scholarly journals A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3143
Author(s):  
István Fazekas ◽  
Attila Barta
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Network Evolution ◽  
Evolution Model ◽  
Mathematical Methods ◽  
Malthusian Parameter ◽  
Limiting Behaviour

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.

A continuous-time network evolution model describing 3-interactions

2021 ◽  
pp. 1-20
Author(s):  
István Fazekas ◽  
Attila Barta ◽  
Csaba Noszály ◽  
Bettina Porvázsnyik
Keyword(s):  
Continuous Time ◽  
Network Evolution ◽  
Evolution Model

scholarly journals Period-Life of a Branching Process with Migration and Continuous Time

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 868
Author(s):  
Khrystyna Prysyazhnyk ◽  
Iryna Bazylevych ◽  
Ludmila Mitkova ◽  
Iryna Ivanochko
Keyword(s):  
Random Process ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Probability Generating Function ◽  
Time Interval ◽  
The Moment ◽  
First Time ◽  
Critical Branching Process ◽  
Number Of Particles

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

scholarly journals Dynamic Evolution Model of a Collaborative Innovation Network from the Resource Perspective and an Application Considering Different Government Behaviors

Information ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 138 ◽  
Author(s):  
Wu ◽  
Shao ◽  
Feng
Keyword(s):  
Network Evolution ◽  
Evolution Model ◽  
Dynamic Evolution ◽  
Innovation Network ◽  
Transfer Policy ◽  
Collaborative Innovation ◽  
Innovation Output ◽  
The Government ◽  
Small Change ◽  
Innovative Behaviors

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.

A note on the subcritical generalized age-dependent branching process

1976 ◽  
Vol 13 (4) ◽  
pp. 798-803 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Malthusian Parameter ◽  
Age Dependent ◽  
The Mean ◽  
Mean Function ◽  
Necessary And Sufficient

For a subcritical Bellman-Harris process for which the Malthusian parameter α exists and the mean function M(t)∼ aeat as t → ∞, a necessary and sufficient condition for e–at (1 –F(s, t)) to have a non-zero limit is known. The corresponding condition is given for the generalized branching process.

The multitype continuous-time Markov branching process in a periodic environment

1980 ◽  
Vol 12 (1) ◽  
pp. 81-93 ◽  
Author(s):  
B. Klein ◽  
P. D. M. MacDonald
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Cell Kinetics ◽  
Initial Conditions ◽  
Random Variable ◽  
Diurnal Rhythms ◽  
Biological Applications ◽  
Regular Case ◽  
Markov Branching Process ◽  
Periodic Environment

The multitype continuous-time Markov branching process has many biological applications where the environmental factors vary in a periodic manner. Circadian or diurnal rhythms in cell kinetics are an important example. It is shown that in the supercritical positively regular case the proportions of individuals of various types converge in probability to a non-random periodic vector, independent of the initial conditions, while the absolute numbers of individuals of various types converge in probability to that vector multiplied by a random variable whose distribution depends on the initial conditions. It is noted that the proofs are straightforward extensions of the well-known results for a constant environment.

scholarly journals On mutations in the branching model for multitype populations

2018 ◽  
Vol 50 (2) ◽  
pp. 543-564 ◽  
Author(s):  
Loïc Chaumont ◽  
Thi Ngoc Anh Nguyen
Keyword(s):  
Infectious Diseases ◽  
Asymptotic Behaviour ◽  
Continuous Time ◽  
Mutation Rates ◽  
Genetic Evolution ◽  
Connected Component ◽  
Branching Model ◽  
Limiting Behaviour ◽  
Number Of Individuals

AbstractThe forest of mutations associated to a multitype branching forest is obtained by merging together all vertices in each of its clusters and by preserving connections between them. (Here, by cluster, we mean a maximal connected component of the forest in which all vertices have the same type.) We first show that the forest of mutations of any multitype branching forest is itself a branching forest. Then we give its progeny distribution and we describe some of its crucial properties in terms of the initial progeny distribution. We also obtain the limiting behaviour of the number of mutations both when the total number of individuals tends to ∞ and when the number of roots tends to ∞. The continuous-time case is then investigated by considering multitype branching forests with edge lengths. When mutations are nonreversible, we give a representation of their emergence times which allows us to describe the asymptotic behaviour of the latter, under certain conditions on the mutation rates. These results have potential relevance for emergence of mutations in population cells, particularly for genetic evolution of cancer or development of infectious diseases.

Markov processes associated with critical Galton-Watson processes with application to extinction probabilities

1976 ◽  
Vol 8 (2) ◽  
pp. 278-295 ◽  
Author(s):  
Michael Sze
Keyword(s):  
Continuous Time ◽  
Branching Process ◽  
Continuous Process ◽  
Regularly Varying Functions ◽  
Original Process ◽  
Additional Information ◽  
Embedding Technique ◽  
Extinction Probabilities ◽  
Watson Process ◽  
The Given

As an alternative to the embedding technique of T. E. Harris, S. Karlin and J. McGregor, we show that given a critical Galton–Watson process satisfying some mild assumptions, we can always construct a continuous-time Markov branching process having the same asymptotic behaviour as the given process. Thus, via the associated continuous process, additional information about the original process is obtained. We apply this technique to the study of extinction probabilities of a critical Galton–Watson process, and provide estimates for the extinction probabilities by regularly varying functions.

A transportation network evolution model based on link prediction

2021 ◽  
Author(s):  
Shuang Gu ◽  
Keping Li ◽  
Yan Liang ◽  
Dongyang Yan
Keyword(s):  
Network Structure ◽  
Link Prediction ◽  
Transportation Networks ◽  
Network Evolution ◽  
Evolution Model ◽  
Civil Aviation ◽  
Node Degree ◽  
Network Efficiency ◽  
Evolution Mechanism ◽  
Proposed Model

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.

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