A pinboard by
Andrea Santoro

PhD Candidate, Queen Mary University of London


I'm a PhD researcher focused on the analysis and modelling of real-world multi-dimensional networks

A mathematical framework can be used to describe many real systems. This assumption underpins my research, which can be placed in the network science field and is focused on complex systems. These systems are made up of a large number of elementary units which, as a whole, show properties that cannot be predicted by the mere knowledge of the individual parts. The standard approach to network description of complex systems consists of studying the mathematical object, also called graph, resulting from the aggregation of all the interactions (edges) observed between a certain set of elementary units (nodes). A social system, for instance, can be described as a set of individuals through an aggregation of friendships, communications, collaborations, and working relationships, just to mention some of them. However, considering all the interactions on an equal footing might in general discard important information about the structure and functioning of the original real system. Therefore, a better description of the system is given by the so-called ``multi-layer networks'', i.e., networks where each node appears in a set of different layers, and each layer describes all the edges of a given type (e.g. a different kind of social interaction). My PhD project aims to develop new measures, based on optimisation principles and information theory techniques, to extract relevant features from large-scale multi-layer networks, by filtering out noise and redundant information. In particular, the identification of key components, which should retain the maximum amount of information, will help to speed up the process of comparison among different multilayer networks and lay the foundation for the construction of a multilayer ''backbone''. These methods can be applied to several aspects of transportation networks, biological systems, and human behaviours, including mobility and social interactions. As an example, we are currently working on the human brain network reconstructed from the medical scans (fMRI and DTI) of several patients. The aim of this research is to extract features from the mathematical formulation, which can be used to distinguish between healthy and non-healthy patients (in our case, patients with Autism Spectrum Disorder).


Multilayer motif analysis of brain networks.

Abstract: In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has made possible to detect the central areas of a neural system and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on anatomical and functional networks as separate entities. The recently developed mathematical framework of multi-layer networks allows us to perform an analysis of the human brain where the structural and functional layers are considered together. In this work, we describe how to classify the subgraphs of a multiplex network, and we extend the motif analysis to networks with an arbitrary number of layers. We then extract multi-layer motifs in brain networks of healthy subjects by considering networks with two layers, anatomical and functional, respectively, obtained from diffusion and functional magnetic resonance imaging. Results indicate that subgraphs in which the presence of a physical connection between brain areas (links at the structural layer) coexists with a non-trivial positive correlation in their activities are statistically overabundant. Finally, we investigate the existence of a reinforcement mechanism between the two layers by looking at how the probability to find a link in one layer depends on the intensity of the connection in the other one. Showing that functional connectivity is non-trivially constrained by the underlying anatomical network, our work contributes to a better understanding of the interplay between the structure and function in the human brain.

Pub.: 01 May '17, Pinned: 23 Jan '18

Identifying the hidden multiplex architecture of complex systems

Abstract: The architecture of many complex systems is well described by multiplex interaction networks, and their dynamics is often the result of several intertwined processes taking place at different levels. However only in a few cases can such multi-layered architecture be empirically observed, as one usually only has experimental access to such structure from an aggregated projection. A fundamental question is thus to determine whether the hidden underlying architecture of complex systems is better modelled as a single interaction layer or results from the aggregation and interplay of multiple layers. Here we show that, by only using local information provided by a random walker navigating the aggregated network, it is possible to decide in a robust way if the underlying structure is a multiplex and, in the latter case, to determine the most probable number of layers. The proposed methodology detects and estimates the optimal architecture capable of reproducing observable non- Markovian dynamics taking place on networks, with applications ranging from human or animal mobility to electronic transport or molecular motors. Furthermore, the mathematical theory extends above and beyond detection of physical layers in networked complex systems, as it provides a general solution for the optimal decomposition of complex dynamics in a Markov switching combination of simple (diffusive) dynamics.

Pub.: 12 May '17, Pinned: 23 Jan '18

Multiplex lexical networks reveal patterns in early word acquisition in children.

Abstract: Network models of language have provided a way of linking cognitive processes to language structure. However, current approaches focus only on one linguistic relationship at a time, missing the complex multi-relational nature of language. In this work, we overcome this limitation by modelling the mental lexicon of English-speaking toddlers as a multiplex lexical network, i.e. a multi-layered network where N = 529 words/nodes are connected according to four relationship: (i) free association, (ii) feature sharing, (iii) co-occurrence, and (iv) phonological similarity. We investigate the topology of the resulting multiplex and then proceed to evaluate single layers and the full multiplex structure on their ability to predict empirically observed age of acquisition data of English speaking toddlers. We find that the multiplex topology is an important proxy of the cognitive processes of acquisition, capable of capturing emergent lexicon structure. In fact, we show that the multiplex structure is fundamentally more powerful than individual layers in predicting the ordering with which words are acquired. Furthermore, multiplex analysis allows for a quantification of distinct phases of lexical acquisition in early learners: while initially all the multiplex layers contribute to word learning, after about month 23 free associations take the lead in driving word acquisition.

Pub.: 25 Apr '17, Pinned: 23 Jan '18