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

Multi-GPU maximum entropy image synthesis for radio astronomy

The maximum entropy method (MEM) is a well known deconvolution technique in radio-interferometry. This method solves a non-linear optimization problem with an entropy regularization term. Other heuristics such as CLEAN are faster but highly user dependent. Nevertheless, MEM has the following advantages: it is unsupervised, it has a statistical basis, it has a better resolution and better image quality under certain conditions. This work presents a high performance GPU version of non-gridding MEM, which is tested using real and simulated data. We propose a single-GPU and a multi-GPU implementation for single and multi-spectral data, respectively. We also make use of the Peer-to-Peer and Unified Virtual Addressing features of newer GPUs which allows to exploit transparently and efficiently multiple GPUs. Several ALMA data sets are used to demonstrate the effectiveness in imaging and to evaluate GPU performance. The results show that a speedup from 1000 to 5000 times faster than a sequential version can be achieved, depending on data and image size. This allows to reconstruct the HD142527 CO(6-5) short baseline data set in 2.1 minutes, instead of 2.5 days that takes a sequential version on CPU.Comment: 11 pages, 13 figure

On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding

The spectrum of the Hamiltonian of the double compactified D=11 supermembrane with non-trivial central charge or equivalently the non-commutative symplectic super Maxwell theory is analyzed. In distinction to what occurs for the D=11 supermembrane in Minkowski target space where the bosonic potential presents string-like spikes which render the spectrum of the supersymmetric model continuous, we prove that the potential of the bosonic compactified membrane with non-trivial central charge is strictly positive definite and becomes infinity in all directions when the norm of the configuration space goes to infinity. This ensures that the resolvent of the bosonic Hamiltonian is compact. We find an upper bound for the asymptotic distribution of the eigenvalues.Comment: 11 pages, LaTe

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

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

Supersymmetric exact sequence, heat kernel and super KdV hierarchy

We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super KdV hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator.We obtain the explicit expression for the Green's function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when $t\to0^+$ of the Green's function for the super heat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.Comment: 20 pages, to be published in JM

Interacting Multiple Try Algorithms with Different Proposal Distributions

We propose a new class of interacting Markov chain Monte Carlo (MCMC) algorithms designed for increasing the efficiency of a modified multiple-try Metropolis (MTM) algorithm. The extension with respect to the existing MCMC literature is twofold. The sampler proposed extends the basic MTM algorithm by allowing different proposal distributions in the multiple-try generation step. We exploit the structure of the MTM algorithm with different proposal distributions to naturally introduce an interacting MTM mechanism (IMTM) that expands the class of population Monte Carlo methods. We show the validity of the algorithm and discuss the choice of the selection weights and of the different proposals. We provide numerical studies which show that the new algorithm can perform better than the basic MTM algorithm and that the interaction mechanism allows the IMTM to efficiently explore the state space

Imaging Tests for Predicting the Presence of Difficult Airway in Head and Neck Cancer Patients Undergoing Otorhinolaryngological Surgery

Patients with head and neck cancers represent a challenge for the surgical team from many points of view, but, especially, the surgical moment where greater stress generated corresponds to the perioperative management of the airway, because in many occasions we can face unexpected situations, most of the time, incidental findings can hinder ventilation and endotracheal intubation. Gutierrez et al., in 2018, decided to study four tomography measures and their correlation in anesthesia records with airway management difficulties. Material and methods: A retrospective, observational study was carried out in 104 patients operated by head and neck cancers over a period of 36 months, only in those with access to tomographic records. Four tomographic measurements were considered and were statistically related to the extreme degrees of visualization of the glottis (Cormack III–IV) and the presence of the physical examination of Mallampati III–IV. Results: After performing a multivariate model in the group of extreme degrees of visualization of the glottis, the results were not statistically significant (p > 0.05; 95% CI: 0.030–2.31: EPI/PPW, 0.018–1.37 TB/PPW). In the Mallampati III–IV group, in the multivariate model only the VC/PPW showed clinically significant results (p < 0.05; 95% CI: 0.104–8.53). Conclusions: Tomographic measurements and the physical examination predictors could represent a useful guide in the prediction of the difficult airway in these patients

Perfiles paleokarsticos en el techo de la unidad intermedia del mioceno de la cuenca de Madrid

An intra-Vallesian (Upper Miocene) paleokarst developed at the top of the Intermediate Miocene Unit in the continental Madrid basin is recognized. This paleokarst is a early shallow, tabular-shaped karst that shows a marked control by the depositional facies pattern and lithologies. By integrating morphological, petrological and geochemica1 data, three hydrogeological or environmental zones have been established throughout the paleokarstic profiles: (i) a vadose zone, characterized by vertically elongated caves and discontinuous speleothems and vadose cements (ii) a 3-7 m thick water table fringe, characterized by the wide development of stratiform breccia bodies, the superimposition of both vadose and phreatic features, and the lowest Fe and Mn contents in host-rock carbonates; and (iii) a phreatic zone characterized by an increase of 6I3C values and the predominance of phreatic cementation. The paleogeographic reconstruction for the intra-Vallesian paleokarst using paleokarstic profiles reveals relative topographic highs to the north and topographic lows to the south drawing the paleokarst landscape.En el techo de la Unidad Intermedia del Mioceno de la Cuenca de Madrid se ha desarrollado un paleokarst temprano, somero y de forma tabular que muestra un marcado control litológico y del dispositivo de facies deposicionales en su génesis. Integrando criterios geomorfológicos, petrográficos y geoquímicos se ha establecido una zonación hidrogeológica en los perfiles paleokársticos estudiados, diferenciándose: (i) una zona vadosa caracterizada por la existencia de cavidades alargadas en la vertical tapizadas discontinuamente por espeleotemas y otros cementos vadosos; (ii) una franja de oscilación del nivel freático de unos 3-7 metros de espesor, caracterizado por el desarrollo extensivo de cuerpos brechoides estratiformes, la yuxtaposición de cementos vadosos y freáticos y los contenidos más bajos en Fe y Mn en el material encajante, y (iii) una zona freática caracterizada por un aumento en los valores de 613C y el predominio de la cementación freática. La correlación de los perfiles paleokárticos revela una paleogeografía para el techo de la Unidad Intermedia con un paisaje topográficamente descendente de norte a sur en la cuenca para el Vallesiense

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