We introduce a new distributional invariance principle, called ‘partial spreadability’, which emerges from the representation theory of Thompson monoid F+ in noncommutative probability spaces. show that partially spreadable sequence random variables is adapted to local Markov filtration. Conversely we large class stationary sequences provides representations F+. In particular case classical spa...

We study a variant of the stochastic multiarmed bandit problem where the set of available arms varies arbitrarily with time (also known as the sleeping bandit problem). We focus on the Thompson Sampling algorithm and consider a regret notion defined with respect to the best available arm. Our main result is anO(log T ) regret bound for Thompson Sampling, which generalizes a similar bound known ...

We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson-Stein groups F (n1, ..., nk) such that n1 − 1|ni − 1 ∀i ∈ {1, ..., k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the ThompsonStein groups. This result al...

Q1: Au: Ryan is listed in the References as McDonough-Ryan. Please confirm the correct author name and revise where necessary. Q2: Au: Should Szucs be spelled Szücs?. Q3: Au: Wood, Willmens, Nuerk, & Fischer, 2008, is listed in the References as Wood, Nuerk, Willmens, & Fischer, 2008, and Willmens is spelled Willmes. Please confirm the correct author order and correct spelling of Willmens vs. W...

Barron, E. S. G. & Singer, T. P. (1945). J. biol. Chem. 157, 221. Cohen, A., King, H. & Strangeways, W. I. (1931). J. chem. Soc. p. 3043. Eagle, H. (1939). J. Pharmacol. 66, 436. Hopkins, F. G. & Morgan, E. J. (1938). Biochem. J. 32,611. Peters, R. A., Sinclair, H. M. & Thompson, R. H. S. (1940). Report to Ministry of Supply, no. 4.* Peters, R. A., Sinclair, H. M. & Thompson, R. H. S. (1946). B...