The Burrows-Wheeler-Transform (BWT), a reversible string transformation, is one of the fundamental components of many current data structures in string processing. It is central in data compression, as well as in efficient query algorithms for sequence data, such as webpages, genomic and other biological sequences, or indeed any textual data. The BWT lends itself well to compression because its number of equal-letterruns (usually referred to as r) is often considerably lower than that of the original string; in particular, it is well suited for strings with many repeated factors. In fact, much attention has been paid to the r parameter as measure of repetitiveness, especially to evaluate the performance in terms of both space and time of compressed indexing data structures.In this paper, we investigate ρ(v), the ratio of r and of the number of runs of the BWT of the reverse of v. Kempa and Kociumaka [FOCS 2020] gave the first non-trivial upper bound as ρ(v) = O(log 2 (n)), for any string v of length n. However, nothing is known about the tightness of this upper bound. We present infinite families of binary strings for which ρ(v) = Θ(log n) holds, thus giving the first non-trivial lower bound on ρ(n), the maximum over all strings of length n.Our results suggest that r is not an ideal measure of the repetitiveness of the string, since the number of repeated factors is invariant between the string and its reverse. We believe that there is a more intricate relationship between the number of runs of the BWT and the string's combinatorial properties.
BackgroundThe aims of this study were to estimate the existence of clusters of AROs in the municipalities of the Marches Region (Central Italy) after complaints from residents living near an abandoned landfill site.MethodsCases of AROs (i.e., congenital malformation, chromosomal abnormalities, and low birth weight) were retrieved from hospital discharge data. SaTScan and GeoDa were used to check for the presence of clusters at a regional and a small area level. Moreover, at a small area/neighborhood level, smoothed rates were calculated, and a case–control approach was used to assess the residence in proximity to the abandoned landfill as an independent risk factor for AROs.ResultsAROs were associated with the price per square meter of the accommodations in the area of residence (OR 2.53, 95 % CI 2.06-3.10). On the other hand, residence within one kilometer of the landfill (OR 0.04, 95 % CI 0.01-0.23) and maternal age greater than 35 years (OR 0.96, 95 % CI 0.92-0.99) were protective.ConclusionsResidency in proximity to the abandoned landfill was not a risk factor for the occurrence of AROs. The results show that basic information, such as the price of accommodations in different neighborhoods, could be of interest in order to target training programs for women living in difficult conditions and highlights the potential role of the building environment in perinatal health. However, we note that aside from the data provided by Geographic Information Systems in public health, collection of the patient’s residential address was unreliable for selected conditions. Future efforts should emphasize the patient’s residential address as information important for evaluating the health of individuals instead of being merely administrative data.
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