972 resultados para T-squared statistics


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This paper summarizes the main results of a unique firm survey conducted in Vietnam in 2011 on product-related environmental regulations (PRERs). The results of this survey are compared with the results of a corresponding survey of firms in Penang, Malaysia (Michida, et al. 2014b). The major findings are as follows. First, adaptation to PRERs involves changes in input procurement and results in market diversification, which potentially alters the structure of supply chains. This finding is consistent with the Malaysian survey result. Second, connections to global supply chains are key to compliance, but this requires firms to meet more stringent customer requirements. Third, government policy can play an important role in assisting firms to comply with PRERs.

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We present an analysis of the space-time dynamics of oceanic sea states exploiting stereo imaging techniques. In particular, a novel Wave Acquisition Stereo System (WASS) has been developed and deployed at the oceanographic tower Acqua Alta in the Northern Adriatic Sea, off the Venice coast in Italy. The analysis of WASS video measurements yields accurate estimates of the oceanic sea state dynamics, the associated directional spectra and wave surface statistics that agree well with theoretical models. Finally, we show that a space-time extreme, defined as the expected largest surface wave height over an area, is considerably larger than the maximum crest observed in time at a point, in agreement with theoretical predictions.

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Hunting is assuming a growing role in the current European forestry and agroforestry landscape. However, consistent statistical sources that provide quantitative information for policy-making, planning and management of game resources are often lacking. In addition, in many instances statistical information can be used without sufficient evaluation or criticism. Recently, the European Commission has declared the importance of high quality hunting statistics and the need to set up a common scheme in Europe for their collection, interpretation and proper use. This work aims to contribute to this current debate on hunting statistics in Europe by exploring data from the last 35 years of Spanish hunting statistics. The analysis focuses on the three major pillars underpinning hunting activity: hunters, hunting grounds and game animals. First, the study aims to provide a better understanding of official hunting statistics for use by researchers, game managers and other potential users. Second, the study highlights the major strengths and weaknesses of the statistical information that was collected. The results of the analysis indicate that official hunting statistics can be incomplete, dispersed and not always homogeneous over a long period of time. This is an issue of which one should be aware when using official hunting data for scientific or technical work. To improve statistical deficiencies associated with hunting data in Spain, our main suggestion is the adoption of a common protocol on data collection to which different regions agree. This protocol should be in accordance with future European hunting statistics and based on robust and well-informed data collection methods. Also it should expand the range of biological, ecological and economic concepts currently included to take account of the profound transformations experienced by the hunting sector in recent years. As much as possible, any future changes in the selection of hunting statistics should allow for comparisons between new variables with the previous ones.

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In this work, the capacity and the interference statistics of the uplink of high-altitude platforms (HAPs) for asynchronous and synchronous WCDMA system assuming finite transmission power and imperfect power control are studied. Propagation loss used to calculate the received signal power is due to the distance, shadowing, and wall insertion loss. The uplink capacity for 3- and 3.75-G services is given for different cell radius assuming outdoor and indoor voice users only, data users only and a combination of the two services. For 37 macrocells HAP, the total uplink capacity is 3,034 outdoor voice users or 444 outdoor data users. When one or more than one user is an indoor user, the uplink capacity is 2,923 voice users or 444 data users when the walls entry loss is 10 dB. It is shown that the effect of the adjacent channels interference is very small.

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The peak temperature in the corona of plasma ejected by a laser-irradiated slab is discussed in terms of a one-electron-temperature model. Both heat-flux saturation and pulse rise-time effects are considered;the intensity in the rising half of the pulse is approximated by a linear function of time, I(t) = Iot/r. The temperature is found to be proportional to (IQX2)273 and a function of I0X4/r. Above a certain value of I0X4/T, the plasma presents two characteristic temperatures (at saturation and at the critical surface) which can be identified with experimentally observed cold- and hot-electron temperatures. The results are compared with extensive experimental data available for both nd and CO2 lasers, I0(W'cnf2) X2 (/um) starting around 1012. The agreement is good if substantial flux inhibition is assumed (flux-limit factor f = 0.03), and fails for I0X2 above 1O1S. Results for both ablation pressure and mass ablation rate are also given.

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The aim of the study was to evaluate the inter-operator reliability of OPTA Client System which is used to collect live football match statistics by OPTA Sportsdata Company. Two groups of experienced operators were required to analyze a Spanish league match independently. Results showed that team events coded by independent operators reached a very good agreement (kappa values were 0.92 and 0.94) and average difference of event time was 0.06±0.04 s. The reliability of goalkeeper actions was also at high level, kappa values were 0.92 and 0.86. The high intra-class correlation coefficients (ranged from 0.88 to 1.00) and low standardized typical errors (varied from 0.00 to 0.37) of different match actions and indicators of individual outfield players showed a high level of inter-operator reliability as well. These results suggest that the OPTA Client System is reliable to be used to collect live football match statistics by well trained operators.

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In this work, we use large eddy simulations (LES) and Lagrangian tracking to study the influence of gravity on particle statistics in a fully developed turbulent upward/downward flow in a vertical channel and pipe at matched Kàrmàn number. Only drag and gravity are considered in the equation of motion for solid particles, which are assumed to have no influence on the flow field. Particle interactions with the wall are fully elastic. Our findings obtained from the particle statistics confirm that: (i) the gravity seems to modify both the quantitative and qualitative behavior of the particle distribution and statistics of the particle velocity in wall normal direction; (ii) however, only the quantitative behavior of velocity particle in streamwise direction and the root mean square of velocity components is modified; (iii) the statistics of fluid and particles coincide very well near the wall in channel and pipe flow with equal Kàrmàn number; (iv) pipe curvature seems to have quantitative and qualitative influence on the particle velocity and on the particle concentration in wall normal direction.

