Lepton flavour violating slepton decays to test type-I and II seesaw at the LHC

Searches at the LHC of lepton flavour violation (LFV) in slepton decays can indirectly test both type-I and II seesaw mechanisms. Assuming universal flavour-blind boundary conditions, LFV in the neutrino sector is related to LFV in the slepton sector by means of the renormalization group equations. Ratios of LFV slepton decay rates result to be a very effective way to extract the imprint left by the neutrino sector. Some neutrino scenarios within the type-I seesaw mechanism are studied. Moreover, for both type-I and II seesaw mechanisms, a scan over the minimal supergravity parameter space is performed to estimate how large LFV slepton decay rates can be, while respecting current low-energy constraints.Comment: 4 pages; to appear in the proceedings of the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY09), Boston (MA), USA, 5-10 Jun 200

A Berry-Esseen theorem for Feynman-Kac and interacting particle models

In this paper we investigate the speed of convergence of the fluctuations of a general class of Feynman-Kac particle approximation models. We design an original approach based on new Berry-Esseen type estimates for abstract martingale sequences combined with original exponential concentration estimates of interacting processes. These results extend the corresponding statements in the classical theory and apply to a class of branching and genealogical path-particle models arising in nonlinear filtering literature as well as in statistical physics and biology.Comment: Published at http://dx.doi.org/10.1214/105051604000000792 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Genealogical particle analysis of rare events

In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman--Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.Comment: Published at http://dx.doi.org/10.1214/105051605000000566 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On the Geometry of Sculpting-like Gauging Processes

Recently, a new gauging procedure called Sculpting mechanism was proposed to obtain the M-theory origin of type II gauged Supergravity theories in 9D. We study this procedurein detail and give a better understanding of the different deformations and changes in fiber bundles, that are able to generate new relevant physical gauge symmetries in the theory. We discuss the geometry involved in the standard approach (Noether-like) and in the new Scultping-like one and comment on possible new applications.Comment: 9 pages, latex, Notation and typos reviewed, more clear explanations, results unchange

Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations

We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolutions depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behavior of these iterative algorithms which relies on measure-valued processes and semigroup techniques. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.Comment: Published in at http://dx.doi.org/10.1214/09-AAP628 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonasymptotic analysis of adaptive and annealed Feynman-Kac particle models

Sequential and quantum Monte Carlo methods, as well as genetic type search algorithms can be interpreted as a mean field and interacting particle approximations of Feynman-Kac models in distribution spaces. The performance of these population Monte Carlo algorithms is strongly related to the stability properties of nonlinear Feynman-Kac semigroups. In this paper, we analyze these models in terms of Dobrushin ergodic coefficients of the reference Markov transitions and the oscillations of the potential functions. Sufficient conditions for uniform concentration inequalities w.r.t. time are expressed explicitly in terms of these two quantities. We provide an original perturbation analysis that applies to annealed and adaptive Feynman-Kac models, yielding what seems to be the first results of this kind for these types of models. Special attention is devoted to the particular case of Boltzmann-Gibbs measures' sampling. In this context, we design an explicit way of tuning the number of Markov chain Monte Carlo iterations with temperature schedule. We also design an alternative interacting particle method based on an adaptive strategy to define the temperature increments. The theoretical analysis of the performance of this adaptive model is much more involved as both the potential functions and the reference Markov transitions now depend on the random evolution on the particle model. The nonasymptotic analysis of these complex adaptive models is an open research problem. We initiate this study with the concentration analysis of a simplified adaptive models based on reference Markov transitions that coincide with the limiting quantities, as the number of particles tends to infinity.Comment: Published at http://dx.doi.org/10.3150/14-BEJ680 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm