Example of Monte Carlo uncertainty assessment in the field of radionuclide metrology

This chapter presents possible uses and examples of Monte Carlo methods for the evaluation of uncertainties in the field of radionuclide metrology. The method is already well documented in GUM supplement 1, but here we present a more restrictive approach, where the quantities of interest calculated by the Monte Carlo method are estimators of the expectation and standard deviation of the measurand, and the Monte Carlo method is used to propagate the uncertainties of the input parameters through the measurement model. This approach is illustrated by an example of the activity calibration of a 103Pd source by liquid scintillation counting and the calculation of a linear regression on experimental data points. An electronic supplement presents some algorithms which may be used to generate random numbers with various statistical distributions, for the implementation of this Monte Carlo calculation method.

A New Model to Determine the Dispersion of Fatigue Damage Evaluations

Reliable predictions of remaining lives of civil or mechanical structures subjected to fatigue damage are very difficult to be made. In general, fatigue damage is extremely sensitive to the random variations of material mechanical properties, environment and loading. These variations may induce large dispersions when the structural fatigue life has to be predicted. Wirsching (1970) mentions dispersions of the order of 30 to 70 % of the mean calculated life. The presented paper introduces a model to estimate the fatigue damage dispersion based on known statistical distributions of the fatigue parameters (material properties and loading). The model is developed by expanding into Taylor series the set of equations that describe fatigue damage for crack initiation.

Bio-inspired optimization & sampling technique for side-chain packing in MCCE

The prediction of proteins' conformation helps to understand their exhibited functions, allows for modeling and allows for the possible synthesis of the studied protein. Our research is focused on a sub-problem of protein folding known as side-chain packing. Its computational complexity has been proven to be NP-Hard. The motivation behind our study is to offer the scientific community a means to obtain faster conformation approximations for small to large proteins over currently available methods. As the size of proteins increases, current techniques become unusable due to the exponential nature of the problem. We investigated the capabilities of a hybrid genetic algorithm / simulated annealing technique to predict the low-energy conformational states of various sized proteins and to generate statistical distributions of the studied proteins' molecular ensemble for pKa predictions. Our algorithm produced errors to experimental results within .acceptable margins and offered considerable speed up depending on the protein and on the rotameric states' resolution used.

Modélisation bayésienne avec des splines du comportement moyen d'un échantillon de courbes

Cette thèse porte sur l'analyse bayésienne de données fonctionnelles dans un contexte hydrologique. L'objectif principal est de modéliser des données d'écoulements d'eau d'une manière parcimonieuse tout en reproduisant adéquatement les caractéristiques statistiques de celles-ci. L'analyse de données fonctionnelles nous amène à considérer les séries chronologiques d'écoulements d'eau comme des fonctions à modéliser avec une méthode non paramétrique. Dans un premier temps, les fonctions sont rendues plus homogènes en les synchronisant. Ensuite, disposant d'un échantillon de courbes homogènes, nous procédons à la modélisation de leurs caractéristiques statistiques en faisant appel aux splines de régression bayésiennes dans un cadre probabiliste assez général. Plus spécifiquement, nous étudions une famille de distributions continues, qui inclut celles de la famille exponentielle, de laquelle les observations peuvent provenir. De plus, afin d'avoir un outil de modélisation non paramétrique flexible, nous traitons les noeuds intérieurs, qui définissent les éléments de la base des splines de régression, comme des quantités aléatoires. Nous utilisons alors le MCMC avec sauts réversibles afin d'explorer la distribution a posteriori des noeuds intérieurs. Afin de simplifier cette procédure dans notre contexte général de modélisation, nous considérons des approximations de la distribution marginale des observations, nommément une approximation basée sur le critère d'information de Schwarz et une autre qui fait appel à l'approximation de Laplace. En plus de modéliser la tendance centrale d'un échantillon de courbes, nous proposons aussi une méthodologie pour modéliser simultanément la tendance centrale et la dispersion de ces courbes, et ce dans notre cadre probabiliste général. Finalement, puisque nous étudions une diversité de distributions statistiques au niveau des observations, nous mettons de l'avant une approche afin de déterminer les distributions les plus adéquates pour un échantillon de courbes donné.

