The Conditional Bivariate Probability Function analysis further explained the impact of local traffic emissions and other sources on PM pollution under varying wind conditions.

Long-term change in winter aerosol composition and sources in Guiyang Southwest China (2003–2020)

This study presents a comprehensive analysis of air quality in China, Southwest China, over four winter seasons: 2003–2004, 2004–2005, 2017–2018 and 2019–2020. We initially collected Total Suspended Particles (TSP) samples during the earlier periods and PM2.5 samples during the later periods. Our goal was to illustrate the changes in sources of atmospheric pollutants over time. By focusing on the chemical composition of water-soluble inorganic ions (WSIIs), we highlighted significant long-term changes in air quality and pollution sources in Guiyang alongside the effectiveness of recent pollution treatment strategies. Historically affected by acid rain and acid pollution, Guiyang has shown notable improvements in air quality. Notably, sulfate pollution, primarily from coal combustion, has significantly decreased, with the sulfates concentration declining from an estimated 19.04 μg m−3 to 30.46 μg m−3 during the winter of 2003–2004, to just 7.37 μg m−3 in PM2.5 during the winter of 2019–2020. Additionally, the mean mass concentration of PM2.5 dropped by 18% between the 2017–2018 and 2019–2020 winters. An increasing ratio of nitrate to sulfate in the aerosols indicates a shift in pollution sources, with secondary nitrate pollution, largely from vehicle emissions, becoming increasingly prevalent. Positive Matrix Factorization (PMF) model analysis identified five major pollution sources, highlighting a transition from secondary sulfate to secondary nitrate as the primary contributors to air pollution in Guiyang, and secondary nitrate pollution mainly from vehicles emission was increasingly severe meanwhile the significance of ammonium should not be overlooked. The results stress the importance of local pollution sources and suggest a need for revised pollution control policies that address the evolving characteristics of aerosols and prioritize the major pollutants in Guiyang, especially during winter months.

Contamination Characteristics and Source Apportionment of Heavy Metal in the Topsoil of a Small Watershed in South Taihang

With the rapid development of industrialization and urbanization, the issue of soil environmental pollution is becoming more and more prominent, especially concerning heavy metal contamination, which has garnered significant scholarly attention. The surface watershed formed by waterline is influenced by various factors such as topography, industrial emissions, and agricultural runoff, resulting in a complex process of migration and accumulation of heavy metal elements from multiple sources. In this study, the pollution characteristics and sources of heavy metal elements Hg, As, Pb, Ni, Cd, Cr, Cu and Zn in 165 surface soil samples from the Manghe River watershed in Jiyuan City were comprehensively analyzed using a variety of methods, including statistics, geostatistics, enriched factor analysis and the Positive Matrix Factorization Model (PMF). The results showed that the concentrations of Hg, Cd, As, Cu, Pb and Zn exceeded their corresponding background values with varying degrees of enrichment. Notably, the average contents of Cd, Hg and Pb were 26.70 times, 3.69 times and 4.49 times higher than those in Chinese soils on average, respectively, showing obvious enrichment characteristics. Moreover, there were distinct spatial distribution patterns for each heavy metal element; Ni and Cr exhibited similar trends mainly controlled by the parent material, while human activities significantly affect the other six elements forming high-value areas around mining and related industries. It is noteworthy that Cu, Hg and Zn were influenced by dominant wind direction in autumn and winter, forming sub-high-value zones in southern forested areas; meanwhile, Cu and Zn were also influenced by agricultural fertilizer application as well as surface runoff, leading to secondary high-value areas in the dryland areas. Further analysis revealed a significant positive correlation among these heavy metal elements, suggesting that they may share common sources. Through the PMF Model, four main factors were identified, with factor 2 (36.25%), factor 1 (23.00%), factor 3 (21.20%) and factor 4 (19.55%) ranked in descending order of contribution rate. The heavy metal pollution in the study area was attributed to anthropogenic activities and natural factors, accounting for 63.75% and 36.25%, respectively. Coal mining, chemical industry smelting, vehicle emissions and excessive use of agrochemicals were identified as the main sources of heavy metal pollution. These pollutants entered the soil through direct emissions, atmospheric deposition, transportation and agricultural activities, exerting a significant impact on the soil environment. Therefore, delving into the spatial distribution pattern of soil heavy metal pollution and precise analysis of its sources are of great importance for effective treatment and remediation of soil heavy metal pollution in small watersheds, maintaining healthy soil ecology and safeguarding human health.

