375,836 research outputs found
Families of sequences with good family complexity and cross-correlation measure
In this paper we study pseudorandomness of a family of sequences in terms of
two measures, the family complexity (-complexity) and the cross-correlation
measure of order . We consider sequences not only on binary alphabet but
also on -symbols (-ary) alphabet. We first generalize some known methods
on construction of the family of binary pseudorandom sequences. We prove a
bound on the -complexity of a large family of binary sequences of
Legendre-symbols of certain irreducible polynomials. We show that this family
as well as its dual family have both a large family complexity and a small
cross-correlation measure up to a rather large order. Next, we present another
family of binary sequences having high -complexity and low cross-correlation
measure. Then we extend the results to the family of sequences on -symbols
alphabet.Comment: 13 pages. Comments are welcome
Interpreting 16S metagenomic data without clustering to achieve sub-OTU resolution
The standard approach to analyzing 16S tag sequence data, which relies on
clustering reads by sequence similarity into Operational Taxonomic Units
(OTUs), underexploits the accuracy of modern sequencing technology. We present
a clustering-free approach to multi-sample Illumina datasets that can identify
independent bacterial subpopulations regardless of the similarity of their 16S
tag sequences. Using published data from a longitudinal time-series study of
human tongue microbiota, we are able to resolve within standard 97% similarity
OTUs up to 20 distinct subpopulations, all ecologically distinct but with 16S
tags differing by as little as 1 nucleotide (99.2% similarity). A comparative
analysis of oral communities of two cohabiting individuals reveals that most
such subpopulations are shared between the two communities at 100% sequence
identity, and that dynamical similarity between subpopulations in one host is
strongly predictive of dynamical similarity between the same subpopulations in
the other host. Our method can also be applied to samples collected in
cross-sectional studies and can be used with the 454 sequencing platform. We
discuss how the sub-OTU resolution of our approach can provide new insight into
factors shaping community assembly.Comment: Updated to match the published version. 12 pages, 5 figures +
supplement. Significantly revised for clarity, references added, results not
change
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