Estrategias de monitorización de CO2 y otros gases en los estudios de análogos naturales

La Universidad Politécnica de Madrid (UPM) y la Università degli Studi di Firenze (UniFi), bajo la coordinación técnica de AMPHOS21, participan desde 2009 en el proyecto de investigación “Estrategias de Monitorización de CO2 y otros gases en el estudio de Análogos Naturales”, financiado por la Fundación Ciudad de la Energía (CIUDEN) en el marco del Proyecto Compostilla OXYCFB300 (http://www.compostillaproject.eu), del Programa “European Energy Program for Recovery - EEPR”. El objetivo principal del proyecto fue el desarrollo y puesta a punto de metodologías de monitorización superficiales para su aplicación en el seguimiento y control de los emplazamientos donde se realice el almacenamiento geológico de CO2, analizando técnicas que permitan detectar y cuantificar las posibles fugas de CO2 a la atmósfera. Los trabajos se realizaron tanto en análogos naturales (españoles e italianos) como en la Planta de Desarrollo Tecnológico de Almacenamiento de CO2 de Hontomín. Las técnicas analizadas se centran en la medición de gases y aguas superficiales (de escorrentía y manantiales). En cuanto a la medición de gases se analizó el flujo de CO2 que emana desde el suelo a la atmósfera y la aplicabilidad de trazadores naturales (como el radón) para la detección e identificación de las fugas de CO2. En cuanto al análisis químico de las aguas se analizaron los datos geoquímicos e isotópicos y los gases disueltos en las aguas de los alrededores de la PDT de Hontomín, con objeto de determinar qué parámetros son los más apropiados para la detección de una posible migración del CO2 inyectado, o de la salmuera, a los ambientes superficiales. Las medidas de flujo de CO2 se realizaron con la técnica de la cámara de acúmulo. A pesar de ser una técnica desarrollada y aplicada en diferentes ámbitos científicos se estimó necesario adaptar un protocolo de medida y de análisis de datos a las características específicas de los proyectos de captura y almacenamiento de CO2 (CAC). Donde los flujos de CO2 esperados son bajos y en caso de producirse una fuga habrá que detectar pequeñas variaciones en los valores flujo con un “ruido” en la señal alto, debido a actividad biológica en el suelo. La medida de flujo de CO2 mediante la técnica de la cámara de acúmulo se puede realizar sin limpiar la superficie donde se coloca la cámara o limpiando y esperando al reequilibrio del flujo después de la distorsión al sistema. Sin embargo, los resultados obtenidos después de limpiar y esperar muestran menor dispersión, lo que nos indica que este procedimiento es el mejor para la monitorización de los complejos de almacenamiento geológico de CO2. El protocolo de medida resultante, utilizado para la obtención de la línea base de flujo de CO2 en Hontomín, sigue los siguiente pasos: a) con una espátula se prepara el punto de medición limpiando y retirando el recubrimiento vegetal o la primera capa compacta de suelo, b) se espera un tiempo para la realización de la medida de flujo, facilitando el reequilibrio del flujo del gas tras la alteración provocada en el suelo y c) se realiza la medida de flujo de CO2. Una vez realizada la medición de flujo de CO2, y detectada si existen zonas de anomalías, se debe estimar la cantidad de CO2 que se está escapando a la atmósfera (emanación total), con el objetivo de cuantificar la posible fuga. Existen un amplio rango de metodologías para realizar dicha estimación, siendo necesario entender cuáles son las más apropiadas para obtener el valor más representativo del sistema. En esta tesis se comparan seis técnicas estadísticas: media aritmética, estimador insegado de la media (aplicando la función de Sichel), remuestreo con reemplazamiento (bootstrap), separación en diferentes poblaciones mediante métodos gráficos y métodos basados en criterios de máxima verosimilitud, y la simulación Gaussiana secuencial. Para este análisis se realizaron ocho campañas de muestreo, tanto en la Planta de Desarrollo Tecnológico de Hontomón como en análogos naturales (italianos y españoles). Los resultados muestran que la simulación Gaussiana secuencial suele ser el método más preciso para realizar el cálculo, sin embargo, existen ocasiones donde otros métodos son más apropiados. Como consecuencia, se desarrolla un procedimiento de actuación para seleccionar el método que proporcione el mejor estimador. Este procedimiento consiste, en primer lugar, en realizar un análisis variográfico. Si existe una autocorrelación entre los datos, modelizada mediante el variograma, la mejor técnica para calcular la emanación total y su intervalo de confianza es la simulación Gaussiana secuencial (sGs). Si los datos son independientes se debe comprobar la distribución muestral, aplicando la media aritmética o el estimador insesgado de la media (Sichel) para datos normales o lognormales respectivamente. Cuando los