DMFVAE: miRNA-disease associations prediction based on deep matrix factorization method with variational autoencoder

MicroRNAs (miRNAs) are closely related to numerous complex human diseases, therefore, exploring miRNA-disease associations (MDAs) can help people gain a better understanding of complex disease mechanism. An increasing number of computational methods have been developed to predict MDAs. However, the sparsity of the MDAs may hinder the performance of many methods. In addition, many methods fail to capture the nonlinear relationships of miRNA-disease network and inadequately leverage the features of network and neighbor nodes. In this study, we propose a deep matrix factorization model with variational autoencoder (DMFVAE) to predict potential MDAs. DMFVAE first decomposes the original association matrix and the enhanced association matrix, in which the enhanced association matrix is enhanced by self-adjusting the nearest neighbor method, to obtain sparse vectors and dense vectors, respectively. Then, the variational encoder is employed to obtain the nonlinear latent vectors of miRNA and disease for the sparse vectors, and meanwhile, node2vec is used to obtain the network structure embedding vectors of miRNA and disease for the dense vectors. Finally, sample features are acquired by combining the latent vectors and network structure embedding vectors, and the final prediction is implemented by convolutional neural network with channel attention. To evaluate the performance of DMFVAE, we conduct five-fold cross validation on the HMDD v2.0 and HMDD v3.2 datasets and the results show that DMFVAE performs well. Furthermore, case studies on lung neoplasms, colon neoplasms, and esophageal neoplasms confirm the ability of DMFVAE in identifying potential miRNAs for human diseases.

Explainable deep learning and biomechanical modeling for TMJ disorder morphological risk factors.

Clarifying multifactorial musculoskeletal disorder etiologies supports risk analysis, development of targeted prevention, and treatment modalities. Deep learning enables comprehensive risk factor identification through systematic analyses of disease data sets but does not provide sufficient context for mechanistic understanding, limiting clinical applicability for etiological investigations. Conversely, multiscale biomechanical modeling can evaluate mechanistic etiology within the relevant biomechanical and physiological context. We propose a hybrid approach combining 3D explainable deep learning and multiscale biomechanical modeling; we applied this approach to investigate temporomandibular joint (TMJ) disorder etiology by systematically identifying risk factors and elucidating mechanistic relationships between risk factors and TMJ biomechanics and mechanobiology. Our 3D convolutional neural network recognized TMJ disorder patients through participant-specific morphological features in condylar, ramus, and chin. Driven by deep learning model outputs, biomechanical modeling revealed that small mandibular size and flat condylar shape were associated with increased TMJ disorder risk through increased joint force, decreased tissue nutrient availability and cell ATP production, and increased TMJ disc strain energy density. Combining explainable deep learning and multiscale biomechanical modeling addresses the "mechanism unknown" limitation undermining translational confidence in clinical applications of deep learning and increases methodological accessibility for smaller clinical data sets by providing the crucial biomechanical context.

Development of Prediction Model for Oil Formation Volume Factor for Sudanese Crude Oil

Understanding Oil Formation Volume Factor βo is crucial for effective oil field development, impacting well performance analysis, reservoir simulation, and production engineering calculations. Traditionally, βo is determined through costly and time-consuming laboratory tests, prompting the need for accurate mathematical correlations. Existing correlations such as Vasquez-Beggs, Standing-Glaso, and others have been widely used but show varying degrees of accuracy across different operating conditions. In this study, these correlations were evaluated against 95 datasets of experimental βo data for Sudanese crude oils. Statistical analysis revealed that Vasquez-Beggs and Standing- Glaso models performed best, with average absolute errors of 3.4219 and 3.4477, and correlation coefficients of 0.7563 and 0.7213 respectively. Motivated by the limitations of existing correlations, a new ap- proach using Polynomial Neural Networks (PNN) was developed. This model utilized reservoir temperature, gas gravity, gas oil ratio, and API as input parameters, trained on 70% of the dataset and tested on the remaining 30%. The PNN model exhibited superior predictive performance with a relative average absolute error of 2.8607 and a correlation coefficient of 0.9080. This study contributes a robust predictive tool for estimating βo in Sudanese oil fields, offering enhanced accuracy over traditional correlations and facilitating more reliable reservoir management decisions.

