Coefficient of Partial Correlation and Its Calculation

This thesis offers the general concept of coefficient of partial correlation.Starting with regres-sion analysis,the paper,by using samples,infers the general formula of expressing coefficient of partial correlation by way of simple correlation coefficient.

Partial Correlation Analysis Based Identification of Distribution Network Topology

Accurately identifying distribution network topol-ogy,which tends to be a mesh configuration with increasing penetration rate of distributed energy resources(DERs),is critical for reliable operation of a smart distribution network.Multicollinearity among node voltages makes existing topology identification methods unstable and inaccurate.Considering partial correlation analysis can reveal the intrinsic correlation of two variables by eliminating the influence of other variables,this paper develops a novel data-driven method based on partial correlation analysis to identify distribution network topology(radial,mesh,or including DERs)using only historical voltage amplitude data.First,maximum spanning tree of network is generated through Prim algorithm.Then,the loops of network are identified by taking tree neighbors as controlling variables in partial correlation analysis.Finally,a new topology verification mechanism based on partial correlation analysis is developed to correct wrong connections caused by multicollinearity.Test results on IEEE 33-node system,IEEE 123-node system and practical distribution network demonstrate that our method outperforms common data-driven methods,and can robustly identify both radial and mesh distribution network with DERs.IndexTerms-Data-driven,linear correlation,partial correlation,smart meter,topology identification.

Inferring Functional Connectivity in fMRI Using Minimum Partial Correlation

Functional connectivity has emerged as a promising approach to study the functional organisation of the brain and to define features for prediction of brain state. The most widely used method for inferring functional connectivity is Pearson＇s correlation, but it cannot differentiate direct and indirect effects. This disadvantage is often avoided by computing the partial correlation between two regions controlling all other regions, but this method suffers from Berkson＇s paradox. Some advanced methods, such as regularised inverse covariance, have been applied. However, these methods usually depend on some parameters. Here we propose use of minimum partial correlation as a parameter-free measure for the skeleton of functional connectivity in functional magnetic resonance imaging （flVIRI）. The minimum partial correlation between two regions is the minimum of absolute values of partial correlations by controlling all possible subsets of other regions. Theoretically, there is a direct effect between two regions if and only if their minimum partial correlation is non-zero under faithfulness and Gaussian assumptions. The elastic PC-algorithm is designed to efficiently approximate minimum partial correlation within a computational time budget. The simulation study shows that the proposed method outperforms others in most cases and its application is illustrated using a resting-state fMRI dataset from the human connectome project.

Generalized bounds on the partial periodic correlation of complex roots of unity sequence set

In this paper,the generalized bounds are derived on the partial periodic correlation of complex roots of unity sequence set with zero or low correlation zone(ZCZ/LCZ)as the important criteria of the sequence design and application.The derived bounds are with respect to family size,subsequence length,maximum partial autocorrelation sidelobe,maximum partial cross-correlation value and the ZCZ/LCZ.The results show that the derived bounds include the previous periodic bounds,such as Sarwate bound,Welch bound,Peng-Fan bound and Paterson-Lothian bound,as special cases.

Impact of climate and human activity on NDVI of various vegetation types in the Three-River Source Region, China

The Three-River Source Region(TRSR)in China holds a vital position and exhibits an irreplaceable strategic importance in ecological preservation at the national level.On the basis of an in-depth study of the vegetation evolution in the TRSR from 2000 to 2022,we conducted a detailed analysis of the feedback mechanism of vegetation growth to climate change and human activity for different vegetation types.During the growing season,the spatiotemporal variations of normalized difference vegetation index(NDVI)for different vegetation types in the TRSR were analyzed using the Moderate Resolution Imaging Spectroradiometer(MODIS)-NDVI data and meteorological data from 2000 to 2022.In addition,the response characteristics of vegetation to temperature,precipitation,and human activity were assessed using trend analysis,partial correlation analysis,and residual analysis.Results indicated that,after in-depth research,from 2000 to 2022,the TRSR's average NDVI during the growing season was 0.3482.The preliminary ranking of the average NDVI for different vegetation types was as follows:shrubland(0.5762)>forest(0.5443)>meadow(0.4219)>highland vegetation(0.2223)>steppe(0.2159).The NDVI during the growing season exhibited a fluctuating growth trend,with an average growth rate of 0.0018/10a(P<0.01).Notably,forests displayed a significant development trend throughout the growing season,possessing the fastest rate of change in NDVI(0.0028/10a).Moreover,the upward trends in NDVI for forests and steppes exhibited extensive spatial distributions,with significant increases accounting for 95.23%and 93.80%,respectively.The sensitivity to precipitation was significantly enhanced in other vegetation types other than highland vegetation.By contrast,steppes,meadows,and highland vegetation demonstrated relatively high vulnerability to temperature fluctuations.A further detailed analysis revealed that climate change had a significant positive impact on the TRSR from 2000 to 2022,particularly in its northwestern areas,accounting for 85.05%of the total area.Meanwhile,human activity played a notable positive role in the southwestern and southeastern areas of the TRSR,covering 62.65%of the total area.Therefore,climate change had a significantly higher impact on NDVI during the growing season in the TRSR than human activity.

