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

Surtsey and Mount St. Helens: a comparison of early succession rates

Surtsey and Mount St. Helens are celebrated but very different volcanoes. Permanent plots allow for comparisons that reveal mechanisms that control succession and its rate and suggest general principles. We estimated rates from structure development, species composition using detrended correspondence analysis (DCA), changes in Euclidean distance (ED) of DCA vectors, and by principal components analysis (PCA) of DCA. On Surtsey, rates determined from DCA trajectory analyses decreased as follows: gull colony on lava with sand > gull colony on lava, no sand ≫ lava with sand > sand spit > block lava > tephra. On Mount St. Helens, plots on lahar deposits near woodlands were best developed. The succession rates of open meadows declined as follows: <i>Lupinus</i>-dominated pumice > protected ridge with <i>Lupinus</i> > other pumice and blasted sites > isolated lahar meadows > barren plain. Despite the prominent contrasts between the volcanoes, we found several common themes. Isolation restricted the number of colonists on Surtsey and to a lesser degree on Mount St. Helens. Nutrient input from outside the system was crucial. On Surtsey, seabirds fashioned very fertile substrates, while on Mount St. Helens wind brought a sparse nutrient rain, then <i>Lupinus</i> enhanced fertility to promote succession. Environmental stress limits succession in both cases. On Surtsey, bare lava, compacted tephra and infertile sands restrict development. On Mount St. Helens, exposure to wind and infertility slow succession

Non-abelian D=11 Supermembrane

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes.Comment: Contribution to the Proceedings of the Dubna International SQS'09 Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3, 2009. 12pg, Late

On Chern-Simons Quivers and Toric Geometry

We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V^2.Comment: 14pg, 1 Figure, late

Invisible Higgs Boson Decays in Spontaneously Broken R-Parity

The Higgs boson may decay mainly to an invisible mode characterized by missing energy, instead of the Standard Model channels. This is a generic feature of many models where neutrino masses arise from the spontaneous breaking of ungauged lepton number at relatively low scales, such as spontaneously broken R-parity models. Taking these models as framework, we reanalyze this striking suggestion in view of the recent data on neutrino oscillations that indicate non-zero neutrino masses. We show that, despite the smallness of neutrino masses, the Higgs boson can decay mainly to the invisible Goldstone boson associated to the spontaneous breaking of lepton number. This requires a gauge singlet superfield coupling to the electroweak doublet Higgses, as in the Next to Minimal Supersymmetric Standard Model (NMSSM) scenario for solving the $\mu$-problem. The search for invisibly decaying Higgs bosons should be taken into account in the planning of future accelerators, such as the Large Hadron Collider and the Next Linear Collider.Comment: 24 pages, 10 figures; typos corrected, published versio

Bayesian Additive Regression Trees with Model Trees

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of non-linearity and high-order interactions. In this paper, we introduce an extension of BART, called Model Trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a linear predictor is estimated considering the covariates that have been used as the split variables in the corresponding tree. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART. Via simulation studies and real data applications, we compare MOTR-BART to its main competitors. R code for MOTR-BART implementation is available at https://github.com/ebprado/MOTR-BART

On the Geometry of Supersymmetric Quantum Mechanical Systems

We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the considered systems to higher dimensions and more complicated potentials.Comment: 18 page

On The spectrum of a Noncommutative Formulation of the D=11 Supermembrane with Winding

A regularized model of the double compactified D=11 supermembrane with nontrivial winding in terms of SU(N) valued maps is obtained. The condition of nontrivial winding is described in terms of a nontrivial line bundle introduced in the formulation of the compactified supermembrane. The multivalued geometrical objects of the model related to the nontrivial wrapping are described in terms of a SU(N) geometrical object which in the $N\to \infty$ limit, converges to the symplectic connection related to the area preserving diffeomorphisms of the recently obtained non-commutative description of the compactified D=11 supermembrane.(I. Martin, J.Ovalle, A. Restuccia. 2000,2001) The SU(N) regularized canonical lagrangian is explicitly obtained. In the $N\to \infty$ limit it converges to the lagrangian in (I.Martin, J.Ovalle, A.Restuccia. 2000,2001) subject to the nontrivial winding condition. The spectrum of the hamiltonian of the double compactified D=11 supermembrane is discussed. Generically, it contains local string like spikes with zero energy. However the sector of the theory corresponding to a principle bundle characterized by the winding number $n \neq 0$, described by the SU(N) model we propose, is shown to have no local string-like spikes and hence the spectrum of this sector should be discrete.Comment: 16 pages.Latex2