Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

Proposing a way forward: a review of standardisation in the use of age categories and ageing techniques in osteological analysis (2004 to 2009)

This study assesses the current state of adult skeletal age-at-death estimation in biological anthropology through analysis of data published in recent research articles from three major anthropological and archaeological journals (2004–2009). The most commonly used adult ageing methods, age of ‘adulthood’, age ranges and the maximum age reported for ‘mature’ adults were compared. The results showed a wide range of variability in the age at which individuals were determined to be adult (from 14 to 25 years), uneven age ranges, a lack of standardisation in the use of descriptive age categories and the inappropriate application of some ageing methods for the sample being examined. Such discrepancies make comparisons between skeletal samples difficult, while the inappropriate use of some techniques make the resultant age estimations unreliable. At a time when national and even global comparisons of past health are becoming prominent, standardisation in the terminology and age categories used to define adults within each sample is fundamental. It is hoped that this research will prompt discussions in the osteological community (both nationally and internationally) about what defines an ‘adult’, how to standardise the age ranges that we use and how individuals should be assigned to each age category. Skeletal markers have been proposed to help physically identify ‘adult’ individuals.

The distribution of the ring current: Cluster observations

Extending previous studies, a full-circle investigation of the ring current has been made using Cluster 4-spacecraft observations near perigee, at times when the Cluster array had relatively small separations and nearly regular tetrahedral configurations, and when the Dst index was greater than −30 nT (non-storm conditions). These observations result in direct estimations of the near equatorial current density at all magnetic local times (MLT) for the first time and with sufficient accuracy, for the following observations. The results confirm that the ring current flows westward and show that the in situ average measured current density (sampled in the radial range accessed by Cluster 4–4.5RE) is asymmetric in MLT, ranging from 9 to 27 nAm−2. The direction of current is shown to be very well ordered for the whole range of MLT. Both of these results are in line with previous studies on partial ring extent. The magnitude of the current density, however, reveals a distinct asymmetry: growing from 10 to 27 nAm−2 as azimuth reduces from about 12:00MLT to 03:00 and falling from 20 to 10 nAm−2 less steadily as azimuth reduces from 24:00 to 12:00MLT. This result has not been reported before and we suggest it could reflect a number of effects. Firstly, we argue it is consistent with the operation of region-2 field aligned-currents (FACs), which are expected to flow upward into the ring current around 09:00MLT and downward out of the ring current around 14:00MLT. Secondly, we note that it is also consistent with a possible asymmetry in the radial distribution profile of current density (resulting in higher peak at 4– 4.5RE). We note that part of the enhanced current could reflect an increase in the mean AE activity (during the periods in which Cluster samples those MLT).

Performance assessment of a volcanic ash transport model mini-ensemble used for inverse modeling of the 2010 Eyjafjallajökull eruption

The requirement to forecast volcanic ash concentrations was amplified as a response to the 2010 Eyjafjallajökull eruption when ash safety limits for aviation were introduced in the European area. The ability to provide accurate quantitative forecasts relies to a large extent on the source term which is the emissions of ash as a function of time and height. This study presents source term estimations of the ash emissions from the Eyjafjallajökull eruption derived with an inversion algorithm which constrains modeled ash emissions with satellite observations of volcanic ash. The algorithm is tested with input from two different dispersion models, run on three different meteorological input data sets. The results are robust to which dispersion model and meteorological data are used. Modeled ash concentrations are compared quantitatively to independent measurements from three different research aircraft and one surface measurement station. These comparisons show that the models perform reasonably well in simulating the ash concentrations, and simulations using the source term obtained from the inversion are in overall better agreement with the observations (rank correlation = 0.55, Figure of Merit in Time (FMT) = 25–46%) than simulations using simplified source terms (rank correlation = 0.21, FMT = 20–35%). The vertical structures of the modeled ash clouds mostly agree with lidar observations, and the modeled ash particle size distributions agree reasonably well with observed size distributions. There are occasionally large differences between simulations but the model mean usually outperforms any individual model. The results emphasize the benefits of using an ensemble-based forecast for improved quantification of uncertainties in future ash crises.

