Topological Measure Locating the Effective Crossover between Segregation and Integration in a Modular Network

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is expressed in terms of the algebraic connectivity of an associated hyper-graph. The rigorous treatment of the simplified case of cliques of equal size that are gradually rewired until they become completely merged, allows us to show that this topological crossover can be made to coincide with a dynamical crossover from cluster to global synchronization of a system of coupled phase oscillators. The dynamical crossover is signaled by a peak in the product of the measures of intra-cluster and global synchronization, which we propose as a dynamical measure of complexity. This quantity is much easier to compute than the entropy (of the average frequencies of the oscillators), and displays a behavior which closely mimics that of the dynamical complexity index based on the latter. The proposed toplogical measure simultaneously provides information on the dynamical behavior, sheds light on the interplay between modularity vs total integration and shows how this affects the capability of the network to perform both local and distributed dynamical tasks

Breathing synchronization in interconnected networks

Global synchronization in a complex network of oscillators emerges from the interplay between its topology and the dynamics of the pairwise interactions among its numerous components. When oscillators are spatially separated, however, a time delay appears in the interaction which might obstruct synchronization. Here we study the synchronization properties of interconnected networks of oscillators with a time delay between networks and analyze the dynamics as a function of the couplings and communication lag. We discover a new breathing synchronization regime, where two groups appear in each network synchronized at different frequencies. Each group has a counterpart in the opposite network, one group is in phase and the other in anti-phase with their counterpart. For strong couplings, instead, networks are internally synchronized but a phase shift between them might occur. The implications of our findings on several socio-technical and biological systems are discussed.Comment: 7 pages, 3 figures + 3 pages of Supplemental Materia

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.Comment: 25 pages, 4 figure

How product market reforms lubricate shock adjustment in the euro area

The essay sets out what product market reforms are, as well as the main measurement issues, followed by an analysis of how such reforms lubricate adjustment processes in EMU, in particular via the “competitiveness channelâ€. Attention is paid to the short-run and longer-run aspects of adjustments to shocks and the scant empirical evidence on the role of product markets in adjustment is discussed.  The essay investigates empirically the need for product market reforms in the euro area, based on the KLEMS data set. Two questions are addressed: how likely is it for euro area countries to experience an asymmetric shock, and what empirical evidence can we deduce about eurozone countries' capacities to adjust to asymmetric shocks? The approach is disaggregated and highlights (especially services) sectors with relatively greater adjustment problems.  The record of product market reforms of the euro area countries is briefly summarized. The paper shows that substantial reforms have been undertaken, yet, there is considerable evidence that the eurozone, and in particular with respect to services, could significantly intensify product market reforms and thereby augment the net benefits of having a single currency. Subsequently, product market reforms are placed in the context of wider reforms efforts (complementarities e.g. with labour and financial markets) as well as in the two-tier institutional structure of the euro area and the EU at large (given cross-border spillovers and the case for coordination). Designing reforms in this euro area context is briefly discussed. A final section with five “policy messages†concludes the essay.adjustment, product market reforms, asymmetric shocks, Pelkmans, Acedo Montoya, Maravalle

Network community detection via iterative edge removal in a flocking-like system

We present a network community-detection technique based on properties that emerge from a nature-inspired system of aligning particles. Initially, each vertex is assigned a random-direction unit vector. A nonlinear dynamic law is established so that neighboring vertices try to become aligned with each other. After some time, the system stops and edges that connect the least-aligned pairs of vertices are removed. Then the evolution starts over without the removed edges, and after enough number of removal rounds, each community becomes a connected component. The proposed approach is evaluated using widely-accepted benchmarks and real-world networks. Experimental results reveal that the method is robust and excels on a wide variety of networks. Moreover, for large sparse networks, the edge-removal process runs in quasilinear time, which enables application in large-scale networks