Evaluation and prediction of regional human capital based on optimised BP neural network

Keyan Zhao

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

Journal Details

Format: Journal
eISSN: 2444-8656
First Published: 01 Jan 2016
Publication timeframe: 2 times per year
Languages: English

High-quality development means that the knowledge-intensive economic structure will gradually replace the labour-intensive economic structure, and human resources will gradually replace the fundamental position of natural resources. In addition, the low price of labour force will no longer be competitive, and making a strong accumulation of human capital will become the greatest advantage [1, 2]. At present, human capital has become an irreplaceable core in the process of high-quality economic development. The premise of making human capital play a better role is to elucidate the actual role of human capital in economic and social development at present. Previous studies have shown that [3, 4] human capital is vital in the process of economic growth, which can impact monetary development in numerous ways. On the other hand, the change and redesigning of modern construction is a dire undertaking in China. In this manner, it is of pragmatic importance to concentrate on the impact of human resources, especially to clarify the influence effect of current human capital.

With the increasing role of knowledge and technology in economy, human capital has become the decisive factor of economic development and social progress. Measuring, evaluating or predicting the level of regional human capital within a country can grasp the investment policy of human capital as a whole. The theories and methods of predicting and evaluating the level of human capital at home and abroad are mostly classical calculation methods under precise thinking, without considering that human capital is a typical complex system with the characteristics of nonlinearity, uncertainty and fuzziness [5–7]. These methods have achieved good results, but in the actual evaluation, the weight assignment is extremely subjective, the amount of information is lost in dimension reduction, and the information contained in the evaluation index system cannot be fully utilised, which is lack of self-learning and self-adapting ability. There are many factors influencing human capital investment, which have a complex nonlinear mapping relationship [8, 9] between themselves and the level of human capital. Therefore, further research on the prediction of regional human capital level is a work of practical significance and application value.

Prediction of regional human capital

2.1

The concept of human capital

Human capital exists relative to physical capital, and it shows the knowledge, skills, experience and health possessed by people. It mainly includes [10] the capital of simple labour, education, health and technology. The first three are investment capital, which can only be obtained through certain investment, and they constitute the core content of human capital. Any investment that can improve workers’ knowledge, skills and physical strength is called human capital investment. Human capital investment is concentrated in the followings: (1)

Medical care offices and administration, including all expenses that influence people’s future, actual strength and perseverance, energy and imperativeness;

(2)

On-the-job training, hands on preparing, including the old apprenticeship framework coordinated by the organisation;

(3)

Formal essential, optional and advanced education;

(4)

Adult training programmes that are not coordinated by the organisation, particularly off-grounds concentrate on programmes in agribusiness;

(5)

Individual and family migration to adapt to changing employment opportunities.

Therefore, human capital is summed up as education and training, medical care, scientific and technological experience and labour force.

Migration, social security and other five aspects of investment formation.

2.2

Construction of evaluation index system

2.2.1

Selection of indicators

To assess the degree of human capital in various regions of China more accurately and objectively, we need to construct a reasonable evaluation index system of human capital investment. Considering the availability and comparability of data, based on the principle of reflecting the inherent requirements of human capital and facilitating management, in this paper, 15 original indicators or generated indicators based on 5 categories are selected to constitute the index system of regional human capital investment evaluation, which is described in Table 1.

Table 1

Index system of regional human capital investment evaluation.

Category	Index system
Educational training	X1 per capita education expenditure (10,000 yuan/person), X2 average education level index, X3 teacher-student ratio in school, X4 population with college degree or above, X5 professional and technical personnel
Development of science and technology	X6 R&D expenditure as a percentage of GDP (%), labour productivity of X7 employees, X8 technological achievements (million yuan), X9 patent applications of employees
Medical care	X10 The number of beds owned by 100,000 people, X11 the number of health technicians, X12 the medical care expenditure per capita
Labour migration	X13 proportion of employees in the total population (%), X14 number of employment agencies
Social security	X15 social security coverage rate (%)

2.2.2

Acquisition of benchmark data

There is correlation among the evaluation indexes of regional human capital investment in China. To accurately evaluate the degree of regional human capital, it is necessary to reduce its dimension. Principal component analysis (PCA) can better solve the correlation problem among indicators. PCA is a multivariate statistical analysis of data compression and feature extraction, which uses the idea of dimension reduction. The original numerous and relevant indicators are recombined into low-dimensional and unrelated comprehensive indicators, and these comprehensive indicators can reflect the main information of the original multiple indicators [11]. According to 15 evaluation indexes of regional human capital investment in China, PCA is carried out by using the evaluation method of economic and social indicators by experts from China Economic Reform and Development Research Institute of Renmin University of China, as shown in Figure 1.

