Percolation on coupled networks with multiple effective dependency links.

The ubiquitous coupled relationship between network systems has become an essential paradigm to depict complex systems. A remarkable property in the coupled complex systems is that a functional node should have multiple external support associations in addition to maintaining the connectivity of the local network. In this paper, we develop a theoretical framework to study the structural robustness of the coupled network with multiple useful dependency links. It is defined that a functional node has the broadest connectivity within the internal network and requires at least M support link of the other network to function. In this model, we present exact analytical expressions for the process of cascading failures, the fraction of functional nodes in the stable state, and provide a calculation method of the critical threshold. The results indicate that the system undergoes an abrupt phase transition behavior after initial failure. Moreover, the minimum inner and inter-connectivity density to maintain system survival is graphically presented at different multiple effective dependency links. Furthermore, we find that the system needs more internal connection densities to avoid collapse when it requires more effective support links. These findings allow us to reveal the details of a more realistic coupled complex system and develop efficient approaches for designing resilient infrastructure.

A quantification method of non-failure cascading spreading in a network of networks.

The cascading spreading process in social and economic networks is more complicated than that in physical systems. These networks' multiple nodes and edges increase their structural complexity and recoverability, enabling the system to lose partial functionality rather than completely fail. However, these phenomena in social and economic networks introduce challenges to the existing network robustness models, where a node is either in a functional state or a failed state. This research uses a network of networks (NoN) to simulate multiple types of nodes and edges. A non-failure cascading process is utilized to model the nodes' self-adaptation and recoverability. The main contribution of this research is proposing a spreading model to extend the non-failure cascading process to the NoN, which can be used in predicting real-world system damage suffering from special events. The case study of this research evaluated the effect degree of crude oil trade changes on each sector from 2015 to 2016.

Repulsive synchronization in complex networks.

Synchronization in complex networks characterizes what happens when an ensemble of oscillators in a complex autonomous system become phase-locked. We study the Kuramoto model with a tunable phase-lag parameter α in the coupling term to determine how phase shifts influence the synchronization transition. The simulation results show that the phase frustration parameter leads to desynchronization. We find two global synchronization regions for α∈[0,2π) when the coupling is sufficiently large and detect a relatively rare network synchronization pattern in the frustration parameter near α=π. We call this frequency-locking configuration as "repulsive synchronization," because it is induced by repulsive coupling. Since the repulsive synchronization cannot be described by the usual order parameter r, the parameter frequency dispersion is introduced to detect synchronization.

Spatial reciprocity in the evolution of cooperation.

Cooperation is key to the survival of all biological systems. The spatial structure of a system constrains who interacts with whom (interaction partner) and who acquires new traits from whom (role model). Understanding when and to what degree a spatial structure affects the evolution of cooperation is an important and challenging topic. Here, we provide an analytical formula to predict when natural selection favours cooperation where the effects of a spatial structure are described by a single parameter. We find that a spatial structure promotes cooperation (spatial reciprocity) when interaction partners overlap role models. When they do not, spatial structure inhibits cooperation even without cooperation dilemmas. Furthermore, a spatial structure in which individuals interact with their role models more often shows stronger reciprocity. Thus, imitating individuals with frequent interactions facilitates cooperation. Our findings are applicable to both pairwise and group interactions and show that strong social ties might hinder, while asymmetric spatial structures for interaction and trait dispersal could promote cooperation.

Robustness of partially interdependent networks under combined attack.

We thoroughly study the robustness of partially interdependent networks when suffering attack combinations of random, targeted, and localized attacks. We compare analytically and numerically the robustness of partially interdependent networks with a broad range of parameters including coupling strength, attack strength, and network type. We observe the first and second order phase transition and accurately characterize the critical points for each combined attack. Generally, combined attacks show more efficient damage to interdependent networks. Besides, we find that, when robustness is measured by the critical removing ratio and the critical coupling strength, the conclusion drawn for a combined attack is not always consistent.

Interactive social contagions and co-infections on complex networks.

What we are learning about the ubiquitous interactions among multiple social contagion processes on complex networks challenges existing theoretical methods. We propose an interactive social behavior spreading model, in which two behaviors sequentially spread on a complex network, one following the other. Adopting the first behavior has either a synergistic or an inhibiting effect on the spread of the second behavior. We find that the inhibiting effect of the first behavior can cause the continuous phase transition of the second behavior spreading to become discontinuous. This discontinuous phase transition of the second behavior can also become a continuous one when the effect of adopting the first behavior becomes synergistic. This synergy allows the second behavior to be more easily adopted and enlarges the co-existence region of both behaviors. We establish an edge-based compartmental method, and our theoretical predictions match well with the simulation results. Our findings provide helpful insights into better understanding the spread of interactive social behavior in human society.