Analysis of precipitation climatology simulated by high resolution coupled global models over the South America

The results of coupled high resolution global models (CGCMs) over South America are discussed. HiGEM1.2 and HadGEM1.2 simulations, with horizontal resolution of ~90 and 135 km, respectively, are compared. Precipitation estimations from CMAP (Climate Prediction Center—Merged Analysis of Precipitation), CPC (Climate Prediction Center) and GPCP (Global Precipitation Climatology Project) are used for validation. HiGEM1.2 and HadGEM1.2 simulated seasonal mean precipitation spatial patterns similar to the CMAP. The positioning and migration of the Intertropical Convergence Zone and of the Pacific and Atlantic subtropical highs are correctly simulated by the models. In HiGEM1.2 and HadGEM1.2, the intensity and locations of the South Atlantic Convergence Zone are in agreement with the observed dataset. The simulated annual cycles are in phase with estimations of rainfall for most of the six regions considered. An important result is that HiGEM1.2 and HadGEM1.2 eliminate a common problem of coarse resolution CGCMs, which is the simulation of a semiannual cycle of precipitation due to the semiannual solar forcing. Comparatively, the use of high resolution in HiGEM1.2 reduces the dry biases in the central part of Brazil during austral winter and spring and in most part of the year over an oceanic box in eastern Uruguay.

Estimating the direct aerosol radiative perturbation: impact of ocean surface representation and aerosol non-sphericity

Atmospheric aerosols are now actively studied, in particular because of their radiative and climate impacts. Estimations of the direct aerosol radiative perturbation, caused by extinction of incident solar radiation, usually rely on radiative transfer codes and involve simplifying hypotheses. This paper addresses two approximations which are widely used for the sake of simplicity and limiting the computational cost of the calculations. Firstly, it is shown that using a Lambertian albedo instead of the more rigorous bidirectional reflectance distribution function (BRDF) to model the ocean surface radiative properties leads to large relative errors in the instantaneous aerosol radiative perturbation. When averaging over the day, these errors cancel out to acceptable levels of less than 3% (except in the northern hemisphere winter). The other scope of this study is to address aerosol non-sphericity effects. Comparing an experimental phase function with an equivalent Mie-calculated phase function, we found acceptable relative errors if the aerosol radiative perturbation calculated for a given optical thickness is daily averaged. However, retrieval of the optical thickness of non-spherical aerosols assuming spherical particles can lead to significant errors. This is due to significant differences between the spherical and non-spherical phase functions. Discrepancies in aerosol radiative perturbation between the spherical and non-spherical cases are sometimes reduced and sometimes enhanced if the aerosol optical thickness for the spherical case is adjusted to fit the simulated radiance of the non-spherical case.

Bollène-2002 experiment: radar quantitative precipitation estimation in the Cévennes–Vivarais region, France

The Bollène-2002 Experiment was aimed at developing the use of a radar volume-scanning strategy for conducting radar rainfall estimations in the mountainous regions of France. A developmental radar processing system, called Traitements Régionalisés et Adaptatifs de Données Radar pour l’Hydrologie (Regionalized and Adaptive Radar Data Processing for Hydrological Applications), has been built and several algorithms were specifically produced as part of this project. These algorithms include 1) a clutter identification technique based on the pulse-to-pulse variability of reflectivity Z for noncoherent radar, 2) a coupled procedure for determining a rain partition between convective and widespread rainfall R and the associated normalized vertical profiles of reflectivity, and 3) a method for calculating reflectivity at ground level from reflectivities measured aloft. Several radar processing strategies, including nonadaptive, time-adaptive, and space–time-adaptive variants, have been implemented to assess the performance of these new algorithms. Reference rainfall data were derived from a careful analysis of rain gauge datasets furnished by the Cévennes–Vivarais Mediterranean Hydrometeorological Observatory. The assessment criteria for five intense and long-lasting Mediterranean rain events have proven that good quantitative precipitation estimates can be obtained from radar data alone within 100-km range by using well-sited, well-maintained radar systems and sophisticated, physically based data-processing systems. The basic requirements entail performing accurate electronic calibration and stability verification, determining the radar detection domain, achieving efficient clutter elimination, and capturing the vertical structure(s) of reflectivity for the target event. Radar performance was shown to depend on type of rainfall, with better results obtained with deep convective rain systems (Nash coefficients of roughly 0.90 for point radar–rain gauge comparisons at the event time step), as opposed to shallow convective and frontal rain systems (Nash coefficients in the 0.6–0.8 range). In comparison with time-adaptive strategies, the space–time-adaptive strategy yields a very significant reduction in the radar–rain gauge bias while the level of scatter remains basically unchanged. Because the Z–R relationships have not been optimized in this study, results are attributed to an improved processing of spatial variations in the vertical profile of reflectivity. The two main recommendations for future work consist of adapting the rain separation method for radar network operations and documenting Z–R relationships conditional on rainfall type.

