Adaptive Wavelet Schwarz Methods for the Navier-Stokes Equation

In this article, we are concerned with domain decomposition methods for the stationary incompressible Navier-Stokes equation. We construct an adaptive additive Schwarz method based on discretization by means of a divergence-free wavelet frame. We prove that the method is convergent and asymptotically optimal with respect to the degrees of freedom involved.     

On a Finite Difference Scheme for an Inverse Integro-Differential Problem Using Semigroup Theory: A Functional Analytic Approach

In this article, the problem of reconstructing an unknown memory kernel from an integral overdetermination in an abstract linear (of convolution type) evolution equation of parabolic type is considered. After illustrating some results of the existence and uniqueness of a solution for the differential problem, we study its approximation by Rothe's method. We prove a result of stability and another concerning the order of approximation of the solution in dependence of its regularity. The main tool is a maximal regularity result for solutions to abstract parabolic finite difference schemes. Two model problems to which the results are applicable are illustrated.     

Use of the bromine isotope ratio in HPLC-ICP-MS and HPLC-ESI-MS analysis of a new drug in development

A combination of inductively coupled plasma mass spectrometry (ICP-MS) and electrospray ionization mass spectrometry (ESI-MS) was deployed for the metabolite profiling and metabolite identification of a new antituberculosis compound (R207910, also known as TMC207) that is currently in drug development. R207910 contains one bromine atom, allowing the detection by ICP-MS. Fluctuations in the Br sensitivity caused by the HPLC gradient were counteracted by the use of species-unspecific isotope dilution. In order to evaluate the method developed, the results obtained were compared with those acquired via radioactivity detection. HPLC-ESI-MS was used for the structural identification of R207910 and its metabolites. The ⁷⁹Br/⁸¹Br isotope ratio is also valuable in the search for metabolites in the complex background of endogenous compounds obtained using HPLC-ESI-MS analyses. Data-dependent scanning using isotope recognition with an ion trap mass spectrometer or processing of Q-Tof data provides HPLC-ICP-MS-like “bromatograms”. The combination of accurate mass measurements and the fragmentation behavior in the MS² spectra obtained using the Q-Tof Ultima mass spectrometer or MSⁿ spectra acquired using the LTQ-Orbitrap allowed structural characterization of the main metabolites of R207910 in methanolic dog and rat faeces extracts taken 0–24 h post-dose. Figure Analyses of a rat faeces extract taken 0–24 h post-dose: a HPLC-ICP-MS using isotope dilution, b corresponding Br mass flow chromatogram, c radio-HPLC, d Q-Tof ESI-MS TIC, e Q-Tof ESI-MS bromatogram after Br stripping, f LTQ-Orbitrap ESI-MS² TIC obtained with isotopic-data-dependent scanning     

Integrated project views: decision support platform for drug discovery project teams

Drug discovery teams continuously have to decide which compounds to progress and which experiments to perform next, but the data required to make informed decisions is often scattered, inaccessible, or inconsistent. In particular, data tend to be stored and represented in a compound-centric or assay-centric manner rather than project-centric as often needed for effective use in drug discovery teams. The Integrated Project Views (IPV) system has been created to fill this gap; it integrates and consolidates data from various sources in a project-oriented manner. Its automatic gathering and updating of project data not only ensures that the information is comprehensive and available on a timely basis, but also improves the data consistency. Due to the lack of suitable off-the-shelf solutions, we were prompted to develop custom functionality and algorithms geared specifically to our drug discovery decision making process. In 10 years of usage, the resulting IPV application has become very well-accepted and appreciated, which is perhaps best evidenced by the observation that standalone Excel spreadsheets are largely eliminated from project team meetings.     

