Uniformly reweighted belief propagation for distributed Bayesian hypothesis testing

Belief propagation (BP) is a technique for distributed inference in wireless networks and is often used even when the underlying graphical model contains cycles. In this paper, we propose a uniformly reweighted BP scheme that reduces the impact of cycles by weighting messages by a constant ?edge appearance probability? rho ? 1. We apply this algorithm to distributed binary hypothesis testing problems (e.g., distributed detection) in wireless networks with Markov random field models. We demonstrate that in the considered setting the proposed method outperforms standard BP, while maintaining similar complexity. We then show that the optimal ? can be approximated as a simple function of the average node degree, and can hence be computed in a distributed fashion through a consensus algorithm.

Regression analysis of top of descent location for idle-thrust descents

In this paper, multiple regression analysis is used to model the top of descent (TOD) location of user-preferred descent trajectories computed by the flight management system (FMS) on over 1000 commercial flights into Melbourne, Australia. In addition to recording TOD, the cruise altitude, final altitude, cruise Mach, descent speed, wind, and engine type were also identified for use as the independent variables in the regression analysis. Both first-order and second-order models are considered, where cross-validation, hypothesis testing, and additional analysis are used to compare models. This identifies the models that should give the smallest errors if used to predict TOD location for new data in the future. A model that is linear in TOD altitude, final altitude, descent speed, and wind gives an estimated standard deviation of 3.9 nmi for TOD location given the trajectory parame- ters, which means about 80% of predictions would have error less than 5 nmi in absolute value. This accuracy is better than demonstrated by other ground automation predictions using kinetic models. Furthermore, this approach would enable online learning of the model. Additional data or further knowledge of algorithms is necessary to conclude definitively that no second-order terms are appropriate. Possible applications of the linear model are described, including enabling arriving aircraft to fly optimized descents computed by the FMS even in congested airspace.

Impacto del entorno institucional en la financiación público-privada de infraestructuras de transporte

Actualmente el sector privado posee un papel relevante en la provisión y gestión de infraestructuras de transporte en los países de ingreso medio‐bajo, principalmente a través de los proyectos de participación público‐privada (PPPs). Muchos países han impulsado este tipo de proyectos con el fin de hacer frente a la gran demanda de infraestructuras de transporte existente, debido a la escasez de recursos públicos y a la falta de eficiencia en la provisión de los servicios públicos. Como resultado, las PPPs han experimentado un crecimiento importante en las últimas dos décadas a nivel mundial. A pesar de esta tendencia creciente, muchos países no han sido capaces de atraer la participación del sector privado para la provisión de sus infraestructuras o no han logrado el nivel de participación privada que habrían requerido para alcanzar sus objetivos. Según numerosos autores, el desarrollo y el éxito de los proyectos PPP de infraestructuras de transporte de cualquier país está condicionado por una diversidad de factores, siendo uno de ellos la calidad de su entorno institucional. La presente tesis tiene como objetivo principal analizar la influencia del entorno institucional en el volumen de inversión en proyectos de participación público‐privada de infraestructuras de transporte en los países de ingreso medio‐bajo. Para acometer dicho objetivo se ha realizado un análisis empírico de 81 países distribuidos en seis regiones del mundo, durante el periodo 1996‐2013. En el análisis se han desarrollado dos modelos empíricos aplicando principalmente dos metodologías: el contraste de hipótesis y los modelos de datos de panel Tobit. El desarrollo de estos modelos ha permitido analizar de una forma exhaustiva el tema de estudio. Los resultados obtenidos aportan evidencia de que la calidad del entorno institucional posee una influencia significativa en el volumen de inversión en los proyectos PPP de transporte. En general, en esta tesis se muestran evidencias empíricas de que el sector privado ha tendido a invertir en mayor medida en países con entornos institucionales fuertes, es decir, en aquellos países en los que ha existido un mayor nivel de Estado de derecho, estabilidad política y regulatoria, efectividad del gobierno, así como un mayor control de la corrupción. Además, aquellos países donde se ha registrado una mejora en el nivel de su calidad institucional también han experimentado un incremento en el volumen de inversión en PPP de transporte. The private sector has an important role in the provision and management of transport infrastructure in countries of medium‐low income, primarily through projects of public‐private partnerships (PPPs). Many countries have developed PPP projects to meet the high demand of transport infrastructure, due to the scarcity of public resources and the lack of efficiency in the provision of public services. As a result, PPPs have experienced a significant growth, worldwide, in the past two decades. Despite this growing trend, many countries have not been able to attract private sector participation in the provision of infrastructure or have not accomplished the level of private participation that would have required to achieve its objectives. According to various authors, the development of PPP projects for transport infrastructure is determined by a number of factors, one of them being the quality of the institutional environment. The main objective of this dissertation is to analyze the influence of the institutional environment on the volume of investment, in projects of public‐private partnerships for transport infrastructure in countries of medium‐low income. In order to meet this objective, we conducted an empirical analysis of 81 countries, in six regions of the world, during the period of 1996‐2013. The analysis used two empirical models, implementing different methodologies and various statistical techniques: hypothesis testing, and Tobit model using panel data. The development of these models allowed to carry out a more comprehensive analysis. The results show that the quality of the institutional environment has a significant influence on the volume of investment in PPP projects of transport. Overall, this dissertation shows that the private sector tends to invest more in countries with stronger institutional environments, i.e. countries where there has been a higher level of Rule of Law, political and regulatory stability, and an effective control of corruption. In addition, those that have improved the level of institutional quality have also experienced an increase in the volume of investment in PPP of transport.

