We present the first comprehensive characterization of the diffusion of ideas on Twitter, studying more than 5.96 million topics that include both popular and less popular topics. On a data set containing approximately 10 million users and a comprehensive scraping of 196 million tweets, we perform a rigorous temporal and spatial analysis, investigating the time-evolving properties of the subgraphs formed by the users discussing each topic. We focus on two different notions of the spatial: the network topology formed by follower-following links on Twitter, and the geospatial location of the users. We investigate the effect of initiators on the popularity of topics and find that users with a high number of followers have a strong impact on topic popularity. We deduce that topics become popular when disjoint clusters of users discussing them begin to merge and form one giant component that grows to cover a significant fraction of the network. Our geospatial analysis shows that highly popular topics are those that cross regional boundaries aggressively.

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Scientific communities are increasingly adopting machine learning and deep learning models in their applications to accelerate scientific insights. High performance computing systems are pushing the frontiers of performance with a rich diversity of hardware resources and massive scale-out capabilities. There is a critical need to understand fair and effective benchmarking of machine learning applications that are representative of real-world scientific use cases. MLPerf TM is a community-driven standard to benchmark machine learning workloads, focusing on end-to-end performance metrics. In this paper, we introduce MLPerf HPC, a benchmark suite of largescale scientific machine learning training applications, driven by the MLCommons TM Association. We present the results from the first submission round including a diverse set of some of the world's largest HPC systems. We develop a systematic framework for their joint analysis and compare them in terms of data staging, algorithmic convergence and compute performance. As a result, we gain a quantitative understanding of optimizations on different subsystems such as staging and on-node loading of data, compute-unit utilization and communication scheduling enabling overall > 10× (end-to-end) performance improvements through system scaling. Notably, our analysis shows a scale-dependent interplay between the dataset size, a system's memory hierarchy and training convergence that underlines the importance of nearcompute storage. To overcome the data-parallel scalability challenge at large batch-sizes, we discuss specific learning techniques and hybrid data-and-model parallelism that are effective on large systems. We conclude by characterizing each benchmark with respect to low-level memory, I/O and network behaviour to parameterize extended roofline performance models in future rounds.

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