Contribución al estudio de las metodologías de cálculo realista con incertidumbre (BEPU), dentro del análisis determinista de seguridad de plantas nucleares

El análisis determinista de seguridad (DSA) es el procedimiento que sirve para diseñar sistemas, estructuras y componentes relacionados con la seguridad en las plantas nucleares. El DSA se basa en simulaciones computacionales de una serie de hipotéticos accidentes representativos de la instalación, llamados escenarios base de diseño (DBS). Los organismos reguladores señalan una serie de magnitudes de seguridad que deben calcularse en las simulaciones, y establecen unos criterios reguladores de aceptación (CRA), que son restricciones que deben cumplir los valores de esas magnitudes. Las metodologías para realizar los DSA pueden ser de 2 tipos: conservadoras o realistas. Las metodologías conservadoras utilizan modelos predictivos e hipótesis marcadamente pesimistas, y, por ello, relativamente simples. No necesitan incluir un análisis de incertidumbre de sus resultados. Las metodologías realistas se basan en hipótesis y modelos predictivos realistas, generalmente mecanicistas, y se suplementan con un análisis de incertidumbre de sus principales resultados. Se les denomina también metodologías BEPU (“Best Estimate Plus Uncertainty”). En ellas, la incertidumbre se representa, básicamente, de manera probabilista. Para metodologías conservadores, los CRA son, simplemente, restricciones sobre valores calculados de las magnitudes de seguridad, que deben quedar confinados en una “región de aceptación” de su recorrido. Para metodologías BEPU, el CRA no puede ser tan sencillo, porque las magnitudes de seguridad son ahora variables inciertas. En la tesis se desarrolla la manera de introducción de la incertidumbre en los CRA. Básicamente, se mantiene el confinamiento a la misma región de aceptación, establecida por el regulador. Pero no se exige el cumplimiento estricto sino un alto nivel de certidumbre. En el formalismo adoptado, se entiende por ello un “alto nivel de probabilidad”, y ésta corresponde a la incertidumbre de cálculo de las magnitudes de seguridad. Tal incertidumbre puede considerarse como originada en los inputs al modelo de cálculo, y propagada a través de dicho modelo. Los inputs inciertos incluyen las condiciones iniciales y de frontera al cálculo, y los parámetros empíricos de modelo, que se utilizan para incorporar la incertidumbre debida a la imperfección del modelo. Se exige, por tanto, el cumplimiento del CRA con una probabilidad no menor a un valor P0 cercano a 1 y definido por el regulador (nivel de probabilidad o cobertura). Sin embargo, la de cálculo de la magnitud no es la única incertidumbre existente. Aunque un modelo (sus ecuaciones básicas) se conozca a la perfección, la aplicación input-output que produce se conoce de manera imperfecta (salvo que el modelo sea muy simple). La incertidumbre debida la ignorancia sobre la acción del modelo se denomina epistémica; también se puede decir que es incertidumbre respecto a la propagación. La consecuencia es que la probabilidad de cumplimiento del CRA no se puede conocer a la perfección; es una magnitud incierta. Y así se justifica otro término usado aquí para esta incertidumbre epistémica: metaincertidumbre. Los CRA deben incorporar los dos tipos de incertidumbre: la de cálculo de la magnitud de seguridad (aquí llamada aleatoria) y la de cálculo de la probabilidad (llamada epistémica o metaincertidumbre). Ambas incertidumbres pueden introducirse de dos maneras: separadas o combinadas. En ambos casos, el CRA se convierte en un criterio probabilista. Si se separan incertidumbres, se utiliza una probabilidad de segundo orden; si se combinan, se utiliza una probabilidad única. Si se emplea la probabilidad de segundo orden, es necesario que el regulador imponga un segundo nivel de cumplimiento, referido a la incertidumbre epistémica. Se denomina nivel regulador de confianza, y debe ser un número cercano a 1. Al par formado por los dos niveles reguladores (de probabilidad y de confianza) se le llama nivel regulador de tolerancia. En la Tesis se razona que la mejor manera de construir el CRA BEPU es separando las incertidumbres, por dos motivos. Primero, los expertos defienden el tratamiento por separado de incertidumbre aleatoria y epistémica. Segundo, el CRA separado es (salvo en casos excepcionales) más conservador que el CRA combinado. El CRA BEPU no es otra cosa que una hipótesis sobre una distribución de probabilidad, y su comprobación se realiza de forma estadística. En la tesis, los métodos estadísticos para comprobar el CRA BEPU en 3 categorías, según estén basados en construcción de regiones de tolerancia, en estimaciones de cuantiles o en estimaciones de probabilidades (ya sea de cumplimiento, ya sea de excedencia de límites reguladores). Según denominación propuesta recientemente, las dos primeras categorías corresponden a los métodos Q, y la tercera, a los métodos P. El propósito de la clasificación no es hacer un inventario de los distintos métodos en cada categoría, que son muy numerosos y variados, sino de relacionar las distintas categorías y citar los métodos más utilizados y los mejor considerados desde el punto de vista