Thompson-type formulae

Let X and Y be two nxn Hermitian matrices. In the article "Proof of a conjectured exponential formula" (Linear and Multilinear Algebra (19) 1986, 187-197) R. C. Thompson proved that there exist two nxn unitary matrices U and V such that $$e^{i X}e^{i Y}=e^{i (UXU^*+VBV^*)}.$$ In this note we consider extensions of this result to compact operators as well as to operators in an embeddable II$_1$ factor

Stacked Thompson Bandits

We introduce Stacked Thompson Bandits (STB) for efficiently generating plans that are likely to satisfy a given bounded temporal logic requirement. STB uses a simulation for evaluation of plans, and takes a Bayesian approach to using the resulting information to guide its search. In particular, we show that stacking multiarmed bandits and using Thompson sampling to guide the action selection process for each bandit enables STB to generate plans that satisfy requirements with a high probability while only searching a fraction of the search space.Comment: Accepted at SEsCPS @ ICSE 201

William Francis Thompson (1888–1965) and His Pioneering Studies of the Pacific Halibut, Hippoglossus stenolepis

William Francis Thompson (1888–1965), as a temporary employee of the British Columbia Provincial Fisheries Department, was assigned in 1914 to under-take full-time studies of the Pacific halibut, Hippoglossus stenolepis. The fishery was showing signs of depletion, so Thompson undertook the inquiry into this resource, the first intensive study on the Pacific halibut. Three years later, Thompson, working alone, had provided a basic foundation of knowledge for the subsequent management of this resource. He published seven land-mark papers on this species, and this work marked the first phase of a career in fisheries science that was to last nearly 50 years