Hypergraph-based convex semi-supervised unconstraint symmetric matrix factorization for image clustering

Semi-supervised symmetric nonnegative matrix factorization (SNMF) has been extensively utilized in both linear and nonlinear data clustering tasks. However, the current SNMF model's non-convex objective function faces challenges in global optimization and time efficiency. In this study, we leverage label information to propose a convex and unconstrained symmetric matrix factorization (SMF) model that is thoroughly analyzed for its convexity properties. In order to capture high-order relationships among data, a hypergraph is utilized in the model, which is computationally simple, translation invariant, and naturally normalized. Moreover, based on the analysis and the corresponding experiments in the paper, the model exhibits robustness towards outliers to some extent. Due to the convexity of our proposed model without constraint, it can be efficiently optimized using the Conjugate Gradient (CG) method, one of the most efficient methods available. Therefore, we propose a novel Convex Combination-based Sufficient Descent CG (CSDCG) method, which outperforms other methods across 284 optimization problems within the CUTEst library. In order to evaluate the effectiveness of the proposed method, the semi-supervised clustering experiments are conducted on the eight datasets by comparison with ten state-of-the-art matrix factorization (MF) methods. The experiment results demonstrate its superiority over the other compared methods to handle the clustering problem with better performance and less computational time. The code is available at https://github.com/Pokemer/HCSSMF.

CTF-DDI: Constrained tensor factorization for drug–drug interactions prediction

Computational approaches for predicting drug–drug interactions (DDI) can significantly facilitate combination therapy and drug discovery. Existing similarity-based methods often overlook simple yet valuable structural information or ignore multiple relationships from biological entities (e.g., target proteins and enzymes). Meanwhile, matrix factorization-based methods can alleviate the inherent sparsity issues in DDI data. However, this line of work usually only considers the original association information of DDI pairs. To address these issues, we proposed a novel tensor factorization strategy with effective constraint terms (CTF-DDI) for potential DDI prediction. Specifically, we first obtained drug features by constructing specific similarity matrices based on drug structure and drug-related biological associations. Then, a novel constrained tensor factorization (CTF) module was designed to further reconstruct drug similarity by introducing Hessian and L2,1 regularization as constraints. Finally, we trained a deep neural network to extract nonlinear features for DDI prediction. Experimental results on two benchmark datasets demonstrated that the proposed CTF-DDI model outperforms classical tensor factorization and deep learning models. Furthermore, ablation and case studies validated the performance of CTF-DDI in DDI prediction. The source code of CTF-DDI is available at https://github.com/angelfacedac/CTF_DDI.

On solving a rank regularized minimization problem via equivalent factorized column-sparse regularized models

On solving a rank regularized minimization problem via equivalent factorized column-sparse regularized models

Distribution Characteristics, Risk Assessment, and Source Analysis of Heavy Metals in Farmland Soil of a Karst Area in Southwest China

Soil environmental quality related to the residents’ life, health, and safety, has been the hotspot issues in science of ecological environment protection. Evaluating the distribution characteristics, ecological risk, and source of heavy metals in farmland is important for protecting soil resources. The agricultural area of Lianhua town, Gongcheng County, Guilin is a typical karst landform. In response to the problem of heavy metal pollution and complex sources in the soil of this area, the characteristics and sources of heavy metal pollution in the soil profiles from farmland, abandoned land, and forest were studied using the single-factor index method, the geoaccumulation index (Igeo) principal component analysis (PCA) and positive matrix factorization (PMF) model. The results showed that: (1) that the contents of cadmium (Cd), chromium (Cr), copper (Cu), nickel (Ni), lead (Pb), and zinc (Zn) in the soil profile of the study area were higher than that of the soil elements background values in Guangxi. The total and available forms contents of all heavy metal elements exhibited the characteristics of accumulation in the surface profile; (2) among the six heavy elements, the contents of Cd were in a moderately to heavily polluted state. The contents of Cd in some soil profiles exceeded the control standard for agricultural land soil pollution. The contents of Zn and Ni were from slightly to moderately polluted in areas with frequent agricultural activities; (3) according to the PCA and PMF model, there were three main sources of heavy metals in the study area. Among them, Cd, Cu, Ni, and Zn are related to agricultural activities; the elements As, Cd, Cr, and Hg are closely related to geological background; Pb and Zn are mainly affected by atmospheric sedimentation of transportation. Agricultural activities and natural geological background are the main contribution sources of heavy metals in soil. Human activities are the main factors that cause the accumulation of heavy metals in soil. This research has theoretical guidance and practical significance for the prevention and control of soil heavy metal pollution and the protection of farmland environmental quality in the region.