regulador. Se hace mención especial del método más utilizado hasta el momento: el método no paramétrico de Wilks, junto con su extensión, hecha por Wald, al caso multidimensional. Se decribe su método P homólogo, el intervalo de Clopper-Pearson, típicamente ignorado en el ámbito BEPU. En este contexto, se menciona el problema del coste computacional del análisis de incertidumbre. Los métodos de Wilks, Wald y Clopper-Pearson requieren que la muestra aleatortia utilizada tenga un tamaño mínimo, tanto mayor cuanto mayor el nivel de tolerancia exigido. El tamaño de muestra es un indicador del coste computacional, porque cada elemento muestral es un valor de la magnitud de seguridad, que requiere un cálculo con modelos predictivos. Se hace especial énfasis en el coste computacional cuando la magnitud de seguridad es multidimensional; es decir, cuando el CRA es un criterio múltiple. Se demuestra que, cuando las distintas componentes de la magnitud se obtienen de un mismo cálculo, el carácter multidimensional no introduce ningún coste computacional adicional. Se prueba así la falsedad de una creencia habitual en el ámbito BEPU: que el problema multidimensional sólo es atacable desde la extensión de Wald, que tiene un coste de computación creciente con la dimensión del problema. En el caso (que se da a veces) en que cada componente de la magnitud se calcula independientemente de los demás, la influencia de la dimensión en el coste no se puede evitar. Las primeras metodologías BEPU hacían la propagación de incertidumbres a través de un modelo sustitutivo (metamodelo o emulador) del modelo predictivo o código. El objetivo del metamodelo no es su capacidad predictiva, muy inferior a la del modelo original, sino reemplazar a éste exclusivamente en la propagación de incertidumbres. Para ello, el metamodelo se debe construir con los parámetros de input que más contribuyan a la incertidumbre del resultado, y eso requiere un análisis de importancia o de sensibilidad previo. Por su simplicidad, el modelo sustitutivo apenas supone coste computacional, y puede estudiarse exhaustivamente, por ejemplo mediante muestras aleatorias. En consecuencia, la incertidumbre epistémica o metaincertidumbre desaparece, y el criterio BEPU para metamodelos se convierte en una probabilidad simple. En un resumen rápido, el regulador aceptará con más facilidad los métodos estadísticos que menos hipótesis necesiten; los exactos más que los aproximados; los no paramétricos más que los paramétricos, y los frecuentistas más que los bayesianos. El criterio BEPU se basa en una probabilidad de segundo orden. La probabilidad de que las magnitudes de seguridad estén en la región de aceptación no sólo puede asimilarse a una probabilidad de éxito o un grado de cumplimiento del CRA. También tiene una interpretación métrica: representa una distancia (dentro del recorrido de las magnitudes) desde la magnitud calculada hasta los límites reguladores de aceptación. Esta interpretación da pie a una definición que propone esta tesis: la de margen de seguridad probabilista. Dada una magnitud de seguridad escalar con un límite superior de aceptación, se define el margen de seguridad (MS) entre dos valores A y B de la misma como la probabilidad de que A sea menor que B, obtenida a partir de las incertidumbres de A y B. La definición probabilista de MS tiene varias ventajas: es adimensional, puede combinarse de acuerdo con las leyes de la probabilidad y es fácilmente generalizable a varias dimensiones. Además, no cumple la propiedad simétrica. El término margen de seguridad puede aplicarse a distintas situaciones: distancia de una magnitud calculada a un límite regulador (margen de licencia); distancia del valor real de la magnitud a su valor calculado (margen analítico); distancia desde un límite regulador hasta el valor umbral de daño a una barrera (margen de barrera). Esta idea de representar distancias (en el recorrido de magnitudes de seguridad) mediante probabilidades puede aplicarse al estudio del conservadurismo. El margen analítico puede interpretarse como el grado de conservadurismo (GC) de la metodología de cálculo. Utilizando la probabilidad, se puede cuantificar el conservadurismo de límites de tolerancia de una magnitud, y se pueden establecer indicadores de conservadurismo que sirvan para comparar diferentes métodos de construcción de límites y regiones de tolerancia. Un tópico que nunca se abordado de manera rigurosa es el de la validación de metodologías BEPU. Como cualquier otro instrumento de cálculo, una metodología, antes de poder aplicarse a análisis de licencia, tiene que validarse, mediante la comparación entre sus predicciones y valores reales de las magnitudes de seguridad. Tal comparación sólo puede hacerse en escenarios de accidente para los que existan valores medidos de las magnitudes de seguridad, y eso ocurre, básicamente en instalaciones experimentales. El objetivo último del establecimiento de los CRA consiste en verificar que se cumplen para los valores reales de las magnitudes de seguridad, y no sólo para sus valores calculados. En la tesis se demuestra que una condición suficiente para este objetivo último es la conjunción del cumplimiento de 2 criterios: el CRA BEPU de licencia