[ES] En la presente tesis se construyen modelos matemáticos para el análisis de tiempos de respuesta (TR) a estímulos visuales en experimentos informatizados. Es conocido que existe una correlación estrecha entre los tiempos de reacción y diversos trastornos cognitivos, tales como el Trastorno por Déficit de Atención e Hiperactividad (TDAH). Sin embargo, no existe consenso en la explicación de estas correlaciones. Una primera aportación, más práctica, de este trabajo, es el desarrollo de una metodología para la clasificación de un grupo coetáneo de niños en edad escolar. La función ex-Gaussiana, originada por la convolución entre una Gaussiana y una exponencial decreciente, se utiliza para representar las funciones de distribución empíricas de tiempos de respuesta. La metodología de clasificación propuesta utiliza las distribuciones de los parámetros de la ex-Gaussiana mu, sigma y tau en una muestra de 168 niños, así como la distribución de la moda, obtenida de las distribuciones empíricas de los TR. También utiliza diferentes definiciones de norma del vector de componentes (mu, sigma, tau) también analizado en la muestra. Entre los criterios utilizados para detectar los niños más alejados de un comportamiento normativo y, por tanto, con mayor probabilidad de tener algún trastorno cognitivo, se encuentra, por ejemplo, el porcentaje medio de prevalencia mundial de TDAH (7 %) y el hecho de que los niños con alteraciones cognitivas presentan respuestas más lentas o más rápidas pero con un mayor número de errores. En una segunda parte de la tesis, con un marcado aporte teórico, se analizan las correlaciones existentes entre los tiempos de respuesta de los participantes. Se ha aplicado una metodología propia basada en la transformada rápida de Fourier de las series temporales de las respuestas de los niños a lo largo de estímulos consecutivos y un análisis de correlaciones basado en la Entropía de Shannon espectral (por frecuencia). Los resultados obtenidos son muy novedosos, ya que se evidencia una correlación elevada entre las respuestas de los niños, aun cuando han hecho los experimentos de manera totalmente independiente. A partir de la evidencia empírica de la existencia de correlaciones entre las series temporales de las respuestas de los niños, lo que apunta hacia la existencia de una colectividad, se propone un modelo inspirado en la Física para entender y explicar las correlaciones. Específicamente, se demuestra la existencia de un paralelismo entre las partículas independientes de un gas ideal y los cerebros de los niños, que serían, en última instancia, los que generan las respuestas observables. La distribución de Maxwell-Boltzmann, conocida en Física por describir la distribución de velocidades de un Gas Ideal en equilibrio termodinámico, emerge del análisis de los tiempos de respuesta, en términos de los momentos de las funciones ex-Gaussianas que los representan. La posibilidad de contar con una función de distribución de probabilidades, que describa el comportamiento natural de una colectividad, ofrece muchas posibilidades de aplicación en diferentes áreas. Una de ellas es la posibilidad de clasificar a los individuos con respecto al grupo natural al que pertenecen. Las implicaciones de las aportaciones conceptuales de esta tesis se discuten al final, donde se comenta la continuidad de este trabajo. / [CA] En la present tesi es construeixen models matemàtics per a l'anàlisi de temps de resposta (TR) a estímuls visuals en experiments informatitzats. És conegut que existeix una correlació estreta entre els temps de reacció i diversos trastorns cognitius, com ara el Trastorn per Dèficit d'Atenció i Hiperactivitat (TDAH). No obstant això, no existeix consens en l'explicació d'aquestes correlacions. Una primera aportació, més pràctica, d'aquest treball, és el desenvolupament d'una metodologia per a la classificació d'un grup coetani de xiquets en edat escolar. La funció ex-Gaussiana, originada per la convolució entre una Gaussiana i una exponencial decreixent, s'utilitza per a representar les funcions de distribució empíriques de temps de resposta. La metodologia de classificació proposada utilitza les distribucions dels paràmetres de la ex-Gaussiana mu, sigma i tau en una mostra de 168 xiquets, així com la distribució de la moda, obtinguda de les distribucions empíriques dels TR. També utilitza diferents definicions de norma del vector de components (mu, sigma, tau), també analitzat en la mostra. Entre els criteris utilitzats per a detectar els xiquets més allunyats d'un comportament normatiu i, per tant, amb major probabilitat de tenir algun trastorn cognitiu, es troba, per exemple, el percentatge mitjà de prevalença mundial de TDAH (7%) i el fet que els xiquets amb alteracions cognitives presenten respostes més lentes o més ràpides però amb un major nombre d'errors. En una segona part de la tesi, amb una marcada aportació teòrica, s'analitzen les correlacions existents entre els temps de resposta dels participants. S'ha aplicat una metodologia pròpia basada en la transformada ràpida de Fourier de les sèries temporals de les respostes dels xiquets al llarg d'estímuls consecutius i una anàlisi de correlacions basat en l'Entropia de Shannon espectral (per freqüència). Els resultats obtinguts són molt nous, ja que, s'evidencia una correlació elevada entre les respostes dels xiquets, tot i que han fet els experiments de manera totalment independent. A partir de l'evidència empírica de l'existència de correlacions entre les sèries temporals de les respostes dels xiquets, la qual cosa apunta cap a l'existència d'una col·lectivitat, es proposa un model inspirat en la Física per a entendre i explicar les correlacions. Específicament, es demostra l'existència d'un paral·lelisme entre les partícules independents d'un gas ideal i els cervells dels xiquets, que serien, en última instància, els que generen les respostes observables. La distribució de Maxwell-Boltzmann, coneguda de la Física per descriure la distribució de velocitats d'un Gas Ideal en equilibri termodinàmic, emergeix de l'anàlisi dels temps de resposta, en termes dels moments de les funcions ex-Gaussianas que els representen. La possibilitat de comptar amb una funció de distribució de probabilitats, que descriga el comportament natural d'una col·lectivitat, ofereix moltes possibilitats d'aplicació en diferents àrees. Una d'elles és la possibilitat de classificar als individus respecte al grup natural al qual pertanyen. Les implicacions de les aportacions conceptuals d'aquesta tesi es discuteixen al final, on es comenta la continuïtat d'aquest treball. / [EN] Mathematical models are built to analyse response time data to visual stimuli in computerized experiments. The actual correlation between reaction times and cognitive disorders, such as Attention Deficit Hyperactivity (ADHD) disorder, is well known in the literature. However, there is no clear consensus about how to explain this correlation. A first practical contribution of this work is a classification methodology of a coetaneous group of school-aged children. The ex-Gaussian function, originated by the convolution of a Gaussian and an exponential decay functions is used to represent the experimental probability distributions of reaction times. The classification methodology proposed in this work utilizes the probability distributions of the ex-Gaussian parameters mu, sigma and tau across a sample of 168 children, as well as the mode of the empirical probability distributions of the reaction times. Also, some definitions of the norm of the vector with components (mu, sigma, tau) are used. The detection of those children who lie furthest from the normative behaviour, and then, are more likely to suffer a cognitive disorder is performed by including the following criteria: the world prevalence percentage of ADHD (7 %) and the fact that children with this disorder show slower and faster responses. In the case of the fast responses, they should be given along with a higher rate of mistakes. In a second part of this work more conceptual contributions are provided. The evidenced correlations between the children's responses along consecutive visual stimuli are analysed by using the fast Fourier transform and the Shannon's Entropy in spectral form (per frequency). The outcome is surprising as correlations among the children are manifested, even when they carry out the experiments independently. This fact strongly suggests the existence of a collective of children. In order to gain insights into this finding, a Physics-inspired model is proposed. Specifically, the results indicate the existence of a parallelism between the independent particles forming an Ideal Gas and the group of individuals. Then, the Maxwell-Boltzmann distribution of the velocities of the particles of an Ideal Gas, emerges here when the moments of the ex-Gaussian distributions are considered across the sample. This opens many possibilities of applications in different fields as a natural distribution of the response times of the collective is available. For instance, the behaviour of an individual in relation to the natural group it belongs to can be known. The potential applications and impact of these developments are included at the end of this work where the continuity of this work is commented. / Hernaiz Guijarro, M. (2021). Tiempos de respuesta a estímulos visuales: vinculando el comportamiento individual y colectivo a través de las leyes de la Física [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/168120 / TESIS

本篇論文主要考慮成群資料的存活分析，其特點為群內個體間具有相關性，並假定群內個體具有相同但無法觀測到的事故傾向。首先，探討事故傾向服從任一連續分配時混合Weibull迴歸模式的特性，接著，推導出事故傾向服從血Inverse Gaussian吧時之混合Weibull模式，並介紹參數的估計問題。然後，推導出群內個體是否獨立之分數檢定統計量，以分別就兩種最常見的存活資料型態一完整型態與右設限型態：檢定模式中事故傾向的效應是否存在。最後，並以實例說明分數檢定之程序。 / In this paper, we study survival analysis for grouped data, where the within group correlations are considered. It is also assumed that individuals within the same group share a common but unobservable random frailty. First, we discuss the properties of the Weibull regression model mixed by any continuous distribution. Next, we derive an Inverse Gaussan mixture of Weibull regression model, and discuss the estimation problem. Then, we derive the score test for testing independence between components within the same group, where the two most common cases are discussed the complete data case and the right censoring case. Finally, the testing procedures are illustrated by two examples.

