Dynamics on and of Complex Networks IX / Mining and learning for complex networks  (DOAO) Session 1

Abstract: Community-detection methods that describe large-scale patterns in the dynamics on and of networks suffer from effects of arbitrary time scales that need to be imposed a priori. We develop a variable-order hidden Markov chain model that generalizes the stochastic block model for discrete time-series as well as temporal networks. With our model, the relevant time scales are inferred from data, instead of being determined beforehand. The temporal model does not require the aggregation of events into discrete intervals, and instead takes full advantage of the time-ordering of the tokens or edges. When the edge ordering is random, we recover the traditional static block model as a special case. We formulate an efficient nonparametric Bayesian framework that can select the most appropriate Markov order and number of communities, based solely on statistical evidence and without overfitting. Close

Abstract: Complex network theory provides an elegant and powerful framework to statisticallyinvestigate different types of systems such as society, brain or the structure of local andlong-range dynamical interrelationships in the climate system. Network links in correlation,so-called climate networks typically imply information, mass or energy exchange.However, the specific connection between oceanic or atmospheric flows and the climatenetwork?s structure is still unclear. We propose a theoretical approach of flow-networks forverifying relations between the correlation matrix and the flow structure, generalizingprevious studies and overcoming the restriction to stationary flows [1]. We studied acomplex interrelation between the velocity field and the correlation network measures.Our methods are developed for correlations of a scalar quantity (temperature, for example)which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation.Our approach reveals the insensitivity of correlation networks to steady sources and sinksand the profound impact of the signal decay rate on the network topology. We illustrate ourresults with calculations of degree and clustering for a meandering flow resembling ageophysical ocean jet.Moreover, we discuss the follow-up approaches and application of the flow-networksmethod [2].[1] "Correlation networks from flows. The case of forced and time-dependent advectiondiffusiondynamics" L.Tupikina, N.Molkenthin, C.Lopez, E.Hernandes-Garcia, N.Marwan,J.Kurths, Plos One. 2016[2] "A geometric perspective on spatially embedded networks. Quantification of edgeanisotropy and application to flow networks", H.Kutza, N.Molkenthin, L.Tupikina, J.Donges,N.Marwan, U.Feudel, J.Kurths, R.Donner under rev.in Chaos Close

Abstract: When modelling dynamical systems on networks, it is often assumed that the process is Markovian, that is future states depend only upon the present state and not on the sequence of events that preceded it. Examples include diffusion of ideas or diseases on social networks, or synchronisation of interacting dynamical units. In each case, the dynamics is governed by coupled differential equation, where the coupling is defined by the adjacency matrix of the underlying network. The main purpose of this talk is to challenge this Markovian picture. We will argue that non-Markovian models can provide a more realistic picture in the case of temporal networks where edges change in time, or in situations when pathways can be measured empirically. We will focus on the importance of non-Poisson temporal statistics, and show analytically the impact of burstiness on diffusive dynamics, before turning to applications and incorporating memory kernels in predictive models of retweet dynamics. Close

Abstract: In this talk I will talk about approaches for understanding transition behavior on networks. In particular I will first introduce HypTrails - a Bayesian framework for comparing different hypothesesabout human transition behavior in networks. Then I will introduce SubTrails - an approach for identifying subgroups of users with exceptional transition behaviors. I will conclude with open challengesand problems in the field. Close

Abstract: In almost any network analytic project, we make multiple, innocent, and seemingly inconsequential modeling decisions - however, some of them might have a profound impact on the results. In this talk, I will discuss how to evaluate the most simple centrality index, the degree, of a node in multiplex networks. Of course, any ranking of all nodes in a multiplex network requires first, some normalization of the degrees to put them on the same scale, and second, some aggregation over the different layers. You might opt for the sum, the average, the mean, the minimum or the maximum as an aggregation strategy. In this talk I will show that the combination of these two strategies, i.e., normalization and aggregation, may result in nodes being identified as either top central or least central. It thus emphasizes the need to properly describe, check, and evaluate even the most simple modeling decisions. Close

Abstract: In every choice we make, repetitive interactions within our social networks and our susceptibility to influence impact our decisions. This research investigates such mechanisms with the framework of threshold models of social contagion. We find that a strong positive correlation between the degree (representing the strength of influence) and the threshold (displaying acceptance level) slows the dynamics and segregates the opinions. Close