Research Of Bi-layer Network、Community And Cascade Event

Based on Reductionism, modern physics has obtained great success, which is contributing to the production and development of modern scientific technology. However, typical complex systems, like biological system and social system, being a whole not equal to the simple combination of the sub parts due to their features of self-organization and self-adoption, are essentially not in accordance with Reductionism. Therefore, how to set up quantitative scientific system in complex system has for long been a hot concern in scientific community. The study of complex system, been particularly stressed in recent twenty years, has been greatly promoted at the end of the last century by the study tide of complex network, a description tool of complex system. Our project group also devote ourselves to the study of complex system and complex network. The first two parts of the thesis address two hot issues of complex network:associated bi-layer network and community division. The next two parts concentrate specifically on avalanche, one major phenomenon in a complex system, and scientific research article publication system, an important complex system.One typical system can be divided into many intricately related layers and subsystems, in which lots of interacting basic units exist. Thus, it is a hard and strenuous work to have a thorough study about the system as a whole. People always naturally focus on one type of basic unit at first, without taking into any account of their relationship with other basic units. And this is the main reason why most studies about complex network up to now cover only one kind of node and their interactions. The network is named layered network. Apparently, a typical complex system must be described from the perspective of many complicatedly interrelated layered networks. This more sophisticated network is called super network, or network of network, or interrelated network. They have been universally known as the most important complex network research direction. For example, in September2003, an International conference, held in Rome, concentrating on the topic "Growing Networks and Graphs in Statistical Physics, Finance, Biology and Social Systems" posed the top ten most urgent research issues, one of which is the network of network. But there are still some difficulties lying in direct study of network of network. Taking for the starting stage, many researchers brought about study on a small number of interrelated layered networks. The first part of the thesis covers our study on bi-layer network.In previous researches, the bus-transport system or the railway system of a city can be mapped into two spaces:Space P and Space L. In the two spaces, each node represents either a bus-stop or a railway station. In space P one edge indicates that at least one bus or train route provides direct service, while in space L, the line between two nodes is a sign, to say the least, that they are the adjoining stops of one route. As we know, in spite of the fact that there are many researches about topological property of two independent spaces, till now, there is still a blank in consideration about relationship between topological property of space P and topological property of space L. Similar to concepts in Kurant’s relevant articles, we hold the idea that space P describes traffic flow and space L approximately represents the road to embody the traffic flow, in other words, they are the infrastructure of traffic flow. Undoubtedly, study about the relationship between topological properties of the two spaces is conducive to have a good knowledge of relationship between transport infrastructure and traffic flow. With the aid of some rational assumptions, we come to the comprehension of correlation of two types of topological property:degree and clustering coefficient, of the same transport vehicle in double layer network composite of space L and space P. The conclusion is corresponding to the result of empirical study about Railway System in China and public traffic system of three Chinese cities. The result, which is in keeping with our tuition, demonstrates that, on statistical average, weighty hubs in space L has the same vital role in space P, and secondary nodes are also subordinate in space P. Similarly, space L and space P share the same dense part. This kind of description method of bi-layer network is also effective in other practical systems. Therefore, the above understanding about relationship between topological properties of two networks is useful for design and control of some systems. Study about this part has been published in Phys. Lett. A, with myself as the first author.A large amount of empirical study have proved that most of complex networks have the so-called "community" structure, which is composed of net nodes for some reasons, compact internally and sparse externally. Consequently,"community" structure division or identification is one of the most important issues in the study of complex network. In present "community" division algorithms, they are almost divided or identified according to topological structure. However, in some cases,"community" identification does not only rely on structure, but also on some other information. For example, fellows in a research group usually discuss very often in their common working place and many other places, forming a dense idea communication community; however, often they do not publish papers together (e.g., each of them only publishes papers with their common supervisor). So, if we set up a co-authorship bipartite network in ordinary way by defining the authors as actors and an edge between two authors as the co-authorship in a paper, the communities identified only by topological information are often very different from the practical research cooperation groups. The main reason for this is that some members of the researching group may publish papers with some scientists outside the group. Then they may belong to another dense part of the network if their out-group papers are jointly done by a great many authors, inducing more edges. The question is, having assumption that we have no idea to which project group one author belongs and project group is a rational community, then, is it possible to divide the community reasonably only by topological structure information, which is under influence of the division of project groups. According to the study we have done, there are few articles touching upon this issue at present. The third chapter of the thesis adopts one example to illustrate, based on the assumption that project group is a rational community, that weighted Newman algorithm is the best choice, for it can obtain the most close community division of the project group on the basis of topological information. These ideas have reference value to community division of other practical complex networks. Study about this part has been published in Chin. Phys. B, with myself as the first author.A widely existing phenomenon,"avalanche" or "cascade failure", has attracted attentions for a long time. The name of "cascade failure" bears more information than "avalanche" does. It is called " cascade" because the transmission process of an event undergoes the chain reactions, i.e., one generation events induce the next. It is called "failure" due to the disaster or catastrophe is has brought about. Snow avalanche or landslide avalanche, and blackout induced by cascade failures in power grids can serve as examples. Since some cascades do not cause disasters, we address this kind of cascading phenomenon as "cascade events"(CE). Why CE often cause disaster or catastrophe? We find that there are two important factors. The first one is that in most cases one event produces more than one next generation events. An uncontrolled increase of CE may bring about disaster even if the single event is harmless. The second important factor is that the frequency of CE becomes higher and higher, namely, time duration between two neighboring generations decreases so rapidly that a lash-up becomes impossible, such as in the courses of snow avalanche, landslide avalanche, and the power blackout. Disaster and catastrophe are frightening because they happened in such a short time that people completely have no time or ability to react to them. Accordingly, we first classify the cascading phenomena into two categories:the cascading disasters that result in large-scale functional failures and the cascading events that do not lead to disasters. We present a simplified sandpile model and a heuristic logistic map to show the characteristics of two kinds of CE. Our present findings contribute to the understanding of the transition between different cascading events, providing a basis for further understanding of the transitions among more general critical events. Study about this part has been published in Physica A, with myself as the first author.In recent decade, more and more physicists have realized the importance of complex system study and threw themselves into the research. Social system, as one of the most complicated complex systems, has become a promising research object, attracting interest of many physics. Human being’s scientific activities, including scientific paper publication, being a very important social system, has been attached great importance and studied broadly. In social system studies, it often happens that a sociologist has a brilliant qualitative idea, but cannot present a quantitative description. Mathematical experts may have a quantitative description to the thoughts, which would contribute to uncovering new general laws. The fifth chapter covers an investigation, made from a totally different angle, into the complex system of the scientific research article publication. It is intuitionist that a higher quality scientific journal accepts articles from higher academic level authors and invites even higher level authors being its editorial board members. This can be viewed as a kind of cooperation and competition between the journals, authors and editorial board members. Recently, quantitative study on complex systems becomes an attracting research area for physicists. Human scientific activity, including scientific paper publication, is one of the important complex systems therefore deserves an investigation. In this thesis we present a very simple model describing interaction between journals, authors and editorial. board members. In the model both the probabilities, with which a journal accepts papers from an author or invites him being an editorial board member, obey normal distributions. However, the most probable value of the later distribution shifts so that the journal can have higher level authors being its editorial board members. The model analytic conclusion is in rather good agreement with the empirical observation in15 real world journals with different influence factors. We successfully obtained a quantitative expression of an intuitional idea by a simple and appropriate model. This quantitative expression describes the relation functions between journals, authors and editorial board members which is important for scientists and, may be, also for the scientific administrations. Study about this part has been published in Chin. Phys. Lett., with myself as the first author.