y un criterio análogo, pero aplicado a validación. Y el criterio de validación debe demostrarse en escenarios experimentales y extrapolarse a plantas nucleares. El criterio de licencia exige un valor mínimo (P0) del margen probabilista de licencia; el criterio de validación exige un valor mínimo del margen analítico (el GC). Esos niveles mínimos son básicamente complementarios; cuanto mayor uno, menor el otro. La práctica reguladora actual impone un valor alto al margen de licencia, y eso supone que el GC exigido es pequeño. Adoptar valores menores para P0 supone menor exigencia sobre el cumplimiento del CRA, y, en cambio, más exigencia sobre el GC de la metodología. Y es importante destacar que cuanto mayor sea el valor mínimo del margen (de licencia o analítico) mayor es el coste computacional para demostrarlo. Así que los esfuerzos computacionales también son complementarios: si uno de los niveles es alto (lo que aumenta la exigencia en el cumplimiento del criterio) aumenta el coste computacional. Si se adopta un valor medio de P0, el GC exigido también es medio, con lo que la metodología no tiene que ser muy conservadora, y el coste computacional total (licencia más validación) puede optimizarse. ABSTRACT Deterministic Safety Analysis (DSA) is the procedure used in the design of safety-related systems, structures and components of nuclear power plants (NPPs). DSA is based on computational simulations of a set of hypothetical accidents of the plant, named Design Basis Scenarios (DBS). Nuclear regulatory authorities require the calculation of a set of safety magnitudes, and define the regulatory acceptance criteria (RAC) that must be fulfilled by them. Methodologies for performing DSA van be categorized as conservative or realistic. Conservative methodologies make use of pessimistic model and assumptions, and are relatively simple. They do not need an uncertainty analysis of their results. Realistic methodologies are based on realistic (usually mechanistic) predictive models and assumptions, and need to be supplemented with uncertainty analyses of their results. They are also termed BEPU (“Best Estimate Plus Uncertainty”) methodologies, and are typically based on a probabilistic representation of the uncertainty. For conservative methodologies, the RAC are simply the restriction of calculated values of safety magnitudes to “acceptance regions” defined on their range. For BEPU methodologies, the RAC cannot be so simple, because the safety magnitudes are now uncertain. In the present Thesis, the inclusion of uncertainty in RAC is studied. Basically, the restriction to the acceptance region must be fulfilled “with a high certainty level”. Specifically, a high probability of fulfillment is required. The calculation uncertainty of the magnitudes is considered as propagated from inputs through the predictive model. Uncertain inputs include model empirical parameters, which store the uncertainty due to the model imperfection. The fulfillment of the RAC is required with a probability not less than a value P0 close to 1 and defined by the regulator (probability or coverage level). Calculation uncertainty is not the only one involved. Even if a model (i.e. the basic equations) is perfectly known, the input-output mapping produced by the model is imperfectly known (unless the model is very simple). This ignorance is called epistemic uncertainty, and it is associated to the process of propagation). In fact, it is propagated to the probability of fulfilling the RAC. Another term used on the Thesis for this epistemic uncertainty is metauncertainty. The RAC must include the two types of uncertainty: one for the calculation of the magnitude (aleatory uncertainty); the other one, for the calculation of the probability (epistemic uncertainty). The two uncertainties can be taken into account in a separate fashion, or can be combined. In any case the RAC becomes a probabilistic criterion. If uncertainties are separated, a second-order probability is used; of both are combined, a single probability is used. On the first case, the regulator must define a level of fulfillment for the epistemic uncertainty, termed regulatory confidence level, as a value close to 1. The pair of regulatory levels (probability and confidence) is termed the regulatory tolerance level. The Thesis concludes that the adequate way of setting the BEPU RAC is by separating the uncertainties. There are two reasons to do so: experts recommend the separation of aleatory and epistemic uncertainty; and the separated RAC is in general more conservative than the joint RAC. The BEPU RAC is a hypothesis on a probability distribution, and must be statistically tested. The Thesis classifies the statistical methods to verify the RAC fulfillment in 3 categories: methods based on tolerance regions, in quantile estimators and on probability (of success or failure) estimators. The former two have been termed Q-methods, whereas those in the third category are termed P-methods. The purpose of our categorization is not to make an exhaustive survey of the very numerous existing methods. Rather, the goal is to relate the three categories and examine the most used methods from a regulatory standpoint. Special mention