The number of records in a sequence of nonidentically distributed random variables

One obtains limit theorems for the number of records and for the times of the attainment of the record values in a sequence of independent random variables.Translated from Veroyatnostnye Raspredeleniya i Matematicheskaya Statistika, pp. 373–388, 1986.     

On families of distributions characterized by certain properties of ordered random variables

In this work, we obtain new characterizations of certain probability distributions by relations with different ordered random variables. Such variables include order statistics, sequential maxima, and records. We consider relations that include not only upper, but also lower record values. The presented ordered objects are based on sequences of independent random variables with a common continuous distribution function. We also investigate equalities in the distribution of sequential maxima exposed by various random shifts. These shifts (one-sided or two-sided) have exponential distributions. Certain theorems and their corollaries present corresponding characterizations of distributions by relations of such a type. In addition, we consider exponentially shifted order statistics such that simple relations among them also characterize certain probability distributions. All of the presented results yield a set of characterizations of various distributions. For particular cases, we present the relations that characterize families of classical exponential and logistic distributions.     

NMR “Crystallography” for Uniformly (13C, 15N)-Labeled Oriented Membrane Proteins

In oriented-sample (OS) solid-state NMR of membrane proteins, the angular-dependent dipolar couplings and chemical shifts provide a direct input for structure calculations. However, so far only ¹H–¹⁵N dipolar couplings and ¹⁵N chemical shifts have been routinely assessed in oriented ¹⁵N-labeled samples. The main obstacle for extending this technique to membrane proteins of arbitrary topology has remained in the lack of additional experimental restraints. We have developed a new experimental triple-resonance NMR technique, which was applied to uniformly doubly (¹⁵N, ¹³C)-labeled Pf1 coat protein in magnetically aligned DMPC/DHPC bicelles. The previously inaccessible ¹H_α–¹³C_α dipolar couplings have been measured, which make it possible to determine the torsion angles between the peptide planes without assuming α-helical structure a priori. The fitting of three angular restraints per peptide plane and filtering by Rosetta scoring functions has yielded a consensus α-helical transmembrane structure for Pf1 protein.     

Rotational diffusion of membrane proteins in aligned phospholipid bilayers by solid-state NMR spectroscopy

Solid-state NMR experiments on mechanically aligned bilayer and magnetically aligned bicelle samples demonstrate that membrane proteins undergo rapid rotational diffusion about the normal in phospholipid bilayers. Narrow single-line resonances are observed from 15N labeled sites in the trans-membrane helix of the channel-forming domain of the protein Vpu from HIV-1 in phospholipid bilayers with their normals at angles of 0 degrees, 20 degrees, 40 degrees, and 90 degrees, and bicelles with their normals at angles of 0 degrees and 90 degrees with respect to the direction of the applied magnetic field. This could only occur if the entire polypeptide undergoes rotational diffusion about the bilayer normal. Comparisons between experimental and simulated spectra are consistent with a rotational diffusion coefficient (DR) of approximately 10(5)s-1.     

Quasifixed-point scenario in a modified nonminimal supersymmetric standard model

The modified next-to-minimal supersymmetric standard model is the simplest model that is obtained as an extension of the minimal supersymmetric standard model and which is compatible with the LEP II experimental constraint on the mass of the lightest Higgs boson at tan β～1. The renormalization of Yukawa coupling constants and of the parameters of a soft breakdown of supersymmetry is investigated within this model. The possibility of unifying the Yukawa coupling constants for the b quark and the τ lepton at the Grand Unification scale M _X is studied. The spectrum of particles is analyzed in the vicinity of a quasifixed point where solutions to the renormalization-group equations are concentrated at the electroweak scale.     

On some regression relationships relating sample means and successive maxima

In recent years, a number of papers have appeared in which characterizations of a series of distributions in terms of regression properties of order statistics were obtained. In particular, characterizations of the Student’s t ₂-distribution in terms of linear regression relation-ships, including the sample median X _{2, 3} and the sample mean T ₃, were obtained in 2002. Later, similar results were also established for samples of larger sizes, and characterizations of families of distributions containing the t ₂-distribution were put forward. These characterizations are based, in particular, on linear regression relationships relating sample means T _{2k + 1} and sample medians X _{k + 1, 2k + 1}, k = 1, 2, ...     

Ergodicity and efficiency of cross-polarization in NMR of static solids

Cross-polarization transfer is employed in virtually every solid-state NMR experiment to enhance magnetization of low-gamma spins. Theory and experiment is used to assess the magnitude of the final quasistationary magnetization amplitude. The many-body density matrix equation is solved for relatively large (up to N=14) spin systems without the spin-temperature assumption for the final spin states. Simulations show that about 13% of the thermodynamic limit is still retained within the proton bath. To test this theoretical prediction, a combination of a reverse cross-polarization experiment and multiple contacts is employed to show that the thermodynamic limit of magnetization cannot be transferred from high- to low-gamma nuclei in a single contact. Multiple contacts, however, fully transfer the maximum magnetization. A simple diffusion on a cone model shows that slow dynamics can affect the build up profile for the transferred magnetization.