datos no son normales o corresponden a una mezcla de poblaciones la mejor técnica de estimación es la de remuestreo con reemplazamiento (bootstrap). Siguiendo este procedimiento el máximo valor del intervalo de confianza estuvo en el orden del ±20/25%, con la mayoría de valores comprendidos entre ±3,5% y ±8%. La identificación de las diferentes poblaciones muestrales en los datos de flujo de CO2 puede ayudar a interpretar los resultados obtenidos, toda vez que esta distribución se ve afectada por la presencia de varios procesos geoquímicos como, por ejemplo, una fuente geológica o biológica del CO2. Así pues, este análisis puede ser una herramienta útil en el programa de monitorización, donde el principal objetivo es demostrar que no hay fugas desde el reservorio a la atmósfera y, si ocurren, detectarlas y cuantificarlas. Los resultados obtenidos muestran que el mejor proceso para realizar la separación de poblaciones está basado en criterios de máxima verosimilitud. Los procedimientos gráficos, aunque existen pautas para realizarlos, tienen un cierto grado de subjetividad en la interpretación de manera que los resultados son menos reproducibles. Durante el desarrollo de la tesis se analizó, en análogos naturales, la relación existente entre el CO2 y los isótopos del radón (222Rn y 220Rn), detectándose en todas las zonas de emisión de CO2 una relación positiva entre los valores de concentración de 222Rn en aire del suelo y el flujo de CO2. Comparando la concentración de 220Rn con el flujo de CO2 la relación no es tan clara, mientras que en algunos casos aumenta en otros se detecta una disminución, hecho que parece estar relacionado con la profundidad de origen del radón. Estos resultados confirmarían la posible aplicación de los isótopos del radón como trazadores del origen de los gases y su aplicación en la detección de fugas. Con respecto a la determinación de la línea base de flujo CO2 en la PDT de Hontomín, se realizaron mediciones con la cámara de acúmulo en las proximidades de los sondeos petrolíferos, perforados en los ochenta y denominados H-1, H-2, H-3 y H-4, en la zona donde se instalarán el sondeo de inyección (H-I) y el de monitorización (H-A) y en las proximidades de la falla sur. Desde noviembre de 2009 a abril de 2011 se realizaron siete campañas de muestreo, adquiriéndose más de 4.000 registros de flujo de CO2 con los que se determinó la línea base y su variación estacional. Los valores obtenidos fueron bajos (valores medios entre 5 y 13 g•m-2•d-1), detectándose pocos valores anómalos, principalmente en las proximidades del sondeo H-2. Sin embargo, estos valores no se pudieron asociar a una fuente profunda del CO2 y seguramente estuvieran más relacionados con procesos biológicos, como la respiración del suelo. No se detectaron valores anómalos cerca del sistema de fracturación (falla Ubierna), toda vez que en esta zona los valores de flujo son tan bajos como en el resto de puntos de muestreo. En este sentido, los valores de flujo de CO2 aparentemente están controlados por la actividad biológica, corroborado al obtenerse los menores valores durante los meses de otoño-invierno e ir aumentando en los periodos cálidos. Se calcularon dos grupos de valores de referencia, el primer grupo (UCL50) es 5 g•m-2•d-1 en las zonas no aradas en los meses de otoño-invierno y 3,5 y 12 g•m-2•d-1 en primavera-verano para zonas aradas y no aradas, respectivamente. El segundo grupo (UCL99) corresponde a 26 g•m-2•d- 1 durante los meses de otoño-invierno en las zonas no aradas y 34 y 42 g•m-2•d-1 para los meses de primavera-verano en zonas aradas y no aradas, respectivamente. Flujos mayores a estos valores de referencia podrían ser indicativos de una posible fuga durante la inyección y posterior a la misma. Los primeros datos geoquímicos e isotópicos de las aguas superficiales (de escorrentía y de manantiales) en el área de Hontomín–Huermeces fueron analizados. Los datos sugieren que las aguas estudiadas están relacionadas con aguas meteóricas con un circuito hidrogeológico superficial, caracterizadas por valores de TDS relativamente bajos (menor a 800 mg/L) y una fácie hidrogeoquímica de Ca2+(Mg2+)-HCO3 −. Algunas aguas de manantiales se caracterizan por concentraciones elevadas de NO3 − (concentraciones de hasta 123 mg/l), lo que sugiere una contaminación antropogénica. Se obtuvieron concentraciones anómalas de of Cl−, SO4 2−, As, B y Ba en dos manantiales cercanos a los sondeos petrolíferos y en el rio Ubierna, estos componentes son probablemente indicadores de una posible mezcla entre los acuíferos profundos y superficiales. El estudio de los gases disueltos en las aguas también evidencia el circuito superficial de las aguas. Estando, por lo general, dominado por la componente atmosférica (N2, O2 y Ar). Sin embargo, en algunos casos el gas predominante fue el CO2 (con concentraciones que llegan al 63% v/v), aunque los valores isotópicos del carbono (<-17,7 ‰) muestran que lo más probable es que esté relacionado con un origen biológico. Los datos geoquímicos e isotópicos de las aguas superficiales obtenidos en la zona de Hontomín se pueden considerar como el valor de fondo con el que comparar durante la fase operacional, la clausura y posterior a la clausura. En este sentido, la composición de los elementos mayoritarios y traza, la composición isotópica del carbono del CO2 disuelto y del TDIC (Carbono inorgánico disuelto) y algunos elementos traza se pueden considerar como parámetros adecuados para detectar la migración del CO2 a los ambientes superficiales. ABSTRACT Since 2009, a group made up of Universidad Politécnica de Madrid (UPM; Spain) and Università degli Studi Firenze (UniFi; Italy) has been taking part in a joint project called “Strategies for Monitoring CO2 and other Gases in Natural analogues”. The group was coordinated by AMPHOS XXI, a private company established in Barcelona. The Project was financially supported by Fundación Ciudad de la Energía (CIUDEN; Spain) as a part of the EC-funded OXYCFB300 project (European Energy Program for Recovery -EEPR-; www.compostillaproject.eu). The main objectives of the project were aimed to develop and optimize analytical methodologies to be applied at the surface to Monitor and Verify the feasibility of geologically stored carbon dioxide. These techniques were oriented to detect and quantify possible CO2 leakages to the atmosphere. Several investigations were made in natural analogues from Spain and Italy and in the Tecnchnological Development Plant for CO2 injection al Hontomín (Burgos, Spain). The studying techniques were mainly focused on the measurements of diffuse soil gases and surface and shallow waters. The soil-gas measurements included the determination of CO2 flux and the application to natural trace gases (e.g. radon) that may help to detect any CO2 leakage. As far as the water chemistry is concerned, geochemical and isotopic data related to surface and spring waters and dissolved gases in the area of the PDT of Hontomín were analyzed to determine the most suitable parameters to trace the migration of the injected CO2 into the near-surface environments. The accumulation chamber method was used to measure the diffuse emission of CO2 at the soil-atmosphere interface. Although this technique has widely been applied in different scientific areas, it was considered of the utmost importance to adapt the optimum methodology for measuring the CO2 soil flux and estimating the total CO2 output to the specific features of the site where CO2 is to be stored shortly. During the pre-injection phase CO2 fluxes are expected to be relatively low where in the intra- and post-injection phases, if leakages are to be occurring, small variation in CO2 flux might be detected when the CO2 “noise” is overcoming the biological activity of the soil (soil respiration). CO2 flux measurements by the accumulation chamber method could be performed without vegetation clearance or after vegetation clearance. However, the results obtained after clearance show less dispersion and this suggests that this procedure appears to be more suitable for monitoring CO2 Storage sites. The measurement protocol, applied for the determination of the CO2 flux baseline at Hontomín, has included the following steps: a) cleaning and removal of both the vegetal cover and top 2 cm of soil, b) waiting to reduce flux perturbation due to the soil removal and c) measuring the CO2 flux. Once completing the CO2 flux measurements and detected whether there were anomalies zones, the total CO2 output was estimated to quantify the amount of CO2 released to the atmosphere in each of the studied areas. There is a wide range of methodologies for the estimation of the CO2 output, which were applied to understand which one was the most representative. In this study six statistical methods are presented: arithmetic mean, minimum variances unbiased estimator, bootstrap resample, partitioning of data into different populations with a graphical and a maximum likelihood procedures, and sequential Gaussian simulation. Eight campaigns were carried out in the Hontomín CO2 Storage Technology Development Plant and in natural CO2 analogues. The results show that sequential Gaussian simulation is the most accurate method to estimate the total CO2 output and the confidential interval. Nevertheless, a variety of statistic methods were also used. As a consequence, an application procedure for selecting the most realistic method was developed. The first step to estimate the total emanation rate was the variogram analysis. If the relation among the data can be explained with the variogram, the best technique to calculate the total CO2 output and its confidence interval is the sequential Gaussian simulation method (sGs). If the data are independent, their distribution is to be analyzed. For normal and log-normal distribution