deserves the most used method, due to Wilks, and its extension to multidimensional variables (due to Wald). The counterpart P-method of Wilks’ is Clopper-Pearson interval, typically ignored in the BEPU realm. The problem of the computational cost of an uncertainty analysis is tackled. Wilks’, Wald’s and Clopper-Pearson methods require a minimum sample size, which is a growing function of the tolerance level. The sample size is an indicator of the computational cost, because each element of the sample must be calculated with the predictive models (codes). When the RAC is a multiple criteria, the safety magnitude becomes multidimensional. When all its components are output of the same calculation, the multidimensional character does not introduce additional computational cost. In this way, an extended idea in the BEPU realm, stating that the multi-D problem can only be tackled with the Wald extension, is proven to be false. When the components of the magnitude are independently calculated, the influence of the problem dimension on the cost cannot be avoided. The former BEPU methodologies performed the uncertainty propagation through a surrogate model of the code, also termed emulator or metamodel. The goal of a metamodel is not the predictive capability, clearly worse to the original code, but the capacity to propagate uncertainties with a lower computational cost. The emulator must contain the input parameters contributing the most to the output uncertainty, and this requires a previous importance analysis. The surrogate model is practically inexpensive to run, so that it can be exhaustively analyzed through Monte Carlo. Therefore, the epistemic uncertainty due to sampling will be reduced to almost zero, and the BEPU RAC for metamodels includes a simple probability. The regulatory authority will tend to accept the use of statistical methods which need a minimum of assumptions: exact, nonparametric and frequentist methods rather than approximate, parametric and bayesian methods, respectively. The BEPU RAC is based on a second-order probability. The probability of the safety magnitudes being inside the acceptance region is a success probability and can be interpreted as a fulfillment degree if the RAC. Furthermore, it has a metric interpretation, as a distance (in the range of magnitudes) from calculated values of the magnitudes to acceptance regulatory limits. A probabilistic definition of safety margin (SM) is proposed in the thesis. The same from a value A to other value B of a safety magnitude is defined as the probability that A is less severe than B, obtained from the uncertainties if A and B. The probabilistic definition of SM has several advantages: it is nondimensional, ranges in the interval (0,1) and can be easily generalized to multiple dimensions. Furthermore, probabilistic SM are combined according to the probability laws. And a basic property: probabilistic SM are not symmetric. There are several types of SM: distance from a calculated value to a regulatory limit (licensing margin); or from the real value to the calculated value of a magnitude (analytical margin); or from the regulatory limit to the damage threshold (barrier margin). These representations of distances (in the magnitudes’ range) as probabilities can be applied to the quantification of conservativeness. Analytical margins can be interpreted as the degree of conservativeness (DG) of the computational methodology. Conservativeness indicators are established in the Thesis, useful in the comparison of different methods of constructing tolerance limits and regions. There is a topic which has not been rigorously tackled to the date: the validation of BEPU methodologies. Before being applied in licensing, methodologies must be validated, on the basis of comparisons of their predictions ad real values of the safety magnitudes. Real data are obtained, basically, in experimental facilities. The ultimate goal of establishing RAC is to verify that real values (aside from calculated values) fulfill them. In the Thesis it is proved that a sufficient condition for this goal is the conjunction of 2 criteria: the BEPU RAC and an analogous criterion for validation. And this las criterion must be proved in experimental scenarios and extrapolated to NPPs. The licensing RAC requires a minimum value (P0) of the probabilistic licensing margin; the validation criterion requires a minimum value of the analytical margin (i.e., of the DG). These minimum values are basically complementary; the higher one of them, the lower the other one. The regulatory practice sets a high value on the licensing margin, so that the required DG is low. The possible adoption of lower values for P0 would imply weaker exigence on the RCA fulfillment and, on the other hand, higher exigence on the conservativeness of the methodology. It is important to highlight that a higher minimum value of the licensing or analytical margin requires a higher computational cost. Therefore, the computational efforts are also complementary. If medium levels are adopted, the required DG is also medium, and the methodology does not need to be very conservative. The total computational effort (licensing plus validation) could be optimized.

