Vincenzo Nicosia

The behaviour and functioning of a variety of complex physical and biological systems depend on the spatial organisation of their constituent units, and on the presence and formation of clusters of functionally similar or related individuals. Here we study the properties of clusters in spatially-embedded networks where nodes are coloured according to a given colouring process. This characterisation will allow us to use spatial networks with uniformly-coloured nodes as a null-model against which the importance, relevance, and significance of clusters of related units in a given real-world system can be assessed. We show that even a uniform and uncorrelated random colouring process can generate coloured clusters of substantial size and interesting shapes, which can be distinguished by using simple dynamical measures, like the average time needed for a random walk to escape from the cluster. We provide a mean-field approach to study the properties of those clusters in large two-dimensional lattices, and we show that the analytical treatment agrees very well with the numerical results. Finally, we will show how a dynamical approach can be used to explore some of the properties of such clusters, shedding light on a fresh and novel perspective for characterising spatial motifs.

The signature of early cancer dynamics on the spatial arrangement of tumour cells is poorly understood, and yet could encode information about how sub-clones grew within the expanding tumour. Novel methods of quantifying spatial tumour data at the cellular scale are required to link evolutionary dynamics to the resulting spatial architecture of the tumour. Here, we propose a framework using first passage times of random walks to quantify the complex spatial patterns of tumour cell population mixing. First, using a simple model of cell mixing we demonstrate how first passage time statistics can distinguish between different pattern structures. We then apply our method to simulated patterns of mutated and non-mutated tumour cell population mixing, generated using an agent-based model of expanding tumours, to explore how first passage times reflect mutant cell replicative advantage, time of emergence and strength of cell pushing. Finally, we explore applications to experimentally measured human colorectal cancer, and estimate parameters of early sub-clonal dynamics using our spatial computational model. We infer a wide range of sub-clonal dynamics, with mutant cell division rates varying between 1 and 4 times the rate of non-mutated cells across our sample set. Some mutated sub-clones emerged after as few as 100 non-mutant cell divisions, and others only after 50,000 divisions. The majority were consistent with boundary driven growth or short-range cell pushing. By analysing multiple sub-sampled regions in a small number of samples, we explore how the distribution of inferred dynamics could inform about the initial mutational event. Our results demonstrate the efficacy of first passage time analysis as a new methodology in spatial analysis of solid tumour tissue, and suggest that patterns of sub-clonal mixing can provide insights into early cancer dynamics.

Integrating structural information and metadata, such as gender, social status, or interests, enriches networks and enables a better understanding of the large-scale structure of complex systems. However, existing approaches to augment networks with metadata for community detection only consider immediately adjacent nodes and cannot exploit the nonlocal relationships between metadata and large-scale network structure present in many spatial and social systems. Here, we develop a flow-based community detection framework based on the map equation that integrates network information and metadata of distant nodes and reveals more complex relationships. We analyze social and spatial networks and find that our methodology can detect functional metadata-informed communities distinct from those derived solely from network information or metadata. For example, in a mobility network of London, we identify communities that reflect the heterogeneity of income distribution, and in a European power grid network, we identify communities that capture relationships between geography and energy prices beyond country borders.

Socioeconomic segregation has an important role in the emergence of large-scale inequalities in urban areas. Most of the available measures of spatial segregation depend on the scale and size of the system under study, or neglect large-scale spatial correlations, or rely on ad-hoc parameters, making it hard to compare different systems on equal grounds. We propose here a family of non-parametric measures for spatial distributions, based on the statistics of the trajectories of random walks on graphs associated to a spatial system. These quantities provide a consistent estimation of segregation in synthetic spatial patterns, and we use them to analyse the ethnic segregation of metropolitan areas in the US and the UK. We show that the spatial diversity of ethnic distributions, as measured through diffusion on graphs, allow us to compare the ethnic segregation of urban areas having different size, shape, or peculiar microscopic characteristics, and exhibits a strong association with socio-economic deprivation.

The ongoing COVID-19 pandemic is the first epidemic in human history in which digital contact tracing has been deployed at a global scale. Tracking and quarantining all the contacts of individuals who test positive for a virus can help slow down an epidemic, but the impact of contact tracing is severely limited by the generally low adoption of contact-tracing apps in the population. We derive here an analytical expression for the effectiveness of contact-tracing app installation strategies in a susceptible-infected-recovered (SIR) model on a given contact graph. We propose a decentralized heuristic to improve the effectiveness of contact tracing under fixed adoption rates, which targets a set of individuals to install contact-tracing apps and can be easily implemented. Simulations on a large number of real-world contact networks confirm that this heuristic represents a feasible alternative to the current state of the art.

