Serendipitous synthesis of a ditwistane: a one-step access!

4-tert-Butyl-2-cyclohexen-1-one dimerizes in THF solution via its kinetic enolate, leading to di-tert-butylditwistane 8 in up to 36% yield (−78 °C → room temp., protonolysis, flash chromatography). X-ray crystallography shows that 8 incorporates one R and one S enantiomer of the starting ketone; none of the diastereomeric ditwistanes epi-8, epi’-8 or iso-8 was isolated. This means that the formation of 8 proceeds with mutual kinetic resolution and 100% induced diastereoselectivity.     

Non-projectability of polytope skeleta

We investigate necessary conditions for the existence of projections of polytopes that preserve full k-skeleta. More precisely, given the combinatorics of a polytope and the dimension e of the target space, what are obstructions to the existence of a geometric realization of a polytope with the given combinatorial type such that a linear projection to e-space strictly preserves the k-skeleton. Building on the work of Sanyal (2009), we develop a general framework to calculate obstructions to the existence of such realizations using topological combinatorics. Our obstructions take the form of graph colorings and linear integer programs. We focus on polytopes of product type and calculate the obstructions for products of polygons, products of simplices, and wedge products of polytopes. Our results show the limitations of constructions for the deformed products of polygons of Sanyal and Ziegler (2010) and the wedge product surfaces of Rörig and Ziegler (2011) and complement their results.     

A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s

In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces.     

Structure-function analysis of an enzymatic prenyl transfer reaction identifies a reaction chamber with modifiable specificity

Fungal indole prenyltransferases participate in a multitude of biosynthetic pathways. Their ability to prenylate diverse substrates has attracted interest for potential use in chemoenzymatic synthesis. The fungal indole prenyltransferase FtmPT1 catalyzes the prenylation of brevianamide F in the biosynthesis of fumitremorgin-type alkaloids, which show diverse pharmacological activities and are promising candidates for the development of antitumor agents. Here, we report crystal structures of unliganded Aspergillus fumigatus FtmPT1 as well as of a ternary complex of FtmPT1 bound to brevianamide F and an analogue of its isoprenoid substrate dimethylallyl diphosphate. FtmPT1 assumes a rare α/β-barrel fold, consisting of 10 circularly arranged β-strands surrounded by α-helices. Catalysis is performed in a hydrophobic reaction chamber at the center of the barrel. In combination with mutagenesis experiments, our analysis of the liganded and unliganded structures provides insight into the mechanism of catalysis and the determinants of regiospecificity. Sequence conservation of key features indicates that all fungal indole prenyltransferases possess similar active site architectures. However, while the dimethylallyl diphosphate binding site is strictly conserved in these enzymes, subtle changes in the reaction chamber likely allow for the accommodation of diverse aromatic substrates for prenylation. In support of this concept, we were able to redirect the regioselectivity of FtmPT1 by a single mutation of glycine 115 to threonine. This finding provides support for a potential use of fungal indole prenyltransferases as modifiable bioreactors that can be engineered to catalyze highly specific prenyl transfer reactions.     

Fermionic atoms in a three dimensional optical lattice: observing Fermi surfaces, dynamics, and interactions

We have studied interacting and noninteracting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Because of the confining potential, gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied, and the time scale is measured to be an order of magnitude larger than the tunneling time in the lattice. Using a Feshbach resonance, we increase the interaction between atoms in two different spin states and dynamically induce a coupling between the lowest energy bands. We observe a shift of this coupling with respect to the Feshbach resonance in free space which is anticipated for strongly confined atoms.     

Explicit Solution of a Non-Linear Filtering Problem for Lévy Processes with Application to Finance

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time inhomogeneity of the jump size density. We apply the explicit formula to obtain the optimal filter for the corresponding filtering problem.     

Zur Natur der Aluminiumsilicatniederschläge aus Na2H2SiO4-und AlCl3-Lösungen bei neutraler Reaktion

On addition, at neutral reaction, of increasing amounts of AlCl₃ solutions to 0.005 m Na-silicate solutions, in which the silicate anions are monomeric, amorphous, almost Na⁺-free precipitates are formed being at first characterised by a higher atomic Al:Si ratio than the total Al:Si mixing ratio. With increasing Al:Si addition, the Al:Si ratio of the precipitates increases until — at a 3:1 ratio in both the liquid and the solid phase — a definite, “saturated” compound, {[(OH)₂AlO]₃SiOH · aq}, is formed. In this compound the silicate anions are monomeric and not condensable at room temperature. This is valid, too, for precipitates from Al:Si > 3 which contain, besides the “saturated” compound, free Al hydroxide. The first-mentioned precipitates with Al:Si < 3, however, contain polymeric Si units which easily condense to more high-polymeric silicate anions.