Correlation Degree and Correlation Coefficient of Multi-Output Functions

We present definitions of the correlation degree and correlation coefficient of multi-output functions. Two relationships about the correlation degree of multi-output functions are proved. One is between the correlation degree and independency, the other is between the correlation degree and balance. Especially the paper discusses the correlation degree of affine multioutput functions. We demonstrate properties of the correlation coefficient of multi-output functions. One is the value range of the correlation coefficient, one is the relationship between the correlation coefficient and independency, and another is the sufficient and necessary condition that two multi-output functions are equivalent to each other.

Application of Grey Correlation Degree Analysis in Broad Bean Strain Screening

[Objectives] The aim was to clarify the target and approach to purifying and selecting Baoshan Touxinlv broad bean. [Methods] In 2012,5 homozygous strains were selected successfully as the material,and completely randomized block arrangement was adopted with 3 repeated trials to analyze the effects of plant height,effective length of podding branches,branch number per plant,pod number per plant,grain number per pod and 100-grain weight on the yield of each plant in the system. [Results] The results showed that the effects of the various factors on the yield of Baoshan broad beans were in the order of grain number per pod 〉 effective length of podding branches 〉 100-grain weight 〉 pod number per plant 〉 branch number per plant 〉 plant height. [Conclusions]In breeding new strains of Baoshan broad beans,under the premise of ensuring the seed nature and quality of the original variety,priority should be given to the gain number per pod and the increment of effective length of podding branches,followed by the pod number per plant,branch number per plant,plant height,which is the best way to breed new strains of Baoshan Touxinlv broad beans.

A Two-Stage Feature Selection Method for Text Categorization by Using Category Correlation Degree and Latent Semantic Indexing

With the purpose of improving the accuracy of text categorization and reducing the dimension of the feature space,this paper proposes a two-stage feature selection method based on a novel category correlation degree(CCD)method and latent semantic indexing(LSI).In the first stage,a novel CCD method is proposed to select the most effective features for text classification,which is more effective than the traditional feature selection method.In the second stage,document representation requires a high dimensionality of the feature space and does not take into account the semantic relation between features,which leads to a poor categorization accuracy.So LSI method is proposed to solve these problems by using statistically derived conceptual indices to replace the individual terms which can discover the important correlative relationship between features and reduce the feature space dimension.Firstly,each feature in our algorithm is ranked depending on their importance of classification using CCD method.Secondly,we construct a new semantic space based on LSI method among features.The experimental results have proved that our method can reduce effectively the dimension of text vector and improve the performance of text categorization.

The effects of degree correlations on network topologies and robustness

Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.

Three vertex degree correlations of fixed act-size collaboration networks

A rate equation approach was presented for the exact computation of the three vertex degree correlations of the fixed act-size collaboration networks.Measurements of the three vertex degree correlations were based on a rate equation in the continuous degree and time approximation for the average degree of the nearest neighbors of vertices of degree k,with an appropriate boundary condition.The rate equation proposed can be generalized in more sophisticated growing network models,and also extended to deal with related correlation measurements.Finally,in order to check the theoretical prediction,a numerical example was solved to demonstrate the performance of the degree correlation function.

Effect of degree correlation on edge controllability of real networks

We use the controllability limit theory to study impact of correlation between in- and out-degrees (degree correlation) on edge controllability of real networks. Simulation results and analytic calculations show that the degree correlation plays an important role in the edge controllability of real networks, especially dense real networks. The upper and lower controllability limits hold for all kinds of real networks. Any edge controllability in between the limits is achievable by properly adjusting the degree correlation. In addition, we find that the edge dynamics in some real networks with positive degree correlation may be difficult to control, and explain the rationality of this anomaly based on the controllability limit theory.

Analysis on the Change Characteristics of the Correlation between Land Use Structure and Energy Consumption and Carbon Emissions in Kunming from 1997 to 2017

This study takes Kunming City, Yunnan Province, China as the research area, to provide reference basis for revealing the change law of land use structure and energy consumption and carbon emissions in Kunming, optimizing land use structure and realizing the development of low-carbon city. Based on the data of land use structure and energy consumption in Kunming from 1997 to 2017, based on the estimation of total energy consumption carbon emissions, carbon intensity and per capita carbon emissions, the correlation between land use structure and energy consumption carbon emissions in Kunming has been calculated and analyzed in the past 20 years. Results: 1) The total amount of carbon emissions in Kunming has increased significantly in the past 20 years. It increased from 34.46 × 105 t to 95.09 × 105 t, an increase of about 2.8 times. 2) The types of land use with the highest correlation between land use structure and total carbon emissions of energy consumption, carbon emission intensity and per capita carbon emissions are urban and village and industrial and mining land (0.8258), cultivated land (0.8733) and garden land (0.7971) respectively. 3) The correlation between construction land and total carbon emissions is greater than that of agricultural land. Conclusion: There is a close correlation between land use structure and carbon emissions from energy consumption in Kunming.

