Minimal Absent Words in a Sliding Window and Applications to On-Line Pattern Matching

International audienceAn absent (or forbidden) word of a word y is a word that does not occur in y. It is then called minimal if all its proper factors occur in y. There exist linear-time and linear-space algorithms for computing all minimal absent words of y (Crochemore et al. in Inf Process Lett 67:111–117, 1998; Belazzougui et al. in ESA 8125:133–144, 2013; Barton et al. in BMC Bioinform 15:388, 2014). Minimal absent words are used for data compression (Crochemore et al. in Proc IEEE 88:1756–1768, 2000, Ota and Morita in Theoret Comput Sci 526:108–119, 2014) and for alignment-free sequence comparison by utilizing a metric based on minimal absent words (Chairungsee and Crochemore in Theoret Comput Sci 450:109–116, 2012). They are also used in molecular biology; for instance, three minimal absent words of the human genome were found to play a functional role in a coding region in Ebola virus genomes (Silva et al. in Bioinformatics 31:2421–2425, 2015). In this article we introduce a new application of minimal absent words for on-line pattern matching. Specifically, we present an algorithm that, given a pattern x and a text y, computes the distance between x and every window of size |x| on y. The running time is O(σ|y|)O(σ|y|) , where σσ is the size of the alphabet. Along the way, we show an O(σ|y|)O(σ|y|) -time and O(σ|x|)O(σ|x|) -space algorithm to compute the minimal absent words of every window of size |x| on y, together with some new combinatorial insight on minimal absent words

Current Understanding of Cu-Exchanged Chabazite Molecular Sieves for Use as Commercial Diesel Engine DeNO(x) Catalysts

Selective catalytic reduction (SCR) of NOx with ammonia using metal-exchanged molecular sieves with a chabazite structure has recently been commercialized on diesel vehicles. One of the commercialized catalysts, i.e., Cu-SSZ-13, has received much attention for both practical and fundamental studies. For the latter, the particularly well-defined structure of this zeolite is allowing long-standing issues of the catalytically active site for SCR in metal-exchanged zeolites to be addressed. In this review, recent progress is summarized with a focus on two areas. First, the technical significance of Cu-SSZ-13 as compared to other Cu ion-exchanged zeolites (e.g., Cu-ZSM-5 and Cu-beta) is highlighted. Specifically, the much enhanced hydrothermal stability for Cu-SSZ-13 compared to other zeolite catalysts is addressed via performance measurements and catalyst characterization using several techniques. The enhanced stability of Cu-SSZ-13 is rationalized in terms of the unique small pore structure of this zeolite catalyst. Second, the fundamentals of the catalytically active center; i.e., the chemical nature and locations within the SSZ-13 framework are presented with an emphasis on understanding structure-function relationships. For the SCR reaction, traditional kinetic studies are complicated by intra-crystalline diffusion limitations. However, a major side reaction, nonselective ammonia oxidation by oxygen, does not suffer from mass-transfer limitations at relatively low temperatures due to significantly lower reaction rates. This allows structure-function relationships that are rather well understood in terms of Cu ion locations and redox properties. Finally, some aspects of the SCR reaction mechanism are addressed on the basis of in situ spectroscopic studies.close2