Non-Markovian temporal networks with auto- and cross-correlated link dynamics

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often observed to be non-Markovian, and the dynamics of their links are often correlated. Hence, to accurately model these networks, predict their evolution, and understand how information and other relevant quantities propagate over them, the inclusion of both memory and dynamical dependencies between links is key. In this article we introduce a general class of models of temporal networks based on discrete autoregressive processes for link dynamics. As a concrete and useful case study, we then concentrate on a specific model within this class, which allows to generate temporal networks with a specified underlying structural backbone, and with precise control over the dynamical dependencies between links and the strength and length of their memories. In this network model the presence of each link is influenced not only by its past activity, but also by the past activities of other links, as specified by a coupling matrix, which directly controls the causal relations, and hence the correlations, among links. We propose a maximum likelihood method for estimating the model's parameters from data, showing how the model allows a more realistic description of real-world temporal networks and also to predict their evolution. Due to the flexibility of maximum likelihood inference, we illustrate how to deal with heterogeneity and time-varying patterns, possibly including also nonstationary network dynamics. We then use our network model to investigate the role that, both the features of memory and the type of correlations in the dynamics of links have on the properties of processes occurring over a temporal network. Namely, we study the speed of a spreading process, as measured by the time it takes for diffusion to reach equilibrium. Through both numerical simulations and analytical results, we are able to separate the roles of autocorrelations and neighborhood correlations in link dynamics, showing that not only is the speed of diffusion nonmonotonically dependent on the memory length, but also that correlations among neighboring links help to speed up the spreading process, while autocorrelations slow it back down. Our results have implications in the study of opinion formation, the modeling of social networks, and the spreading of epidemics through mobile populations

Controllability of Social Networks and the Strategic Use of Random Information

This work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception. Our research is based on a model of knowledge diffusion applied to a time-varying adaptive network, and considers two well-known strategies for influencing social contexts. One is the selection of few influencers for manipulating their actions in order to drive the whole network to a certain behavior; the other, instead, drives the network behavior acting on the state of a large subset of ordinary, scarcely influencing users. The two approaches have been studied in terms of network and diffusion effects. The network effect is analyzed through the changes induced on network average degree and clustering coefficient, while the diffusion effect is based on two ad-hoc metrics defined to measure the degree of knowledge diffusion and skill level, as well as the polarization of agent interests. The results, obtained through simulations on synthetic networks, show a rich dynamics and strong effects on the communication structure and on the distribution of knowledge and skills, supporting our hypothesis that the strategic use of random information could represent a realistic approach to social network controllability, and that with both strategies, in principle, the control effect could be remarkable

Early Warning Analysis for Social Diffusion Events

There is considerable interest in developing predictive capabilities for social diffusion processes, for instance to permit early identification of emerging contentious situations, rapid detection of disease outbreaks, or accurate forecasting of the ultimate reach of potentially viral ideas or behaviors. This paper proposes a new approach to this predictive analytics problem, in which analysis of meso-scale network dynamics is leveraged to generate useful predictions for complex social phenomena. We begin by deriving a stochastic hybrid dynamical systems (S-HDS) model for diffusion processes taking place over social networks with realistic topologies; this modeling approach is inspired by recent work in biology demonstrating that S-HDS offer a useful mathematical formalism with which to represent complex, multi-scale biological network dynamics. We then perform formal stochastic reachability analysis with this S-HDS model and conclude that the outcomes of social diffusion processes may depend crucially upon the way the early dynamics of the process interacts with the underlying network's community structure and core-periphery structure. This theoretical finding provides the foundations for developing a machine learning algorithm that enables accurate early warning analysis for social diffusion events. The utility of the warning algorithm, and the power of network-based predictive metrics, are demonstrated through an empirical investigation of the propagation of political memes over social media networks. Additionally, we illustrate the potential of the approach for security informatics applications through case studies involving early warning analysis of large-scale protests events and politically-motivated cyber attacks

How Realistic Should Knowledge Diffusion Models Be?

Knowledge diffusion models typically involve two main features: an underlying social network topology on one side, and a particular design of interaction rules driving knowledge transmission on the other side. Acknowledging the need for realistic topologies and adoption behaviors backed by empirical measurements, it becomes unclear how accurately existing models render real-world phenomena: if indeed both topology and transmission mechanisms have a key impact on these phenomena, to which extent does the use of more or less stylized assumptions affect modeling results? In order to evaluate various classical topologies and mechanisms, we push the comparison to more empirical benchmarks: real-world network structures and empirically measured mechanisms. Special attention is paid to appraising the discrepancy between diffusion phenomena (i) on some real network topologies vs. various kinds of scale-free networks, and (ii) using an empirically-measured transmission mechanism, compared with canonical appropriate models such as threshold models. We find very sensible differences between the more realistic settings and their traditional stylized counterparts. On the whole, our point is thus also epistemological by insisting that models should be tested against simulation-based empirical benchmarks.Agent-Based Simulation, Complex Systems, Empirical Calibration and Validation, Knowledge Diffusion, Model Comparison, Social Networks

Dynamic Core Community Detection and Information Diffusion Processes on Networks

Interest in network science has been increasingly shared among various research communities due to its broad range of applications. Many real world systems can be abstracted as networks, a group of nodes connected by pairwise edges, and examples include friendship networks, metabolic networks, and world wide web among others. Two of the main research areas in network science that have received a lot of focus are community detection and information diffusion. As for community detection, many well developed algorithms are available for such purposes in static networks, for example, spectral partitioning and modularity function based optimization algorithms. As real world data becomes richer, community detection in temporal networks becomes more and more desirable and algorithms such as tensor decomposition and generalized modularity function optimization are developed. One scenario not well investigated is when the core community structure persists over long periods of time with possible noisy perturbations and changes only over periods of small time intervals. The contribution of this thesis in this area is to propose a new algorithm based on low rank component recovery of adjacency matrices so as to identify the phase transition time points and improve the accuracy of core community structure recovery. As for information diffusion, traditionally it was studied using either threshold models or independent interaction models as an epidemic process. But information diffusion mechanism is different from epidemic process such as disease transmission because of the reluctance to tell stale news and to address this issue other models such as DK model was proposed taking into consideration of the reluctance of spreaders to diffuse the information as time goes by. However, this does not capture some cases such as the losing interest of information receivers as in viral marketing. The contribution of this thesis in this area is we proposed two new models coined susceptible-informed-immunized (SIM) model and exponentially time decaying susceptible-informed (SIT) model to successfully capture the intrinsic time value of information from both the spreader and receiver points of view. Rigorous analysis of the dynamics of the two models were performed based mainly on mean field theory. The third contribution of this thesis is on the information diffusion optimization. Controlling information diffusion has been widely studied because of its important applications in areas such as social census, disease control and marketing. Traditionally the problem is formulated as identifying the set of k seed nodes, informed initially, so as to maximize the diffusion size. Heuristic algorithms have been developed to find approximate solutions for this NP-hard problem, and measures such as k-shell, node degree and centrality have been used to facilitate the searching for optimal solutions. The contribution of this thesis in this field is to design a more realistic objective function and apply binary particle swarm optimization algorithm for this combinatorial optimization problem. Instead of fixating the seed nodes size and maximize the diffusion size, we maximize the profit defined as the revenue, which is simply the diffusion size, minus the cost of setting those seed nodes, which is designed as a function of degrees of the seed nodes or a measure that is similar to the centrality of nodes. Because of the powerful algorithm, we were able to study complex scenarios such as information diffusion optimization on multilayer networks.PHDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145937/1/wbao_1.pd