Taking 31 regions in China as evaluation objects, and 15 evaluation indexes of human capital investment: X1, X2, …, X15 constitute the original data matrix $X_{31 \times 15}^{*}$ . The specific steps are as follows: (1)

Standardise the original data matrix $X_{31 \times 15}^{*}$ to eliminate the influence of dimension and the difference of magnitude. Get the standardised sample data matrix $X_{31 \times 15}^{*}$ ;

(2)

Calculate the sample correlation coefficient matrix: $R = (r_{i j})_{15 \times 15}, (i, j = 1, 2, \dots, 15)$ , in which r_ij is an correlation coefficient of indicator X_i and indicator X_j;

(3)

Find the correlation coefficient matrix by Jacobian method R, non-negative eigenvalue of $(λ_{1}, λ_{2}, \dots, λ_{15})$ and the corresponding eigenvectors. $a_{i} = (a_{i 1}, a_{i 2}, \dots, a_{i 15}), (i = 1, 2, \dots, 15)$ . 15 principal components were obtained: $Y 1, Y 2, \dots, Y 15$ and Y_i are the linear combination of variable. $X 1, X 2, \dots, X 15$ , that is, $Y_{i} = a_{i 1} X 1 + a_{i 2} X 2 + \dots + a_{i 15} X 15, (i = 1, 2, \dots, 15)$ ;

(4)

The first n principal components are selected according to the cumulative contribution rate of principal components: $Y 1, Y 2, \dots, Y n$ ; the cumulative contribution rate of $\sum_{k = 1}^{n} λ_{k} / \sum_{k = 1}^{15} λ_{k}$ exceeds 85%. The n principal components are used to replace the original 15 evaluation indexes, and a new index system is obtained to reflect the original evaluation object;

(5)

Calculate the principal component score as: $Y_{k} = a_{i k}^{T} X^{T}$ , $(k = 1, 2, \dots, n)$ . The scores of principal calculated n components can be taken as training samples.

(6)

According to the corresponding n principal component scores of each region in China, the comprehensive principal component scores of human capital level in 31 regions are calculated as the benchmark target data of the subsequent model.

Application of BP neural network

3.1

Application basis

BP neural network is a feed-forward network with blunder back engendering calculation as its learning calculation, which has strong nonlinear mapping ability. For a given sample set: ${(x (t), y (t)) | x (t) \in R_{n}, y (t) \in R_{m}, t =$ $1, 2, \dots, k}$ , BP network can understand profoundly nonlinear planning from contribution to yield, that is, there is a mapping: $F : R_{n} \to R_{m}$ , make $F (x (t)) = y (t)$ .

Therefore, we can regard the prediction of human capital level as a functional mapping from investment index of human capital to evaluation conclusion, and then an evaluation model reflecting the nonlinear mapping relationship can be established, as shown in Figure 2.

Nonlinear mapping relation of evaluation model.

In addition, BP network can accurately describe the mapping relationship between factors without establishing a specific mathematical function model, which shows that it is feasible to predict the level of human capital.

3.2

Optimisation of BP neural network

In the research of prediction, BP neural network and PSO algorithm are all suitable for solving nonlinear problems, but with their own characteristics [12, 13].

(1)

BP neural network has the characteristics of nonlinear mapping, distributed storage and parallel processing of information, self-organisation, self-learning and self-adaptation, which is suitable for modelling complex systems with uncertain factors. However, its error function has local minimum, and its convergence speed is slow;

(2)

Determine the structure of BP neural network, provide preliminary optimisation results by using the mutation ability and global search ability of PSO, and roughly search the weights and thresholds in the optimal solution space;

(3)

Adopt PSO to strengthen local search, improve convergence speed, and carry out fine search to get the optimal weights and thresholds for BP network training;

(4)

Take the loads and edges obtained above as the underlying loads and edges of BP brain network preparing.

