We present integration vectors for Staphylococcus aureus encoding the fluorescent reporters mAmetrine, CFP, sGFP, YFP, mCherry and mKate. The expression is driven either from the sarA-P1 promoter or from any other promoter of choice. The reporter can be inserted markerless in the chromosome of a wide range of S. aureus strains. The integration site chosen does not disrupt any open reading frame, provides good expression, and has no detectable effect on the strains physiology. As an intermediate construct, we present a set of replicating plasmids containing the same fluorescent reporters. Also in these reporter plasmids the sarA-P1 promoter can be replaced by any other promoter of interest for expression studies. Cassettes from the replication plasmids can be readily swapped with the integration vector. With these constructs it becomes possible to monitor reporters of separate fluorescent wavelengths simultaneously.
The Fréchet distance is a commonly used similarity measure between curves. It is known how to compute the continuous Fréchet distance between two polylines with m and n vertices in R d in O(mn(log log n) 2 ) time; doing so in strongly subquadratic time is a longstanding open problem. Recent conditional lower bounds suggest that it is unlikely that a strongly subquadratic algorithm exists. Moreover, it is unlikely that we can approximate the Fréchet distance to within a factor 3 in strongly subquadratic time, even if d = 1. The best current results establish a tradeoff between approximation quality and running time. Specifically, Colombe and Fox (SoCG, 2021) give an O(α)-approximate algorithm that runs in O((n 3 /α 2 ) log n) time for any α ∈ [ √ n, n], assuming m ≤ n. In this paper, we improve this result with an O(α)-approximate algorithm that runs in O((n + mn/α) log 3 n) time for any α ∈ [1, n], assuming m ≤ n and constant dimension d.
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