First passage time analysis of spatial mutation patterns reveals sub-clonal evolutionary dynamics in colorectal cancer.

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.

Pareto Optimality in Multilayer Network Growth.

We model the formation of multilayer transportation networks as a multiobjective optimization process, where service providers compete for passengers, and the creation of routes is determined by a multiobjective cost function encoding a trade-off between efficiency and competition. The resulting model reproduces well real-world systems as diverse as airplane, train, and bus networks, thus suggesting that such systems are indeed compatible with the proposed local optimization mechanisms. In the specific case of airline transportation systems, we show that the networks of routes operated by each company are placed very close to the theoretical Pareto front in the efficiency-competition plane, and that most of the largest carriers of a continent belong to the corresponding Pareto front. Our results shed light on the fundamental role played by multiobjective optimization principles in shaping the structure of large-scale multilayer transportation systems, and provide novel insights to service providers on the strategies for the smart selection of novel routes.

Collective Phenomena Emerging from the Interactions between Dynamical Processes in Multiplex Networks.

We introduce a framework to intertwine dynamical processes of different nature, each with its own distinct network topology, using a multilayer network approach. As an example of collective phenomena emerging from the interactions of multiple dynamical processes, we study a model where neural dynamics and nutrient transport are bidirectionally coupled in such a way that the allocation of the transport process at one layer depends on the degree of synchronization at the other layer, and vice versa. We show numerically, and we prove analytically, that the multilayer coupling induces a spontaneous explosive synchronization and a heterogeneous distribution of allocations, otherwise not present in the two systems considered separately. Our framework can find application to other cases where two or more dynamical processes such as synchronization, opinion formation, information diffusion, or disease spreading, are interacting with each other.

Multilayer motif analysis of brain networks.

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.

Phase transition in the economically modeled growth of a cellular nervous system.

Spatially embedded complex networks, such as nervous systems, the Internet, and transportation networks, generally have nontrivial topological patterns of connections combined with nearly minimal wiring costs. However, the growth rules shaping these economical tradeoffs between cost and topology are not well understood. Here, we study the cellular nervous system of the nematode worm Caenorhabditis elegans, together with information on the birth times of neurons and on their spatial locations. We find that the growth of this network undergoes a transition from an accelerated to a constant increase in the number of links (synaptic connections) as a function of the number of nodes (neurons). The time of this phase transition coincides closely with the observed moment of hatching, when development switches metamorphically from oval to larval stages. We use graph analysis and generative modeling to show that the transition between different growth regimes, as well as its coincidence with the moment of hatching, may be explained by a dynamic economical model that incorporates a tradeoff between topology and cost that is continuously negotiated and renegotiated over developmental time. As the body of the animal progressively elongates, the cost of longer-distance connections is increasingly penalized. This growth process regenerates many aspects of the adult nervous system's organization, including the neuronal membership of anatomically predefined ganglia. We expect that similar economical principles may be found in the development of other biological or manmade spatially embedded complex systems.

Remote synchronization reveals network symmetries and functional modules.

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Components in time-varying graphs.

Real complex systems are inherently time-varying. Thanks to new communication systems and novel technologies, today it is possible to produce and analyze social and biological networks with detailed information on the time of occurrence and duration of each link. However, standard graph metrics introduced so far in complex network theory are mainly suited for static graphs, i.e., graphs in which the links do not change over time, or graphs built from time-varying systems by aggregating all the links as if they were concurrent in time. In this paper, we extend the notion of connectedness, and the definitions of node and graph components, to the case of time-varying graphs, which are represented as time-ordered sequences of graphs defined over a fixed set of nodes. We show that the problem of finding strongly connected components in a time-varying graph can be mapped into the problem of discovering the maximal-cliques in an opportunely constructed static graph, which we name the affine graph. It is, therefore, an NP-complete problem. As a practical example, we have performed a temporal component analysis of time-varying graphs constructed from three data sets of human interactions. The results show that taking time into account in the definition of graph components allows to capture important features of real systems. In particular, we observe a large variability in the size of node temporal in- and out-components. This is due to intrinsic fluctuations in the activity patterns of individuals, which cannot be detected by static graph analysis.

Quantifying ethnic segregation in cities through random walks.

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.

Mapping nonlocal relationships between metadata and network structure with metadata-dependent encoding of random walks.

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.

