Recent research has highlighted limitations of studying complex systems with time-varying topologies from the perspective of static, time-aggregated networks. Non-Markovian characteristics resulting from the ordering of interactions in temporal networks were identified as one important mechanism that alters causality and affects dynamical processes. So far, an analytical explanation for this phenomenon and for the significant variations observed across different systems is missing. Here we introduce a methodology that allows to analytically predict causality-driven changes of diffusion speed in non-Markovian temporal networks. Validating our predictions in six data sets we show that compared with the time-aggregated network, non-Markovian characteristics can lead to both a slow-down or speed-up of diffusion, which can even outweigh the decelerating effect of community structures in the static topology. Thus, non-Markovian properties of temporal networks constitute an important additional dimension of complexity in time-varying complex systems.

We study correlations in temporal networks and introduce the notion of betweenness preference. It allows to quantify to what extent paths, existing in time-aggregated representations of temporal networks, are actually realizable based on the sequence of interactions. We show that betweenness preference is present in empirical temporal network data and that it influences the length of shortest time-respecting paths. Using four different data sets, we further argue that neglecting betweenness preference leads to wrong conclusions about dynamical processes on temporal networks.Recent works have argued that properties of dynamical processes evolving on complex networks change profoundly when the dynamics of the network topology is taken into account. For a number of empirical temporal networks obtained from time-stamped contact data, simulations have shown that their topological dynamics can both slow down [5,1,6] or speed up spreading processes [17]. At the same time, it has been observed that, compared to time-aggregated topologies, the exploration dynamics of random walks in temporal networks is significantly slower [18]. Furthermore, it has been shown that network dynamics alone can give rise to collective phenomena like synchronization [19]. These observations have generated significant interest in the mechanism underlying these phenomena. A series of recent works focused on the influence of inter-event time distributions and temporal correlations in the time series of interactions [4,6,18,15,9]. Bursty activity patterns of nodes have been identified as one possible source that slows down spreading [6] and random walk processes [16]. Similarly, bursty node activities have been suggested to slow down information diffusion, particularly when the diffusion process is initiated in phases of low activity [13]. Furthermore, for a number of social contact networks, it has been shown that heterogeneous inter-event times increase the length of time-respecting paths [12]. Apart from inter-event time distributions, it has been argued that link appearance frequencies and their correlation with community structures are another characteristic of temporal networks that can slow down spreading dynamics [6]. Another line of research is concerned with the study of temporal motifs [8,20], i.e. whether there are classes of frequently occurring temporal contact patterns. It was shown that the presence of certain temporal motifs (like e.g. "chains" of consec-

We address the question to what extent the success of scientific articles is due to social influence. Analyzing a data set of over 100,000 publications from the field of Computer Science, we study how centrality in the coauthorship network differs between authors who have highly cited papers and those who do not. We further show that a Machine Learning classifier, based only on coauthorship network centrality metrics measured at the time of publication, is able to predict with high precision whether an article will be highly cited five years after publication. By this we provide quantitative insight into the social dimension of scientific publishingchallenging the perception of citations as an objective, socially unbiased measure of scientific success.

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdős-Rényi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems. Message-passing algorithms have over the last two decades turned out to be an important paradigm in fields as distant as iterative decoding, image processing and AI, see [1] for the intuition behind Belief Propagation (BP) in AI, and [2, 3, 4] for more recent reviews. It has been realized that systems where the message-passing algorithms are effective can often be assimilated to disordered systems in statistical physics, and that the message-passing algorithms themselves are closely related to the Bethe approximation [5]. Most applications pursued concern inference in static models; how to do this effectively (if approximately), and when these methods work. In another direction, Consensus Propagation (CP) has been proposed as a message-passing scheme to average measurement values in a network of connected nodes [6]. This is a naturally dynamic setting, where, in large networks, and in many scenarios of interest, one must allow the measurement values, and perchance the network itself, to change on the same time scale as the averaging process. The two strands of inquiry are connected by the fact that CP is equivalent to BP on a class of Gauss-Markov random fields [6,9].In this contribution we study CP both in a static network with changing measurement values (dynamic data), and in a network where the strengths of the interconnections also change (dynamic network). We will show that the method has very good scalability, i.e. that its performance degrades very slowly as the systems grow. In a sense, to be made precise below, performance does not degrade with size at all. This should make CP a very interesting method for aggregation tasks in large and dynamic networks, possibly competitive to alternative schemes such as gossiping [7]. From a physics perspective the salient points are the following: (i) CP with dynamic data is (after a transient) a linear averaging process; (ii) the kernel of this averaging process, being the linearization of Gaussian BP, is related to the second variation of the Bethe free energy...