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Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same…
Structure identification in cosmological simulations plays an important role in analysing simulation outputs. The definition of these structures directly impacts the inferred properties derived from these simulations. This paper proposes a…
Symmetries found through automorphisms or graph fibrations provide important insights in network analysis. Symmetries identify clusters of robust synchronization in the network which improves the understanding of the functionality of…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
Biclustering is an unsupervised data mining technique that aims to unveil patterns (biclusters) from gene expression data matrices. In the framework of this thesis, we propose new biclustering algorithms for microarray data. The latter is…
The need to harmonise apparently irreconcilable arrangements in an ecosystem --nestedness and segregation-- has triggered so far different strategies. Methodological refinements, or the inclusion of behavioural preferences to the network…
Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts,…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
Estimating a covariance matrix is central to high-dimensional data analysis. Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging, among others, consistently reveal strong…
In this paper we propose weighted symmetric binary matrix factorization (wSBMF) framework to detect overlapping communities in bipartite networks, which describe relationships between two types of nodes. Our method improves performance by…
Interconnected networks are mathematical representation of systems where two or more simple networks are coupled to each other. Depending on the coupling weight between the two components, the interconnected network can function in two…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Uncovering structural properties of ecological networks is a crucial starting point of studying the system's stability in response to various types of perturbations. We analyze pollination and seed disposal networks, which are…
The latent space approach to complex networks has revealed fundamental principles and symmetries, enabling geometric methods. However, the conditions under which network topology implies geometricity remain unclear. We provide a…
Many networks can be usefully decomposed into a dense core plus an outlying, loosely-connected periphery. Here we propose an algorithm for performing such a decomposition on empirical network data using methods of statistical inference. Our…
Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used…
We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative…
The minimal number of nodes required to multilaterate a network endowed with geodesic distance (i.e., to uniquely identify all nodes based on shortest path distances to the selected nodes) is called its metric dimension. This quantity is…