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With human help, the mammals can defy'the world's most fundamental natural boundaries.' Breakthroughs, discoveries, and DIY tips sent every weekday. Despite not exactly being world-renowned swimmers, pigs have spread across the Asia-Pacific region for thousands of years . With the genetic and archeological data from over 700 pigs, a team of scientists documented how people helped the mammals make their way across thousands of miles. "This research reveals what happens when people transport animals enormous distances, across one of the world's most fundamental natural boundaries," evolutionary geneticist and study co-author author Dr. David Stanton of the University of Cardiff and Queen Mary University of London said in a statement. "These movements led to pigs with a melting pot of ancestries. These patterns were technically very difficult to disentangle, but have ultimately helped us understand how and why animals came to be distributed across the Pacific islands."

This essay develops a parallel between the Fundamental Theorem of Galois Theory and the Stone--Weierstrass theorem: both can be viewed as assertions that tie the distinguishing power of a class of objects to their expressive power. We provide an elementary theorem connecting the relevant notions of "distinguishing power". We also discuss machine learning and data science contexts in which these theorems, and more generally the theme of links between distinguishing power and expressive power, appear. Finally, we discuss the same theme in the context of linguistics, where it appears as a foundational principle, and illustrate it with several examples.

For example, in the Pandemic Response Challenge experiment, the context consisted of data about the geographic region for which the predictions were made, e.g., historical data of COVID-19 cases and intervention policies; actions were future schedules of intervention policies for the region; and outcomes were predicted future cases of COVID-19 along with the stringency

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