MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Impact of Delivery Mode on Morbidity in Preterm Infants with Very Low Birth Weights (<1500 Grams)

The mode of delivery and gestational age for very-low-birth-weight (VLBW) preterm infants are not yet well established and are constant topics of debate. Objective: To analyze the impact of delivery mode on morbidity in preterm infants weighing less than 1500 g. Results: Among 21,957 births, 81 were analyzed;53 were delivered vaginally, and 28 were delivered by cesarean section. The median maternal age, gestational age and body mass index among those delivered vaginally and by cesarean section were 20 years and 22.5 years, 27.6 weeks and 30.1 weeks, and 26.0 kg/m2 and 27.8 kg/m2, respectively. With respect to neonatal blood gas parameters, for those born vaginally and by cesarean section, the median pH was 7.32 and 7.24, the pCO2 was 41.5 mmHg and 51.1 mmHg, and the pO2 was 22.3 mmHg and 16 mmHg. The median fetal weight among those born by cesarean section and vaginally were 1180 g and 955 g, respectively. The median Apgar scores at the first and fifth minutes among those born by cesarean section and vaginally were 5.00 and 8.00 and 4.50 and 7.00, respectively. Conclusion: There was no significant difference between the results of vaginal and cesarean delivery for VLBW infants. Thus, further studies on this subject are needed.

Transfer learning for well logging formation evaluation using similarity weights

Machine learning has been widely applied in well logging formation evaluation studies.However,several challenges negatively impacted the generalization capabilities of machine learning models in practical imple-mentations,such as the mismatch of data domain between training and testing datasets,imbalances among sample categories,and inadequate representation of data model.These issues have led to substantial insufficient identification for reservoir and significant deviations in subsequent evaluations.To improve the transferability of machine learning models within limited sample sets,this study proposes a weight transfer learning framework based on the similarity of the labels.The similarity weighting method includes both hard weights and soft weights.By evaluating the similarity between test and training sets of logging data,the similarity results are used to estimate the weights of training samples,thereby optimizing the model learning process.We develop a double experts’network and a bidirectional gated neural network based on hierarchical attention and multi-head attention(BiGRU-MHSA)for well logs reconstruction and lithofacies classification tasks.Oil field data results for the shale strata in the Gulong area of the Songliao Basin of China indicate that the double experts’network model performs well in curve reconstruction tasks.However,it may not be effective in lithofacies classification tasks,while BiGRU-MHSA performs well in that area.In the study of constructing large-scale well logging processing and formation interpretation models,it is maybe more beneficial by employing different expert models for combined evaluations.In addition,although the improvement is limited,hard or soft weighting methods is better than unweighted(i.e.,average-weighted)in significantly different adjacent wells.The code and data are open and available for subsequent studies on other lithofacies layers.

Stability Prediction in Smart Grid Using PSO Optimized XGBoost Algorithm with Dynamic Inertia Weight Updation

Prediction of stability in SG(Smart Grid)is essential in maintaining consistency and reliability of power supply in grid infrastructure.Analyzing the fluctuations in power generation and consumption patterns of smart cities assists in effectively managing continuous power supply in the grid.It also possesses a better impact on averting overloading and permitting effective energy storage.Even though many traditional techniques have predicted the consumption rate for preserving stability,enhancement is required in prediction measures with minimized loss.To overcome the complications in existing studies,this paper intends to predict stability from the smart grid stability prediction dataset using machine learning algorithms.To accomplish this,pre-processing is performed initially to handle missing values since it develops biased models when missing values are mishandled and performs feature scaling to normalize independent data features.Then,the pre-processed data are taken for training and testing.Following that,the regression process is performed using Modified PSO(Particle Swarm Optimization)optimized XGBoost Technique with dynamic inertia weight update,which analyses variables like gamma(G),reaction time(tau1–tau4),and power balance(p1–p4)for providing effective future stability in SG.Since PSO attains optimal solution by adjusting position through dynamic inertial weights,it is integrated with XGBoost due to its scalability and faster computational speed characteristics.The hyperparameters of XGBoost are fine-tuned in the training process for achieving promising outcomes on prediction.Regression results are measured through evaluation metrics such as MSE(Mean Square Error)of 0.011312781,MAE(Mean Absolute Error)of 0.008596322,and RMSE(Root Mean Square Error)of 0.010636156 and MAPE(Mean Absolute Percentage Error)value of 0.0052 which determine the efficacy of the system.

