We prove that, given a double sequence w over the alphabet A (i.e. a mapping from Z Z 2 to A), if there exists a pair (n 0 ; m 0) 2 Z Z 2 such that p w (n 0 ; m 0) < 1 100 n 0 m 0 , then w has a periodicity vector, where p w of w is the complexity function of w.
Getting and analyzing biological interaction networks is at the core of systems biology. To help understanding these complex networks, many recent works have suggested to focus on motifs which occur more frequently than expected in random. To identify such exceptional motifs in a given network, we propose a statistical and analytical method which does not… (More)
For discrete sets coded by the Freeman chain describing their contour, several linear algorithms have been designed for determining their shape properties. Most of them are based on the assumption that the boundary word forms a closed and non-intersecting discrete curve. In this article, we provide a linear time and space algorithm for deciding whether a… (More)
The aim of the paper is to introduce techniques in order to optimize the parallel execution time of sorting on heterogeneous platforms (processors speeds are related by a constant factor). We develop a constant time technique for mastering processor load balancing and execution time in an heterogeneous environment. We develop an analytical model for the… (More)
Discovering patterns or frequent episodes in transactions is an important problem in data-mining for the purpose of infering deductive rules from them. Because of the huge size of the data to deal with, parallel algorithms have been designed for reducing both the execution time and the number of repeated passes over the database in order to reduce, as much… (More)
The aim of the paper is to introduce techniques in order to tune sequential in-core sorting algorithms in the frameworks of two applications. The first application is parallel sorting when the processor speeds are not identical in the parallel system. The second application is the Zeta-Data Project (Koskas , 2003) whose aim is to develop novel algorithms… (More)
Change point problems arise in many genomic analyses such as the detection of copy number variations or the detection of transcribed regions. The expanding Next Generation Sequencing technologies now allow to locate change points at the nucleotide resolution. Because of its complexity which is almost linear in the sequence length when the maximal number of… (More)