Impacts of climate change and human activities on vegetation dynamics on the Mongolian Plateau, East Asia from 2000 to 2023

The Mongolian Plateau in East Asia is one of the largest contingent arid and semi-arid areas of the world.Under the impacts of climate change and human activities,desertification is becoming increasingly severe on the Mongolian Plateau.Understanding the vegetation dynamics in this region can better characterize its ecological changes.In this study,based on Moderate Resolution Imaging Spectroradiometer(MODIS)images,we calculated the kernel normalized difference vegetation index(kNDVI)on the Mongolian Plateau from 2000 to 2023,and analyzed the changes in kNDVI using the Theil-Sen median trend analysis and Mann-Kendall significance test.We further investigated the impact of climate change on kNDVI change using partial correlation analysis and composite correlation analysis,and quantified the effects of climate change and human activities on kNDVI change by residual analysis.The results showed that kNDVI on the Mongolian Plateau was increasing overall,and the vegetation recovery area in the southern region was significantly larger than that in the northern region.About 50.99%of the plateau showed dominant climate-driven effects of temperature,precipitation,and wind speed on kNDVI change.Residual analysis showed that climate change and human activities together contributed to 94.79%of the areas with vegetation improvement.Appropriate human activities promoted the recovery of local vegetation,and climate change inhibited vegetation growth in the northern part of the Mongolian Plateau.This study provides scientific data for understanding the regional ecological environment status and future changes and developing effective ecological protection measures on the Mongolian Plateau.

Zonal Differences in Correlation Patterns Between Soil Organic Carbon and Climate Factors at Multi-extent

Studying the relationship between climate factors and soil organic carbon （SOC） is vitally important. However, how SOC responses to climate （temperature and precipitation） at cohesive extents is poorly studied. Two transects of approximately the same length （transect P and transect T） were selected to examine the variation of SOC content in relation to mean annual temperature （MAT） and mean annual precipitation （MAP）. The coefficients of partial correlation between SOC density and MAT （Rt） and MAP （Rp） were determined to quantify the relationships between SOC density and the two climate factors. The results indicated that for transect T, Rt was statistically significant once the extent level was greater than or equal to two fundamental extent units, while for transect P, Rp showed statistical significance only at extent levels which were greater than two fundamental extent traits. At the same extent levels but in different transects, Rts exhibited no zonal difference, but Rps did once the extent level was greater than two fundamental extent units. Therefore, to study the relationship between SOC density and different climate factors, different minimum extent levels should be ex- amined. The results of this paper could deepen the understanding of the impacts that SOC pool has on terrestrial ecosystem and global carbon cycling.

On Testing Equality of K Multiple Correlation Matrices

Coutsourides derived an ad hoc nuisance paratmeter removal test for testing equality of two multiple correlation matrices of two independent p variate normal populations under the assumption that a sample of size n is available from each population. This paper presents a likelihood ratio test criterion for testing equality of K multiple correlation matrices and extends the results to the testing of equality of K partial correlation matrices.

Trade-offs and Synergies of Ecosystem Services in Karst Area of China Driven by Grain-for-Green Program

As an important means regulating the relationship between human and natural ecosystem,ecological restoration program plays a key role in restoring ecosystem functions.The Grain-for-Green Program(GFGP,One of the world’s most ambitious ecosystem conservation set-aside programs aims to transfer farmland on steep slopes to forestland or grassland to increase vegetation coverage)has been widely implemented from 1999 to 2015 and exerted significant influence on land use and ecosystem services(ESs).In this study,three ecological models(In VEST,RUSLE,and CASA)were used to accurately calculate the three key types of ESs,water yield(WY),soil conservation(SC),and net primary production(NPP)in Karst area of southwestern China from 1982 to 2015.The impact of GFGP on ESs and trade-offs was analyzed.It provides practical guidance in carrying out ecological regulation in Karst area of China under global climate change.Results showed that ESs and trade-offs had changed dramatically driven by GFGP.In detail,temporally,SC and NPP exhibited an increasing trend,while WY exhibited a decreasing trend.Spatially,SC basically decreased from west to east;NPP basically increased from north to south;WY basically increased from west to east;NPP and SC,SC and WY developed in the direction of trade-offs driven by the GFGP,while NPP and WY developed in the direction of synergy.Therefore,future ecosystem management and restoration policy-making should consider trade-offs of ESs so as to achieve sustainable provision of ESs.

