arXiv subjects

Liming Pan

Publications and source records attributed to Liming Pan.

30 records · Page 2Linked to original sources

arXiv2020

Phase diagrams of interacting spreading dynamics in complex networks

Epidemic spreading processes in the real world can interact with each other in a cooperative, competitive, or asymmetric way, requiring a description based on coevolution dynamics. Rich phenomena such as discontinuous outbreak transitions and hystereses can arise, but a full picture of these behaviors in the parameter space is lacking. We develop a theory for interacting spreading dynamics on complex networks through spectral dimension reduction. In particular, we derive from the microscopic quenched mean-field equations a two-dimensional system in terms of the macroscopic variables, which enables a full phase diagram to be determined analytically. The diagram predicts critical phenomena that were known previously but only numerically, such as the interplay between discontinuous transition and hysteresis as well as the emergence and role of tricritical points.

physics.soc-ph↗

arXiv2020

Effective edge-based approach for promoting the spreading of SIR model

Promoting some typical spreading dynamics, for instance, the spreading of information, commercial message, vaccination guidance, innovation, and political movement, can bring benefits to all aspects of the socio-economic systems. In this study, we propose a strategy for promoting the spreading of the susceptible-infected-recovered model, which is widely applied to describe these common spreading dynamics in real life. Specifically, we first quantify the potential influence that the addition of each latent edge (that is, edges that do not exist before) could cause to the spreading dynamics. Then, we strategically add the latent edges to the original networks according to the potential influence of each latent edge. Numerical simulations verify the effectiveness of our strategy and demonstrate that our strategy outperforms several static strategies, namely, adding the latent edges between nodes with the largest degree or eigenvector centrality. This study provides an effective way of promoting the spreading of the susceptible-infected-recovered model by modifying the network structure slightly and helps in understanding what a better network structure for the spreading dynamics is. Besides, the theoretical framework established in this study provides inspirations for the further investigations of edge-based promoting strategies for other spreading models.

physics.soc-ph↗

arXiv2020

The optimal edge for containing the spreading of SIS model

Numerous real-world systems, for instance, the communication platforms and transportation systems, can be abstracted into complex networks. Containing spreading dynamics (e.g., epidemic transmission and misinformation propagation) in networked systems is a hot topic in multiple fronts. Most of the previous strategies are based on the immunization of nodes. However, sometimes, these node--based strategies can be impractical. For instance, in the train transportation networks, it is dramatic to isolating train stations for flu prevention. On the contrary, temporarily suspending some connections between stations is more acceptable. Thus, we pay attention to the edge-based containing strategy. In this study, we develop a theoretical framework to find the optimal edge for containing the spreading of the susceptible-infected-susceptible model on complex networks. In specific, by performing a perturbation method to the discrete-Markovian-chain equations of the SIS model, we derive a formula that approximately provides the decremental outbreak size after the deactivation of a certain edge in the network. Then, we determine the optimal edge by simply choosing the one with the largest decremental outbreak size. Note that our proposed theoretical framework incorporates the information of both network structure and spreading dynamics. Finally, we test the performance of our method by extensive numerical simulations. Results demonstrate that our strategy always outperforms other strategies based only on structural properties (degree or edge betweenness centrality). The theoretical framework in this study can be extended to other spreading models and offers inspirations for further investigations on edge-based immunization strategies.

physics.soc-ph↗

arXiv2019

Containing rumors spreading on correlated multiplex networks

Rumors flooding on rapidly-growing online social networks has geared much attention from many fronts. Individuals can transmit rumors via numerous channels since they can be active on multiple platforms. However, no systematic theoretical research of rumors containing dynamics on multiplex networks has been conducted yet. In this study, we propose a family of containing strategies based on the degree product $\mathcal{K}$ of each user on the multiplex networks. Then, we develop a heterogeneous edge-based compartmental theory to comprehend the containing dynamics. The simulation results demonstrate that strategies with preference to block users with large $\mathcal{K}$ can significantly reduce the rumor outbreak size and enlarge the threshold. Besides, better performance can be expected on heterogeneous multiplex networks with the increasing of preference intensity and degree heterogeneity. Moreover, take the inter-layer degree correlations $r_s$ into consideration, the strategy performs best on multiplex networks with $r_s=-1$, $r_s=1$ the second, and $r_s=0$ the last. On the contrary, if we prefer to block users with small $\mathcal{K}$ rather than large $\mathcal{K}$, the containing performance will be worse than that of blocking users randomly on most multiplex networks except for uncorrelated multiplex networks with uniform degree distribution. We found that the blocking preferences have no influence on the containing results on uncorrelated multiplex networks with uniform degree distribution. Our theoretical analysis can well predict the rumors containing results and performance differences in all the cases studied. The systematic theoretical research of rumors containing dynamics on multiplex networks in this study will offer inspirations for further investigations on this issue.

physics.soc-ph↗

arXiv2019

Misinformation spreading on correlated multiplex networks

The numerous expanding online social networks offer fast channels for misinformation spreading, which could have a serious impact on socioeconomic systems. Researchers across multiple areas have paid attention to this issue with a view of addressing it. However, no systematical theoretical study has been performed to date on observing misinformation spreading on correlated multiplex networks. In this study, we propose a multiplex network-based misinformation spreading model, considering the fact that each individual can obtain misinformation from multiple platforms. Subsequently, we develop a heterogeneous edge-base compartmental theory to comprehend the spreading dynamics of our proposed model. In addition, we establish an analytical method based on stability analysis to obtain the misinformation outbreak threshold. On the basis of these theories, we finally analyze the influence of different dynamical and structural parameters on the misinformation spreading dynamics. Results show that the misinformation outbreak size $R(\infty)$ grows continuously with the effective transmission probability $β$ once $β$ exceeds a certain value, that is, the outbreak threshold $β_c$. A large average degrees, strong degree heterogeneity, or positive inter-layer correlation will reduce $β_c$, accelerating the outbreak of misinformation. Besides, increasing the degree heterogeneity or a more positive inter-layer correlation will both enlarge (reduce) $R(\infty)$ for small (large) values of $β$. Our systematic theoretical analysis results agree well with the numerical simulation results. Our proposed model and accurate theoretical analysis will serve as a useful framework to understand and predict the spreading dynamics of misinformation on multiplex networks, and thereby pave the way to address this serious issue.

physics.soc-ph↗

arXiv2019

Optimizing spreading dynamics in interconnected networks

Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focus on the case of adding a single edge, the theoretical optimal strategy for adding multiple edges still need to be studied. In this study, based on the susceptible-infected-susceptible (SIS) model, we investigate the problem of maximizing the stationary spreading prevalence in interconnected networks. For two isolated networks, we maximize the spreading prevalence near the critical point by choosing multiple interconnecting edges. We present a theoretical analysis based on the discrete-time Markov chain approach to derive the approximate optimal strategy. The optimal inter-layer structure predicted by the strategy maximizes the spreading prevalence, meanwhile minimizes the spreading outbreak threshold for the interconnected network simultaneously. Numerical simulations on synthetic and real-world networks show that near the critical point, the proposed strategy gives better performance than connecting large degree nodes and randomly connecting.

physics.soc-ph↗

arXiv2019

Optimal interlayer structure for promoting spreading of SIS model in two-layer networks

Real-world systems, ranging from social and biological to infrastructural, can be modeled by multilayer networks. Promoting spreading dynamics in multilayer networks may significantly facilitate electronic advertising and predicting popular scientific publications. In this study, we propose a strategy for promoting the spreading dynamics of the susceptible-infected-susceptible model by adding one interconnecting edge between two isolated networks. By applying a perturbation method to the discrete Markovian chain approach, we derive an index that estimates the spreading prevalence in the interconnected network. The index can be interpreted as a variant of Katz centrality, where the adjacency matrix is replaced by a weighted matrix with weights depending on the dynamical information of the spreading process. Edges that are less infected at one end and its neighborhood but highly infected at the other will have larger weights. We verify the effectiveness of the proposed strategy on small networks by exhaustively examining all latent edges and demonstrate that performance is optimal or near-optimal. For large synthetic and real-world networks, the proposed method always outperforms other static strategies such as connecting nodes with the highest degree or eigenvector centrality.

physics.soc-ph↗

arXiv2018

Free energy of bipartite Sherrington-Kirkpatrick model

In this paper we study the bipartite version of Sherrington-Kirkpatrick model. We prove that the free energy density is given by an analogue of the Parisi formula, that contains both the usual overlap and an additional new type of overlap. Following Panchenko, we prove the upper bound of the formula by Guerra's replica symmetry breaking interpolation, then the matching lower bound by Ghirlanda-Guerra identities and the Aizenman-Sims-Starr scheme. Based on this result we study the stability of the replica symmetric solution. A new phase exhibiting partial replica symmetry breaking is observed, where the broken phase is realized in the larger group only.

cond-mat.dis-nn↗

arXiv2016

Link Prediction via Matrix Completion

Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to understand the mechanisms by which new links are added to the networks. We introduce the method of robust principal component analysis (robust PCA) into link prediction, and estimate the missing entries of the adjacency matrix. On one hand, our algorithm is based on the sparsity and low rank property of the matrix, on the other hand, it also performs very well when the network is dense. This is because a relatively dense real network is also sparse in comparison to the complete graph. According to extensive experiments on real networks from disparate fields, when the target network is connected and sufficiently dense, whatever it is weighted or unweighted, our method is demonstrated to be very effective and with prediction accuracy being considerably improved comparing with many state-of-the-art algorithms.

cs.SI↗

arXiv2016

Effective information spreading based on local information in correlated networks

Using network-based information to facilitate information spreading is an essential task for spreading dynamics in complex networks, which will benefit the promotion of technical innovations, healthy behaviors, new products, etc. Focusing on degree correlated networks, we propose a preferential contact strategy based on the local network structure and local informed density to promote the information spreading. During the spreading process, an informed node will preferentially select a contact target among its neighbors, basing on their degrees or local informed densities. By extensively implementing numerical simulations in synthetic and empirical networks, we find that when only consider the local structure information, the convergence time of information spreading will be remarkably reduced if low-degree neighbors are favored as contact targets. Meanwhile, the minimum convergence time depends non-monotonically on degree-degree correlation, and moderate correlation coefficients result in most efficient information spreading. Incorporating the informed density information into contact strategy, the convergence time of information spreading can be further reduced. Finally, we show that by using local informed density is more effective as compared with the global case.

physics.soc-ph↗

arXiv2016

Lower bound of assortativity coefficient in scale-free networks

The degree-degree correlation is important in understanding the structural organization of a network and the dynamics upon a network. Such correlation is usually measured by the assortativity coefficient $r$, with natural bounds $r \in [-1,1]$. For scale-free networks with power-law degree distribution $p(k) \sim k^{-γ}$, we analytically obtain the lower bound of assortativity coefficient in the limit of large network size, which is not -1 but dependent on the power-law exponent $γ$. This work challenges the validation of assortativity coefficient in heterogeneous networks, suggesting that one cannot judge whether a network is positively or negatively correlated just by looking at its assortativity coefficient.

physics.soc-ph↗

arXiv2014

Zero-Determinant Strategies in the Iterated Public Goods Game

Recently, Press and Dyson have proposed a new class of probabilistic and conditional strategies for the two-player iterated Prisoner's Dilemma, so-called zero-determinant strategies. A player adopting zero-determinant strategies is able to pin the expected payoff of the opponents or to enforce a linear relationship between his own payoff and the opponents' payoff, in a unilateral way. This paper considers zero-determinant strategies in the iterated public goods game, a representative multi-player evolutionary game where in each round each player will choose whether or not put his tokens into a public pot, and the tokens in this pot are multiplied by a factor larger than one and then evenly divided among all players. The analytical and numerical results exhibit a similar yet different scenario to the case of two-player games: (i) with small number of players or a small multiplication factor, a player is able to unilaterally pin the expected total payoff of all other players; (ii) a player is able to set the ratio between his payoff and the total payoff of all other players, but this ratio is limited by an upper bound if the multiplication factor exceeds a threshold that depends on the number of players.

cs.GT↗