A polynomial eigenvalue approach for multiplex networks

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive interesting results based on an interpretation of the traditional eigenvalue problem. More specifically, we reduce the dimensionality of our matrices but increase the power of the characteristic polynomial, i.e, a polynomial eigenvalue problem. Such an approach may sound counterintuitive at first glance, but it allows us to relate the quadratic problem for a 2-Layer multiplex system with the spectra of the aggregated network and to derive bounds for the spectra, among many other interesting analytical insights. Furthermore, it also permits to directly obtain analytical and numerical insights on the eigenvalue behavior as a function of the coupling between layers. Our study includes the supra-adjacency, supra-Laplacian, and the probability transition matrices, which enable us to put our results under the perspective of structural phases in multiplex networks. We believe that this formalism and the results reported will make it possible to derive new results for multiplex networks in the future.Comment: 15 pages including figures. Submitted for publicatio

On degree-degree correlations in multilayer networks

We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to weighted networks and provides information about correlations considering pairs of layers. By analyzing the multilayer representation of the airport transportation network, we show that contrasting results are obtained when the layers are analyzed independently or as an interconnected system. Finally, we study the impact of the level of assortativity and heterogeneity between layers on the spreading of diseases. Our results highlight the need of studying degree-degree correlations on multilayer systems, instead of on aggregated networks.Comment: 8 pages, 3 figure

Layer degradation triggers an abrupt structural transition in multiplex networks

Network robustness is a central point in network science, both from a theoretical and a practical point of view. In this paper, we show that layer degradation, understood as the continuous or discrete loss of links' weight, triggers a structural transition revealed by an abrupt change in the algebraic connectivity of the graph. Unlike traditional single layer networks, multiplex networks exist in two phases, one in which the system is protected from link failures in some of its layers and one in which all the system senses the failure happening in one single layer. We also give the exact critical value of the weight of the intra-layer links at which the transition occurs for continuous layer degradation and its relation to the value of the coupling between layers. This relation allows us to reveal the connection between the transition observed under layer degradation and the one observed under the variation of the coupling between layers.Comment: 8 pages, and 8 figures in Revtex style. Submitted for publicatio

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < \gamma \leq 3$, in line with what has been observed for other dynamical processes in such networks. For $\gamma > 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators

Centrality anomalies in complex networks as a result of model over-simplification

Tremendous advances have been made in our understanding of the properties and evolution of complex networks. These advances were initially driven by information-poor empirical networks and theoretical analysis of unweighted and undirected graphs. Recently, information-rich empirical data complex networks supported the development of more sophisticated models that include edge directionality and weight properties, and multiple layers. Many studies still focus on unweighted undirected description of networks, prompting an essential question: how to identify when a model is simpler than it must be? Here, we argue that the presence of centrality anomalies in complex networks is a result of model over-simplification. Specifically, we investigate the well-known anomaly in betweenness centrality for transportation networks, according to which highly connected nodes are not necessarily the most central. Using a broad class of network models with weights and spatial constraints and four large data sets of transportation networks, we show that the unweighted projection of the structure of these networks can exhibit a significant fraction of anomalous nodes compared to a random null model. However, the weighted projection of these networks, compared with an appropriated null model, significantly reduces the fraction of anomalies observed, suggesting that centrality anomalies are a symptom of model over-simplification. Because lack of information-rich data is a common challenge when dealing with complex networks and can cause anomalies that misestimate the role of nodes in the system, we argue that sufficiently sophisticated models be used when anomalies are detected.Comment: 14 pages, including 9 figures. APS style. Accepted for publication in New Journal of Physic

Disease Localization in Multilayer Networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure

Genomic analysis of eight native plasmids of the phytopathogen Pseudomonas syringae

