Fall 2016

A Topological Approach to Compositionality in Complex Systems

Thursday, Dec. 8, 2016 11:50 am12:10 pm PST

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Calvin Lab Auditorium

According to Frege’s principle of compositionality, the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This talk will try to show how this principle acquires new unexpected features in the context of complex systems – which are composed of many non-identical elements, entangled in loops of nonlinear interactions – due to the characteristic 'emergence' effects. Indeed, representing expression composition as a path algebra construct in data space (the space on which composition rules operate) and embedding the latter in a simplicial complex – geometric and at the same time combinatorial notion coming from algebraic topology – provides us with a mathematical structure that naturally allows for a finer classification of compositional rules in equivalence classes not identifiable otherwise.