Application of grey weighted related degree to the ambient air quality assessment

It is difficult to establish the integrated method to assess the ambient air quality because the atmospheric environmental system is composed of several environmental elements, which contains many contanination factors. In view of the typical grey system character of the monitored data in the ambient air, this paper introduces the weighted value to obtain related degree during applying the method of grey related degree analvsis to assess ambient air quality by each polluting factor producing different effects on the environment quality. This method could give more reasonable and reliable evaluating results. Taking the monitored data of Harbin, a provincial city of Heilongjiang, for example in this paper, the result of assessment by this method was coincide,It with the actual environmental quality of Harbin.

Fusion and Classification of Beijing-1 Small Satellite Remote Sensing Image for Land Cover Monitoring in Mining Area

In order to promote the application of Beijing-1 small satellite(BJ-1) remote sensing data,the multispectral and panchromatic images captured by BJ-1 were used for land cover classification in Pangzhuang Coal Mining.An improved Intensity-Hue-Saturation(IHS) fusion algorithm is proposed to fuse panchromatic and multispectral images,in which intensity component and panchromatic image are combined using the weights determined by edge pixels in the panchromatic image identified by grey absolute correlation degree.This improved IHS fusion algorithm outper-forms traditional IHS fusion method to a certain extent,evidenced by its ability in preserving spectral information and enhancing spatial details.Dempster-Shafer(D-S) evidence theory was adopted to combine the outputs of three member classifiers to generate the final classification map with higher accuracy than that by any individual classifier.Based on this study,we conclude that Beijing-1 small satellite remote sensing images are useful to monitor and analyze land cover change and ecological environment degradation in mining areas,and the proposed fusion algorithms at data and decision levels can integrate the advantages of multi-resolution images and multiple classifiers,improve the overall accuracy and produce a more reliable land cover map.

Nutrients Determination in Nuts from Different Torreya grandis Cultivars

[Objectives]This study aimed to investigate the differences in nutritional properties of nuts from different Torreya grandis cultivars.[Methods]Seven T.grandis cultivars were selected to analyze the protein,soluble carbohydrate,vitamin E,amino acids and fatty acid composition,and evaluate nutritional value of T.grandis nuts from different cultivars using gray correlation analysis.[Results]The kernels of T.grandis contained 9.47%-13.3% protein,1.92%-2.36% soluble carbohydrate,0.16-0.22 mg/g vitamin E,8.40%-11.55% amino acids,and 42.09%-49.29% fatty acid including 35.14%-40.14% oleic acid.And the coefficient of variation ranged from 5.02% to 18.9% among different cultivars.Meanwhile,the average contents of essential amino acids(E),nonessential amino acids(N)and children essential amino acids(C)were 3.88%,6.07% and 0.99%,respectively.The ratios of E/T and E/N were quite stable and in fully compliance with the recommendation standards of amino acids composition from WHO/FAO.[Conclusions]Overall,the nutritional value of tested seven cultivars could be ranked in the following decreasing order using gray correlation analysis:T.grandis cv.Dong No.2>T.grandis cv.Longfeng>T.grandis cv.Dingshan>T.grandis cv.Merrilli>T.grandis cv.Dong No.3>T.grandis cv.Dong No.1>T.grandis cv.Zhuyan.

Identification of Time-Varying Modal Parameters for Thermo-Elastic Structure Subject to Unsteady Heating

A time-varying modal parameter identification method combined with Bayesian information criterion(BIC)and grey correlation analysis(GCA)is presented for a kind of thermo-elastic structures with sparse natural frequencies and subject to an unsteady temperature field.To demonstrate the method,the thermo-elastic structure to be identified is taken as a simply-supported beam with an axially movable boundary and subject to both random excitation and an unsteady temperature field,and the dynamic outputs of the beam are first simulated as the measured data for the identification.Then,an improved time-varying autoregressive(TVAR)model is generated from the simulated input and output of the system.The time-varying coefficients of the TVAR model are expanded as a finite set of time basis functions that facilitate the time-varying coefficients to be time-invariant.According to the BIC for preliminarily determining the scope of the order number,the grey system theory is introduced to determine the order of TVAR and the dimension of the basis functions simultaneously via the absolute grey correlation degree(AGCD).Finally,the time-varying instantaneous frequencies of the system are estimated by using the recursive least squares method.The identified results are capable of tracking the slow time-varying natural frequencies with high accuracy no matter for noise-free or noisy estimation.

Application of Grey-correlated Spectral Region Selection in Analysis of Near-infrared Spectra

The optimal selection method of spectral region based on the grey correlation analysis was applied in the analysis of near-infrared（NIR） spectra. In order to compute ＂characteristic＂ spectral region, 160 samples of tobacco were surveyed by NIR. Next, the whole spectral region was randomly divided into six regions, and the values of association coefficients and correlation orders of different regions were computed for total sugar, reducing sugar and nicotine. Moreover, two regions that owned the largest value of association coefficient were regarded as ＂characteristic＂ spectral region of a model. Finally, the quantitative analysis models of different components were established via the partial least squares method, and the common selection methods of spectral region were compared. The simulation results indicate that the models to choose the spectral region based on grey correlation analysis are more effective than the common selection methods of spectral region, the optimized time of algorithm is shorter, the prediction precision of the models is higher and generalization ability for quantitative analysis results is stronger. This research can provide the support for the quantitative analysis models of NIR spectra and new idea for commercial analysis software of NIR. So, it has a high application value in the analysis of NIR spectra.

Impact of demographic dynamics on CO_2 emissions in Sichuan,China

Global climate change is one of the major environmental issues faced by humans.Existing evidence indicates that the anthropogenic push for a rise in the atmospheric concentration of greenhouse gases(GHGs)(particularly CO_2) has been a primary cause for global warming.Aside from economic and teclinological factors,demographic dynamics(including human consumption in a broad demographic sense) has been a major driver for CO_2 emissions.In this paper,we performed both nonlinear regression analysis(based on the STIRPAT model) and gray correlation degree analysis(based on gray system theory) on the impact of demographic dynamics on CO_2 emissions.Our results reveal that CO_2 emissions are positively correlated with population size and GDP per capita and negatively correlated with energy intensity.We also show that gray con-elation degree with CO_2 emissions for five variables(i.e.,household consumption,urbanization rate,household size,population aging rate,population size) varies substantially:household consumption > urbanization rate >household size > population aging rate > population size,with household consumption being the highest,and population size the lowest.To mitigate the impact of demographic dynamics on CO_2 emissions,it is of vital significance to nurture people's awareness of sustainable consumption and to adhere to current population control policies.

Application of Improved Matter-element Extension Method in Comprehensive Assessment of Shallow Groundwater

Taking shallow groundwater in Jinjiang City,Fujian Province for example,it was found that the classical element-matter analysis shows deficiency in calculation of correlation function,so the improved matter-element method was applied for the comprehensive assessment of shallow groundwater in Jinjiang City,and the spatial distribution was shown in maps.The assessment results demonstrated that ground water quality of most regions in the study area belonged to Grade I and II,thus the overall quality of shallow groundwater was good.The groundwater of Grade IV and V(relatively poor and extremely poor) was mainly distributed in Dongshi Town,Chendi Town,Zimao Town,and Shenhu Town,major exceeding-standard factors that influence shallow groundwater quality in the local area included TDS,Mn^(2+),NO_3,NO_2,NH_4^+ and Cl^-,which mainly owed to invasion of seawater,original geological conditions,industrial and agricultural discharge,and human life.

Information diffusion on adaptive network

Based on the adaptive network, the feedback mechanism and interplay between the network topology and the diffusive process of information are studied. The results reveal that the adaptation of network topology can drive systems into the scale-free one with the assortative or disassortative degree correlations, and the hierarchical clustering. Meanwhile, the processes of the information diffusion are extremely speeded up by the adaptive changes of network topology.

Decision with Grey Correlation and AHP

On the basis of the theories of grey system correlation degree and analytic hierarchy process,this paper studies the problem of plan decision for the exploitation of water conservancy project.According to the data army of correlation degree,the optimized plan can be selected objectively and scientifically.Practical example given in this paper have proved the validity of the method.