Multi-Purpose Forensics of Image Manipulations Using Residual-Based Feature

The multi-purpose forensics is an important tool for forge image detection.In this paper,we propose a universal feature set for the multi-purpose forensics which is capable of simultaneously identifying several typical image manipulations,including spatial low-pass Gaussian blurring,median filtering,re-sampling,and JPEG compression.To eliminate the influences caused by diverse image contents on the effectiveness and robustness of the feature,a residual group which contains several high-pass filtered residuals is introduced.The partial correlation coefficient is exploited from the residual group to purely measure neighborhood correlations in a linear way.Besides that,we also combine autoregressive coefficient and transition probability to form the proposed composite feature which is used to measure how manipulations change the neighborhood relationships in both linear and non-linear way.After a series of dimension reductions,the proposed feature set can accelerate the training and testing for the multi-purpose forensics.The proposed feature set is then fed into a multi-classifier to train a multi-purpose detector.Experimental results show that the proposed detector can identify several typical image manipulations,and is superior to the complicated deep CNN-based methods in terms of detection accuracy and time efficiency for JPEG compressed image with low resolution.

EFFECTS OF ENSO ON THE RELATIONSHIP BETWEEN IOD AND SUMMER RAINFALL IN CHINA

Based on the data of 1950 – 1999 monthly global SST from Hadley Center, NCAR/NCEP reanalysis data and rainfall over 160 weather stations in China, investigation is conducted into the difference of summer rainfall in China (hereafter referred to as the "CS rainfall") between the years with the Indian Ocean Dipole (IOD) occurring independently and those with IOD occurring along with ENSO so as to study the effects of El Ni?o - Southern Oscillation (ENSO) on the relationship between IOD and the CS rainfall. It is shown that CS rainfall will be more than normal in South China (centered in Hunan province) in the years of positive IOD occurring independently; the CS rainfall will be less (more) than normal in North China (Southeast China) in the years of positive IOD occurring together with ENSO. The effect of ENSO is offsetting (enhancing) the relationship between IOD and summer rainfall in Southwest China, the region joining the Yangtze River basin with the Huaihe River basin (hereafter referred to as the "Yangtze-Huaihe basin") and North China (Southeast China). The circulation field is also examined for preliminary causes of such an influence.

AR Model Based on Time Series Modeling for Predicting Egg Market Price in 2021

Eggs,as a meat consumer product in China,are closely related to the vegetable basket project.Exploring and predicting the future trend of egg market price is of great significance for stabilizing egg price and market supply.In this study,the time series AR model was used for fitting the egg market prices in the 66 d from January 1 to March 7,2021,and the delay operator nlag18 was used for white noise test,giving pr>probability of chisq<0.005.The time series was not a white noise series,and then the stationary series was used for modeling.The optimal model was selected as the AR series(BIC(3,0)),and finally,the egg market price model AM was obtained as X_(t)=9.0556+(1+0.8926)ε_(t),which was the optimal model.The model showed that the egg price fluctuations in 2021 will be clustered,and the later price will be significantly affected by external factors in the previous period.The dynamic prediction results of the model showed that the egg price would stop falling in March 2020,and the egg price would continue to slow down in March.

Energy consumption hierarchical analysis based on interpretative structural model for ethylene production

Interpretative structural model(ISM) can transform a multivariate problem into several sub-variable problems to analyze a complex industrial structure in a more efficient way by building a multi-level hierarchical structure model. To build an ISM of a production system, the partial correlation coefficient method is proposed to obtain the adjacency matrix, which can be transformed to ISM. According to estimation of correlation coefficient, the result can give actual variable correlations and eliminate effects of intermediate variables. Furthermore, this paper proposes an effective approach using ISM to analyze the main factors and basic mechanisms that affect the energy consumption in an ethylene production system. The case study shows that the proposed energy consumption analysis method is valid and efficient in improvement of energy efficiency in ethylene production.

New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation

Recently, Chung et al. gave a general method to construct frequency-hopping sequence set(FHS set) with low-hit-zone(LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.

Parameter Sensitivity and Qualitative Analysis of Dynamics of Ovarian Tumor Growth Model with Treatment Strategy

In this paper, we are interested to find the most sensitive parameter, local and global stability of ovarian tumor growth model. For sensitivity analysis, we use Latin Hypercube Sampling (LHS) method to generate sample points and Partial Rank Correlation Coefficient (PRCC) method, uses those sample points to find out which parameters are important for the model. Based on our findings, we suggest some treatment strategies. We investigate the sensitivity of the parameters for tumor volume, y, cell nutrient density, Q and maximum tumor size, ymax. We also use Scatter Plot method using LHS samples to show the consistency of the results obtained by using PRCC. Moreover, we discuss the qualitative analysis of ovarian tumor growth model investigating the local and global stability.

