Castelnuovo-Mumford regularity by approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.     

Rapid synthesis of pomalidomide-conjugates for the development of protein degrader libraries

Current methods for the preparation of heterobifunctional pomalidomide-conjugates rely on methods that are often low yielding and produce intractable byproducts. Herein we describe our strategy for the reliable and succinct preparation of pomalidomide-linkers which is essential to the formation of these conjugates. We present the preparation of 18 pomalidomide-linkers in high yield compared to current literature methods. Our findings show that secondary amines consistently afford greater yields than their primary counterparts, a trend that we were able to exploit in the synthesis of several new pomalidomide homo-dimers in enhanced yields compared to similar literature syntheses. This trend was further utilised to develop the first one-pot synthesis of JQ1-pomalidomide conjugates in yields up to 62%, providing a method that is suited to rapid preparation of conjugate libraries as is frequently required for the development of new protein degraders.

Current methods for the preparation of heterobifunctional pomalidomide-conjugates rely on methods that are often low yielding and produce intractable byproducts. Herein we describe our strategy for the succinct preparation of pomalidomide-linkers.     

Photolysis of diacyl peroxides: a radical-based approach for the synthesis of functionalized amino acids

[reaction: see text] Photolysis of the amino acid derived symmetrical and unsymmetrical diacyl peroxides at 254 nm at low temperature (-78 to -196 degrees C) generates various bis(amino acids) in a concise manner and with orthogonal protection. The methodology was applied to the synthesis of (4R)-5-propyl-L-leucine (PrLeu), a component of HUN-7293.     

Hilbert series of subspace arrangements

The vanishing ideal I of a subspace arrangement V₁∪V₂∪?∪V_m⊆V is an intersection I₁∩I₂∩?∩I_m of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of the product ideal J=I₁I₂?I_m without any assumptions about the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. We will also apply our results to generalized principal component analysis (GPCA), a tool that is useful for computer vision and image processing.     

On the Canonical Decomposition of Quiver Representations

Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the canonical decomposition for quivers with three vertices gives us fractal-like pictures.     

Confined and Agitated Swirling Flows with Applications in Chemical Engineering

Turbulent, swirling flows are encountered frequently in chemical engineering practice. In this article, experiments and simulations on two classes of swirling flows, viz. agitated flows (stirred tanks), and confined swirling flows are discussed. Results of large-eddy simulations of stirred tank flow are compared with experimental data, mainly phase-resolved LDA data of the flow in the vicinity of the impeller. Next to the average velocity field, also the turbulent kinetic energy, and the anisotropy of the Reynolds stress tensor have been assessed. An important application of confined swirling flow is the cyclone separator (hydrocyclones for the separation of liquids, gas cyclones for gas-solid separation). The flow in a swirl tube geometry exhibiting many of the typical features of swirl flows (e.g. vortex breakdown) is discussed. Furthermore, a large-eddy simulation of the gas flow in a high-efficiency Stairmand cyclone separator is presented. Two examples of process modeling based on flow simulations are briefly treated: orthokinetic agglomeration of crystals in a stirred tank, and particle separation in a cyclone. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simulations of thixotropic liquids

In thixotropic liquids the rheological properties depend on the liquid’s deformation history. Clay suspensions (as encountered in oil sands mining) are a prominent example. Activated clay particles form a network. As a consequence of (ionic) transport limitations, the network is not an instantaneous feature; it takes time to build up, and also to break down, the latter as a result of deformation in the liquid. In this paper a procedure for detailed simulations of flow of viscous thixotropic liquids is outlined. The local viscosity of the liquid relates to the level of integrity of the network. The time-dependence of the liquid’s rheology is due to the finite rate with which the network in the liquid builds up or breaks down. This concept has been incorporated in a lattice-Boltzmann discretization of the flow equations. With this methodology the way thixotropic liquids are mobilized in mixing tanks and the drag force experienced by dense assemblies of coarse particles (e.g. sand) in thixotropic liquids have been studied.     

Microextraction of Reseda luteola-Dyed Wool and Qualitative Analysis of Its Flavones by UHPLC-UV,NMR and MS

Detailed knowledge on natural dyes is important for agronomy and quality control as well as the fastness, stability, and analysis of dyed textiles. Weld (Reseda luteola L.), which is a source of flavone-based yellow dye, is the focus of this study. One aim was to reduce the required amount of dyed textile to ≤50 μg for a successful chromatographic analysis. The second aim was to unambiguously confirm the identity of all weld flavones. By carrying out the extraction of 50 μg dyed wool with 25 μL of solvent and analysis by reversed-phase UHPLC at 345 nm, reproducible chromatographic fingerprints could be obtained with good signal to noise ratios. Ten baseline separated peaks with relative areas ≥1% were separated in 6 min. Through repeated polyamide column chromatography and prepHPLC, the compounds corresponding with the fingerprint peaks were purified from dried weld. Each was unequivocally identified, including the position and configuration of attached sugars, by means of 1D and 2D NMR and high-resolution MS. Apigenin-4′-O-glucoside and luteolin-4′-O-glucoside were additionally identified as two trace flavones co-eluting with other flavone glucosides, the former for the first time in weld. The microextraction might be extended to other used dye plants, thus reducing the required amount of precious historical textiles.     

Maximum common binding modes (MCBM): consensus docking scoring using multiple ligand information and interaction fingerprints

Improving the scoring functions for small molecule-protein docking is a highly challenging task in current computational drug design. Here we present a novel consensus scoring concept for the prediction of binding modes for multiple known active ligands. Similar ligands are generally believed to bind to their receptor in a similar fashion. The presumption of our approach was that the true binding modes of similar ligands should be more similar to each other compared to false positive binding modes. The number of conserved (consensus) interactions between similar ligands was used as a docking score. Patterns of interactions were modeled using ligand receptor interaction fingerprints. Our approach was evaluated for four different data sets of known cocrystal structures (CDK-2, dihydrofolate reductase, HIV-1 protease, and thrombin). Docking poses were generated with FlexX and rescored by our approach. For comparison the CScore scoring functions from Sybyl were used, and consensus scores were calculated thereof. Our approach performed better than individual scoring functions and was comparable to consensus scoring. Analysis of the distribution of docking poses by self-organizing maps (SOM) and interaction fingerprints confirmed that clusters of docking poses composed of multiple ligands were preferentially observed near the native binding mode. Being conceptually unrelated to commonly used docking scoring functions our approach provides a powerful method to complement and improve computational docking experiments.