On the clustering of winter storm loss events over Germany

During the last decades, several windstorm series hit Europe leading to large aggregated losses. Such storm series are examples of serial clustering of extreme cyclones, presenting a considerable risk for the insurance industry. Clustering of events and return periods of storm series for Germany are quantified based on potential losses using empirical models. Two reanalysis data sets and observations from German weather stations are considered for 30 winters. Histograms of events exceeding selected return levels (1-, 2- and 5-year) are derived. Return periods of historical storm series are estimated based on the Poisson and the negative binomial distributions. Over 4000 years of general circulation model (GCM) simulations forced with current climate conditions are analysed to provide a better assessment of historical return periods. Estimations differ between distributions, for example 40 to 65 years for the 1990 series. For such less frequent series, estimates obtained with the Poisson distribution clearly deviate from empirical data. The negative binomial distribution provides better estimates, even though a sensitivity to return level and data set is identified. The consideration of GCM data permits a strong reduction of uncertainties. The present results support the importance of considering explicitly clustering of losses for an adequate risk assessment for economical applications.

Combining satellite observations and reanalysis energy transports to estimate global net surface energy fluxes 1985-2012

Two methods are developed to estimate net surface energy fluxes based upon satellite-based reconstructions of radiative fluxes at the top of atmosphere and the atmospheric energy tendencies and transports from the ERA-Interim reanalysis. Method 1 applies the mass adjusted energy divergence from ERA-Interim while method 2 estimates energy divergence based upon the net energy difference at the top of atmosphere and the surface from ERA-Interim. To optimise the surface flux and its variability over ocean, the divergences over land are constrained to match the monthly area mean surface net energy flux variability derived from a simple relationship between the surface net energy flux and the surface temperature change. The energy divergences over the oceans are then adjusted to remove an unphysical residual global mean atmospheric energy divergence. The estimated net surface energy fluxes are compared with other data sets from reanalysis and atmospheric model simulations. The spatial correlation coefficients of multi-annual means between the estimations made here and other data sets are all around 0.9. There are good agreements in area mean anomaly variability over the global ocean, but discrepancies in the trend over the eastern Pacific are apparent.

Ratings of age of acquisition of 299 words across 25 languages: is there a cross-linguistic order of words?

We present a new set of subjective age-of-acquisition (AoA) ratings for 299 words (158 nouns, 141 verbs) in 25 languages from five language families (Afro-Asiatic: Semitic languages; Altaic: one Turkic language: Indo-European: Baltic, Celtic, Germanic, Hellenic, Slavic, and Romance languages; Niger-Congo: one Bantu language; Uralic: Finnic and Ugric languages). Adult native speakers reported the age at which they had learned each word. We present a comparison of the AoA ratings across all languages by contrasting them in pairs. This comparison shows a consistency in the orders of ratings across the 25 languages. The data were then analyzed (1) to ascertain how the demographic characteristics of the participants influenced AoA estimations and (2) to assess differences caused by the exact form of the target question (when did you learn vs. when do children learn this word); (3) to compare the ratings obtained in our study to those of previous studies; and (4) to assess the validity of our study by comparison with quasi-objective AoA norms derived from the MacArthur–Bates Communicative Development Inventories (MB-CDI). All 299 words were judged as being acquired early (mostly before the age of 6 years). AoA ratings were associated with the raters’ social or language status, but not with the raters’ age or education. Parents reported words as being learned earlier, and bilinguals reported learning them later. Estimations of the age at which children learn the words revealed significantly lower ratings of AoA. Finally, comparisons with previous AoA and MB-CDI norms support the validity of the present estimations. Our AoA ratings are available for research or other purposes.

Taxes, corruption, and entry

Tax policies and corruption are important institutional considerations which can shape entrepreneurship. We investigate how tax rates, and the interaction between corruption and tax rates, influence variations in entry across a panel of 72 countries in the period 2005–2011. We use a series of panel estimations as well as several robustness checks to test these effects, using relevant controls for economic development, the size of the state, and other regulatory and tax policy measures. We find that higher tax rates consistently discourage entry. Further, we find that although the direct influence of corruption on entry is also consistently negative, the interaction influence of corruption and tax rate is positive. This indicates that corruption can offset the negative influence of high taxes on entry. We discuss the implications of our findings for policymakers and future research.

Chirikov diffusion in the asteroidal three-body resonance (5,-2,-2)

The theory of diffusion in many-dimensional Hamiltonian system is applied to asteroidal dynamics. The general formulation developed by Chirikov is applied to the NesvornA1/2-Morbidelli analytic model of three-body (three-orbit) mean-motion resonances (Jupiter-Saturn-asteroid). In particular, we investigate the diffusion along and across the separatrices of the (5, -2, -2) resonance of the (490) Veritas asteroidal family and their relationship to diffusion in semi-major axis and eccentricity. The estimations of diffusion were obtained using the Melnikov integral, a Hadjidemetriou-type sympletic map and numerical integrations for times up to 10(8) years.

