Coherent-mode decomposition of general anisotropic Gaussian Schell-model beams

We present a complete solution to the problem of coherent-mode decomposition of the most general anisotropic Gaussian Schell-model (AGSM) beams, which constitute a ten-parameter family. Our approach is based on symmetry considerations. Concepts and techniques familiar from the context of quantum mechanics in the two-dimensional plane are used to exploit the Sp(4, R) dynamical symmetry underlying the AGSM problem. We take advantage of the fact that the symplectic group of first-order optical system acts unitarily through the metaplectic operators on the Hilbert space of wave amplitudes over the transverse plane, and, using the Iwasawa decomposition for the metaplectic operator and the classic theorem of Williamson on the normal forms of positive definite symmetric matrices under linear canonical transformations, we demonstrate the unitary equivalence of the AGSM problem to a separable problem earlier studied by Li and Wolf [Opt. Lett. 7, 256 (1982)] and Gori and Guattari [Opt. Commun. 48, 7 (1983)]. This conn ction enables one to write down, almost by inspection, the coherent-mode decomposition of the general AGSM beam. A universal feature of the eigenvalue spectrum of the AGSM family is noted.

The Gaussian Toeplitz matrix

An analytical expression for the LL(T) decomposition for the Gaussian Toeplitz matrix with elements T(ij) = [1/(2-pi)1/2-sigma] exp[-(i - j)2/2-sigma-2] is derived. An exact expression for the determinant and bounds on the eigenvalues follows. An analytical expression for the inverse T-1 is also derived.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

The stretching of single poly-ubiquitin molecules: Static versus dynamic disorder in the non-exponential kinetics of chain unfolding

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernandez, Proc. Natl. Acad. Sci. U. S. A. 107, 11336 (2010)]. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzig's indirect approach to noise averaging Acc. Chem. Res. 23, 148 (1990)]. In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman J. Chem. Phys. 58, 4009 (1973); ibid. 60, 866 (1974)], this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely. (C) 2011 American Institute of Physics.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Physics based basis function for vibration analysis of high speed rotating beams

The natural frequencies of continuous systems depend on the governing partial differential equation and can be numerically estimated using the finite element method. The accuracy and convergence of the finite element method depends on the choice of basis functions. A basis function will generally perform better if it is closely linked to the problem physics. The stiffness matrix is the same for either static or dynamic loading, hence the basis function can be chosen such that it satisfies the static part of the governing differential equation. However, in the case of a rotating beam, an exact closed form solution for the static part of the governing differential equation is not known. In this paper, we try to find an approximate solution for the static part of the governing differential equation for an uniform rotating beam. The error resulting from the approximation is minimized to generate relations between the constants assumed in the solution. This new function is used as a basis function which gives rise to shape functions which depend on position of the element in the beam, material, geometric properties and rotational speed of the beam. The results of finite element analysis with the new basis functions are verified with published literature for uniform and tapered rotating beams under different boundary conditions. Numerical results clearly show the advantage of the current approach at high rotation speeds with a reduction of 10 to 33% in the degrees of freedom required for convergence of the first five modes to four decimal places for an uniform rotating cantilever beam.

Least path criterion (LPC) for unique indexing in a two-dimensional decagonal quasilattice

The least path criterion or least path length in the context of redundant basis vector systems is discussed and a mathematical proof is presented of the uniqueness of indices obtained by applying the least path criterion. Though the method has greater generality, this paper concentrates on the two-dimensional decagonal lattice. The order of redundancy is also discussed; this will help eventually to correlate with other redundant but desirable indexing sets.