Valuing water resources in developing countries: A semiparametric approach to valuation models

Valuation of projects for the preservation of water resources provides important information to policy makers and funding institutions. Standard contingent valuation models rely on distributional assumptions to provide welfare measures. Deviations from assumed and actual distribution of benefits are important when designing policies in developing countries, where inequality is a concern. This article applies semiparametric methods to obtain estimates of the benefit from a project for the preservation of an important Brazilian river basin. These estimates lead to significant differences from those obtained using the standard parametric approach.

Technical, allocative, cost and scale efficiencies in Bangladesh rice cultivation: A non-parametric approach

Applying programming techniques to detailed data for 406 rice farms in 21 villages, for 1997, produces inefficiency measures, which differ substantially from the results of simple yield and unit cost measures. For the Boro (dry) season, mean technical efficiency was efficiency was 56.2 per cent and 69.4 per cent, allocative efficiency was 81.3 per cent, cost efficiency was 56.2 per cent and scale efficiency 94.9 per cent. The Aman (wet) season results are similar, but a few points lower. Allocative inefficiency is due to overuse of labour, suggesting population pressure, and of fertiliser, where recommended rates may warrant revision. Second-stage regressions show that large families are more inefficient, whereas farmers with better access to input markets, and those who do less off-farm work, tend to be more efficient. The information on the sources of inter-farm performance differentials could be used by the extension agents to help inefficient farmers. There is little excuse for such sub-optimal use of survey data, which are often collected at substantial costs.

Electrohysterogram signal component cataloging with spectral and time-frequency methods

The Electrohysterogram (EHG) is a new instrument for pregnancy monitoring. It measures the uterine muscle electrical signal, which is closely related with uterine contractions. The EHG is described as a viable alternative and a more precise instrument than the currently most widely used method for the description of uterine contractions: the external tocogram. The EHG has also been indicated as a promising tool in the assessment of preterm delivery risk. This work intends to contribute towards the EHG characterization through the inventory of its components which are: • Contractions; • Labor contractions; • Alvarez waves; • Fetal movements; • Long Duration Low Frequency Waves; The instruments used for cataloging were: Spectral Analysis, parametric and non-parametric, energy estimators, time-frequency methods and the tocogram annotated by expert physicians. The EHG and respective tocograms were obtained from the Icelandic 16-electrode Electrohysterogram Database. 288 components were classified. There is not a component database of this type available for consultation. The spectral analysis module and power estimation was added to Uterine Explorer, an EHG analysis software developed in FCT-UNL. The importance of this component database is related to the need to improve the understanding of the EHG which is a relatively complex signal, as well as contributing towards the detection of preterm birth. Preterm birth accounts for 10% of all births and is one of the most relevant obstetric conditions. Despite the technological and scientific advances in perinatal medicine, in developed countries, prematurity is the major cause of neonatal death. Although various risk factors such as previous preterm births, infection, uterine malformations, multiple gestation and short uterine cervix in second trimester, have been associated with this condition, its etiology remains unknown [1][2][3].

Study on period search methods of variable stars: Application to ASAS and CRTS databases

