Die Bestimmung der Halogene in organischen Verbindungen

Ohne Zusammenfassung     

On the restricted homomorphism problem

The restricted homomorphism problem asks: given an input digraph G and a homomorphism g:G→Y, does there exist a homomorphism f:G→H? We prove that if H is hereditarily hard and YH, then is NP-complete. Since non-bipartite graphs are hereditarily hard, this settles in the affirmative a conjecture of Hell and Nešetřil.     

Halomethyl-Triazoles for Rapid,Site-Selective Protein Modification

Post-translational modifications (PTMs) are used by organisms to control protein structure and function after protein translation, but their study is complicated and their roles are not often well understood as PTMs are difficult to introduce onto proteins selectively. Designing reagents that are both good mimics of PTMs, but also only modify select amino acid residues in proteins is challenging. Frequently, both a chemical warhead and linker are used, creating a product that is a misrepresentation of the natural modification. We have previously shown that biotin-chloromethyl-triazole is an effective reagent for cysteine modification to give S-Lys derivatives where the triazole is a good mimic of natural lysine acylation. Here, we demonstrate both how the reactivity of the alkylating reagents can be increased and how the range of triazole PTM mimics can be expanded. These new iodomethyl-triazole reagents are able to modify a cysteine residue on a histone protein with excellent selectivity in 30 min to give PTM mimics of acylated lysine side-chains. Studies on the more complicated, folded protein SCP-2L showed promising reactivity, but also suggested the halomethyl-triazoles are potent alkylators of methionine residues.     

Shear wave caustics and the shadows of surface breaking cracks

A refinement to the detection of defects in rods and pipes by means of their ultrasonic shadows is presented. It has been previously shown that in standard non-destructive test configurations ultrasonic waves inside cylindrical test objects form caustics, surfaces of high sound intensity. Here it is demonstrated that when a crack edge crosses a caustic the diffraction of sound around the defect is enhanced, which allows the point at which this intersection occurs to be detected. Because the caustic is a well-defined geometric entity the position of the crack edge is now known. This effect presents a novel method of sizing defects that extend in from the surface. Experiments were performed in water immersion using 5 MHz sound. The test specimens were 76 mm diameter aluminium cylinders into which slots were cut to act as artificial defects.     

Wavelets for electronic structure calculations

Molecular electronic structure calculations have a multi‐scale character through the presence of a set of singularities corresponding to atomic nuclei, and thus there exists a potential to improve the efficiency of these calculations using fast wavelet transform techniques. We report on the development of a one dimensional prototype benchmark problem of sufficient complexity to capture the features of 3‐D problems that are being solved today in quantum electronics calculations. Theoretical estimates of decay across scales and spatial distribution of wavelet coefficients for the solutions of the 1‐D and 3‐D problems are derived and verified experimentally. Equivalence in a multi‐resolution context of the solutions of the 1‐D prototype and the 3‐D problem is established. This revised version was published online in July 2006 with corrections to the Cover Date.     

Non-stochastic sampling error in quantal analyses for Campylobacter species on poultry products

Using primers and fluorescent probes specific for the most common food-borne Campylobacter species (Campylobacter jejuni and Campylobacter coli), we developed a multiplex, most probable number (MPN) assay using quantitative PCR (qPCR) as the determinant for binomial detection: i.e., number of p positive pathogen growth responses out of n?=?6 observations each of 4 mL (V) per dilution. Working with media washes of thrice frozen-thawed chicken pieces which had been spiked with known levels of C. jejuni and C. coli, we found that about 20 % of the experiments had a significant amount of error in the form of either greater than 25 % MPN calculation error (Δε) and/or a low apparent recovery rate (R less than 1?=?MPN observed ÷ CFU spiked). Assuming such errors were exacerbated by an excessively small n, we examined computer-generated MPN enumeration data from the standpoint of stochastic sampling error (Δ) and found that such binomial-based assays behaved identically to Poisson-based methods (e.g., counting data) except that fewer technical replicates (n) appeared to be required for the same number of cells per test volume (μ). This result implies that the qPCR detection-based MPN protocol discussed herein should accurately enumerate a test population with a μ?≥?1 using n?=?6 observations per dilution. For our protocol, this equates to ≥?8 cells per 400–500 g of sampled product. Based on this analysis, the error rate we saw in spiked experiments (where μ >?>?1) implied a non-stochastic source. In other experiments we present evidence that this source was, at least in part, related to the cell concentration step (i.e., centrifugation). We also demonstrate that the error rate lessened (from ～38 % to ～13 %) at lower Campylobacter levels (μ?≤?40) as would most likely exist in nature. Using this protocol, we were able to quantify 14 to 1,226 MPN per 450 g of naturally contaminated chicken for skinless pieces and 11 to 244 MPN per 450 g for wings, breasts, legs, and thighs (skin on) whereupon about 50 % of the 29 samples tested negative for both species. Four of these chicken wash samples did have substantially lower Campylobacter levels (1 to 6 MPN per 450 g) which might be better enumerated using a larger n. However, we established that the limit of quantification of this protocol diminishes for n?>?6 because one is ever more diluting the sample, or lessening V, to achieve the requisite n.     

