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SUMMARY:Interacting Hopf monoids: the algebra of signal flow diagrams - Fa
 bio Zanasi\,  Radboud University of Nijmegen\, Netherlands
DTSTART:20160129T140000Z
DTEND:20160129T150000Z
UID:TALK62231@talks.cam.ac.uk
CONTACT:Ohad Kammar
DESCRIPTION:This talk illustrates the signal flow calculus\, an algebraic 
 and diagrammatic foundation of signal processing circuits. Signal flow gra
 phs\, a class of circuits that play a foundational role in control theory\
 , are recovered via a Kleene’s theorem\, as the rational fragment of the
  calculus. The high-point of our developments is a sound and complete axio
 matisation for semantic equivalence\, which we call the theory of interact
 ing Hopf monoids (IH). The relevance of IH goes beyond the signal flow cal
 culus: its equations describe the interplay of familiar structures\, such 
 as Frobenius monoids and Hopf monoids\, in a way that appeared independent
 ly in other research threads\, in quantum information theory and concurren
 cy theory. Our approach gives a formal explanation for this ubiquity\, by 
 showing that the equations of IH present categories of linear subspaces 
 — completeness for the signal flow calculus follows as a corollary. This
  characterisation passes through a modular account of IH : its axioms are 
 explained in terms of composition of simpler algebraic theories\, using di
 stributive laws of PROPs as in the work of Steve Lack.\n\nThis talk is bas
 ed on joint work with Filippo Bonchi and Pawel Sobocinski.
LOCATION:SS03
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