Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Random assignment of intervention points in two phase single-case designs: data-division-specific distributions

The present study explores the statistical properties of a randomization test based on the random assignment of the intervention point in a two-phase (AB) single-case design. The focus is on randomization distributions constructed with the values of the test statistic for all possible random assignments and used to obtain p-values. The shape of those distributions is investigated for each specific data division defined by the moment in which the intervention is introduced. Another aim of the study consisted in testing the detection of inexistent effects (i.e., production of false alarms) in autocorrelated data series, in which the assumption of exchangeability between observations may be untenable. In this way, it was possible to compare nominal and empirical Type I error rates in order to obtain evidence on the statistical validity of the randomization test for each individual data division. The results suggest that when either of the two phases has considerably less measurement times, Type I errors may be too probable and, hence, the decision making process to be carried out by applied researchers may be jeopardized.

The co-evolution of culturally inherited altruistic helping and cultural transmission under random group formation.

Limited migration results in kin selective pressure on helping behaviors under a wide range of ecological, demographic and life-history situations. However, such genetically determined altruistic helping can evolve only when migration is not too strong and group size is not too large. Cultural inheritance of helping behaviors may allow altruistic helping to evolve in groups of larger size because cultural transmission has the potential to markedly decrease the variance within groups and augment the variance between groups. Here, we study the co-evolution of culturally inherited altruistic helping behaviors and two alternative cultural transmission rules for such behaviors. We find that conformist transmission, where individuals within groups tend to copy prevalent cultural variants (e.g., beliefs or values), has a strong adverse effect on the evolution of culturally inherited helping traits. This finding is at variance with the commonly held view that conformist transmission is a crucial factor favoring the evolution of altruistic helping in humans. By contrast, we find that under one-to-many transmission, where individuals within groups tend to copy a "leader" (or teacher), altruistic helping can evolve in groups of any size, although the cultural transmission rule itself hitchhikes rather weakly with a selected helping trait. Our results suggest that culturally determined helping behaviors are more likely to be driven by "leaders" than by popularity, but the emergence and stability of the cultural transmission rules themselves should be driven by some extrinsic factors.

Les Passions filmées: des codes en appropriation, un cinéma en canonisation

Constituant l'un des premiers « genres » de l'histoire du cinéma (dont Burch et Gaudreault ont montré le rôle fondateur dans la standardisation des procédures de montage institutionnalisées), les films mettant en scène la Vie et la Passion du Christ fixent leurs normes en s'appropriant des codes iconographiques préétablis. Dans cet article, Valentine Robert s'attache à déployer le « palimpseste » de ces Passions des premiers temps, à démêler les « séries culturelles » impliquées, à dégager les phénomènes de reprises d'une bande à l'autre, et à replacer certains de ces jeux référentiels dans leur visée de légitimation - ou doit-on dire « canonisation » ? - du médium cinématographique.

Reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns

Treball final de carrera basat en el reconeixement de punts clau en imatges mitjançant l'algorisme Random Ferns.