Genetic structure, phylogeny, and biogeography of Brazilian eyelid-less lizards of genera Calyptommatus and Nothobachia (Squamata, Gymnophthalmidae) as inferred from mitochondrial DNA sequences

Calyptommatus and Nothobachia genera of gymnophthalmid lizards are restricted to sandy open habitats on Sao Francisco River margins, northeastern Brazil. Phylogenetic relationships and geographic distribution of the four recognized species of Calyptommatus were analyzed from partial mitochondrial cyt b, 12S, and 16S rRNA genes sequencing, taking allopatric populations of the monotypic Nothobachia ablephara as the outgroup. In Calyptommatus a basal split separated C. sinebrachiatus, a species restricted to the eastern bank of the river, from the three other species. In this clade, C. confusionibus, found on western margin, was recovered as the sister group of the two other species, C. leiolepis and C. nicterus, from opposite margins. According to approximate date estimations, C. sinebrachiatus would have separated from the other congeneric species by 4.4-6.5 my, and C. nicterus, also from eastern bank, would be diverging by 1.8-2.6 my from C. leiolepis, the sister species on the opposite margin. C. confusionibus and C. leiolepis, both from western sandy areas, would be differentiating by 2.8-5.0 my. Divergence times of about 3.0-4.0 my were estimated for allopatric populations of Nothobachia restricted to western margin. Significant differences in 16S rRNA secondary structure relatively to other vertebrates are reported. Distinct evolutionary patterns are proposed for different taxa in those sandy areas, probably related to historical changes in the course of Sao Francisco River. (C) 2010 Elsevier Inc. All rights reserved.

Unraveling an antique subduction process from metamorphic basement around Medellin city, Central Cordillera of Colombian Andes

In the surroundings of Caldas and El Retiro cities (Colombia) metamorphic rocks derived from basic and pelitic protoliths comprise the Caldas amphibole schist and the Ancon schist respectively. Subordinated metamorphosed granite bodies (La Miel gneiss) are associated to these units, and The El Retiro amphibolites, migmatites and granulites crops out eastwards of these units, separated by shear zones. The Caldas amphibole schist and the Ancon schist protoliths could have been formed in a distal marine reduced environment and amalgamated to the South American continent in an apparent Triassic subduction event. The El Retiro rocks are akin to a continental basement and possible include impure metasediments of continental margin, whose metamorphism originated granulite facies rocks and migmatites as a result of the anatexis of quartz-feldspathic rocks. The metamorphism was accompanied by intense deformation, which has juxtaposed both migmatites and granulite blocks. Afterward, heat and fluid circulation associated with the emplacement of minor igneous intrusions resulted in intense fluid-rock interaction, variations in the grain size of the minerals and, especially, intense retrograde metamorphic re-equilibrium. Thermobarometric estimations for the Caldas amphibole schist indicate metamorphism in the Barrovian amphibolite fades. The metamorphic path is counter-clockwise, but retrograde evolution could not be precisely defined. The pressures of the metamorphism in these rocks range from 6.3 to 13.5 kbar, with narrow temperature ranging from 550 to 630 degrees C. For the Ancon schist metapelites the P-T path is also counter-clockwise, with a temperature increase evidenced by the occurrence of sillimanite and the cooling by later kyanite. The progressive metamorphism event occurred at pressures of 7.6-7.2 kbar and temperatures of 645-635 degrees C for one sample and temperature between 500 and 600 degrees C under constant pressure of 6 kbar. The temperature estimated for these rocks varies between 400 and 555 degrees C at pressures of 5-6 kbar in the retrograde metamorphic path. The El Retiro rocks evidence strong decompression with narrow variation in temperature, showing pressure values between 8.7 and 2.7 kbar at temperatures of 740-633 degrees C. These metamorphic fragments of the basement in the Central Cordillera of the Colombian Andes could represent a close relationship with an antique subduction zone. (C) 2011 Elsevier Ltd. All rights reserved.

A GUI for online presentation of steel and steelmaking ladle temperature data and simulation.

Continuous casting is a casting process that produces steel slabs in a continuous manner with steel being poured at the top of the caster and a steel strand emerging from the mould below. Molten steel is transferred from the AOD converter to the caster using a ladle. The ladle is designed to be strong and insulated. Complete insulation is never achieved. Some of the heat is lost to the refractories by convection and conduction. Heat losses by radiation also occur. It is important to know the temperature of the melt during the process. For this reason, an online model was previously developed to simulate the steel and ladle wall temperatures during the ladle cycle. The model was developed as an ODE based model using grey box modeling technique. The model’s performance was acceptable and needed to be presented in a user friendly way. The aim of this thesis work was basically to design a GUI that presents steel and ladle wall temperatures calculated by the model and also allow the user to make adjustments to the model. This thesis work also discusses the sensitivity analysis of different parameters involved and their effects on different temperature estimations.