Sparseness-controlled non-negative tensor factorization and its application in machinery fault diagnosis

Aiming at the problems of bispectral analysis when applied to machinery fault diagnosis, a machinery fault feature extraction method based on sparseness-controlled non-negative tensor factorization （SNTF） is proposed. First, a non-negative tensor factorization（NTF） algorithm is improved by imposing sparseness constraints on it. Secondly, the bispectral images of mechanical signals are obtained and stacked to form a third-order tensor. Thirdly, the improved algorithm is used to extract features, which are represented by a series of basis images from this tensor. Finally, coefficients indicating these basis images＇ weights in constituting original bispectral images are calculated for fault classification. Experiments on fault diagnosis of gearboxes show that the extracted features can not only reveal some nonlinear characteristics of the system, but also have intuitive meanings with regard to fault characteristic frequencies. These features provide great convenience for the interpretation of the relationships between machinery faults and corresponding bispectra.

Local hierarchical non-negative tensor factorization and its application in machinery fault diagnosis

Aiming at the slow convergence and low accuracy problems of the traditional non-negative tensor factorization, a local hierarchical non-negative tensor factorization method is proposed by applying the local objective function theory to non- negative tensor factorization and combining the three semi-non- negative matrix factorization（NMF） model. The effectiveness of the method is verified by the facial feature extraction experiment. Through the decomposition of a series of an air compressor＇s vibration signals composed in the form of a bispectrum by this new method, the basis images representing the fault features and corresponding weight matrices are obtained. Then the relationships between characteristics and faults are analyzed and the fault types are classified by importing the weight matrices into the BP neural network. Experimental results show that the accuracy of fault diagnosis is improved by this new method compared with other feature extraction methods.

NEW SHADOWED C-MEANS CLUSTERING WITH FEATURE WEIGHTS

Partition-based clustering with weighted feature is developed in the framework of shadowed sets. The objects in the core and boundary regions, generated by shadowed sets-based clustering, have different impact on the prototype of each cluster. By integrating feature weights, a formula for weight calculation is introduced to the clustering algorithm. The selection of weight exponent is crucial for good result and the weights are updated iteratively with each partition of clusters. The convergence of the weighted algorithms is given, and the feasible cluster validity indices of data mining application are utilized. Experimental results on both synthetic and real-life numerical data with different feature weights demonstrate that the weighted algorithm is better than the other unweighted algorithms.

Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

Three methods for generating monotonic OWA operator weights with given orness level

Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples.

Some OWA operator weights determination methods with RIM quantifier

Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA weights generating method is modified to make the generated weights be monotonic,which can be used to express the decision maker's consistent preference information.Finally,both of these weights generating methods are extended to their generic forms,so that they can generate the OWA weights for any ordinary elements set with any given aggregated value.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

New approach to determine common weights in DEA efficiency evaluation model

Data envelopment analysis（DEA） is a mathematical programming approach to appraise the relative efficiencies of peer decision-making unit（DMU）,which is widely used in ranking DMUs.However,almost all DEA-related ranking approaches are based on the self-evaluation efficiencies.In other words,each DMU chooses the weights it prefers to most,so the resulted efficiencies are not suitable to be used as ranking criteria.Therefore this paper proposes a new approach to determine a bundle of common weights in DEA efficiency evaluation model by introducing a multi-objective integer programming.The paper also gives the solving process of this multi-objective integer programming,and the solution is proven a Pareto efficient solution.The solving process ensures that the obtained common weight bundle is acceptable by a great number of DMUs.Finally a numeral example is given to demonstrate the approach.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

Genome-Wide Association Study for Certain Carcass Traits and Organ Weights in a Large White×Minzhu Intercross Porcine Population

Porcine carcass traits and organ weights have important economic roles in the swine industry. A total of 576 animals from a Large White×Minzhu intercross population were genotyped using the Illumina PorcineSNP60K Beadchip and were phenotyped for 10 traits, speciifcally, backfat thickness （6-7 libs）, carcass length, carcass weight, foot weight, head weight, heart weight, leaf fat weight, liver weight, lung weight and slaughter body weight. The genome-wide association study （GWAS） was assessed by Genome Wide Rapid Association using the mixed model and regression-genomic control approach. A total of 31 single nucleotide polymorphisms （SNPs） （with the most signiifcant SNP being MARC0033464, P value=6.80×10-13） were located in a 9.76-Mb （31.24-41.00 Mb） region on SSC7 and were found to be signiifcantly associated with one or more carcass traits and organ weights. High percentage of phenotypic variance explanation was observed for each trait ranging from 31.21 to 67.42%. Linkage analysis revealed one haplotype block of 495 kb, in which the most signiifcant SNP being MARC0033464 was contained, on SSC7 at complete linkage disequilibrium. Annotation of the pig reference genome suggested 6 genes （GRM4, HMGA1, NUDT3, RPS10, SPDEF and PACSIN1） in this candidate linkage disequilibrium （LD） interval. Functional analysis indicated that the HMGA1 gene presents the prime biological candidate for carcass traits and organ weights in pig, with potential application in breeding programs.