3.3

Description of core issues

3.3.1

Selection of initial parameters

Improving BP network with PSO algorithm is mainly to optimise the weights of network connection and neuron thresholds. The specific implementation method is as follows:

The neural network trained by PSO algorithm adopts real number coding; matrix A, B, respectively, represent the connection weights and thresholds: $A = (\begin{array}{cccc} a_{11} & a_{12} & \dots & a_{1 (n + 1)} \\ a_{21} & a_{22} & \dots & a_{2 (n + 1)} \\ ⋮ & ⋮ & \dots & ⋮ \\ a_{h 1} & a_{h 1} & \dots & a_{h (n + 1)} \end{array}) B = (\begin{array}{cccc} b_{11} & b_{12} & \dots & b_{1 (h + 1)} \\ b_{21} & b_{22} & \dots & b_{2 (h + 1)} \\ ⋮ & ⋮ & \dots & ⋮ \\ b_{o 1} & b_{o 1} & \dots & b_{o (h + 1)} \end{array})$ \[A=\left(\begin{array}{cccc} {a_{11} } & {a_{12} } & {\cdots } & {a_{1(n+1)} } \\ {a_{21} } & {a_{22} } & {\cdots } & {a_{2(n+1)} } \\ {\vdots } & {\vdots } & {\cdots } & {\vdots } \\ {a_{h1} } & {a_{h1} } & {\cdots } & {a_{h(n+1)} } \end{array}\right)\, \, \, B=\left(\begin{array}{cccc} {b_{11} } & {b_{12} } & {\cdots } & {b_{1(h+1)} } \\ {b_{21} } & {b_{22} } & {\cdots } & {b_{2(h+1)} } \\ {\vdots } & {\vdots } & {\cdots } & {\vdots } \\ {b_{o1} } & {b_{o1} } & {\cdots } & {b_{o(h+1)} } \end{array}\right)\] where h is the number of neurons in the hidden layer, n is the number of neurons, o is the number of output neurons, and other values are the connection weights of neurons in the hidden and output layers.

The code string used for PSO algorithm optimisation comprises four sections: the association weight of stowed away layer and information layer, the association weight of result layer and secret layer, the edge of stowed away layer and the edge of result layer. Arranging matrices A and B into row vectors with row priority is as follows: $(a_{11}, a_{12}, \dots \dots, a_{1 n}, a_{1 (n + 1)}, a_{21}, \dots \dots, a_{h (n + 1)}, b_{11}, b_{12}, \dots \dots, b_{1 h}, b_{1 (h + 1)}, b_{21}, \dots \dots, b_{o (h + 1)})$ \[\left(a_{11} ,a_{12} ,\ldots \ldots ,a_{1n} ,a_{1(n+1)} ,\, a_{21} ,\ldots \ldots ,a_{h(n+1)} ,\, \, b_{11} ,b_{12} ,\ldots \ldots ,b_{1h} ,b_{1(h+1)} ,b_{21} ,\ldots \ldots ,b_{o(h+1)} \right)\]

3.3.2

Construction of genetic algorithm

To obtain satisfactory optimisation results, the mixing degree of the PSO algorithm can be quantified by the ratio of PSO population number m to BP population number s (m/s). Specifically, it can be divided into four steps as shown in Figure 3: (1)

Coding: For numerical optimisation, the average efficiency of real coding is higher than that of binary coding, which avoids the tedious back-and-forth coding and decoding, so real coding is selected in this paper.

(2)

Fitness function (individual evaluation method) is vital to the genetic algorithm. Because of the fitness, there exists competition among individuals, and the result of the competition is that the surviving individuals are getting better and better, and the individuals with the highest fitness are the individuals that best meet the solution objectives (optimal solutions). The function of individual fitness is called Fitness function $F_{1} (i) = 1 / E (i)$ , in which $E (i) = \sum_{p} | | o_{i} - y_{i} | |^{2}$ . E(i) is the objective function, p is the number of output nodes, p = 1, o_i is the actual output vector of the network with respect to the ith individual and y_i is the ideal output vector of the ith individual in the sample.

(3)

Plan the hereditary operator: the determination activity utilises the corresponding choice operator, the hybrid activity utilises the single-point hybrid operator and the transformation activity utilises the essential digit change operator.