A generalization of random matrix theory and its application to statistical physics.

To study the statistical structure of crosscorrelations in empirical data, we generalize random matrix theory and propose a new method of cross-correlation analysis, known as autoregressive random matrix theory (ARRMT). ARRMT takes into account the influence of auto-correlations in the study of cross-correlations in multiple time series. We first analytically and numerically determine how auto-correlations affect the eigenvalue distribution of the correlation matrix. Then we introduce ARRMT with a detailed procedure of how to implement the method. Finally, we illustrate the method using two examples taken from inflation rates for air pressure data for 95 US cities.

Unification of theoretical approaches for epidemic spreading on complex networks.

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.

Predicting the Lifetime of Dynamic Networks Experiencing Persistent Random Attacks.

Estimating the critical points at which complex systems abruptly flip from one state to another is one of the remaining challenges in network science. Due to lack of knowledge about the underlying stochastic processes controlling critical transitions, it is widely considered difficult to determine the location of critical points for real-world networks, and it is even more difficult to predict the time at which these potentially catastrophic failures occur. We analyse a class of decaying dynamic networks experiencing persistent failures in which the magnitude of the overall failure is quantified by the probability that a potentially permanent internal failure will occur. When the fraction of active neighbours is reduced to a critical threshold, cascading failures can trigger a total network failure. For this class of network we find that the time to network failure, which is equivalent to network lifetime, is inversely dependent upon the magnitude of the failure and logarithmically dependent on the threshold. We analyse how permanent failures affect network robustness using network lifetime as a measure. These findings provide new methodological insight into system dynamics and, in particular, of the dynamic processes of networks. We illustrate the network model by selected examples from biology, and social science.

Modeling simple amphiphilic solutes in a Jagla solvent.

Methanol is an amphiphilic solute whose aqueous solutions exhibit distinctive physical properties. The volume change upon mixing, for example, is negative across the entire composition range, indicating strong association. We explore the corresponding behavior of a Jagla solvent, which has been previously shown to exhibit many of the anomalous properties of water. We consider two models of an amphiphilic solute: (i) a "dimer" model, which consists of one hydrophobic hard sphere linked to a Jagla particle with a permanent bond, and (ii) a "monomer" model, which is a limiting case of the dimer, formed by concentrically overlapping a hard sphere and a Jagla particle. Using discrete molecular dynamics, we calculate the thermodynamic properties of the resulting solutions. We systematically vary the set of parameters of the dimer and monomer models and find that one can readily reproduce the experimental behavior of the excess volume of the methanol-water system as a function of methanol volume fraction. We compare the pressure and temperature dependence of the excess volume and the excess enthalpy of both models with experimental data on methanol-water solutions and find qualitative agreement in most cases. We also investigate the solute effect on the temperature of maximum density and find that the effect of concentration is orders of magnitude stronger than measured experimentally.

Heuristic segmentation of a nonstationary time series.

Many phenomena, both natural and human influenced, give rise to signals whose statistical properties change under time translation, i.e., are nonstationary. For some practical purposes, a nonstationary time series can be seen as a concatenation of stationary segments. However, the exact segmentation of a nonstationary time series is a hard computational problem which cannot be solved exactly by existing methods. For this reason, heuristic methods have been proposed. Using one such method, it has been reported that for several cases of interest-e.g., heart beat data and Internet traffic fluctuations-the distribution of durations of these stationary segments decays with a power-law tail. A potential technical difficulty that has not been thoroughly investigated is that a nonstationary time series with a (scalefree) power-law distribution of stationary segments is harder to segment than other nonstationary time series because of the wider range of possible segment lengths. Here, we investigate the validity of a heuristic segmentation algorithm recently proposed by Bernaola-Galván et al. [Phys. Rev. Lett. 87, 168105 (2001)] by systematically analyzing surrogate time series with different statistical properties. We find that if a given nonstationary time series has stationary periods whose length is distributed as a power law, the algorithm can split the time series into a set of stationary segments with the correct statistical properties. We also find that the estimated power-law exponent of the distribution of stationary-segment lengths is affected by (i) the minimum segment length and (ii) the ratio R identical with sigma(epsilon)/sigma(x), where sigma(x) is the standard deviation of the mean values of the segments and sigma(epsilon) is the standard deviation of the fluctuations within a segment. Furthermore, we determine that the performance of the algorithm is generally not affected by uncorrelated noise spikes or by weak long-range temporal correlations of the fluctuations within segments.

Perimeter growth of a branched structure: application to crackle sounds in the lung.

