EXACT SOLUTION OF THE DEGREE DISTRIBUTION FOR AN EVOLVING NETWORK

In this paper we propose a simple evolving network with link additions as well as removals. The preferential attachment of link additions is similar to BA model’s, while the removal rule is newly added. From the perspective of Markov chain, we give the exact solution of the degree distribution and show that whether the network is scale-free or not depends on the parameter m, and the degree exponent varying in （3, 5] is also depend on m if scale-free.

Evolving networks: from topology to dynamics

A multi-local-world model is introduced to describe the evolving networks that have a localization property such as the Internet. Based on this model, we show that the traffic load defined by 'betweenness centrality' on the multi-local-world scale-free networks' model also follows a power law form. In this kind of network, a few vertices have heavier loads and so play more important roles than the others in the network.

A new local-world evolving network model

In some real complex networks, only a few nodes can obtain the global information about the entire networks, but most of the nodes own only local connections therefore own only local information of the networks. A new local-world evolving network model is proposed in this paper. In the model, not all the nodes obtain local network information, which is different from the local world network model proposed by Li and Chen （LC model）. In the LC model, each node has only the local connections therefore owns only local information about the entire networks. Theoretical analysis and numerical simulation show that adjusting the ratio of the number of nodes obtaining the global information of the network to the total number of nodes can effectively control the valuing range for the power-law exponent of the new network. Therefore, if the topological structure of a complex network, especially its exponent of power-law degree distribution, needs controlling, we just add or take away a few nodes which own the global information of the network.

Effects of Vertex Activity and Self-organized Criticality Behavior on a Weighted Evolving Network

Effects of vertex activity have been analyzed on a weighted evolving network.The network is characterized by the probability distribution of vertex strength,each edge weight and evolution of the strength of vertices with different vertex activities.The model exhibits self-organized criticality behavior.The probability distribution of avalanche size for different network sizes is also shown.In addition,there is a power law relation between the size and the duration of an avalanche and the average of avalanche size has been studied for different vertex activities.

Evolving Network Model with Local-Area Preference for Mobile Ad Hoc Network

To accurately describe the evolving features of Mobile Ad Hoc Networks (MANETs) and to improve the performance of such networks, an evolving topology model with local-area preference is proposed. The aim of the model, which is analyzed by the mean field theory, is to optimize network structures based on users' behaviors in MANETs. The analysis results indicate that the network generated by this evolving model is a kind of scale-free network. This evolving model can improve the fault-tolerance performance of networks by balancing the connectivity and two factors, i.e., the remaining energy and the distance to nodes. The simulation results show that the evolving topology model has superior performance in reducing the traffic load and the energy consumption, prolonging network lifetime and improving the scalability of networks. It is an available approach for establishing and analyzing actual MANETs.

Markov Chain-based Degree Distributions of Evolving Networks

In this paper, we study a class of stochastic processes, called evolving network Markov chains, in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains. We investigate the evolving network Markov chains, thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not. With this new method, we finally obtain a rigorous, exact and unified solution of the steady degree distribution of the evolving network.

A Collaboration Network Model with Multiple Evolving Factors

To describe the empirical data of collaboration networks, several evolving mechanisms have been proposed, which usually introduce different dynamics factors controlling the network growth. These models can reasonably reproduce the empirical degree distributions for a number of we11-studied real-world collaboration networks. On the basis of the previous studies, in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors, including partial preferential attachment, partial random attachment and network growth speed. By using a rate equation method, we obtain an analytical formula for the act degree distribution. We discuss the dependence of the act degree distribution on these different dynamics factors. By fitting to the empirical data of two typical collaboration networks, we can extract the respective contributions of these dynamics factors to the evolution of each networks.

Integrated Evolving Spiking Neural Network and Feature Extraction Methods for Scoliosis Classification

