Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.     

Phase II monitoring of changes in mean from high‐dimensional data

The generalized T² chart (GT‐chart), which is composed of the T² statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T² control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T² control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature.     

Convergence Theory for Preconditioned Eigenvalue Solvers in a Nutshell

Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using multilevel preconditioning for elliptic differential operators or graph Laplacian eigenvalue problems, exhibit almost optimal complexity in practice; i.e., their computational costs to calculate a fixed number of eigenvalues and eigenvectors grow linearly with the matrix problem size. Theoretical justification of their optimality requires convergence rate bounds that do not deteriorate with the increase of the problem size. Such bounds were pioneered by E. D’yakonov over three decades ago, but to date only a handful have been derived, mostly for symmetric eigenvalue problems. Just a few of known bounds are sharp. One of them is proved in doi: 10.1016/S0024-3795(01)00461-X for the simplest preconditioned eigensolver with a fixed step size. The original proof has been greatly simplified and shortened in doi: 10.1137/080727567 by using a gradient flow integration approach. In the present work, we give an even more succinct proof, using novel ideas based on Karush–Kuhn–Tucker theory and nonlinear programming.     

Uniform antibacterial cylindrical nanoparticles for enhancing the strength of nanocomposite hydrogels

Crystallization-driven self-assembly (CDSA) was employed for the preparation of monodisperse cationic cylindrical nanoparticles with controllable sizes, which were subsequently explored for their effect on antibacterial activity and the mechanical properties of nanocomposite hydrogels. Poly(ɛ-caprolactone)-block-poly(methyl methacrylate)-block-poly[2-(tert-butylamino) ethyl methacrylate] (PCL-b-PMMA-b-PTA) triblock copolymers were synthesized using combined ring-opening and RAFT polymerizations, and then self-assembled into polycationic cylindrical micelles with controllable lengths by epitaxial growth. The polycationic cylinders exhibited intrinsic cell-type-dependent antibacterial capabilities against gram-positive and gram-negative bacteria under physiological conditions, without quaternization or loading of any additional antibiotics. Furthermore, when the cylinders were combined into anionic alginate hydrogel networks, the mechanical response of the hydrogel composite was tunable and enhanced up to 51%, suggesting that cationic polymer fibers with controlled lengths are promising mimics of the fibrous structures in natural extracellular matrix to support scaffolds. Overall, this polymer fiber/hydrogel nanocomposite shows potential as an injectable antibacterial biomaterial, with possible application in implant materials as bacteriostatic agents or bactericides against various infections.     

Enantioselective Rhodium-Catalyzed Pauson–Khand Reactions of 1,6-Chloroenynes with 1,1-Disubstituted Olefins

An enantioselective rhodium(I)-catalyzed Pauson–Khand reaction (PKR) using 1,6-chloroenynes that contain challenging 1,1-disubstituted olefins is described. In contrast to the previous studies with these types of substrates, which are only suitable for a single type of tether and alkyne substituent, the new approach results in a more expansive substrate scope, including carbon and heteroatom tethers with polar and non-polar substituents on the alkene. DFT calculations provide critical insight into the role of the halide, which pre-polarizes the alkyne to lower the barrier for metallacycle formation and provides the proper steric profile to promote a favorable enantiodetermining interaction between substrate and chiral diphosphine ligand. Hence, the chloroalkyne enables the efficient and enantioselective PKR with 1,6-enynes that contain challenging 1,1-disubstituted olefins, thereby representing a new paradigm for enantioselective reactions involving 1,6-enynes.     

Quantitative Nanoscale Secondary Ion Mass Spectrometry (NanoSIMS) Imaging of Individual Vesicles to Investigate the Relation between Fraction of Chemical Release and Vesicle Size

We used correlative transmission electron microscopy (TEM) and nanoscale secondary ion mass spectrometry (NanoSIMS) imaging to quantify the contents of subvesicular compartments, and to measure the partial release fraction of ¹³C-dopamine in cellular nanovesicles as a function of size. Three modes of exocytosis comprise full release, kiss-and-run, and partial release. The latter has been subject to scientific debate, despite a growing amount of supporting literature. We tailored culturing procedures to alter vesicle size and definitively show no size correlation with the fraction of partial release. In NanoSIMS images, vesicle content was indicated by the presence of isotopic dopamine, while vesicles which underwent partial release were identified by the presence of an ¹²⁷I-labelled drug, to which they were exposed during exocytosis allowing entry into the open vesicle prior to its closing again. Demonstration of similar partial release fractions indicates that this mode of exocytosis is predominant across a wide range of vesicle sizes.     

