Inferring interdependencies in climate networks constructed at inter-annual, intra-season and longer time scales

We study global climate networks constructed by means of ordinal time series analysis. Climate interdependencies among the nodes are quantified by the mutual information, computed from time series of monthly-averaged surface air temperature anomalies, and from their symbolic ordinal representation (OP). This analysis allows identifying topological changes in the network when varying the time-interval of the ordinal pattern. We consider intra-season time-intervals (e.g., the patterns are formed by anomalies in consecutive months) and inter-annual time-intervals (e.g., the patterns are formed by anomalies in consecutive years). We discuss how the network density and topology change with these time scales, and provide evidence of correlations between geographically distant regions that occur at specific time scales. In particular, we find that an increase in the ordinal pattern spacing (i.e., an increase in the timescale of the ordinal analysis), results in climate networks with increased connectivity on the equatorial Pacific area. On the contrary, the number of significant links decreases when the ordinal analysis is done with a shorter timescale (by comparing consecutive months), and interpret this effect as due to more stochasticity in the time-series in the short timescale. As the equatorial Pacific is known to be dominated by El Niño-Southern Oscillation (ENSO) on scales longer than several months, our methodology allows constructing climate networks where the effect of ENSO goes from mild (monthly OP) to intense (yearly OP), independently of the length of the ordinal pattern and of the thresholding method employed.     

Connectivity and percolation in simulated grain-boundary networks

Random percolation theory is a common basis for modelling intergranular phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.     

Measuring information networks

Traffic and communication between different parts of a complex system are fundamental elements in maintaining its overall cooperativity. Because a complex system consists of many different parts, it matters where signals are transmitted. Thus signaling and traffic are in principle specific, with each message going from a unique sender to a specific recipient. In the current paper we review some measures of network topology that are related to its ability to direct specific communication.     

Advances in dynamic temporal networks: Understanding the temporal dynamics of complex adaptive networks

Complex networks have been extensively studied in the past 15 years and with increasing details. However, research on the temporal dynamics of complex networks is largely a new territory yet to map out. The present volume presents a collection of papers dealing with various aspects of the problem and this editorial introduces the field as well as the papers.     

Burstiness and spreading on temporal networks

We discuss how spreading processes on temporal networks are impacted by the shape of their inter-event time distributions. Through simple mathematical arguments and toy examples, we find that the key factor is the ordering in which events take place, a property that tends to be affected by the bulk of the distributions and not only by their tail, as usually considered in the literature. We show that a detailed modeling of the temporal patterns observed in complex networks can change dramatically the properties of a spreading process, such as the ergodicity of a random walk process or the persistence of an epidemic.     

Invasion exponents in biological networks

This article is concerned with the characterization of invasion exponents in biological networks defined by a population of replicating elements: molecules, cells, higher organisms. We show that the outcome of competition between an invader and a resident population is a stochastic process, determined by the rate at which a population returns to its steady state after a random perturbation in the parameters that characterize the replicating elements. This return rate is defined by the macroscopic parameter evolutionary entropy, a measure of the diversity of the interaction between the individuals in the population. We also show that the evolutionary stability of a population, that is the invulnerability of a resident to the introduction of an invader competing for the available resources, are given by extremal states of entropy. These results which pertain to networks of interacting molecules, cells and higher organisms, are generalizations of results established for demographic networks, that is populations of replicating organisms parametrized by the ages at which they reproduce and die.     

Coverage centralities for temporal networks

Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the importance of a temporal vertex, which is a pair of vertex index and time. In this paper, we define two centrality measures of a temporal vertex based on the fastest temporal paths which use the temporal vertex. The definition is free from parameters and robust against the change in time scale on which we focus. In addition, we can efficiently compute these centrality values for all temporal vertices. Using the two centrality measures, we reveal that distributions of these centrality values of real-world temporal networks are heterogeneous. For various datasets, we also demonstrate that a majority of the highly central temporal vertices are located within a narrow time window around a particular time. In other words, there is a bottleneck time at which most information sent in the temporal network passes through a small number of temporal vertices, which suggests an important role of these temporal vertices in spreading phenomena.     

PageRank centrality for temporal networks

In this paper, we propose a new centrality measure for ranking the nodes and time layers of temporal networks simultaneously, referred to as the f-PageRank centrality. The f-PageRank values of nodes and time layers in temporal networks are obtained by solving the eigenvector of a multi-homogeneous map. The existence and uniqueness of the proposed centrality measure are also guaranteed by existing results, under some reasonable conditions. The numerical experiments on a synthetic temporal network and two real-world temporal networks (i.e., Email-Eu-core and CollegeMsg temporal networks) show that the proposed centrality outperforms some existing centrality measures.     

Sequences in neural networks with temporal association

We solve the dynamics of the strongly diluted version of a model recently proposed by Herz et al. to store sequences of patterns with spatio-temporal retrieval properties. We analyze the spurious sequence solutions and we find the region in the (,T) plane where the only relevant attractors are the learnt cycles.     

