Linear systems on projective spaces

In the paper the propertiesÑ _p (a generalization of the propertiesN _p for projectively normal embeddings of projective varieties) are investigated for noncomplete Veronese embeddings. It is shown that the linear projection of a complete Veronese embedding ? _n →? _N from a general linear subspace of ? _N of low dimension satisfies propertyÑ ₀. Moreover, Theorem 3.1 yields an upper bound forp for a noncomplete Veronese embedding of the projective plane ?₂ to satisfy propertyÑ _p .     

Stereoselective synthesis of a novel carbamoyl oxybiotin

Utilizing an l-serine derived enantiopure aminobutenolide as a chiral template, an efficient synthesis of a doubly modified novel biotin analog has been achieved. In view of the renewed interest in understanding the various biological roles of biotin, the title analog could provide some as yet unreported structure-activity relationship information on this important vitamin.     

Multilevel-in-width training for deep neural network regression

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. We draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.     

Structure Elucidation and Activity of Kolossin A,the D‐/L‐Pentadecapeptide Product of a Giant Nonribosomal Peptide Synthetase

The largest continuous bacterial nonribosomal peptide synthetase discovered so far is described. It consists of 15 consecutive modules arising from an uninterrupted, fully functional gene in the entomopathogenic bacterium Photorhabdus luminescens. The identification of its cryptic biosynthesis product was achieved by using a combination of genome analysis, promoter exchange, isotopic labeling experiments, and total synthesis of a focused collection of peptide candidates. Although it belongs to the growing class of D ‐/ L ‐peptide natural products, the encoded metabolite kolossin A was found to be largely devoid of antibiotic activity and is likely involved in interspecies communication. A stereoisomer of this peculiar natural product displayed high activity against Trypanosoma brucei rhodesiense, a recalcitrant parasite that causes the deadly disease African sleeping sickness.     

Efficient Regioselective Ring Opening of Activated Aziridine-2-Carboxylates with [18F]Fluoride

Aziridines can undergo a range of ring-opening reactions with nucleophiles. The regio- and stereochemistry of the products depend on the substituents on the aziridine. Aziridine ring-opening reactions have rarely been used in radiosynthesis. Herein we report the ring opening of activated aziridine-2-carboxylates with [¹⁸F]fluoride. The aziridine was activated for nucleophilic attack by substitution of various groups on the aziridine nitrogen atom. Fluorine-18 radiolabelling was followed by ester hydrolysis and removal of the activation group. Totally regioselective ring opening and subsequent deprotection was achieved with tert-butyloxycarbonyl- and carboxybenzyl-activated aziridines to give α-[¹⁸F]fluoro-β-alanine in good radiochemical yield.     

Different Complexation Behavior of P‐Functionalized Ferrocene Derivatives Towards SnCl2, SnCl4 and SnPh2Cl2: Auto‐ionization and Redox‐Type Reactions

The novel phosphonyl‐substituted ferrocene derivatives [Fe(η⁵‐Cp)(η⁵‐C₅H₃{P(O)(O‐iPr)₂}₂‐1,2)] ( Fc^1,2 ) and [Fe{η⁵‐C₅H₄P(O)(O‐iPr)₂}₂] ( Fc^1,1′ ) react with SnCl₂, SnCl₄, and SnPh₂Cl₂, giving the corresponding complexes [(Fc^1,2)₂SnCl][SnCl₃] ( 1 ), [{(Fc^1,1′)SnCl₂}_n] ( 2 ), [(Fc^1,1′)SnCl₄] ( 3 ), [{(Fc^1,1′)SnPh₂Cl₂}_n] ( 4 ), and [(Fc^1,2)SnCl₄] ( 5 ), respectively. The compounds are characterized by elemental analyses, ¹H, ¹³C, ³¹P, ¹¹⁹Sn NMR and IR spectroscopy, ³¹P and ¹¹⁹Sn CP‐MAS NMR spectroscopy, cyclovoltammetry, electrospray ionization mass spectrometry, and single‐crystal as well as powder X‐ray diffraction analyses. The experimental work is accompanied by DFT calculations, which help to shed light on the origin for the different reaction behavior of Fc^1,1′ and Fc^1,2 towards tin(II) chloride.     

Influence of metal loading and humic acid functional groups on the complexation behavior of trivalent lanthanides analyzed by CE-ICP-MS

The complexation behavior of Aldrich humic acid (AHA) and a modified humic acid (AHA-PB) with blocked phenolic hydroxyl groups for trivalent lanthanides (Ln) is compared, and their influence on the mobility of Ln(III) in an aquifer is analyzed. As speciation technique, capillary electrophoresis (CE) was hyphenated with inductively coupled plasma mass spectrometry (ICP-MS). For metal loading experiments 25 mg L⁻¹ of AHA and different concentrations (c_Ln(Eu+Gd) = 100–6000 μg L⁻¹) of Eu(III) and Gd(III) in 10 mM NaClO₄ at pH 5 were applied. By CE-ICP-MS, three Ln-fractions, assumed to be uncomplexed, weakly and strongly AHA-complexed metal can be detected. For the used Ln/AHA-ratios conservative complex stability constants log β_LnAHA decrease from 6.33 (100 μg L⁻¹ Ln³⁺) to 4.31 (6000 μg L⁻¹ Ln³⁺) with growing Ln-content. In order to verify the postulated weaker and stronger humic acid binding sites for trivalent Eu and Gd, a modified AHA with blocked functional groups was used. For these experiments 500 μg L⁻¹ Eu and 25 mg L⁻¹ AHA and AHA-PB in 10 mM NaClO₄ at pH-values ranging from 3 to 10 have been applied. With AHA-PB, where 84% of the phenolic OH-groups and 40% of the COOH-groups were blocked, Eu complexation was significantly lower, especially at the strong binding sites. The log β-values decrease from 6.11 (pH 10) to 5.61 at pH 3 (AHA) and for AHA-PB from 6.01 (pH 7) to 3.94 at pH 3. As a potential consequence, particularly humic acids with a high amount of strong binding sites (e.g. phenolic OH- and COOH-groups) can be responsible for a higher metal mobility in the aquifer due to the formation of dissolved negatively charged metal-humate species.     

Synthesis and potent cytotoxic activity of 8- and 9-anilinophenanthridine-7,10-diones

A series of 8-anilino and 9-anilinophenanthridine-7,10-diones was prepared and screened against various cancer cell lines to measure anti-proliferative activity. The compounds tested display potent cytotoxic activity in the micromolar and sub-micromolar range. These compounds are promising new leads for developing anticancer compounds.     

Dihydroxy(4-thiomorpholinomethyl)benzoic acid: from molecular asymmetry to diode characteristics

One of the challenges in molecular electronics is to design molecules which can be used as functional units in electronic devices. The subject of our investigations is an asymmetrical molecule, dihydroxy(4-thiomorpholinomethyl)benzoic acid (TMBA), whose structural and electronic properties are characterized. The self-assembly behavior of TMBA on Au(111) surfaces resulting in highly ordered monolayers is obtained using scanning tunneling microscopy (STM). Furthermore, investigations on the electronic properties of the combined metal/molecule system reveal an orbital mediated tunneling process and tunneling decay constants for the carboxylic and thiomorpholino group. Thus, a diode-like character of TMBA is shown to be caused by intrinsic electronic properties of different molecular moieties.