On friendly index sets of 2-regular graphs

Let G be a graph with vertex set V and edge set E, and let A be an abelian group. A labeling f:V→A induces an edge labeling f^∗:E→A defined by f^∗(xy)=f(x)+f(y). For i∈A, let v_f(i)=card{v∈V:f(v)=i} and e_f(i)=card{e∈E:f^∗(e)=i}. A labeling f is said to be A-friendly if |v_f(i)−v_f(j)|≤1 for all (i,j)∈A×A, and A-cordial if we also have |e_f(i)−e_f(j)|≤1 for all (i,j)∈A×A. When A=Z₂, the friendly index set of the graph G is defined as {|e_f(1)−e_f(0)|:the vertex labelingf is Z₂-friendly}. In this paper we completely determine the friendly index sets of 2-regular graphs. In particular, we show that a 2-regular graph of order n is cordial if and only if n?2 (mod 4).     

Strong edge-magic graphs of maximum size

An edge-magic total labeling on G is a one-to-one map λ from V(G)∪E(G) onto the integers 1,2,…,|V(G)∪E(G)| with the property that, given any edge (x,y), λ(x)+λ(x,y)+λ(y)=k for some constant k. The labeling is strong if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most 2|V(G)|-3 edges. In this paper we study graphs of this maximum size.     

Selective lighting up of segments around Gly,Ala and Ser/Thr in proteins

Direct detection of ¹³C nucleus can be used as a valuable alternative where ¹H detection poses a challenge due to relaxation effects, chemical exchange and poor chemical shift dispersion. In this context, we have designed a suite of 2D ¹³C^α‐detected hNCA experiments that provide sequential correlations of ¹³C^α with ¹⁵N on one hand and efficient spectroscopic labeling of certain groups of residues, namely, Gly, Ala, Ser and Thr, on the other. These residues act as checkpoints in the sequential walk, which in turn offer new possibilities of backbone assignment of small proteins from a set of 2D experiments, thereby providing great economy in terms of spectrometer time. The direct identification of peptide segments around Gly, Ala, Ser and Thr residues along a protein chain will be highly valuable for deriving important information on sites of ligand binding, phosphorylation, inhibitor/substrate binding, understanding protein folding pathways, comprehending local conformational dynamics etc. without having to obtain complete sequence‐specific assignments, which can be time consuming and at times formidable, especially in large proteins. We have illustratively demonstrated the multifaceted applications of these variants of 2D experiments on ubiquitin and M‐crystallin. We foresee that these 2D hNCA experiments will provide economic and efficient strategies for studying the structure and function of proteins. Copyright © 2012 John Wiley & Sons, Ltd.     

有向图n·■_m的优美性

给定有向图D(V,E),如果存在一个单射f:V(D)→{0,1,…,|E|}使得对于每条有向边(u,v),诱导函数f′:E(D)→{1,2,…,|E|}是一个双射函数,其中,f′(u,v)=[f(v)-f(u)](mod(|E|+1)),则f称为有向图D(V,E)的优美标号,f′称为有向图D(V,E)的诱导的边的优美标号.本文讨论了有向图n.■m的优美性,并且证明了当m=23且n为偶数时,n.■m是优美有向图.     

POPMUSIC for the point feature label placement problem

Point feature label placement is the problem of placing text labels adjacent to point features on a map so as to maximize legibility. The goal is to choose positions for the labels that do not give rise to label overlaps and that minimize obscuration of features. A practical goal is to minimize the number of overlaps while considering cartographic preferences. This article proposes a new heuristic for solving the point feature label placement problem based on the application of the POPMUSIC frame. Computational experiments show that the proposed heuristic outperformed other recent metaheuristics approaches in the literature. Experiments with problem instances involving up to 10 million points show that the computational time of the proposed heuristic increases almost linearly with the problem size. New problem instances based on real data with more than 13,000 labels are proposed.     

Synthesis of C-8 Deuterated Glycosides of 3-Deoxy-D-manno-oct-2-ulosonic Acid (Kdo) Related to Chlamydial Lipopolysaccharides

Summary.  Methyl glycosides of Kdo and a (2→8)-linked Kdo disaccharide were prepared which contain a deuterium label at C-8 of the reducing unit. The label was introduced in fair diastereoselectivity upon reduction of an aldehyde group using a chiral borane complex derived from N-benzyloxycarbonyl-(S)-proline which produced the 8-(S)-deuterated derivative as the major isomer. Further coupling with a Kdo bromide gave the α-(2→8)-linked disaccharide in good yield. The deprotected disaccharide serves as a model for NMR spectroscopic studies on the side chain conformation of a carbohydrate epitope from the bacterial pathogen Chlamydia. Received September 17, 2001. Accepted October 17, 2001     

Rapid labeling of amino acid neurotransmitters with a fluorescent thiol in the presence of o‐phthalaldehyde

LIF detection often requires labeling of analytes with fluorophores; and fast fluorescent derivatization is valuable for high‐throughput analysis with flow‐gated CE. Here, we report a fast fluorescein‐labeling scheme for amino acid neurotransmitters, which were then rapidly separated and detected in flow‐gated CE. This scheme was based on the reaction between primary amines and o‐phthalaldehyde in the presence of a fluorescent thiol, 2‐((5‐fluoresceinyl)aminocarbonyl)ethyl mercaptan (FACE‐SH). The short reaction time (<30 s) was suited for on‐line mixing and derivatization that was directly coupled with flow‐gated CE for rapid electrophoretic separation and sensitive LIF detection. To maintain the effective concentration of reactive FACE‐SH, Tris(2‐carboxyethyl)phosphine was added to the derivatization reagents to prevent thiol loss due to oxidation. This labeling scheme was applied to the detection of neurotransmitters by coupling in vitro microdialysis with online derivatization and flow‐gated CE. It is also anticipated that this fluorophore tagging scheme would be valuable for on‐chip labeling of proteins retained on support in SPE.     

A convenient synthesis of deuterium labeled tertiary aliphatic nitro ketones and nitriles - starting materials for preparation of deuterated cyclic nitrones, isomeric hydroxylamines, and corresponding C-nitroso compounds

Tertiary aliphatic β- and γ-nitro nitriles and ketones deuterated in (several) selected positions had been synthesized. The deuterated nitro compounds served as a starting material for the corresponding deuterium labeled nitrones or hydroxylamines (reducing with aluminum amalgam). Further oxidation of the last two groups of compounds with sodium periodate or m-CPBA afforded the relevant deuterated tertiary C-nitroso compounds.