Diamond a sorting method for vector machines

A method for parallel sorting in vector machines is described. It is shown that it has complexityO(N(logN)²).     

The effect of double scattering on critical fluid Rayleigh linewidth measurements

We apply recent work on the intensity correlation function of light double scattered from a system of brownian diffusing balls to the case of a fluid near the critical point. We evaluate the relative intensities and intensity correlation times of the polarized and depolarized components of the double scattered light as a function of k₀ξ. We compare these correlation times to those found for single scattering and find that the more intense polarized component of the double scattered light has a correlation time nearly equal to the singly scattered light in the critical region where $\text{k}{}_0\text{ξ ? 8}$.     

The configuration of aurones

The configurations of 6-methoxyaurone prepared by the condensation of 6-methoxy- coumaran-3-one and benzaldehyde and of its photoisomer are assigned on the basis of chemical and NMR evidence.     

Conformational studies by far infrared and Raman spectra of gases

One of the major goals of conformational analysis is the calculation of the energy difference between two or more conformers, ΔE, as well as the energy necessary for interconversion. The calculation of these energy quantities is facilitated by using a potential function which describes the vibrational motion, or internal rotation (torsion), as a function of the dihedral angle, α. The potential function is called asymmetric because both the frame and top portions of the molecule have no symmetry element higher than a plane. The most common type of potential function where at least one of the minima coincides with the plane of symmetry is of the type: V(α) = $\text{1}\text{2}$ΣV_i(1 - cos iα). The kinetic energy term, F(α), is extremely complicated. In general, if the only data being used to calculate the potential function are torsional transitions, and if one continues within the boundary conditions of a one-dimensional problem, then a cosine expansion of F(α) should be adequate: F(α) = F₀ + ΣF_i cos iα. For those systems where there is an equilibrium between a planar form and two non-planar forms, V₃ is usually the predominant term. This is because V₃ represents a three maxima/three minima potential per 2π (360°) internal rotation. In a similar fashion, V₂ is found to be the predominant term in the potential function for a system consisting of two equivalent non-planar conformers. Several examples of our most recent studies are given where the potential function for interconversion of two conformers has been determined.     

Quantifying polypeptide conformational space: sensitivity to conformation and ensemble definition

Quantifying the density of conformations over phase space (the conformational distribution) is needed to model important macromolecular processes such as protein folding. In this work, we quantify the conformational distribution for a simple polypeptide (N-mer polyalanine) using the cumulative distribution function (CDF), which gives the probability that two randomly selected conformations are separated by less than a "conformational" distance and whose inverse gives conformation counts as a function of conformational radius. An important finding is that the conformation counts obtained by the CDF inverse depend critically on the assignment of a conformation's distance span and the ensemble (e.g., unfolded state model): varying ensemble and conformation definition (1 --> 2 A) varies the CDF-based conformation counts for Ala(50) from 10(11) to 10(69). In particular, relatively short molecular dynamics (MD) relaxation of Ala(50)'s random-walk ensemble reduces the number of conformers from 10(55) to 10(14) (using a 1 A root-mean-square-deviation radius conformation definition) pointing to potential disconnections in comparing the results from simplified models of unfolded proteins with those from all-atom MD simulations. Explicit waters are found to roughen the landscape considerably. Under some common conformation definitions, the results herein provide (i) an upper limit to the number of accessible conformations that compose unfolded states of proteins, (ii) the optimal clustering radius/conformation radius for counting conformations for a given energy and solvent model, (iii) a means of comparing various studies, and (iv) an assessment of the applicability of random search in protein folding.