Random Access to Grammar Compressed Strings

Grammar based compression, where one replaces a long string by a small context-free grammar that generates the string, is a simple and powerful paradigm that captures many popular compression schemes. In this paper, we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string. Let $S$ be a string of length $N$ compressed into a context-free grammar $\mathcal{S}$ of size $n$. We present two representations of $\mathcal{S}$ achieving $O(\log N)$ random access time, and either $O(n\cdot \alpha_k(n))$ construction time and space on the pointer machine model, or $O(n)$ construction time and space on the RAM. Here, $\alpha_k(n)$ is the inverse of the $k^{th}$ row of Ackermann's function. Our representations also efficiently support decompression of any substring in $S$: we can decompress any substring of length $m$ in the same complexity as a single random access query and additional $O(m)$ time. Combining these results with fast algorithms for uncompressed approximate string matching leads to several efficient algorithms for approximate string matching on grammar-compressed strings without decompression. For instance, we can find all approximate occurrences of a pattern $P$ with at most $k$ errors in time $O(n(\min\{|P|k, k^4 + |P|\} + \log N) + occ)$, where $occ$ is the number of occurrences of $P$ in $S$. Finally, we generalize our results to navigation and other operations on grammar-compressed ordered trees. All of the above bounds significantly improve the currently best known results. To achieve these bounds, we introduce several new techniques and data structures of independent interest, including a predecessor data structure, two "biased" weighted ancestor data structures, and a compact representation of heavy paths in grammars.Comment: Preliminary version in SODA 201

Cross-Document Pattern Matching

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem

X-ray emission from the remarkable A-type star HR 8799

We present a Chandra observation of the exceptional planet bearing A5V star HR 8799, more precisely classified as a kA5hF0mA5 star and search for intrinsic X-ray emission. We clearly detect HR 8799 at soft X-ray energies with the ACIS-S detector in a 10 ks exposure; minor X-ray brightness variability is present during the observation. The coronal plasma is described well by a model with a temperature of around 3 MK and an X-ray luminosity of about Lx = 1.3 x 10^28 erg/s in the 0.2-2.0 keV band, corresponding to an activity level of log Lx/Lbol ~ -6.2. Altogether, these findings point to a rather weakly active and given a RASS detection, long-term stable X-ray emitting star. The X-ray emission from HR 8799 resembles those of a late A/early F-type stars, in agreement with its classification from hydrogen lines and effective temperature determination and thus resolving the apparent discrepancy with the standard picture of magnetic activity that predicts mid A-type stars to be virtually X-ray dark.Comment: 4 pages, 3 figures, accepted by A&

Efficient Seeds Computation Revisited

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in $O(n^2)$ time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an $O(n\log{(n/m)})$ time algorithm checking if the shortest seed has length at least $m$ and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).Comment: 14 pages, accepted to CPM 201

Searching for Radio Pulsars in 3EG Sources at Urumqi Observatory

Since mid-2005, a pulsar searching system has been operating at 18 cm on the 25-m radio telescope of Urumqi Observatory. Test observations on known pulsars show that the system can perform the intended task. The prospect of using this system to observe 3EG sources and other target searching tasks is discussed.Comment: a training project about MSc thesi

Five-Year Optical and Near Infrared Observations of the Extremely Slow Nova V1280 Scorpii

We present optical ($B$, $V$, $R_{\rm c}$, $I_{\rm c}$ and $y$) and near infrared ($J$, $H$ and $K_{\rm s}$) photometric and spectroscopic observations of a classical nova V1280 Scorpii for five years from 2007 to 2011. Our photometric observations show a declining event in optical bands shortly after the maximum light which continues $\sim$ 250 days. The event is most probably caused by a dust formation. The event is accompanied by a short ($\sim$ 30 days) re-brightening episode ($\sim$ 2.5 mag in $V$), which suggests a re-ignition of the surface nuclear burning. After 2008, the $y$ band observations show a very long plateau at around $y$ = 10.5 for more than 1000 days until April 2011 ($\sim$ 1500 days after the maximum light). The nova had taken a very long time ($\sim$ 50 months) before entering the nebular phase (clear detection of both [\ion{O}{iii}] 4959 and 5007) and is still continuing to generate the wind caused by H-burning. The finding suggests that V1280 Sco is going through the historically slowest evolution. The interval from the maximum light (2007 February 16) to the beginning of the nebular phase is longer than any previously known slow novae: V723 Cas (18 months), RR Pic (10 months), or HR Del (8 months). It suggests that the mass of a white dwarf in the V1280 Sco system might be 0.6 M_\mathrm{\sun} or smaller. The distance, based on our measurements of the expansion velocity combined with the directly measured size of the dust shell, is estimated to be 1.1 $\pm$ 0.5 kpc.Comment: 17 pages, 14 figures, accepted for publication in A&

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Generation of Multiple Circular Walls on a Thin Film of Nematic Liquid Crystal by Laser Scanning

We found that multiple circular walls (MCW) can be generated on a thin film of a nematic liquid crystal through a spiral scanning of a focused IR laser. The ratios between radii of adjacent rings of MCW were almost constant. These constant ratios can be explained theoretically by minimization of the Frank elastic free energy of nematic medium. The director field on a MCW exhibits chiral symmetry-breaking although the elastic free energies of both chiral MCWs are degenerated, i.e., the director on a MCW can rotate clockwise or counterclockwise along the radial direction.Comment: 10 pages, 5 figures. Submitted to Chemical Physics Letters 2nd Editio