Structural basis for poor uracil excision from hairpin DNA

Two-dimensional NMR and molecular dynamics simulations have been used to determine the three-dimensional structures of two hairpin DNA structures: d-CTAGAG GATCCUTTTGGATCCT (abbreviated as U1-hairpin) and d-CTAGAGGATCCTTUTGGATCCT (abbreviated as U3-hairpin). The (1) H resonances of both of these hairpin structures have been assigned almost completely. NMR restrained molecular dynamics and energy minimization procedures have been used to describe the three-dimensional structures of these hairpins. This study and concurrent NMR structural studies on two other d-CTAGAGGA TCCTUTTGGATCCT (abbreviated as U2-hairpin) and d-CTAGAGGATCCTTTUGGATCCT (abbreviated as U4-hairpin) have shed light upon various interactions reported between Echerichia coli uracil DNA glycosylase (UDG) and uracil-containing DNA. The backbone torsion angles, which partially influence the local conformation of U12 and U14 in U1 and U3-hairpins, respectively, are probably locked in the trans conformation as in the case of U-13 in the U2-hairpin. Such a stretched-out backbone conformation in the vicinity of U-12 and U-14 is thought to be the reason why the K-m value is poor for U1- and U3-hairpins as it is for the U2-hairpin. Furthermore, the bases U-12 and U-14 in both U1- and U3-hairpins adopt an anti conformation, in contrast with the base conformation of U-13 in the U2-hairpin, which adopts a syn conformation. The clear discrepancy observed in the U-base orientation with respect to the sugar moieties could explain why the V-max value is 10- to 20-fold higher for the U1- and U3-hairpins compared with the U2-hairpin. Taken together, these observations support our interpretation that the unfavourable backbone results in a poor K-m value, whereas the unfavourable nucleotide conformation results in a poor V-max value. These two parameters therefore make the U1- and U3-hairpins better substrates for UDG compared with the U2-hairpin, as reported earlier [Kumar, N. V. & Varshney, U. (1997) Nucleic Acids Res. 25, 2336-2343.].

A Grobner basis for certain affine monomial curves

Let K be a field and let m(0),...,m(e-1) be a sequence of positive integers. Let W be a monomial curve in the affine e-space A(K)(e), defined parametrically by X-0 = T-m0,...,Xe-1 = Tme-1 and let p be the defining ideal of W. In this article, we assume that some e-1 terms of m(0), m(e-1) form an arithmetic sequence and produce a Grobner basis for p.

Tree structure for efficient data mining using rough sets

In data mining, an important goal is to generate an abstraction of the data. Such an abstraction helps in reducing the space and search time requirements of the overall decision making process. Further, it is important that the abstraction is generated from the data with a small number of disk scans. We propose a novel data structure, pattern count tree (PC-tree), that can be built by scanning the database only once. PC-tree is a minimal size complete representation of the data and it can be used to represent dynamic databases with the help of knowledge that is either static or changing. We show that further compactness can be achieved by constructing the PC-tree on segmented patterns. We exploit the flexibility offered by rough sets to realize a rough PC-tree and use it for efficient and effective rough classification. To be consistent with the sizes of the branches of the PC-tree, we use upper and lower approximations of feature sets in a manner different from the conventional rough set theory. We conducted experiments using the proposed classification scheme on a large-scale hand-written digit data set. We use the experimental results to establish the efficacy of the proposed approach. (C) 2002 Elsevier Science B.V. All rights reserved.

Conformational basis for substrate recognition and regulation of catalytic activity in Staphylococcus aureus nucleoside di-phosphate kinase

Nucleoside diphosphate kinases (NDK) are characterized by high catalytic turnover rates and diverse substrate specificity. These features make this enzyme an effective activator of a pro-drug an application that has been actively pursued for a variety of therapeutic strategies. The catalytic mechanism of this enzyme is governed by a conserved histidine that coordinates a magnesium ion at the active site. Despite substantial structural and biochemical information on NDK, the mechanistic feature of the phospho-transfer that leads to auto-phosphorylation remains unclear. While the role of the histidine residue is well documented, the other active site residues, in particular the conserved serine remains poorly characterized. Studies on some homologues suggest no role for the serine residue at the active site, while others suggest a crucial role for this serine in the regulation and quaternary association of this enzyme in some species. Here we report the biochemical features of the Staphylococcus aureus NDK and the mutant enzymes. We also describe the crystal structures of the apo-NDK, as a transition state mimic with vanadate and in complex with different nucleotide substrates. These structures formed the basis for molecular dynamics simulations to understand the broad substrate specificity of this enzyme and the role of active site residues in the phospho-transfer mechanism and oligomerization. Put together, these data suggest that concerted changes in the conformation of specific residues facilitate the stabilization of nucleotide complexes thereby enabling the steps involved in the ping-pong reaction mechanism without large changes to the overall structure of this enzyme. (C) 2011 Elsevier B.V. All rights reserved.