Analysis and Simulation of Transverse Random Fracture of Long Fibre Reinforced Composites

La present tesi proposa una metodología per a la simulació probabilística de la fallada de la matriu en materials compòsits reforçats amb fibres de carboni, basant-se en l'anàlisi de la distribució aleatòria de les fibres. En els primers capítols es revisa l'estat de l'art sobre modelització matemàtica de materials aleatoris, càlcul de propietats efectives i criteris de fallada transversal en materials compòsits. El primer pas en la metodologia proposada és la definició de la determinació del tamany mínim d'un Element de Volum Representatiu Estadístic (SRVE) . Aquesta determinació es du a terme analitzant el volum de fibra, les propietats elàstiques efectives, la condició de Hill, els estadístics de les components de tensió i defromació, la funció de densitat de probabilitat i les funcions estadístiques de distància entre fibres de models d'elements de la microestructura, de diferent tamany. Un cop s'ha determinat aquest tamany mínim, es comparen un model periòdic i un model aleatori, per constatar la magnitud de les diferències que s'hi observen. Es defineix, també, una metodologia per a l'anàlisi estadístic de la distribució de la fibra en el compòsit, a partir d'imatges digitals de la secció transversal. Aquest anàlisi s'aplica a quatre materials diferents. Finalment, es proposa un mètode computacional de dues escales per a simular la fallada transversal de làmines unidireccionals, que permet obtenir funcions de densitat de probabilitat per a les variables mecàniques. Es descriuen algunes aplicacions i possibilitats d'aquest mètode i es comparen els resultats obtinguts de la simulació amb valors experimentals.

Sensitivity of feature-based analysis methods of storm tracks to the form of background field removal

For the tracking of extrema associated with weather systems to be applied to a broad range of fields it is necessary to remove a background field that represents the slowly varying, large spatial scales. The sensitivity of the tracking analysis to the form of background field removed is explored for the Northern Hemisphere winter storm tracks for three contrasting fields from an integration of the U. K. Met Office's (UKMO) Hadley Centre Climate Model (HadAM3). Several methods are explored for the removal of a background field from the simple subtraction of the climatology, to the more sophisticated removal of the planetary scales. Two temporal filters are also considered in the form of a 2-6-day Lanczos filter and a 20-day high-pass Fourier filter. The analysis indicates that the simple subtraction of the climatology tends to change the nature of the systems to the extent that there is a redistribution of the systems relative to the climatological background resulting in very similar statistical distributions for both positive and negative anomalies. The optimal planetary wave filter removes total wavenumbers less than or equal to a number in the range 5-7, resulting in distributions more easily related to particular types of weather system. For the temporal filters the 2-6-day bandpass filter is found to have a detrimental impact on the individual weather systems, resulting in the storm tracks having a weak waveguide type of behavior. The 20-day high-pass temporal filter is less aggressive than the 2-6-day filter and produces results falling between those of the climatological and 2-6-day filters.

Spherical nonparametric estimators applied to the UGAMP model integration for AMIP

The aim of this paper is essentially twofold: first, to describe the use of spherical nonparametric estimators for determining statistical diagnostic fields from ensembles of feature tracks on a global domain, and second, to report the application of these techniques to data derived from a modern general circulation model. New spherical kernel functions are introduced that are more efficiently computed than the traditional exponential kernels. The data-driven techniques of cross-validation to determine the amount elf smoothing objectively, and adaptive smoothing to vary the smoothing locally, are also considered. Also introduced are techniques for combining seasonal statistical distributions to produce longer-term statistical distributions. Although all calculations are performed globally, only the results for the Northern Hemisphere winter (December, January, February) and Southern Hemisphere winter (June, July, August) cyclonic activity are presented, discussed, and compared with previous studies. Overall, results for the two hemispheric winters are in good agreement with previous studies, both for model-based studies and observational studies.

