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Based on those meetings, we argue that the rapid proliferation of digital data generators, the unprecedented growth in the volume and diversity of the data they generate, and the intense evolution of the methods for analyzing and using that data are radically reshaping the landscape of scientific computing. The most critical problems involve the logistics of wide-area, multistage workflows that will move back and forth across the computing continuum, between the multitude of distributed sensors, instruments and other devices at the networks edge, and the centralized resources of commercial clouds and HPC centers. We suggest that the prospects for the future integration of technological infrastructures and research ecosystems need to be considered at three different levels. First, we discuss the convergence of research applications and workflows that establish a research paradigm that combines both HPC and HDA, where ongoing progress is already motivating efforts at the other two levels. Second, we offer an account of some of the problems involved with creating a converged infrastructure for peripheral environments, that is, a shared infrastructure that can be deployed throughout the network in a scalable manner to meet the highly diverse requirements for processing, communication, and buffering\/storage of massive data workflows of many different scientific domains. Third, we focus on some opportunities for software ecosystem convergence in big, logically centralized facilities that execute large-scale simulations and models and\/or perform large-scale data analytics. 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