— We study three sequences of polynomials defined as successive derivatives with respect to a differential operator associated with a grammar (one of these sequences was originally introduced by Ramanujan). Combinatorial interpretations for these polynomials are found in terms of rooted trees and graphs of mappings from [n] to [n]. Introduction Dans [Ra], [B], Ramanujan (et B. Berndt à sa suite...

Gossip-based protocols are simple, robust and scalable and have been consistently applied in many distributed, mostly wired, settings. Most validation in this area has been so far empirical and there is a clear lack of a theoretical counterpart clearly defining what can and cannot be computed with gossip-based protocols. Population protocols, on the other hand, provide a clear and formal model ...

We address the question of typing noninterference (NI) in Milner’s Calculus of Communicating Systems (CCS), in such a way that Milner’s translation of a standard parallel imperative language into CCS preserves both an existing NI property and the associated type system. Recently, Focardi, Rossi and Sabelfeld have shown that a variant of Milner’s translation, restricted to the sequential fragmen...

Let X and Y be finite-type CW-spaces (X connected, Y simply connected), such that the ring H∗(Y,Q) is a k-rescaling of H∗(X,Q). If H∗(X,Q) is a Koszul algebra, then the graded Lie algebra π∗(ΩY )⊗Q is the k-rescaling of gr∗(π1X)⊗Q. If Y is a formal space, then the converse holds, and Y is coformal. Furthermore, if X is formal, with Koszul cohomology algebra, there exist filtered group isomorphi...

Snow cover is often measured as snow water equivalent (SWE), which refers to the amount of water stored in a snow-pack that would be available upon melting. Snow cover and SWE represent the source of local snow melt release, and are sensitive to regional and global atmospheric circulation, and changes in climate. Monitoring SWE using satellite-based passive microwave radiometry has provided nea...

The notion of a (pointed) Galois pretopos (“catégorie galoisienne”) was considered originally by Grothendieck in [12] in connection with the fundamental group of an scheme. In that paper Galois theory is conceived as the axiomatic characterization of the classifying pretopos of a profinite group G. The fundamental theorem takes the form of a representation theorem for Galois pretopos (see [10] ...

A message adversary is a daemon that suppresses messages in round-based message-passing synchronous systems in which no process crashes. A property imposed on a message adversary defines a subset of messages that cannot be eliminated by the adversary. It has recently been shown that when a message adversary is constrained by a property denoted TOUR (for tournament), the corresponding synchronou...

ion : règle (comb-K). M est de la forme fun z → C où C est soit une variable différente de z, soit un opérateur, soit un setm, soit un getm. Dans ce cas, [M ] vaut K C. On cherche à montrer que fun z → C ≃ (fun x → fun y → x)C. Or on a : (fun x → fun y → x)C / s → fun y → C / s (on suppose ici que C n’est pas la variable y pour éviter les considérations sur l’alpha-conversion lors de l’applicat...

To a given analytic function germ f : (R, 0) → (R, 0), we associate zeta functions Zf,+, Zf,− ∈ Z[[T ]], defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence ...