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1 Distributed Adaptive Networks: A Graphical Evolutionary GameTheoretic View
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A novel analytical method for evolutionary graph theory problems
, 2013
"... Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general di ..."
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Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide nontrivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a nontrivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.
Evolutionary Dynamics of Information Diffusion Over Social Networks
"... Abstract—Current social networks are of extremely largescale generating tremendous information flows at every moment. How information diffuses over social networks has attracted much attention from both industry and academics. Most of the existing works on information diffusion analysis are based o ..."
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Abstract—Current social networks are of extremely largescale generating tremendous information flows at every moment. How information diffuses over social networks has attracted much attention from both industry and academics. Most of the existing works on information diffusion analysis are based on machine learning methods focusing on social network structure analysis and empirical data mining. However, the network users ’ decisions, actions, and socioeconomic interactions are generally ignored by most of existing works. In this paper, we propose an evolutionary game theoretic framework to model the dynamic information diffusion process in social networks. Specifically, we derive the information diffusion dynamics in complete networks, uniform degree, and nonuniform degree networks, with the highlight of two special networks, the Erdős–Rényi random network and the Barabási–Albert scalefree network. We find that the dynamics of information diffusion over these three kinds of networks are scalefree and all the three dynamics are same with each other when the network scale is sufficiently large. To verify our theoretical analysis, we perform simulations for the information diffusion over synthetic networks and realworld Facebook networks. Moreover, we also conduct an experiment on a Twitter hashtags dataset, which shows that the proposed game theoretic model can well fit and predict the information diffusion over real social networks. Index Terms—Evolutionary game, game theory, information diffusion, information spreading, social networks. I.
The molecular clock of neutral evolution can be accelerated or slowed by asymmetric spatial structure. PLoS Computational Biology. 2015; 11(2):e1004108. doi: 10.1371/journal.pcbi.1004108 PMID: 25719560
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(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters.
Modeling information diffusion dynamics over social networks
 In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP
, 2014
"... Information diffusion over social networks becomes a hot topic recently. Most of the existing works are based on the machine learning method with social network structure analysis and empirical data mining. However, the results learned from some specific dataset may not apply to the future networ ..."
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Information diffusion over social networks becomes a hot topic recently. Most of the existing works are based on the machine learning method with social network structure analysis and empirical data mining. However, the results learned from some specific dataset may not apply to the future networks, since the social network structure is in a highly dynamic environment. Moreover, the dynamics of information diffusion are also heavily influenced by network users ’ decisions, actions and their socioeconomic interactions, which is generally ignored by existing works. In this paper, we propose an evolutionary game theoretic framework to model the dynamic information diffusion process in social networks, which focuses on the users ’ behavior analysis from a microeconomics points of view. We also conduct experiments by using realworld Twitter information diffusion dataset, which shows that the proposed evolutionary game theoretic model is effective and practical in modeling the social network users ’ information diffusion dynamics. Index Terms — Social networks, information diffusion, information spreading, game theory, evolutionary game.
rspb.royalsocietypublishing.org Research
, 2013
"... thirdparty punishment, evolutionary Author for correspondence: Patrick Roos High strengthofties and low on February 26, ..."
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thirdparty punishment, evolutionary Author for correspondence: Patrick Roos High strengthofties and low on February 26,
Formal properties of the probability of fixation: identities, inequalities and approximations
"... The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent ..."
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The formula for the probability of fixation of a new mutation is widely used in theoretical population genetics and molecular evolution. Here we derive a series of identities, inequalities and approximations for the exact probability of fixation of a new mutation under the Moran process (equivalent results hold for the approximate probability of fixation under the WrightFisher process, after an appropriate change of variables). We show that the logarithm of the fixation probability has a particularly simple behavior when the selection coefficient is measured as a difference of Malthusian fitnesses, and we exploit this simplicity to derive inequalities and approximations. We also present a comprehensive comparison of both existing and new approximations for the fixation probability, highlighting those approximations that induce a reversible Markov chain when used to describe the dynamics of evolution under weak mutation. ∗To whom correspondence should be addressed.