Synthesis of Rhodomyrtone Analogs Modified at C7

We developed a route to rhodomyrtone analogs that feature different acyl groups at C7. Since electrophilic substitution reactions on the aryl part of the rhodomyrtone core led to C5 derivatives, the C5 position was blocked by a chlorine. Subsequent Duff type formylation followed by Grignard addition to the aldehyde group and oxidation gave various phenones. The benzyl protecting groups were removed by hydrogenation or boron tribromide. Some derivatives turned out to be quite active against multiple resistant Staphylococcus aureus strains and a rhodomyrtone resistant mutant (Rom^R). The chlorine at C5 seems to have a beneficial effect on the antibacterial activity.     

Digital Microfluidics and Magnetic Bead-Based Intact Proteoform Elution for Quantitative Top-down Nanoproteomics of Single C. elegans Nematodes

While most nanoproteomics approaches for the analysis of low-input samples are based on bottom-up proteomics workflows, top-down approaches enabling proteoform characterization are still underrepresented. Using mammalian cell proteomes, we established a facile one-pot sample preparation protocol based on protein aggregation on magnetic beads and intact proteoform elution using 40 % formic acid. Performed on a digital microfluidics device, the workflow enabled sensitive analyses of single Caenorhabditis elegans nematodes, thereby increasing the number of proteoform identifications compared to in-tube sample preparation by 46 %. Label-free quantification of single nematodes grown under different conditions allowed to identify changes in the abundance of proteoforms not distinguishable by bottom-up proteomics. The presented workflow will facilitate proteoform-directed analysis on samples of limited availability.     

Understanding the Buoy Effect of Surface-Enriched Pt Complexes in Ionic Liquids: A Combined ARXPS and Pendant Drop Study**

Recently, we demonstrated that Pt catalyst complexes dissolved in the ionic liquid (IL) [C₄C₁Im][PF₆] can be deliberately enriched at the IL surface by introducing perfluorinated substituents, which act like buoys dragging the metal complex towards the surface. Herein, we extend our previous angle-resolved X-ray photoelectron spectroscopy (ARXPS) studies at complex concentrations between 30 and 5 %_mol down to 1 %_mol and present complementary surface tension pendant drop (PD) measurements under ultraclean vacuum conditions. This combination allows for connecting the microscopic information on the IL/gas interface derived from ARXPS with the macroscopic property surface tension. The surface enrichment of the Pt complexes is found to be most pronounced at 1 %_mol. It also displays a strong temperature dependence, which was not observed for 5 %_mol and above, where the surface is already saturated with the complex. The surface enrichment deduced from ARXPS is also reflected by the pronounced decrease in surface tension with increasing concentration of the catalyst. We furthermore observe by ARXPS and PD a much stronger surface affinity of the buoy-complex as compared to the free ligands in solution. Our results are highly interesting for an optimum design of IL-based catalyst systems with large contact areas to the surrounding reactant/product phase, such as in supported IL phase (SILP) catalysis.     

A generalization of Euler's hypergeometric transformation

Euler's transformation formula for the Gauss hypergeometric function  is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but not linearly. Its consequences for hypergeometric summation are explored. It has as a corollary a summation formula of Slater. From this formula new one-term evaluations of and are derived by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of with linearly constrained parameters are derived as well.

     

On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

By formally invoking the Wiener–Hopf method, we explicitly solve a one‐dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called surface plasmon‐polariton (SPP), of small wavelength on a semiinfinite, flat conducting sheet irradiated by a plane wave in two spatial dimensions. This setting is germane to wave diffraction by edges of large sheets of single‐layer graphene. Our analytical approach includes (i) formulation of a functional equation in the Fourier domain; (ii) evaluation of a split function, which is expressed by a contour integral and is a key ingredient of the Wiener–Hopf factorization; and (iii) extraction of the SPP as a simple‐pole residue of a Fourier integral. Our analytical solution is in good agreement with a finite‐element numerical computation.     

Protection of flows under targeted attacks

We present a new robust optimization model for the problem of maximizing the amount of flow surviving the attack of an interdictor. Given some path flow, our model allows the interdictor to specify the amount of flow removed from each path individually. In contrast to previous models, for which no efficient algorithms are known, the most important basic variants of our model can be solved in poly-time. We also consider extensions where there is a budget to set the interdiction costs.     

Colliding stacks: A large deviations analysis

We analyze the performance of a prototypical scheme for shared storage allocation: two initially empty stacks evolving in a contiguous block of memory of size m. We treat the case in which the stacks are more likely to shrink than grow, but with the probabilities of insertion and deletion allowed to depend arbitrarily on stack height as a fraction of m. New results are obtained on the m → ∞ asymptotics of the stack collision time, and of the final stack heights. The results of Wentzell and Freidlin on the large deviations of Markov chains are used, and the relation of their formalism to the Hamiltonian formulation of classical mechanics is emphasized. Certain results on higher-order asymptotics follow from WKB expansions.     

COMPUTATIONAL MULTISCALE METHODS FOR LINEAR HETEROGENEOUS POROELASTICITY

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.     

On the Asymptotics of Fekete-Type Points for Univariate Radial Basis Interpolation

Suppose that K ^d is compact and that we are given a function fC(K) together with distinct points x_iK, 1in. Radial basis interpolation consists of choosing a fixed (basis) function g : ⁺→ and looking for a linear combination of the translates g(|x−x_j|) which interpolates f at the given points. Specifically, we look for coefficients c_j such that has the property that F(x_i)=f(x_i), 1in. The Fekete-type points of this process are those for which the associated interpolation matrix [g(|x_i−x_j|)]_1i,jn has determinant as large as possible (in absolute value). In this work, we show that, in the univariate case, for a broad class of functions g, among all point sequences which are (strongly) asymptotically distributed according to a weight function, the equally spaced points give the asymptotically largest determinant. This gives strong evidence that the Fekete points themselves are indeed asymptotically equally spaced.