This survey presents a unified and essentially self-contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the average-case analysis of algorithms. It relies on the Mellin transform, a close relative of the integral transforms of Laplace and Fourier. The method… (More)
We establish a fundamental isomorphism between discrete-time balanced urn processes and certain ordinary differential systems, which are nonlinear, autonomous, and of a simple monomial form. As a consequence, all balanced urn processes with balls of two colours are proved to be analytically solvable in finite terms. The corresponding generating functions… (More)
RÉSUMÉ. Nous étudions le comportement asymptotique d'une classe de suites mahlériennes dont les séries génératrices sont des produits infinis. Un exemple caractéristique est celui de l'estima-tion des coefficients de Taylor de 03A0+~k=0(1 + z2k + z2k+1)-1, voisin des partitions binaires étudiées par De Bruijn. Le résultat obtenu illustre un cas typique… (More)
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)
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)
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)