(4)

Determine the operating parameters of genetic algorithm, where population size is s, termination evolution algebra is G, crossover probability is p_c, mutation probability is p_m and so on.

Construction of prediction model

4.1

Initialisation of data

4.1.1

Input of training samples

In the prediction of improved BP network model, the benchmark data of regional human capital is divided into P initial training sample sets and Q prediction sample sets. Initial training sample set is the BP network input original data matrix X_n×P, and training target set matrix Y corresponding to the input data, while prediction sample set is data matrix Y_n×Q, where n is the number of neurons in the input layer.

The establishment of BP network must be based on a large number of sample data training, so providing sufficient and comprehensive training samples is the key to establish a correct and practical network. In the prediction simulation of human capital level based on BP network, it is found that the data of P×n input training samples is less, and the simulation effect is not obvious. Add some noise to the learning samples. Although some samples are similar, other samples will be different, which can prevent the network from falling into local optimum in learning, and thus solving the problem of insufficient training sample data of BP neural network. Therefore, this paper adds ‘noise samples’ based on the original data, and its remarkable effect has been verified in the simulation. By adopting the rand function in MATLAB software, the original data matrix X corresponding to the training is recombined as the extended data matrix for BP network training, so the number of input original data corresponding to the training is expanded to P × n × R.

4.1.2

Input of training target set

According to the 15 evaluation indexes of human capital investment, the PCA is completed by using the evaluation method of economic and social indexes by experts from the university. The first n principal components are selected to replace the original 15 indexes, and the scores of the corresponding human capital levels in 31 regions of China are calculated as the original target data, which is expressed by matrix Y. Corresponding to the training sample data, the matrix Y is recombined as the extended target data set for BP network training.

If the input value is too large, the neurons may be saturated and lose their learning ability, so it is necessary to limit the input data to a certain range. In addition, to eliminate the influence of dimension and the magnitude difference, we must standardise the expanded raw data [14]. Therefore, the original data is initialised by the mapminmax function in MATLAB software, and normalised to the interval [1, 1] as the input data after the initialisation of BP network.

4.2

Implementation of the model

The neural network toolbox is one of the magnificent tool compartments created in the MATLAB era. In light of the hypothesis of fake brain organisation, the MATLAB programming language is taken to build numerous commonplace brain network actuation capacities, which is convenient for users to call the design, training and simulation programs of neural network. The MATLAB2019 simulation platform is selected to combine the PSO-optimised algorithm with BP network toolbox, construct a prediction model, and simulate the prediction of regional human capital level.

(1)

Adopt MATLAB to program, complete PCA, determine the original data needed for prediction and initialise the original data.

In this paper, a ‘noise sample’ is added to the original data to make it an expanded original data. Specifically, in the programming, rand function in MATLAB is used to make each element x_i in the original data matrix X corresponding to the training to be executed for R consecutive times: $X . * (1 + 0.2 * (r a n d (n, P) - 0.5))$ sentence, generate R uniformly distributed random numbers in $[x_{i} - 0.1, x_{i} + 0.1]$ interval and recombine them as an extended data matrix for BP network training. The original input data corresponding to training is expanded to P × n × R.

(2)

Establish the BP neural network prediction model of regional human capital level optimised by PSO, and the parameters of the prediction model are set, so that the level of regional human capital can be predicted and simulated.

(3)

The parameter settings in MATLAB programming are as follows:

The population number s in PSO algorithm is set as 250; terminating evolution algebra G = 100; and cross probability p_c = 0.90. The adaptive mutation probability is adopted as $p_{m} = 0.10 - [1 : 1 : s] \times 0.01 / s$ , that is, the mutation probability is related to fitness; the smaller the fitness, the greater the mutation probability. By adjusting the mixing degree, the appropriate population number of PSO can be set. According to experience, the mixing degree is selected at about 20%; when the particle number of population m = 30 ∼ 50, the simulation effect of regional human capital prediction in China is relatively good at ΔV = 0.9; and T = 100000, ΔT = 0.95 in simulated annealing algorithm.