Study on variable stars is an important topic of modern astrophysics. After the invention of powerful telescopes and high resolving powered CCD’s, the variable star data is accumulating in the order of peta-bytes. The huge amount of data need lot of automated methods as well as human experts. This thesis is devoted to the data analysis on variable star’s astronomical time series data and hence belong to the inter-disciplinary topic, Astrostatistics. For an observer on earth, stars that have a change in apparent brightness over time are called variable stars. The variation in brightness may be regular (periodic), quasi periodic (semi-periodic) or irregular manner (aperiodic) and are caused by various reasons. In some cases, the variation is due to some internal thermo-nuclear processes, which are generally known as intrinsic vari- ables and in some other cases, it is due to some external processes, like eclipse or rotation, which are known as extrinsic variables. Intrinsic variables can be further grouped into pulsating variables, eruptive variables and flare stars. Extrinsic variables are grouped into eclipsing binary stars and chromospheri- cal stars. Pulsating variables can again classified into Cepheid, RR Lyrae, RV Tauri, Delta Scuti, Mira etc. The eruptive or cataclysmic variables are novae, supernovae, etc., which rarely occurs and are not periodic phenomena. Most of the other variations are periodic in nature. Variable stars can be observed through many ways such as photometry, spectrophotometry and spectroscopy. The sequence of photometric observa- xiv tions on variable stars produces time series data, which contains time, magni- tude and error. The plot between variable star’s apparent magnitude and time are known as light curve. If the time series data is folded on a period, the plot between apparent magnitude and phase is known as phased light curve. The unique shape of phased light curve is a characteristic of each type of variable star. One way to identify the type of variable star and to classify them is by visually looking at the phased light curve by an expert. For last several years, automated algorithms are used to classify a group of variable stars, with the help of computers. Research on variable stars can be divided into different stages like observa- tion, data reduction, data analysis, modeling and classification. The modeling on variable stars helps to determine the short-term and long-term behaviour and to construct theoretical models (for eg:- Wilson-Devinney model for eclips- ing binaries) and to derive stellar properties like mass, radius, luminosity, tem- perature, internal and external structure, chemical composition and evolution. The classification requires the determination of the basic parameters like pe- riod, amplitude and phase and also some other derived parameters. Out of these, period is the most important parameter since the wrong periods can lead to sparse light curves and misleading information. Time series analysis is a method of applying mathematical and statistical tests to data, to quantify the variation, understand the nature of time-varying phenomena, to gain physical understanding of the system and to predict future behavior of the system. Astronomical time series usually suffer from unevenly spaced time instants, varying error conditions and possibility of big gaps. This is due to daily varying daylight and the weather conditions for ground based observations and observations from space may suffer from the impact of cosmic ray particles. Many large scale astronomical surveys such as MACHO, OGLE, EROS, xv ROTSE, PLANET, Hipparcos, MISAO, NSVS, ASAS, Pan-STARRS, Ke- pler,ESA, Gaia, LSST, CRTS provide variable star’s time series data, even though their primary intention is not variable star observation. Center for Astrostatistics, Pennsylvania State University is established to help the astro- nomical community with the aid of statistical tools for harvesting and analysing archival data. Most of these surveys releases the data to the public for further analysis. There exist many period search algorithms through astronomical time se- ries analysis, which can be classified into parametric (assume some underlying distribution for data) and non-parametric (do not assume any statistical model like Gaussian etc.,) methods. Many of the parametric methods are based on variations of discrete Fourier transforms like Generalised Lomb-Scargle peri- odogram (GLSP) by Zechmeister(2009), Significant Spectrum (SigSpec) by Reegen(2007) etc. Non-parametric methods include Phase Dispersion Minimi- sation (PDM) by Stellingwerf(1978) and Cubic spline method by Akerlof(1994) etc. Even though most of the methods can be brought under automation, any of the method stated above could not fully recover the true periods. The wrong detection of period can be due to several reasons such as power leakage to other frequencies which is due to finite total interval, finite sampling interval and finite amount of data. Another problem is aliasing, which is due to the influence of regular sampling. Also spurious periods appear due to long gaps and power flow to harmonic frequencies is an inherent problem of Fourier methods. Hence obtaining the exact period of variable star from it’s time series data is still a difficult problem, in case of huge databases, when subjected to automation. As Matthew Templeton, AAVSO, states “Variable star data analysis is not always straightforward; large-scale, automated analysis design is non-trivial”. Derekas et al. 2007, Deb et.al. 2010 states “The processing of xvi huge amount of data in these databases is quite challenging, even when looking at seemingly small issues such as period determination and classification”. It will be beneficial for the variable star astronomical community, if basic parameters, such as period, amplitude and phase are obtained more accurately, when huge time series databases are subjected to automation. In the present thesis work, the theories of four popular period search methods are studied, the strength and weakness of these methods are evaluated by applying it on two survey databases and finally a modified form of cubic spline method is intro- duced to confirm the exact period of variable star. For the classification of new variable stars discovered and entering them in the “General Catalogue of Vari- able Stars” or other databases like “Variable Star Index“, the characteristics of the variability has to be quantified in term of variable star parameters.

Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.

