Nonclassical Recrystallization

Applications in the fields of materials science and nanotechnology increasingly demand monodisperse nanoparticles in size and shape. Up to now, no general purification procedure exists to thoroughly narrow the size and shape distributions of nanoparticles. Here, we show by analytical ultracentrifugation (AUC) as an absolute and quantitative high-resolution method that multiple recrystallizations of nanocrystals to mesocrystals is a very efficient tool to generate nanocrystals with an excellent and so-far unsurpassed size-distribution (PDI_c=1.0001) and shape. Similar to the crystallization of molecular building blocks, nonclassical recrystallization removes “colloidal” impurities (i.e., nanoparticles, which are different in shape and size from the majority) by assembling them into a mesocrystal. In the case of nanocrystals, this assembly can be size- and shape-selective, since mesocrystals show both long-range packing ordering and preferable crystallographic orientation of nanocrystals. Besides the generation of highly monodisperse nanoparticles, these findings provide highly relevant insights into the crystallization of mesocrystals.     

Tensor method for optimal control problems constrained by fractional three-dimensional elliptic operator with variable coefficients

We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional two- (2D) and three-dimensional (3D) elliptic operators with variable coefficients. We solve the governing equation for the control function which includes a sum of the fractional operator and its inverse, both discretized over large 3D $n\times n\times n$ spacial grids. Using the diagonalization of the arising matrix-valued functions in the eigenbasis of the one-dimensional Sturm–Liouville operators, we construct the rank-structured tensor approximation with controllable precision for the discretized fractional elliptic operators and the respective preconditioner. The right-hand side in the constraining equation (the optimal design function) is supposed to be represented in a form of a low-rank canonical tensor. Then the equation for the control function is solved in a tensor structured format by using preconditioned CG iteration with the adaptive rank truncation procedure that also ensures the accuracy of calculations, given an $\epsilon$-threshold. This method reduces the numerical cost for solving the control problem to $O(n\log n)$ (plus the quadratic term $O(n^2)$ with a small weight), which outperforms traditional approaches with $O(n^3\log n)$ complexity in the 3D case. The storage for the representation of all 3D nonlocal operators and functions involved is also estimated by $O(n\log n)$. This essentially outperforms the traditional methods operating with fully populated $n^3\times n^3$ matrices and vectors in ${?}^{n^3}$. Numerical tests for 2D/3D control problems indicate the almost linear complexity scaling of the rank truncated preconditioned conjugate gradient iteration in the univariate grid size n.     

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.     

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.     

Determination of Testosterone Metabolites in Rat Hepatocytes with and without Cryopreservation by On-Line SPE Column-Switching LC and MS Detection

In a recently published paper development of a sensitive automated “on-line” solid-phase extraction (SPE)/RP-HPLC assay for 6β-hydroxytestosterone (6β-OHT) with corticosterone as the internal standard (IS) was reported and its potential for quantification of various testosterone metabolites in culture media reflecting metabolic activity of cultured human and animal hepatocytes demonstrated [1]. In this following contribution the technique has been extended to determination of another five testosterone metabolites in cultured rat hepatocytes using an identical “on-line” SPE/RP-HPLC procedure and detection by tandem MS-MS with an atmospheric pressure chemical ionization (APCI) source in the selected reaction monitoring (SRM) mode as that described in [1]. All six testosterone metabolites, namely 2α-OHT, 2β-OHT, 6α-OHT, 6β-OHT, 7α-OHT and 16α-OHT, could be sufficiently separated from each other and thus an unequivocal assignment to the individual structures was achieved. Validation data are presented specifying the limits of quantitation as well as the mean values of the coefficients of variation (CV) for the target analytes and the accuracy obtained at five different days. Regio- and stereoselective testosterone hydroxylation by rat hepatocytes was measured in a long-term culture system with and without exposure to rifampicin as an inducer of liver CYP 3A4 activity. In addition, testosterone hydroxylation was analyzed in cultures of cryopreserved hepatocytes that had been stored at −196 °C. The rat hepatocytes were cultured after thawing for up to 11 days and induction of testosterone hydroxylase activity could be demonstrated in cultures which underwent a new cryopreservation protocol. This paper is dedicated to Professor Hinrich Cramer on the occasion of his 75th birthday.     

Aldehyde

Ohne Zusammenfassung     

Freezing point osmometry of milk to determine the additional water content – an issue in general quality control and German food regulation

Background  

The determination of the osmolality of aqueous samples using a freezing point osmometer is a well-established, routine laboratory method. In addition to their use in clinical and pharmaceutical laboratories, freezing point osmometers are also employed in food testing laboratories. One application is the determination of the osmolality of milk. Although cow's milk is a natural product whose water content is approximately 87%, the osmolality of milk is a significant value when the milk is collected from a larger population of animals. This value is used in milk processing to control the water content, based on the German Food Control Regulations for Milk.     

Matroid bases with cardinality constraints on the intersection

Mathematical Programming - Given two matroids $$\mathcal {M}_{1} = (E, \mathcal {B}_{1})$$ and $$\mathcal {M}_{2} = (E, \mathcal {B}_{2})$$ on a common ground set E with base sets $$\mathcal...