Regiochemistry of the Condensation of 2-Aroyl-cyclohexanones and 2-Cyanoacetamide: (13)C-Labeling Studies and Semiempirical MO Calculations

Hydroxy-aryl-5,6,7,8-tetrahydroisoquinoline-4-carbonitriles represent interesting chemical scaffolds, but synthetic access to these compounds is limited. The reaction of 2-aroyl-cyclohexanones with 2-cyanoacetamide and base in ethanol has been reported to lead to the formation of the tetrahydroisoquinoline isomer. We show that depending on the electronic nature of the para-substituent on the aryl ring, formation of the regioisomeric tetrahydroquinoline isomer can significantly compete. The electron-donating or -withdrawing properties of the para-substituent of the aryl ring determines the ratio of product isomers. A series of 2-aroyl-cyclohexanones, with para-substituents ranging from electron-donating to electron-withdrawing, were reacted with [2-(13)C]-cyanoacetamide. The product ratio and absolute regiochemistry were directly determined by quantitative (13)C, HMBC, and NOESY NMR spectroscopy on the reaction mixtures. A clear relationship between the regioisomeric product ratio and the Hammett sigma values of the substituents is demonstrated. This is explained by the separate in situ yields, which reveal that the pathway leading to the tetrahydroquinoline regioisomer is significantly more sensitive toward the electronic nature of the para-substituent than the pathway leading to the tetrahydroisoquinoline. Semiempirical AM1 molecular orbital calculations on the starting electrophile 2-aroyl-cyclohexanone support a correlation between the energy of the LUMOs and the regioisomeric product ratio. Our results facilitate synthetic access to a range of these interesting synthetic intermediates.     

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.     

Wavelets with patchwise cancellation properties

We construct wavelets on general -dimensional domains or manifolds via a domain decomposition technique, resulting in so-called composite wavelets. With this construction, wavelets with supports that extend to more than one patch are only continuous over the patch interfaces. Normally, this limited smoothness restricts the possibility for matrix compression, and with that the application of these wavelets in (adaptive) methods for solving operator equations. By modifying the scaling functions on the interval, and with that on the -cube that serves as parameter domain, we obtain composite wavelets that have patchwise cancellation properties of any required order, meaning that the restriction of any wavelet to each patch is again a wavelet. This is also true when the wavelets are required to satisfy zeroth order homogeneous Dirichlet boundary conditions on (part of) the boundary. As a result, compression estimates now depend only on the patchwise smoothness of the wavelets that one may choose. Also taking stability into account, our composite wavelets have all the properties for the application to the (adaptive) solution of well-posed operator equations of orders for .

     

Whitney towers and gropes in 4-manifolds

Many open problems and important theorems in low-dimensional topology have been formulated as statements about certain 2-complexes called gropes. This paper describes a precise correspondence between embedded gropes in 4-manifolds and the failure of the Whitney move in terms of iterated `towers' of Whitney disks. The `flexibility' of these Whitney towers is used to demonstrate some geometric consequences for knot and link concordance connected to -solvability, -cobordism and grope concordance. The key observation is that the essential structure of gropes and Whitney towers can be described by embedded unitrivalent trees which can be controlled during surgeries and Whitney moves. It is shown that a Whitney move in a Whitney tower induces an IHX (Jacobi) relation on the embedded trees.

     

Asteropine A, a sialidase-inhibiting conotoxin-like peptide from the marine sponge Asteropus simplex

Marine sponges contain structurally intriguing and biologically active peptides of nonribosomal peptide synthase origin, often containing amino acids with novel structures. Here we report the discovery of asteropine A (APA), a cystine knot to be isolated from marine sponges. The solution structure of APA as determined by NMR belongs to the four-loop class of cystine knots similar to those of some conotoxins and spider toxins. However, the highly negatively charged surface of APA is uncommon among other cystine knots. APA competitively inhibits bacterial sialidases, but not a viral sialidase. APA was inactive against all other enzymes tested and did not have any apparent antitumor activity. Our data suggest that APA and other knotting peptides may be important leads for antibacterial and even antiviral drug development.