Hardness of Approximation for Crossing Number

We show that, if $\mathrm{P}\not=\mathrm{NP}$ , there is a constant c ₀>1 such that there is no c ₀-approximation algorithm for the crossing number, even when restricted to 3-regular graphs.     

Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians

The classic Cayley identity states that

det(∂)(detX)^s=s(s+1)?(s+n−1)(detX)^s−1$\det (\partial ){(\det X)}^s=s(s+1)?(s+n-1){(\det X)}^{s-1}$

where X=(_xij)$X=(x_{ij})$ is an n×n$n\times n$ matrix of indeterminates and ∂=(∂/∂_xij)$\partial =(\partial /\partial x_{ij})$ is the corresponding matrix of partial derivatives. In this paper we present straightforward algebraic/combinatorial proofs of a variety of Cayley-type identities, both old and new. The most powerful of these proofs employ Grassmann algebra (= exterior algebra) and Grassmann–Berezin integration. Among the new identities proven here are a pair of “diagonal-parametrized” Cayley identities, a pair of “Laplacian-parametrized” Cayley identities, and the “product-parametrized” and “border-parametrized” rectangular Cayley identities.     

The generalized second law in the emergent universe

This Letter studies whether the generalized second law of thermodynamics is fulfilled in the transition from a generic initial Einstein static phase to the inflationary phase, with constant Hubble rate, and from the end of the latter to the conventional era of thermal radiation dominated expansion. As it turns out, the said law is satisfied provided the radiation component does not largely contribute to the total energy of the static phase.     

A suggested statistical test for measuring bivariate nonlinear dependence

We devise a new asymptotic statistical test to assess independence in bivariate continuous distributions. Our approach is based on the Cramér–von Mises test, in which the empirical process is viewed as the Kullback–Leibler divergence, that is, as the distance between the data under the independence hypothesis and the data empirically observed. We derive the theoretical characteristic function of the limit distribution of the test statistic and find the critical values through computer simulation. A Monte Carlo experiment is considered as assessing the validation and power performance of the test by assuming a bivariate nonlinear dependence structure with fat tails. Two extra examples, respectively, consider stationary and conditionally nonstationary series. Results confirm that our suggested test is consistent and powerful in the presence of bivariate nonlinear dependence even if the environment is non-Gaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.     

Convex domination in the composition and cartesian product of graphs

In this paper we characterize the convex dominating sets in the composition and Cartesian product of two connected graphs. The concepts of clique dominating set and clique domination number of a graph are defined. It is shown that the convex domination number of a composition G[H] of two non-complete connected graphs G and H is equal to the clique domination number of G. The convex domination number of the Cartesian product of two connected graphs is related to the convex domination numbers of the graphs involved.     

Comparison of several extraction procedures for the determination of biopesticides in soil samples by ultrahigh pressure LC-MS/MS

A new procedure has been proposed for the determination of biopesticides (nicotine, sabadine, veratridine, rotenone, azadirachtin, cevadine, deguelin, spynosad D, and pyrethrins) and piperonyl butoxide in agricultural soils. Several extraction procedures such as solid-liquid extraction using mechanical shaking, sonication, pressurized liquid extraction, and modified QuEChERS (quick, easy, cheap, effective, rugged, and safe) have been tested, obtaining better results when QuEChERS procedure without further cleanup steps was applied. The determination of the compounds was carried out by ultra high pressure liquid chromatography coupled to tandem mass spectrometry, using methanol and aqueous solution of ammonium formate 5 mM as mobile phase. The method was validated for all compounds at concentrations ranging from 10 to 100 μg/kg and recoveries ranged from 68 to 116%, except for nicotine and sabadine, with recoveries lower than 50%. Precision was estimated through intra- and inter-day studies, obtaining intra-day precision lower than 20% for most of the compounds, and inter-day precision was lower than 25%. Limits of detection and quantification were also estimated, obtaining limits of quantification equal or lower than 10 μg/kg. Finally, the method was applied to the analysis of 20 real agricultural soil samples and no biopesticide residues were found over the limit of quantification.     

A methodology for the fabrication by FIB of needle-shape specimens around sub-surface features at the nanometre scale

A novel methodology for the preparation by focused ion beam (FIB) of needle-shape specimens in specific sites underneath the sample surface for their study by electron tomography (ET) is proposed. In particular, we demonstrate this methodology for the fabrication of needles containing InAs/InP quantum dots (QDs). The main challenge of this methodology is the location of specific QDs in the FIB equipment, as they are not visible with the secondary electrons detector. In order to overcome this difficulty, a series of marks visible both in conventional transmission electron microscopy and in the FIB are introduced before the preparation of the needles. The conditions for the fabrication by FIB of needles with optimized characteristics for their study by ET are also detailed.     

Ionically Self-Assembled, Multi-Luminophore One-Dimensional Micro- and Nanoscale Aggregates of Thiacarbocyanine GUMBOS

Groups of uniform materials based on organic salts (GUMBOS), derived from thiacarbocyanine (TC)-based dyes with increasing methyne chain lengths, were prepared through a single-step metathesis reaction between the iodide form of the TC dye and lithium bis(perfluoroethylsulfonyl)imide as the lipophilic anion source. Ionic self-assembly of these fluorescent hydrophobic GUMBOS resulted in aqueous dispersions of one-dimensional micro-and nano-scale molecular aggregates. Blended binary and ternary aggregates containing multiple TC GUMBOS were also prepared. These nanostructures exhibited a variety of aspect ratios, affording tunable F?rster resonance energy transfer (FRET) and aggregation-dependent spectroscopic properties.