ANALYSIS OF BENDING, VIBRATION AND STABILITY FOR THIN PLATE ON ELASTIC FOUNDATION BY THE MULTIVARIABLE SPLINE ELEMENT METHOD

In this paper, the bicubic splines in product form are used to construct the multi-field functions for bending moments, twisting moment and transverse displacement of the plate on elastic foundation. The multivariable spline element equations are derived, based on the mixed variational principle. The analysis and calculations of bending, vibration and stability of the plates on elastic foundation are presented in the paper. Because the field functions of plate on elastic foundation are assumed independently, the precision of the field variables of bending moments and displacement is high.

AN ALGEBRAIC METHOD FOR POLE PLACEMENT IN MULTIVARIABLE SYSTEMS

This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.

A NEW METHOD FOR THE CONSTRUCTIONOF MULTIVARIATE MINIMALINTERPOLATION POLYNOMIAL

The extended Hermite interpolation problem on segment points set over n-dimensional Euclidean space is considered. Based on the algorithm to compute the Gr?bner basis of Ideal given by dual basis a new method to construct minimal multivariate polynomial which satisfies the interpolation conditions is given.

The Method for Optimum Estimation of COVID-19 Variant Type Virus Infection Status Analysis by the Multivariate Analysis Considering the Environmental Variability Impact in Japan

Currently, the estimated value of the effective reproduction number (ERN), which is an index for grasping the COVID-19 infection status, is used for important planning and evaluation of infection prevention measures. Since ERN in the Sequential SIR model fluctuates in multiple dimensions due to changes in the surrounding environment, it is difficult to set the appropriate accuracy of the uncertainty region of the estimated data. The challenge in this study is to build a mathematical model of infectious disease according to the characteristics and data characteristics of the infectious disease and select an appropriate estimation method. Highly accurate quantitative research that analyzes the validity of “how infectious diseases prevail” from an academic point of view is the key to prediction and estimation in appropriate infection situation analysis. In this study, we adopted a statistical multivariate analysis method (T method) that enables evaluation and prediction of important factors related to ERN estimation and analysis of phenomena that change in real time (time series analysis). It was clarified that it is possible to estimate with higher accuracy by applying the T method to the estimated value of ERN by the current SIR mathematical model.

Spatial variation assessment of groundwater quality using multivariate statistical analysis(Case Study:Fasa Plain,Iran)

Groundwater is considered as one of the most important sources for water supply in Iran.The Fasa Plain in Fars Province,Southern Iran is one of the major areas of wheat production using groundwater for irrigation.A large population also uses local groundwater for drinking purposes.Therefore,in this study,this plain was selected to assess the spatial variability of groundwater quality and also to identify main parameters affecting the water quality using multivariate statistical techniques such as Cluster Analysis(CA),Discriminant Analysis(DA),and Principal Component Analysis(PCA).Water quality data was monitored at 22 different wells,for five years(2009-2014)with 10 water quality parameters.By using cluster analysis,the sampling wells were grouped into two clusters with distinct water qualities at different locations.The Lasso Discriminant Analysis(LDA)technique was used to assess the spatial variability of water quality.Based on the results,all of the variables except sodium absorption ratio(SAR)are effective in the LDA model with all variables affording 92.80%correct assignation to discriminate between the clusters from the primary 10 variables.Principal component(PC)analysis and factor analysis reduced the complex data matrix into two main components,accounting for more than 95.93%of the total variance.The first PC contained the parameters of TH,Ca2+,and Mg2+.Therefore,the first dominant factor was hardness.In the second PC,Cl-,SAR,and Na+were the dominant parameters,which may indicate salinity.The originally acquired factors illustrate natural(existence of geological formations)and anthropogenic(improper disposal of domestic and agricultural wastes)factors which affect the groundwater quality.

