Asymptotic normality in random graphs with given vertex degrees

We consider random graphs with a given degree sequence and show, under weak technical conditions, asymptotic normality of the number of components isomorphic to a given tree, first for the random multigraph given by the configuration model and then, by a conditioning argument, for the simple uniform random graph with the given degree sequence. Such conditioning is standard for convergence in probability, but much less straightforward for convergence in distribution as here. The proof uses the method of moments, and is based on a new estimate of mixed cumulants in a case of weakly dependent variables. The result on small components is applied to give a new proof of a recent result by Barbour and Röllin on asymptotic normality of the size of the giant component in the random multigraph; moreover, we extend this to the random simple graph.     

Random graphs with given vertex degrees and switchings

Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that, assuming essentially a bounded second moment of the degree distribution, this construction with the simplest types of switchings yields a simple random graph with an almost uniform distribution, in the sense that the total variation distance is o(1). This construction can be used to transfer results on distributional convergence from the configuration model multigraph to the uniform random simple graph with the given vertex degrees. As examples, we give a few applications to asymptotic normality. We show also a weaker result yielding contiguity when the maximum degree is too large for the main theorem to hold.     

Excitation energy transfer in atom—molecule interactions of sodium and potassium vapours

The mechanism of energy transfer, from optically excited sodium and potassium molecules to sodium and potassium atoms has been investigated by the method of sensitized fluorescence. The rate constants of collisional energy transfer have been determined.     

A laser extraction/combustion technique for in situ delta(13)C analysis of organic and inorganic materials

A CO(2) laser extraction system is described for in situ delta(13)C analysis of organic and inorganic materials. Carbonaceous compounds volatilized by the laser are quantitatively converted to CO(2) gas by a combustion furnace mounted after the sample chamber. Gases produced by the laser and combustion processes are swept by helium carrier gas and separated by a packed gas chromatography column prior to their introduction to an isotope ratio monitoring mass spectrometer. A sample of lentil bean was analyzed at a spatial resolution of 200 μm and yielded delta(13)C values with precision of +/- 0.3 per thousand. The accuracy of delta(13)C measurements was better than +/- 0.5 per thousand from NBS 22 (mineral oil), USGS 24 (graphite), and IAEA CO-1 (calcium carbonate). Copyright 1999 John Wiley & Sons, Ltd.     

Separation and purification of puerarin using beta-cyclodextrin-coupled agarose gel media

The isoflavonoid puerarin, a well-known traditional Chinese drug, has been purified in one step from an extract of Radix puerariae (root of the plant Pueralria lobata) by adsorption chromatography on an epichlorohydrin polymerized beta-cyclodextrin ligand coupled to brominated allyl-group substituted Sepharose HP. Acetic acid (10%) was used as the mobile phase and the optimum loading capacity was around 1.2 mg crude extract/ml packed gel. The purity of the collected puerarin was about 98% with a recovery of about 62%.     

Production, purification and characterization of recombinant human interferon gamma.

An essentially three-step chromatographic purification procedure, i.e., ion-exchange, immobilized metal ion affinity and size-exclusion chromatography, is described for the purification to homogeneity of recombinant human interferon-gamma (rhIFN-gamma) from the inclusion bodies produced in genetically transformed Escherichia coli cells. Batchwise adsorption of the cloudy solution of renatured rhIFN-gamma obviated the need for high-speed centrifugation to clarify the suspension. This step effectively removed about 70% of extraneous protein impurities. The established purification process is reproducible and leads to a total recovery of 32%. Pilot-scale processing of E. coli cells grown in a 30-l fermentor gave about 70 mg of a homogeneous preparation of rhIFN-gamma. The specific biological activity of purified rhIFN-gamma is ca. 3.4 x 10(7) I.U./mg protein, which is comparable to that of its natural counterpart. It is basic protein (pI greater than pH 9) with a monomer relative molecular mass of 15,000. It behaves, however, as a dimer on size-exclusion chromatography. Its partial NH2-terminal sequence is identical with that established for the rhIFN-gamma. However, its amino acid composition and its relative molecular mass (15,067 as determined by electrospray mass spectrometry) indicate that the purified protein is a truncated form lacking fifteen amino acid residues from its carboxyl-terminal side. This modification does not seem to have any adverse effect on its biological potency. The levels of DNA, bacterial endotoxins and Ni(II) ions in the final product were determined.     

Investigation of the adsorption behavior of glycine peptides on 12% cross-linked agarose gel media

The highly cross-linked 12% agarose gel Superose 12 10/300 GL causes retardation of glycine peptides when mobile phases containing varying concentrations of acetonitrile in water are used. An investigation has been made into the retention mechanism behind this retardation using the glycine dipeptide (GG) and tripeptide (GGG) as models. The dependence of retention times of analytical-size peaks under different experimental conditions was interpreted such that the adsorption most probably was caused by the formation of hydrogen bonds but that electrostatic interactions cannot be ruled out. Thereafter, a nonlinear adsorption study was undertaken at different acetonitrile content in the eluent, using the elution by characteristic points (ECPs) method on strongly overloaded GG and GGG peaks. With a new evaluation tool, the adsorption energy distribution (AED) could be calculated prior to the model selection. These calculations revealed that when the acetonitrile content in the eluent was varied from 0% to 20% the interactions turned from (i) being homogenous (GG) or mildly heterogeneous (GGG), (ii) via a more or less stronger degree of heterogeneity around one site to (iii) finally a typical bimodal energy interaction comprising of two sites (GG at 20% and GGG at 10% and 20%). The Langmuir, Tóth and bi-Langmuir models described these interesting adsorption trends excellently. Thus, the retardation observed for these glycine peptides is interpreted as being of mixed-mode character composed of electrostatic bonds and hydrogen bonds.