Survival of freeze dried Lactobacillus plantarum in instant fruit powders and reconstituted fruit juices

The aim of this study was to investigate the survival of freeze dried Lactobacillus plantarum cells mixed with several freeze dried instant fruit powders (strawberry, pomegranate, blackcurrant and cranberry) during storage for 12 months as well as after reconstitution with water each month. Inulin and gum arabic were also added to the instant fruit powders at two levels (10% and 20% w/w of dry weight) to improve the cell survival and functional properties of the product. The best cell survival over the 12 months of storage was observed for the blackcurrant powder (almost no decrease) followed by strawberry (~ 0.3 log decrease), pomegranate (~ 0.9 log decrease), whereas the worst survival was obtained in cranberry powder (~ 4.5 logs). To explain these results multiple regression analysis was conducted with the log decrease [log10N0 month − log10N12 months] as the dependent variable and water activity, pH, citric acid, dietary fibre and total phenol as the independent variables. The results indicated that among all the examined factors, the [log10N0 month − log10N12 months] depended only on the water activity (P < 0.05). Inulin and gum arabic demonstrated a substantial protective effect on cell survival (1–1.5 log) in the case of cranberry, which was likely due to a physical interaction between the cells and the carbohydrates. After reconstituting the dried fruit powders at room temperature and measuring cell viability for up to 4 h, it was shown that in the case of strawberry juice there was no decrease, and very little in the case of pomegranate and blackcurrant juices (< 0.5 log). On the other hand, a significant decrease was observed for cranberry juice (P < 0.05), which increased as the storage time of the dried cranberry powder increased, indicating that the cells became more susceptible with prolonged storage. Multiple regression analysis indicated that the main factors influencing cell survival were water activity and pH, while citric acid, dietary fibre and total phenol did not have an effect. Furthermore, inulin and gum arabic addition did not have a significant (P > 0.05) effect upon reconstitution of the dried fruit powder. This study showed that instant juice powders are very good carriers of probiotic cells and constitute good alternatives to highly acidic fruit juices.

Is the unfolding of the group discussion off-pattern? Improving coordination support in educational forums using mobile devices

A forum is a valuable tool to foster reflection in an in-depth discussion; however, it forces the course mediator to continually pay close attention in order to coordinate learners` activities. Moreover, monitoring a forum is time consuming given that it is impossible to know in advance when new messages are going to be posted. Additionally, a forum may be inactive for a long period and suddenly receive a burst of messages forcing forum mediators to frequently log on in order to know how the discussion is unfolding to intervene whenever it is necessary. Mediators also need to deal with a large amount of messages to identify off-pattern situations. This work presents a piece of action research that investigates how to improve coordination support in a forum using mobile devices for mitigating mediator`s difficulties in following the status of a forum. Based on summarized information extracted from message meta-data, mediators consult visual information summaries on PDAs and receive textual notifications in their mobile phone. This investigation revealed that mediators used the mobile-based coordination support to keep informed on what is taking place within the forum without the need to log on their desktop computer. (C) 2009 Elsevier Ltd. All rights reserved.

