In modern times, the innovation ability of college students is a focus of college education. However, the cultivation and improvement of this ability are constrained by many factors, and the ability is too complex to be evaluated accurately. To solve the problems, this paper puts forward an extension model suitable for evaluating the cultivation and improvement of the said ability. Firstly, the research problem was defined clearly as the evaluation of the cultivation and improvement for the innovation ability of college students. Based on the extension theory, an evaluation model was established for the cultivation and improvement of the said ability, the workflow of model implementation was explained, and the corresponding evaluation algorithm was designed in details. Finally, the proposed model and algorithm were proved operable through case analysis. The research results provide support to the solution of complex systematic decision-making problems.

Many studies have considered the preferential attachment mechanism to cause scale-free networks. On the contrary, a network evolution model based on nonpreferential attachment is proposed to explain some non-scale-free network, and the existence of a stable degree distribution of the model is theoretically proven. Three methods are suggested to estimate the distribution. The model’s significance shows that preferential attachment is not the only mechanism of tail power-law distribution, which gives a reasonable explanation to non-scale-free phenomenon. Our results provide a new train of thought for understanding the degree distribution of network.

Revealing synaptic connections between neurons is of great significance and practical value to biomedicine and bioneurology. We present a general approach to reconstruct neuronal synapses, which is based on compressive sensing and special data processing. And this approach is more suitable for nervous system with peak time series. Numerical simulations illustrate the feasibility and effectiveness of the proposed approach. Moreover, this approach not only adapts to the asymmetry of neural connections and the diversity of coupling strength, but also adapts to the excitability and inhibition of neural node classification. In addition, the effects of the factors on the synaptic connection identification performance and their optimal states for the synaptic connection recovery are discussed. Besides, it is of great practical significance to control the order of Taylor expansion to improve the performance of synaptic connection recognition.

Many practical systems can be considered as networks of nodes interacting. Explicit network topology is a straightforward method to understand the actual system, so it is of practical significance to obtain the complete network topology from the empirically measured time series. With the premise that the dynamics equations and coupling matrix are known, a method to reconstruct the network topology from the measured time series is proposed, and based on regression theory the estimated matrix form of the adjacency matrix is given. Also, the method is suitable for predicting arbitrary weights of network connections, and its practicality is verified by numerical simulations. Importantly for the 0 − 1 matrix, a new method for judging the prediction performance of the model using the false negative rate is proposed. It can estimate the accuracy of model prediction with only partial sampling data when the information of network topology is unknown. In addition, a method that can control false positives is proposed, and the feasibility of the method is verified by numerical simulation. Finally, two factors that affect model performance, the amount of sample data and the intensity of noise, are discussed. INDEX TERMSReconstruction, false negative rate, regress theory. XUE ZHANG received the B.S. degree in mathematics from the University of Jinan, Jinan, China, in 2015. She is currently pursuing the master's degree with Wenzhou University. Her research interest includes complex systems. CHUANKUI YAN received the Master of Science (M.Sc.

Networks are prevalent in real life, and the study of network evolution models is very important for understanding the nature and laws of real networks. The distribution of the initial degree of nodes in existing classical models is constant or uniform. The model we proposed shows binomial distribution, and it is consistent with real network data. The theoretical analysis shows that the proposed model is scale-free at different probability values and its clustering coefficients are adjustable, and the Barabasi-Albert model is a special case of p = 0 in our model. In addition, the analytical results of the clustering coefficients can be estimated using mean-field theory. The mean clustering coefficients calculated from the simulated data and the analytical results tend to be stable. The model also exhibits small-world characteristics and has good reproducibility for short distances of real networks. Our model combines three network characteristics, scale-free, high clustering coefficients, and small-world characteristics, which is a significant improvement over traditional models with only a single or two characteristics. The theoretical analysis procedure can be used as a theoretical reference for various network models to study the estimation of clustering coefficients. The existence of stable equilibrium points of the model explains the controversy of whether scale-free is universal or not, and this explanation provides a new way of thinking to understand the problem.