Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

Local Stereology of Tensors of Convex Bodies

In this paper, we present local stereological estimators of Minkowski tensors defined on convex bodies in ℝ d . Special cases cover a number of well-known local stereological estimators of volume and surface area in ℝ3, but the general set-up also provides new local stereological estimators of various types of centres of gravity and tensors of rank two. Rank two tensors can be represented as ellipsoids and contain information about shape and orientation. The performance of some of the estimators of centres of gravity and volume tensors of rank two is investigated by simulation.

A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method

We present a novel approach to the reconstruction of depth from light field data. Our method uses dictionary representations and group sparsity constraints to derive a convex formulation. Although our solution results in an increase of the problem dimensionality, we keep numerical complexity at bay by restricting the space of solutions and by exploiting an efficient Primal-Dual formulation. Comparisons with state of the art techniques, on both synthetic and real data, show promising performances.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Relative abundance and ranges of selected diatoms from Pliocene-Pleistocene sections of ODP Leg 177, Atlantic sector of the Southern Ocean

During Ocean Drilling Program (ODP) Leg 177, seven sites were drilled aligned on a transect across the Antarctic Circumpolar Current in the Atlantic sector of the Southern Ocean. The primary scientific objective of Leg 177 was the study of the Cenozoic paleoceanographic and paleoclimatic history of the southern high latitudes and its relationship with the Antarctic cryosphere development. Of special emphasis was the recovery of Pliocene-Pleistocene sections, allowing paleoceanographic studies at millennial or higher time resolution, and the establishment of refined biostratigraphic zonations tied to the geomagnetic polarity record and stable isotope records. At most sites, multiple holes were drilled to ensure complete recovery of the section. A description of the recovered sections and the construction of a multihole splice for the establishment of a continuous composite is presented in the Leg 177 Initial Reports volume for each of the sites (Gersonde, Hodell, Blum, et al., 1999). Here we present the relative abundance pattern and the stratigraphic ranges of diatom taxa encountered from shore-based light microscope studies completed on the Pliocene-Pleistocene sequences from six of the drilled sites (Sites 1089-1094). No shore-based diatom studies have been conducted on the Pliocene-Pleistocene sediments obtained at Site 1088, located on the northern crest of the Agulhas Ridge, because of the scattered occurrence and poor preservation of diatoms in these sections (Shipboard Scientific Party, 1999b). The data included in our report present the baseline of a diatom biostratigraphic study of Zielinski and Gersonde (2002), which (1) includes a refinement of the southern high-latitude Pliocene-Pleistocene diatom zonation, in particular for the middle and late Pleistocene, and (2) presents a biostratigraphic framework for the establishment of age models of the recovered sediment sections. Zielinski and Gersonde (2002) correlated the diatom ranges with the geomagnetic polarity record established shipboard (Sites 1090 and 1092) (Shipboard Scientific Party, 1999c, 1999d) and on shore (Sites 1089, 1091, 1093, and 1094) by Channell and Stoner (2002). The Pliocene-Pleistocene diatom zonation proposed by Zielinski and Gersonde (2002) relies on a diatom zonation from Gersonde and Bárcena (1998) for the northern belt of the Southern Ocean. Because of latitudinal differentiation of sea-surface temperature, nutrients, and salinity between Antarctic and Subantarctic/subtropical water masses, the Pliocene-Pleistocene stratigraphic marker diatoms are not uniformly distributed in the Southern Ocean (Fenner, 1991; Gersonde and Bárcena, 1998). As a consequence, Zielinski and Gersonde (2002) propose two diatom zonations for application in the Antarctic Zone south of the Polar Front (Southern Zonation, Sites 1094 and 1093) and the area encompassing the Polar Front Zone (PFZ) and the Subantarctic Zone (Northern Zonation, Sites 1089-1092). This accounts especially for the Pleistocene zonation where Hemidiscus karstenii, whose first abundant occurrence datum and last occurrence datum defines the subzonation of the northern Thalassiosira lentiginosa Zone, occurs only sporadically in the cold-water realm south of the PFZ and thus is not applicable in sections from this area. However, newly established marker species assigned to the genus Rouxia (Rouxia leventerae and Rouxia constricta) are more related to cold-water environments and allow a refinement of the Pleistocene stratigraphic zonation for the southern cold areas. A study relying on quantitative counts of both Rouxia species confirms the utility of these stratigraphic markers for the identification of sequences attributed to marine isotope Stages 6 and 8 in the southern Southern Ocean (Zielinski et al., 2002).

Uniformly reweighted belief propagation for distributed Bayesian hypothesis testing

Belief propagation (BP) is a technique for distributed inference in wireless networks and is often used even when the underlying graphical model contains cycles. In this paper, we propose a uniformly reweighted BP scheme that reduces the impact of cycles by weighting messages by a constant ?edge appearance probability? rho ? 1. We apply this algorithm to distributed binary hypothesis testing problems (e.g., distributed detection) in wireless networks with Markov random field models. We demonstrate that in the considered setting the proposed method outperforms standard BP, while maintaining similar complexity. We then show that the optimal ? can be approximated as a simple function of the average node degree, and can hence be computed in a distributed fashion through a consensus algorithm.