Generation, description and storage of dendritic morphology data

It is generally assumed that the variability of neuronal morphology has an important effect on both the connectivity and the activity of the nervous system, but this effect has not been thoroughly investigated. Neuroanatomical archives represent a crucial tool to explore structure–function relationships in the brain. We are developing computational tools to describe, generate, store and render large sets of three–dimensional neuronal structures in a format that is compact, quantitative, accurate and readily accessible to the neuroscientist. Single–cell neuroanatomy can be characterized quantitatively at several levels. In computer–aided neuronal tracing files, a dendritic tree is described as a series of cylinders, each represented by diameter, spatial coordinates and the connectivity to other cylinders in the tree. This ‘Cartesian’ description constitutes a completely accurate mapping of dendritic morphology but it bears little intuitive information for the neuroscientist. In contrast, a classical neuroanatomical analysis characterizes neuronal dendrites on the basis of the statistical distributions of morphological parameters, e.g. maximum branching order or bifurcation asymmetry. This description is intuitively more accessible, but it only yields information on the collective anatomy of a group of dendrites, i.e. it is not complete enough to provide a precise ‘blueprint’ of the original data. We are adopting a third, intermediate level of description, which consists of the algorithmic generation of neuronal structures within a certain morphological class based on a set of ‘fundamental’, measured parameters. This description is as intuitive as a classical neuroanatomical analysis (parameters have an intuitive interpretation), and as complete as a Cartesian file (the algorithms generate and display complete neurons). The advantages of the algorithmic description of neuronal structure are immense. If an algorithm can measure the values of a handful of parameters from an experimental database and generate virtual neurons whose anatomy is statistically indistinguishable from that of their real counterparts, a great deal of data compression and amplification can be achieved. Data compression results from the quantitative and complete description of thousands of neurons with a handful of statistical distributions of parameters. Data amplification is possible because, from a set of experimental neurons, many more virtual analogues can be generated. This approach could allow one, in principle, to create and store a neuroanatomical database containing data for an entire human brain in a personal computer. We are using two programs, L–NEURON and ARBORVITAE, to investigate systematically the potential of several different algorithms for the generation of virtual neurons. Using these programs, we have generated anatomically plausible virtual neurons for several morphological classes, including guinea pig cerebellar Purkinje cells and cat spinal cord motor neurons. These virtual neurons are stored in an online electronic archive of dendritic morphology. This process highlights the potential and the limitations of the ‘computational neuroanatomy’ strategy for neuroscience databases.

Evaluation of ice cloud representation in the ECMWF and UK Met Office models using CloudSat and CALIPSO data

Ice cloud representation in general circulation models remains a challenging task, due to the lack of accurate observations and the complexity of microphysical processes. In this article, we evaluate the ice water content (IWC) and ice cloud fraction statistical distributions from the numerical weather prediction models of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the UK Met Office, exploiting the synergy between the CloudSat radar and CALIPSO lidar. Using the last three weeks of July 2006, we analyse the global ice cloud occurrence as a function of temperature and latitude and show that the models capture the main geographical and temperature-dependent distributions, but overestimate the ice cloud occurrence in the Tropics in the temperature range from −60 °C to −20 °C and in the Antarctic for temperatures higher than −20 °C, but underestimate ice cloud occurrence at very low temperatures. A global statistical comparison of the occurrence of grid-box mean IWC at different temperatures shows that both the mean and range of IWC increases with increasing temperature. Globally, the models capture most of the IWC variability in the temperature range between −60 °C and −5 °C, and also reproduce the observed latitudinal dependencies in the IWC distribution due to different meteorological regimes. Two versions of the ECMWF model are assessed. The recent operational version with a diagnostic representation of precipitating snow and mixed-phase ice cloud fails to represent the IWC distribution in the −20 °C to 0 °C range, but a new version with prognostic variables for liquid water, ice and snow is much closer to the observed distribution. The comparison of models and observations provides a much-needed analysis of the vertical distribution of IWC across the globe, highlighting the ability of the models to reproduce much of the observed variability as well as the deficiencies where further improvements are required.