Nonparametric versus Parametric Statistical Approaches for Genetic Anticipation: The Pancreatic Cancer Case

2000 Mathematics Subject Classi cation: 62N01, 62N05, 62P10, 92D10, 92D30.

Esophageal Ulcer in Brazilian Patients with HIV: Prevalence and Comparative Analysis Among Diagnostic Methods

Esophageal ulcer (EU) represents an important comorbidity in AIDS. We evaluated the prevalence of EU, the accuracy of the endoscopic and histologic methods used to investigate viral EU in HIV-positive Brazilian patients and the numerical relevance of tissue sampling. A total of 399 HIV-positive patients underwent upper gastrointestinal (UGI) endoscopy. HIV-positive patients with EU determined by UGI endoscopy followed by biopsies were analyzed by the hematoxylin-eosin (HE) and immunohistochemical (IH) methods. EU was detected in 41 patients (mean age, 39.2 years; 23 males), with a prevalence of 10.27%. The median CD4 count was 49 cells/mm(3) (range, 1-361 cells/mm(3)) and the viral load was 58,869 copies per milliliter (range, 50-77,3290 copies per milliliter). UGI endoscopy detected 29 of 41 EU suggestive of cytomegalovirus (CMV) infection and 7 of 41 indicating herpes simplex virus (HSV) infection. HE histology confirmed 4 of 29 ulcers induced by CMV, 2 of 7 induced by HSV, and 1 of 7 induced by HSV plus CMV. IH for CMV and HSV confirmed the HE findings and detected one additional CMV-induced case. UGI endoscopy showed 100% sensitivity and 15% specificity for the diagnosis of EU due to CMV or HSV compared to HE and IH. HE proved to be an adequate method for etiologic evaluation, with 87% sensitivity and 100% specificity compared to IH. The number of samples did not influence the etiologic evaluation. The data support the importance of IH as a complementary method for HE in the diagnosis of EU of viral etiology.

Development and validation of sensitive methods for determination of sibutramine hydrochloride monohydrate and direct enantiomeric separation on a protein-based chiral stationary phase

Sibutramine hydrochloride monohydrate, chemically 1-(4-chlorophenyl)-N,N-dimethyl-alpha-(2-methylpropyl) hydrochloride monohydrate (SB center dot HCl center dot H2O), was approved by the U.S. Food and Drug Administration for the treatment of obesity. The objective of this study was to develop, validate, and compare methods using UV-derivative spectrophotometry (UVDS) and reversed-phase high-performance liquid chromatography (HPLC) for the determination of SB center dot HCl center dot H2O in pharmaceutical drug products. The UVDS and HPLC methods were found to be rapid, precise, and accurate. Statistically, there was no significant difference between the proposed UVDS and HPLC methods. The enantiomeric separation of SB was obtained on an alpha-1 acid glycoprotein column. The R- and S-sibutramine were eluted in < 5 min with baseline separation of the chromatographic peaks (alpha = 1.9 and resolution = 1.9).

Development and validation of high performance liquid chromatographic and UV-derivative spectrophotometric methods for the determination of sotalol hydrochloride in tablets

High performance liquid chromatographic (HPLC) and UV derivative spectrophotometric (UVDS) methods were developed and validated for the quantitative determination of sotalol hydrochloride in tablets. The HPLC method was performed on a C18 column with fluorescence detection. The excitation and emission wavelengths were 235 and 310nm, respectively. The mobile phase was composed of acetonitrile-water containing 0.1% trietylamine (7:93v/v) and pH adjusted to 4.6 with formic acid. The UVDS method was performed taking a signal at 239.1nm in the first derivative. The correlation coefficients (r) obtained were 0.9998 and 0.9997 for HPLC and UVDS methods, respectively. The proposed methods are simple and adaptable to routine analysis.

Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments

We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics.

HPLC-FLD methods to quantify chloroaluminum phthalocyanine in nanoparticles, plasma and tissue: application in pharmacokinetic and biodistribution studies

Analytical and bioanalytical methods of high-performance liquid chromatography with fluorescence detection (HPLC-FLD) were developed and validated for the determination of chloroaluminum phthalocyanine in different formulations of polymeric nanocapsules, plasma and livers of mice. Plasma and homogenized liver samples were extracted with ethyl acetate, and zinc phthalocyanine was used as internal standard. The results indicated that the methods were linear and selective for all matrices studied. Analysis of accuracy and precision showed adequate values, with variations lower than 10% in biological samples and lower than 2% in analytical samples. The recoveries were as high as 96% and 99% in the plasma and livers, respectively. The quantification limit of the analytical method was 1.12 ng/ml, and the limits of quantification of the bioanalytical method were 15 ng/ml and 75 ng/g for plasma and liver samples, respectively. The bioanalytical method developed was sensitive in the ranges of 15-100 ng/ml in plasma and 75-500 ng/g in liver samples and was applied to studies of biodistribution and pharmacokinetics of AlClPc. (C) 2011 Elsevier B.V. All rights reserved.

