On birational Torelli theorems

Archiv der Mathematik - Let G be a simple simply-connected connected linear algebraic group over $${\mathbb {C}}$$ . We prove a 2-birational Torelli theorem for the moduli space of semistable...     

Development and validation of consensus machine learning-based models for the prediction of novel small molecules as potential anti-tubercular agents

Molecular Diversity - Tuberculosis (TB) is an infectious disease and the leading cause of death globally. The rapidly emerging cases of drug resistance among pathogenic mycobacteria have been a...     

Predicting 19F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase–Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor–protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable ¹⁹F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the ¹⁹F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein–inhibitor conformations as well as monomeric and dimeric inhibitor–protein complexes, thus rendering it the largest computational study on chemical shifts of ¹⁹F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Deciphering Internal and External π-Conjugation in C3-Symmetric Multiple Azobenzene Connected Systems in Self-Assembly

Two tripodal C₃-symmetric photoswitchable molecular systems T1 and T2 are reported that have extended conjugation at external and internal positions using an acryl group. The influence of the extended π-bonds in their absorption properties, thermal relaxation of the photoisomers and their propensities in forming supramolecular self-assemblies have been explored through spectroscopy, and microscopic studies. In particular, the investigations on the self-assembly have been carried out using scanning electron microscopy (SEM), transmission electron microscopy (TEM), polarized optical microscopy (POM), X-ray diffraction studies (XRD) and atomic force microscopy (AFM). Remarkably, the position of the acryl group influences the behaviour of the two target molecules in supramolecular assembly, and also in the formation of photoresponsive organic hydrogels or microcrystals.     

Hyperpolarization of Amino Acids in Water Utilizing Parahydrogen on a Rhodium Nanocatalyst

NMR offers many possibilities in chemical analysis, structural investigations, and medical diagnostics. Although it is broadly used, one of NMR spectroscopies main drawbacks is low sensitivity. Hyperpolarization techniques enhance NMR signals by more than four orders of magnitude allowing the design of new contrast agents. Parahydrogen induced polarization that utilizes the para-hydrogen's singlet state to create enhanced signals is of particular interest since it allows to produce molecular imaging agents within seconds. Herein, we present a strategy for signal enhancement of the carbonyl ¹³C in amino acids by using parahydrogen, as demonstrated for glycine and alanine. Importantly, the hyperpolarization step is carried out in water and chemically unmodified canonical amino acids are obtained. Our approach thus offers a high degree of biocompatibility, which is crucial for further application. The rapid sample hyperpolarization (within seconds) may enable the continuous production of biologically useful probes, such as metabolic contrast agents or probes for structural biology.     

IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems

Numerical Algorithms - This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called...     

On the distribution of the sum of digits of sums $$a+b$$ a + b

The Ramanujan Journal - Let $${\mathcal {A}}$$ , $${\mathcal {B}}$$ be large subsets of $$\{1,\ldots ,N\}$$ . We study the distribution of the sum of binary digits of the sums $$a+b$$ with...     

Sustainable challenges on the moon

For a permanently manned outpost on the moon – a moon village – a first holistic concept of a sustainable material flow has been established. From this context three dedicated topics have been investigated to more depth: Additive manufacturing (AM) of Al from disused space crafts, AM of structural elements with local resources, and resource extraction from regolith via thermal processes.     

Dinuclear gold(I)-N-heterocyclic carbene complexes: Synthesis,characterization, and catalytic application for hydrohydrazidation of terminal alkynes

Dinuclear gold(I)-N-heterocyclic carbene complexes were developed for the hydrohydrazidation of terminal alkynes. The gold(I)-N-heterocyclic carbene complexes 2a-2b were synthesized in good yields from silver complexes synthesized in situ, which in turn were obtained from the corresponding imidazolium salts with Ag₂O in dichloromethane as a solvent. The new air-stable gold(I)-NHC complexes, 2a - 2b, were characterized using NMR spectroscopy, elemental analysis, infrared, and mass spectroscopy studies. The gold(I) complex 2a was characterized using X-ray crystallography. Bis-N-heterocyclic carbene–based gold(I) complexes 2a - 2b exhibited excellent catalytic activities for hydrohydrazidation of terminal alkynes yielding acylhydrazone derivatives. The working catalytic system can be used in gram-scale synthesis. In addition, the catalytic reaction mechanism of the hydrohydrazidation of terminal alkynes by gold(I)-NHC complex was studied in detail using density functional theory.