Subdivision Strategies for Boxes in Branch-and-Bound Nonlinear Solvers and Verification

Most verified solvers for nonlinear interval systems of equations comprise two strategies: a branch-and-bound-type “location” phase for excluding regions that cannot contain a solution, and a “verification” phase for proving that the remaining regions do indeed contain solutions. In the first phase, subdivision is crucial for the efficiency of the solvers. We discuss several ways for subdivision and present robust strategies that are suited for a variety of nonlinear systems. Particular focus is on the choice of subdivision directions, subdivision points and the handling of unbounded intervals. Furthermore we discuss a method to discard parts of a box within subdivision. Numerical evaluations are given based on the nonlinear interval solver SONIC. In the verification phase, further subdivision can increase the strength of the verification tests. In this paper, we address methods for the rigorous implementation of symmetrical subdivision which is needed, e.g., in existence tests based on Borsuk’s theorem.     

Development and validation of an LC–MS/MS method for the quantification of artificial sweeteners in human matrices

Artificial sweeteners are widely used as substitutes for sugar. The sweeteners are generally considered safe, however their whereabouts during pregnancy and lactation and the effect on child development are poorly explored. There is a need for new tools to measure these substances during pregnancy and lactation. Here, we describe the development and validation of a sensitive liquid chromatography–tandem mass spectrometry method for the simultaneous quantification of acesulfame, cyclamate, saccharin and sucralose in human plasma, umbilical cord blood, amniotic fluid and breast milk. The samples were prepared by protein precipitation and separated on a Luna Omega Polar C₁₈ column (2.1 × 50 mm, 1.6 μm). Electrospray ionization in negative mode and multiple reaction monitoring were used to monitor the ion transitions. The validated concentration ranges were from 1 to 500 ng/ml (10–500 ng/ml for sucralose). Interassay precisions were all ≤15% and the accuracies were within ±15%. Stability, linearity, dilution integrity, carryover and recovery were also examined and satisfied the validation criteria. Finally, this analytical method was successfully applied on spiked samples of plasma, umbilical cord blood, amniotic fluid and breast milk, proving its suitability for use in clinical studies on artificial sweeteners, including during pregnancy and lactation.     

Carbohydrate Hydrolase-Inhibitory Activity of Juice-Based Phenolic Extracts in Correlation to Their Anthocyanin/Copigment Profile

Red fruits and their juices are rich sources of polyphenols, especially anthocyanins. Some studies have shown that such polyphenols can inhibit enzymes of the carbohydrate metabolism, such as α-amylase and α-glucosidase, that indirectly regulate blood sugar levels. The presented study examined the in vitro inhibitory activity against α-amylase and α-glucosidase of various phenolic extracts prepared from direct juices, concentrates, and purees of nine different berries which differ in their anthocyanin and copigment profile. Generally, the extracts with the highest phenolic content—aronia (67.7 ± 3.2 g GAE/100 g; cyanidin 3-galactoside; chlorogenic acid), pomegranate (65.7 ± 7.9 g GAE/100 g; cyanidin 3,5-diglucoside; punicalin), and red grape (59.6 ± 2.5 g GAE/100 g; malvidin 3-glucoside; quercetin 3-glucuronide)—showed also one of the highest inhibitory activities against α-amylase (326.9 ± 75.8 μg/mL; 789.7 ± 220.9 μg/mL; 646.1 ± 81.8 μg/mL) and α-glucosidase (115.6 ± 32.5 μg/mL; 127.8 ± 20.1 μg/mL; 160.6 ± 68.4 μg/mL) and, partially, were even more potent inhibitors than acarbose (441 ± 30 μg/mL; 1439 ± 85 μg/mL). Additionally, the investigation of single anthocyanins and glycosylated flavonoids demonstrated a structure- and size-dependent inhibitory activity. In the future in vivo studies are envisaged.     

Polarization optics for X-rays

An experimental arrangement for X-rays is described which is analogous to the optical bench for polarization investigations. Using this arrangement elliptically polarized X-rays should be generated and proved. Although the dynamical theory of X-ray diffraction is needed for X-ray optics the polarization phenomena can be phenomenologically interpreted in analogy to visible light optics. The experimental results showed that with a wedge-shaped crystal used as the phase shifter any polarization state of X-rays can be generated.     

Flow measurements below 50 mum: NMR microscopy experiments in lithographic model pore spaces

Quasi two-dimensional random site percolation model objects have been prepared using a synchrotron radiation lithography technique with a spatial resolution better than 50 microm and an aspect ratio of up to 17. Flow of water through the pore space was studied with the aid of an NMR velocity mapping method and compared with a computational fluid dynamics simulation. In order to be able to measure and map widely distributed flow velocities with microscopic resolution (typically 40 x 40 microm), an experimental protocol that permits one to cover an effectively very wide velocity field of view (0.6-10 mm/s) had to be developed.