Analysis of morphological characteristics of gravels based on digital image processing technology and self-organizing map

A comprehensive understanding of spatial distribution and clustering patterns of gravels is of great significance for ecological restoration and monitoring.However,traditional methods for studying gravels are low-efficiency and have many errors.This study researched the spatial distribution and cluster characteristics of gravels based on digital image processing technology combined with a self-organizing map(SOM)and multivariate statistical methods in the grassland of northern Tibetan Plateau.Moreover,the correlation of morphological parameters of gravels between different cluster groups and the environmental factors affecting gravel distribution were analyzed.The results showed that the morphological characteristics of gravels in northern region(cluster C)and southern region(cluster B)of the Tibetan Plateau were similar,with a low gravel coverage,small gravel diameter,and elongated shape.These regions were mainly distributed in high mountainous areas with large topographic relief.The central region(cluster A)has high coverage of gravels with a larger diameter,mainly distributed in high-altitude plains with smaller undulation.Principal component analysis(PCA)results showed that the gravel distribution of cluster A may be mainly affected by vegetation,while those in clusters B and C could be mainly affected by topography,climate,and soil.The study confirmed that the combination of digital image processing technology and SOM could effectively analyzed the spatial distribution characteristics of gravels,providing a new mode for gravel research.

Expanding the Scope of Multivariate Regression Approaches in Cross-Omics Research

Recent technological advancements and developments have led to a dramatic increase in the amount of high-dimensional data and thus have increased the demand for proper and efficient multivariate regression methods.Numerous traditional multivariate approaches such as principal component analysis have been used broadly in various research areas,including investment analysis,image identification,and population genetic structure analysis.However,these common approaches have the limitations of ignoring the correlations between responses and a low variable selection efficiency.Therefore,in this article,we introduce the reduced rank regression method and its extensions,sparse reduced rank regression and subspace assisted regression with row sparsity,which hold potential to meet the above demands and thus improve the interpretability of regression models.We conducted a simulation study to evaluate their performance and compared them with several other variable selection methods.For different application scenarios,we also provide selection suggestions based on predictive ability and variable selection accuracy.Finally,to demonstrate the practical value of these methods in the field of microbiome research,we applied our chosen method to real population-level microbiome data,the results of which validated our method.Our method extensions provide valuable guidelines for future omics research,especially with respect to multivariate regression,and could pave the way for novel discoveries in microbiome and related research fields.

Chemical Characteristics Combined with Bioactivity for Comprehensive Evaluation of Tumuxiang Based on HPLC-DAD and Multivariate Statistical Methods

Background: The dried roots of Inula helenium L.(IH) and Inula racemosa Hook f.(IR) are used commonly as folk medicine under the name of "tumuxiang(TMX)". Phenolic acid compounds and their derivatives, as main active constituents in IH and IR, exhibit prominent anti-inflammation effect.Objective: To develop a holistic method based on chemical characteristic and anti-inflammation effect for systematically evaluating the quality of twenty-seven TMX samples(including 18 IH samples and 9 IR samples) from different origins.Methods: HPLC fingerprints data of AL(Aucklandia lappa Decne.) whose dried root was similar with HR was added for classification analysis. The HPLC fingerprints of twenty-seven TMX samples and four AL samples were evaluated using hierarchical clustering analysis(HCA) and principle component analysis(PCA). The spectrum-efficacy model between HPLC fingerprints and anti-inflammatory activities was investigated by principal component regression(PCR) and partial least squares(PLS).Results: All samples were successfully divided into three main clusters and peaks 7, 9, 11, 22, 24 and 26 had a primary contribution to classify these medicinal herbs. The results were in accord with the appraisal results of herbs. The spectrum-efficacy relationship results indicated that citric acid, quinic acid, caffeic acid-β-D-glucopyranoside, chlorogenic acid, caffeic acid, 1,3-O-dicaffeoyl quinic acid, tianshic acid and 3β-Hydroxypterondontic acid had main contribution to anti-inflammatory activities.Conclusion: This comprehensive strategy was successfully used for identification of IH, IR and AL, which provided a reliable and adequate theoretical basis for the bioactivity relevant quality standards and studying the material basis of anti-inflammatory effect of TMX.

