The Transmission And Spreading Of Information In Big Data Networks

With t,he rapid development of computer technology,the rapid growth of network bandwidth,the popularization of intelligent devices,and the prosperity of social networks,network communication has become the main part of the data communication system,also gradually become an indispensable part of our daily life.At the same time,the amount of data generated and transmitted in the network has reached an astonishing degree.The popularization of the network makes the process of information transmission wider and faster.The advent of the era of big data requires data transmission in a more efficient way.Under the background requirements of these two aspects,the traditional coding theory and complex networks methods no longer perfectly fit the information transmission and communication needs in the era of big data,and many new coding problems and network dynamics problems emerge at the historic moment,which also makes the relevant theoretical disciplines enter a new stage of development.Over the past 70 years,researchers have created many distinguished classes of codes.These code classes are driven by various needs,for example,how to achieve Shannon capacity effectively,construct perfect or good codes in Hamming worst-case model,match the performance of random codes,reduce the complexity of decoding and the application in theoretical computer science,such as:cryptography(secret sharing,private information retrieval,etc.),pseudo-randomness,extractors,or probabilistic proof systems.Among all known codes,Reed-Muller(RM)codes are among the oldest,simplest and most widely used ones.RM codes were introduced by Muller in 1954,shortly after,Reed proposed the first efficient decoding algorithm.RM codes are kinds of channel coding scheme,which is used in wireless communication,especially in deep space communication.From 1969 to 1977,RM codes were used extensively for Mars exploration.Even today,RM codes also have great research value,and their fast decoding algorithms are very suitable for optical fiber communication systems.In addition,because of its good structural and mathematical properties,RM codes have been widely studied in theoretical computer science.In recent years,with the emergence of various spreading phenomena in complex networks,people pay more and more attention to transmission dynamics.Whether it is the study of disease epidemie or the propagation of public opinion,or the study of biological and information transmission models,their main purpose is to study the law of transmission and analyze the process of transmission.It can predict the direction and risk of transmission in real life,promote the dissemination of beneficial information,restrain the diffusion of harmful information,and provide theoretical basis for the discovery,prediction and control of information dissemination.How to quantitatively measure the importance of nodes in complex networks.or how to identify influential nodes in the spreading process of complex networks,is a long-term hot issue in complex network analysis.Successful answers to these questions,namely effective algorithms for identifying influential spreaders in complex networks,can help control the illness outbreaks better,stop the spread of epidemics,optimize the use of limited resources to facilitate the spread of information,publicize new products,prevent catastrophic outages of power grids or the Internet,and so on.This thesis mainly focuses on the transmission and spreading of information on the big data networks.Effective information transmission means that data can resist certain damage and be smoothly transmitted to the receiver,while extensive spreading can be applied to positive information publicity or prevent the spread of epidemic and rumors.Therefore,effective and widespread transmission of information is the basis for ensuring the security of cyberspace.For information transmission,this thesis mainly constructs two new extended cyclic codes sandwiched between two order RM codes.Both of these new codes can reach the channel capacity,that is,they have very effficient information transmission properties.We studied some of their fundamental properties and completely determined the minimal vectors in two special cases.For information spreading,this thesis focuses on influence maximization on the networks,involving the selection of multiple initial spreading nodes and the identification of important nodes.Our research results have theoretical and practical application value for the design and implementation of efficient transmission and wide dissemination of information.The specific research content is as follows.Two new classes of extended cyclic codes sandwiched-between RM codes:The 22m dimensional famous Barnes-Wall lattice BW2m(where m E N)forms an important infinite family of even lattices.One way to construct BW2m is to apply Construction D to the RM codes chains.Recently,Hu and Nebe constructed a series of new 22m dimensional universal strong perfect lattice sandwiched between the Barnes-Wall lattices.These lattices can be obtained by applying Construction D(cyc)to extended cyclic codes chains sandwiched between binary RM codes.In this thesis,we generalized the construction given by Hu and Nebe.Two new classes of extended cyclic codes sandwiched between generalized R.M codes are given by modifying the zeros of RM codes.Then we study the basic properties of these two new classes of codes,including their dimensions,dual codes and lower bounds of minimum distance.Finally,using Newton identities,affine polynomials and other tools,we completely determine the minimum vectors of these two classes of codes in some special cases.Information spreading influence maximization:The existing work on maximizing the spreading range of information with the lowest possible cost mainly focuses on two aspects:identifying multiple influential nodes and identifying important nodes in the networks.First,the distance between initial spreading nodes is a key factor.The greater the distance,the more different the range of spreading,the easier to avoid information congestion.In this thesis,"common neighbor",another statistical index in graph theory,is used to measure the common spreading ranges:and it is combined with the spreading ability of a single node to define the "marginal benefit" when vertex v joins the existing seed set S.On this basis,we propose a.multi-spreading nodes recognition algorithm based on marginal benefit,We test this approach on several data sets,all get better results.In addition,we give some default values for the user-defined parameter involved in this new measurement.Second,many existing centrality methods evaluate the importance of a node based on its neighbor nodes.For example,degree centrality focuses on the number of adjacent nodes,while eigenvector centrality states that the importance of a node is proportional to the sum of the importance of its neighbors.However,in calculating these centralities,the incident edges are ignored or treated equally.To the best of our knowledge,researchers rarely evaluate the centrality of a node by the centrality of its incident edges.In this thesis,we propose an iterative approach framework to obtain centralities of both nodes and edges.The idea is that the centrality of a node is determined by the centrality of its incident edges,whereas the centrality of an edge is determined by the centrality of its two endpoints.We construct a mutually updating iterative framework and prove that the node centers obtained by this framework are actually the principal eigenvectors of the Signless-Laplacian matrix of the input network.We call this new method SignlessLaplacian eigenvector center method.The proposed method is applied to multiple data sets,and the effectiveness of the proposed method is verified and good results are obtained.