We study an invasion percolation process on Cayley trees and find that the dynamics of perimeter growth is strongly dependent on the nature of the invasion process, as well as on the underlying tree structure. We apply this process to model the inflation of the lung in the airway tree, where crackling sounds are generated when airways open. We define the perimeter as the interface between the closed and opened regions of the lung. In this context we find that the distribution of time intervals between consecutive openings is a power law with an exponent beta approximately 2. We generalize the binary structure of the lung to a Cayley tree with a coordination number Z between 2 and 4. For Z=4, beta remains close to 2, while for a chain, Z=2 and beta=1, exactly. We also find a mean field solution of the model.

Intramolecular coupling as a mechanism for a liquid-liquid phase transition.

We study a model for water with a tunable intramolecular interaction J(sigma), using mean-field theory and off-lattice Monte Carlo simulations. For all J(sigma)> or =0, the model displays a temperature of maximum density. For a finite intramolecular interaction J(sigma)>0, our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely preempted by inevitable freezing. For J=0, the liquid-liquid critical point disappears at T=0.

Truncation of power law behavior in "scale-free" network models due to information filtering.

We formulate a general model for the growth of scale-free networks under filtering information conditions-that is, when the nodes can process information about only a subset of the existing nodes in the network. We find that the distribution of the number of incoming links to a node follows a universal scaling form, i.e., that it decays as a power law with an exponential truncation controlled not only by the system size but also by a feature not previously considered, the subset of the network "accessible" to the node. We test our model with empirical data for the World Wide Web and find agreement.

Dependence of conductance on percolation backbone mass

We study , the average conductance of the backbone, defined by two points separated by Euclidean distance r, of mass M(B) on two-dimensional percolation clusters at the percolation threshold. We find that with increasing M(B) and for fixed r, asymptotically decreases to a constant, in contrast with the behavior of homogeneous systems and nonrandom fractals (such as the Sierpinski gasket) in which conductance increases with increasing M(B). We explain this behavior by studying the distribution of shortest paths between the two points on clusters with a given M(B). We also study the dependence of conductance on M(B) above the percolation threshold and find that (i) slightly above p(c), the conductance first decreases and then increases with increasing M(B) and (ii) further above p(c), the conductance increases monotonically for all values of M(B), as is the case for homogeneous systems.

Economic fluctuations and anomalous diffusion

We quantify the relation between trading activity - measured by the number of transactions N(Deltat)-and the price change G(Deltat) for a given stock, over a time interval [t, t+Deltat]. To this end, we analyze a database documenting every transaction for 1000 U.S. stocks for the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of classic diffusion, where the diffusion constant fluctuates drastically in time. We relate the analog for stock price fluctuations of the diffusion constant-known in economics as the volatility-to two microscopic quantities: (i) the number of transactions N(Deltat) in Deltat, which is the analog of the number of collisions and (ii) the variance W(2)(Deltat) of the price changes for all transactions in Deltat, which is the analog of the local mean square displacement between collisions. Our results are consistent with the interpretation that the power-law tails of P(G(Deltat)) are due to P(W(Deltat)), and the long-range correlations in |G(Deltat)| are due to N(Deltat).

Tracer dispersion in a percolation network with spatial correlations

We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolationlike porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the numerical solution of the Navier-Stokes and continuity equations in the pore space. We find that the resulting statistical properties of the tracer show a transition from a subdiffusion regime at low Peclet number to an enhanced diffusion regime at high Peclet number.

Flow between two sites on a percolation cluster

We study the flow of fluid in porous media in dimensions d=2 and 3. The medium is modeled by bond percolation on a lattice of L(d) sites, while the flow front is modeled by tracer particles driven by a pressure difference between two fixed sites ("wells") separated by Euclidean distance r. We investigate the distribution function of the shortest path connecting the two sites, and propose a scaling ansatz that accounts for the dependence of this distribution (i) on the size of the system L and (ii) on the bond occupancy probability p. We confirm by extensive simulations that the ansatz holds for d=2 and 3. Further, we study two dynamical quantities: (i) the minimal traveling time of a tracer particle between the wells when the total flux is constant and (ii) the minimal traveling time when the pressure difference is constant. A scaling ansatz for these dynamical quantities also includes the effect of finite system size L and off-critical bond occupation probability p. We find that the scaling form for the distribution functions for these dynamical quantities for d=2 and 3 is similar to that for the shortest path, but with different critical exponents. Our results include estimates for all parameters that characterize the scaling form for the shortest path and the minimal traveling time in two and three dimensions; these parameters are the fractal dimension, the power law exponent, and the constants and exponents that characterize the exponential cutoff functions.