Bursting of rigid bubbles

We propose here a fluid dynamics video relating the bursting of soap rigid films.Comment: 4 pages and 2 videos included for the Gallery of Fluid Motion 201

Nonparametric estimation of the conditional distribution of the inter-jumping times for piecewise-deterministic Markov processes

This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation example illustrates the behavior of our estimator

Holes and cracks in rigid foam films

The classical problem of foam film rupture dynamics has been investigated when surfaces exhibit very high rigidity due to the presence of specific surfactants. Two new features are reported. First a strong deviation to the well-known Taylor-Culick law is observed. Then, crack-like patterns can be visualized in the film; these patterns are shown to appear at a well defined deformation. The key role of surface active material on these features is quantitatively investigated, pointing the importance of surface elasticity to describe these fast dynamical processes, and thus providing an alternative tool to characterize surface elasticity in conditions extremely far from equilibrium. The origin of the cracks and their consequences on film rupturing dynamics are also discussed

Asymmetry tests for Bifurcating Auto-Regressive Processes with missing data

We present symmetry tests for bifurcating autoregressive processes (BAR) when some data are missing. BAR processes typically model cell division data. Each cell can be of one of two types \emph{odd} or \emph{even}. The goal of this paper is to study the possible asymmetry between odd and even cells in a single observed lineage. We first derive asymmetry tests for the lineage itself, modeled by a two-type Galton-Watson process, and then derive tests for the observed BAR process. We present applications on both simulated and real data

Random coefficients bifurcating autoregressive processes

This paper presents a model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency with a convergence rate, and their asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new important general results in both these frameworks

A general definition of influence between stochastic processes

We extend the study of weak local conditional independence (WCLI) based on a measurability condition made by Commenges and G\'egout-Petit (2009) to a larger class of processes that we call D'. We also give a definition related to the same concept based on certain likelihood processes, using the Girsanov theorem. Under certain conditions, the two definitions coincide on D'. These results may be used in causal models in that we define what may be the largest class of processes in which influences of one component of a stochastic process on another can be described without ambiguity. From WCLI we can contruct a concept of strong local conditional independence (SCLI). When WCLI does not hold, there is a direct influence while when SCLI does not hold there is direct or indirect influence. We investigate whether WCLI and SCLI can be defined via conventional independence conditions and find that this is the case for the latter but not for the former. Finally we recall that causal interpretation does not follow from mere mathematical definitions, but requires working with a good system and with the true probability