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Este trabajo de investigación trata de aportar luz al estudio del tiempo de reacción (TR) en velocistas con y sin discapacidad auditiva desde las Ciencias del Deporte. El planteamiento del presente estudio surgió al cuestionarnos la existencia de las diferencias en cuanto al TR visual y auditivo aplicado a velocistas con y sin discapacidad auditiva, pensando en el desarrollo futuro de competiciones inclusivas entre ambos colectivos. Por ello, este estudio trata de resolver las dificultades que los velocistas con discapacidad se encuentran habitualmente en las competiciones. A priori, los atletas con discapacidad auditiva compiten en inferioridad de condiciones como consecuencia de una salida que no parece la más adecuada para ellos (desde los tacos, han de mirar hacia la pistola del juez o el movimiento de un rival). El documento se divide en tres partes. En la primera parte se realiza la pertinente revisión del marco teórico y justificación del estudio. La segunda parte se centra en los objetivos de la investigación, el material y el método, donde se muestran los resultados, discusión y conclusiones del estudio realizado, así como las limitaciones del presente trabajo y sus futuras líneas de investigación. La tercera parte corresponde a la bibliografía y la cuarta parte a los anexos. En la primera parte, presentamos el marco teórico compuesto por cinco capítulos organizan la fundamentación que hemos realizado como revisión sobre los aspectos más destacados del TR, determinado por las características de la tarea y otros factores que influyen en el TR como objeto de nuestro estudio. Después exponemos los principales aspectos estructurales y funcionales del sistema nervioso (SN) relacionados con el TR visual y auditivo. Tras ello se expone la realidad del deporte para personas con discapacidad auditiva, indagando en sus peculiaridades y criterios de elegibilidad que tiene ese colectivo dentro del ámbito deportivo. A continuación abordamos el estudio de la salida de velocidad en el atletismo, como aspecto clave que va a guiar nuestra investigación, especialmente los parámetros determinantes en la colocación de los tacos de salida para atletas con y sin discapacidad auditiva, la posición de salida y la propia colocación de los estímulos en dicha situación. Es la segunda parte se desarrolla el trabajo de investigación que tiene como objetivos estudiar los valores de TR visual simple manual, TR en salida de tacos y los tiempos de desplazamiento a los 10m y 20m de velocistas con y sin discapacidad auditiva, así como analizar las posibles diferencias en TR según posición y tipo de estímulo luminoso, respecto a ambos grupos de atletas. Como tercer objetivo de estudio se evalúa cualitativamente, por parte de los propios atletas, el dispositivo luminoso utilizado. La toma de datos de este estudio se llevó a cabo entre los meses de febrero y mayo del 2014, en el módulo de atletismo del Centro de Alto Rendimiento Joaquín Blume (Madrid), con dos grupos de estudio, uno de 9 velocistas con discapacidad auditiva (VDA), conformando éstos el 60% de toda la población en España, según el número de las licencias de la FEDS en la modalidad de atletismo (velocistas, pruebas de 100 y 200 m.l.), en el momento del estudio, y otro de 13 velocistas sin discapacidad (VsDA) que se presentaron de manera voluntaria con unos mismos criterios de inclusión para ambos grupos. Para la medición y el registro de los datos se utilizaron materiales como hoja de registro, Medidor de Tiempo de Reacción (MTR), tacos de salida, ReacTime®, dispositivo luminoso conectado a los tacos de salida, células fotoeléctricas, ordenador y software del ReacTime, y cámara de video. La metodología utilizada en este estudio fue de tipo correlacional, analizando los resultados del TR simple manual según vía sensitiva (visual y auditiva) entre los dos grupos de VDA y VsDA. También se estudiaron los TR desde la salida de tacos en función de la colocación del dispositivo luminoso (en el suelo y a 5 metros, vía visual) y pistola de salida atlética (vía auditiva) así como el tiempo de desplazamiento a los 10m (t10m) y 20m (t20m) de ambos grupos de velocistas. Finalmente, se desarrolló y llevó a cabo un cuestionario de evaluación por parte de los atletas VDA con el objetivo de conocer el grado de satisfacción después de haber realizado la serie de experimentos con el dispositivo luminoso y adaptado para sistemas de salida en la velocidad atlética. Con el objetivo de comprobar la viabilidad de la metodología descrita y probar en el contexto de análisis real el protocolo experimental, se realizó un estudio piloto con el fin de conocer las posibles diferencias del TR visual desde los tacos de salida en velocistas con discapacidad auditiva, usando para dicha salida un estímulo visual mediante un dispositivo luminoso coordinado con la señal sonora de salida (Soto-Rey, Pérez-Tejero, Rojo-González y Álvarez-Ortiz, 2015). En cuanto a los procedimientos estadísticos utilizados, con el fin de analizar la distribución de los datos y su normalidad, se aplicó la prueba de Kolmogorov-Smirnof, dicha prueba arrojó resultados de normalidad para todas las variables analizadas de las situaciones experimentales EA, EVsuelo y EV5m. Es por ello que en el presente trabajo de investigación se utilizó estadística paramétrica. Como medidas descriptivas, se calcularon el máximo, mínimo, media y la desviación estándar. En relación a las situaciones experimentales, para estudiar las posibles diferencias en las variables estudiadas dentro de cada grupo de velocistas (intragrupo) en la situación experimental 1 (MTR), se empleó una prueba T de Student para muestras independientes. En las situaciones experimentales 2, 3 y 4, para conocer las diferencias entre ambos grupos de velocistas en cada situación, se utilizó igualmente la prueba T para muestras independientes, mientras que un ANOVA simple (con post hoc Bonferroni) se utilizó para analizar las diferencias para cada grupo (VDA y VsDA) por situación experimental. Así mismo, se utilizó un ANOVA de medidas repetidas, donde el tipo de estímulo (situación experimental) fue la variable intra-grupo y el grupo de velocistas participantes (VDA y VsDA) la entre-grupo, realizándose esta prueba para evaluar en cada situación el TR, t1m0 y t20m y las interacciones entre las variables. Para el tratamiento estadístico fue utilizado el paquete estadístico SPSS 18.0 (Chicago, IL, EEUU). Los niveles de significación fueron establecidos para un ≤0.05, indicando el valor de p en cada caso. Uno de los aspectos más relevantes de este trabajo es la medición en diferentes situaciones, con instrumentación distinta y con situaciones experimentales distintas, del TR en velocistas con y sin discapacidad auditiva. Ello supuso el desarrollo de un diseño de investigación que respondió a las necesidades planteadas por los objetivos del estudio, así como el desarrollo de instrumentación específica (Rojo-Lacal, Soto-Rey, Pérez-Tejero y Rojo-González, 