Analysis of prediction results

Considering the availability and comparability of data, based on the principle of not only reflecting the inherent requirements of human capital, but also being easy to operate, this paper selects 15 original indexes or generated indexes from five aspects, namely education and training, medical care, scientific and technological experience, labour migration and social security, to constitute the evaluation index system of regional human capital. The data of the model simulation come from the National Statistical Bulletin of Science and Technology from 2015 to 2021, and so on. The evaluation data of regional human capital investment in China from 2014 to 2020 are selected. Taking the PCA of China’s regional human capital level in 2020 as an example, through PCA, the first four principal components are selected to replace the original 15 indicators, and the principal component scores of the corresponding human capital levels in 31 regions in China are obtained, as shown in Table 2.

Table 2

Regional horizontal principal component scores in some areas.

Region (Province)	Y1	Y2	Y3	Y4
Beijing	11.217	0.938	3.883	−1.760
Tianjin	4.726	−2.299	−1.106	1.099
Hebei	−0.855	0.347	−0.961	−0.722
Shanxi	−0.259	−1.389	−0.267	−0.514
Inner Mongolia	−0.006	−1.334	−0.849	−0.682
Liaoning	2.087	0.348	−1.545	−0.742
Jilin	0.983	−1.553	−1.373	−1.341
Shanghai	7.810	−0.796	−1.076	2.797
Jiangsu	0.999	3.112	−2.064	0.140
Zhejiang	1.402	2.707	0.203	1.371
Hubei	−0.635	0.342	−0.684	−0.349
Hunan	−1.025	0.553	0.093	−0.424
Guangdong	0.672	2.268	−0.675	1.032
Guangxi	−2.387	−0.182	0.979	0.200
Hainan	−1.519	−1.519	0.544	0.513
Chongqing	−1.551	−0.034	1.473	0.480
Sichuan	−1.858	1.224	0.367	−0.126

Compared with the prediction of standard BP network, the improved model is feasible has certain advantages for the prediction of regional human capital level. In order to test the simulation performance of the optimised BP neural network, the MATLAB command $[m, b, r] = p o s t r e g$ (A, T) is used to conduct linear regression analysis between the simulation output and the target output, where the correlation coefficient r = 0.99882 is obtained, showing that its network performance is good.

As can be seen from Figure 4, the actual output of human capital level in 31 regions in 2020 is obtained, and compared with the target output, the output result of the prediction model is basically consistent with the reality, which indicates that the improved prediction model is more accurate.

Comparison of prediction effect of human capital level.

To clearly explain the advantages in the prediction of human capital level, the error analysis of the prediction results is carried out. The relative error and test error are selected for testing. Table 3 shows the comparison results.

Table 3

Error comparison of simulation results.

Region				Beijing	Tianjin	Hebei	Shanxi	Inner Mongolia	Liaoning	Jilin
Relative error		Improved BP network		7.87	2.51	14.83	18.0	14.9	1.05	42.89
		BP network		6.24	21.9	35.14	44.6	88.5	16.1	290.6
Shanghai	Jiangsu	Zhejiang	Anhui(Province)	Fujian	Jiangxi	Shandong	Henan	Hubei	Hunan	Guangdong
8.2	6.83	1.57	5.85	9.68	6.99	140.4	12.0	19.8	18.1	3.05
4.8	29.51	6.74	7.29	9.24	9.54	152.05	5.54	35.51	15.80	10.64
Hainan	Chongqing	Sichuan	Guizhou	Yunnan	Tibet	Shaanxi	Gansu	Qinghai	Ningxia	Xinjiang
2.06	4.66	10.41	4.39	3.96	2.38	40.44	1.80	4.40	8.75	29.84
5.90	3.83	5.81	10.34	7.11	6.51	106.08	5.88	7.33	9.19	177.05

The results show that compared with BP neural network, the dimension of the training samples in the optimised model is reduced, so the calculation of the model is relatively reduced, so that the prediction accuracy is improved and the error is smaller.

Conclusion

Further research on the prediction of regional human capital level is a work of practical significance and application value. In this paper, the evaluation index system of human capital is constructed, and the data of various regions in China are selected according to the generated index to form the original data sample set. After the data are initialised, the optimised BP neural network model is derived, and the prediction model of regional human capital level is obtained. The test results show that, compared with the BP neural network, the dimension of training samples of the optimised model is reduced, so the calculation of the model is relatively reduced, the prediction accuracy is improved and the error is smaller. At the same time, the output results of the prediction model are basically consistent with the reality, which can provide decision support for the development of regional human capital.

