Time-limited states characterize many dynamical processes on networks: disease-infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited-waiting-time processes, and they are particularly important for systems modeled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting-time temporal paths from a source node and time. We propose a method yielding an orders-of-magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in-or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyze reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak.

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Fully decentralised federated learning enables collaborative training of individual machine learning models on distributed devices on a network while keeping the training data localised. This approach enhances data privacy and eliminates both the single point of failure and the necessity for central coordination. Our research highlights that the effectiveness of decentralised federated learning is significantly influenced by the network topology of connected devices. A simplified numerical model for studying the early behaviour of these systems leads us to an improved artificial neural network initialisation strategy, which leverages the distribution of eigenvector centralities of the nodes of the underlying network, leading to a radically improved training efficiency. Additionally, our study explores the scaling behaviour and choice of environmental parameters under our proposed initialisation strategy. This work paves the way for more efficient and scalable artificial neural network training in a distributed and uncoordinated environment, offering a deeper understanding of the intertwining roles of network structure and learning dynamics.

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BackgroundClassification of medical sciences into its sub-branches is crucial for optimum administration of healthcare and specialty training. Due to the rapid and continuous evolution of medical sciences, development of unbiased tools for monitoring the evolution of medical disciplines is required.Methodology/Principal FindingsNetwork analysis was used to explore how the medical sciences have evolved between 1980 and 2015 based on the shared words contained in more than 9 million PubMed abstracts. The k-clique percolation method was used to extract local research communities within the network. Analysis of the shared vocabulary in research papers reflects the trends of collaboration and splintering among different disciplines in medicine. Our model identifies distinct communities within each discipline that preferentially collaborate with other communities within other domains of specialty, and overturns some common perceptions.Conclusions/SignificanceOur analysis provides a tool to assess growth, merging, splitting and contraction of research communities and can thereby serve as a guide to inform policymakers about funding and training in healthcare.