Reaction mechanisms and kinetics for the oxidations of dimethyl sulfide, dimethyl disulfide, and methyl mercaptan by the nitrate radical

This study examines the initial oxidation routes of the three major reduced sulfur compounds (CH(3)SH, CH(3)SCH(3), and CH(3)SSCH(3)) by the nitrate radical using density functional and ab initio methods. Stationary points along each reaction pathway are examined using different levels of theory and basis sets to ensure the convergence of the results. Kinetics calculations follow on the determined reaction pathways to obtain the rate constants. This study shows that sulfur compounds exhibit a general trend of hydrogen abstraction following the formation of an initial sulfur-nitrate complex. The results are in agreement with experimental work on CH(3)SCH(3) and CH(3)SH, while refuting a proposal of several previous studies that oxygen addition is the dominant oxidation pathway in the case of CH(3)SSCH(3). The rate constants obtained from kinetics calculations are consistent with experimental findings and exhibit negative temperature dependence. Overall, this study confirms the importance of nitrate in the oxidation of reduced sulfur compounds in the atmosphere.     

Polarization instabilities in a multi-transverse-mode vertical-cavity surface-emitting laser with polarized optical feedback

We have experimentally studied polarization instabilities in the multi-transverse-mode regime of a vertical-cavity surface-emitting laser subject to polarized optical feedback. A dynamical regime that is similar to the transition from the so called low frequency fluctuation (LFF) to coherence collapse (CC) in the single-transverse-mode VCSEL is found and investigated. The role of higher order transverse modes is to increase the irregularity of the dynamics as shown experimentally and numerically.     

Photo-induced site-specific nitridation of plasma-deposited B10C2Hx films: A new pathway toward post-deposition doping of semiconducting boron carbides

We show that dopant impurities can be introduced in a controlled, site-specific manner into pre-deposited semiconducting boron carbide films. B―N bond formation has been characterized by X-ray photoelectron spectroscopy for semiconducting B₁₀C₂H_x films exposed to vacuum ultraviolet photons in the presence of NH₃. Core level photoemission data indicate that B―NH₂ bonds are formed at B sites bonded to other boron atoms (B―B), and not at boron atoms adjacent to carbon atoms (B―C) or at carbon atom sites. Nitridation obeys diffusion-limited kinetics. These results indicate that dopant species can be introduced in a controlled, site-specific manner into pre-deposited boron carbide films, as opposed to currently required dopant incorporation during the deposition process.     

Bichromatic and Equichromatic Lines in ℂ2 and ℝ2

Let G and R each be a finite set of green and red points, respectively, such that |G|=n, |R|=n−k, G∩R=∅, and the points of G∪R are not all collinear. Let t be the total number of lines determined by G∪R. The number of equichromatic lines (a subset of bichromatic) is at least (t+2n+3−k(k+1))/4. A slightly weaker lower bound exists for bichromatic lines determined by points in ℂ². For sufficiently large point sets, a proof of a conjecture by Kleitman and Pinchasi is provided. A lower bound of (2t+14n−k(3k+7))/14 is demonstrated for bichromatic lines passing through at most six points. Lower bounds are also established for equichromatic lines passing through at most four, five, or six points.     

Lines, Circles, Planes and Spheres

Let S be a set of n points in ℝ³, no three collinear and not all coplanar. If at most n−k are coplanar and n is sufficiently large, the total number of planes determined is at least 1+k\binomn-k2-\binomk2(\fracn-k2)1+k\binom{n-k}{2}-\binom{k}{2}(\frac{n-k}{2}). For similar conditions and sufficiently large n, (inspired by the work of P.D.T.A. Elliott in Acta Math. Sci. Hung. 18:181–188, 1967) we also show that the number of spheres determined by n points is at least 1+\binomn-13-t₃^orchard(n-1)1+\binom{n-1}{3}-t_{3}^{\mathrm{orchard}}(n-1), and this bound is best possible under its hypothesis. (By t₃^orchard(n)t_{3}^{\mathrm{orchard}}(n), we are denoting the maximum number of three-point lines attainable by a configuration of n points, no four collinear, in the plane, i.e., the classic Orchard Problem.) New lower bounds are also given for both lines and circles.     

Magnetic properties of prussian blue modified Fe3O4 nanocubes

Size controlled cubic Fe₃O₄ nanoparticles in the size range 90–10 nm were synthesized by varying the ferric ion concentration using the oxidation method. A bimodal size distribution was found without ferric ion concentration and the monodispersity increased with higher concentration. The saturation magnetization decreased from 90 to 62 emu/g when the particle size is reduced to 10 nm. The Fe₃O₄ nanoparticles with average particle sizes 10 and 90 nm were surface modified with prussian blue. The attachment of prussian blue with Fe₃O₄ was found to depend on the concentration of HCl and the particle size. The saturation magnetization of prussian blue modified Fe₃O₄ varied from 10 to 80 emu/g depending on the particle size. The increased tendency for the attachment of prussian blue with smaller particle size was explained based on the surface charge. The prussian blue modified magnetite nanoparticles could be used as a radiotoxin remover in detoxification applications.     

Weighted enumeration of spanning subgraphs in locally tree‐like graphs

Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}Using the theory of negative association for measures and the notion of unimodularity for random weak limits of sparse graphs, we establish the validity of the cavity method for counting spanning subgraphs subject to local constraints in asymptotically tree‐like graphs. Specifically, the normalized logarithm of the associated partition function (free energy) is shown to converge along any sequence of graphs whose random weak limit is a tree, and the limit is directly expressed in terms of the unique solution to a limiting cavity equation. On a Galton–Watson tree, the latter simplifies into a recursive distributional equation which can be solved explicitly. As an illustration, we provide a new asymptotic formula for the maximum size of a b‐matching in the Erd?s–Rényi random graph with fixed average degree and diverging size, for any $b\in\mathbb{N}$. To the best of our knowledge, this is the first time that correlation inequalities and unimodularity are combined together to yield a general proof of uniqueness of Gibbs measures on infinite trees. We believe that a similar argument is applicable to other Gibbs measures than those over spanning subgraphs considered here. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Peeking Inside the Black Box: Visualizing Statistical Learning With Plots of Individual Conditional Expectation

This article presents individual conditional expectation (ICE) plots, a tool for visualizing the model estimated by any supervised learning algorithm. Classical partial dependence plots (PDPs) help visualize the average partial relationship between the predicted response and one or more features. In the presence of substantial interaction effects, the partial response relationship can be heterogeneous. Thus, an average curve, such as the PDP, can obfuscate the complexity of the modeled relationship. Accordingly, ICE plots refine the PDP by graphing the functional relationship between the predicted response and the feature for individual observations. Specifically, ICE plots highlight the variation in the fitted values across the range of a covariate, suggesting where and to what extent heterogeneities might exist. In addition to providing a plotting suite for exploratory analysis, we include a visual test for additive structure in the data-generating model. Through simulated examples and real datasets, we demonstrate how ICE plots can shed light on estimated models in ways PDPs cannot. Procedures outlined are available in the R package ICEbox.