High reynolds numbers turbulent boundary layers

Esta tesis estudia las similitudes y diferencias entre los flujos turbulentos de pared de tipo externo e interno, en régimen incompresible, y a números de Reynolds moderada¬mente altos. Para ello consideramos tanto simulaciones numéricas como experimentos de capas límites con gradiente de presiones nulo y de flujos de canal, ambos a números de Reynolds en el rango δ+ ~ 500 - 2000. Estos flujos de cortadura son objeto de numerosas investigaciones debido a la gran importancia que tienen tanto a nivel tecnológico como a nivel de física fundamental. No obstante, todavía existen muchos interrogantes sobre aspectos básicos tales como la universalidad de los perfiles medios y de fluctuación de las velocidades o de la presión, tanto en la zona cercana a la pared como en la zona logarítmica, el escalado y el efecto del número de Reynolds, o las diferencias entre los flujos internos y externos en la zona exterior. En éste estudio hemos utilizado simulaciones numéricas ya existentes de canales y capas límites a números de Reynolds δ+ ~ 2000 y δ+ ~ 700, respectivamente. Para poder comparar ambos flujos a igual número de Reynolds hemos realizado una nueva simulación directa de capa límite en el rango δ+ ~ 1000-2000. Los resultados de la misma son presentados y analizados en detalle. Los datos sin postprocesar y las estadísticas ya postprocesadas están públicamente disponibles en nuestro sitio web.162 El análisis de las estadísticas usando un único punto confirma la existencia de perfiles logarítmicos para las fluctuaciones de la velocidad transversal w'2+ y de la presión p'2+ en ambos tipos de flujos, pero no para la velocidad normal v'2+ o la velocidad longitudinal u'2+. Para aceptar o rechazar la existencia de un rango logarítmico en u'2+ se requieren números de Reynolds más altos que los considerados en éste trabajo. Una de las conse¬cuencias más importantes de poseer tales perfiles es que el valor máximo de la intensidad, que se alcanza cerca de la pared, depende explícitamente del número de Reynolds. Esto ha sido confirmado tras analizar un gran número de datos experimentales y numéricos, cor¬roborando que el máximo de u'2+, p/2+, y w'2+ aumenta proporcionalmente con el log(δ+). Por otro lado, éste máximo es más intenso en los flujos externos que en los internos. La máxima diferencia ocurre en torno a y/δ ~ 0.3-0.5, siendo esta altura prácticamente independiente del número de Reynolds considerado. Estas diferencias se originan como consecuencia del carácter intermitente de las capas límites, que es inexistente en los flujos internos. La estructura de las fluctuaciones de velocidad y de presión, junto con la de los esfuer¬zos de Reynolds, se han investigado por medio de correlaciones espaciales tridimensionales considerando dos puntos de medida. Hemos obtenido que el tamaño de las mismas es gen¬eralmente mayor en canales que en capas límites, especialmente en el caso de la correlación longitudinal Cuu en la dirección del flujo. Para esta correlación se demuestra que las es¬tructuras débilmente correladas presentan longitudes de hasta 0(75), en el caso de capas límites, y de hasta 0(185) en el caso de canales. Estas longitudes se obtienen respecti-vamente en la zona logarítmica y en la zona exterior. Las longitudes correspondientes en la dirección transversal son significativamente menores en ambos flujos, 0(5 — 25). La organización espacial de las correlaciones es compatible con la de una pareja de rollos casi paralelos con dimensiones que escalan en unidades exteriores. Esta organización se mantiene al menos hasta y ~ 0.65, altura a la cual las capas límites comienzan a organi¬zarse en rollos transversales. Este comportamiento es sin embargo más débil en canales, pudiéndose observar parcialmente a partir de y ~ 0.85. Para estudiar si estas estructuras están onduladas a lo largo de la dirección transver¬sal, hemos calculado las correlaciones condicionadas a eventos intensos de la velocidad transversal w'. Estas correlaciones revelan que la ondulación de la velocidad longitudinal aumenta conforme nos alejamos de la pared, sugiriendo que las estructuras están más alineadas en la zona cercana a la pared que en la zona lejana a ella. El por qué de esta ondulación se encuentra posiblemente en la configuración a lo largo de diagonales que presenta w'. Estas estructuras no sólo están onduladas, sino que también están inclinadas