Temporal networks: slowing down diffusion by long lasting interactions

Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal networks and compare it with that of the corresponding aggregate network. First, we show that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks. In large networks without edge condensation, the expected temporal dynamics is a time-rescaled version of the aggregate dynamics. Even for single sequential realizations, diffusive dynamics is slower in temporal networks. These discrepancies are due to the noncommutability of interactions. We illustrate our analytical findings using a simple temporal motif, larger network models and real temporal networks.Comment: 5 pages, 2 figures, v2: minor revision + supplemental materia

Dynamic Modeling of the Electric Transportation Network

We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time causing local overloads that drive the dynamic evolution of the network topology. Our model displays a transition from a fully connected network to a configuration with a non-trivial topology and where global failures are suppressed. The most efficient topology is characterized by an exponential degree distribution, in agreement with the topology of the real electric grid. The model intrinsically presents self-induced break-down events, which can be thought as representative of real black-outs.Comment: (e.g. 7 pages, 5 figures

Collective intelligence: aggregation of information from neighbors in a guessing game

Complex systems show the capacity to aggregate information and to display coordinated activity. In the case of social systems the interaction of different individuals leads to the emergence of norms, trends in political positions, opinions, cultural traits, and even scientific progress. Examples of collective behavior can be observed in activities like the Wikipedia and Linux, where individuals aggregate their knowledge for the benefit of the community, and citizen science, where the potential of collectives to solve complex problems is exploited. Here, we conducted an online experiment to investigate the performance of a collective when solving a guessing problem in which each actor is endowed with partial information and placed as the nodes of an interaction network. We measure the performance of the collective in terms of the temporal evolution of the accuracy, finding no statistical difference in the performance for two classes of networks, regular lattices and random networks. We also determine that a Bayesian description captures the behavior pattern the individuals follow in aggregating information from neighbors to make decisions. In comparison with other simple decision models, the strategy followed by the players reveals a suboptimal performance of the collective. Our contribution provides the basis for the micro-macro connection between individual based descriptions and collective phenomena.Comment: 9 pages, 9 figure

Competition in the presence of aging: order, disorder, and synchronized collective behavior

We study the stochastic dynamics of coupled states with transition probabilities depending on local persistence, this is, the time since a state has changed. When the population has a preference to adopt older states the system orders quickly due to the dominance of the old state. When preference for new states prevails, the system can show coexistence of states or synchronized collective behavior resulting in long ordering times. In this case, the magnetization $m(t)$ of the system oscillates around $m(t)=0$. Implications for social systems are discussed.Comment: 5 pages, 5 figures, lette

From continuous to discontinuous transitions in social diffusion

Models of social diffusion reflect processes of how new products, ideas or behaviors are adopted in a population. These models typically lead to a continuous or a discontinuous phase transition of the number of adopters as a function of a control parameter. We explore a simple model of social adoption where the agents can be in two states, either adopters or non-adopters, and can switch between these two states interacting with other agents through a network. The probability of an agent to switch from non-adopter to adopter depends on the number of adopters in her network neighborhood, the adoption threshold $T$ and the adoption coefficient $a$, two parameters defining a Hill function. In contrast, the transition from adopter to non-adopter is spontaneous at a certain rate $\mu$. In a mean-field approach, we derive the governing ordinary differential equations and show that the nature of the transition between the global non-adoption and global adoption regimes depends mostly on the balance between the probability to adopt with one and two adopters. The transition changes from continuous, via a transcritical bifurcation, to discontinuous, via a combination of a saddle-node and a transcritical bifurcation, through a supercritical pitchfork bifurcation. We characterize the full parameter space. Finally, we compare our analytical results with Montecarlo simulations on annealed and quenched degree regular networks, showing a better agreement for the annealed case. Our results show how a simple model is able to capture two seemingly very different types of transitions, i.e., continuous and discontinuous and thus unifies underlying dynamics for different systems. Furthermore the form of the adoption probability used here is based on empirical measurements.Comment: 7 pages, 3 figure

Voter model dynamics in complex networks: Role of dimensionality, disorder and degree distribution

We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs in the network modifies the linear system size scaling law of the survival time. The size of an ordered domain is sensitive to the network disorder and the average connectivity, decreasing with both; however it seems not to depend on network size and degree heterogeneity.Comment: (8 pages, 12 figures, for simililar work visit http://www.imedea.uib.es/physdept/

Particle velocity controls phase transitions in contagion dynamics

Interactions often require the proximity between particles. The movement of particles, thus, drives the change of the neighbors which are located in their proximity, leading to a sequence of interactions. In pathogenic contagion, infections occur through proximal interactions, but at the same time the movement facilitates the co-location of different strains. We analyze how the particle velocity impacts on the phase transitions on the contagion process of both a single infection and two cooperative infections. First, we identify an optimal velocity (close to half of the interaction range normalized by the recovery time) associated with the largest epidemic threshold, such that decreasing the velocity below the optimal value leads to larger outbreaks. Second, in the cooperative case, the system displays a continuous transition for low velocities, which becomes discontinuous for velocities of the order of three times the optimal velocity. Finally, we describe these characteristic regimes and explain the mechanisms driving the dynamics.Comment: 9 pages, 5 figures, 12 supplementary figure

Bayesian decision making in human collectives with binary choices

Here we focus on the description of the mechanisms behind the process of information aggregation and decision making, a basic step to understand emergent phenomena in society, such as trends, information spreading or the wisdom of crowds. In many situations, agents choose between discrete options. We analyze experimental data on binary opinion choices in humans. The data consists of two separate experiments in which humans answer questions with a binary response, where one is correct and the other is incorrect. The questions are answered without and with information on the answers of some previous participants. We find that a Bayesian approach captures the probability of choosing one of the answers. The influence of peers is uncorrelated with the difficulty of the question. The data is inconsistent with Weber's law, which states that the probability of choosing an option depends on the proportion of previous answers choosing that option and not on the total number of those answers. Last, the present Bayesian model fits reasonably well to the data as compared to some other previously proposed functions although the latter sometime perform slightly better than the Bayesian model. The asset of the present model is the simplicity and mechanistic explanation of the behavior.Comment: 8 pages, 6 figures, 1 tabl

Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model

Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of both network structure and temporal dimensions. Theoretical approaches are much needed for identifying key factors that affect dynamics of epidemics. In particular, what factors make some temporal networks stronger media of infection than other temporal networks is under debate. We develop a theory to understand the susceptible-infected-susceptible epidemic model on arbitrary temporal networks, where each contact is used for a finite duration. We show that temporality of networks lessens the epidemic threshold such that infections persist more easily in temporal networks than in their static counterparts. We further show that the Lie commutator bracket of the adjacency matrices at different times is a key determinant of the epidemic threshold in temporal networks. The effect of temporality on the epidemic threshold, which depends on a data set, is approximately predicted by the magnitude of a commutator norm.Comment: 8 figures, 1 tabl

Binary and Multivariate Stochastic Models of Consensus Formation

A current paradigm in computer simulation studies of social sciences problems by physicists is the emergence of consensus. The question is to establish when the dynamics of a set of interacting agents that can choose among several options (political vote, opinion, cultural features, etc.) leads to a consensus in one of these options, or when a state with several coexisting social options prevail. We consider here stochastic dynamic models naturally studied by computer simulations. We will first review some basic results for the voter model. This is a binary option stochastic model, and probably the simplest model of collective behavior. Next we consider a model proposed by Axelrod for the dissemination of culture. This model can be considered as a multivariable elaboration of the voter model dynamics.Comment: (16 pages, 8 figures; for simililar work visit http://www.imedea.uib.es/physdept