Figures & Tables

Regional horizontal principal component scores in some areas.

Region (Province)	Y1	Y2	Y3	Y4
Beijing	11.217	0.938	3.883	−1.760
Tianjin	4.726	−2.299	−1.106	1.099
Hebei	−0.855	0.347	−0.961	−0.722
Shanxi	−0.259	−1.389	−0.267	−0.514
Inner Mongolia	−0.006	−1.334	−0.849	−0.682
Liaoning	2.087	0.348	−1.545	−0.742
Jilin	0.983	−1.553	−1.373	−1.341
Shanghai	7.810	−0.796	−1.076	2.797
Jiangsu	0.999	3.112	−2.064	0.140
Zhejiang	1.402	2.707	0.203	1.371
Hubei	−0.635	0.342	−0.684	−0.349
Hunan	−1.025	0.553	0.093	−0.424
Guangdong	0.672	2.268	−0.675	1.032
Guangxi	−2.387	−0.182	0.979	0.200
Hainan	−1.519	−1.519	0.544	0.513
Chongqing	−1.551	−0.034	1.473	0.480
Sichuan	−1.858	1.224	0.367	−0.126

Index system of regional human capital investment evaluation.

Category	Index system
Educational training	X1 per capita education expenditure (10,000 yuan/person), X2 average education level index, X3 teacher-student ratio in school, X4 population with college degree or above, X5 professional and technical personnel
Development of science and technology	X6 R&D expenditure as a percentage of GDP (%), labour productivity of X7 employees, X8 technological achievements (million yuan), X9 patent applications of employees
Medical care	X10 The number of beds owned by 100,000 people, X11 the number of health technicians, X12 the medical care expenditure per capita
Labour migration	X13 proportion of employees in the total population (%), X14 number of employment agencies
Social security	X15 social security coverage rate (%)

Error comparison of simulation results.

Region				Beijing	Tianjin	Hebei	Shanxi	Inner Mongolia	Liaoning	Jilin
Relative error		Improved BP network		7.87	2.51	14.83	18.0	14.9	1.05	42.89
		BP network		6.24	21.9	35.14	44.6	88.5	16.1	290.6
Shanghai	Jiangsu	Zhejiang	Anhui(Province)	Fujian	Jiangxi	Shandong	Henan	Hubei	Hunan	Guangdong
8.2	6.83	1.57	5.85	9.68	6.99	140.4	12.0	19.8	18.1	3.05
4.8	29.51	6.74	7.29	9.24	9.54	152.05	5.54	35.51	15.80	10.64
Hainan	Chongqing	Sichuan	Guizhou	Yunnan	Tibet	Shaanxi	Gansu	Qinghai	Ningxia	Xinjiang
2.06	4.66	10.41	4.39	3.96	2.38	40.44	1.80	4.40	8.75	29.84
5.90	3.83	5.81	10.34	7.11	6.51	106.08	5.88	7.33	9.19	177.05

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Applied Mathematics and Nonlinear Sciences

Evaluation and prediction of regional human capital based on optimised BP neural network

Keyan Zhao
Keyan Zhao

Published Online: 24 Jun 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 16 Mar 2022

Accepted: 25 Apr 2022

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

PDF Preview

Article

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Regional horizontal principal component scores in some areas.

Index system of regional human capital investment evaluation.

Error comparison of simulation results.

References

Recent Articles

Plan your remote conference with Sciendo

Applied Mathematics and Nonlinear Sciences

Evaluation and prediction of regional human capital based on optimised BP neural network

Keyan ZhaoKeyan Zhao

Published Online: 24 Jun 2022

Volume & Issue: AHEAD OF PRINT

Page range: -

Received: 16 Mar 2022

Accepted: 25 Apr 2022

Journal & Issue Details

Applied Mathematics and Nonlinear Sciences

PDF Preview

Article

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Regional horizontal principal component scores in some areas.

Index system of regional human capital investment evaluation.

Error comparison of simulation results.

References

Recent Articles

Plan your remote conference with Sciendo

Keyan Zhao
Keyan Zhao