End-to-end correlation for a C-12 hydrocarbon chain

The 19F nuclear spin-lattice relaxation rate constants were measured as a function of magnetic field strength for 1,12-diaminododecane labeled at one end with a nitroxide radical and at the other with a trifluoromethyl group. The magnetic relaxation dispersion profile (MRD) reports the spectral density function appropriate to the end-to-end correlation function for the doubly labeled molecule. After extrapolation to zero concentration to eliminate the intermolecular relaxation contribution to relaxation, the resulting intramolecular MRD profile was compared with several model approaches. The rotational model for the spectral density functions as included in the Solomon-Bloembergen-Morgan equations does not describe the data well. The earlier model of Freed for nuclear spin relaxation induced by a freely diffusing paramagnetic co-solute is not rigorous for this case because the paramagnet is tethered to the observed nuclear spin and only a restricted space in the immediate vicinity of the nuclear spin is accessible for pseudo-translational diffusion of one end of the molecule with respect to the other. A generalization of the Torrey model for magnetic relaxation by translational diffusion developed by Nevzorov and Freed, which includes the effect of restrictions imposed by the finite length of the chain, describes the experiment within experimental errors. A simple modification of the Hwang-Freed model that does not specifically include the dynamical effects of the finite tether also provides a good approximation to the data when the tether chain is sufficiently long.     

Structure determination of aligned samples of membrane proteins by NMR spectroscopy

The paper briefly reviews the process of determining the structures of membrane proteins by NMR spectroscopy of aligned samples, describes the integration of recent developments in the interpretation of spectra of aligned proteins and illustrates the application of these methods to the trans-membrane helical domain of a protein. The emerging methods of interpreting the spectral parameters from aligned samples of isotopically labeled proteins provide opportunities for simultaneously assigning the spectra and determining the structures of the proteins, and also for comparing the results from solid-state NMR experiments on completely aligned samples with those of solution NMR experiments on weakly aligned samples.     

Conditional distributions of record values and characterizations of distributions

We consider some regression relations for record values X(n), n > 0, generated by a sequence of independent random variables X₁, X₂, X₃,... with a common continuous cumulative distribution function F(x). New characterizations of distributions based on regression properties of record values are obtained. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 5–14.     

Inhibition of Acinetobacter baumannii biofilm formation on a methacrylate polymer containing a 2-aminoimidazole subunit

A polymeric composite containing a 2-aminoimidazole derivative was synthesized. It was found that this polymer was resistant to biofilm colonization by Acinetobacter baumannii, no leaching of the 2-aminoimidazole derivative was observed after 2 weeks of treatment with deionized water, and the resulting polymer was not hemolytic.     

Structure determination of a membrane protein with two trans-membrane helices in aligned phospholipid bicelles by solid-state NMR spectroscopy

The structure of the membrane protein MerFt was determined in magnetically aligned phospholipid bicelles by solid-state NMR spectroscopy. With two trans-membrane helices and a 10-residue inter-helical loop, this truncated construct of the mercury transport membrane protein MerF has sufficient structural complexity to demonstrate the feasibility of determining the structures of polytopic membrane proteins in their native phospholipid bilayer environment under physiological conditions. PISEMA, SAMMY, and other double-resonance experiments were applied to uniformly and selectively (15)N-labeled samples to resolve and assign the backbone amide resonances and to measure the associated (15)N chemical shift and (1)H-(15)N heteronuclear dipolar coupling frequencies as orientation constraints for structure calculations. (1)H/(13)C/(15)N triple-resonance experiments were applied to selectively (13)C'- and (15)N-labeled samples to complete the resonance assignments, especially for residues in the nonhelical regions of the protein. A single resonance is observed for each labeled site in one- and two-dimensional spectra. Therefore, each residue has a unique conformation, and all protein molecules in the sample have the same three-dimensional structure and are oriented identically in planar phospholipid bilayers. Combined with the absence of significant intensity near the isotropic resonance frequency, this demonstrates that the entire protein, including the loop and terminal regions, has a well-defined, stable structure in phospholipid bilayers.     

NMSSM Higgs benchmarks near 125 GeV

The recent LHC indications of a SM-like Higgs boson near 125 GeV are consistent not only with the Standard Model (SM) but also with Supersymmetry (SUSY). However naturalness arguments disfavour the Minimal Supersymmetric Standard Model (MSSM). We consider the Next-to-Minimal Supersymmetric Standard Model (NMSSM) with a SM-like Higgs boson near 125 GeV involving relatively light stops and gluinos below 1 TeV in order to satisfy naturalness requirements. We are careful to ensure that the chosen values of couplings do not become non-perturbative below the grand unification (GUT) scale, although we also examine how these limits may be extended by the addition of extra matter to the NMSSM at the two-loop level. We then propose four sets of benchmark points corresponding to the SM-like Higgs boson being the lightest or the second lightest Higgs state in the NMSSM or the NMSSM-with-extra-matter. With the aid of these benchmark points we discuss how the NMSSM Higgs boson near 125 GeV may be distinguished from the SM Higgs boson in future LHC searches.     

Representations of ordered random variables in the terms of the sums or products of independent variables

This is a survey of the available representations capable of expressing dependent ordered variables like order statistics and records as sums of independent summands or as products of independent random multipliers. Some new similar representations are obtained that in a similar manner express the common distributions of representatives of these two types of ordered random variables.     

On the average number of records for sequences of not identically distributed random variables

The scheme of n series of independent random variables X ₁₁, X ₂₁, …, X _k1, X ₁₂, X ₂₂, …, X _k2, …, X _1n , X _2n , …, X _kn is considered. Each of these successive series X _1m , X _2m , …, X _km , m = 1, 2, …, n consists of k variables with continuous distribution functions F ₁, F ₂, …, F _k , which are the same for all series. Let N(nk) be the number of upper records of the given nk random variables, and EN(nk) be the corresponding expected value. For EN(nk) exact upper and lower estimates are obtained. Examples are given of the sets of distribution functions for which these estimates are attained.     

k-th record times and their generalizations

A series of asymptotic results are given for the k-th record times and for their generalizations, the so-called k_n-record times. All possible limiting distributions are obtained for some generalizations of the k-th record variables. These distributions are closely related with the corresponding limit distributions of the extremal order statistics.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 153, pp. 115–121, 1986.     

Record values with constraints

Record values are very popular in probability and mathematical statistics. There are many books and papers concerned with classical record values and record times, i.e., records in sequences of independent equally distributed random variables. In recent times, new types of record values (records in the F ^α-scheme, record values in sequences of unequally distributed random variables, records with confirmations, exceedance record values) have been proposed and examined. The present paper proposes another record scheme (so-called “records with constraint”). Various cases are studied in which these records may be useful. For these record values, we give their joint density functions and discover some of their properties. For particular cases of utmost importance, when the initial random variables are independent and have equal exponential distribution, we obtain fairly simple representations of records with constraints as sums of independent equally distributed random terms.