Distribution, risk evaluation, and source allocation of cesium and strontium in surface soil in a mining city.

Radioactive nuclides cesium (Cs) and strontium (Sr) possess long half-lives, with 135Cs at approximately 2.3 million years and 87Sr at about 49 billion years. Their persistent accumulation can result in long-lasting radioactive contamination of soil ecosystems. This study employed geo-accumulation index (Igeo), pollution load index (PLI), potential ecological risk index (PEPI), health risk assessment model (HRA), and Monte Carlo simulation to evaluate the pollution and health risks of Cs and Sr in the surface soil of different functional areas in a typical mining city in China. Positive matrix factorization (PMF) model was used to elucidate the potential sources of Cs and Sr and the respective contribution rates of natural and anthropogenic sources. The findings indicate that soils in the mining area exhibited significantly higher levels of Cs and Sr pollution compared to smelting factory area, agricultural area, and urban residential area. Strontium did not pose a potential ecological risk in any studied functional area. The non-carcinogenic health risk of Sr to the human body in the study area was relatively low. Because of the lack of parameters for Cs, the potential ecological and human health risks of Cs was not calculated. The primary source of Cs in the soil was identified as the parent material from which the soil developed, while Sr mainly originated from associated contamination caused by mining activities. This research provides data for the control of Cs and Sr pollution in the surface soil of mining city.

Volatile Organic Compounds on Rhodes Island, Greece: Implications for Outdoor and Indoor Human Exposure.

Volatile organic compounds (VOC) are considered a class of pollutants with a significant presence in indoor and outdoor air and serious health effects. The aim of this study was to measure and evaluate the levels of outdoor and indoor VOCs at selected sites on Rhodes Island, Greece, during the cold and warm periods of 2023. Spatial and seasonal variations were evaluated; moreover, cancer and non-cancer inhalation risks were assessed. For this purpose, simultaneous indoor-outdoor air sampling was carried out on the island of Rhodes. VOCs were determined by Thermal Desorption-Gas Chromatography/Mass Spectroscopy (TD-GC/MS). Fifty-six VOCs with frequencies ≥ 50% were further considered. VOC concentrations (∑56VOCs) at all sites were found to be higher in the warm period. In the warm and cold sampling periods, the highest concentrations were found at the port of Rhodes City, while total VOC concentrations were dominated by alkanes. The Positive Matrix Factorization (PMF) model was applied to identify the VOC emission sources. Non-cancer and cancer risks for adults were within the safe levels.

Unveiling nitrate origins in semiarid aquifers: A comparative analysis of Bayesian isotope mixing models using nitrate and boron isotopes and a Positive Matrix Factorization model

Nitrate contamination of groundwater is a pressing global concern, affecting over 80 million people worldwide, with agricultural activities being the primary contributor to nitrogen inputs into aquifers. The primary objective of this study was to identify the predominant sources of nitrate pollution and biogeochemical transformations in the semiarid region of the Meoqui-Delicias aquifer, Mexico. In this region, the uncontrolled use of chemical fertilizers and manure leads to excessive nutrient input, which accelerates the deterioration of groundwater quality. This study introduces an innovative dual-model approach (δ15NNO3 vs. δ11B) to compare the Bayesian Isotope Mixing Model (BIMM) with Positive Matrix Factorization (PMF) for nuanced source apportionment. This approach enhanced the differentiation between manure and sewage as nitrate sources. Results from the δ15NNO3 vs. δ11B model revealed that manure (52.4%) was the most significant source of nitrate pollution in the aquifer, followed by soil (37.4%), chemical fertilizers (5.5%), and sewage (4.7%). The PMF model corroborated this finding and indicated that 60.2% of the NO3–-N pollution in the aquifer was attributed to manure and sewage, confirming the superior performance of the proposed BIMM in source differentiation. Our findings enhance the understanding of nitrate dynamics in semi-arid regions and can serve as a scientific evidence base for targeted interventions in nutrient management in the study area and elsewhere.