Impact of urban structure on infectious disease spreading.

The ongoing SARS-CoV-2 pandemic has been holding the world hostage for several years now. Mobility is key to viral spreading and its restriction is the main non-pharmaceutical interventions to fight the virus expansion. Previous works have shown a connection between the structural organization of cities and the movement patterns of their residents. This puts urban centers in the focus of epidemic surveillance and interventions. Here we show that the organization of urban flows has a tremendous impact on disease spreading and on the amenability of different mitigation strategies. By studying anonymous and aggregated intra-urban flows in a variety of cities in the United States and other countries, and a combination of empirical analysis and analytical methods, we demonstrate that the response of cities to epidemic spreading can be roughly classified in two major types according to the overall organization of those flows. Hierarchical cities, where flows are concentrated primarily between mobility hotspots, are particularly vulnerable to the rapid spread of epidemics. Nevertheless, mobility restrictions in such types of cities are very effective in mitigating the spread of a virus. Conversely, in sprawled cities which present many centers of activity, the spread of an epidemic is much slower, but the response to mobility restrictions is much weaker and less effective. Investing resources on early monitoring and prompt ad-hoc interventions in more vulnerable cities may prove helpful in containing and reducing the impact of future pandemics.

[Health management of Italian workers abroad]. / La gestione dei lavoratori italiani all'estero.

In the last 20 years traveling workers abroad have increased markedly. This resulted in the need for standardized preventive tools available to protect workers-travelers in geographic areas with related additional risk factors. Health surveillance of these workers require a company organization that involves the components of the process prior: the occupational physician, safety service, administrative areas, travel clinic. The application phases of medical surveillance must be differentiated into two main phases: 1. pre-travel, in which successive stages also encoded by the SIMLII guidelines; 2. the return journey, where the paths are different for asymptomatic and symptomatic workers. The evaluation of fitness to perform the job abroad is based on general criteria that allow to correlate the health of the worker with respect to the destination area. The application methods actually available allow modulations of the health surveillance for companies of different dimension.

Diffusion segregation and the disproportionate incidence of COVID-19 in African American communities.

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.

Cholera, the Current Status of Cholera Vaccines and Recommendations for Travellers.

Cholera is endemic in approximately 50 countries, primarily in Africa and South and Southeast Asia, and in these areas, it remains a disease associated with poverty. In developed nations, cholera is rare, and cases are typically imported from endemic areas by returning travellers. Cholera is readily preventable with the tools available to modern medicine. In developing nations, cholera transmission can be prevented through improved water, sanitation, and hygiene services and the use of oral cholera vaccines (OCVs). For travellers, risk can be mitigated by practicing regular hand hygiene and consuming food and water from safe sources. OCVs should be considered for high-risk travellers likely to be exposed to cholera patients or contaminated water and food. There are currently three World Health Organization pre-qualified OCVs, which are based on killed whole-cell strains of Vibrio cholerae. These established vaccines offer significant protection in adults and children for up to 2 years. A novel live attenuated vaccine that provides rapid-onset protection in adults and children is licensed in the USA and Europe only. Live attenuated OCVs may mimic the natural infection of V. cholerae more closely, generating rapid immune responses without the need for repeat dosing. These potential benefits have prompted the ongoing development of several additional live attenuated vaccines. The objective of this article is to provide a general review of the current landscape of OCVs, including a discussion of their appropriate use in international travellers.

Layered social influence promotes multiculturality in the Axelrod model.

Despite the presence of increasing pressure towards globalisation, the coexistence of different cultures is a distinctive feature of human societies. However, how multiculturality can emerge in a population of individuals inclined to imitation, and how it remains stable under cultural drift, i.e. the spontaneous mutation of traits in the population, still needs to be understood. To solve such a problem, we propose here a microscopic model of culture dissemination which takes into account that, in real social systems, the interactions are organised in various layers corresponding to different interests or topics. We show that the addition of multiplexity in the modeling of our society generates qualitatively novel dynamical behavior, producing a new stable regime of cultural diversity. This finding suggests that the layered organisation of social influence typical of modern societies is the key ingredient to explain why and how multiculturality emerges and thrives in our world.

Spatio-Temporal Analysis of Micro Economic Activities in Rome Reveals Patterns of Mixed-Use Urban Evolution.