Descripción de parámetros glóticos basados en el modelado de los pliegues vocales para la detección de patología de la voz

Las patologías de la voz se han transformado en los últimos tiempos en una problemática social con cierto calado. La contaminación de las ciudades, hábitos como el de fumar, el uso de aparatos de aire acondicionado, etcétera, contribuyen a ello. Esto alcanza más relevancia en profesionales que utilizan su voz de manera frecuente, como, por ejemplo, locutores, cantantes, profesores o teleoperadores. Por todo ello resultan de especial interés las técnicas de ayuda al diagnóstico que son capaces de extraer conclusiones clínicas a partir de una muestra de la voz grabada con un micrófono, frente a otras invasivas que implican la exploración utilizando laringoscopios, fibroscopios o videoendoscopios, técnicas en cualquier caso mucho más molestas para los pacientes al exigir la introducción parcial del instrumental citado por la garganta, en actuaciones consideradas de tipo quirúrgico. Dentro de aquellas técnicas se ha avanzado mucho en un período de tiempo relativamente corto. En lo que se refiere al diagnóstico de patologías, hemos pasado en los últimos quince años de trabajar principalmente con parámetros extraídos de la señal de voz –tanto en el dominio del tiempo como en el de la frecuencia– y con escalas elaboradas con valoraciones subjetivas realizadas por expertos a hacerlo también con parámetros procedentes de estimaciones de la fuente glótica. La importancia de utilizar la fuente glótica reside, a grandes rasgos, en que se trata de una señal vinculada directamente al estado de la estructura laríngea del locutor y también en que está generalmente menos influida por el tracto vocal que la señal de voz. Es conocido que el tracto vocal guarda más relación con el mensaje hablado, y su presencia dificulta el proceso de detección de patología vocal. Estas estimaciones de la fuente glótica han sido obtenidas a través de técnicas de filtrado inverso desarrolladas por nuestro grupo de investigación. Hemos conseguido, además, profundizar en la naturaleza de la señal glótica: somos capaces de descomponerla y relacionarla con parámetros biomecánicos de los propios pliegues vocales, obteniendo estimaciones de elementos como la masa, la pérdida de energía o la elasticidad del cuerpo y de la cubierta del pliegue, entre otros. De las componentes de la fuente glótica surgen también los denominados parámetros biométricos, relacionados con la forma de la señal, que constituyen por sí mismos una firma biométrica del individuo. También trabajaremos con parámetros temporales, relacionados con las diferentes etapas que se observan dentro de la señal glótica durante un ciclo de fonación. Por último, consideraremos parámetros clásicos de perturbación y energía de la señal. En definitiva, contamos ahora con una considerable cantidad de parámetros glóticos que conforman una base estadística multidimensional, destinada a ser capaz de discriminar personas con voces patológicas o disfónicas de aquellas que no presentan patología en la voz o con voces sanas o normofónicas. Esta tesis doctoral se ocupa de varias cuestiones: en primer lugar, es necesario analizar cuidadosamente estos nuevos parámetros, por lo que ofreceremos una completa descripción estadística de los mismos. También estudiaremos cuestiones como la distribución de los parámetros atendiendo a criterios como el de normalidad estadística de los mismos, ocupándonos especialmente de la diferencia entre las distribuciones que presentan sujetos sanos y sujetos con patología vocal. Para todo ello emplearemos diferentes técnicas estadísticas: generación de elementos y diagramas descriptivos, pruebas de normalidad y diversos contrastes de hipótesis, tanto paramétricos como no paramétricos, que considerarán la diferencia entre los grupos de personas sanas y los grupos de personas con alguna patología relacionada con la voz. Además, nos interesa encontrar relaciones estadísticas entre los parámetros, de cara a eliminar posibles redundancias presentes en el modelo, a reducir la dimensionalidad del problema y a establecer un criterio de importancia relativa en los parámetros en cuanto a su capacidad discriminante para el criterio patológico/sano. Para ello se aplicarán técnicas estadísticas como la Correlación Lineal Bivariada y el Análisis Factorial basado en Componentes Principales. Por último, utilizaremos la conocida técnica de clasificación Análisis Discriminante, aplicada a diferentes combinaciones de parámetros y de factores, para determinar cuáles de ellas son las que ofrecen tasas de acierto más prometedoras. Para llevar a cabo la experimentación se ha utilizado una base de datos equilibrada y robusta formada por doscientos sujetos, cien de ellos pertenecientes al género femenino y los restantes cien al género masculino, con una proporción también equilibrada entre los sujetos que presentan patología vocal y aquellos que no la presentan. Una de las aplicaciones informáticas diseñada para llevar a cabo la recogida de muestras también es presentada en esta tesis. Los distintos estudios estadísticos realizados nos permitirán identificar aquellos parámetros que tienen una mayor contribución a la hora de detectar la presencia de patología vocal. Alguno de los estudios, además, nos permitirá presentar una ordenación de los parámetros en base a su importancia para realizar la detección. Por otra parte, también concluiremos que en ocasiones es conveniente realizar una reducción de la dimensionalidad de los parámetros para mejorar las tasas de detección. Por fin, las propias tasas de detección constituyen quizá la conclusión más importante del trabajo. Todos los análisis presentes en el trabajo serán realizados para cada uno de los dos géneros, de acuerdo con diversos estudios previos que demuestran que los géneros masculino y femenino deben