respecto a la pared con ángulos que dependen de la variable considerada, de la altura, y de el contorno de correlación seleccionado. Por encima de la zona tampón e independien¬temente del número de Reynolds y tipo de flujo, Cuu presenta una inclinación máxima de unos 10°, las correlaciones Cvv y Cm son esencialmente verticales, y Cww está inclinada a unos 35°. Summary This thesis studies the similitudes and differences between external and internal in¬compressible wall-bounded turbulent flows at moderately-high Reynolds numbers. We consider numerical and experimental zero-pressure-gradient boundary layers and chan¬nels in the range of δ+ ~ 500 — 2000. These shear flows are subjects of intensive research because of their technological importance and fundamental physical interest. However, there are still open questions regarding basic aspects such as the universality of the mean and fluctuating velocity and pressure profiles at the near-wall and logarithmic regions, their scaling and the effect of the Reynolds numbers, or the differences between internal and external flows at the outer layer, to name but a few. For this study, we made use of available direct numerical simulations of channel and boundary layers reaching δ+ ~ 2000 and δ+ ~ 700, respectively. To fill the gap in the Reynolds number, a new boundary layer simulation in the range δ+ ~ 1000-2000 is presented and discussed. The original raw data and the post-processed statistics are publicly available on our website.162 The analysis of the one-point statistic confirms the existence of logarithmic profiles for the spanwise w'2+ and pressure p'2+ fluctuations for both type of flows, but not for the wall-normal v'2+ or the streamwise u'2+ velocities. To accept or reject the existence of a logarithmic range in u'2+ requires higher Reynolds numbers than the ones considered in this work. An important consequence of having such profiles is that the maximum value of the intensities, reached near the wall, depends on the Reynolds number. This was confirmed after surveying a wide number of experimental and numerical datasets, corrob¬orating that the maximum of ul2+, p'2+, and w'2+ increases proportionally to log(δ+). On the other hand, that maximum is more intense in external flows than in internal ones, differing the most around y/δ ~ 0.3-0.5, and essentially independent of the Reynolds number. We discuss that those differences are originated as a consequence of the inter¬mittent character of boundary layers that is absent in internal flows. The structure of the velocity and pressure fluctuations, together with those of the Reynolds shear stress, were investigated using three-dimensional two-point spatial correlations. We find that the correlations extend over longer distances in channels than in boundary layers, especially in the case of the streamwise correlation Cuu in the flow direc-tion. For weakly correlated structures, the maximum streamwise length of Cuu is O(78) for boundary layers and O(188) for channels, attained at the logarithmic and outer regions respectively. The corresponding lengths for the transverse velocities and for the pressure are shorter, 0(8 — 28), and of the same order for both flows. The spatial organization of the velocity correlations is shown to be consistent with a pair of quasi-streamwise rollers that scales in outer units. That organization is observed until y ~ 0.68, from which boundary layers start to organize into spanwise rollers. This effect is weaker in channels, and it appears at y ~ 0.88. We present correlations conditioned to intense events of the transversal velocity, w', to study if these structures meander along the spanwise direction. The results indicate that the streamwise velocity streaks increase their meandering proportionally to the distance to the wall, suggesting that the structures are more aligned close to the wall than far from it. The reason behind this meandering is probably due to the characteristic organization along diagonals of w'. These structures not only meander along the spanwise direction, but they are also inclined to the wall at angles that depend on the distance from the wall, on the variable being considered, and on the correlation level used to define them. Above the buffer layer and independent of the Reynolds numbers and type of flow, the maximum inclination of Cuu is about 10°, Cvv and Cpp are roughly vertical, and Cww is inclined by 35°.

