Random directed graphs are robustly Hamiltonian

A classical theorem of Ghouila‐Houri from 1960 asserts that every directed graph on n vertices with minimum out‐degree and in‐degree at least contains a directed Hamilton cycle. In this paper we extend this theorem to a random directed graph , that is, a directed graph in which every ordered pair (u, v) becomes an arc with probability p independently of all other pairs. Motivated by the study of resilience of properties of random graphs, we prove that if , then a.a.s. every subdigraph of with minimum out‐degree and in‐degree at least contains a directed Hamilton cycle. The constant 1/2 is asymptotically best possible. Our result also strengthens classical results about the existence of directed Hamilton cycles in random directed graphs. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 345–362, 2016     

Crosslinked poly(ethylene oxide) fouling resistant coating materials for oil/water separation

Potential fouling reducing coating materials were synthesized via free-radical photopolymerization of aqueous solutions of poly(ethylene glycol) diacrylate (PEGDA). Crosslinked PEGDA (XLPEGDA) exhibited high water permeability and good fouling resistance to oil/water mixtures. Water permeability increased strongly with increasing the water content in the prepolymerization water mixture, going from 10 to 150 L μm/(m² h bar) as prepolymerization water content increased from 60 to 80 wt.%. However, molecular weight cutoff decreased as water content increased. These materials were applied to polysulfone (PSF) UF membranes to form coatings on the surface of the PSF membranes. Oil/water crossflow filtration experiments showed that the coated PSF membranes had water flux values 400% higher than that of an uncoated PSF membrane after 24 h of operation, and the coated membranes had higher organic rejection than the uncoated membranes.     

Conformational evolution of ubiquitin ions in electrospray mass spectrometry: molecular dynamics simulations at gradually increasing temperatures

Evidence from cross section data indicates that ubiquitin +13 ions lose their secondary and tertiary structure in mass spectrometric experiments. These transitions from the folded state into the near linear final structure occur at the experimental temperatures on time scales that are far too long for conventional molecular dynamics simulations. In this study, an approach to mass spectrometric unfolding processes is developed and a detailed application to an ubiquitin +13 ion system is presented. The approach involves a sequence of molecular dynamics simulations at gradually increasing temperatures leading to identification of major intermediate states, and the unfolding pathway. The unfolding rate at any temperature can then be calculated by a Rice-Ramsperger-Kassel (RRK) approach. For ubiquitin +13, three interesting intermediate states were found and the final near linear geometry was computed. The several relevant energy barriers calculated for the process are in the range of 7 to 15 kcal mol(-1). The unfolding time scale at 300 K was computed to be 2 ms. Cross section calculations using a hard sphere scattering model were carried out for the final structure and found to be in good accord with the results of electrospray experiments supporting the theoretical model used. The approach employed here should be applicable to any other solvent-free protein system.     

Directed-sorting method for synthesis of bead-based combinatorial libraries of heterogeneous catalysts

The synthesis and analysis of inorganic material combinatorial libraries by a directed-sorting, split-pool bead method was demonstrated. Directed-sorting, split-pool, metal-loaded libraries were synthesized by adsorbing metal salts (H2PtCl6, SnCl2, CuCl2, and NiCl2) and metal standards (Pt, Cu, Ni in HCl) onto 2-mg porous gamma-alumina beads in 96- or 384-well plates. A matrix algorithm for the synthesis of bead libraries treated each bead as a member of a row or column of a given matrix. Computer simulations and manual tracking of the sorting process were used to assess library diversity. The bead compositions were analyzed by energy-dispersive X-ray spectroscopy, X-ray fluorescence spectroscopy, electron probe microanalysis, inductively coupled plasma atomic emission spectroscopy, and inductively coupled plasma mass spectroscopy. The metal-loaded beads were analyzed by laser-activated membrane introduction mass spectroscopy (LAMIMS) for catalytic activity using methylcyclohexane dehydrogenation to toluene as a probe reaction. The catalytic activity of individual beads that showed minimal (approximately 20% of that of Pt on alumina) to high conversion could be determined semiquantitatively by LAMIMS. This method, therefore, provides an alternative to screening using microreactors for reactors that employ catalysts in the form of beads. The directed-sorting method offers the potential for synthesis of focused libraries of inorganic materials through relatively simple benchtop split-pool chemistry.     

Low-temperature metallic alloying of copper and silver nanoparticles with gold nanoparticles through digestive ripening

We describe a remarkable and simple alloying procedure in which noble metal intermetallic nanoparticles are produced in gram quantities via digestive ripening. This process involves mixing of separately prepared colloids of pure Au and pure Ag or Cu particles and then heating in the presence of an alkanethiol under reflux. The result after 1 h is alloy nanoparticles. Particles synthesized according to this procedure were characterized by UV-vis spectroscopy, EDX analysis, and high-resolution electron microscopy, the results of which confirm the formation of alloy particles. The particles of 5.6+/-0.5 nm diameter for Au/Ag and 4.8+/-1.0 nm diameter for Cu/Au undergo facile self-assembly to form 3-D superlattice ordering. It appears that during this digestive ripening process, the organic ligands display an extraordinary chemistry in which atom transfer between atomically pure copper, silver, and gold metal nanoparticles yields monodisperse alloy nanoparticles.     

Discrete Kakeya-type problems and small bases

A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erdős and Newman on bases for sets of integers, and to obtain several extensions for other groups.