Characterization of regular Diophantine quadruples

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Characterization of regular Diophantine quadruples

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Low-Light Trees, and Tight Lower Bounds for Euclidean Spanners

We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T)=O(k⋅n ^1/k )⋅w(MST(M)), and a spanning tree T′ with weight w(T′)=O(k)⋅w(MST(M)) and unweighted diameter O(k⋅n ^1/k ). These trees also achieve an optimal maximum degree. Furthermore, we demonstrate that these trees can be constructed efficiently.     

p-type conductivity and green photoluminescence of CuGaS2 grown by iodine transport

Crystals of CuGaS₂ grown from the vapor phase by iodine transport can be made usefully p-type (resistivity of 1 Ω cm at room temperature) by post annealing in saturated sulfur vapor. At 2°K these crystals exhibit efficient green photoluminescence.     

Excited-state proton transfer reactions of 10-hydroxycamptothecin

Time-resolved and steady-state emission characterization of 10-hydroxycamptothecin reveals a rich but less complex proton-transfer behavior than its parent hydroxyquinoline. The electronic effect of the additional electron-withdrawing ring makes the excited-state both less basic and more acidic than the parent and adds to the class of high-acidity excited-state proton donors in photochemistry and photobiology.     

Palladium‐Assisted Cleavage of Peptides and Proteins Containing a Backbone with Thiazolidine Linkage

The design and synthesis of biomolecules that are responsive to external stimuli is of great interest in various research areas, such as in the preparation of smart biomaterial and chemical biology. Polypeptide backbone disassembly as a response to a particular stimulus is of interest, as it leads to a complete loss of the protein tertiary structure and, as a result, to a loss of function. In this study, a strategy based on palladium‐assisted efficient cleavage of backbone thiazolidine linkage in peptides and proteins was developed. Using a fluorescence‐based assay, encompassing ubiquitinated peptide with a quenching florescence pair, it was possible to optimize the cleavage step after rapid screening of various conditions, such as the type of metal complexes and reaction additives. The optimized conditions prompted fast cleavage of the thiazolidine linkage. The straightforward introduction of a backbone thiazolidine linkage in peptide and proteins coupled with the chemical methods used offers new opportunities in controlling macromolecule function and might, with the aid of cellular protein delivery methods, be applied in cellular settings.     

Direct evidence for a three-dimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause

We report the direct detection by three THEMIS spacecraft of a magnetic flux rope flanked by two active X lines producing colliding plasma jets near the center of the flux rope. The observed density depletion and open magnetic field topology inside the flux rope reveal important three-dimensional effects. There was also evidence for nonthermal electron energization within the flux rope core where the fluxes of 1-4 keV superthermal electrons were higher than those in the converging reconnection jets. The observed ion and electron energizations differ from current theoretical predictions.     

Protein‐oligosaccharide conjugates as novel prebiotics

Maintaining a good proportion of gut probiotic bacteria is imperative to health. This may be achieved by consuming “prebiotics,” e.g., galacto‐oligosaccharides (GOS) that selectively promote probiotic bacteria, as they often uniquely express transporters for such oligosaccharides. Proteins are an important source for amino acids essential to probiotic bacteria. As most protein digestion products are absorbed in the small intestine, and there is great competition on the residuals by colonic bacteria, amino acids are scarce (<0.01 mM) in the colonic intercellular fluid, thus limiting probiotics' proliferation. However, no existing prebiotic product contains protein. Herein, we propose a new type of prebiotics: protein‐oligosaccharide conjugates. These conjugates were designed to be selectively targeted to probiotic bacteria in the colon, for enhancing their competitive advantage over undesired microorganisms. The approach was inspired by active targeting of chemotherapy, achieved by conjugating drugs to ligands, which selectively bind to proteins uniquely expressed on cancer cells; except here, we aimed to promote, not eliminate, the targeted cells. We formed these conjugates by mild Maillard‐reaction‐based covalent conjugation of GOS to lactoferrin hydrolysate (LFH), formed by peptic digestion, hence it resists gastric digestion. LFH‐GOS conjugates comprised 76% ± 1% LFH and 25% ± 4% GOS, and self‐assembled into 0.2 to 1.5‐μm microparticles. Most of the conjugates' protein content endured simulated gastrointestinal digestion, hence is expected to reach the colon. Remarkably, we found that the growth rate of a model probiotic bacterium (Lactobacillus casei) on the conjugates was double that on the unconjugated components (0.082 and 0.041 h^?1, respectively). This study proposes the next generation of prebiotics.     

Subdivision Schemes of Sets and the Approximation of Set-Valued Functions in the Symmetric Difference Metric

In this work we construct subdivision schemes refining general subsets of ? ⁿ and study their applications to the approximation of set-valued functions. Differently from previous works on set-valued approximation, our methods are developed and analyzed in the metric space of Lebesgue measurable sets endowed with the symmetric difference metric. The construction of the set-valued subdivision schemes is based on a new weighted average of two sets, which is defined for positive weights (corresponding to interpolation) and also when one weight is negative (corresponding to extrapolation). Using the new average with positive weights, we adapt to sets spline subdivision schemes computed by the Lane–Riesenfeld algorithm, which requires only averages of pairs of numbers. The averages of numbers are then replaced by the new averages of pairs of sets. Among other features of the resulting set-valued subdivision schemes, we prove their monotonicity preservation property. Using the new weighted average of sets with both positive and negative weights, we adapt to sets the 4-point interpolatory subdivision scheme. Finally, we discuss the extension of the results obtained in metric spaces of sets, to general metric spaces endowed with an averaging operation satisfying certain properties.