Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

A decision support method for designing vegetation layers with minimised irrigation need

Annals of Operations Research - Selecting a vegetation layer design goes along with determining its future irrigation need. Therefore, it is essential to take a design decision that is minimising...     

Dextramabs: A Novel Format of Antibody-Drug Conjugates Featuring a Multivalent Polysaccharide Scaffold

Antibody-drug conjugates (ADCs) are multicomponent biomolecules that have emerged as a powerful tool for targeted tumor therapy. Combining specific binding of an immunoglobulin with toxic properties of a payload, they however often suffer from poor hydrophilicity when loaded with a high amount of toxins. To address these issues simultaneously, we developed dextramabs, a novel class of hybrid antibody-drug conjugates. In these architectures, the therapeutic antibody trastuzumab is equipped with a multivalent dextran polysaccharide that enables efficient loading with a potent toxin in a controllable fashion. Our modular chemoenzymatic approach provides an access to synthetic dextramabs bearing monomethyl auristatin as releasable cytotoxic cargo. They possess high drug-to-antibody ratios, remarkable hydrophilicity, and high toxicity in vitro.     

Synthesis and Reactivity of the First Isolated Hydrogen‐Bridged Silanol–Silanolate Anions

We report on the first examples of isolated silanol–silanolate anions, obtained by utilizing weakly coordinating phosphazenium counterions. The silanolate anions were synthesized from the recently published phosphazenium hydroxide hydrate salt with siloxanes. The silanol–silanolate anions are postulated intermediates in the hydroxide‐mediated polymerization of aryl and alkyl siloxanes. The silanolate anions are strong nucleophiles because of the weakly coordinating character of the phosphazenium cation, which is perceptible in their activity in polysiloxane depolymerization.     

Comparison of monomethoxy‐, dimethoxy‐, and trimethoxysilane anchor groups for surface‐initiated RAFT polymerization from silica surfaces

The immobilization of reversible addition–fragmentation chain transfer (RAFT) agents on silica for surface‐initiated RAFT polymerizations (SI‐RAFT) via the Z‐group approach was studied systematically in dependence of the functionality of the RAFT‐agent anchor group. Monoalkoxy‐, dialkoxy‐, and trialkoxy silyl ether groups were incorporated into trithiocarbonate‐type RAFT agents and bound to planar silica surfaces as well as to silica nanoparticles. The immobilization efficiency and the structure of the bound RAFT‐agent film varied strongly in dependence of the used solvent (toluene vs. 1,2‐dimethoxyethane) and the anchor group functionality, as evidenced by atomic force microscopy, transmission electron microscopy, dynamic light scattering, and UV/Vis spectroscopy. Surface‐initiated RAFT polymerizations using functionalized silica nanoparticles revealed that grafted oligomers, which often occur in SI‐RAFT, are not formed within the crosslinked structures that originate from the immobilization, and that RAFT‐agent films that show less aggregation during the immobilization are more efficient during SI‐RAFT in terms of polymer grafting density. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 103–113     

Seeded Polymerization of an Amide-Functionalized Diketopyrrolopyrrole Dye in Aqueous Media

The self-assembly of an amide-functionalized dithienyldiketopyrrolopyrrole (DPP) dye in aqueous media was achieved through seed-initiated supramolecular polymerization. Temperature- and time-dependent studies showed that the spontaneous polymerization of the DPP derivative was temporally delayed upon cooling the monomer solution in a methanol/water mixture. Theoretical calculations revealed that an amide-functionalized DPP derivative adopts an energetically favorable folded conformation in the presence of water molecules due to hydration. This conformational change is most likely responsible for the trapping of monomers in the initial stage of the cooperative supramolecular polymerization in aqueous media. However, the monomeric species can selectively interact with externally added fragmented aggregates as seeds through concerted π-stacking and hydrogen-bonding interactions. Consequently, the time course of the supramolecular polymerization and the morphology of the aggregated state can be controlled, and one-dimensional fibers that exhibit a J-aggregate-like bathochromically shifted absorption band can be obtained.     

“Brown-Ring”-Related Coordination Polymers of the Quartet-{FeNO}7 Chromophore

A conspicuous detail of the so-called brown-ring test (the analytical test on nitrate) is the reddish color of the bottom layer of concentrated sulfuric acid, which develops upon the bleeding of the brown layer into the acid. Crystals of the same color form from a solution of ferrous sulfate in concentrated sulfuric acid on saturation with gaseous nitric oxide. The structure of this H₃O[{Fe(NO)(μ₄-SO₄)(μ₂-SO₄)_0.5}_n/n] ( 1a ) is made up from infinite chessboard-type layers with sulfur on the field junctions and Fe(NO) moieties below the black and above the white fields. An Fe–N–O angle of about 160° causes disorder in the tetragonal space group I4/mmm. A similar crystal pathology was found in the related [{Fe(MeOH)(NO)(μ₄-SO₄)}_n/n] ( 1b ) in the same crystal class. A one-dimensional coordination polymer is formed in crystals of a third compound that comprises the Fe(NO)O₅ coordination pattern, namely the brown oxalato species [{Fe(H₂O)(NO)(μ₂-ox)}_n/n · H₂O] ( 2 ). A still larger NO tilt of about 156° is not obscured by disorder in the triclinic crystals of 2 .     

15‐Hydroperoxy‐PGE2: Intermediate in Mammalian and Algal Prostaglandin Biosynthesis

Arachidonic‐acid‐derived prostaglandins (PGs), specifically PGE₂, play a central role in inflammation and numerous immunological reactions. The enzymes of PGE₂ biosynthesis are important pharmacological targets for anti‐inflammatory drugs. Besides mammals, certain edible marine algae possess a comprehensive repertoire of bioactive arachidonic‐acid‐derived oxylipins including PGs that may account for food poisoning. Described here is the analysis of PGE₂ biosynthesis in the red macroalga Gracilaria vermiculophylla that led to the identification of 15‐hydroperoxy‐PGE₂, a novel precursor of PGE₂ and 15‐keto‐PGE₂. Interestingly, this novel precursor is also produced in human macrophages where it represents a key metabolite in an alternative biosynthetic PGE₂ pathway in addition to the well‐established arachidonic acid‐PGG₂‐PGH₂‐PGE₂ route. This alternative pathway of mammalian PGE₂ biosynthesis may open novel opportunities to intervene with inflammation‐related diseases.