Measuring distances between complex networks

A previously introduced concept of higher order neighborhoods in complex networks, [R.F.S. Andrade, J.G.V. Miranda, T.P. Lobão, Phys. Rev. E 73 (2006) 046101] is used to define a distance between networks with the same number of nodes. With such measure, expressed in terms of the matrix elements of the neighborhood matrices of each network, it is possible to compare, in a quantitative way, how far apart in the space of neighborhood matrices two networks are. The distance between these matrices depends on both the network topologies and the adopted node numberings. While the numbering of one network is fixed, a Monte Carlo algorithm is used to find the best numbering of the other network, in the sense that it minimizes the distance between the matrices. The minimal value found for the distance reflects differences in the neighborhood structures of the two networks that arise only from distinct topologies. This procedure ends up by providing a projection of the first network on the pattern of the second one. Examples are worked out allowing for a quantitative comparison for distances among distinct networks, as well as among distinct realizations of random networks.     

Fast response and temporal coherent oscillations in small-world networks

We have investigated the role that different connectivity regimes play in the dynamics of a network of Hodgkin-Huxley neurons by computer simulations. The different connectivity topologies exhibit the following features: random topologies give rise to fast system response yet are unable to produce coherent oscillations in the average activity of the network; on the other hand, regular topologies give rise to coherent oscillations, but in a temporal scale that is not in accordance with fast signal processing. Finally, small-world topologies, which fall between random and regular ones, take advantage of the best features of both, giving rise to fast system response with coherent oscillations.     

Investigation on a temporal asymmetric oscillating temperature ratchet

We study the directed motion of Brownian particles in a periodic potential due to a periodically oscillating temperature of the thermal environment. The steady average velocity of Brownian particles is evaluated by using the Langevin simulation. The features of current are discussed in detail. The results obtained here show that the periodically oscillating temperature produces a directed transport of the particles in a ratchet system and that through changing some parameters of this system, the magnitude and direction of transport can be controlled. Moreover, it is found that the temporal symmetric temperature oscillation may not be the best choice and the mode of temperature oscillation can be optimized.     

Higher-order aggregate networks in the analysis of temporal networks: path structures and centralities

Despite recent advances in the study of temporal networks, the analysis of time-stampednetwork data is still a fundamental challenge. In particular, recent studies have shownthat correlations in the ordering of links crucially alter causaltopologies of temporal networks, thus invalidating analyses based on static,time-aggregated representations of time-stamped data. These findings not only highlight animportant dimension of complexity in temporal networks, but also call for newnetwork-analytic methods suitable to analyze complex systems with time-varying topologies.Addressing this open challenge, here we introduce a novel framework for the study ofpath-based centralities in temporal networks. Studying betweenness,closeness and reach centrality, we first show than an application of these measures totime-aggregated, static representations of temporal networks yields misleading resultsabout the actual importance of nodes. To overcome this problem, we define path-basedcentralities in higher-order aggregate networks, a recently proposedgeneralization of the commonly used static representation of time-stamped data. Using dataon six empirical temporal networks, we show that the resulting higher-order measuresbetter capture the true, temporal centralities of nodes. Our resultsdemonstrate that higher-order aggregate networks constitute a powerful abstraction, withbroad perspectives for the design of new, computationally efficient data mining techniquesfor time-stamped relational data.     

Self-organization of directed networks through asymmetric coupling

In this Letter, self-organization of directed networks is surveyed. Inspired from the results in neural networks research, we propose an asymmetric coupling scheme with simple edge deleting rules. Results show that all-to-all networks can be organized into scale-free networks with feed-forward structures. Corresponding analysis is also given.     

Totally asymmetric simple exclusion process on networks

We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices crucially modifies the transport features of a network: irregular networks involve homogeneous segments and have a bimodal distribution of edge densities, whereas regular networks are dominated by shocks leading to a unimodal density distribution. The proposed numerical approach of solving for mean-field transport on networks provides a general framework for studying TASEP on large networks, and is expected to generalize to other transport processes.     

Threshold model of cascades in empirical temporal networks

Threshold models try to explain the consequences of social influence like the spread of fads and opinions. Along with models of epidemics, they constitute a major theoretical framework of social spreading processes. In threshold models on static networks, an individual changes her state if a certain fraction of her neighbors has done the same. When there are strong correlations in the temporal aspects of contact patterns, it is useful to represent the system as a temporal network. In such a system, not only contacts but also the time of the contacts are represented explicitly. In many cases, bursty temporal patterns slow down disease spreading. However, as we will see, this is not a universal truth for threshold models. In this work we propose an extension of Watts’s classic threshold model to temporal networks. We do this by assuming that an agent is influenced by contacts which lie a certain time into the past. I.e., the individuals are affected by contacts within a time window. In addition to thresholds in the fraction of contacts, we also investigate the number of contacts within the time window as a basis for influence. To elucidate the model’s behavior, we run the model on real and randomized empirical contact datasets.     

Learning and forgetting on asymmetric,diluted neural networks

It is possible to construct diluted asymmetric models of neural networks for which the dynamics can be calculated exactly. We test several learning schemes, in particular, models for which the values of the synapses remain bounded and depend on the history. Our analytical results on the relative efficiencies of the various learning schemes are qualitatively similar to the corresponding ones obtained numerically on fully connected symmetric networks.     

Ranking important nodes in complex networks by simulated annealing

In this paper, based on simulated annealing a new method to rank important nodes in complex networks is presented.First, the concept of an importance sequence(IS) to describe the relative importance of nodes in complex networks is defined. Then, a measure used to evaluate the reasonability of an IS is designed. By comparing an IS and the measure of its reasonability to a state of complex networks and the energy of the state, respectively, the method finds the ground state of complex networks by simulated annealing. In other words, the method can construct a most reasonable IS. The results of experiments on real and artificial networks show that this ranking method not only is effective but also can be applied to different kinds of complex networks.