Adolescent Idiopathic Scoliosis(AIS)is a deformity of the spine that affects teenagers.The current method for detecting AIS is based on radiographic images which may increase the risk of cancer growth due to radiation.Photogrammetry is another alternative used to identify AIS by distinguishing the curves of the spine from the surface of a human’s back.Currently,detecting the curve of the spine is manually performed,making it a time-consuming task.To overcome this issue,it is crucial to develop a better model that automatically detects the curve of the spine and classify the types of AIS.This research proposes a new integration of ESNN and Feature Extraction(FE)methods and explores the architecture of ESNN for the AIS classification model.This research identifies the optimal Feature Extraction(FE)methods to reduce computational complexity.The ability of ESNN to provide a fast result with a simplicity and performance capability makes this model suitable to be implemented in a clinical setting where a quick result is crucial.A comparison between the conventional classifier(Support Vector Machine(SVM),Multi-layer Perceptron(MLP)and Random Forest(RF))with the proposed AIS model also be performed on a dataset collected by an orthopedic expert from Hospital Universiti Kebangsaan Malaysia(HUKM).This dataset consists of various photogrammetry images of the human back with different types ofMalaysian AIS patients to solve the scoliosis problem.The process begins by pre-processing the images which includes resizing and converting the captured pictures to gray-scale images.This is then followed by feature extraction,normalization,and classification.The experimental results indicate that the integration of LBP and ESNN achieves higher accuracy compared to the performance of multiple baseline state-of-the-art Machine Learning for AIS classification.This demonstrates the capability of ESNN in classifying the types of AIS based on photogrammetry images.

Design of an Interconnection Architecture and Sizing of Two (2) EPC Core Networks: The Case of Orange-Guinea

With the arrival of the 4G and 5G,the telecommunications networks have experienced a large expansion of these networks.That enabled the integration of many services and adequate flow,thus enabling the operators to respond to the growing demand of users.This rapid evolution has given the operators to adapt,their methods to the new technologies that increase.This complexity becomes more important,when these networks include several technologies to access different from the heterogeneous network like in the 4G network.The dimensional new challenges tell the application and the considerable increase in demand for services and the compatibility with existing networks,the management of mobility intercellular of users and it offers a better quality of services.Thus,the proposed solution to meet these new requirements is the sizing of the EPC(Evolved Packet Core)core network to support the 5G access network.For the case of Orange Guinea,this involves setting up an architecture for interconnecting the core networks of Sonfonia and Camayenne.The objectives of our work are of two orders:(1)to propose these solutions and recommendations for the heart network EPC sizing and the deployment to be adopted;(2)supply and architectural interconnection in the heart network EPC and an existing heart network.In our work,the model of traffic in communication that we use to calculate the traffic generated with each technology has link in the network of the heart.

Evolution of Weighted Networks by Duplication-Divergence Mechanism

The duplication and divergence process is ubiquitous in nature and man-made networks. Motivated by the duplication-divergence mechanism which depicts the growth of protein networks, we propose a weighted network model in which topological evolution is coupled with weight dynamics. Large scale numerical results indicate that our model can naturally generate networks with power-law-like distributions of degree, strength and weight. The degree-strength correlation is illustrated as well. These properties are in agreement well with empirical data observed in real-world systems. Furthermore, by altering the retention probability δ, weighted, structured exponential networks are realized.

Modified DM Models for Aging Networks Based on Neighborhood Connectivity

Two modified Dorogovtsev-Mendes （DM） models of aging networks based on the dynamics of connecting nearest-neighbors are introduced. One edge of the new site is connected to the old site with probability - kt^-α as in the DM＇s model, where the degree and age of the old site are k and t, respectively. We consider two cases, i.e. the other edges of the new site attaching to the nearest-neighbors of the old site with uniform and degree connectivity probability, respectively. The network structure changes with an increase of aging exponent α It is found that the networks can produce scale-free degree distributions with small-world properties. And the different connectivity probabilities lead to the different properties of the networks.

Local Events and Dynamics on Weighted Complex Networks

We examine the weighted networks grown and evolved by local events, such as the addition of new vertices and links and we show that depending on frequency of the events, a generalized power-law distribution of strength can emerge. Continuum theory is used to predict the scaling function as well as the exponents, which is in good agreement with the numerical simulation results. Depending on event frequency, power-law distributions of degree and weight can also be expected. Probability saturation phenomena for small strength and degree in many real world networks can be reproduced. Particularly, the non-trivial clustering coefficient, assortativity coefficient and degree-strength correlation in our model are all consistent with empirical evidences.

A Mixed Mechanism of Weighted-Driven and Inner Selection in Networks

For most networks, the weight of connection is changing with their attachment and inner affinity. By introducing a mixed mechanism of weighted-driven and inner selection, the model exhibits wide range power-law distributions of node strength and edge weight, and the exponent can be adjusted by not only the parameter δ but also the probability q. Furthermore, we investigate the weighted average shortest distance, clustering coefficient, and the correlation of our network. In addition, the weighted assortativity coefficient which characterizes important information of weighted topological networks has been discussed, but the variation of coefficients is much smaller than the former researches.