Abstract.We study two fundamental problems concerning the search for interesting regions in sequences: (i) given a sequence of real numbers of length n and an upper bound U , find a consecutive subsequence of length at most U with the maximum sum and (ii) given a sequence of real numbers of length n and a lower bound L, find a consecutive subsequence of length at least L with the maximum average. We present an O(n)-time algorithm for the first problem and an O(n log L)-time algorithm for the second. The algorithms have potential applications in several areas of biomolecular sequence analysis including locating GC-rich regions in a genomic DNA sequence, post-processing sequence alignments, annotating multiple sequence alignments, and computing length-constrained ungapped local alignment. Our preliminary tests on both simulated and real data demonstrate that the algorithms are very efficient and able to locate useful (such as GC-rich) regions.

Periodontitis is an inflammatory disease involving complex interactions between oral microorganisms and the host immune response. Understanding the structure of the microbiota community associated with periodontitis is essential for improving classifications and diagnoses of various types of periodontal diseases and will facilitate clinical decision-making. In this study, we used a 16S rRNA metagenomics approach to investigate and compare the compositions of the microbiota communities from 76 subgingival plagues samples, including 26 from healthy individuals and 50 from patients with periodontitis. Furthermore, we propose a novel feature selection algorithm for selecting features with more information from many variables with a combination of these features and machine learning methods were used to construct prediction models for predicting the health status of patients with periodontal disease. We identified a total of 12 phyla, 124 genera, and 355 species and observed differences between health- and periodontitis-associated bacterial communities at all phylogenetic levels. We discovered that the genera Porphyromonas, Treponema, Tannerella, Filifactor, and Aggregatibacter were more abundant in patients with periodontal disease, whereas Streptococcus, Haemophilus, Capnocytophaga, Gemella, Campylobacter, and Granulicatella were found at higher levels in healthy controls. Using our feature selection algorithm, random forests performed better in terms of predictive power than other methods and consumed the least amount of computational time.

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