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Cooperation abounds in all biological systems. Spatial public goods game (PGG) serves as a baseline model when investigating the evolution of cooperation in collective interactions. Since analyzing collective interactions and dynamics in spatial structures is very complicated, a full theoretical understanding of spatial PGGs is still deficient. Here we generalize spatial PGGs in a three-layer weighted network—investment, benefit allocation, and strategy dispersal layers—which are not necessarily identical and thus cover a wide class of population structures and interaction scenarios. We provide an analytic formula that accurately predicts when cooperation is favored over defection, and that is applicable in populations of any size under weak selection. We prove that in regular networks investment and benefit allocation are essentially symmetric—that exchanging structures of investment and benefit allocation layers does not affect the evolutionary dynamics at all. The success of cooperators relies heavily on the correlation between an individual’s investment in a game and its benefit allocated from the same game. In most cases, the positive correlation, i.e., a greater investment in games with a larger share of benefits, facilitates a cooperative society. Importantly, we also show that diversifying the amounts of investment in different games or benefit allocation to different participants, if implementing improperly, might impede the global cooperation. [ABSTRACT FROM AUTHOR]

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks. [ABSTRACT FROM AUTHOR]

The robustness of complex networks against node failure and malicious attack has been of interest for decades, while most of the research has focused on random attack or hub-targeted attack. In many real-world scenarios, however, attacks are neither random nor hub-targeted, but localized, where a group of neighboring nodes in a network are attacked and fail. In this paper we develop a percolation framework to analytically and numerically study the robustness of complex networks against such localized attack. In particular, we investigate this robustness in Erdős–Rényi networks, random-regular networks, and scale-free networks. Our results provide insight into how to better protect networks, enhance cybersecurity, and facilitate the design of more robust infrastructures. [ABSTRACT FROM AUTHOR]

Proton nuclear magnetic resonance ( 1H NMR) experiments have been performed to measure the spin−lattice, T1, and spin−spin, T2, relaxation times of the three functional groups in water/methanol mixtures at different methanol molar fractions ( XMeOH= 0, 0.04, 0.1, 0.24, 0.5, 1) as a function of temperature in the range 205 K < T< 295 K. The measured relaxation times in the mixtures, at all the methanol molar fractions, are faster than those of pure water and methanol because of strong interactions, resulting in a complex hydrogen bonding dynamics that determines their thermodynamic properties. In particular, we observe how the interplay between hydrophobicity and hydrophilicity changes with temperature and influences the peculiar thermal behavior of the NMR relaxation times of the solution. The obtained results are interpreted in terms of the existence of stable water−methanol clusters at high temperature whereas, upon cooling to low temperature, clusters of single species are present in the mixture. [ABSTRACT FROM AUTHOR]

In the gathered multiplex systems, nodes inherit a part of their original system’s topological features, as in the world economic system, national policies and resource distribution bring industry advantages and resource advantages to the domestic industry. Although they represent one of the important original topological features of nodes, the inherited topological features of nodes have not received sufficient attention and have hardly been analyzed by existing network models. In our research, we defined the inherited topological features of nodes as ‘cluster-based topological features. To accurately calculate the cluster-based topological features of nodes in multiplex networks, we first provide a network model to summarize the multiplex networks into a calculable network of networks (NoN). Based on our network model, we propose a series of algorithms for calculating industries’ cluster-based topological features. Our calculating process contains 2 steps: ‘abstracting’ the NoN into one-layer calculable network; ‘inheriting’ subnetworks’ topological features into the inner nodes. Our network model and calculation algorithms are applied in a series of theoretical and empirical multiplex networks. The results not only confirm the realizability of our model but also produce several interesting findings, the most important of which is that some unremarkable nodes in multiplex network may have a very high contributory value from NoN perspective. [ABSTRACT FROM AUTHOR]

This paper proposes a Hankel matrix-based statistical study to calculate the final synchronization state of the entire network via local observation of just a single node for a time period significantly shorter than the synchronization process. It surfaces that synchronization can be achieved more quickly than the routine rhythm for networks no matter with linear or nonlinear dynamics. This finding refines our understanding of the abundant ultrafast synchronization phenomena observed in nature, which enables the efficient design of self-aligned robots as well. [ABSTRACT FROM AUTHOR]

Network systems with clustering have been given much attention due to their wide occurrence in the real world. One focus of these studies has been on robustness of single clustered networks and interdependent clustered networks under random attack (RA) or hub-targeted attack. However, infrastructure networks could suffer from a damage that is localized, i.e. a group of neighboring nodes attacked or fail, a topic that was not studied earlier on clustered networks. In this paper, we analytically and via simulations study the robustness under localized attack (LA) of single Erdős–Rényi clustered network and interdependent clustered network. For generating networks with clustering we use two models: (i) double Poisson distribution (DPD) and (ii) fixed degree distribution (FDD). For the LA case, the DPD model shows a second order phase transition behavior for a single clustered network, while for dependent networks, the system undergoes a change of percolation phase transition from a first order (abrupt transition) to a second order (continuous) transition when the coupling strength q decreases below a critical value qc. Our results imply that single networks become significantly more vulnerable with increasing clustering coefficient c with respect to LA. This is in contrast to RA where the robustness is almost independent of c. We obtain similar results when testing different real networks. For LA on dependent networks, we also observe that the system becomes more vulnerable as c increases. This is again in contrast to RA, where for, q < qc, the system robustness is almost unaffected by increasing clustering. We also solved analytically the case of LA on random regular networks which are clustered and interdependent and find that as m (the number of clustered networks that each network depends on) or c increases, the system becomes significantly more vulnerable. We also analyzed via simulations the case of generating clustering in networks for the model of keeping a FDD, and find that the influence of clustering on the robustness of two partially interdependent networks under LA is smaller than for DPD, which is very different from these cases under RA. [ABSTRACT FROM AUTHOR]