Uniformly Reweighted Belief Propagation: A Factor Graph Approach

Tree-reweighted belief propagation is a message passing method that has certain advantages compared to traditional belief propagation (BP). However, it fails to outperform BP in a consistent manner, does not lend itself well to distributed implementation, and has not been applied to distributions with higher-order interactions. We propose a method called uniformly-reweighted belief propagation that mitigates these drawbacks. After having shown in previous works that this method can substantially outperform BP in distributed inference with pairwise interaction models, in this paper we extend it to higher-order interactions and apply it to LDPC decoding, leading performance gains over BP.

Efficient algorithms for dynamic probabilistic safety assessment. An application to convex damage domain.

The design of nuclear power plant has to follow a number of regulations aimed at limiting the risks inherent in this type of installation. The goal is to prevent and to limit the consequences of any possible incident that might threaten the public or the environment. To verify that the safety requirements are met a safety assessment process is followed. Safety analysis is as key component of a safety assessment, which incorporates both probabilistic and deterministic approaches. The deterministic approach attempts to ensure that the various situations, and in particular accidents, that are considered to be plausible, have been taken into account, and that the monitoring systems and engineered safety and safeguard systems will be capable of ensuring the safety goals. On the other hand, probabilistic safety analysis tries to demonstrate that the safety requirements are met for potential accidents both within and beyond the design basis, thus identifying vulnerabilities not necessarily accessible through deterministic safety analysis alone. Probabilistic safety assessment (PSA) methodology is widely used in the nuclear industry and is especially effective in comprehensive assessment of the measures needed to prevent accidents with small probability but severe consequences. Still, the trend towards a risk informed regulation (RIR) demanded a more extended use of risk assessment techniques with a significant need to further extend PSA’s scope and quality. Here is where the theory of stimulated dynamics (TSD) intervenes, as it is the mathematical foundation of the integrated safety assessment (ISA) methodology developed by the CSN(Consejo de Seguridad Nuclear) branch of Modelling and Simulation (MOSI). Such methodology attempts to extend classical PSA including accident dynamic analysis, an assessment of the damage associated to the transients and a computation of the damage frequency. The application of this ISA methodology requires a computational framework called SCAIS (Simulation Code System for Integrated Safety Assessment). SCAIS provides accident dynamic analysis support through simulation of nuclear accident sequences and operating procedures. Furthermore, it includes probabilistic quantification of fault trees and sequences; and integration and statistic treatment of risk metrics. SCAIS comprehensively implies an intensive use of code coupling techniques to join typical thermal hydraulic analysis, severe accident and probability calculation codes. The integration of accident simulation in the risk assessment process and thus requiring the use of complex nuclear plant models is what makes it so powerful, yet at the cost of an enormous increase in complexity. As the complexity of the process is primarily focused on such accident simulation codes, the question of whether it is possible to reduce the number of required simulation arises, which will be the focus of the present work. This document presents the work done on the investigation of more efficient techniques applied to the process of risk assessment inside the mentioned ISA methodology. Therefore such techniques will have the primary goal of decreasing the number of simulation needed for an adequate estimation of the damage probability. As the methodology and tools are relatively recent, there is not much work done inside this line of investigation, making it a quite difficult but necessary task, and because of time limitations the scope of the work had to be reduced. Therefore, some assumptions were made to work in simplified scenarios best suited for an initial approximation to the problem. The following section tries to explain in detail the process followed to design and test the developed techniques. Then, the next section introduces the general concepts and formulae of the TSD theory which are at the core of the risk assessment process. Afterwards a description of the simulation framework requirements and design is given. Followed by an introduction to the developed techniques, giving full detail of its mathematical background and its procedures. Later, the test case used is described and result from the application of the techniques is shown. Finally the conclusions are presented and future lines of work are exposed.

Entire functions uniformly bounded on balls of a Banach space

Let X be an in�finite-dimensional complex Banach space. Very recently, several results on the existence of entire functions on X bounded on a given ball B1 � X and unbounded on another given ball B2 � X have been obtained. In this paper we consider the problem of �finding entire functions which are uniformly bounded on a collection of balls and unbounded on the balls of some other collection. RESUMEN. Sea X un espacio de Banach complejo de dimensión infinita. En este trabajo, los autores estudian el problema de encontrar una función entera en X que esté uniformemente acotada en una colección de de bolas en X y que no esté acotada en las bolas de otra colección.

A new UTD for the electromagnetic plane wave scattering by a canonical circular cylinder with an impedance boundary condition

A UTD solution is developed for describing the scattering by a circular cylinder with an impedance boundary condition (IBC), when it is illuminated by an obliquely incident electromagnetic (EM) plane wave. The solution to this canonical problem will be crucial for the construction of a more general UTD solution valid for an arbitrary smooth convex surface with an IBC, when it is illuminated by an arbitrary EM ray optical field. The canonical solution is uniformly valid across the surface shadow boundary that is tangent to the surface at grazing incidence. This canonical solution contains cross polarized terms in the scattered fields, which arise from a coupling of the TEz and TMz waves at the impedance boundary on the cylinder. Here, z is the cylinder axis. Numerical results show very good accuracy for the simpler and efficient UTD solution, when compared to exact but very slowly convergent eigenfunction solution.

Planar point sets with large minimum convex decompositions

We show the existence of sets with n points (n ? 4) for which every convex decomposition contains more than (35/32)n?(3/2) polygons,which refutes the conjecture that for every set of n points there is a convex decomposition with at most n+C polygons. For sets having exactly three extreme pointswe show that more than n+sqr(2(n ? 3))?4 polygons may be necessary to form a convex decomposition.