Assortativity and leadership emergence from anti-preferential attachment in heterogeneous networks

Many real-world networks exhibit degree-assortativity, with nodes of similar degree more likely to link to one another. Particularly in social networks, the contribution to the total assortativity varies with degree, featuring a distinctive peak slightly past the average degree. The way traditional models imprint assortativity on top of pre-defined topologies is via degree-preserving link permutations, which however destroy the particular graph's hierarchical traits of clustering. Here, we propose the first generative model which creates heterogeneous networks with scale-free-like properties and tunable realistic assortativity. In our approach, two distinct populations of nodes are added to an initial network seed: one (the followers) that abides by usual preferential rules, and one (the potential leaders) connecting via anti-preferential attachments, i.e. selecting lower degree nodes for their initial links. The latter nodes come to develop a higher average degree, and convert eventually into the final hubs. Examining the evolution of links in Facebook, we present empirical validation for the connection between the initial anti-preferential attachment and long term high degree. Thus, our work sheds new light on the structure and evolution of social networks

Explosive synchronization in weighted complex networks

The emergence of dynamical abrupt transitions in the macroscopic state of a system is currently a subject of the utmost interest. Given a set of phase oscillators networking with a generic wiring of connections and displaying a generic frequency distribution, we show how combining dynamical local information on frequency mismatches and global information on the graph topology suggests a judicious and yet practical weighting procedure which is able to induce and enhance explosive, irreversible, transitions to synchronization. We report extensive numerical and analytical evidence of the validity and scalability of such a procedure for different initial frequency distributions, for both homogeneous and heterogeneous networks, as well as for both linear and non linear weighting functions. We furthermore report on the possibility of parametrically controlling the width and extent of the hysteretic region of coexistence of the unsynchronized and synchronized states

Los jesuitas y el lulismo

Antes de finales del siglo xvii hay poca información para relacionar directamente la Compañía de Jesús con el pensamiento de Ramón Llull, a pesar de lo que se ha supuesto con relación al padre fundador de la orden y con excepciones como la de Jerónimo Nadal. En el siglo xviii destacan, en cambio, los estudios de los jesuitas mallorquines Andrés Moragues y, sobretodo, de Jaume Custurer, que estuvo en contacto con el editor de la Maguntina. Jean-Baptiste Sollier fue otro gran jesuita lulista. La expulsión de la Compañía en tiempos de Carlos III fue perjudicial para el desarrollo del lulismo. En el siglo xx algunos de los mejores especialistas en Ramón Llull han sido jesuitas, como Eusebi Colomer o Charles Lohr.Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed at sem hendrerit, hendrerit dolor vitae, convallis massa. Nunc eu urna in mi sollicitudin faucibus. Sed a nunc at felis rhoncus imperdiet. Vestibulum consequat posuere tortor vel fringilla. Fusce id nunc lectus. Aenean nec rhoncus risus. Cras a semper diam, ac sodales erat. Sed eget fringilla purus, sed posuere ex. Integer id enim diam. Ut et eleifend nulla, quis dapibus metus. Ut ullamcorper risus ut nisl blandit, in gravida libero pulvinar. Sed ac nisi vitae augue auctor sodales. Vivamus egestas accumsan felis. Mauris vitae nulla eu orci volutpat pulvinar

Relay synchronization in multiplex networks

Relay (or remote) synchronization between two not directly connected oscillators in a network is an important feature allowing distant coordination. In this work, we report a systematic study of this phenomenon in multiplex networks, where inter-layer synchronization occurs between distant layers mediated by a relay layer that acts as a transmitter. We show that this transmission can be extended to higher order relay configurations, provided symmetry conditions are preserved. By first order perturbative analysis, we identify the dynamical and topological dependencies of relay synchronization in a multiplex. We find that the relay synchronization threshold is considerably reduced in a multiplex configuration, and that such synchronous state is mostly supported by the lower degree nodes of the outer layers, while hubs can be de-multiplexed without affecting overall coherence. Finally, we experimentally validated the analytical and numerical findings by means of a multiplex of three layers of electronic circuits.the analytical and numerical findings by means of a multiplex of three layers of electronic circuits

Synchronization centrality and explosive synchronization in complex networks

Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of quantitative tools has hampered so far a systematic study of the mechanisms behind such a collective behavior. We here propose an effective network whose topological properties reflect the interplay between the topology and dynamics of the original network. On that basis, we are able to introduce the "synchronization centrality", a measure which quantifies the role and importance of each network's node in the synchronization process. In particular, we use such a measure to assess the propensity of a graph to synchronize explosively, thus indicating a unified framework for most of the different models proposed so far for such an irreversible transition. Taking advantage of the predicting power of this measure, we furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a small fraction of its nodes

PKI Interoperability: Still an Issue? A Solution in the X. 509 Realm

There exist many obstacles that slow the global adoption of public key infrastructure (PKI) technology. The PKI interoperability problem, being poorly understood, is one of the most confusing. In this paper, we clarify the PKI interoperability issue by exploring both the juridical and technical domains. We demonstrate the origin of the PKI interoperability problem by determining its root causes, the latter being legal, organizational and technical differences between countries, which mean that relying parties have no one to rely on. We explain how difficult it is to harmonize them. Finally, we propose to handle the interoperability problem from the trust management point of view, by introducing the role of a trust broker which is in charge of helping relying parties make informed decisions about X.509 certificates

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

Synchronization interfaces and overlapping communities in complex networks

We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied in the general framework of interacting phase oscillators composed of either dynamical domains (influenced by different forcing processes), or structural domains (modular networks). The obtained results allow to give a functional definition of overlapping structures in modular networks, and suggest a practical method to identify them. As a result, our algorithm could detect information on both single overlapping nodes and overlapping clusters.Comment: 5 pages, 4 figure