Qinghua Chen

Yingyu Du, Qinghua Chen

The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive algorithm of the Crouzeix-Raviart nonconforming element method for the convection-diffusion eigenvalue problems. We give the corresponding a posteriori error estimators, and prove their reliability and efficiency. Finally, the numerical results validate the theoretical analysis and show that the algorithm presented in this paper is efficient.

Dinghua Shi, Zhifeng Chen, Xiang Sun et al.

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions. Since searching for maximum cliques is an NP-complete problem, we use k-core decomposition to determine the computability of a given network. For a computable network, we design a search method with an implementable algorithm for finding cliques of different orders, obtaining also the Euler characteristic number. Then, we compute the Betti numbers by using the ranks of boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans with data from one typical dataset, and find all of its cliques and some cavities of different orders, providing a basis for further mathematical analysis and computation of its structure and function.

Qinghua Chen, Yan Wang, Mengmeng Wang et al.

Corpus-based statistical analysis plays a significant role in linguistic research, and ample evidence has shown that different languages exhibit some common laws. Studies have found that letters in some alphabetic writing languages have strikingly similar statistical usage frequency distributions. Does this hold for Chinese, which employs ideogram writing? We obtained letter frequency data of some alphabetic writing languages and found the common law of the letter distributions. In addition, we collected Chinese literature corpora for different historical periods from the Tang Dynasty to the present, and we dismantled the Chinese written language into three kinds of basic particles: characters, strokes and constructive parts. The results of the statistical analysis showed that, in different historical periods, the intensity of the use of basic particles in Chinese writing varied, but the form of the distribution was consistent. In particular, the distributions of the Chinese constructive parts are certainly consistent with those alphabetic writing languages. This study provides new evidence of the consistency of human languages.