Evaluation of lignin contents in tropical forages using different analytical methods and their correlations with degradation of insoluble fiber

We compared the lignin contents of tropical forages by different analytical methods and evaluated their correlations with parameters related to the degradation of neutral detergent fiber (NDF). The lignin content was evaluated by five methods: cellulose solubilization in sulfuric acid [Lignin (sa)], oxidation with potassium permanganate [Lignin (pm)], the Klason lignin method (KL), solubilization in acetyl bromide from acid detergent fiber (ABLadf) and solubilization in acetyl bromide from the cell wall (ABLcw). Samples from ten grasses and ten legumes were used. The lignin content values obtained by gravimetric methods were also corrected for protein contamination, and the corrected values were referred to as Lignin (sa)p, Lignin (pm)p and KLp. The indigestible fraction of NDF (iNDF), the discrete lag (LAG) and the fractional rate of degradation (kd) of NDF were estimated using an in vitro assay. Correcting for protein resulted in reductions (P < 0.05) in the lignin contents as measured by the Lignin (sa), Lignin (pm) and, especially, the KL methods. There was an interaction (P < 0.05) of analytical method and forage group for lignin content. In general, LKp method provided the higher (P < 0.05) lignin contents. The estimates of lignin content obtained by the Lignin (sa)p, Lignin (pm)p and LKp methods were associated (P > 0.05) with all of the NDF degradation parameters. However, the strongest correlation coefficients for all methods evaluated were obtained with Lignin (pm)p and KLp. The lignin content estimated by the ABLcw method did not correlate (P > 0.05) with any parameters of NDF degradation. There was a correlation (P < 0.05) between the lignin content estimated by the ABLadf method and iNDF content. Nonetheless, this correlation was weaker than those found with gravimetric methods. From these results, we concluded that the gravimetric methods produce residues that are contaminated by nitrogenous compounds. Adjustment for these contaminants is suggested, particularly for the KL method, to express lignin content with greater accuracy. The relationships between lignin content measurements and NDF degradation parameters can be better determined using KLp and Lignin (pm)p methods. (C) 2011 Elsevier B.V. All rights reserved.

The influence of cone-beam computed tomography and periapical radiographic evaluation on the assessment of periapical bone destruction in dog`s teeth

Objective. The aim of this study was to determine the influence of periapical radiographs, cone beam computed tomography (CBCT) sections, and cone beam volumetric data on the determination of periapical bone destruction in endodontically treated distal root canals of premolar canine teeth. Nontreated mesial roots were used as controls. Study design. Enterococcus faecalis strain (ATCC 29212) was inoculated into 30 root canals of 2 mongrel dogs to induce apical periodontitis. After 60 days, the root canals of the distal roots of the 11 mandibular and 4 maxillary premolars were endodontically treated (n = 15). The mesial root canals were used as controls (no treatment). The bone destruction was evaluated after 6 months by 5 evaluators using periapical radiographs and by CBCT (coronal and sagittal sections). After the experimental period, the area of the lesions in periapical radiographs and CBCT sections were measured in mm(2) using the ImageTool software. A single evaluator measured the volumetric data using the OsiriX software. The comparison between the diagnosis methods in treated root canals and controls was performed using parametric and nonparametric criteria. The Pearson correlation coefficient was computed between radiographic values and CBCT volumetric data in treated root canals and controls. Results. The results showed the presence of chronic apical periodontitis in every inoculated tooth. After 6 months, periapical radiographs, coronal CBCT sections, and volumetric data showed lower bone destruction in endodontically treated teeth in comparison with the control group (P < .05). The 5 evaluators found no differences between the apical periodontitis area of treated teeth and controls when CBCT sagittal sections were used (P > .05). No correlation was found between x-ray and CBCT volumetric values in treated root canals. Conclusions. Although selected CBCT sagittal sections showed similar values of bone destruction in endodontically and nontreated root canals, volumetric CBCT data showed that periapical lesions of endodontically treated root canals had half of the volume of periapical lesions in nontreated root canals. No relationship could be found between the periapical values of bone destruction and volumetric data found in CBCT of treated rood canals. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2011; 112: 272-279)