An Analysis of the Correlation between the Economic Barometer and the Postal Service

There are many economic factors that can influence the postal market. In thispaper, by adopting the method of quantitative analysis, the author analyse exhaustively theeconomic factors that influence the postal market and the internal relations between the economicfactors and the postal market.

Climate change and its effect on reference crop evapotranspiration in central and western Inner Mongolia during 1961-2009

Water resource is one of the major constraints to agricultural production in central and western Inner Mongolia, where are characteristic by arid and semi-arid climate. Reference crop evapotranspiration （ETo） is an important part of water cycle in agricultural ecosystem, which has a direct effect on crop growth and yield. The implications of climate change on ETo are of high importance for agriculture regarding water management and irrigation scheduling. The aim of this study was to analyze the variations in climate and its effect on ETo in central and western Inner Mongolia over the period 1961 to 2009 For this purpose, data in ten meteorological stations across study area were collected and the FAO Penman-Monteith 56 method was used. Results showed that the average temperature, maximum temperature and minimum temperature increased by 0.49~C, 0.31~C and 0.70~C per decade during 1961-2009, respectively. In comparison, the daily temperature range decreased by 0.38~C per decade. The air relative humidity, sunshine hour, and 10-m wind speed decreased generally by 0.58%, 40.11 h, and 0.35 rrds per decade, respectively. Annual mean ETo decreased significantly at a rate of 12.2 mm per decade over the periods, this was mainly due to the decrease in wind speed in the study area. The decrease in wind speed may balance the effect of the increase in air temperature on ETo. Variations in spatial distribution of ETo and its main controlling factor were also detected among ten stations. Our results suggested that spatial and temporal distribution of ETo should be considered regarding the optimization of water resource management for agriculture in central and western Inner Mongolia under foreseen climate change.

CHANGES OF PAN EVAPORATION IN THE UPPER REACH OF THE YANGTZE RIVER

The upper reach of the Yangtze River, 4 511 km long from west to east, contains a great amount of water resources of the Yangtze River Basin. This article studies the characteristics of the pan evaporation, the related meteorological variables, and their effects on the pan evaporation, based on the data of the daily pan evaporation （1980-2008） and other meteorological variables （1961-2008）. The results show that the linear trend of the pan evaporation has remarkable regional features, i.e., the decrease trend in the southwest and the increase trend in the northeast of the investigated region, and the Yangtze River is approximately the boundary of these trends. The meteorological variables have different effects on the pan evaporation depending on the fact that they are in the category the thermal variables or the dynamic variables. The thermal meteorological variables （i.e., air temperature, diurnal temperature range, and sunshine duration） have positive partial correlations with the pan evaporation, while the dynamic ones （air pressure, rainfall, and relateive humidity） have negative correlations with the pan evaporation. The correlation of the wind speed remains to be investigated.

Statistical downscaling model for late-winter rainfall over Southwest China

A statistical downscaling model is built for the late-winter rainfall over Southwest China(SWC).A partial-correlation method is used for selecting factors.The results show that the selected factors for late-winter rainfall in SWC are sea level pressure in Western Europe(SNAO)and sea surface temperature in Western Pacific(WPT).SNAO is related to the southern pole of North Atlantic Oscillation(NAO)and excites Southern Eurasian teleconnection,which influences the development of the southern branch trough and the water vapor transport to SWC.WPT indicates the variability of ENSO in the tropical Western Pacific.WPT excites Pacific-East Asia teleconnection and an anticyclone(cyclone)is formed in the southern part of China and suppresses(enhances)rainfall over SWC.A regression statistical downscaling model using SNAO and WPT shows good performance in fitting the variability of late-winter rainfall in the whole SWC region and every observation station,and the model also shows strong robustness in the independent validation.The statistical model can be used for downscaling output from seasonal forecast numerical models and improve the SWC late winter rainfall prediction in the future.

Causality Analysis of Futures Sugar Prices in Zhengzhou Based on Graphical Models for Multivariate Time Series

This paper presents a method of constructing a mixed graph which can be used to analyze the causality for multivariate time series.We construct a partial correlation graph at first which is an undirected graph.For every undirected edge in the partial correlation graph,the measures of linear feedback between two time series can help us decide its direction,then we obtain the mixed graph.Using this method,we construct a mixed graph for futures sugar prices in Zhengzhou（ZF）,spot sugar prices in Zhengzhou（ZS） and futures sugar prices in New York（NF）.The result shows that there is a bi-directional causality between ZF and ZS,an unidirectional causality from NF to ZF,but no causality between NF and ZS.