A continuous-time network evolution model describing 3-interactions

Author(s):  
István Fazekas ◽  
Attila Barta ◽  
Csaba Noszály ◽  
Bettina Porvázsnyik
Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3143
Author(s):  
István Fazekas ◽  
Attila Barta

A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is governed by a multi-type continuous-time branching process. The limiting behaviour of the network is studied by mathematical methods. We prove that the number of triangles and edges have the same magnitude on the event of non-extinction, and it is eαt, where α is the Malthusian parameter. The probability of the extinction and the degree process of a fixed vertex are also studied. The results are illustrated by simulations.


Information ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 138 ◽  
Author(s):  
Wu ◽  
Shao ◽  
Feng

The evolution of a collaborative innovation network depends on the interrelationships among the innovation subjects. Every single small change affects the network topology, which leads to different evolution results. A logical relationship exists between network evolution and innovative behaviors. An accurate understanding of the characteristics of the network structure can help the innovative subjects to adopt appropriate innovative behaviors. This paper summarizes the three characteristics of collaborative innovation networks, knowledge transfer, policy environment, and periodic cooperation, and it establishes a dynamic evolution model for a resource-priority connection mechanism based on innovation resource theory. The network subjects are not randomly testing all of the potential partners, but have a strong tendency to, which is, innovation resource. The evolution process of a collaborative innovation network is simulated with three different government behaviors as experimental objects. The evolution results show that the government should adopt the policy of supporting the enterprises that recently entered the network, which can maintain the innovation vitality of the network and benefit the innovation output. The results of this study also provide a reference for decision-making by the government and enterprises.


Author(s):  
Shuang Gu ◽  
Keping Li ◽  
Yan Liang ◽  
Dongyang Yan

An effective and reliable evolution model can provide strong support for the planning and design of transportation networks. As a network evolution mechanism, link prediction plays an important role in the expansion of transportation networks. Most of the previous algorithms mainly took node degree or common neighbors into account in calculating link probability between two nodes, and the structure characteristics which can enhance global network efficiency are rarely considered. To address these issues, we propose a new evolution mechanism of transportation networks from the aspect of link prediction. Specifically, node degree, distance, path, expected network structure, relevance, population and GDP are comprehensively considered according to the characteristics and requirements of the transportation networks. Numerical experiments are done with China’s high-speed railway network, China’s highway network and China’s inland civil aviation network. We compare receiver operating characteristic curve and network efficiency in different models and explore the degree and hubs of networks generated by the proposed model. The results show that the proposed model has better prediction performance and can effectively optimize the network structure compared with other baseline link prediction methods.


Author(s):  
Yuxin Liu ◽  
Zili Zhang ◽  
Chao Gao ◽  
Yuheng Wu ◽  
Tao Qian

2017 ◽  
Vol 13 (03) ◽  
pp. 4 ◽  
Author(s):  
Hui Gao ◽  
Zhixian Yang

<span style="font-family: 'Times New Roman',serif; font-size: 12pt; mso-fareast-font-family: SimSun; mso-fareast-theme-font: minor-fareast; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;">The Barabási–Albert (BA) model is a famous complex network model that generates scale-free networks. Wireless sensor networks (WSNs) had been thought to be approximately scale-free through lots of empirical research. Based on the BA model, we propose an evolution model for WSNs. According to actual influence factors such as the remainder energy of each sensor and physical link capability of each sensor, our evolution model constructs WSNs by using a preferential attachment mechanism. Through simulation and analysis, we can prove that our evolution model would make the total energy consumption of the WSNs more efficient and have a superior random node error tolerance.</span>


2019 ◽  
Vol 56 (2) ◽  
pp. 416-440 ◽  
Author(s):  
István Fazekas ◽  
Csaba Noszály ◽  
Attila Perecsényi

AbstractA new network evolution model is introduced in this paper. The model is based on cooperations of N units. The units are the nodes of the network and the cooperations are indicated by directed links. At each evolution step N units cooperate, which formally means that they form a directed N-star subgraph. At each step either a new unit joins the network and it cooperates with N − 1 old units, or N old units cooperate. During the evolution both preferential attachment and uniform choice are applied. Asymptotic power law distributions are obtained both for in-degrees and for out-degrees.


2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Yang Peng ◽  
Paul Scott ◽  
Ruikang Tao ◽  
Hua Wang ◽  
Yan Wu ◽  
...  

The molecular circuits of cell cycle control serve as a key hub to integrate from endogenous and environmental signals into a robust biological decision driving cell growth and division. Dysfunctional cell cycle control is highlighted in a wide spectrum of human cancers. More importantly the mainstay anticancer treatment such as radiation therapy and chemotherapy targets the hallmark of uncontrolled cell proliferation in cancer cells by causing DNA damage, cell cycle arrest, and cell death. Given the functional importance of cell cycle control, the regulatory mechanisms that drive the cell division have been extensively investigated in a huge number of studies by conventional single-gene approaches. However the complexity of cell cycle control renders a significant barrier to understand its function at a network level. In this study, we used mathematical modeling through modern graph theory and differential equation systems. We believe our network evolution model can help us understand the dynamic cell cycle control in tumor evolution and optimizing dosing schedules for radiation therapy and chemotherapy targeting cell cycle.


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