2014; Soto-Rey et al., 2015) y distintas situaciones experimentales que reprodujeran las condiciones de práctica y competición real de VsDA y VDA en las pruebas atléticas de velocidad, y más concretamente, en las salidas. El análisis estadístico mostró diferencias significativas entre los estímulos visuales y sonoros medidos con el MTR, siendo menor el TR ante el estímulo visual que ante el sonoro, tanto para los atletas con discapacidad auditiva como para los que no la presentaron (TR visual, 0.195 s ± 0.018 vs 0.197 s ± 0.022, p≤0.05; TR sonoro 0.230 s ± 0.016 vs 0.237 s ± 0.045, p≤0.05). Teniendo en cuenta los resultados según población objeto de estudio y situación experimental, se registraron diferencias significativas entre ambas poblaciones, VDA y VsDA, siendo más rápidos los VDA que VsDA en la situación experimental con el estímulo visual en el suelo (EVsuelo, 0.191 ±0.025 vs 0.210 ±0.025, p≤0.05, respectivamente) y los VsDA en la situación experimental con el estímulo auditivo (EA, 0.396 ±0.045 vs 0.174 ±0.021, p≤0.05), aunque sin diferencias entre ambos grupos en la situación experimental con el estímulo visual a 5m de los tacos de salida. Es de destacar que en el TR no hubo diferencias significativas entre EA para VsDA y EVsuelo para VDA. El ANOVA simple registró diferencias significativas en todas las situaciones experimentales dentro de cada grupo y para todas las variables, por lo que estadísticamente, las situaciones experimentales fueron diferentes entre sí. En relación al de ANOVA medidas repetidas, la prueba de esfericidad se mostró adecuada, existiendo diferencias significativas en las varianzas de los pares de medias: el valor de F indicó que existieron diferencias entre las diferentes situaciones experimentales en cuanto a TR, incluso cuando éstas se relacionaban con el factor discapacidad (factor interacción, p≤0,05). Por ello, queda patente que las situaciones son distintas entre sí, también teniendo en cuenta la discapacidad. El η2 (eta al cuadrado, tamaño del efecto, para la interacción) indica que el 91.7% de la variación se deben a las condiciones del estudio, y no al error (indicador de la generalización de los resultados del estudio). Por otro lado, la evaluación del dispositivo luminoso fue positiva en relación a la iluminación, comodidad de uso, ubicación, color, tamaño, adecuación del dispositivo y del equipamiento necesario para adaptar al sistema de salida. La totalidad de los atletas afirman rotundamente que el dispositivo luminoso favorecería la adaptación al sistema de salida atlética para permitir una competición inclusiva. Asimismo concluyen que el dispositivo luminoso favorecería el rendimiento o mejora de marca en la competición. La discusión de este estudio presenta justificación de las diferencias demostradas que el tipo de estímulo y su colocación son clave en el TR de esta prueba, por lo que podríamos argumentar la necesidad de contar con dispositivos luminosos para VDA a la hora de competir con VsDA en una misma prueba, inclusiva. El presente trabajo de investigación ha demostrado, aplicando el método científico, que el uso de estos dispositivos, en las condiciones técnicas y experimentales indicadas, permite el uso por parte del VDA, usando su mejor TR visual posible, que se muestra similar (ns) al TR auditivo de VsDA, lo que indica que, para competiciones inclusivas, la salida usando el semáforo (para VDA) y la salida habitual (estímulo sonoro) para VsDA, puede ser una solución equitativa en base a la evidencia demostrada en este estudio. De esta manera, y como referencia, indicar que la media de los TR de los velocistas en la final de los 100 m.l. en los Juegos Olímpicos de Londres 2012 fue de 0.162 ±0.015. De esta manera, creemos que estos parámetros sirven de referencia a técnicos deportivos, atletas y futuros trabajos de investigación. Las aplicaciones de este trabajo permitirán modificaciones y reflexiones en forma de apoyo al entrenamiento y la competición para el entrenador, o juez de salida en la competición que, creemos, es necesaria para proporcionar a este colectivo una atención adecuada en las salidas, especialmente en situaciones inclusivas de práctica. ABSTRACT This research aims to study of reaction time (RT) in sprinters with and without hearing impairment from the Sports Science perspective. The approach of this study came asking whether there were differences in the visual and auditory RT applied to sprinters with and without hearing impairment, thinking about the future development of inclusive competition between the two groups. Therefore, this study attempts to resolve the difficulties commonly founded by sprinters with hearing impairments during competitions. A priori, sprinters with hearing impairment would compete in a disadvantage situation as a result of the use of a staring signal not suitable for them (from the blocks, they have to look to the judge´s pistol or the movement of an opponent). The document is divided into three parts. In the first part of the review of relevant theoretical framework and justification of the study is presented. The second part focuses on the research objectives, material and method, where results, discussion and conclusions of the study, as well as the limitations of this study and future research are presented. The third part contains references and the fourth, annexes. In the first part, we present the theoretical framework consisting of five chapters, organizing the state of the art of RT, determined by the characteristics of the task and other factors that influence the RT as object of our study. Then we present the main structural and functional aspects of the nervous system associated with visual and auditory RT. After that, sport for people with hearing disabilities is presented, investigating its peculiarities and eligibility criteria is that group within the deaf sport. Finally, we discuss the theoretical foundation of the study of start speed in athletics as a key aspect that will guide our research, especially the determining parameters in placing the starting blocks for athletes with and without hearing impairment, the starting position and the actual placement of stimuli in such a situation. The second part of the research aims to study the values of simple manual visual RT, RT start from blocks and travel times up to 10m and 20m of sprinters with and without hearing impairment, and to analyze possible differences in RT as position and type of light stimulus with respect to both groups of athletes. The third objective of the study is to assess the pertinence of the lighting device developed and used in the study, in a qualitatively way by athletes themselves. Data collection for this study was carried out between February and May 2014, in the Athletics module at the High Performance Centre Joaquin Blume (Madrid) with the two study groups: 9 sprinters with hearing impairments(VDA, reaching 60% of the population in Spain, according to the number of licenses for athletics at FEDS: sprint, 100 and 200 m.l., at the time of the study), and another 13 sprinters without disability (VsDA) who voluntarily presented themselves, with same inclusion criteria for both groups. For measuring and data collection materials such as recording sheet, gauge reaction time (MTR), starting blocks, ReacTime®, luminous device connected to the starting blocks, photocells, computer and software ReacTime, and video camera were used. The methodology used in this study was correlational, analyzing the results of simple manual RT according sensory pathway (visual and auditory) between the two groups (VsDA and VDA). Also auditory and visual RT was studied depending the placement of the start light signal (on the ground and 5 meters, visual pathway) and athletic start gun signal (auditory pathway, conventional situation) and travel time up to 10m (t10m) and 20m (t20m) for both groups of sprinters. Finally, we developed and carried out an evaluation questionnaire for VDA athletes in order to determine the degree of satisfaction after completing the series of experiments with lighting device and adapted to start systems in athletic speed. In order to test the feasibility of the methodology described and tested in the context of real analysis of the experimental protocol, a pilot study in order to know the possible differences visual RT from the starting blocks in sprinters with hearing impairments was performed, to said output using a visual stimulus coordinated by a lighting device with sound output signal (Soto-Rey Perez-Tejero, Rojo-González y Álvarez-Ortiz, 2015). For the statistical procedures, in order to analyze the distribution of the data and their normality, Kolmogorov-Smirnov test was applied, this test yielded normal results for all variables analyzed during EA, EVsuelo and EV5m experimental situations. Parametric statistics were used in this research. As descriptive measures, the maximum, minimum, mean and standard deviation were calculated. In relation to experimental situations, to study possible differences in the variables studied in each group sprinters (intragroup) in the experimental situation 1 (MTR), a Student t test was used for independent samples. Under the experimental situations 2, 3 and 4, to know the differences between the two groups of sprinters in every situation, the T test for independent samples was used, while a simple ANOVA (with post hoc Bonferroni) was used to analyze differences for each group (VDA and VsDA) by experimental situation. Likewise, a repeated measures ANOVA, where the type of stimulus (experimental situation) was variable intra-group and participants sprinters group (VDA and VsDA) the variable between-group, was performed to assess each situation for RT, t10m and t20m, and also interactions between variables. For the statistical treatment SPSS 18.0 (Chicago, IL, USA) was used. Significance levels were set for  ≤0.05, indicating the value of p in each case. One of the most important aspects of this work is the measurement of RT in sprinters with and without hearing impairment in different situations, with different instrumentation and different experimental situations. This involved the development of a research design that responded to the needs raised by the study aims and the development of specific instrumentation (Rojo-Lacal, Soto-Rey Perez-Tejero and Rojo-Gonzalez, 2014; Soto-Rey et al., 2015) and different experimental situations to reproduce the conditions of practical and real competition VsDA and VDA in athletic sprints, and more specifically, at the start. Statistical analysis showed significant differences between the visual and sound stimuli measured by the MTR, with lower RT to the visual stimulus that for sound, both for athletes with hearing disabilities and for those without (visual RT, 0.195 s ± 0.018 s vs 0.197 ± 0.022, p≤0.05; sound RT 0.230 s ± 0.016 vs 0.237 s ± 0.045, p≤0.05). Considering the results according to study population and experimental situation, significant differences between the two populations, VDA and VsDA were found, being faster the VDA than VsDA in the experimental situation with the visual stimulus on the floor (EVsuelo, recorded 0.191 s ± 0.025 vs 0.210 s ± 0.025, p≤0.05, respectively) and VsDA in the experimental situation with the auditory stimulus (EA, 0.396 s ± 0.045 vs 0.174 s ± 0.021, p≤0.05), but no difference between groups in the experimental situation with the 5m visual stimulus to the starting blocks. It is noteworthy that no significant differences in EA and EVsuelo between VsDA to VDA, respectively, for RT. Simple ANOVA showed significant differences in all experimental situations within each group and for all variables, so statistically, the experimental situations were different. Regarding the repeated measures ANOVA, the sphericity test showed adequate, and there were significant differences in the variances of the pairs of means: the value of F indicated that there were differences between the different experimental situations regarding RT, even when they were related to the disability factor (factor interaction, p≤0.05). Therefore, it is clear that the situations were different from each other, also taking into account impairment. The η2 (eta squared, effect size, for interaction) indicates that 91.7% of the variation is due to the conditions of the study, not by error (as indicator of the generalization potential of the study results). On the other hand, evaluation of the light signal was positively related to lighting, ease of use, location, color, size, alignment device and equipment necessary to adapt the start system. All the athletes claim strongly in favor of the lighting device adaptation system to enable athletic competition inclusive. Also they concluded that light device would enhance performance or would decrease their RT during the competition. The discussion of this study justify the type of stimulus and the start light positioning as key to the RT performance, so that we could argue the need for lighting devices for VDA when competing against VsDA the same competition, inclusive. This research has demonstrated, applying the scientific method, that the use of these devices, techniques and given experimental conditions, allows the use of the VDA, using his best visual RT, shown similar (ns) auditory RT of VsDA, indicating that for inclusive competitions, the start signal using the light (for VDA) and the usual start (sound stimulus) to VsDA can be an equitable solution based on the evidence shown in this study. Thus, and as a reference, indicate that the average of the RT sprinters in the 100 m. final at the 2012 Summer Olympic Games was 0.162 s ± 0.015. Thus, we believe that these parameters become a reference to sports coaches, athletes and future research. Applications of this work will allow modifications and reflections in the form of support for training and competition for the coach, or judge, as we believe is necessary to provide adequate attention to VDA in speed starts, especially in inclusive practice situations.

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Background: This project’s idea arose derived of the need of the professors of the department “Computer Languages and Systems and Software Engineering (DLSIIS)” to develop exams with multiple choice questions in a more productive and comfortable way than the one they are currently using. The goal of this project is to develop an application that can be easily used by the professors of the DLSIIS when they need to create a new exam. The main problems of the previous creation process were the difficulty in searching for a question that meets some specific conditions in the previous exam files; and the difficulty for editing exams because of the format of the employed text files. Result: The results shown in this document allow the reader to understand how the final application works and how it addresses successfully every customer need. The elements that will help the reader to understand the application are the structure of the application, the design of the different components, diagrams that show the workflow of the application and some selected fragments of code. Conclusions: The goals stated in the application requirements are finally met. In addition, there are some thoughts about the work performed during the development of the application and how it improved the author skills in web development.

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Non peer reviewed

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Although 1–24% of T cells are alloreactive, i.e., respond to MHC molecules encoded by a foreign haplotype, it is generally believed that T cells cannot recognize foreign peptides binding foreign MHC molecules. We show using a quantitative model that, if T cell selection and activation are affinity-driven, then an alloreactivity of 1–24% is incompatible with the textbook notion that self MHC restriction is absolute. If an average of 1% of clones are alloreactive, then according to our model, at most 20-fold more clones should, on average, be activated by antigens presented on self MHC than by antigens presented on foreign MHC. This ratio is at best 5 if alloreactivity is 5%. These results describe average properties of the murine immune system, but not the outcome of individual experiments. Using supercomputer technology, we simulated 100,000 MHC restriction experiments. Although the average restriction ratio was 7.1, restriction was absolute in 10% of the simulated experiments, greater than 100, although not absolute, in 29%, and below 6 in 24%. This extreme variability agrees with experimental estimates. Our analysis suggests that alloreactivity and average self MHC restriction both cannot be high, but that a low average restriction level is compatible with high levels in a significant number of experiments.