Prediction of lateral wall deflections of excavations in water-rich sands by a modified multivariate-adaptiveregression- splines method

Machine learning methods have advantages in predicting excavation-induced lateral wall displacements.Due to lack of sufficient field data,training data for prediction models were often derived from the results of numerical simulations,leading to poor prediction accuracy.Based on a specific quantity of data,a multivariate adaptive regression splines method(MARS)was introduced to predict lateral wall deflections caused by deep excavations in thick water-rich sands.Sensitivity of lateral wall deflections to affecting factors was analyzed.It is disclosed that dewatering mode has the most significant influence on lateral wall deflections,while the soil cohesion has the least influence.Using crossvalidation analysis,weights were introduced to modify the MARS method to optimize the prediction model.Comparison of the predicted and measured deflections shows that the prediction based on the modified multivariate adaptive regression splines method(MMARS)is more accurate than that based on the traditional MARS method.The prediction model established in this paper can help engineers make predictions for wall displacement,and the proposed methodology can also serve as a reference for researchers to develop prediction models.

MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS

This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity,orthogonality of Fourier basis system, partial sum of Fourier series and its approximation behavior, can be moved on the new non tensor-product partition case.

A Comparative Analysis of Binary Logistic Regression and Analytical Hierarchy Process for Landslide Susceptibility Assessment in the Dobrovǎt River Basin,Romania

A correct assessment of the landslide susceptibility component is extremely useful for the diminution of associated potential risks to local economic development, particularly in regard to land use planning and soil conservation. The purpose of the present study was to compare the usefulness of two methods, i.e., binary logistic regression(BLR) and analytical hierarchy process(AHP), for the assessment of landslide susceptibility over a 130-km^2 area in the Moldavian Plateau(eastern Romania) region, where landslides affect large areas and render them unsuitable for agriculture. A large scale inventory mapping of all types of landslides(covering 13.7% of the total area) was performed using orthophoto images, topographical maps, and field surveys. A geographic information system database was created, comprising the nine potential factors considered as most relevant for the landsliding process. Five factors(altitude, slope angle, slope aspect, surface lithology, and land use) were further selected for analysis through the application of a tolerance test and the stepwise filtering procedure of BLR. For each predictor, a corresponding raster layer was built and a dense grid of equally spaced points was generated, with an approximately equal number of points inside and outside the landslide area, in order to extract the values of the predictors from raster layers. Approximately half of the total number of points was used for model computation, while the other half was used for validation. Analytical hierarchy process was employed to derive factor weights, with several pair-wise comparison matrices being tested for this purpose. The class weights, on a scale of 0 to 1, were taken as normalized landslide densities. A comparison of results achieved through these two approaches showed that BLR was better suited for mapping landslide susceptibility, with 82.8% of the landslide area falling into the high and very high susceptibility classes. The susceptibility class separation using standard deviation was superior to either the equal interval or the natural break method. Results from the study area suggest that the statistical model achieved by BLR could be successfully extrapolated to the entire area of the Moldavian Plateau.

Two-component Brownian coagulation: Monte Carlo simulation and process characterization

The compositional distribution within aggregates of a given size is essential to the functionality of com- posite aggregates that are usually enlarged by rapid Brownian coagulation, There is no analytical solution for the process of such two-component systems, Monte Carlo method is an effective numerical approach for two-component coagulation, In this paper, the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation, respectively, in the continuum regime, the free-molecular regime and the transition regime. It is found that （1） for Brownian coagulation in the continuum regime and in the free-molecular regime, the mono-variate compositional distribution, i.e., the number density distribution function of one component amount （in the form of volume of the component in aggregates） satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; （2） however, for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and （3） the bivariate compositional distribution, i.e., the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form. Moreover, other new features inherent to aggregative mixing are also demonstrated; e.g., the degree of mixing between components, which is largely controlled by the initial compositional mass fraction, improves as aggregate size increases.

A review of 20 years of naive tests of significance for high-dimensional mean vectors and covariance matrices

We introduce the so-called naive tests and give a brief review of the new developments. Naive testing methods are easy to understand and perform robustly, especially when the dimension is large. We focus mainly on reviewing some naive testing methods for the mean vectors and covariance matrices of high-dimensional populations, and we believe that this naive testing approach can be used widely in many other testing problems.