Experimental Confirmation of a Predicted Porous Hydrogen-Bonded Organic Framework

Hydrogen-bonded organic frameworks (HOFs) with low densities and high porosities are rare and challenging to design because most molecules have a strong energetic preference for close packing. Crystal structure prediction (CSP) can rank the crystal packings available to an organic molecule based on their relative lattice energies. This has become a powerful tool for the a priori design of porous molecular crystals. Previously, we combined CSP with structure-property predictions to generate energy-structure-function (ESF) maps for a series of triptycene-based molecules with quinoxaline groups. From these ESF maps, triptycene trisquinoxalinedione (TH5) was predicted to form a previously unknown low-energy HOF (TH5-A) with a remarkably low density of 0.374 g cm⁻³ and three-dimensional (3D) pores. Here, we demonstrate the reliability of those ESF maps by discovering this TH5-A polymorph experimentally. This material has a high accessible surface area of 3,284 m² g⁻¹, as measured by nitrogen adsorption, making it one of the most porous HOFs reported to date.     

Spatially Directed Pyrolysis via Thermally Morphing Surface Adducts

Combustion is often difficult to spatially direct or tune associated kinetics—hence a run-away reaction. Coupling pyrolytic chemical transformation to mass transport and reaction rates (Damköhler number), however, we spatially directed ignition with concomitant switch from combustion to pyrolysis (low oxidant). A ‘surface-then-core’ order in ignition, with concomitant change in burning rate,is therefore established. Herein, alkysilanes grafted onto cellulose fibers are pyrolyzed into non-flammable SiO₂ terminating surface ignition propagation, hence stalling flame propagating. Sustaining high temperatures, however, triggers ignition in the bulk of the fibers but under restricted gas flow (oxidant and/or waste) hence significantly low rate of ignition propagation and pyrolysis compared to open flame (Liñán's equation). This leads to inside-out thermal degradation and, with felicitous choice of conditions, formation of graphitic tubes. Given the temperature dependence, imbibing fibers with an exothermically oxidizing synthon (MnCl₂) or a heat sink (KCl) abets or inhibits pyrolysis leading to tuneable wall thickness. We apply this approach to create magnetic, paramagnetic, or oxide containing carbon fibers. Given the surface sensitivity, we illustrate fabrication of nm- and μm-diameter tubes from appropriately sized fibers.     

A General Strategy Toward pH-Resistant Phenolic Fluorophores for High-Fidelity Sensing and Bioimaging Applications

Aryl alcohol-type or phenolic fluorophores offer diverse opportunities for developing bioimaging agents and fluorescence probes. Due to the inherently acidic hydroxyl functionality, phenolic fluorophores provide pH-dependent emission signals. Therefore, except for developing pH probes, the pH-dependent nature of phenolic fluorophores should be considered in bioimaging applications but has been neglected. Here we show that a simple structural remedy converts conventional phenolic fluorophores into pH-resistant derivatives, which also offer “medium-resistant” emission properties. The structural modification involves a single-step introduction of a hydrogen-bonding acceptor such as morpholine nearby the phenolic hydroxyl group, which also leads to emission bathochromic shift, increased Stokes shift, enhanced photo-stability and stronger emission for several dyes. The strategy greatly expands the current fluorophores’ repertoire for reliable bioimaging applications, as demonstrated here with ratiometric imaging of cells and tissues.     

Engineered Biocatalytic Synthesis of β-N-Substituted-α-Amino Acids

Non-canonical amino acids (ncAAs) are useful synthons for the development of new medicines, materials, and probes for bioactivity. Recently, enzyme engineering has been leveraged to produce a suite of highly active enzymes for the synthesis of β-substituted amino acids. However, there are few examples of biocatalytic N-substitution reactions to make α,β-diamino acids. In this study, we used directed evolution to engineer the β-subunit of tryptophan synthase, TrpB, for improved activity with diverse amine nucleophiles. Mechanistic analysis shows that high yields are hindered by product re-entry into the catalytic cycle and subsequent decomposition. Additional equivalents of l -serine can inhibit product reentry through kinetic competition, facilitating preparative scale synthesis. We show β-substitution with a dozen aryl amine nucleophiles, including demonstration on a gram scale. These transformations yield an underexplored class of amino acids that can serve as unique building blocks for chemical biology and medicinal chemistry.