tratarse de forma independiente debido a las diferencias orgánicas observadas entre ambos. Sin embargo, en lo referente a la detección de patología vocal contemplaremos también la posibilidad de trabajar con la base de datos unificada, comprobando que las tasas de acierto son también elevadas. Abstract Voice pathologies have become recently in a social problem that has reached a certain concern. Pollution in cities, smoking habits, air conditioning, etc. contributes to it. This problem is more relevant for professionals who use their voice frequently: speakers, singers, teachers, actors, telemarketers, etc. Therefore techniques that are capable of drawing conclusions from a sample of the recorded voice are of particular interest for the diagnosis as opposed to other invasive ones, involving exploration by laryngoscopes, fiber scopes or video endoscopes, which are techniques much less comfortable for patients. Voice quality analysis has come a long way in a relatively short period of time. In regard to the diagnosis of diseases, we have gone in the last fifteen years from working primarily with parameters extracted from the voice signal (both in time and frequency domains) and with scales drawn from subjective assessments by experts to produce more accurate evaluations with estimates derived from the glottal source. The importance of using the glottal source resides broadly in that this signal is linked to the state of the speaker's laryngeal structure. Unlike the voice signal (phonated speech) the glottal source, if conveniently reconstructed using adaptive lattices, may be less influenced by the vocal tract. As it is well known the vocal tract is related to the articulation of the spoken message and its influence complicates the process of voice pathology detection, unlike when using the reconstructed glottal source, where vocal tract influence has been almost completely removed. The estimates of the glottal source have been obtained through inverse filtering techniques developed by our research group. We have also deepened into the nature of the glottal signal, dissecting it and relating it to the biomechanical parameters of the vocal folds, obtaining several estimates of items such as mass, loss or elasticity of cover and body of the vocal fold, among others. From the components of the glottal source also arise the so-called biometric parameters, related to the shape of the signal, which are themselves a biometric signature of the individual. We will also work with temporal parameters related to the different stages that are observed in the glottal signal during a cycle of phonation. Finally, we will take into consideration classical perturbation and energy parameters. In short, we have now a considerable amount of glottal parameters in a multidimensional statistical basis, designed to be able to discriminate people with pathologic or dysphonic voices from those who do not show pathology. This thesis addresses several issues: first, a careful analysis of these new parameters is required, so we will offer a complete statistical description of them. We will also discuss issues such as distribution of the parameters, considering criteria such as their statistical normality. We will take special care in the analysis of the difference between distributions from healthy subjects and the distributions from pathological subjects. To reach these goals we will use different statistical techniques such as: generation of descriptive items and diagramas, tests for normality and hypothesis testing, both parametric and nonparametric. These latter techniques consider the difference between the groups of healthy subjects and groups of people with an illness related to voice. In addition, we are interested in finding statistical relationships between parameters. There are various reasons behind that: eliminate possible redundancies in the model, reduce the dimensionality of the problem and establish a criterion of relative importance in the parameters. The latter reason will be done in terms of discriminatory power for the criterion pathological/healthy. To this end, statistical techniques such as Bivariate Linear Correlation and Factor Analysis based on Principal Components will be applied. Finally, we will use the well-known technique of Discriminant Analysis classification applied to different combinations of parameters and factors to determine which of these combinations offers more promising success rates. To perform the experiments we have used a balanced and robust database, consisting of two hundred speakers, one hundred of them males and one hundred females. We have also used a well-balanced proportion where subjects with vocal pathology as well as subjects who don´t have a vocal pathology are equally represented. A computer application designed to carry out the collection of samples is also presented in this thesis. The different statistical analyses performed will allow us to determine which parameters contribute in a more decisive way in the detection of vocal pathology. Therefore, some of the analyses will even allow us to present a ranking of the parameters based on their importance for the detection of vocal pathology. On the other hand, we will also conclude that it is sometimes desirable to perform a dimensionality reduction in order to improve the detection rates. Finally, detection rates themselves are perhaps the most important conclusion of the work. All the analyses presented in this work have been performed for each of the two genders in agreement with previous studies showing that male and female genders should be treated independently, due to the observed functional differences between them. However, with regard to the detection of vocal pathology we will consider the possibility of working with the unified database, ensuring that the success rates obtained are also high.