Application of portable Raman spectroscopy and benchtop spatially offset Raman spectroscopy to interrogate concealed biomaterials

In this paper, we demonstrate the ability of portable Raman spectroscopy and benchtop spatially offset Raman spectroscopy (SORS) techniques to rapidly identify real and fake ivory samples. Both techniques were able to identify exposed genuine from fake ivory samples. In contrast to conventional Raman spectroscopy, SORS was, in addition, able to identify ivory concealed by plastics, paints, varnishes and cloth. Application of the SORS technique allows the interrogation of biomaterial samples through materials in which conventional Raman spectroscopic instrumentation cannot penetrate. Copyright © 2009 John Wiley & Sons, Ltd.     

Graph homomorphism reconfiguration and frozen H-colorings

We say that a graph $F$ strongly arrows a pair of graphs $\left(G,H\right)$ and write $\text{◂→▸}F\stackrel{\text{ind}}{\to }\left(G,H\right)$ if any coloring of its edges with red and blue leads to either a red $G$ or a blue $H$ appearing as induced subgraphs of $F$. The induced Ramsey number, $\text{◂...▸}\text{IR}\left(G,H\right)$, is defined as $\text{◂lim▸}\min \text{◂{}▸}\{|V\left(F\right)|:\text{◂→▸}F\stackrel{\text{ind}}{\to }\left(G,H\right)\}$. We consider the connection between the induced Ramsey number for a pair of two connected graphs $\text{◂...▸}\text{IR}\left(G,H\right)$ and the induced Ramsey number for multiple copies of these graphs $\text{IR}\text{◂()▸}\left(sG,tH\right)$, where $xG$ denotes the pairwise vertex-disjoint union of $x$ copies of $G$. It is easy to see that if $\text{◂→▸}F\stackrel{\text{ind}}{\to }\left(G,H\right)$, then $\text{◂⋅▸}\left(s+t-1\right)F\stackrel{\text{ind}}{\to }\text{◂()▸}\left(sG,tH\right)$. This implies that $$\text{◂...▸}\text{IR}\text{◂≤▸}\text{◂()▸}\left(sG,tH\right)\le \left(s+t-1\right)\text{IR}\left(G,H\right).$$ For several specific graphs, such as a path on three vertices vs a complete multipartite graph, a matching vs a complete graph, or a matching vs another matching, it is known that the above inequality is tight. On the other hand, the inequality is also strict for some graphs. However, even in the simplest case when $H$ is an edge and $t=2$, it is not known for what $G$ and for what $s$ the above inequality is tight. We show that it is tight if $G$ is connected and $s$ is at least as large as the order of $G$. In addition, we make further progress in determining induced Ramsey numbers for multiple copies of graphs, such as paths and triangles.     

Building blocks for the variety of absolute retracts

Given a graph H with a labelled subgraph G, a retraction of H to G is a homomorphism r:H→G such that r(x)=x for all vertices x in G. We call G a retract of H. While deciding the existence of a retraction to a fixed graph G is NP-complete in general, necessary and sufficient conditions have been provided for certain classes of graphs in terms of holes, see for example Hell and Rival.For any integer k?2 we describe a collection of graphs that generate the variety AR_k of graphs G with the property that G is a retract of H whenever G is a subgraph of H and no hole in G of size at most k is filled by a vertex of H. We also prove that AR_k⊂NUF_k+1, where NUF_k+1 is the variety of graphs that admit a near unanimity function of arity k+1.