Fast Searching in Packed Strings

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let $m \leq n$ be the lengths $P$ and $Q$, respectively, and let $\sigma$ denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time O\left(\frac{n}{\log_\sigma n} + m + \occ\right). Here \occ is the number of occurrences of $P$ in $Q$. For $m = o(n)$ this improves the $O(n)$ bound of the Knuth-Morris-Pratt algorithm. Furthermore, if $m = O(n/\log_\sigma n)$ our algorithm is optimal since any algorithm must spend at least \Omega(\frac{(n+m)\log \sigma}{\log n} + \occ) = \Omega(\frac{n}{\log_\sigma n} + \occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.Comment: To appear in Journal of Discrete Algorithms. Special Issue on CPM 200

Non-relativistic limit of Randall-Sundrum model: solutions, applications and constraints

In the Randall-Sundrum model with one brane, we found the approximate and exact solutions for gravitational potentials and accelerations of test bodies in these potentials for different geometrical configurations. We applied these formulas for calculation of the gravitational interaction between two spheres and found the approximate and exact expressions for the relative force corrections to the Newton's gravitational force. We demonstrated that the difference between relative force corrections for the approximate and exact cases increases with the parameter $l$ (for the fixed distance $r$ between centers of the spheres). On the other hand, this difference increases with decreasing of the distance between the centers of the spheres (for the fixed curvature scale parameter $l$). We got the upper limit for the curvature scale parameter $l\lesssim 10\, \mu$m. For these values of $l$, the difference between the approximate and exact solutions is negligible.Comment: LaTex 11 pages, 3 figure

Continuous wave optical parametric oscillator for quartz-enhanced photoacoustic trace gas sensing

A continuous wave optical parametric oscillator, generating up to 300 mW idler output in the 3–4 μm wavelength region, and pumped by a fiber-amplified DBR diode laser is used for trace gas detection by means of quartz-enhanced photoacoustic spectroscopy (QEPAS). Mode-hop-free tuning of the OPO output over 5.2 cm-1 and continuous spectral coverage exceeding 16.5 cm-1 were achieved via electronic pump source tuning alone. Online monitoring of the idler wavelength, with feedback to the DBR diode laser, provided an automated closed-loop control allowing arbitrary idler wavelength selection within the pump tuning range and locking of the idler wavelength with a stability of 1.7×10-3 cm-1 over at least 30 min.\ud \ud Using this approach, we locked the idler wavelength at an ethane absorption peak and obtained QEPAS data to verify the linear response of the QEPAS signal at different ethane concentrations (100 ppbv-20 ppmv) and different power levels. The detection limit for ethane was determined to be 13 ppbv (20 s averaging), corresponding to a normalized noise equivalent absorption coefficient of 4.4×10-7 cm-1  W/Hz1/2

Vortex dynamics and states of artificially layered superconducting films with correlated defects

Linear resistances and $IV$-characteristics have been measured over a wide range in the parameter space of the mixed phase of multilayered a-TaGe/Ge films. Three films with varying interlayer coupling and correlated defects oriented at an angle $\approx 25$ from the film normal were investigated. Experimental data were analyzed within vortex glass models and a second order phase transition from a resistive vortex liquid to a pinned glass phase. Various vortex phases including changes from three to two dimensional behavior depending on anisotropy have been identified. Careful analysis of $IV$-characteristics in the glass phases revealed a distinctive $T$ and $H$-dependence of the glass exponent $\mu$. The vortex dynamics in the Bose-glass phase does not follow the predicted behavior for excitations of vortex kinks or loops.Comment: 16 pages, 10 figures, 3 table

Boson Expansion Methods in (1+1)-dimensional Light-Front QCD

We derive a bosonic Hamiltonian from two dimensional QCD on the light-front. To obtain the bosonic theory we find that it is useful to apply the boson expansion method which is the standard technique in quantum many-body physics. We introduce bilocal boson operators to represent the gauge-invariant quark bilinears and then local boson operators as the collective states of the bilocal bosons. If we adopt the Holstein-Primakoff type among various representations, we obtain a theory of infinitely many interacting bosons, whose masses are the eigenvalues of the 't Hooft equation. In the large $N$ limit, since the interaction disappears and the bosons are identified with mesons, we obtain a free Hamiltonian with infinite kinds of mesons.Comment: 20 pages, latex, no figures, journal version (no significant changes), to appear in Phys. Rev.