2-Acetamino-1,2-dideoxynojirimycin—lysine hybrids as hexosaminidase inhibitors

Cyclisation by double reductive amination of 2-acetamino-2-deoxy-d-xylo-hexos-5-ulose with N-2 protected l-lysine derivatives provided 2-acetamino-1,2-dideoxynojirimycin derivatives without any observable epimer formation at C-5. Modifications on the lysine moiety gave access to lipophilic derivatives that exhibited improved hexosaminidase inhibitory activities.     

Set-valued average value at risk and its computation

New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ’regulator’ version is independent from any market model whereas the second version, called the market extension, takes trading opportunities into account. Essential properties of both versions are proven and an algorithmic approach is provided which admits to compute the values of both versions over finite probability spaces. Several examples illustrate various features of the theoretical constructions.     

The expected degree of minimal spanning forests

We give a lower bound on the expected degree of the free minimal spanning forest of a vertex transitive graph in terms of its spectral radius. This result answers a question of Lyons-Peres-Schramm and simplifies the Gaboriau-Lyons proof of the measurable-group-theoretic solution to von Neumann’s problem.In the second part we study a relative version of the free minimal spanning forest. As a consequence of this study we can show that non-torsion unitarizable groups have fixed price one.