Projections of global warming-induced impacts on winter storm losses in the German private household sector

We present projections of winter storm-induced insured losses in the German residential building sector for the 21st century. With this aim, two structurally most independent downscaling methods and one hybrid downscaling method are applied to a 3-member ensemble of ECHAM5/MPI-OM1 A1B scenario simulations. One method uses dynamical downscaling of intense winter storm events in the global model, and a transfer function to relate regional wind speeds to losses. The second method is based on a reshuffling of present day weather situations and sequences taking into account the change of their frequencies according to the linear temperature trends of the global runs. The third method uses statistical-dynamical downscaling, considering frequency changes of the occurrence of storm-prone weather patterns, and translation into loss by using empirical statistical distributions. The A1B scenario ensemble was downscaled by all three methods until 2070, and by the (statistical-) dynamical methods until 2100. Furthermore, all methods assume a constant statistical relationship between meteorology and insured losses and no developments other than climate change, such as in constructions or claims management. The study utilizes data provided by the German Insurance Association encompassing 24 years and with district-scale resolution. Compared to 1971–2000, the downscaling methods indicate an increase of 10-year return values (i.e. loss ratios per return period) of 6–35 % for 2011–2040, of 20–30 % for 2041–2070, and of 40–55 % for 2071–2100, respectively. Convolving various sources of uncertainty in one confidence statement (data-, loss model-, storm realization-, and Pareto fit-uncertainty), the return-level confidence interval for a return period of 15 years expands by more than a factor of two. Finally, we suggest how practitioners can deal with alternative scenarios or possible natural excursions of observed losses.

A semi-distributed ntegrated itrogen model for multiple source assessment in tchments (INCA): Part I — model structure and process equations

A new model has been developed for assessing multiple sources of nitrogen in catchments. The model (INCA) is process based and uses reaction kinetic equations to simulate the principal mechanisms operating. The model allows for plant uptake, surface and sub-surface pathways and can simulate up to six land uses simultaneously. The model can be applied to catchment as a semi-distributed simulation and has an inbuilt multi-reach structure for river systems. Sources of nitrogen can be from atmospheric deposition, from the terrestrial environment (e.g. agriculture, leakage from forest systems etc.), from urban areas or from direct discharges via sewage or intensive farm units. The model is a daily simulation model and can provide information in the form of time series at key sites, or as profiles down river systems or as statistical distributions. The process model is described and in a companion paper the model is applied to the River Tywi catchment in South Wales and the Great Ouse in Bedfordshire.

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Power law distribution in education: Effect of economical, teaching, and study conditions in university entrance examination

We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study - day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects axe due to the nature of the subjects themselves. Further and better study, teaching and economical conditions axe more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

Study of Hybrid Silica-Polyethyleneglycol Xerogels by Eu3+ Luminescence Spectroscopy

Good optical quality Eu3+-doped silica-polyethyleneglycol hybrids were prepared by the sol-gel process. Thermomechanical analysis showed an increase of the glass transition temperature, due to the stiffness of the polymeric network, as the amount of Eu3+ increased. Europium luminescent properties were used to study structural evolution during the sol-gel transition. For lower doping concentrations dried gels present statistical distributions of Eu3+, typical of an amorphous environment, while for higher concentrations a crystalline-like environment of Eu3+ was observed. A broad emission band was observed in the visible part of the electromagnetic spectrum and assigned to the intrinsic emission from the hybrid polymeric network.

Power law distribution in education: University entrance examination

We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.