Vertical representation of C∞C^{\infty}-words

We present a new framework for dealing with $C^{\infty}$-words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of $C^{\infty}$-words through an infinite directed acyclic graph $G$. This graph is defined by a map acting on the frontiers of $C^{\infty}$-words. We show that this map can be defined recursively and with no explicit references to $C^{\infty}$-words. We then show that some important conjectures on $C^{\infty}$-words follow from analogous statements on the structure of the graph $G$.Comment: Published in Theoretical Computer Scienc

Equitable (d,m)(d,m)-edge designs

The paper addresses design of experiments for classifying the input factors of a multi-variate function into negligible, linear and other (non-linear/interaction) factors. We give constructive procedures for completing the definition of the clustered designs proposed Morris 1991, that become defined for arbitrary number of input factors and desired clusters' multiplicity. Our work is based on a representation of subgraphs of the hyper-cube by polynomials that allows the formal verification of the designs' properties. Ability to generate these designs in a systematic manner opens new perspectives for the characterisation of the behaviour of the function's derivatives over the input space that may offer increased discrimination

La doctrine du Logos chez Justin : enjeux philosophiques et théologiques

La doctrine du Logos tient une place centrale dans la pensée de Justin. L’article en explique la signification sur la base de l’Apologie. Il montre comment Justin a compris la médiation du Logos entre Dieu et le monde, et commente ensuite ses affirmations sur le « Logos spermatikos » et les « semences du Logos ». Il montre que la pensée de Justin ne doit pas être interprétée à la lumière de l’arianisme ultérieur, mais que, considérée dans son contexte, elle représente une importante contribution à la compréhension du rapport entre Dieu et le monde. Il souligne enfin que sa doctrine du « Logos spermatikos » n’implique pas d’abord une « hellénisation » du christianisme ; elle est plutôt, pour Justin, une manière d’affirmer l’universalité du don de Dieu.The doctrine of the Logos has a central place in the thought of Justin. The article explains its meaning on the basis of the Apology. It shows how Justin understood the mediation of the Logos between God and the world; then it comments his assertions on the “Logos spermatikos” and the “seeds of the Logos”. It shows that the thought of Justin should not be interpreted in the light of the later Arianism, but that, considered in its context, it represents an important contribution to the understanding of the relationship between God and the world. It underlines finally that his doctrine of “Logos spermatikos” does not imply an “hellenization” of Christianity; it is rather, for Justin, a way of asserting the universality of the gift of God

Extending Morris Method: identification of the interaction graph using cycle-equitabe designs

International audienceThe paper presents designs that allow detection of mixed effects when performing preliminary screening of the inputs of a scalar function of $d$ input factors, in the spirit of Morris' Elementary Effects approach. We introduce the class of $(d,c)$-cycle equitable designs as those that enable computation of exactly $c$ second order effects on all possible pairs of input factors. Using these designs, we propose a fast Mixed Effects screening method, that enables efficient identification of the interaction graph of the input variables. Design definition is formally supported on the establishment of an isometry between sub-graphs of the unit cube $Q_d$ equipped of the Manhattan metric, and a set of polynomials in $(X_1,\ldots, X_d)$ on which a convenient inner product is defined. In the paper we present systems of equations that recursively define these $(d,c)$-cycle equitable designs for generic values of $c\geq 1$, from which direct algorithmic implementations are derived. Application cases are presented, illustrating the application of the proposed designs to the estimation of the interaction graph of specific functions

Effects over one year of low-intensity endurance exercise targeted at the level of maximal lipid oxidation

International audienc

Automata and Differentiable Words

We exhibit the construction of a deterministic automaton that, given k > 0, recognizes the (regular) language of k-differentiable words. Our approach follows a scheme of Crochemore et al. based on minimal forbidden words. We extend this construction to the case of C\infinity-words, i.e., words differentiable arbitrary many times. We thus obtain an infinite automaton for representing the set of C\infinity-words. We derive a classification of C\infinity-words induced by the structure of the automaton. Then, we introduce a new framework for dealing with \infinity-words, based on a three letter alphabet. This allows us to define a compacted version of the automaton, that we use to prove that every C\infinity-word admits a repetition in C\infinity whose length is polynomially bounded.Comment: Accepted for publicatio

́Evaluer la qualité d’une fragmentation de graphe multi-niveaux

International audienc

Derivative based global sensitivity measures

The method of derivative based global sensitivity measures (DGSM) has recently become popular among practitioners. It has a strong link with the Morris screening method and Sobol' sensitivity indices and has several advantages over them. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is generally much lower than that for estimation of Sobol' sensitivity indices. This paper presents a survey of recent advances in DGSM concerning lower and upper bounds on the values of Sobol' total sensitivity indices $S\_{i}^{tot}$. Using these bounds it is possible in most cases to get a good practical estimation of the values of $S\_{i}^{tot}$. Several examples are used to illustrate an application of DGSM

Effets chroniques de l’exercice ciblé au niveau d’oxydation maximale des lipides (LIPOXmax) sur le comportement alimentaire de sujets obèses sédentaires

