On the number of connected convex subgraphs of a connected acyclic digraph

A digraph D is connected if the underlying undirected graph of D is connected. A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. We find the minimum and maximum possible number of connected convex subgraphs in a connected acyclic digraph of order n. Connected convex subgraphs of connected acyclic digraphs are of interest in the area of modern embedded processors technology.     

Quantitative real-time measurements of DNA hybridization with alkylated nonoxidized silicon nanowires in electrolyte solution

The quantitative, real-time detection of single-stranded oligonucleotides with silicon nanowires (SiNWs) in physiologically relevant electrolyte solution is demonstrated. Debye screening of the hybridization event is circumvented by utilizing electrostatically adsorbed primary DNA on an amine-terminated NW surface. Two surface functionalization chemistries are compared: an amine-terminated siloxane monolayer on the native SiO2 surface of the SiNW, and an amine-terminated alkyl monolayer grown directly on a hydrogen-terminated SiNW surface. The SiNWs without the native oxide exhibit improved solution-gated field-effect transistor characteristics and a significantly enhanced sensitivity to single-stranded DNA detection, with an accompanying 2 orders of magnitude improvement in the dynamic range of sensing. A model for the detection of analyte by SiNW sensors is developed and utilized to extract DNA-binding kinetic parameters. Those values are directly compared with values obtained by the standard method of surface plasmon resonance (SPR) and demonstrated to be similar. The nanowires, however, are characterized by higher detection sensitivity. The implication is that SiNWs can be utilized to quantitate the solution-phase concentration of biomolecules at low concentrations. This work also demonstrates the importance of surface chemistry for optimizing biomolecular sensing with silicon nanowires.     

Effect of hydrophobicity inside PEO-PPO-PEO block copolymer micelles on the stabilization of gold nanoparticles: experiments

In this paper we present the effect of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymer micelles and their hydrophobicity on the stabilization of gold nanoparticles. Gold nanoparticles were prepared by a method developed by Sakai et al. (Sakai, T.; Alexandridis, P. Langmuir 2004, 20, 8426). An absorption centered at 300-400 nm in time-dependent UV spectra provided evidence that the very first step of the synthesis was to form primary gold clusters. Then the gold clusters grew in size and were stabilized by block copolymer micelles. The stabilization capacities of the micelles were modulated by tuning the block copolymer concentration and composition and by adding salts. With good stabilization, gold particles were spherical and uniform in size with a diameter of 5-10 nm. Otherwise they were aggregates with irregular shapes such as triangular, hexagonal, and rodlike. The presence of a small amount of NaF significantly increased the stabilization capacity of the micelles and consequently modified the quality of the gold particles. Using FTIR and 1H NMR spectroscopy, micellization of the block copolymers and hydrophobicity of the micelles were proven very important for the stabilization. A higher hydrophobicity of the micelle cores was expected to favor the entrapment of primary gold clusters and the stabilization of gold nanoparticles.     

High resolution spectra and conformational analysis of 2-butoxy radical

We have recorded five high resolution (200 MHz), rotationally resolved, vibrational bands of the B-X electronic transition of 2-butoxy. Two bands of the 2-butoxy spectrum have been rotationally analyzed and assigned to two different geometrical conformers of the molecule. The analyses allow the determination of the six experimental rotational constants defined by the geometry of the species in the ground (X) and excited (B) electronic states and also four spin-rotation constants for the X electronic state of the conformers. Comparison of the experimental rotational constants with the results of ab initio computations provides unambiguous conformational assignment of these bands. This approach can be extended to assign two other spectral bands to the third 2-butoxy conformer.     

ε-Amino acids based on bicyclic skeleton: bicyclo[3.3.0]octane-5-amino-1-carboxylic acids

Tsc-protected ε-amino acids, bicyclo[3.3.0]octane-5-amino-1-carboxylic acids (1), ready to use in the solid-phase synthesis, are prepared from 4,4-diethylcarboxylic bicyclo[3.3.0]oct-2-enone (3), which is available in bulk from 2 through the catalytic Pauson-Khand reaction.     

Time-Resolved Fluorescence Anisotropy Study of the Interaction Between DNA and a Peptide Truncated from the p53 Protein Core Domain

Time-resolved fluorescence anisotropy spectroscopy was applied to study the interaction between a peptide truncated from the binding site of tumor suppressor p53 protein and the DNAs covalently labeled with 6-carboxyfluorescein (FAM) dye. Fluorescence intensity quenching and changes of anisotropy decay lifetime were monitored when FAM labeled DNA formed complex with the peptide. The results demonstrated that the sequence of DNA could not define the binding specificity between the peptide and DNA. But the anisotropy decay of FAM can be used to examine the binding affinity of the peptide to DNA. The fluorescent dynamics of FAM can also be used to represent the rigidity of the complex formed between the peptide and DNA.     

