Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

The Coronation mantle and the Westminster sanctuary pavement

The Great Sanctuary pavement at Westminster Abbey, on which the kings of England were crowned, features a design of rotated squares, around a central roundel of unusual Egyptian alabaster, set within a circle of bright blue glass. The roundel’s visual resemblance to the world and the firmament is underlined by a surrounding inscription, identifying it as the world, the macrocosm. This paper proposes that the design and meaning of the Great Sanctuary pavement reflect the square macrocosmic mantle in which the English king was wrapped during the coronation ceremony. This paper underlines the special nature of the English coronation mantle within the context of other royal and imperial cosmic mantles. Its square form was unique, and it featured in the English coronation liturgies in a way that European mantles did not. The English liturgies stressed its role as a representation of the world or macrocosm

Effects of dietary urea levels on milk protein fractions of Holstein cows

The aim of this study was to evaluate the effects of substituting soybean meal for urea on milk protein fractions (casein, whey protein and non-protein nitrogen) of dairy cows in three dietary levels. Nine mid-lactation Holstein cows were used in a 3 x 3 Latin square arrangement, composed of 3 treatments, 3 periods of 21 days each, and 3 squares. The treatments consisted of three different diets fed to lactating cows, which were randomly assigned to three groups of three animals: (A) no urea inclusion, providing 100% of crude protein (CP), rumen undegradable protein (RUP) and rumen degradable protein (RDP) requirements, using soybean meal and sugarcane as roughage; (B) urea inclusion at 7.5 g/kg DM in partial substitution of soybean meal CP equivalent; (C) urea inclusion at 15 g/kg DM in partial substitution of soybean meal CP equivalent. Rations were isoenergetic and isonitrogenous-1 60 g/kg DM of crude protein and 6.40 MJ/kg DM of net energy for lactation. When the data were analyzed by simple polynomial regression, no differences were observed among treatments in relation to milk CP content, true protein, casein, whey protein, non-casein and non-protein nitrogen, or urea. The milk true protein:crude protein and casein:true protein ratios were not influenced by substituting soybean meal for urea in the diet. Based on the results it can be concluded that the addition of urea up to 15 g/kg of diet dry matter in substitution of soybean meal did not alter milk protein concentration casein, whey protein and its non-protein fractions, when fed to lactating dairy cows. (c) 2007 Elsevier B.V. All rights reserved.

Upper-mantle seismic structure beneath SE and Central Brazil from P- and S-wave regional traveltime tomography

We present models for the upper-mantle velocity structure beneath SE and Central Brazil using independent tomographic inversions of P- and S-wave relative arrival-time residuals (including core phases) from teleseismic earthquakes. The events were recorded by a total of 92 stations deployed through different projects, institutions and time periods during the years 1992-2004. Our results show correlations with the main tectonic structures and reveal new anomalies not yet observed in previous works. All interpretations are based on robust anomalies, which appear in the different inversions for P-and S-waves. The resolution is variable through our study volume and has been analyzed through different theoretical test inversions. High-velocity anomalies are observed in the western portion of the Sao Francisco Craton, supporting the hypothesis that this Craton was part of a major Neoproterozoic plate (San Franciscan Plate). Low-velocity anomalies beneath the Tocantins Province (mainly fold belts between the Amazon and Sao Francisco Cratons) are interpreted as due to lithospheric thinning, which is consistent with the good correlation between intraplate seismicity and low-velocity anomalies in this region. Our results show that the basement of the Parana Basin is formed by several blocks, separated by suture zones, according to model of Milani & Ramos. The slab of the Nazca Plate can be observed as a high-velocity anomaly beneath the Parana Basin, between the depths of 700 and 1200 km. Further, we confirm the low-velocity anomaly in the NE area of the Parana Basin which has been interpreted by VanDecar et al. as a fossil conduct of the Tristan da Cunha Plume related to the Parana flood basalt eruptions during the opening of the South Atlantic.

