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Register a new userMissing Link Identifcation Using SIS Epidemic Traces
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The study of SIS epidemics on networks has stressed the role of the network topology on the spreading process. However, accurate models of SIS epidemics rely on the complete knowledge of the network topology, which is often not available. This paper tackles the problem of inferring the network topology from observed infection time traces, especially where the network topology is partially known or known with some uncertainty. We propose a Bayesian method to infer the posterior probability of uncertain links in the network, and we derive closed form equations for these probabilities. We also propose a numerical approach based on a Gibbs sampling when the number of uncertain links is large such that using the closed form equations becomes impractical. Numerical results show the capability of the proposed approach to assign high probability to existing links and low probability to non-existing links of the network when the SIS traces are sufficiently long.
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To provide a comprehensive view for dynamics of and on many real-world temporal networks, we investigate the interplay of temporal connectivity patterns and spreading phenomena, in terms of the susceptible-infected-removed (SIR) model on the modified activity-driven temporal network (ADTN) with memory. In particular, we focus on how the epidemic threshold of the SIR model is affected by the heterogeneity of nodal activities and the memory strength in temporal and static regimes, respectively. While strong ties (memory) between nodes inhibit the spread of epidemic to be localized, the heterogeneity of nodal activities enhances it to be globalized initially. Since the epidemic threshold of the SIR model is very sensitive to the degree distribution of nodes in static networks, we test the SIR model on the modified ADTNs with the possible set of the activity exponents and the memory exponents that generates the same degree distributions in temporal networks. We also discuss the role of spatiotemporal scaling properties of the largest cluster and the maximum degree in the epidemic threshold. It is observed that the presence of highly active nodes enables to trigger the initial spread of epidemic in a short period of time, but it also limits its final spread to the entire network. This implies that there is the trade-off between the spreading time of epidemic and its outbreak size. Finally, we suggest the phase diagram of the SIR model on ADTNs and the optimal condition for the spread of epidemic under the circumstances.
In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $lambda$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate $epsilon_{c}(l)$ above which a finite fraction of the population becomes permanently infected. From the mean-field solution and computer simulations on hypercubic lattices we find evidences that the upper critical dimension is 6 like in the SIR model, which can be mapped in ordinary percolation.
A traffic incident analysis method based on extended spectral envelope (ESE) method is presented to detect the key incident time. Sensitivity analysis of parameters (the length of time window, the length of sliding window and the study period) are discussed on four real traffic incidents in Beijing. The results show that: (1) Moderate length of time window got the best accurate in detection. (2) The shorter the sliding window is, the more accurate the key incident time are detected. (3) If the study period is too short, the end time of an incident cannot be detected. Empirical studies show that the proposed method can effectively discover the key incident time, which can provide a theoretic basis for traffic incident management.
We investigate the accumulated wealth distribution by adopting evolutionary games taking place on scale-free networks. The system self-organizes to a critical Pareto distribution (1897) of wealth $P(m)sim m^{-(v+1)}$ with $1.6 < v <2.0$ (which is in agreement with that of U.S. or Japan). Particularly, the agents personal wealth is proportional to its number of contacts (connectivity), and this leads to the phenomenon that the rich gets richer and the poor gets relatively poorer, which is consistent with the Matthew Effect present in society, economy, science and so on. Though our model is simple, it provides a good representation of cooperation and profit accumulation behavior in economy, and it combines the network theory with econophysics.
Moderate length of time window can get the best accurate result in detecting the key incident time using extended spectral envelope. This paper presents a method to calculate the moderate length of time window. Two factors are mainly considered: (1) The significant vertical lines consist of negative elements of eigenvectors; (2) the least amount of interruption. The elements of eigenvectors are transformed into binary variable to eliminate the interruption of positive elements. Sine transform is introduced to highlight the significant vertical lines of negative elements. A novel Quality Index (QI) is proposed to measure the effect of different lengths of time window. Empirical studies on four real traffic incidents in Beijing verify the validity of this method.
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