Artificial intelligence and all its supporting tools, e.g. machine and deep learning in computational intelligence-based systems, are rebuilding our society (economy, education, life-style, etc.) and promising a new era for the social welfare state. In this paper we summarize recent advances in data science and artificial intelligence within the interplay between natural and artificial computation. A review of recent works published in the latter field and the state the art are summarized in a comprehensive and self-contained way to provide a baseline framework for the international community in artificial intelligence. Moreover, this paper aims to provide a complete analysis and some relevant discussions of the current trends and insights within several theoretical and application fields covered in the essay, from theoretical models in

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