复杂网络与效率模型及其计算-应用数学专业论文.docxVIP

II II Complex networks and Efficiency model with computation Abstract Complex networks widely exist in our reality. Recently, the dynamics research of complex networks has become an important aspect in the research of complex networks. The effects of communities are found in biology, as well as in economy. A lot of researches are related to this subject. The work in this paper can be divided into three parts: the first is the research on General Purposed GPU. In recent years, because of the deficiency of CPU( e.g. the parallel deficiency, too expensive, etc), the discussing of GPGPU is been becoming very popular. In this paper, four aspects of GPU are considered: 1. the convenience of the GPU’s programming; 2. the cheap price of GPU; 3. the speed between CPU and GPU in some calculations; 4. the precision of GPU. At last, we confirm that the common researchers can learn to code the GPU although it is a little more complex than the CPU program. And the GPU is much cheaper than CPU if the flops are the same. Moreover, in some calculations, the precision is OK. The other part of this paper is about the efficiency model on the complex networks. As the efficiency model on small-world and scale-free networks with no communities had been studied, we studied the same networks but with communities where we considered the identical networks with two communities, with the help of GPU. The results of simulations are: as long as there is just one edge between two Small-World networks, the efficiency of one community increases if the other is increases. On the other hand, the Scale-Free networks with communities have the similar results. Both of them have the same reason. That is the distance of the total network is decreased if edges are added between the communities, which causes the efficiency increases. The last part of this paper is the degree distribution of PPI( Protein-Protein Interaction). We fitted the degree distribution of PPI, and found the stretched exponent function