Saturation in random graphs

A graph H is K_s ‐saturated if it is a maximal K_s ‐free graph, i.e., H contains no clique on s vertices, but the addition of any missing edge creates one. The minimum number of edges in a K_s ‐saturated graph was determined over 50 years ago by Zykov and independently by Erd?s, Hajnal and Moon. In this paper, we study the random analog of this problem: minimizing the number of edges in a maximal K_s ‐free subgraph of the Erd?s‐Rényi random graph G (n, p ). We give asymptotically tight estimates on this minimum, and also provide exact bounds for the related notion of weak saturation in random graphs. Our results reveal some surprising behavior of these parameters. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 169–181, 2017     

A new hybrid algorithm for finding the lowest minima of potential surfaces: approach and application to peptides

A new algorithm is presented for finding the global minimum, and other low-lying minima, of a potential energy surface (PES) of biological molecules. The algorithm synergetically combines three well-known global optimization methods: the diffusion equation method (DEM), which involves smoothing the PES; a simulated annealing (SA) algorithm; and evolutionary programming (EP), whose population-oriented approach allows for a parallel search over different regions of the PES. Tests on five peptides having between 6 and 9 residues show that the code implementing the new combined algorithm is efficient and is found to outperform the constituent methods, DEM and SA. Results of the algorithm, in the gas phase and with the GBSA implicit solvent model, are compared with crystallographic data for the test peptides; good accord is found in all cases. Also, for all but one of the examples, our hybrid algorithm finds a minimum deeper than those obtained by a very extensive scan. TINKERs implementation of the OPLS-AA force field is employed for the structure prediction. The results show that the new algorithm is a powerful structure predictor, when a reliable potential function is available. Our implementation of the algorithm is time-efficient, and requires only modest computational resources. Work is underway on applications of the new algorithm to structural prediction of proteins and other biological macro-molecules.     

Investigation of mixed oxidation state cyanide-bridged Re(V)oxo (acac(2)en/pn) and Re(I)(bipy)(CO)3 complexes

A series of cyanide-bridged complexes that combine a low-valent photoacceptor rhenium(I) metal center with an electroactive midvalent rhenium(V) complex were prepared. The synthesis involved the preparation of novel asymmetric rhenium(V) oxo compounds, cis-Re(V)O(CN)(acac(2)en) (1) and cis-Re(V)O(CN)(acac(2)pn) (2), formed by reacting trans-[Re(V)O(OH(2))(acac(2)en)]Cl or trans-Re(V)O(acac(2)pn)Cl with [NBu(4)][CN]. The μ-bridged cyanide mixed-oxidation Re(V)-Re(I) complexes were prepared by incubating the asymmetric complexes, 1 or 2, with fac-[Re(I)(bipy)(CO)(3)][OTf] to yield cis-[Re(V)O(acac(2)en)(μ-CN-1κC:2κN)-fac-Re(I)(bipy)(CO)(3)][PF(6)] (3) and [cis-Re(V)O(acac(2)pn)(μ-CN-1κC:2κN)-fac-Re(I)(bipy)(CO)(3)][PF(6)] (4), respectively.     

Stability of noble-gas hydrocarbons in an organic liquid-like environment: HXeCCH in acetylene

Noble-gas hydrides such as HXeCCH are prepared in cryogenic noble-gas matrices where they are stable. Molecular dynamics simulations reported here predict that HXeCCH is chemically stable in clusters of acetylene, and that stability prevails for temperatures of at least 150 K, at which the clusters are liquid-like. The HXeCCH(C(2)H(2))(n) clusters are studied for sizes up to n = 7. Ab Initio Molecular Dynamics trajectories of 10 ps duration are computed using BLYP-D DFT potential. The liquid-like nature of the system at 150 K is reflected in large amplitude motion of intermolecular distances and orientations. In addition, structures, energetics, NBO charges and bonding analysis at equilibrium are also reported. Complexation is found to be energetically favorable, and to increase the stability of the HXeCCH molecule. The significance of the existence of stable liquid-like complexes of noble-gas hydrides is discussed.     

Spectra of lifted Ramanujan graphs

A random n-lift of a base-graph G is its cover graph H on the vertices [n]×V(G), where for each edge uv in G there is an independent uniform bijection π, and H has all edges of the form (i,u),(π(i),v). A main motivation for studying lifts is understanding Ramanujan graphs, and namely whether typical covers of such a graph are also Ramanujan.Let G be a graph with largest eigenvalue λ₁ and let ρ be the spectral radius of its universal cover. Friedman (2003) [12] proved that every “new” eigenvalue of a random lift of G is with high probability, and conjectured a bound of ρ+o(1), which would be tight by results of Lubotzky and Greenberg (1995) [15]. Linial and Puder (2010) [17] improved Friedman?s bound to . For d-regular graphs, where λ₁=d and , this translates to a bound of O(d2/3), compared to the conjectured .Here we analyze the spectrum of a random n-lift of a d-regular graph whose nontrivial eigenvalues are all at most λ in absolute value. We show that with high probability the absolute value of every nontrivial eigenvalue of the lift is . This result is tight up to a logarithmic factor, and for λ?d2/3−ε it substantially improves the above upper bounds of Friedman and of Linial and Puder. In particular, it implies that a typical n-lift of a Ramanujan graph is nearly Ramanujan.     

Carbon Dots Integrated NiCo2O4 Hierarchical Nanoneedle Arrays Supported on Ni Foam as Efficient and Stable Electrode for Hydrogen and Oxygen Evolution Reactions

The production of hydrogen and oxygen via water electrolysis has become a sustainable and encouraging pathway for the establishment of new energy sources. Herein, we report the successful growth of hierarchical NiCo₂O₄‐carbon dots (CDs) nanoneedle arrays supported on nickel foam through a simple and environmentally benign hydrothermal self‐assembly technique. The designed material acts as a binder free electrode and shows bifunctional electrocatalytic activity for both hydrogen evolution reaction (HER) as well as oxygen evolution reaction (OER) in alkaline medium. An electrocatalyst sample with an optimal loading of CDs (25 mg) requires a low overpotential of 146 mV to achieve a current density of 10 mA/cm² for the HER in an alkaline medium, whereas it requires an overpotential of 390 mV to achieve a current density of 50 mA/cm² for the OER in the same alkaline medium. The excellent electrocatalytic activities of the sample with loading of CD can be ascribed due to the presence of large number of exposed active sites offered by CD/NiCo₂O₄ and the enhanced electron transfer processes occurring as a result of hierarchical structure composed of three‐dimensional nickel foam and the NiCo₂O₄?CDs nanoneedle arrays. Thus, the synthesis method introduced in this present work is a facile and cost‐effective approach for the construction of bifunctional electrocatalysts with high reactivity and excellent durability.     

Reactive characterization of nanothermites

Conventional thermal analysis techniques (TG and DSC) give valuable information on the activation energy and the reactivity of energetic materials such as organic explosives. Here, we discuss the use of these methods for characterizing nanothermites, energetic compositions made of metallic oxides and a fuel (often a reducing metal). The experimental limitations of these analysis techniques are identified. It is difficult to ignite nanothermites with slow heating rates as those used in DSC. This is due to the inorganic nature of the thermite components and because the reaction involves interparticular heat and matter transfers. In addition, during the progressive decomposition of nanothermites, there is no change in mass, so it cannot be observed by thermogravimetric analysis. The use of laser ignition to prime the abrupt combustion of nanothermite pellets allows determining the ignition energy and analyzing the propagation of the combustion front. It also provides qualitative data that can be used to understand the combustion mechanism and to correlate it to the microstructure of the nanothermites. By analyzing several examples, we will show that the coupling of high speed video to existing thermal analysis techniques could significantly extend their utilization range for the characterization of new energetic materials.     

Effects of physical aging on solubility,diffusivity, and permeability of propane and n-butane in poly(4-methyl-2-pentyne)

The effects of physical aging on the solubility, diffusivity, and permeability of propane and n-butane in a hydrocarbon-based disubstituted polyacetylene, poly(4-methyl-2-pentyne) (PMP), were studied. As the relative pressure of propane and n-butane increased, the solubility of both hydrocarbons increased. Like other glassy polymers, the sorption isotherms for propane and n-butane in all PMP films were concave to the relative pressure axis, indicating dual-mode sorption behavior. The diffusion of propane and n-butane in PMP followed typical Fickian diffusion in a plane sheet. The propane diffusivity in both the unaged and aged films increased with increasing concentration of propane sorbed in the film. The n-butane diffusivity in aged films also increased with increasing n-butane concentration. However, unaged films showed the opposite behavior: the diffusivity decreased with increasing n-butane concentration. These diffusion phenomena are a consequence of the interplay between thermodynamic and mobility factors. The permeabilities of propane and n-butane decreased monotonically with increasing penetrant concentration, similar to the behavior observed in other common glassy polymers. The relaxation of the nonequilibrium excess free volume in PMP films induced the decrease in both solubility and diffusivity. As a result, the permeability of propane and n-butane in PMP decreased upon physical aging. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2407–2418, 2004     

Cr(III) and Cr(VI) speciation measurements in environmental reference materials

The production of reference materials for quality control of Cr(III) and Cr(VI) speciation in environmental samples is described. It concerns in the first place two lyophilized solutions containing Cr(III) and Cr(VI) at different concentrations, respectively representative for drinking water and filter leaching solutions, and in the second place filters loaded with welding dust. Twenty-four laboratories with experience in the field participated in an intercomparison exercise organized to validate the suitability of the reference materials and to gauge the state-of-the-art of Cr speciation throughout Europe. The outcome of this exercise is discussed.     

Inorganic‐Base‐Mediated Hydroamination of Alkenyl Oximes for the Synthesis of Cyclic Nitrones

A method based on hydroamination mediated by inorganic base was developed for the synthesis of cyclic nitrones from alkenyl oximes. DFT calculations of the reaction pathway suggested that this hydroamination could proceed through an unprecedented nucleophilic amination of the unactivated alkene by the oxime nitrogen atom. The transition state of this reaction is stabilized by an ionic interaction between a metal cation such as K⁺ and the oxime oxygen and negatively charged alkene moiety.