The footprint left by early cancer dynamics on the spatial arrangement of tumour cells is poorly understood, and yet could encode information about how therapy resistant sub-clones grew within the expanding tumour. Novel methods of quantifying spatial tumour data at the cellular scale are required to link evolutionary dynamics to the resulting spatial architecture of the tumour. Here, we propose a framework using first passage times of random walks to quantify the complex spatial patterns of tumour cell population mixing. First, using a toy model of cell mixing we demonstrate how first passage time statistics can distinguish between different pattern structures. We then apply our method to simulated patterns of wild-type and mutated tumour cell population mixing, generated using an agent-based model of expanding tumours, to explore how first passage times reflect mutant cell replicative advantage, time of emergence and strength of cell pushing. Finally, we analyse experimentally measured patterns of genetic point mutations in human colorectal cancer, and estimate parameters of early sub-clonal dynamics using our spatial computational model. We uncover a wide range of mutant cell replicative advantages and timings, with the majority of sampled tumours consistent with boundary driven growth or short-range cell pushing. By analysing multiple sub-sampled regions in a small number of samples, we explore how the distribution of inferred dynamics could inform about the initial mutational event. Our results demonstrate the efficacy of first passage time analysis as a new methodology for quantifying cell mixing patterns in vivo , and suggest that patterns of sub-clonal mixing can provide insights into early cancer dynamics.

Virtually all the emergent properties of complex systems are rooted in the non-homogeneous nature of the behaviours of their elements and of the interactions among them. However, heterogeneity and correlations appear simultaneously at multiple relevant scales, making it hard to devise a systematic approach to quantify them. We develop here a scalable and non-parametric framework to characterise the presence of heterogeneity and correlations in a complex system, based on normalised mean first passage times between preassigned classes of nodes. We showcase a variety of concrete applications, including the quantification of polarisation in the UK Brexit referendum and the roll-call votes in the US Congress, the identification of key players in disease spreading, and the comparison of spatial segregation of US cities. These results show that the diffusion structure of a system is indeed a defining aspect of the complexity of its organisation and functioning.

One of the most concerning aspects of the ongoing COVID-19 pandemic is that it disproportionately affects people from some specific ethnic and socio-economic minorities. In particular, since from the beginning of the pandemic it has been clear that people from Black and African American backgrounds seem to be hit especially hard by the virus, creating a substantial infection gap. The observed abnormal impact on these ethnic groups could probably be due to the co-occurrence of other known risk factors, including co-morbidity, poverty, level of education, access to healthcare, residential segregation and response to cures, although those factors do not seem able to explain fully and in depth the excess incidence of infections and deaths among African Americans. Here, we introduce the concept of diffusion segregation, that is the extent to which a given group of people is internally clustered or exposed to other groups, as a result of mobility and commuting habits. By analysing census and mobility data on major US cities, we found that the weekly excess COVID-19 incidence and mortality in African American communities at the beginning of the COVID-19 pandemic is significantly associated with their level of diffusion segregation. The results confirm that knowing where people commute to, rather than where they live, is potentially much more important to contain and curb the spreading of infectious diseases.

Virtually all the emergent properties of complex systems are rooted in the non-homogeneous nature of the behaviours of their elements and of the interactions among them. However, heterogeneity and correlations appear simultaneously at multiple relevant scales, making it hard to devise a systematic approach to quantify them. We develop here a scalable and non-parametric framework to characterise the presence of heterogeneity and correlations in a complex system, based on normalised mean first passage times between pre-assigned classes of nodes. We showcase a variety of concrete applications, including the quantification of polarisation in the UK Brexit referendum and the roll-call votes in the US Congress, the identification of key players in disease spreading, and the comparison of spatial segregation of US cities. These results show that the diffusion structure of a system is indeed a defining aspect of the complexity of its structure and function.

Socioeconomic segregation is considered one of the main factors behind the emergence of large-scale inequalities in urban areas, and its characterisation is an active area of research in urban studies. There are currently many available measures of spatial segregation, but almost all of them either depend in non-trivial ways on the scale and size of the system under study, or mostly neglect the importance of large-scale spatial correlations, or depend on parameters which make it hard to compare different systems on equal grounds. We propose here two non-parametric measures of spatial variance and local spatial diversity, based on the statistical properties of the trajectories of random walks on graphs. We show that these two quantities provide a consistent and intuitive estimation of segregation of synthetic spatial patterns, and we use them to analyse and compare the ethnic segregation of large metropolitan areas in the US and the UK. The results confirm that the spatial variance and local diversity as measured through simple diffusion on graphs provides meaningful insights about the spatial organisation of ethnicities across a city, and allows us to efficiently compare the ethnic segregation of urban areas across the world irrespective of their size, shape, or peculiar microscopic characteristics.