the proper methods are the arithmetic mean and minimum variances unbiased estimator, respectively. If the data are not normal (log-normal) or are a mixture of different populations the best approach is the bootstrap resampling. According to these steps, the maximum confidence interval was about ±20/25%, with most of values between ±3.5% and ±8%. Partitioning of CO2 flux data into different populations may help to interpret the data as their distribution can be affected by different geochemical processes, e.g. geological or biological sources of CO2. Consequently, it may be an important tool in a monitoring CCS program, where the main goal is to demonstrate that there are not leakages from the reservoir to the atmosphere and, if occurring, to be able to detect and quantify it. Results show that the partitioning of populations is better performed by maximum likelihood criteria, since graphical procedures have a degree of subjectivity in the interpretation and results may not be reproducible. The relationship between CO2 flux and radon isotopes (222Rn and 220Rn) was studied in natural analogues. In all emissions zones, a positive relation between 222Rn and CO2 was observed. However, the relationship between activity of 220Rn and CO2 flux is not clear. In some cases the 220Rn activity indeed increased with the CO2 flux in other measurements a decrease was recognized. We can speculate that this effect was possibly related to the route (deep or shallow) of the radon source. These results may confirm the possible use of the radon isotopes as tracers for the gas origin and their application in the detection of leakages. With respect to the CO2 flux baseline at the TDP of Hontomín, soil flux measurements in the vicinity of oil boreholes, drilled in the eighties and named H-1 to H-4, and injection and monitoring wells were performed using an accumulation chamber. Seven surveys were carried out from November 2009 to summer 2011. More than 4,000 measurements were used to determine the baseline flux of CO2 and its seasonal variations. The measured values were relatively low (from 5 to 13 g•m-2•day-1) and few outliers were identified, mainly located close to the H-2 oil well. Nevertheless, these values cannot be associated to a deep source of CO2, being more likely related to biological processes, i.e. soil respiration. No anomalies were recognized close to the deep fault system (Ubierna Fault) detected by geophysical investigations. There, the CO2 flux is indeed as low as other measurement stations. CO2 fluxes appear to be controlled by the biological activity since the lowest values were recorded during autumn-winter seasons and they tend to increase in warm periods. Two reference CO2 flux values (UCL50 of 5 g•m-2•d-1 for non-ploughed areas in autumn-winter seasons and 3.5 and 12 g•m-2•d-1 for in ploughed and non-ploughed areas, respectively, in spring-summer time, and UCL99 of 26 g•m-2•d-1 for autumn-winter in not-ploughed areas and 34 and 42 g•m-2•d-1 for spring-summer in ploughed and not-ploughed areas, respectively, were calculated. Fluxes higher than these reference values could be indicative of possible leakage during the operational and post-closure stages of the storage project. The first geochemical and isotopic data related to surface and spring waters and dissolved gases in the area of Hontomín–Huermeces (Burgos, Spain) are presented and discussed. The chemical and features of the spring waters suggest that they are related to a shallow hydrogeological system as the concentration of the Total Dissolved Solids approaches 800 mg/L with a Ca2+(Mg2+)-HCO3 − composition, similar to that of the surface waters. Some spring waters are characterized by relatively high concentrations of NO3 − (up to 123 mg/L), unequivocally suggesting an anthropogenic source. Anomalous concentrations of Cl−, SO4 2−, As, B and Ba were measured in two springs, discharging a few hundred meters from the oil wells, and in the Rio Ubierna. These contents are possibly indicative of mixing processes between deep and shallow aquifers. The chemistry of the dissolved gases also evidences the shallow circuits of the Hontomín– Huermeces, mainly characterized by an atmospheric source as highlighted by the contents of N2, O2, Ar and their relative ratios. Nevertheless, significant concentrations (up to 63% by vol.) of isotopically negative CO2 (<−17.7‰ V-PDB) were found in some water samples, likely related to a biogenic source. The geochemical and isotopic data of the surface and spring waters in the surroundings of Hontomín can be considered as background values when intra- and post-injection monitoring programs will be carried out. In this respect, main and minor solutes, the isotopic carbon of dissolved CO2 and TDIC (Total Dissolved Inorganic Carbon) and selected trace elements can be considered as useful parameters to trace the migration of the injected CO2 into near-surface environments.

