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Register a new userSmall But Slow World: How Network Topology and Burstiness Slow Down Spreading
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Communication networks show the small-world property of short paths, but the spreading dynamics in them turns out slow. We follow the time evolution of information propagation through communication networks by using the SI model with empirical data on contact sequences. We introduce null models where the sequences are randomly shuffled in different ways, enabling us to distinguish between the contributions of different impeding effects. The slowing down of spreading is found to be caused mostly by weight-topology correlations and the bursty activity patterns of individuals.
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Online social media have greatly affected the way in which we communicate with each other. However, little is known about what are the fundamental mechanisms driving dynamical information flow in online social systems. Here, we introduce a generative model for online sharing behavior that is analytically tractable and which can reproduce several characteristics of empirical micro-blogging data on hashtag usage, such as (time-dependent) heavy-tailed distributions of meme popularity. The presented framework constitutes a null model for social spreading phenomena which, in contrast to purely empirical studies or simulation-based models, clearly distinguishes the roles of two distinct factors affecting meme popularity: the memory time of users and the connectivity structure of the social network.
This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network, wherein the disease in one network can spread to the other. Theoretical analysis is provided for each model to reveal that the global epidemic threshold in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks. In particular, in an interconnected homogenous network, detailed theoretical analysis is presented, which allows quick and accurate calculations of the global epidemic threshold. Moreover, in an interconnected heterogeneous network with inter-layer correlation between node degrees, it is found that the inter-layer correlation coefficient has little impact on the epidemic threshold, but has significant impact on the total prevalence. Simulations further verify the analytical results, showing that cooperative epidemic processes promote the spreading of diseases.
We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node`s attractiveness. The developed model reveals that increasing either the network`s mean degree or the ``choosiness`` exercised during pair-formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair-formation. By iterating over model mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.
In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity $Phi_S(t)$, namely, the probability that a given neighbor of a node is susceptible at time $t$, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time $t_c$ above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time $t_c$. Our theoretical results are confirmed by extensive simulations of the SIR process.
We compute the wall velocity in the MSSM. We therefore generalize the SM equations of motion for bubble walls moving through a hot plasma at the electroweak phase transition and calculate the friction terms which describe the viscosity of the plasma. We give the general expressions and apply them to a simple model where stops, tops and W bosons contribute to the friction. In a wide range of parameters including those which fulfil the requirements of baryogenesis we find a wall velocity of order v = 0.05-0.1 much below the SM value.
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