Comunicación a conferenciaThe pPT23A family of plasmids (PFPs) appears to be indigenous to the plant pathogen Pseudomonas syringae and these plasmids are widely distributed and widely transferred among pathovars of P. syringae and related species. PFPs are sources of accessory genes for their hosts that can include genes important for virulence and epiphytic colonization of plant leaf surfaces. Further understanding of the evolution of the pPT23A plasmid family and the role of these plasmids in P. syringae biology and pathogenesis, requires the determination and analysis of additional complete, closed plasmid genome sequences. Therefore, our main objective was to obtain complete genome sequences from PFPs from three different P. syringae pathovars and perform a comparative genomic analysis. In this work plasmid DNA isolation, purification by CsCl-EtBr gradients, and sequencing using 454 platform, were used to obtain the complete sequence of P. syringae plasmids. Different bioinformatic tools were used to analyze the plasmid synteny, to identify virulence genes (i.e. type 3 effectors) and to unravel the evolutionary history of PFPs. Our sequence analysis revealed that PFPs from P. syringae encode suites of accessory genes that are selected at different levels (universal, interpathovar and intrapathovar). The conservation of type IVSS encoding conjugation functions also contributes to the distribution of these plasmids within P. syringae populations. Thus, this study contributes to unravel the genetic basis of the role of PFPs in different P. syringae lifestyles.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Isolation, characterization and selection of bacterial isolates from a suppressive soil with beneficial traits to plants

Backgrounds This study focused on the characterization and selection of bacterial strains obtained from a suppressive soil displaying antifungal activity against the soilborne phytopathogenic fungi Rosellinia necatrix. Bacterial profile from this suppressive soil were first obtained by 16S rRNA gene sequencing, revealing a significant increase in the bacterial class Gammaproteobacteria, especially in some antagonistic representatives of Pseudomonas spp. Objectives To obtain and characterize a collection of 246 bacterial isolates obtained from this suppressive soil, in order to identify new strains with antifungal activity against fungal phytopathogens. Methods To obtain the bacterial collection, we performed an isolation on a selective medium for Pseudomonas-like microorganisms. Further characterization tests were used in order to analyse the bacterial collection, including identification of the general metabolic profile of glucose, the profiling of antifungals produced, including both the putative production of antifungal compounds and lytic exoenzymes, and the evaluation of traits related with beneficial effects on plants. Conclusions A final selection of representative strains resulted in antifungal isolates belonging to the genus Pseudomonas, but also some representatives of the genera Serratia and Stenotrophomonas. These selected strains were tested for plant protection by an in vivo experiment using avocado and wheat plants challenged by the pathogen R. necatrix, showing all of them an antifungal ability and plant disease protection. Pseudomonas-like strains isolated from suppressive soils constitute an excellent source for novel microbial biocontrol agents against soilborne fungal pathogens. This work was supported by grant AGL2014-52518-C2-1-R. Carmen Vida and Sandra Tienda are supported by a PhD fellowship from the FPI program of the Spanish Government.This work was supported by grant AGL2014-52518-C2-1-R. Carmen Vida and Sandra Tienda are supported by a PhD fellowship from the FPI program of the Spanish Government; Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Comparative genomic analysis of native pseudomonas syringae plasmids belonging to the ppt23 a family reveals their role in p. Syringae epiphytic and pathogenic lifestyles

Backgrounds The pPT23A family of plasmids (PFPs) appears to be indigenous to the plant pathogen Pseudomonas syringae and these plasmids are widely distributed and widely transferred among pathovars of P. syringae and related species. PFPs are sources of accessory genes for their hosts that can include genes important for virulence and epiphytic colonization of plant leaf surfaces. Objectives Further understanding of the evolution of the pPT23A plasmid family and the role of these plasmids in P. syringae biology and pathogenesis, requires the determination and analysis of additional complete, closed plasmid genome sequences. Therefore, our main objective was to obtain complete genome sequences of PFPs from three different P. syringae pathovars and perform a comprehensive comparative genomic analysis. Methods In this work plasmid DNA isolation, purification by CsCl-EtBr gradients, and sequencing using 454 platform, were carried out to obtain the complete sequence of P. syringae plasmids. Different bioinformatic tools were used to analyze the plasmid synteny, to identify virulence genes (i.e. type 3 effectors) and to unravel the evolutionary history of PFPs. Conclusions Our sequence analysis revealed that PFPs from P. syringae encode suites of accessory genes that are selected at different levels (universal, interpathovar and intrapathovar). The conservation of type IVSS encoding conjugation functions also contributes to the distribution of these plasmids within P. syringae populations. Thus, this study contributes to unravel the genetic bases of the role of PFPs in different P. syringae lifestyles. This work was supported by grants Proyecto de Excelencia, Junta de Andalucía (P07-AGR-02471; P12-AGR-1473) and by Michigan State University AgBioResearch.This work was supported by grants Proyecto de Excelencia, Junta de Andalucía (P07-AGR-02471; P12-AGR-1473) and by Michigan State University AgBioResearch; Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech