Convergence of U-statistics for interacting particle systems

The convergence of U-statistics has been intensively studied for estimators based on families of i.i.d. random variables and variants of them. In most cases, the independence assumption is crucial [Lee90, de99]. When dealing with Feynman-Kac and other interacting particle systems of Monte Carlo type, one faces a new type of problem. Namely, in a sample of N particles obtained through the corresponding algorithms, the distributions of the particles are correlated -although any finite number of them is asymptotically independent with respect to the total number N of particles. In the present article, exploiting the fine asymptotics of particle systems, we prove convergence theorems for U-statistics in this framework

On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering

We analyse the exponential stability properties of a class of measure-valued equations arising in nonlinear multi-target filtering problems. We also prove the uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean eld particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter, yielding what seems to be the first results of this kind in this subject

Production and decays of supersymmetric Higgs bosons in spontaneously broken R-parity

We study the mass spectra, production and decay properties of the lightest supersymmetric CP-even and CP-odd Higgs bosons in models with spontaneously broken R-parity (SBRP). We compare the resulting mass spectra with expectations of the Minimal Supersymmetric Standard Model (MSSM), stressing that the model obeys the upper bound on the lightest CP-even Higgs boson mass. We discuss how the presence of the additional scalar singlet states affects the Higgs production cross sections, both for the Bjorken process and the "associated production". The main phenomenological novelty with respect to the MSSM comes from the fact that the spontaneous breaking of lepton number leads to the existence of the majoron, denoted J, which opens new decay channels for supersymmetric Higgs bosons. We find that the invisible decays of CP-even Higgses can be dominant, while those of the CP-odd bosons may also be sizeable.Comment: 21 pages, 8 figures; minor changes, final version for publicatio

On particle Gibbs Markov chain Monte Carlo models

This article analyses a new class of advanced particle Markov chain Monte Carlo algorithms recently introduced by Andrieu, Doucet, and Holenstein (2010). We present a natural interpretation of these methods in terms of well known unbiasedness properties of Feynman-Kac particle measures, and a new duality with many-body Feynman-Kac models. This perspective sheds a new light on the foundations and the mathematical analysis of this class of methods. A key consequence is the equivalence between the backward and ancestral particle Markov chain Monte Carlo methods, and Gibbs sampling of a many-body Feynman-Kac target distribution. Our approach also presents a new stochastic differential calculus based on geometric combinatorial techniques to derive explicit non-asymptotic Taylor type series of the semigroup of a class of particle Markov chain Monte Carlo models around their invariant measures with respect to the population size of the auxiliary particle sampler. These results provide sharp quan- titative estimates of the convergence properties of conditional particle Markov chain models with respect to the time horizon and the size of the systems. We illustrate the implication of these results with sharp estimates of the contraction coefficient and the Lyapunov exponent of conditional particle samplers, and explicit and non-asymptotic Lp-mean error decompositions of the law of the random states around the limiting invariant measure. The abstract framework developed in the article also allows the design of natural extensions to island (also called SMC2) type particle methodologies

Degenerate neutrinos from a supersymmetric A_4 model

We investigate the supersymmetric A_4 model recently proposed by Babu, Ma and Valle. The model naturally gives quasi-degenerate neutrinos that are bi-largely mixed, in agreement with observations. Furthermore, the mixings in the quark sector are constrained to be small, making it a complete model of the flavor structure. Moreover, it has the interesting property that CP-violation in the leptonic sector is maximal (unless vanishing). The model exhibit a close relation between the slepton and lepton sectors and we derive the slepton spectra that are compatible with neutrino data and the present bounds on flavor-violating charged lepton decays. The prediction for the branching ratio of the decay tau -> mu gamma has a lower limit of 10^{-9}. In addition, the overall neutrino mass scale is constrained to be larger than 0.3 eV. Thus, the model will be tested in the very near future.Comment: 11 pages, 6 figures. Talk given at the International Workshop on Astroparticle and High Energy Physics (AHEP), Valencia, Spain, 14-18 Oct. 200

Biotechnological approaches to develop nitrogen-fixing cereals: A review

Funding: This work has been funded by the Junta de Andalucia through the research group AGR123.Agricultural yields are often limited by nitrogen (N) availability, especially in countries of the developing world, whereas in industrialized nations the application of chemical N fertilizers has reached unsustainable levels that have resulted in severe environmental consequences. Finding alternatives to inorganic fertilizers is critical for sustainable and secure food production. Although gaseous nitrogen (N2) is abundant in the atmosphere, it cannot be assimilated by most living organisms. Only a selected group of microorganisms termed diazotrophs, have evolved the ability to reduce N2 to generate NH3 in a process known as biological nitrogen fixation (BNF) catalysed by nitrogenase, an oxygen-sensitive enzyme complex. This ability presents an opportunity to improve the nutrition of crop plants, through the introduction into cereal crops of either the N fixing bacteria or the nitrogenase enzyme responsible for N fixation. This review explores three potential approaches to obtain N-fixing cereals: (a) engineering the nitrogenase enzyme to function in plant cells; (b) engineering the legume symbiosis into cereals; and (c) engineering cereals with the capability to associate with N-fixing bacteria.Junta de Andaluci

Minimal supergravity radiative effects on the tri-bimaximal neutrino mixing pattern

We study the stability of the Harrison-Perkins-Scott (HPS) mixing pattern, assumed to hold at some high energy scale, against supersymmetric radiative corrections. We work in the framework of a reference minimal supergravity model (mSUGRA) where supersymmetry breaking is universal and flavor-blind at unification. The radiative corrections considered include both RGE running as well as threshold effects. We find that in this case the solar mixing angle can only increase with respect to the HPS reference value, while the atmospheric and reactor mixing angles remain essentially stable. Deviations from the solar angle HPS prediction towards lower values would signal novel contributions from physics beyond the simplest mSUGRA model.Comment: 13 pages, 3 figures; added reference; final version for publicatio

Predicting Neutrinoless Double Beta Decay

We give predictions for the neutrinoless double beta decay rate in a simple variant of the A_4 family symmetry model. We show that there is a lower bound for the neutrinoless double beta decay amplitude even in the case of normal hierarchical neutrino masses, corresponding to an effective mass parameter |m_{ee}| >= 0.17 \sqrt{\Delta m^2_{ATM}}. This result holds both for the CP conserving and CP violating cases. In the latter case we show explicitly that the lower bound on |m_{ee}| is sensitive to the value of the Majorana phase. We conclude therefore that in our scheme, neutrinoless double beta decay may be accessible to the next generation of high sensitivity experiments.Comment: 4 pages, 5 figures, 1 tabl