Integrated marine gravity field in the Brazilian coast from altimeter-derived sea surface gradient and shipborne gravity

Sea surface gradients derived from the Geosat and ERS-1 satellite altimetry geodetic missions were integrated with marine gravity data from the National Geophysical Data Center and Brazilian national surveys. Using the least squares collocation method, models of free-air gravity anomaly and geoid height were calculated for the coast of Brazil with a resolution of 2` x 2`. The integration of satellite and shipborne data showed better statistical results in regions near the coast than using satellite data only, suggesting an improvement when compared to the state-of-the-art global gravity models. Furthermore, these results were obtained with considerably less input information than was used by those reference models. The least squares collocation presented a very low content of high-frequency noise in the predicted gravity anomalies. This may be considered essential to improve the high resolution representation of the gravity field in regions of ocean-continent transition. (C) 2010 Elsevier Ltd. All rights reserved.

Effects of roads, topography, and land use on forest cover dynamics in the Brazilian Atlantic Forest

Roads and topography can determine patterns of land use and distribution of forest cover, particularly in tropical regions. We evaluated how road density, land use, and topography affected forest fragmentation, deforestation and forest regrowth in a Brazilian Atlantic Forest region near the city of Sao Paulo. We mapped roads and land use/land cover for three years (1962, 1981 and 2000) from historical aerial photographs, and summarized the distribution of roads, land use/land cover and topography within a grid of 94 non-overlapping 100 ha squares. We used generalized least squares regression models for data analysis. Our models showed that forest fragmentation and deforestation depended on topography, land use and road density, whereas forest regrowth depended primarily on land use. However, the relationships between these variables and forest dynamics changed in the two studied periods; land use and slope were the strongest predictors from 1962 to 1981, and past (1962) road density and land use were the strongest predictors for the following period (1981-2000). Roads had the strongest relationship with deforestation and forest fragmentation when the expansions of agriculture and buildings were limited to already deforested areas, and when there was a rapid expansion of development, under influence of Sao Paulo city. Furthermore, the past(1962)road network was more important than the recent road network (1981) when explaining forest dynamics between 1981 and 2000, suggesting a long-term effect of roads. Roads are permanent scars on the landscape and facilitate deforestation and forest fragmentation due to increased accessibility and land valorization, which control land-use and land-cover dynamics. Topography directly affected deforestation, agriculture and road expansion, mainly between 1962 and 1981. Forest are thus in peril where there are more roads, and long-term conservation strategies should consider ways to mitigate roads as permanent landscape features and drivers facilitators of deforestation and forest fragmentation. (C) 2009 Elsevier B.V. All rights reserved.

Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

Resampling Strategies for Deforming MLS Surfaces

Moving-least-squares (MLS) surfaces undergoing large deformations need periodic regeneration of the point set (point-set resampling) so as to keep the point-set density quasi-uniform. Previous work by the authors dealt with algebraic MLS surfaces, and proposed a resampling strategy based on defining the new points at the intersections of the MLS surface with a suitable set of rays. That strategy has very low memory requirements and is easy to parallelize. In this article new resampling strategies with reduced CPU-time cost are explored. The basic idea is to choose as set of rays the lines of a regular, Cartesian grid, and to fully exploit this grid: as data structure for search queries, as spatial structure for traversing the surface in a continuation-like algorithm, and also as approximation grid for an interpolated version of the MLS surface. It is shown that in this way a very simple and compact resampling technique is obtained, which cuts the resampling cost by half with affordable memory requirements.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

Statistical analysis of the Doppler broadening coincidence spectrum of electron-positron annihilation radiation in silicon

We report a statistical analysis of Doppler broadening coincidence data of electron-positron annihilation radiation in silicon using a (22)Na source. The Doppler broadening coincidence spectrum was fit using a model function that included positron annihilation at rest with 1s, 2s, 2p, and valence band electrons. In-flight positron annihilation was also fit. The response functions of the detectors accounted for backscattering, combinations of Compton effects, pileup, ballistic deficit, and pulse-shaping problems. The procedure allows the quantitative determination of positron annihilation with core and valence electron intensities as well as their standard deviations directly from the experimental spectrum. The results obtained for the core and valence band electron annihilation intensities were 2.56(9)% and 97.44(9)%, respectively. These intensities are consistent with published experimental data treated by conventional analysis methods. This new procedure has the advantage of allowing one to distinguish additional effects from those associated with the detection system response function. (C) 2009 Elsevier B.V. All rights reserved.

Intermolecular Contacts Influencing the Conformational and Geometric Features of the Pharmaceutically Preferred Mebendazole Polymorph C

Mebendazole (MBZ) is a common benzimidazole anthelmintic that exists in three different polymorphic forms, A, B, and C. Polymorph C is the pharmaceutically preferred form due to its adequated aqueous solubility. No single crystal structure determinations depicting the nature of the crystal packing and molecular conformation and geometry have been performed on this compound. The crystal structure of mebendazole form C is resolved for the first time. Mebendazole form C crystallizes in the triclinic centrosymmetric space group and this drug is practically planar, since the least-squares methyl benzimidazolylcarbamate plane is much fitted on the forming atoms. However, the benzoyl group is twisted by 31(1)degrees from the benzimidazole ring, likewise the torsional angle between the benzene and carbonyl moieties is 27(1)degrees. The formerly described bends and other interesting intramolecular geometry features were viewed as consequence of the intermolecular contacts occurring within mebendazole C structure. Among these features, a conjugation decreasing through the imine nitrogen atom of the benzimidazole core and a further resonance path crossing the carbamate one were described. At last, the X-ray powder diffractogram of a form C rich mebendazole mixture was overlaid to the calculated one with the mebendazole crystal structure. (C) 2008 Wiley-Liss, Inc. and the American Pharmacists Association J Pharm Sci 98:2336-2344, 2009

Structural basis for selective inhibition of trypanosomatid glyceraldehyde-3-phosphate dehydrogenase: Molecular docking and 3D QSAR studies

The glycolytic enzyme glyceraldehyde-3 -phosphate dehydrogenase (GAPDH) is as an attractive target for the development of novel antitrypanosomatid agents. In the present work, comparative molecular field analysis and comparative molecular similarity index analysis were conducted on a large series of selective inhibitors of trypanosomatid GAPDH. Four statistically significant models were obtained (r(2) > 0.90 and q(2) > 0.70), indicating their predictive ability for untested compounds. The models were then used to predict the potency of an external test set, and the predicted values were in good agreement with the experimental results. Molecular modeling studies provided further insight into the structural basis for selective inhibition of trypanosomatid GAPDH.

OSCILLATOR STRENGTHS AND LIFETIMES FOR THE P XII

Semi-empirical weighted oscillator strengths (gf) and lifetimes presented in this work for all experimentally known electric dipole P XII spectral lines and energy levels were computed within a multiconfiguration Hartree-Fock relativistic approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure in order to improve the adjustment to experimental energy levels. The method produces lifetime and gf values that are in agreement with intensity observations used for the interpretation of spectrograms of solar and laboratory plasmas.

Exact penalties for variational inequalities with applications to nonlinear complementarity problems

In this paper, we present a new reformulation of the KKT system associated to a variational inequality as a semismooth equation. The reformulation is derived from the concept of differentiable exact penalties for nonlinear programming. The best theoretical results are presented for nonlinear complementarity problems, where simple, verifiable, conditions ensure that the penalty is exact. We close the paper with some preliminary computational tests on the use of a semismooth Newton method to solve the equation derived from the new reformulation. We also compare its performance with the Newton method applied to classical reformulations based on the Fischer-Burmeister function and on the minimum. The new reformulation combines the best features of the classical ones, being as easy to solve as the reformulation that uses the Fischer-Burmeister function while requiring as few Newton steps as the one that is based on the minimum.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.