# Optimal Computation of Avoided Words

**Solon Pissis**,

**Kings College** –

## Abstract:

The deviation of the observed frequency of a word w from its

expected frequency in a given sequence x is used to determine whether

or not the word is avoided. This concept is particularly useful in DNA

linguistic analysis. The value of the standard deviation of w, denoted by

std(w), effectively characterises the extent of a word by its edge contrast

in the context in which it occurs. A word w of length k > 2 is a ρ-avoided

word in x if std(w) ≤ ρ, for a given threshold ρ < 0. Notice that such a
word may be completely absent from x. Hence computing all such words
naïvely can be a very time-consuming procedure, in particular for large
k. In this talk, we propose an O(n)-time and O(n)-space algorithm
to compute all ρ-avoided words of length k in a given sequence x of
length n over a fixed-sized alphabet. We also present a time-optimal
O(σn)-time algorithm to compute all ρ-avoided words (of any length) in
a sequence of length n over an integer alphabet of size σ.

## Bio

http://www.inf.kcl.ac.uk/staff/solon/

Date: 2016-Jun-28 Time: 14:00:00 Room: 408

For more information:

- luis.russo@tecnico.ulisboa.pt
- 21 31 00272

### Upcoming Events

### Workshop “Metabolism and mathematical models: Two for a tango” – 2nd Edition

**Title: ** Workshop Metabolism and mathematical models: Two for a tango – 2nd Edition

**Dates:** October 25-26, 2022

**Location:** This workshop will be held in a virtual way

The topic of this workshop is metabolism in general, with a special focus, although not exclusive, on parasitology. Besides an exploration of the biological, biochemical and biomedical aspects, the workshop will also aim at presenting some of the mathematical modelling, algorithmic theory and software development that have become crucial to explore such aspects.

This workshop is being organised in the context of two projects, both with the Inria European Team Erable. One of the projects involves a partnership with the University of São Paulo (USP), in São Paulo, Brazil, more specifically the Institute of Mathematics and Statistics (IME) and the Institute of Biomedical Sciences – Inria Associated Team Capoeira – and the other involves the Inesc-ID/IST in Portugal, ETH in Zürich and EMBL in Heidelberg – H2020 Twinning Project Olissipo.

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