Large-scale testing of proficiency in English: Back to multiple choice?

The paper analyses whether that a properly designed multiple choice test can discriminate with a high level of accuracy if a student in our context has reached a B2 level according to the CEFRL.

A general framework to testing the effect of transport policy measures to achieve a modal shift: a sequental hybrid model

In order to achieve to minimize car-based trips, transport planners have been particularly interested in understanding the factors that explain modal choices. In the transport modelling literature there has been an increasing awareness that socioeconomic attributes and quantitative variables are not sufficient to characterize travelers and forecast their travel behavior. Recent studies have also recognized that users? social interactions and land use patterns influence travel behavior, especially when changes to transport systems are introduced, but links between international and Spanish perspectives are rarely deal. In this paper, factorial and path analyses through a Multiple-Indicator Multiple-Cause (MIMIC) model are used to understand and describe the relationship between the different psychological and environmental constructs with social influence and socioeconomic variables. The MIMIC model generates Latent Variables (LVs) to be incorporated sequentially into Discrete Choice Models (DCM) where the levels of service and cost attributes of travel modes are also included directly to measure the effect of the transport policies that have been introduced in Madrid during the last three years in the context of the economic crisis. The data used for this paper are collected from a two panel smartphone-based survey (n=255 and 190 respondents, respectively) of Madrid.

Design, development and construction of an outdoor testing facility for semi-transparent photovoltaic modules

Building-integrated Photovoltaics (BIPV) is one of the most promising technologies enabling buildings to generate on-site part of their electricity needs while performing architectural functionalities. A clear example of BIPV products consists of semi-transparent photovoltaic modules (STPV), designed to replace the conventional glazing solutions in building façades. Accordingly, the active building envelope is required to perform multiple requirements such as provide solar shading to avoid overheating, supply solar gains and thermal insulation to reduce heat loads and improve daylight utilization. To date, various studies into STPV systems have focused on their energy performance based on existing simulation programs, or on the modelling, normally validated by limited experimental data, of the STPV modules thermal behaviour. Taking into account that very limited experimental research has been conducted on the energy performance of STPV elements and that the characterization in real operation conditions is necessary to promote an energetically efficient integration of this technology in the building envelope, an outdoor testing facility has been designed, developed and built at the Solar Energy Institute of the Technical University of Madrid. In this work, the methodology used in the definition of the testing facility, its capability and limitations are presented and discussed.

