Searching for Fixed-Length Patterns

We present an algorithm, RQ for finding all occurrences of a fixed-length pattern, Pi,J?2\u3e * * * »Pp , in a text string, where each p,- can match an arbitrary set of characters. Our algorithm is optimal in that it examines the minimum average number of text characters, which is not necessarily the same as being optimal in running time. This paper answers the question of optimal string searching put forth in [KMP77]. Let a = the alphabet size, P= the length of the string matched by the pattern, T= the length of the text, W= the word size in bits of the underlying machine, and $(i?Q) = the average number of text characters examined RQvWe derive an asymptotic approximation for$(RQ) when P\u3c a. We also show that &(RQ) \u3c (4 Ioga P/3)(T/P), when P \u3e a. In the worst case, RQ examines T characters. Our algorithm requires space 0(||II|| |P/W|). In addition, our method of analysis is applicable to other algorithms modeled by a finite automaton. We present an efficient implementation of our algorithm when P \u3c W. In practice, compared to the Boyer-Moore algorithm, RQ requires slightly more space, accepts a more general range of patterns, and runs in comparable time

Receptor Editing and Marginal Zone B Cell Development Are Regulated by the Helix-Loop-Helix Protein, E2A

Previous studies have indicated that the E2A gene products are required to initiate B lineage development. Here, we demonstrate that E2A+/− B cells that express an autoreactive B cell receptor fail to mature due in part to an inability to activate secondary immunoglobulin (Ig) light chain gene rearrangement. Both RAG1/2 gene expression and RS deletion are severely defective in E2A+/− mice. Additionally, we demonstrate that E2A+/− mice show an increase in the proportion of marginal zone B cells with a concomitant decrease in the proportion of follicular B cells. In contrast, Id3-deficient splenocytes show a decline in the proportion of marginal zone B cells. Based on these observations, we propose that E-protein activity regulates secondary Ig gene rearrangement at the immature B cell stage and contributes to cell fate determination of marginal zone B cells. Additionally, we propose a model in which E-proteins enforce the developmental checkpoint at the immature B cell stage

Elimination of unoccupied state summations in it ab initio self-energy calculations for large supercells

We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for 8 or more silicon atoms per unit cell

Density-functional-based predictions of Raman and IR spectra for small Si clusters

We have used a density-functional-based approach to study the response of silicon clusters to applied electric fields. For the dynamical response, we have calculated the Raman activities and infrared (IR) intensities for all of the vibrational modes of several clusters (SiN with N=3-8, 10, 13, 20, and 21) using the local density approximation (LDA). For the smaller clusters (N=3-8) our results are in good agreement with previous quantum-chemical calculations and experimental measurements, establishing that LDA-based IR and Raman data can be used in conjunction with measured spectra to determine the structure of clusters observed in experiment. To illustrate the potential of the method for larger clusters, we present calculated IR and Raman data for two low-energy isomers of Si10 and for the lowest-energy structure of Si13 found to date. For the static response, we compare our calculated polarizabilities for N=10, 13, 20, and 21 to recent experimental measurements. The calculated results are in rough agreement with experiment, but show less variation with cluster size than the measurements. Taken together, our results show that LDA calculations can offer a powerful means for establishing the structures of experimentally fabricated clusters and nanoscale systems

Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps

Density-functional calculations of the phonon spectrum and electron-phonon coupling in MgB$_2$ are presented. The $E_{2g}$ phonons, which involve in-plane B displacements, couple strongly to the $p_{x,y}$ electronic bands. The isotropic electron-phonon coupling constant is calculated to be about 0.8. Allowing for different order parameters in different bands, the superconducting $\lambda$ in the clean limit is calculated to be significantly larger. The $E_{2g}$ phonons are strongly anharmonic, and the non-linear contribution to the coupling between the $E_{2g}$ modes and the p$_{x,y}$ bands is significant.Comment: 4 pages, 3 figure

Reevaluating electron-phonon coupling strengths: Indium as a test case for ab initio and many-body-theory methods

Using indium as a test case, we investigate the accuracy of the electron-phonon coupling calculated with state-of-the-art ab initio and many-body theory methods. The ab initio calculations -- where electrons are treated in the local-density approximation, and phonons and the electron-phonon interaction are treated within linear response -- predict an electron-phonon spectral function alpha^2 F(omega) which translates into a relative tunneling conductance that agrees with experiment to within one part in 1000. The many-body theory calculations -- where alpha^2 F(omega) is extracted from tunneling data by means of the McMillan-Rowell tunneling inversion method -- provide spectral functions that depend strongly on details of the inversion process. For the the most important moment of alpha^2 F(omega), the mass-renormalization parameter lambda, we report 0.9 +/- 0.1, in contrast to the value 0.805 quoted for nearly three decades in the literature. The ab initio calculations also provide the transport electron-phonon spectral function alpha_{tr}^2 F(omega), from which we calculate the resistivity as a function of temperature in good agreement with experiment.Comment: 16 pages, 5 figure

Ab initio calculations of bulk moduli and comparison with experiment

Published versio

First-principles calculation of the thermal properties of silver

The thermal properties of silver are calculated within the quasi-harmonic approximation, by using phonon dispersions from density-functional perturbation theory, and the pseudopotential plane-wave method. The resulting free energy provides predictions for the temperature dependence of various quantities such as the equilibrium lattice parameter, the bulk modulus, and the heat capacity. Our results for the thermal properties are in good agreement with available experimental data in a wide range of temperatures. As a by-product, we calculate phonon frequency and Grueneisen parameter dispersion curves which are also in good agreement with experiment.Comment: 9 pages, 8 figures, submitted to Phys. Rev. B April 30, 1998). Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Linear-response theory and lattice dynamics: a muffin-tin orbital approach

A detailed description of a method for calculating static linear-response functions in the problem of lattice dynamics is presented. The method is based on density functional theory and it uses linear muffin-tin orbitals as a basis for representing first-order corrections to the one-electron wave functions. As an application we calculate phonon dispersions in Si and NbC and find good agreement with experiments.Comment: 18 pages, Revtex, 2 ps figures, uuencoded, gzip'ed, tar'ed fil

Exchange-correlation kernels for excited states in solids

The performance of several common approximations for the exchange-correlation kernel within time-dependent density-functional theory is tested for elementary excitations in the homogeneous electron gas. Although the adiabatic local-density approximation gives a reasonably good account of the plasmon dispersion, systematic errors are pointed out and traced to the neglect of the wavevector dependence. Kernels optimized for atoms are found to perform poorly in extended systems due to an incorrect behavior in the long-wavelength limit, leading to quantitative deviations that significantly exceed the experimental error bars for the plasmon dispersion in the alkali metals.Comment: 7 pages including 5 figures, RevTe