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Explore advanced database query processing foundations in this comprehensive lecture by Professor Dan Olteanu from the University of Oxford. Delve into worst-case optimal join algorithms for various data representation formalisms, including LeapFrog TrieJoin for relational data and FDB for factorized data. Examine recent developments in computing functional aggregate queries over joins, which are widely used across Computer Science disciplines. Discover how to apply this theory to in-database computation of optimization problems in machine learning, focusing on algorithms and complexity for problems solved over database joins. Access the full slide deck for in-depth study and explore a related lecture for more information on machine learning applications in database systems.