数学建模论文汇总.docx

1、数学建模论文汇总Contents1. Introduction2. Restatement of the Problem3. Convention 3.1Terminology 3.2 Variables3.3Assumptions4.The Model4.1 the co-author network of the Erdos1 authors4.1.1 Complete co-author network4.1.2 Streamlined co-author network4.2 NMIM Model To Find the Most Influential Author4.2.1 Why

2、 is NMIM (Networks multi-attribute indicator method)4.2.2 Definition of Measure Indicators4.2.3 Model Establishment4.2.4 Summary of the NMIM 4.3The Journal Citation Networks Model4.3.1 Model establishment4.3.2 Model solution and analysis4.3.3 The influence measure of an individual network researcher

3、4.3.4 The influence measure of a journal5. Application of the Model:the Influential Actors in Fengs 6. Further Discussion6.1 Discussion about the Science, Understanding and Utility6.2 Further Discussion:Help Society in Preventing spread of rumor7. Conclusion8.Strengths and Weaknesses9.Reference1. In

4、troductionAs an ordinary person, we would never think of that there is an intersection point with the world-famous mathematician. If we want to know the intersection point, so easy, just visit the websites about Erds Number. As we all know, Paul Erds is a very talented math genius, he has published

5、1457 papers and has collaborated with 511 people in his life. Because the co-authors are too many, so Erds number is born. Erdss Erds Number is zero. The Erds Number of people who has writed papers directly with Erds is one, if someone has writed with an Erds Number one person, his Erds Number will

6、be two, and so on. So if we go to test, it is possible to find the Erds Number that belongs to ourselves. What is marvelous is Erds is not only the center of Erds Number network, but also focus on the study of network science.Network science is an interdisciplinary academic field which studies the q

7、ualitative and quantitative laws of complex networks such as social networks, computer, telecommunication networks, biological networks and so on. The The United States National Research Council defines network science as the study of network representations of physical, biological, and social pheno

8、mena leading to predictive models of these phenomena.2.Restatement of the Problem2.1 Problems we are confrontingIn a word, our task is to analyze influence and impact in research networks and other areas of society. And specific problems are as below: First, we are allowed to build the co-author net

9、work of the Erdos1 authors. Then analyze the properties of the network. Create a method to measure the influence so as to determine who in this Erdos1 network has significant influence within the network. The problem talks about another type of influence measure to compare the significance of a rese

10、arch paper. Use the papers in the attached list to build a model to determine which paper is in the center of the citation network. Besides, discuss the similar method to measure the influence of network researcher, university, department or journal in the network. Apply the model into different typ

11、es of network and analyze the importance of nodes in the net. Finally, discuss the influence methodology to solve the actual problems in the life.2.2 Solutions to solve these problems According to the appendix Erdos1.htm, we get a mass of data about 511 researchers who coauthored a paper with Erds a

12、nd their links and we use Microsoft Excel and Java Compiler to disposaldata.For the first question, we can draw a complex network to build the co-author network of the Erdos1 authors. Before we do this, we should get rid of people outside the Erdos1 network. Then, regard every person as a node. We u

13、se to analyze and visualize large networks. And we should take some measures, just like reducing the number of edges, deleting some nodes that have minor effect on the whole network. Finally, we can analyze the properties of this network with the help of network figures. After referencing some paper

14、s associated with co-author network, we have learned several centrality indicators deciding the importance of nodes. We know that single index may cause the assessing become one sided inevitably. So we adopt the NMIM model also as ”key nodes in complex networks identified by multi-attribute indicato

15、r method” to find the most influential nodes in the network. There are four kinds of indictors are introduced to obtain a comprehensive result .Use to calculate the value of these centrality indicators. Then we adopt Analytic Hierarchy Process to get the weight of each indicator. According to the in

16、tegrated analysis we can draw the conclusion that the most influential author in Erdos network is ALON, NOGA M. The third problem is similar to the second one. The difference is that the connections between papers have directions. We can also calculate the value of centrality indicators using. Some