Understanding urban growth is one with understanding how society evolves to satisfy the needs of its individuals in sharing a common space and adapting to the territory. We propose here a quantitative analysis of the historical development of a large urban area by investigating the spatial distribution and the age of commercial activities in the whole city of Rome. We find that the age of activities of various categories presents a very interesting double exponential trend, with a transition possibly related to the long-term economical effects determined by the oil crisis of the Seventies. The diversification of commercial categories, studied through various measures of entropy, shows, among other interesting features, a saturating behaviour with the density of activities. Moreover, different couples of commercial categories exhibit over the years a tendency to attract in space. Our results demonstrate that the spatio-temporal distribution of commercial activities can provide important insights on the urbanisation processes at work, revealing specific and non trivial socio-economical dynamics, as the presence of crisis periods and expansion trends, and contributing to the characterisation of the maturity of urban areas.

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.

Homophily and missing links in citation networks.

Citation networks have been widely used to study the evolution of science through the lenses of the underlying patterns of knowledge flows among academic papers, authors, research sub-fields, and scientific journals. Here we focus on citation networks to cast light on the salience of homophily, namely the principle that similarity breeds connection, for knowledge transfer between papers. To this end, we assess the degree to which citations tend to occur between papers that are concerned with seemingly related topics or research problems. Drawing on a large data set of articles published in the journals of the American Physical Society between 1893 and 2009, we propose a novel method for measuring the similarity between articles through the statistical validation of the overlap between their bibliographies. Results suggest that the probability of a citation made by one article to another is indeed an increasing function of the similarity between the two articles. Our study also enables us to uncover missing citations between pairs of highly related articles, and may thus help identify barriers to effective knowledge flows. By quantifying the proportion of missing citations, we conduct a comparative assessment of distinct journals and research sub-fields in terms of their ability to facilitate or impede the dissemination of knowledge. Findings indicate that Electromagnetism and Interdisciplinary Physics are the two sub-fields in physics with the smallest percentage of missing citations. Moreover, knowledge transfer seems to be more effectively facilitated by journals of wide visibility, such as Physical Review Letters, than by lower-impact ones. Our study has important implications for authors, editors and reviewers of scientific journals, as well as public preprint repositories, as it provides a procedure for recommending relevant yet missing references and properly integrating bibliographies of papers.

Measuring and modeling correlations in multiplex networks.

The interactions among the elementary components of many complex systems can be qualitatively different. Such systems are therefore naturally described in terms of multiplex or multilayer networks, i.e., networks where each layer stands for a different type of interaction between the same set of nodes. There is today a growing interest in understanding when and why a description in terms of a multiplex network is necessary and more informative than a single-layer projection. Here we contribute to this debate by presenting a comprehensive study of correlations in multiplex networks. Correlations in node properties, especially degree-degree correlations, have been thoroughly studied in single-layer networks. Here we extend this idea to investigate and characterize correlations between the different layers of a multiplex network. Such correlations are intrinsically multiplex, and we first study them empirically by constructing and analyzing several multiplex networks from the real world. In particular, we introduce various measures to characterize correlations in the activity of the nodes and in their degree at the different layers and between activities and degrees. We show that real-world networks exhibit indeed nontrivial multiplex correlations. For instance, we find cases where two layers of the same multiplex network are positively correlated in terms of node degrees, while other two layers are negatively correlated. We then focus on constructing synthetic multiplex networks, proposing a series of models to reproduce the correlations observed empirically and/or to assess their relevance.

Network structure of multivariate time series.

Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range tools and techniques for time series analysis already exist, the increasing availability of massive data structures calls for new approaches for multidimensional signal processing. We present here a non-parametric method to analyse multivariate time series, based on the mapping of a multidimensional time series into a multilayer network, which allows to extract information on a high dimensional dynamical system through the analysis of the structure of the associated multiplex network. The method is simple to implement, general, scalable, does not require ad hoc phase space partitioning, and is thus suitable for the analysis of large, heterogeneous and non-stationary time series. We show that simple structural descriptors of the associated multiplex networks allow to extract and quantify nontrivial properties of coupled chaotic maps, including the transition between different dynamical phases and the onset of various types of synchronization. As a concrete example we then study financial time series, showing that a multiplex network analysis can efficiently discriminate crises from periods of financial stability, where standard methods based on time-series symbolization often fail.

Structural reducibility of multilayer networks.

Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.