Large-scale assessment of language proficiency: theoretical and pedagogical reflections on the use of multiple-choice tests

The new requirement placed on students in tertiary settings in Spain to demonstrate a B1 or a B2 proficiency level of English, in accordance with the Common European Framework of Reference for Languages (CEFRL), has led most Spanish universities to develop a program of certification or accreditation of the required level. The first part of this paper aims to provide a rationale for the type of test that has been developed at the Universidad Politécnica de Madrid for the accreditation of a B2 level, a multiple choice version, and to describe how it was constructed and validated. Then, in the second part of the paper, the results from its application to 924 students enrolled in different degree courses at a variety of schools and faculties at the university are analyzed based on a final test version item analysis. To conclude, some theoretical as well as practical conclusions about testing grammar that affect the teaching and learning process are drawn. RESUMEN. Las nuevas exigencias sobre niveles de competencia B1 y B2 en inglés según el Marco Común Europeo de Referencia para las Lenguas (MCERL) que se imponen sobre los estudiantes de grado y posgrado han llevado a la mayoría de las universidades españolas a desarrollar programas de acreditación o de certificación de estos niveles. La primera parte de este trabajo trata sobre las razones que fundamentan la elección de un tipo concreto de examen para la acreditación del nivel B2 de lengua inglesa en la Universidad Politécnica de Madrid. Se trata de un test de opción múltiple y en esta parte del trabajo se describe cómo fue diseñado y validado. En la segunda parte, se analizan los resultados de la aplicación del test a gran escala a un total de 924 estudiantes matriculados en varias escuelas y Facultades de la Universidad. Para terminar, se apuntan una serie de conclusiones teóricas y prácticas sobre la evaluación de la gramática y de qué modo influye en los procesos de enseñanza y aprendizaje.

REST service testing based on inferred XML schemas

The concept of service oriented architecture has been extensively explored in software engineering, due to the fact that it produces architectures made up of several interconnected modules, easy to reuse when building new systems. This approach to design would be impossible without interconnection mechanisms such as REST (Representationa State Transfer) services, which allow module communication while minimizing coupling. . However, this low coupling brings disadvantages, such as the lack of transparency, which makes it difficult to sistematically create tests without knowledge of the inner working of a system. In this article, we present an automatic error detection system for REST services, based on a statistical analysis over responses produced at multiple service invocations. Thus, a service can be systematically tested without knowing its full specification. The method can find errors in REST services which could not be identified by means of traditional testing methods, and provides limited testing coverage for services whose response format is unknown. It can be also useful as a complement to other testing mechanisms.

Testing of Android testing tools: development of a benchmark for the evaluation

With the ever growing trend of smart phones and tablets, Android is becoming more and more popular everyday. With more than one billion active users i to date, Android is the leading technology in smart phone arena. In addition to that, Android also runs on Android TV, Android smart watches and cars. Therefore, in recent years, Android applications have become one of the major development sectors in software industry. As of mid 2013, the number of published applications on Google Play had exceeded one million and the cumulative number of downloads was more than 50 billionii. A 2013 survey also revealed that 71% of the mobile application developers work on developing Android applicationsiii. Considering this size of Android applications, it is quite evident that people rely on these applications on a daily basis for the completion of simple tasks like keeping track of weather to rather complex tasks like managing one’s bank accounts. Hence, like every other kind of code, Android code also needs to be verified in order to work properly and achieve a certain confidence level. Because of the gigantic size of the number of applications, it becomes really hard to manually test Android applications specially when it has to be verified for various versions of the OS and also, various device configurations such as different screen sizes and different hardware availability. Hence, recently there has been a lot of work on developing different testing methods for Android applications in Computer Science fraternity. The model of Android attracts researchers because of its open source nature. It makes the whole research model more streamlined when the code for both, application and the platform are readily available to analyze. And hence, there has been a great deal of research in testing and static analysis of Android applications. A great deal of this research has been focused on the input test generation for Android applications. Hence, there are a several testing tools available now, which focus on automatic generation of test cases for Android applications. These tools differ with one another on the basis of their strategies and heuristics used for this generation of test cases. But there is still very little work done on the comparison of these testing tools and the strategies they use. Recently, some research work has been carried outiv in this regard that compared the performance of various available tools with respect to their respective code coverage, fault detection, ability to work on multiple platforms and their ease of use. It was done, by running these tools on a total of 60 real world Android applications. The results of this research showed that although effective, these strategies being used by the tools, also face limitations and hence, have room for improvement. The purpose of this thesis is to extend this research into a more specific and attribute-­‐ oriented way. Attributes refer to the tasks that can be completed using the Android platform. It can be anything ranging from a basic system call for receiving an SMS to more complex tasks like sending the user to another application from the current one. The idea is to develop a benchmark for Android testing tools, which is based on the performance related to these attributes. This will allow the comparison of these tools with respect to these attributes. For example, if there is an application that plays some audio file, will the testing tool be able to generate a test input that will warrant the execution of this audio file? Using multiple applications using different attributes, it can be visualized that which testing tool is more useful for which kinds of attributes. In this thesis, it was decided that 9 attributes covering the basic nature of tasks, will be targeted for the assessment of three testing tools. Later this can be done for much more attributes to compare even more testing tools. The aim of this work is to show that this approach is effective and can be used on a much larger scale. One of the flagship features of this work, which also differentiates it with the previous work, is that the applications used, are all specially made for this research. The reason for doing that is to analyze just that specific attribute in isolation, which the application is focused on, and not allow the tool to get bottlenecked by something trivial, which is not the main attribute under testing. This means 9 applications, each focused on one specific attribute. The main contributions of this thesis are: A summary of the three existing testing tools and their respective techniques for automatic test input generation of Android Applications. • A detailed study of the usage of these testing tools using the 9 applications specially designed and developed for this study. • The analysis of the obtained results of the study carried out. And a comparison of the performance of the selected tools.

