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A neutral network is a subgraph of a Hamming graph, and its principal eigenvalue determines its robustness: the ability of a population evolving on it to withstand errors. Here we consider the most robust small neutral networks: the graphs that interpolate pointwise between hypercube graphs of consecutive dimension (the point, line, line and point in the square, square, square and point in the cube, and so on). We prove that the principal eigenvalue of the adjacency matrix of these graphs is bounded by the logarithm of the number of vertices, and we conjecture an analogous result for Hamming graphs of alphabet size greater than two. [ABSTRACT FROM AUTHOR]

Abstract: We are developing a system to predict the arrival of interplanetary (IP) shocks at the Earth. These events are routinely detected by the Electron, Proton, and Alpha Monitor (EPAM) instrument aboard NASA’s ACE spacecraft, which is positioned at Lagrange Point 1 (L1). In this work, we use historical EPAM data to train an IP shock forecasting algorithm. Our approach centers on the observation that these shocks are often preceded by identifiable signatures in the energetic particle intensity data. Using EPAM data, we trained an artificial neural network to predict the time remaining until the shock arrival. After training this algorithm on 37 events, it was able to forecast the arrival time for 19 previously unseen events. The average uncertainty in the prediction 24h in advance was 8.9h, while the uncertainty improved to 4.6h when the event was 12h away. This system is accessible online, where it provides predictions of shock arrival times using real-time EPAM data. [Copyright &y& Elsevier]