Three‐dimensional visible‐light capsule enclosing perfect supersized darkness via antiresolution

Supersized darkness in three dimensions surrounded by all light in free space is demonstrated theoretically and experimentally in the visible regime. The object staying in the darkness is similar to staying in an empty light capsule because light just bypasses it by resorting to destructive interference. A binary‐optical system is designed and fabricated based on achieving antiresolution (AR), by which electromagnetic energy flux avoids and bends smoothly around a nearly perfect darkness region. AR remains an unexplored topic hitherto, in contrast to the super‐resolution for realizing high spatial resolution. This novel scheme replies on smearing out the point spread function and thus poses less stringent limitations upon the object's size and position since the created dark (zero‐field) area reach 8 orders of magnitude larger than λ² in cross‐sectional size. It functions very well with arbitrarily polarized beams in three dimensions, which is also frequency scalable in the whole electromagnetic spectrum.     

Optimization‐free superoscillatory lens using phase and amplitude masks

A superoscillatory focusing lens has been experimentally demonstrated by optimizing Fresnel zone plates (FZP), with limited physical insight as to how the lens feature contributes to the focal formation. It is therefore imperative to establish a generalized viable account for both FZP (amplitude mask) and binary optics (phase mask). Arbitrary superoscillatory spots can now be customized and realized by a realistic optical device, without using optimization. It is counterintuitively found that high spatial frequency with small amplitude and destructive interference are favorable in superfocusing of a superoscillation pattern. The inevitably high sidelobe is pushed 15λ away from the central subwavelength spot, resulting in significantly enlarged field of view for viable imaging applications. This work therefore not only reveals the explicit physical role of any given metallic/dielectric rings but also provides an alternative design roadmap of superresolution imaging. The robust method is readily applicable in superthin longitudinally polarized needle light, quantum physics and information theory.     

Stereochemical analysis of ferrocene and the uncertainty of fluorescence XAFS data

Methods for the quantification of statistically valid measures of the uncertainties associated with X‐ray absorption fine structure (XAFS) data obtained from dilute solutions using fluorescence measurements are developed. Experimental data obtained from 10 mM solutions of the organometallic compound ferrocene, Fe(C₅H₅)₂, are analysed within this framework and, following correction for various electronic and geometrical factors, give robust estimates of the standard errors of the individual measurements. The reliability of the refinement statistics of standard current XAFS structure approaches that do not include propagation of experimental uncertainties to assess subtle structural distortions is assessed in terms of refinements obtained for the staggered and eclipsed conformations of the C₅H₅ rings of ferrocene. Standard approaches (XFIT, IFEFFIT) give refinement statistics that appear to show strong, but opposite, preferences for the different conformations. Incorporation of experimental uncertainties into an IFEFFIT‐like analysis yield refinement statistics for the staggered and eclipsed forms of ferrocene which show a far more realistic preference for the eclipsed form which accurately reflects the reliability of the analysis. Moreover, the more strongly founded estimates of the refined parameter uncertainties allow more direct comparison with those obtained by other techniques. These XAFS‐based estimates of the bond distances have accuracies comparable with those obtained using single‐crystal diffraction techniques and are superior in terms of their use in comparisons of experimental and computed structures.     

Dangling-bond logic gates on a Si(100)-(2 × 1)-H surface

Atomic-scale Boolean logic gates (LGs) with two inputs and one output (i.e. OR, NOR, AND, NAND) were designed on a Si(100)-(2 × 1)-H surface and connected to the macroscopic scale by metallic nano-pads physisorbed on the Si(100)-(2 × 1)-H surface. The logic inputs are provided by saturating and unsaturating two surface Si dangling bonds, which can, for example, be achieved by adding and extracting two hydrogen atoms per input. Quantum circuit design rules together with semi-empirical elastic-scattering quantum chemistry transport calculations were used to determine the output current intensity of the proposed switches and LGs when they are interconnected to the metallic nano-pads by surface atomic-scale wires. Our calculations demonstrate that the proposed devices can reach ON/OFF ratios of up to 2000 for a running current in the 10 μA range.