Invited Speakers
Baruch Barzel
Bar-Ilan University, Israel
Title: Navigating network
dynamics
Abstract: Universal network characteristics, such as the scale-free degree distribution and the small world phenomenon, are the bread and butter of network science. But how do we translate such topological features into an understanding of the system's dynamic behavior: for instance, how does the small world structure impact the patterns of flow in the system? Or how does the presence of hubs affect the distribution of influence? These questions touch on the interplay between the network structure and its intrinsic nonlinear dynamics - a challenging combination that rarely succumbs to analytical treatment. It is therefore, no surprise that, upon observation, network dynamics seem diverse and unpredictable - a zoo of diverging timescales, propagation patterns, spreading dynamics and critical transitions. Hence, it seems that the concept of universality, which ignited the field of network science at the turn of the century - this concept breaks down when it comes to dynamics, as diversity wins over universality. How, then, can we understand, predict and influence the network's actual behavior? Our research over the past decade offers an optimistic view on this question, by exposing the deep universality that characterizes network dynamics. This universality allows a systematic translation of structure into dynamics, from state transitions, to propagation timescales, localization, and spectral analysis. It allows us to expose the relevant parameters that actually control the system's behavior, and - ultimately - steer the system towards desired states with minimal
intervention.
Stefano Boccaletti
Institute of Complex Systems, National Research Council, Italy
Title: The transition to synchronization of networked dynamical systems
Abstract: From brain dynamics and neuronal firing, to power grids or financial markets, synchronization of networked units is the collective behavior characterizing the normal functioning of most natural and man made systems. As a control parameter (typically the coupling strength in each link of the network) increases, a transition occurs between a fully disordered and gaseous-like phase (where the units evolve in a totally incoherent manner) to an ordered or solid-like phase (in which, instead, all units follow the same trajectory in time). The transition between such two phases can be discontinuous and irreversible, or smooth, continuous, and reversible. The first case is known as Explosive Synchronization, and refers to an abrupt onset of synchronization following an infinitesimally small change in the control parameter. The second case is the most commonly observed one, and corresponds to a second-order phase transition, resulting in intermediate states emerging in between the two phases. Namely, the path to synchrony is here characterized by a sequence of events where structured states emerge made of different functional modules (or clusters), each one evolving in unison. In my talk, I will assume that, during the transition, the synchronous solution of each cluster does not differ substantially from that of the entire network and, under such an approximation, I will introduce a (simple, effective, and limited in computational demand) method which is able to: i) predict the entire sequence of events that are taking place during the transition, ii) identify exactly which graph's node is belonging to each of the emergent clusters, iii) provide a well approximated calculation of the critical coupling strength value at which each of such clusters is observed to synchronize, and iv) use the cluster properties to suitably control and tame cluster synchronization. I will also demonstrate that, under the assumed approximation, the sequence of events is in fact universal, in that it is independent of the specific dynamical system operating in each network's node and depends, instead, only on the graph's structure.
Hocine Cherifi
University of Burgundy, France
Title:
Community-Aware Centrality and Beyond
Shlomo Havlin
Bar-Ilan University, Israel
Title: General Theory for Mechanisms behind Abrupt and Continuous Phase Transitions in Nature and Technology.
Huijuan Wang
Delft University of Technology, the Netherlands
Title: Temporal Network Prediction and Interpretation