Seminars are given every Friday from 2:00 to 3:00 in room 178. You are welcome 10 minutes earlier for tea, coffee and cake.

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Next talks:

Vendredi 13 décembre 2019 - 9h-9h45 - Graph representation of circular codes - François Pirot (G-SCOP).

The discovery of the DNA structure by Watson and Crick in 1953 spurred a new branch of mathematical biology, which overlaps the theory of block codes, that is, codes consisting of words of a fixed length over some finite alphabet. There are several relevant notions associated to block codes; from most to less restrictive, a block code X can be strong-comma-free (the words of X do not overlap), comma-free (no word from X appears as a proper factor of a word in X2), or k-circular (every word of Xk admits a unique decomposition into words of X when read of a cycle) — if X is k-circular for every k∈N, we say that it is circular. In biology, all these properties imply that it is always possible to retrieve the reading frame in a DNA sequence in order to decompose it into codons (words of length 3).

We describe a graph representation of codes which encapsulates its various properties. By taking advantage of this representation, we are able to give a full characterisation of maximum codes on dinucleotides (words of length 2), of maximal strong-comma-free codes on ℓ-nucleotides (words of any fixed length ℓ), and of maximum comma-free codes on trinucleotides (words of length 3). Finally, we will discuss the optimal value of k(n,ℓ) such that k(n,ℓ)-circularity implies circularity, for all codes on ℓ-nucleotides over an alphabet of cardinality n.

Vendredi 13 décembre 2019 - 9h45-10h30 - Sur les cycles dans les graphes planaires et 1-planaires - François Dross (University of Warsaw, Poland).

Vendredi 13 décembre 2019 - 10h45-11h30 - Composing DP algorithms by treewidth to solve diversity problems - Julien Baste (Universität Ulm, Germany).

Vendredi 13 décembre 2019 - 11h30-12h15 - Counting independent sets in strongly orderable graphs - Marc Heinrich (University of Leeds, United Kingdom).

Vendredi 13 décembre - 12h15-13h30 - Pique-nique de thème.

Vendredi 13 décembre 2019 - 13h30-14h - Pré-audition de François Pirot (G-SCOP).

Vendredi 13 décembre 2019 - 14h15-14h45 - Pré-audition de François Dross (University of Warsaw, Poland).

Vendredi 13 décembre 2019 - 15h-15h30 - Pré-audition de Julien Baste (Universität Ulm, Germany).

Vendredi 13 décembre 2019 - 15h45-16h15 - Pré-audition de Marc Heinrich (University of Leeds, United Kingdom).



GT Graphs and Optimization


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