Motif formation and emergence of mesoscopic structure in complex networks

PhDNetwork structures can encode information from datasets that have a natural representation in terms of networks, for example datasets describing collaborations or social relations among individuals in science or society, as well as from data that can be mapped into graphs due to their intrinsic correlations, such as time series or images. Developing models and algorithms to characterise the structure of complex networks at the micro and mesoscale is thus of fundamental importance to extract relevant information from and to understand real world complex data and systems. In this thesis we will investigate how modularity, a mesoscopic feature observed almost universally in real world complex networks can emerge, and how this phenomenon is related to the appearance of a particular type of network motif, the triad. We will shed light on the role that motifs play in shaping the mesoscale structure of complex networks by considering two special classes of networks, multiplex networks, that describe complex systems where interactions of different nature are involved, and visibility graphs, a family of graphs that can be extracted from the time series of dynamical processes. This thesis is based on the research papers listed below, in particular on the first five, published between 2014 and 2016: 1. Bianconi, G., Darst R. K., Iacovacci J., Fortunato S., Triadic closure as a basic generating mechanism of communities in complex networks, Phys. Rev. E 90 (4), 042806 (2014). 2. Iacovacci J., Wu Z., Bianconi G., Mesoscopic structures reveal the network between the layers of multiplex data sets, Phys. Rev. E. 92 (4), 042806 (2015). 3. Battiston F., Iacovacci J., Nicosia V., Bianconi G., Latora V., Emergence of multiplex communities in collaboration networks, PloS one 11 (1), e0147451 (2016). 4. Iacovacci J., Lacasa L., Sequential visibility-graph motifs, Phys. Rev. E. 93 (4), 042309 (2016). 5. Iacovacci J., Lacasa L., Sequential motif pro le of natural visibility-graphs, Phys. Rev. E. 94 (5), 052309 (2016). 6. Iacovacci J., Bianconi G., Extracting information from multiplex networks, Chaos: An Interdisciplinary Journal of Nonlinear Science 26 (6), 065306 (2016). 7. Iacovacci J., Rahmede C., Arenas A., Bianconi G., Functional Multiplex PageRank, EPL (Europhysics Letters) 116(2), 28004 (2016). 8. Lacasa L, Iacovacci J., Visibility graphs of random scalar elds and spatial data, arXiv preprint arXiv:1702.07813 (2017). 9. Rahmede C, Iacovacci J, Arenas A, Bianconi G., Centralities of Nodes and In infuences of Layers in Large Multiplex Network, arXiv preprint arXiv:1703.05833 (2017)

Extraction and Integration of Genetic Networks from Short-Profile Omic Data Sets.

Mass spectrometry technologies are widely used in the fields of ionomics and metabolomics to simultaneously profile the intracellular concentrations of, e.g., amino acids or elements in genome-wide mutant libraries. These molecular or sub-molecular features are generally non-Gaussian and their covariance reveals patterns of correlations that reflect the system nature of the cell biochemistry and biology. Here, we introduce two similarity measures, the Mahalanobis cosine and the hybrid Mahalanobis cosine, that enforce information from the empirical covariance matrix of omics data from high-throughput screening and that can be used to quantify similarities between the profiled features of different mutants. We evaluate the performance of these similarity measures in the task of inferring and integrating genetic networks from short-profile ionomics/metabolomics data through an analysis of experimental data sets related to the ionome and the metabolome of the model organism S. cerevisiae. The study of the resulting ionome-metabolome Saccharomyces cerevisiae multilayer genetic network, which encodes multiple omic-specific levels of correlations between genes, shows that the proposed measures can provide an alternative description of relations between biological processes when compared to the commonly used Pearson's correlation coefficient and have the potential to guide the construction of novel hypotheses on the function of uncharacterised genes

Sequential motif profile of natural visibility graphs

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Extracting information from multiplex networks

11 pages; 5 figure

Visibility graphs of random scalar fields and spatial data

The family of visibility algorithms were recently introduced as mappings between time series and graphs. Here we extend this method to characterize spatially extended data structures by mapping scalar fields of arbitrary dimension into graphs. After introducing several possible extensions, we provide analytical results on some topological properties of these graphs associated to some types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension, extending a well known result in one-dimensional time series. As this result holds independently of the field's marginal distribution, we show that it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatio-temporal chaos. We finally discuss the range of potential applications of this combinatorial framework, which include image processing in engineering, the description of surface growth in material science, soft matter or medicine and the characterization of potential energy surfaces in chemistry, disordered systems and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed

Extraction and Integration of Genetic Networks from Short-Profile Omic Data Sets

Mass spectrometry technologies are widely used in the fields of ionomics and metabolomics to simultaneously profile the intracellular concentrations of, e.g., amino acids or elements in genome-wide mutant libraries. These molecular or sub-molecular features are generally non-Gaussian and their covariance reveals patterns of correlations that reflect the system nature of the cell biochemistry and biology. Here, we introduce two similarity measures, the Mahalanobis cosine and the hybrid Mahalanobis cosine, that enforce information from the empirical covariance matrix of omics data from high-throughput screening and that can be used to quantify similarities between the profiled features of different mutants. We evaluate the performance of these similarity measures in the task of inferring and integrating genetic networks from short-profile ionomics/metabolomics data through an analysis of experimental data sets related to the ionome and the metabolome of the model organism S. cerevisiae. The study of the resulting ionome−metabolome Saccharomyces cerevisiae multilayer genetic network, which encodes multiple omic-specific levels of correlations between genes, shows that the proposed measures can provide an alternative description of relations between biological processes when compared to the commonly used Pearson’s correlation coefficient and have the potential to guide the construction of novel hypotheses on the function of uncharacterised genes

Emergence of Multiplex Communities in Collaboration Networks.

Community structures in collaboration networks reflect the natural tendency of individuals to organize their work in groups in order to better achieve common goals. In most of the cases, individuals exploit their connections to introduce themselves to new areas of interests, giving rise to multifaceted collaborations which span different fields. In this paper, we analyse collaborations in science and among movie actors as multiplex networks, where the layers represent respectively research topics and movie genres, and we show that communities indeed coexist and overlap at the different layers of such systems. We then propose a model to grow multiplex networks based on two mechanisms of intra and inter-layer triadic closure which mimic the real processes by which collaborations evolve. We show that our model is able to explain the multiplex community structure observed empirically, and we infer the strength of the two underlying social mechanisms from real-world systems. Being also able to correctly reproduce the values of intra-layer and inter-layer assortativity correlations, the model contributes to a better understanding of the principles driving the evolution of social networks

Community activity vs layer activity for the EU Airports multiplex.

<p>(A) Largest link community of the European Multiplex Air Transportation Network. Lufthansa’s flights are shown in blue, the other airlines in pink. (B) Second largest link community. Ryanair’s flights are shown in blue, the other airlines in pink. (C) Community vs. layer activity of the EU airports. While the layer activity appears to have a positive correlation with the communities activity, there are large differences in the communities activity between airports with large layer activity (compare for instance Amsterdam (AMS) and Vienna (VIE)). The multilink communities are detected using <i>ϵ</i> = 0.4, <i>z</i> = 0.6.</p