Gestión de ideas innovadoras

El trabajo de fin de grado que se va a definir detalladamente en esta memoria, trata de poner de manifiesto muchos de los conocimientos que he adquirido a lo largo de la carrera, aplicándolos en un proyecto real. Se ha desarrollado una plataforma capaz de albergar ideas, escritas por personas de todo el mundo que buscan compartirlas con los demás, para que estas sean comentadas, valoradas y entre todos poder mejorarlas. Estas ideas pueden ser de cualquier ámbito, por tanto, se da la posibilidad de clasificarlas en las categorías que mejor encajen con la idea. La aplicación ofrece una API RESTful muy descriptiva, en la que se ha identificado y estructurado cada recurso, para que a través de los “verbos http” se puedan gestionar todos los elementos de una forma fácil y sencilla, independientemente del cliente que la utilice. La arquitectura está montada siguiendo el patrón de diseño modelo vista-controlador, utilizando las últimas tecnologías del mercado como Spring, Liferay, SmartGWT y MongoDB (entre muchas otras) con el objetivo de crear una aplicación segura, escalable y modulada, por lo que se ha tenido que integrar todos estos frameworks. Los datos de la aplicación se hacen persistentes en dos tipos de bases de datos, una relacional (MySQL) y otra no relacional (MongoDB), aprovechando al máximo las características que ofrecen cada una de ellas. El cliente propuesto es accesible mediante un navegador web, se basa en el portal de Liferay. Se han desarrollado varios “Portlets o Widgets”, que componen la estructura de contenido que ve el usuario final. A través de ellos se puede acceder al contenido de la aplicación, ideas, comentarios y demás contenidos sociales, de una forma agradable para el usuario, ya que estos “Portlets” se comunican entre sí y hacen peticiones asíncronas a la API RESTful sin necesidad de recargar toda la estructura de la página. Además, los usuarios pueden registrarse en el sistema para aportar más contenidos u obtener roles que les dan permisos para realizar acciones de administración. Se ha seguido una metodología “Scrum” para la realización del proyecto, con el objetivo de dividir el proyecto en tareas pequeñas y desarrollarlas de una forma ágil. Herramientas como “Jenkins” me han ayudado a una integración continua y asegurando mediante la ejecución de los test de prueba, que todos los componentes funcionan. La calidad ha sido un aspecto principal en el proyecto, se han seguido metodologías software y patrones de diseño para garantizar un diseño de calidad, reutilizable, óptimo y modulado. El uso de la herramienta “Sonar” ha ayudado a este cometido. Además, se ha implementado un sistema de pruebas muy completo de todos los componentes de la aplicación. En definitiva, se ha diseñado una aplicación innovadora de código abierto, que establece unas bases muy definidas para que si algún día se pone en producción, sirva a las personas para compartir pensamientos o ideas ayudando a mejorar el mundo en el que vivimos. ---ABSTRACT---The Final Degree Project, described in detail in this report, attempts to cover a lot of the knowledge I have acquired during my studies, applying it to a real project. The objective of the project has been to develop a platform capable of hosting ideas from people all over the world, where users can share their ideas, comment on and rate the ideas of others and together help improving them. Since these ideas can be of any kind, it is possible to classify them into suitable categories. The application offers a very descriptive API RESTful, where each resource has been identified and organized in a way that makes it possible to easily manage all the elements using the HTTP verbs, regardless of the client using it. The architecture has been built following the design pattern model-view-controller, using the latest market technologies such as Spring, Liferay, Smart GWT and MongoDB (among others) with the purpose of creating a safe, scalable and adjustable application. The data of the application are persistent in two different kinds of databases, one relational (MySQL) and the other non-relational (MongoDB), taking advantage of all the different features each one of them provides. The suggested client is accessible through a web browser and it is based in Liferay. Various “Portlets" or "Widgets” make up the final content of the page. Thanks to these Portlets, the user can access the application content (ideas, comments and categories) in a pleasant way as the Portlets communicate with each other making asynchronous requests to the API RESTful without the necessity to refresh the whole page. Furthermore, users can log on to the system to contribute with more contents or to obtain administrator privileges. The Project has been developed following a “Scrum” methodology, with the main objective being that of dividing the Project into smaller tasks making it possible to develop each task in a more agile and ultimately faster way. Tools like “Jenkins” have been used to guarantee a continuous integration and to ensure that all the components work correctly thanks to the execution of test runs. Quality has been one of the main aspects in this project, why design patterns and software methodologies have been used to guarantee a high quality, reusable, modular and optimized design. The “Sonar” technology has helped in the achievement of this goal. Furthermore, a comprehensive proofing system of all the application's components has been implemented. In conclusion, this Project has consisted in developing an innovative, free source application that establishes a clearly defined basis so that, if it someday will be put in production, it will allow people to share thoughts and ideas, and by doing so, help them to improve the World we live in.

Integrated and Personalized Digital Information Services

Digital information services are gradually becoming integrated with other systems and services such as library automation systems, student information services, and electronic learning systems. Users demand seamless access to a multitude of digital information services without leaving their desktop computers. They prefer using systems that recognize them when they log on, acknowledge their rights and privileges, and thus provide personalized information services. This paper summarizes the recent developments concerning integrated and personalized digital information services. It first emphasizes the role of the Internet in providing information services and then goes on to discuss the integration and personalization issues by emphasizing their importance for digital information services.

An investigation on multi-vehicle motorcycle crashes using log-linear models

Motorcyclists are the most crash-prone road-user group in many Asian countries including Singapore; however, factors influencing motorcycle crashes are still not well understood. This study examines the effects of various roadway characteristics, traffic control measures and environmental factors on motorcycle crashes at different location types including expressways and intersections. Using techniques of categorical data analysis, this study has developed a set of log-linear models to investigate multi-vehicle motorcycle crashes in Singapore. Motorcycle crash risks in different circumstances have been calculated after controlling for the exposure estimated by the induced exposure technique. Results show that night-time influence increases crash risks of motorcycles particularly during merging and diverging manoeuvres on expressways, and turning manoeuvres at intersections. Riders appear to exercise more care while riding on wet road surfaces particularly during night. Many hazardous interactions at intersections tend to be related to the failure of drivers to notice a motorcycle as well as to judge correctly the speed/distance of an oncoming motorcycle. Road side conflicts due to stopping/waiting vehicles and interactions with opposing traffic on undivided roads have been found to be as detrimental factors on motorcycle safety along arterial, main and local roads away from intersections. Based on the findings of this study, several targeted countermeasures in the form of legislations, rider training, and safety awareness programmes have been recommended.

