James Hook works at the intersection of Tropical Mathematics, Numerical Linear Algebra, Dynamical Systems and Machine Learning. James completed a PhD in Dynamical Systems, under the supervision of Professor David Broomhead, at the University of Manchester in 2012, where he became interested in max-plus algebra and queuing systems. After a one year EPSRC Doctoral Prize Fellowship he took a Postdoc position at Manchester with Professor Francoise Tisseur, developing applications of max-plus algebra in conventional numerical linear algebra. In 2016 he took up a Prize Fellowship at the University of Bath.

AG 1, AG 2, AG 3, AG 4, AG 5, SWS, RG1, MMCI   Info

Expert Audience

English

60 Minutes

Saarbrücken

Tropical algebra concerns any semiring whose ‘addition’ operation is max or min. In my talk I will focus on the max-plus semiring Rmax = [R∪{−∞},⊕,⊗], with a⊕b = max{a,b} and a⊗b = a+b, for all a,b ∈ Rmax. Tropical algebra has the potential to describe certain classically non-linear phenomena in a linear way. For example many queuing models turn out to be linear over Rmax. Similarly many discrete optimizations problems including shortest paths problems have a tropically linear structure.
When dealing with datasets from such applications it is natural to ask whether tropical analogues of classical linear algebra approaches will be effective. To this end I will discuss using max-plus linear regression to analyze time series data recorded from a queuing system and using max-plus low rank approximate matrix factorization to reveal structure in large networks.

Daniela Alessi

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