Triangulations in CGAL

This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library .     

Simplified liquid chromatographic determination of glyphosate and metabolite residues in environmental water using post-column fluorogenic labelling

Glyphosate and its metabolite aminomethylphosphonic acid in environmental water can be preconcentrated with an anion-exchange column, eluted with potassium citrate solution and determined directly by liquid chromatography with a post-column reactor and a fluorescence detector. The limit of detection and average recovery are 1 μg 1^?1 and 89.3% for glyphosate and 0.4 μg l^?1 and 86.3% for the metabolite.     

Total Synthesis of Albicidin: A Lead Structure from Xanthomonas albilineans for Potent Antibacterial Gyrase Inhibitors

The peptide antibiotic albicidin, which is synthesized by the plant pathogenic bacterium Xanthomonas albilineans, displays remarkable antibacterial activity against various Gram‐positive and Gram‐negative microorganisms. The low amounts of albicidin obtainable from the producing organism or through heterologous expression are limiting factors in providing sufficient material for bioactivity profiling and structure–activity studies. Therefore, we developed a convergent total synthesis route toward albicidin. The unexpectedly difficult formation of amide bonds between the aromatic amino acids was achieved through a triphosgene‐mediated coupling strategy. The herein presented synthesis of albicidin confirms the previously determined chemical structure and underlines the extraordinary antibacterial activity of this compound. The synthetic protocol will provide multigram amounts of albicidin for further profiling of its drug properties.     

Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization

We consider the problem of minimizing a continuous function f over a compact set \({\mathbf {K}}\). We analyze a hierarchy of upper bounds proposed by Lasserre (SIAM J Optim 21(3):864–885, 2011), obtained by searching for an optimal probability density function h on \({\mathbf {K}}\) which is a sum of squares of polynomials, so that the expectation \(\int _{{\mathbf {K}}} f(x)h(x)dx\) is minimized. We show that the rate of convergence is no worse than \(O(1/\sqrt{r})\), where 2r is the degree bound on the density function. This analysis applies to the case when f is Lipschitz continuous and \({\mathbf {K}}\) is a full-dimensional compact set satisfying some boundary condition (which is satisfied, e.g., for convex bodies). The rth upper bound in the hierarchy may be computed using semidefinite programming if f is a polynomial of degree d, and if all moments of order up to \(2r+d\) of the Lebesgue measure on \({\mathbf {K}}\) are known, which holds, for example, if \({\mathbf {K}}\) is a simplex, hypercube, or a Euclidean ball.     

A Grobman–Hartman Theorem for Control Systems

We consider the problem of locally linearizing a control system via topological transformations. According to [2,3], there is no naive generalization of the classical Grobman–Hartman theorem for ODEs to control systems: a generic control system, when viewed as a set of under-determined differential equations parametrized by the control, cannot be linearized using pointwise transformations on the state and the control values. However, if we allow the transformations to depend on the control at a functional level (open loop transformations), we are able to prove a version of the Grobman–Hartman theorem for control systems.     

Biomimetic membrane arrays on cast hydrogel supports

Lipid bilayers are intrinsically fragile and require mechanical support in technical applications based on biomimetic membranes. Tethering the lipid bilayer membranes to solid substrates, either directly through covalent or ionic substrate-lipid links or indirectly on substrate-supported cushions, provides mechanical support but at the cost of small molecule transport through the membrane-support sandwich. To stabilize biomimetic membranes while allowing transport through a membrane-support sandwich, we have investigated the feasibility of using an ethylene tetrafluoroethylene (ETFE)/hydrogel sandwich as the support. The sandwich is realized as a perforated surface-treated ETFE film onto which a hydrogel composite support structure is cast. We report a simple method to prepare arrays of lipid bilayer membranes with low intrinsic electrical conductance on the highly permeable, self-supporting ETFE/hydrogel sandwiches. We demonstrate how the ETFE/hydrogel sandwich support promotes rapid self-thinning of lipid bilayers suitable for hosting membrane-spanning proteins.     

The design, synthesis and photochemical study of a biomimetic cyclodextrin model of photoactive yellow protein (PYP)

The design, synthesis and study of the photophysical and photochemical properties of the first biomimetic cyclodextrin (CD) model of photoactive yellow protein (PYP) are described. This model bears a deprotonated trans-p-coumaric acid chromophore, covalently linked via a cysteine moiety to a permethylated 6-monoamino β-CD. NMR and UV/Visible spectroscopy studies showed the formation of strong self-inclusion complexes in water at basic pH. Steady-state photolysis demonstrated that, unlike the free chromophore in solution, excitation of the model molecule leads to the formation of a photoproduct identified as the cis isomer by NMR spectroscopy. These observations provide evidence that the restricted CD cavity offers a promising framework for the design of biomimetic models of the PYP hydrophobic pocket.     

An explicit model of default time with given survival probability

For a given filtered probability space (Ω,F,P), an F-adapted continuous increasing process Λ and a positive P-F local martingale N such that Λ₀=0 and N_te^−Λ_t≤1, we construct a probability measure Q^Z and a random time τ such that Q|_F∞=P|_F∞ and Q[τ>t|F_t]=Z_t. The probability Q^Z is linked with the well-known Cox model by an explicit density function. Various properties exist, which characterize Q^Z from others. Let G=(G_t)_t≥0 with G_t=F_t∨σ({τ≤s}:s≤t). We establish the (H^′)-property between the filtrations F and G, and we provide the enlargement of filtration formula.