Algorithms for Computing Abelian Periods of Words

Constantinescu and Ilie (Bulletin EATCS 89, 167--170, 2006) introduced the notion of an \emph{Abelian period} of a word. A word of length $n$ over an alphabet of size $\sigma$ can have $\Theta(n^{2})$ distinct Abelian periods. The Brute-Force algorithm computes all the Abelian periods of a word in time $O(n^2 \times \sigma)$ using $O(n \times \sigma)$ space. We present an off-line algorithm based on a \sel function having the same worst-case theoretical complexity as the Brute-Force one, but outperforming it in practice. We then present on-line algorithms that also enable to compute all the Abelian periods of all the prefixes of $w$.Comment: Accepted for publication in Discrete Applied Mathematic

Fast Computation of Abelian Runs

Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word $w$ of length $n$ over an alphabet of cardinality $\sigma$ and a Parikh vector $\mathcal{P}$, returns all the abelian runs of period $\mathcal{P}$ in $w$ in time $O(n)$ and space $O(\sigma+p)$, where $p$ is the norm of $\mathcal{P}$, i.e., the sum of its components. We also present an online algorithm that computes all the abelian runs with periods of norm $p$ in $w$ in time $O(np)$, for any given norm $p$. Finally, we give an $O(n^2)$-time offline randomized algorithm for computing all the abelian runs of $w$. Its deterministic counterpart runs in $O(n^2\log\sigma)$ time.Comment: To appear in Theoretical Computer Scienc

A Note on Easy and Efficient Computation of Full Abelian Periods of a Word

Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.Comment: Accepted for publication in Discrete Applied Mathematic

Design of an undervoltage load shedding scheme for the Hydro-Québec system

This paper deals with the control logic of an undervoltage, closed-loop load shedding scheme aimed at protecting the Hydro-Quebec system against long-term voltage instability. This scheme relies on a set of "if-then" rules whose parameters are determined through combinatorial optimisation, relying on the system dynamic response over a set of scenarios. Preliminary results of the above optimisation technique are given, besides a brief description of the foreseen implementation

Design of Load Shedding Schemes against Voltage Instability using Combinatorial Optimization

This paper proposes a methodology for the design of automatic load shedding against voltage instability. In a first step, we describe a method allowing to find the minimal shedding required in a given unstable scenario. In a second step, we describe the structure of various controllers and identify the parameters to be optimized. Next, we present an optimization approach to find the controller parameters which optimize an overall performance objective. Results are presented on the Hydro-Québec system, in which load shedding is presently planned

Efficient validation and construction of border arrays

In this article we present an on-line linear time and space algorithm to check if an integer array f is the border array of at least one string w built on a bounded or unbounded size alphabet Σ. We first show some relations between the border array of some string w and the skeleton of the DFA recognizing Σ ∗ · w, independently of the explicit knowledge of w. This enables us to design algorithms for validating and generating border arrays that outperform existing ones [4, 3]. The validating algorithm lowers the delay (time spent on one element of the array) from O(|w|) to O(min{|Σ|, |w|}) comparing to algorithms in [4, 3]. Finally we give some results on the numbers of distinct border arrays on some alphabet sizes.

Les films de propagande sanitaire de Lortac et O’Galop (1918-1919)

Cette étude s’attache à présenter, de façon succincte, le volet cinématographique de la première grande campagne de santé publique, menée en France, entre 1917 et 1919 à l’initiative du Comité national d’assistance aux anciens militaires tuberculeux. L’accent y est tout particulièrement mis sur la douzaine de dessins animés qui en constituèrent l’un des fleurons. Ces courts-métrages, produits par Pathé, furent réalisés par O’Galop et Lortac, sous la direction du Dr Jean Comandon.This article is a brief presentation of the role played by cinema in the first major public health campaign organised by the “National Committee of Assistance for Tubercular Ex-Soldiers” in France between 1917 and 1919. The focus is more specifically on the dozen animated films that featured in this campaign. These short films were produced by Pathé and made by O’Galop and Lortac, under the supervision of D r Jean Comandon

La Société d’histoire de la pharmacie d’un siècle à l’autre

Fondée à Paris en février 1913 à l’initiative d’un médecin bibliothécaire (Paul Dorveaux), d’un jeune chartiste (Eugène-Humbert Guitard) et d’un pharmacien industriel (Charles Buchet), la Société d’histoire de la pharmacie fut la première société consacrée à l’histoire de cette profession et de cet art. Elle édite depuis plus de cent ans la Revue d’histoire de la pharmacie (anciennement Bulletin de la Société d’histoire de la pharmacie). L’article évoque les principaux réseaux qui la constituèrent à l’origine et l’enrichissement mutuel qui en résulta. Aujourd’hui, la Société d’histoire de la pharmacie demeure toujours très active, malgré le désengagement de l’industrie qui l’avait portée sur les fonts baptismaux

Témoignage de Pierre Bichet

Né en 1922, peintre de vocation, Pierre Bichet accompagna Haroun Tazieff dans son périple autour du monde des volcans et se chargea des prises de vues 35 mm. Il nous a accordé un entretien le 14 octobre 2002

Filmer la bombe A : Premières images, premiers usages

Alors ma terreur redoubla à l'aspect de l'abîme, car je vis des feux et j'entendis des pleurs, et, tout tremblant, je me ramassai sur moi-même. Et je compris alors, aux grandes douleurs qui s'approchaient de toutes parts, ce que je n'avais pas compris auparavant, que je tournais et que je descendais. Juillet-août 1945 : en l'espace de quelques jours, trois bombes atomiques explosèrent en trois points différents du globe, causant pour deux d'entre elles un nombre effrayant de victimes. Sans né..