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Register a new userOptimal Stabilization of Boolean Networks through Collective Influence
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The stability of Boolean networks has attracted much attention due to its wide applications in describing the dynamics of biological systems. During the past decades, much effort has been invested in unveiling how network structure and update rules will affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. By minimizing the largest eigenvalue of a modified non-backtracking matrix, we propose a method using the collective influence theory to identify the influential nodes in Boolean networks with high computational efficiency. We test the performance of collective influence on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes than other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying the virulence genes that lead to serious disease.
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The whole frame of interconnections in complex networks hinges on a specific set of structural nodes, much smaller than the total size, which, if activated, would cause the spread of information to the whole network [1]; or, if immunized, would prevent the diffusion of a large scale epidemic [2,3]. Localizing this optimal, i.e. minimal, set of structural nodes, called influencers, is one of the most important problems in network science [4,5]. Despite the vast use of heuristic strategies to identify influential spreaders [6-14], the problem remains unsolved. Here, we map the problem onto optimal percolation in random networks to identify the minimal set of influencers, which arises by minimizing the energy of a many-body system, where the form of the interactions is fixed by the non-backtracking matrix [15] of the network. Big data analyses reveal that the set of optimal influencers is much smaller than the one predicted by previous heuristic centralities. Remarkably, a large number of previously neglected weakly-connected nodes emerges among the optimal influencers. These are topologically tagged as low-degree nodes surrounded by hierarchical coronas of hubs, and are uncovered only through the optimal collective interplay of all the influencers in the network. Eventually, the present theoretical framework may hold a larger degree of universality, being applicable to other hard optimization problems exhibiting a continuous transition from a known phase [16].
Novel aspects of human dynamics and social interactions are investigated by means of mobile phone data. Using extensive phone records resolved in both time and space, we study the mean collective behavior at large scales and focus on the occurrence of anomalous events. We discuss how these spatiotemporal anomalies can be described using standard percolation theory tools. We also investigate patterns of calling activity at the individual level and show that the interevent time of consecutive calls is heavy-tailed. This finding, which has implications for dynamics of spreading phenomena in social networks, agrees with results previously reported on other human activities.
Network reconstruction is fundamental to understanding the dynamical behaviors of the networked systems. Many systems, modeled by multiplex networks with various types of interactions, display an entirely different dynamical behavior compared to the corresponding aggregated network. In many cases, unfortunately, only the aggregated topology and partial observations of the network layers are available, raising an urgent demand for reconstructing multiplex networks. We fill this gap by developing a mathematical and computational tool based on the Expectation-Maximization framework to reconstruct multiplex layer structures. The reconstruction accuracy depends on the various factors, such as partial observation and network characteristics, limiting our ability to predict and allocate observations. Surprisingly, by using a mean-field approximation, we discovered that a discrimination indicator that integrates all these factors universally determines the accuracy of reconstruction. This discovery enables us to design the optimal strategies to allocate the fixed budget for deriving the partial observations, promoting the optimal reconstruction of multiplex networks. To further evaluate the performance of our method, we predict beside structure also dynamical behaviors on the multiplex networks, including percolation, random walk, and spreading processes. Finally, applying our method on empirical multiplex networks drawn from biological, transportation, and social domains, corroborate the theoretical analysis.
We study the betweenness centrality of fractal and non-fractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality $C$ of nodes is much weaker in fractal network models compared to non-fractal models. We also show that nodes of both fractal and non-fractal scale-free networks have power law betweenness centrality distribution $P(C)sim C^{-delta}$. We find that for non-fractal scale-free networks $delta = 2$, and for fractal scale-free networks $delta = 2-1/d_{B}$, where $d_{B}$ is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776), yeast (N=1458), WWW (N=2526), and a sample of Internet network at AS level (N=20566), where $N$ is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to non-fractal networks upon adding random edges to a fractal network. We show that the crossover length $ell^{*}$, separating fractal and non-fractal regimes, scales with dimension $d_{B}$ of the network as $p^{-1/d_{B}}$, where $p$ is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with $p$.
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