A nova família de distribuições odd log-logística: teoria e aplicações

Neste trabalho, foi proposta uma nova família de distribuições, a qual permite modelar dados de sobrevivência quando a função de risco tem formas unimodal e U (banheira). Ainda, foram consideradas as modificações das distribuições Weibull, Fréchet, half-normal generalizada, log-logística e lognormal. Tomando dados não-censurados e censurados, considerou-se os estimadores de máxima verossimilhança para o modelo proposto, a fim de verificar a flexibilidade da nova família. Além disso, um modelo de regressão locação-escala foi utilizado para verificar a influência de covariáveis nos tempos de sobrevida. Adicionalmente, conduziu-se uma análise de resíduos baseada nos resíduos deviance modificada. Estudos de simulação, utilizando-se de diferentes atribuições dos parâmetros, porcentagens de censura e tamanhos amostrais, foram conduzidos com o objetivo de verificar a distribuição empírica dos resíduos tipo martingale e deviance modificada. Para detectar observações influentes, foram utilizadas medidas de influência local, que são medidas de diagnóstico baseadas em pequenas perturbações nos dados ou no modelo proposto. Podem ocorrer situações em que a suposição de independência entre os tempos de falha e censura não seja válida. Assim, outro objetivo desse trabalho é considerar o mecanismo de censura informativa, baseado na verossimilhança marginal, considerando a distribuição log-odd log-logística Weibull na modelagem. Por fim, as metodologias descritas são aplicadas a conjuntos de dados reais.

Size frequency distribution of the β-amyloid (aβ) deposits in dementia with Lewy bodies with associated Alzheimer’s disease pathology

The objective is to study beta-amyloid (Abeta) deposition in dementia with Lewy bodies (DLB) with Alzheimer's disease (AD) pathology (DLB/AD). The size frequency distributions of the Abeta deposits were studied and fitted by log-normal and power-law models. Patients were ten clinically and pathologically diagnosed DLB/AD cases. Size distributions had a single peak and were positively skewed and similar to those described in AD and Down's syndrome. Size distributions had smaller means in DLB/AD than in AD. Log-normal and power-law models were fitted to the size distributions of the classic and diffuse deposits, respectively. Size distributions of Abeta deposits were similar in DLB/AD and AD. Size distributions of the diffuse deposits were fitted by a power-law model suggesting that aggregation/disaggregation of Abeta was the predominant factor, whereas the classic deposits were fitted by a log-normal distribution suggesting that surface diffusion was important in the pathogenesis of the classic deposits.

Size frequency distribution of prion protein (PrP) aggregates in variant Creutzfeldt-Jakob disease (vCJD)

The frequency distribution of aggregate size of the diffuse and florid-type prion protein (PrP) plaques was studied in various brain regions in cases of variant Creutzfeldt-Jakob disease (vCJD). The size distributions were unimodal and positively skewed and resembled those of β-amyloid (Aβ) deposits in Alzheimer's disease (AD) and Down's syndrome (DS). The frequency distributions of the PrP aggregates were log-normal in shape, but there were deviations from the expected number of plaques in specific size classes. More diffuse plaques were observed in the modal size class and fewer in the larger size classes than expected and more florid plaques were present in the larger size classes compared with the log-normal model. It was concluded that the growth of the PrP aggregates in vCJD does not strictly follow a log-normal model, diffuse plaques growing to within a more restricted size range and florid plaques to larger sizes than predicted. © Springer-Verlag 2005.