A comparison of models for predicting the maximum spreading factor in droplet impingement

The maximum spreading factor during droplet impact on a dry surface is a pivotal parameter of a range of applications, including inkjet printing, anti-icing, and micro-droplet transportation. It is determined by a combination of the inertial force, viscous force, surface tension, and fluid–solid interaction. There are currently a series of qualitative and quantitative prediction models for the maximum spreading factor rooted in both momentum and energy conservation. However, the performance of these models on consistent experimental samples remains ambiguous. In this work, a comprehensive set of 785 experimental samples spanning the last four decades is compiled. These samples encompass Weber numbers ranging from 0.038 to 2447.7 and Reynolds numbers from 9 to 34 339. A prediction model is introduced that employs a neural network, which achieves an average relative error of less than 16.6% with a standard error of 0.018 08 when applied to the test set. Following this, a fair comparison is presented of the accuracy, generality, and stability of different prediction models. Although the neural network model provides superior accuracy and generality, its stability is weaker than that of Scheller's We-Re-dependent formula, chiefly due to the absence of physical constraints. Subsequently, a physics-informed prediction model is introduced by considering a physical loss term. This model demonstrates comprehensive enhancements compared to the original neural network, and the average relative and standard errors for this model are reduce to 13.6% and 0.010 59, respectively. This novel model should allow for the rapid and precise prediction of the maximum spreading factor across a broad range of parameters for various applications.

Learning Single Spectral Abundance for Hyperspectral Subpixel Target Detection.

Due to the limitation of target size and spatial resolution, targets of interest in hyperspectral images (HSIs) often appear as subpixel targets, which makes hyperspectral target detection still faces an important bottleneck, that is, subpixel target detection. In this article, we propose a new detector by learning single spectral abundance for hyperspectral subpixel target detection (denoted as LSSA). Different from most existing hyperspectral detectors that are designed based on a match of the spectrum assisted by spatial information or focusing on the background, the proposed LSSA addresses the problem of detecting subpixel targets by learning a spectral abundance of the target of interest directly. In LSSA, the abundance of the prior target spectrum is updated and learned, while the prior target spectrum is fixed in a nonnegative matrix factorization (NMF) model. It turns out that such a way is quite effective to learn the abundance of subpixel targets and contributes to detecting subpixel targets in hyperspectral imagery (HSI). Numerous experiments are conducted on one simulated dataset and five real datasets, and the results indicate that the LSSA yields superior performance in hyperspectral subpixel target detection and outperforms its counterparts.

Robust and Effective: A Deep Matrix Factorization Framework for Classification.

For complex data, high dimension and high noise are challenging problems, and deep matrix factorization shows great potential in data dimensionality reduction. In this article, a novel robust and effective deep matrix factorization framework is proposed. This method constructs a dual-angle feature for single-modal gene data to improve the effectiveness and robustness, which can solve the problem of high-dimensional tumor classification. The proposed framework consists of three parts, deep matrix factorization, double-angle decomposition, and feature purification. First, a robust deep matrix factorization (RDMF) model is proposed in the feature learning, to enhance the classification stability and obtain better feature when faced with noisy data. Second, a double-angle feature (RDMF-DA) is designed by cascading the RDMF features with sparse features, which contains the more comprehensive information in gene data. Third, to avoid the influence of redundant genes on the representation ability, a gene selection method is proposed to purify the features by RDMF-DA, based on the principle of sparse representation (SR) and gene coexpression. Finally, the proposed algorithm is applied to the gene expression profiling datasets, and the performance of the algorithm is fully verified.