Estimates of the rate of convergence of sums of order statistics to the normal law. II

Some results are obtained on the rate of convergence of trimmed means to the normal Law. The work continues the investigations begun in the paper [3].Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 55, pp. 165–174, 1976.     

Structural fitting of PISEMA spectra of aligned proteins

An algorithm for fitting protein structures to PISEMA spectra is described, and its application to helical proteins in aligned samples is demonstrated using both simulated and experimental results. The formulation of the algorithm in terms of rotation operators yields compact recursion relations that provide a fast and effective way of obtaining peptide plane orientations from chemical and torsion angle constraints. The algorithm in combination with experimental solid-state NMR data results in a method for determining the backbone structures of proteins, since it yields the orientation of a helix as a whole, including its tilt and twist angles, and describes kinks and curves with atomic resolution. Although the algorithm can be applied in an "assignment-free" manner to spectra of uniformly labeled proteins, the precision of the structural fitting is improved by the addition of assignment information, for example the identification of resonances by residue type from spectra of selectively labeled proteins.     

A "magic sandwich" pulse sequence with reduced offset dependence for high-resolution separated local field spectroscopy

A pulse sequence for high resolution separated local field spectroscopy based on "magic sandwich" elements is demonstrated on a single crystal sample. Simulations and experimental results show that this pulse sequence has a reduced frequency offset dependence compared to PISEMA (polarization inversion spin exchange at the magic angle). As a result, it has a larger effective range of homonuclear decoupling, reduced zero-frequency spectral distortions, and more reliable scale factors for individual resonances. In addition, it is easier to setup on commercial spectrometers.     

Maximum of cumulative sums for the Cauchy distribution

Limit theorems for the maximum of cumulative sums of stable random variables are discussed. Some new results are obtained for the Cauchy distribution.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 169–174, 1979.     

Record values in sequences of sample ranges

The classical representation of record values in sequences of independent random variables with the standard exponential distribution E(1) as sums of exponentially distributed random summands plays an important role in the mathematical theory of records. A generalization of this representation is proposed. A new similar result that makes it possible to express the record values of sample ranges as sums of independent exponentially distributed random variables is obtained.     

Selective averaging for high-resolution solid-state NMR spectroscopy of aligned samples

Solid-state NMR experiments benefit from being performed at high fields, and this is essential in order to obtain spectra with the resolution and sensitivity required for applications to protein structure determination in aligned samples. Since the amount of rf power that can be applied is limited, especially for aqueous protein samples, the most important pulse sequences suffer from bandwidth limitations resulting from the same spread in chemical shift frequencies that aids resolution. SAMPI4 is a pulse sequence that addresses these limitations. It yields separated local field spectra with narrower and more uniform linewidths over the entire spectrum than the currently used PISEMA and SAMMY experiments. In addition, it is much easier to set up on commercial spectrometers and can be incorporated as a building block into other multidimensional pulse sequences. This is illustrated with a two-dimensional HETCOR experiment, where it is crucial to transfer polarization from the amide protons to their directly bonded nitrogens over a wide range of chemical shift frequencies. A quantum-mechanical treatment of the spin Hamiltonians under high-power rf pulses is presented which gives the scaling factor for SAMPI4 as well as the durations of the rf pulses to achieve optimal decoupling.     

Ordered Random Variables

We discuss methods, which enable us to express distributions of ordered random variables (classical order statistics, induced order statistics, records and generalized order statistics) via distributions of sums of independent terms.     

Higgs Boson with Mass around 125 GeV in SUSY Extensions of the SM

Physics of Atomic Nuclei - The presence of the 125-GeV Higgs boson in the particle spectrum of the minimal supersymmetric (SUSY) standard model (MSSM) implies that the SUSY breaking scale has to be...     

On a limit relation between order statistics and records

Let a distribution function (d.f.) F belong to the domain of minimal attraction of some d.f. L. It is shown that the limit distribution of suitably normalized order statistics X_k,n corresponding to the d.f. F, coincides with the distribution of the record value X(k) corresponding to the d.f. L. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 244, 1997, pp. 218–226. Translated by A. Sudakov.