Factors determining the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease

The size frequency distributions of discrete β-amyloid (Aβ) deposits were studied in single sections of the temporal lobe from patients with Alzheimer's disease. The size distributions were unimodal and positively skewed. In 18/25 (72%) tissues examined, a log normal distribution was a good fit to the data. This suggests that the abundances of deposit sizes are distributed randomly on a log scale about a mean value. Three hypotheses were proposed to account for the data: (1) sectioning in a single plane, (2) growth and disappearance of Aβ deposits, and (3) the origin of Aβ deposits from clusters of neuronal cell bodies. Size distributions obtained by serial reconstruction through the tissue were similar to those observed in single sections, which would not support the first hypothesis. The log normal distribution of Aβ deposit size suggests a model in which the rate of growth of a deposit is proportional to its volume. However, mean deposit size and the ratio of large to small deposits were not positively correlated with patient age or disease duration. The frequency distribution of Aβ deposits which were closely associated with 0, 1, 2, 3, or more neuronal cell bodies deviated significantly from a log normal distribution, which would not support the neuronal origin hypothesis. On the basis of the present data, growth and resolution of Aβ deposits would appear to be the most likely explanation for the log normal size distributions.

Income distribution dependence of poverty measure:a theoretical analysis

Using a modified deprivation (or poverty) function, in this paper, we theoretically study the changes in poverty with respect to the 'global' mean and variance of the income distribution using Indian survey data. We show that when the income obeys a log-normal distribution, a rising mean income generally indicates a reduction in poverty while an increase in the variance of the income distribution increases poverty. This altruistic view for a developing economy, however, is not tenable anymore once the poverty index is found to follow a pareto distribution. Here although a rising mean income indicates a reduction in poverty, due to the presence of an inflexion point in the poverty function, there is a critical value of the variance below which poverty decreases with increasing variance while beyond this value, poverty undergoes a steep increase followed by a decrease with respect to higher variance. Identifying this inflexion point as the poverty line, we show that the pareto poverty function satisfies all three standard axioms of a poverty index [N.C. Kakwani, Econometrica 43 (1980) 437; A.K. Sen, Econometrica 44 (1976) 219] whereas the log-normal distribution falls short of this requisite. Following these results, we make quantitative predictions to correlate a developing with a developed economy. © 2006 Elsevier B.V. All rights reserved.

EUSAAR size distribution analysis database

Two years of harmonized aerosol number size distribution data from 24 European field monitoring sites have been analysed. The results give a comprehensive overview of the European near surface aerosol particle number concentrations and number size distributions between 30 and 500 nm of dry particle diameter. Spatial and temporal distribution of aerosols in the particle sizes most important for climate applications are presented. We also analyse the annual, weekly and diurnal cycles of the aerosol number concentrations, provide log-normal fitting parameters for median number size distributions, and give guidance notes for data users. Emphasis is placed on the usability of results within the aerosol modelling community. We also show that the aerosol number concentrations of Aitken and accumulation mode particles (with 100 nm dry diameter as a cut-off between modes) are related, although there is significant variation in the ratios of the modal number concentrations. Different aerosol and station types are distinguished from this data and this methodology has potential for further categorization of stations aerosol number size distribution types. The European submicron aerosol was divided into characteristic types: Central European aerosol, characterized by single mode median size distributions, unimodal number concentration histograms and low variability in CCN-sized aerosol number concentrations; Nordic aerosol with low number concentrations, although showing pronounced seasonal variation of especially Aitken mode particles; Mountain sites (altitude over 1000 m a.s.l.) with a strong seasonal cycle in aerosol number concentrations, high variability, and very low median number concentrations. Southern and Western European regions had fewer stations, which decreases the regional coverage of these results. Aerosol number concentrations over the Britain and Ireland had very high variance and there are indications of mixed air masses from several source regions; the Mediterranean aerosol exhibit high seasonality, and a strong accumulation mode in the summer. The greatest concentrations were observed at the Ispra station in Northern Italy with high accumulation mode number concentrations in the winter. The aerosol number concentrations at the Arctic station Zeppelin in Ny-Ålesund in Svalbard have also a strong seasonal cycle, with greater concentrations of accumulation mode particles in winter, and dominating summer Aitken mode indicating more recently formed particles. Observed particles did not show any statistically significant regional work-week or weekday related variation in number concentrations studied. Analysis products are made for open-access to the research community, available in a freely accessible internet site. The results give to the modelling community a reliable, easy-to-use and freely available comparison dataset of aerosol size distributions.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.