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This talk gives a general introduction to the asymptotic study of harmonic sums arising in many concrete applications, especially the analysis of algorithms.

We give a new and simple proof of the fact that a finite family of analytic functions has a zero Wronskian only if it is linearly dependent.

We study the differential probability adp ⊕ of exclusive-or when differences are expressed using addition modulo 2 N. This function is important when analysing symmetric primitives that mix exclusive-or and addition—especially when addition is used to add in the round keys. (Such primitives include idea, Mars, rc6 and Twofish.) We show that adp ⊕ can be… (More)

We give a randomized algorithm in deterministic time O(N log M) for estimating the score vector of matches between a text string of length N and a pattern string of length M , i.e., the vector obtained when the pattern is slid along the text, and the number of matches is counted for each position. A direct application is approximate string matching. The… (More)

- Serena Bernacchi, Séverine Freisz, Clarisse Maechling, Bernard Spiess, Roland Marquet, Philippe Dumas +1 other
- Nucleic acids research
- 2007

Owing to a striking, and most likely fortuitous, structural and sequence similarity with the bacterial 16 S ribosomal A site, the RNA kissing-loop complex formed by the HIV-1 genomic RNA dimerization initiation site (DIS) specifically binds 4,5-disubstituted 2-deoxystreptamine (2-DOS) aminoglycoside antibiotics. We used chemical probing, molecular modeling,… (More)

- Eric Ennifar, Jean-Christophe Paillart, Anne Bodlenner, Philippe Walter, Jean-Marc Weibel, Anne-Marie Aubertin +3 others
- Nucleic acids research
- 2006

The kissing-loop complex that initiates dimerization of genomic RNA is crucial for Human Immunodeficiency Virus Type 1 (HIV-1) replication. We showed that owing to its strong similitude with the bacterial ribosomal A site it can be targeted by aminoglycosides. Here, we present its crystal structure in complex with neamine, ribostamycin, neomycin and… (More)

We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using elementary tools from analysis and linear algebra, and more sophisticated tools from analytic number theory. We show that a probability distribution function describes the asymptotic behaviour of the rational series… (More)

The generating series of a radix-rational sequence is a rational formal power series from formal language theory viewed through a fixed radix numeration system. For each radix-rational sequence with complex values we provide an asymptotic expansion for the sequence of its Cesàro means. The precision of the asymptotic depends on the joint spectral radius of… (More)

- Philippe Dumas
- 1993