International audiencePhysical exercise has both a satiating and an orexigenic effect. The latter seems to be favored by glycogen depletion and thus by high intensity exercise. The balance between these two effects is likely to strongly determine the effect of muscle activity on fat loss. Our hypothesis is that the efficiency of training targeted in the zone of maximal lipid oxidation is at least in part explained by alterations in eating behavior. We studied 25 overweight and obese subjects, including 21 women and 4 men. On the whole these subjects lost weight: –2.05 ± 0.8 kg; P < 0.02 and this loss was due to a loss in fat mass (–1.68 ± 0.81 kg; P < 0.05) while FFM was preserved. Five subjects (20%) gained weight (ranging from 0.1 to 1.9 kg), two (8%) had a stable weight and 18 (72%) lost weight (from 0.4 to 21.2 kg). After the first session of training: satiety was unchanged, but hunger was increased (1.15 ± 0.53; P < 0.05) and the subjects were less thinking of food (P < 0.05). Throughout the sessions there was a gradual increase in the satiety score (P < 0.05), and subjects were less thinking of food (P < 0.05). After training, the acute effect of an exercise session on the appetite scale was modified. The acute orexigenic effect (increased hunger) decreases (–1.17 ± 0.40; P < 0.01) as well as the desire to eat (–1.35 ± 0.61, P < 0.05), the amount of food we could eat (–1.25 ± 0.57, P < 0.05) and the will to eat food (–1.78 ± 0.58, P < 0.01). Caloric intake decreased after 8 weeks by 362.69 ± 91.2 kcal/d (P < 0.01) due to a decrease in fat intake (0.17 ± 0.06 g/kg/day; P < 0.02) which was explained in turn by a decrease in the percentage of fat in diet (from 25% to 21% P < 0.05) and reduced snacking that goes from 44% to 18% of subjects tested (P < 0.01). This decrease in snacking is correlated with that of the item “I think about food” on the scale (Spearman rank correlation r = 0.634 P = 0.003). This work therefore shows that LIPOXmax training in obese subjects increases satiety at rest and decreases the orexigenic effect of a single session, and decreased caloric intake and snacking at a correspondingly lower thoughts directed towards the food, resulting in weight loss in 72% of subjects. The slimming effect of training at LIPOXmax seems to be explained at least in part by an increase in satiating effect and decreased orexigenic effect of exercise, resulting in a measurable decrease in calorie intake. These results thus evidence a new mechanism that increases the interest in this variety of training in the management of obesity.L’exercice physique a un effet satiétogène et un effet orexigène, ce dernier semblant favorisé par la déplétion glycogénique et les exercices à haute intensité. L’équilibre entre ces deux effets semble déterminer fortement l’effet de l’activité musculaire sur l’adiposité. Notre hypothèse est que l’efficacité du réentraînement au LIPOXmax s’expliquerait partiellement par une modulation du comportement alimentaire. L’effet chronique de l’entraînement ciblé au LIPOXmax a été étudié chez 25 sujets en surpoids (IMC ≥ 25 kg/m2) et obèses (IMC ≥ 30 kg/m2) dont 21 femmes et 4 hommes. Dans l’ensemble les 25 sujets ont maigri : –2,05 ± 0,8 kg ; p < 0,02 en perdant de la MG (–1,68 ± 0,81 kg ; p < 0,05) et pas de la MM. Cinq sujets (20 %) ont grossi (de 0,1 à 1,9), deux (8 %) ont eu un poids stable et 18 (72 %) ont maigri (de 0,4 à 21,2 kg). L’échelle de Hill est modifiée par la première séance de réentraînement : juste après celle-ci la satiété est inchangée, la faim augmente (+1,15 ± 0,53 ; p < 0,05) et les sujets pensent moins à la nourriture (p < 0,05). Au fil des séances, on voit augmenter le score de satiété (p < 0,05), et les sujets pensent moins à la nourriture (p < 0,05). L’effet immédiat d’une séance sur l’échelle de Hill se modifie. L’effet orexigène aigu de celle-ci (augmentation de faim) diminue (–1,17 ± 0,40 p < 0,01) ainsi que l’intensité du désir de manger. L’envie de manger (–1,35 ± 0,61 ; p < 0,05), et la quantité de nourriture que l’on pourrait manger (–1,25 ± 0,57 ; p < 0,05) et on pense moins à la nourriture (–1,78 ± 0,58 ; p < 0,01). La ration alimentaire des sujets après 8 semaines de réentraînement au LIPOXmax a baissé de 362,69 ± 91,2 kcal/j (p < 0,01) en raison d’une baisse de la ration lipidique de 0,17 ± 0,06 g/kg/j (p < 0,02) ce qui représente une diminution de pourcentage de lipides dans la ration alimentaire passant de 25 % à 21 % (p < 0,05) et une baisse du grignotage qui passe de 44 % à 18 % des sujets testés (p < 0,01). Cette baisse du grignotage est corrélée à celle de l’item (je pense à la nourriture) de l’échelle de Hill (corrélation des rangs de Spearman r = 0,634, p = 0,003). Ce travail montre donc que l’entraînement au LIPOXmax des sujets obèses augmente la sensation de satiété au repos, diminue progressivement l’effet orexigène d’une séance isolée, et diminue la consommation calorique et le grignotage corrélativement à une diminution des pensées dirigées vers la nourriture, déterminant une perte de poids chez 72 % des sujets. L’effet amaigrissant du réentraînement au LIPOXmax semble donc s’expliquer au moins en partie par une augmentation de l’effet satiétogène et une diminution de l’effet orexigène de l’exercice, entraînant une modification mesurable de la prise alimentaire. Ces résultats mettent ainsi en évidence un nouveau mécanisme qui renforce l’intérêt de ce type de réentraînement dans la prise en charge de l’obésité

Simulation of chemical vapor infiltration and deposition based on 3D images: a local scale approach

International audienceA numerical solution for the simulation of chemical vapor infiltration of ceramic matrix composites is presented. This computational model requires a 3D representation of the preform. Gas transport and chemical reaction are simulated by a Monte Carlo random walk technique. The developed algorithm can also be used for determination of effective transport and reaction properties in a porous medium. It is firstly validated by considering the simple case of diffusion and reaction in a flat pore. Results of infiltration of an actual fiber arrangement are described and discussed. Extension to deposition on a thin substrate with asperities is also studied