A new registration method based on Log-Euclidean tensor metrics and its application to genetic studies

In structural brain MRI, group differences or changes in brain structures can be detected using Tensor-Based Morphometry (TBM). This method consists of two steps: (1) a non-linear registration step, that aligns all of the images to a common template, and (2) a subsequent statistical analysis. The numerous registration methods that have recently been developed differ in their detection sensitivity when used for TBM, and detection power is paramount in epidemological studies or drug trials. We therefore developed a new fluid registration method that computes the mappings and performs statistics on them in a consistent way, providing a bridge between TBM registration and statistics. We used the Log-Euclidean framework to define a new regularizer that is a fluid extension of the Riemannian elasticity, which assures diffeomorphic transformations. This regularizer constrains the symmetrized Jacobian matrix, also called the deformation tensor. We applied our method to an MRI dataset from 40 fraternal and identical twins, to revealed voxelwise measures of average volumetric differences in brain structure for subjects with different degrees of genetic resemblance.

Influence of site, storage and steaming on Eucalyptus nitens log-end splitting

Key message Log-end splitting is one of the single most important defects in veneer logs. We show that log-end splitting in the temperate plantation species Eucalyptus nitens varies across sites and within-tree log position and increases with time in storage. Context Log-end splitting is one of the single most important defects in veneer logs because it can substantially reduce the recovery of veneer sheets. Eucalyptus nitens can develop log-end splits, but factors affecting log-end splitting in this species are not well understood. Aims The present study aims to describe the effect of log storage and steaming on the development of log-end splitting in logs from different plantations and log positions within the tree. Methods The study was conducted on upper and lower logs from each of 41 trees from three 20–22-year-old Tasmanian E. nitens plantations. Log-end splitting was assessed immediately after felling, after transport and storage in a log-yard, and just before peeling. A pre-peeling steam treatment was applied to half the logs. Results Site had a significant effect on splitting, and upper logs split more than lower logs with storage. Splitting increased with tree diameter breast height (DBH), but this relationship varied with site. The most rapidly growing site had more splitting even after accounting for DBH. No significant effect of steaming was detected. Conclusion Log-end splitting varied across sites and within-tree log position and increased with time in storage.

Estimating Sensor Motion from Wide-Field Optical Flow on a Log-Dipolar Sensor

Log-polar image architectures, motivated by the structure of the human visual field, have long been investigated in computer vision for use in estimating motion parameters from an optical flow vector field. Practical problems with this approach have been: (i) dependence on assumed alignment of the visual and motion axes; (ii) sensitivity to occlusion form moving and stationary objects in the central visual field, where much of the numerical sensitivity is concentrated; and (iii) inaccuracy of the log-polar architecture (which is an approximation to the central 20°) for wide-field biological vision. In the present paper, we show that an algorithm based on generalization of the log-polar architecture; termed the log-dipolar sensor, provides a large improvement in performance relative to the usual log-polar sampling. Specifically, our algorithm: (i) is tolerant of large misalignmnet of the optical and motion axes; (ii) is insensitive to significant occlusion by objects of unknown motion; and (iii) represents a more correct analogy to the wide-field structure of human vision. Using the Helmholtz-Hodge decomposition to estimate the optical flow vector field on a log-dipolar sensor, we demonstrate these advantages, using synthetic optical flow maps as well as natural image sequences.

On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

A comparative study on the modified Max-Log-MAP turbodecoding by extrinsic information scaling

A simple but effective technique to improve the performance of the Max-Log-MAP algorithm is to scale the extrinsic information exchanged between two MAP decoders. A comprehensive analysis of the selection of the scaling factors according to channel conditions and decoding iterations is presented in this paper. Choosing a constant scaling factor for all SNRs and iterations is compared with the best scaling factor selection for changing channel conditions and decoding iterations. It is observed that a constant scaling factor for all channel conditions and decoding iterations is the best solution and provides a 0.2-0.4 dB gain over the standard Max- Log-MAP algorithm. Therefore, a constant scaling factor should be chosen for the best compromise.

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades <-1 to >9) were separated, and each fraction was analysed for its chemical composition. The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø <8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar). To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend. Key words: sediment, geochemistry, grain size, regression, step function

On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.