Metric projection for dynamic multiplex networks

Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time series is still an open problem. Here we propose a two-steps strategy to tackle this problem based on the concept of distance (metric) between networks. Given a multiplex graph, first a network of networks is built for each time steps, and then a real valued time series is obtained by the sequence of (simple) networks by evaluating the distance from the first element of the series. The effectiveness of this approach in detecting the occurring changes along the original time series is shown on a synthetic example first, and then on the Gulf dataset of political events

Detecting change points in the large-scale structure of evolving networks

Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving networks is change-point detection, in which we both identify the times at which the large-scale pattern of interactions changes fundamentally and quantify how large and what kind of change occurred. Here, we formalize for the first time the network change-point detection problem within an online probabilistic learning framework and introduce a method that can reliably solve it. This method combines a generalized hierarchical random graph model with a Bayesian hypothesis test to quantitatively determine if, when, and precisely how a change point has occurred. We analyze the detectability of our method using synthetic data with known change points of different types and magnitudes, and show that this method is more accurate than several previously used alternatives. Applied to two high-resolution evolving social networks, this method identifies a sequence of change points that align with known external "shocks" to these networks

Intrinsically Dynamic Network Communities

Community finding algorithms for networks have recently been extended to dynamic data. Most of these recent methods aim at exhibiting community partitions from successive graph snapshots and thereafter connecting or smoothing these partitions using clever time-dependent features and sampling techniques. These approaches are nonetheless achieving longitudinal rather than dynamic community detection. We assume that communities are fundamentally defined by the repetition of interactions among a set of nodes over time. According to this definition, analyzing the data by considering successive snapshots induces a significant loss of information: we suggest that it blurs essentially dynamic phenomena - such as communities based on repeated inter-temporal interactions, nodes switching from a community to another across time, or the possibility that a community survives while its members are being integrally replaced over a longer time period. We propose a formalism which aims at tackling this issue in the context of time-directed datasets (such as citation networks), and present several illustrations on both empirical and synthetic dynamic networks. We eventually introduce intrinsically dynamic metrics to qualify temporal community structure and emphasize their possible role as an estimator of the quality of the community detection - taking into account the fact that various empirical contexts may call for distinct `community' definitions and detection criteria.Comment: 27 pages, 11 figure

Optimizing surveillance for livestock disease spreading through animal movements

The spatial propagation of many livestock infectious diseases critically depends on the animal movements among premises; so the knowledge of movement data may help us to detect, manage and control an outbreak. The identification of robust spreading features of the system is however hampered by the temporal dimension characterizing population interactions through movements. Traditional centrality measures do not provide relevant information as results strongly fluctuate in time and outbreak properties heavily depend on geotemporal initial conditions. By focusing on the case study of cattle displacements in Italy, we aim at characterizing livestock epidemics in terms of robust features useful for planning and control, to deal with temporal fluctuations, sensitivity to initial conditions and missing information during an outbreak. Through spatial disease simulations, we detect spreading paths that are stable across different initial conditions, allowing the clustering of the seeds and reducing the epidemic variability. Paths also allow us to identify premises, called sentinels, having a large probability of being infected and providing critical information on the outbreak origin, as encoded in the clusters. This novel procedure provides a general framework that can be applied to specific diseases, for aiding risk assessment analysis and informing the design of optimal surveillance systems.Comment: Supplementary Information at https://sites.google.com/site/paolobajardi/Home/archive/optimizing_surveillance_ESM_l.pdf?attredirects=

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table

Fast filtering and animation of large dynamic networks

Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted graph and visualize it by either creating a movie, or by streaming it to an interactive network visualization tool. The algorithm is an approximation of exponential sliding time-window that scales linearly with the number of interactions. We compare the algorithm against rectangular and exponential sliding time-window methods. Our network filtering algorithm: i) captures persistent trends in the structure of dynamic weighted networks, ii) smoothens transitions between the snapshots of dynamic network, and iii) uses limited memory and processor time. The algorithm is publicly available as open-source software.Comment: 6 figures, 2 table

Can co-location be used as a proxy for face-to-face contacts?

Technological advances have led to a strong increase in the number of data collection efforts aimed at measuring co-presence of individuals at different spatial resolutions. It is however unclear how much co-presence data can inform us on actual face-to-face contacts, of particular interest to study the structure of a population in social groups or for use in data-driven models of information or epidemic spreading processes. Here, we address this issue by leveraging data sets containing high resolution face-to-face contacts as well as a coarser spatial localisation of individuals, both temporally resolved, in various contexts. The co-presence and the face-to-face contact temporal networks share a number of structural and statistical features, but the former is (by definition) much denser than the latter. We thus consider several down-sampling methods that generate surrogate contact networks from the co-presence signal and compare them with the real face-to-face data. We show that these surrogate networks reproduce some features of the real data but are only partially able to identify the most central nodes of the face-to-face network. We then address the issue of using such down-sampled co-presence data in data-driven simulations of epidemic processes, and in identifying efficient containment strategies. We show that the performance of the various sampling methods strongly varies depending on context. We discuss the consequences of our results with respect to data collection strategies and methodologies