17、of them are divided into outdegree indicator and indegree indicator. Besides, we should consider the importance of other papers connected with the paper we study. Finally, list Top 5 papers in each indicator in a table. Analyze the data in the table to get results. The left two small problems are th

18、e application and improvement of the citation network model. Calculate results and modify some parts of model can solve the problem easily. The fourth problem requires us to implement our algorithm on a completely different network. We should choose the representative network,and it must be easy to

19、achive.our choose positioned in the actors who have performed in Fengs movie(directed by Xiaogang Feng).Then use the NMIM model to select the influential actors. First,we should discuss the the Science, Understanding and Utility of our model basing on the process of model establishment.Then analyze

20、the possibility that to help society in preventing spread of rumor by our models.3. Convention3.1 Variables3.2 Assumptions We think the influence and impact mentioned in the problem are equivalent to significance and the destructiveness of the network after deleting the specific node. In our paper,

21、the influence and impact of someone or something in network We assume that in the co-author network the influence is only related to the four 4. The Model4.1 the co-author network of the Erdos1 authors4.1.1 Complete co-author networkWe pick out the 511 author inside the Erdos1 network by utilizing M

22、icrosoft Excel and Java program. Sort themalphabetically. Forconveniencesake,we use 1 to 511 to stand for the 511 author respectively(as their ID). Get anadjacency matrix with 511 rows and 511 columns to show the relationship between the coauthors.It is obvious that the relationship between the coau

23、thors is mutual(if A collaborates with B,B collaborateswith A).So the adjacency matrix is symmetric.We can just draw an undirectedgraph. By adopting Pajek,a complex network is presented in Figure 1.Figure 1.Complete co-author networkIn Figure 1,we can distinguish the diffirent degrees of nodes accor

24、ding to the colors of nodes. The correspondences between the degrees and the colors base on the Default Vertex Color in where we set up the Partition Color in Pajek . Tabel 1 shows part of the correspondences.Table 1 The correspondences between the degrees and the colorspartition01234567ColorCyanYel

25、lowLimeGreenRedBluePinkWhiteOrangepartition89101112131415ColorPurpleCadetBlueTealBlueOliveGreenGrayBlackMaroomLightGreen4.1.2 Streamlined co-author networkHowever, the number of edges is so large that the lines cover each other.We hardly look into the characteristic and laws among nodes ,edges,and c

26、olors.So we limit the size of network.For a node,we suspect that close relations to other nodes means major influence.We have degrees of nodes embody those relations for the time being.So,we select the nodes whose degree is greaterthan 210.There are 21 nodes that meet requirements.We draw the networ

27、k drawing consisting of these nodes and edges associated with the nodes.Now,we can observe clear in Figure 2.Figure 2 Streamlined co-author networkIn Figure 2,we is in virtue of not only color,but also diameter distinguish the diffirent degrees of nodes.We just have understood how color realizesthis

28、 purpose. The correspondences between the degrees and the colors in Figure 2 are same with them in Figure 1. Using diameter to attain like color is easy too.That is :larger the nodes are,larger the diameter of nodes are. We reach the following properties of this network for the present from Figure2:

29、 The number 10 (Liu, Andy C. F. ) has most degree,and he has the most direct connection with others. From the point of view of this, the number 10 will be the most influential. To facilitate the explanation,we call these nodes that have major directly connected edges Big Note.And we found that most

30、of directly connected edges of Big Note are directly connected edges of other Big Note.That is to say ,the direct relation between Big Note is much more than other combinations. These conclusion by perceiving subjectively and analyzing qualitatively will get modification and perfection in the next m

31、odeling.4.2 NMIM Model To Find the Most Influential Author4.2.1 Why is NMIM (Networks multi-attribute indicator method)The “Networks multi-attribute indicator method”(NMIM),known also as”key nodes in complex networks identified by multi-attribute indicator method ”. The Erdos1 network (do not includ

32、e Erds) is also involves a set of items(authors),which we will call nodes or sometimes vertices,with connections between them,called edges.In effect,the researcher who has significant influence within the network is the key node.4.2.2 Definition of Measure IndicatorsFor a given graph G=(V,E)is a non-directional network without self-rings,is set of all the nodes and is the set of edges between the