Epidemic Threshold in Continuous-Time Evolving Networks

Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold in continuous time through the infection propagator approach. We introduce the {\em weak commutation} condition allowing the interpretation of annealed networks, activity-driven networks, and time scale separation into one formalism. Our work provides a coherent connection between discrete and continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure

Understanding Communication Patterns in MOOCs: Combining Data Mining and qualitative methods

Massive Open Online Courses (MOOCs) offer unprecedented opportunities to learn at scale. Within a few years, the phenomenon of crowd-based learning has gained enormous popularity with millions of learners across the globe participating in courses ranging from Popular Music to Astrophysics. They have captured the imaginations of many, attracting significant media attention - with The New York Times naming 2012 "The Year of the MOOC." For those engaged in learning analytics and educational data mining, MOOCs have provided an exciting opportunity to develop innovative methodologies that harness big data in education.Comment: Preprint of a chapter to appear in "Data Mining and Learning Analytics: Applications in Educational Research

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

Efficient detection of contagious outbreaks in massive metropolitan encounter networks

Physical contact remains difficult to trace in large metropolitan networks, though it is a key vehicle for the transmission of contagious outbreaks. Co-presence encounters during daily transit use provide us with a city-scale time-resolved physical contact network, consisting of 1 billion contacts among 3 million transit users. Here, we study the advantage that knowledge of such co-presence structures may provide for early detection of contagious outbreaks. We first examine the "friend sensor" scheme --- a simple, but universal strategy requiring only local information --- and demonstrate that it provides significant early detection of simulated outbreaks. Taking advantage of the full network structure, we then identify advanced "global sensor sets", obtaining substantial early warning times savings over the friends sensor scheme. Individuals with highest number of encounters are the most efficient sensors, with performance comparable to individuals with the highest travel frequency, exploratory behavior and structural centrality. An efficiency balance emerges when testing the dependency on sensor size and evaluating sensor reliability; we find that substantial and reliable lead-time could be attained by monitoring only 0.01% of the population with the highest degree.Comment: 4 figure

Quantifying the effect of temporal resolution on time-varying networks

Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the description of a dynamical process taking place upon a time-varying network. We focus on the elementary random walk, and put forth a simple mathematical framework that well describes the behavior observed on real datasets. The analytical description of the bias introduced by time integrating techniques represents a step forward in the correct characterization of dynamical processes on time-varying graphs