Correlation Analysis for the Attack of Respiratory Diseases and Meteorological Factors

Objective：To investigate the relationship between respiratory diseases onset and the meteorological factors in the same period and in a specific environment.Methods：By using the data of daily incidence of respiratory diseases obtained from Dongzhimen Hospital Affiliated to Beijing University of Chinese Medicine from January 1, 1998 to December 31,2007,and the data of 16 items of meteorological factors（such as the average,maximum, and minimum temperatures,etc.,including meteorological factors derived） obtained from the Beijing Municipal Meteorological Observatory,mathematical statistical methods were applied to achieve the non-linear correlation analysis,or the correlation test,between the incidence of respiratory diseases and the time-related meteorological factors.Results：The simple correlation coefficients of the relationship between the incidence of respiratory diseases and 9 meteorological elements,including the average values of temperature,maximum temperature,minimum temperature,degree of comfort,precipitation,vapor pressure,low cloud cover,change of vapor pressure,and change of wind speed,were all greater than 0.8286,in which one of the relationship between the incidence of respiratory diseases and the maximum temperature is as high as 0.9670.Statistical tests showed RRα=0.05 and FFα=0.05.Conclusions：The incidence of respiratory diseases was closely correlated to meteorological factors,such as air temperature,vapor pressure,precipitation,wind speed,etc.To a certain extent,this conclusion confirmed the scientificity and objectivity of the theory of five evolutive phases and six climatic factors（Wu Yun Liu Qi,五运六气） in Huang Di Nei Jing（黄帝内经,The Yellow Emperor＇s Canon of Internal Medicine）.

A dynamic signal coordination control method for urban arterial roads and its application

We propose a novel dynamic traffic signal coordination method that takes account of the special traffic flow characteristics of urban arterial roads. The core of this method includes a control area division module and a signal coordination control module. Firstly, we analyze and model the influences of segment distance, traffic flow density, and signal cycle time on the correlation degree between two neighboring intersections. Then, we propose a fuzzy computing method to estimate the correlation degree based on a hierarchical structure and a method to divide the control area of urban arterial roads into subareas based on correlation degrees. Subarea coordination control arithmetic is used to calculate the public cycle time of the control subarea, up-run offset and down-run offset of the section, and the split of each intersection. An application of the method in Shaoxing City, Zhejiang Province, China shows that the method can reduce the average travel time and the average stop rate effectively.

Optimization of structural parameters for elliptical cross-section spiral equal-channel extrusion dies based on grey theory

The elliptical cross-section spiral equal-channel extrusion （ECSEE） process is simulated by using Deform-3D finite element software. The ratio m of major-axis to minor-axis length for ellipse-cross-section, the torsion angle u, the round-ellipse cross-section transitional channel L1, the elliptical rotation cross-section transitional channel L2 and the ellipse-round cross-section transitional channel L3 are destined for the extrusion process parameters. The average effective strain eave on cross-section of blank, the deformation uniformity coefficient a and the value of maximum damage dmax are chosen to be the optimize indexes, and the virtual orthogonal experiment of L16 （45） is designed. The correlation degree of the process factors affecting eave, a and dmax is analyzed by the numerical simulation results using the weights and grey association model. The process parameters are optimized by introducing the grey situation decision theory and the ECSEE optimal combination of process parameters is obtained： u of 120 , m of 1.55, L1 of 7 mm, L2 of 10 mm, and L3 of 10 mm. Simulation and experimental results show that the material can be refined with the optimized structural parameters of die. Therefore, the optimization results are satisfactory.

Dynamic Evaluation and Analysis of Regional Innovation Capability in Eastern China from the Perspective of High-quality Development

The economy of China has turned to the stage of high-quality development. In this sense,the connotation of regional innovation capacity should reflect more aspects, such as better economic effectiveness, people-centered philosophy of development and better living conditions. This study aims at establishing the evaluation index system of regional innovation capacity under high-quality perspective.Then the dynamic evaluation method based on gray correlation degree and TOPSIS is improved. And the improved method is applied to evaluate the regional innovation capacity under high-quality development perspective. The results show that: 1) The regional innovation capacity of Jiangsu, Zhejiang,Shanghai and Guangdong under high-quality development perspective is better than other regions,while the regional innovation capacity of Beijing-Tianjin-Hebei is imbalanced. Regional innovation capability of Fujian, Shandong, and Hainan from a high-quality perspective is at the middle and lower levels. 2) From the perspective of development trends, the gap of regional innovation capacity between Beijing, Jiangsu, Zhejiang, Shanghai, Guangdong and Fujian, Hebei, Shandong is gradually narrowing.3) An in-depth analysis of the regional innovation capability of the eastern provinces and cities from the perspective of high-quality development through different dimensions shows that Beijing, Guangdong, Jiangsu perform well in all dimensions, while Fujian and Hainan need to pay more attention to innovation input and the creation of a better innovation environment to enhance innovation output and promote innovation effectiveness. At last, based on above analysis, relevant policy recommendations are proposed.