Testing of crop Models for Accurate Predictions of Evapotranspiration and crop Water Use

All crop models, whether site-specific or global-gridded and regardless of crop, simulate daily crop transpiration and soil evaporation during the crop life cycle, resulting in seasonal crop water use. Modelers use several methods for predicting daily potential evapotranspiration (ET), including FAO-56, Penman-Monteith, Priestley-Taylor, Hargreaves, full energy balance, and transpiration water efficiency. They use extinction equations to partition energy to soil evaporation or transpiration, depending on leaf area index. Most models simulate soil water balance and soil-root water supply for transpiration, and limit transpiration if water uptake is insufficient, and thereafter reduce dry matter production. Comparisons among multiple crop and global gridded models in the Agricultural Model Intercomparison and Improvement Project (AgMIP) show surprisingly large differences in simulated ET and crop water use for the same climatic conditions. Model intercomparisons alone are not enough to know which approaches are correct. There is an urgent need to test these models against field-observed data on ET and crop water use. It is important to test various ET modules/equations in a model platform where other aspects such as soil water balance and rooting are held constant, to avoid compensation caused by other parts of models. The CSM-CROPGRO model in DSSAT already has ET equations for Priestley-Taylor, Penman-FAO-24, Penman-Monteith-FAO-56, and an hourly energy balance approach. In this work, we added transpiration-efficiency modules to DSSAT and AgMaize models and tested the various ET equations against available data on ET, soil water balance, and season-long crop water use of soybean, fababean, maize, and other crops where runoff and deep percolation were known or zero. The different ET modules created considerable differences in predicted ET, growth, and yield.

On multiple-path sonic anemometer measurement theory

In this paper, a model of the measuring process of sonic anemometers with more than one measuring path is presented. The main hypothesis of the work is that the time variation of the turbulent speed field during the sequence of pulses that produces a measure of the wind speed vector affects the measurement. Therefore, the previously considered frozen flow, or instantaneous averaging, condition is relaxed. This time variation, quantified by the mean Mach number of the flow and the time delay between consecutive pulses firings, in combination with both the full geometry of sensors (acoustic path location and orientation) and the incidence angles of the mean with speed vector, give rise to significant errors in the measurement of turbulence which are not considered by models based on the hypothesis of instantaneous line averaging. The additional corrections (relative to the ones proposed by instantaneous line-averaging models) are strongly dependent on the wave number component parallel to the mean wind speed, the time delay between consecutive pulses, the Mach number of the flow, the geometry of the sensor and the incidence angles of mean wind speed vector. Kaimal´s limit k W1=1/l (where k W1 is the wave number component parallel to mean wind speed and l is the path length) for the maximum wave numbers from which the sonic process affects the measurement of turbulence is here generalized as k W1=C l /l, where C l is usually lesser than unity and depends on all the new parameters taken into account by the present model.