Spatial assessment for groundwater quality based on GIS and improved fuzzy comprehensive assessment with entropy weights

The objective of the research is to evaluate spatial groundwater quality based on improved fuzzy comprehensive assessment model with entropy weights(FCAEW)in geographical information system(GIS)environment.This paper explores the method of comprehensive evaluation of groundwater and sets up an evaluation model applying GIS and FCAEW.Groundwater samples were collected and analyzed from 29 wells in Zhenping County,China.Six parameters were chosen including chloride,sulfate,total hardness,nitrate,fluoride and color.Better spatial interpolation methods for evaluated parameters are found out and selected according to the minimum cross-validation errors from the interpolation methods.FCAEW model was carried out with the help of GIS which makes the evaluating process simpler and easier and more automatically,effectively,efficiently and intelligently.The result embodies the feasibility and effectiveness of FCAEW in GIS when compared with other comprehensive evaluation methods.

Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

GIS Predictive Model for Producing Hydrothermal Gold Potential Map Using Weights of Evidence Approach in Gengma Region, Sanjiang District, China

Gengma region, Sanjiang district is known to have some large-scale gold deposits. GIS predictive model for hydrothermal gold potential was carried out in this region using weights of evidence modeling technique. Datasets used include large-scale hydrothermal gold deposit records, geological, geophysical and remote sensing imagery. Based on the geological and mineral characteristics of areas with known gold occurrences in Sanjiang, several geological features were thought to be indicative of areas with potential for the occurrence of hydrothermal gold deposits. Indicative features were extracted from geoexploration datasets for use as input in the predictive model. The features include host rock lithology, geologic structures, wallrock alteration and associated (volcanic-plutonic) igneous rocks. To determine which of the indicative geological features are important spatial predictors of area with potential for gold deposits, spatial analysis was done through the modeling method. The input maps were buffered and the optimum distance of spatial association for each geological feature was determined by calculating the contrast and studentized contrast. Five feature maps were converted to binary predictor patterns and used as evidential layers for predictive modeling. The binary patterns were integrated in two combinations, each of which consists of four patterns in order to avoid over prediction due to the effect of duplicate features in the two structural evidences. The two produced potential maps define almost similar favorable zones. Areas of intersections between these zones in the two potential maps placed the highest predictive favorable zones in the region.

Method for multi-attribute group decision-making based on the compromise weights

Multi-attribute group decision-making problems are considered where information on both attribute weights and value scores of consequences is incomplete.In group decision analysis,if preference information about alternatives is provided by participants,it should be verified whether there exist compromise weights that can support all the preference relations.The different compromise weight vectors may differ for the ranking of the alternatives.In the case that compromise weights exist,the method is proposed to find out all the compromise weight vectors in order to rank the alternatives.Based on the new feasible domain of attribute weights determined by all the compromise weight vectors and the incomplete information on value scores of consequences,dominance relations between alternatives are checked by a nonlinear goal programming model which can be transformed into a linear one by adopting a transformation.The checked dominance relations uniformly hold for all compromise weight vectors and the incomplete information on value scores of consequences.A final ranking of the alternatives can be obtained by aggregating these dominance relations.

Mining Weights of Land Evaluation Factors Based on Cloud Model and Correlation Analysis

The veracity of land evaluation is tightly related to the reasonable weights of land evaluation fac- tors. By mapping qualitative linguistic words into a fine-changeable cloud drops and translating the uncertain factor conditions into quantitative values with the uncertain illation based on cloud model, and then, inte- grating correlation analysis, a new way of figuring out the weight of land evaluation factors is proposed. It may solve the limitations of the conventional ways.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graphregularization for non-negative matrix factorization(TV-GNMF).The method utilizes non-negative matrix factorization by total variation constraint and graph regularization.The main contributions of our work are the following.First,total variation is incorporated into NMF to control the diffusion speed.The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information.Second,we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power.Third,the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.