Ultra Wideband (UWB) communication has recently drawn considerable attention from academia and industry. This is mainly owing to the ultra high speeds and cognitive features it could offer. The employability of UWB in numerous areas including but not limited to Wireless Personal Area Networks, WPAN's, Body Area Networks, BAN's, radar and medical imaging etc. has opened several avenues of research and development. However, still there is a disagreement on the standardization of UWB. Two contesting radios for UWB are Multiband Orthogonal Frequency Division Multiplexing (MB-OFDM) and DS-UWB (Direct Sequence Ultra Wideband). As nearly all of the reported research on UWB hasbeen about a very narrow/specific area of the communication system, this thesis looks at the end-to-end performance of an MB-OFDM approach. The overall aim of this project has been to first focus on three different aspects i.e. interference, antenna and propagation aspects of an MB-OFDM system individually and then present a holistic or an end-to-end system analysis finally. In the first phase of the project the author investigated the performance of MB-OFDM system under the effect of his proposed generic or technology non-specific interference. Avoiding the conventional Gaussian approximation, the author has employed an advanced stochastic method. A total of two approaches have been presented in this phase of the project. The first approach is an indirect one which involves the Moment Generating Functions (MGF's) of the Signal-to-Interference-plus-Noise-Ratio (SINR) and the Probability Density Function (pdf) of the SINR to calculate the Average Probabilities of Error of an MB-OFDM system under the influence of proposed generic interference. This approach assumed a specific two-dimensional Poisson spatial/geometric placement of interferers around the victim MB-OFDM receiver. The second approach is a direct approach and extends the first approach by employing a wider class of generic interference. In the second phase of the work the author designed, simulated, prototyped and tested novel compact monopole planar antennas for UWB application. In this phase of the research, compact antennas for the UWB application are presented. These designs employ low-loss Rogers duroid substrates and are fed by Copla-nar Waveguides. The antennas have a proposed feed-line to the main radiating element transition region. This transition region is formed by a special step-generating function-set called the "Inverse Parabolic Step Sequence" or IPSS. These IPSS-based antennas are simulated, prototyped and then tested in the ane-choic chamber. An empirical approach, aimed to further miniaturize IPSS-based antennas, was also derived in this phase of the project. The empirical approach has been applied to derive the design of a further miniaturized antenna. More-over, an electrical miniaturization limit has been concluded for the IPSS-based antennas. The third phase of the project has investigated the effect of the indoor furnishing on the distribution of the elevation Angle-of-Arrival (AOA) of the rays at the receiver. Previously, constant distributions for the AOA of the rays in the elevation direction had been reported. This phase of the research has proposed that the AOA distribution is not fixed. It is established by the author that the indoor elevation AOA distributions depend on the discrete levels of furnishing. A joint time-angle-furnishing channel model is presented in this research phase. In addition, this phase of the thesis proposes two vectorial or any direction AOA distributions for the UWB indoor environments. Finally, the last phase of this thesis is presented. As stated earlier, the overall aim of the project has been to look at three individual aspects of an MB-OFDM system, initially, and then look at the holistic system, finally. Therefore, this final phase of the research presents an end-to-end MB-OFDM system analysis. The interference analysis of the first phase of the project is revisited to re-calculate the probability of bit error with realistic/measured path loss exponents which have been reported in the existing literature. In this method, Gaussian Quadrature Rule based approximations are computed for the average probability of bit error. Last but not the least, an end-to-end or comprehensive system equation/impulse response is presented. The proposed system equation covers more aspects of an indoor UWB system than reported in the existing literature.

En fiabilité et en analyse de survie, les distributions qui ont une fonction de hasard unimodale ne sont pas nombreuses, qu'on peut citer: Gaussienne inverse ,log-normale, log-logistique, de Birnbaum-Saunders, de Weibull exponentielle et de Weibullgénéralisée. Dans cette thèse, nous développons les tests modifiés du Chi-deux pour ces distributions tout en comparant la distribution Gaussienne inverse avec les autres. Ensuite nousconstruisons le modèle AFT basé sur la distribution Gaussienne inverse et les systèmes redondants basés sur les distributions de fonction de hasard unimodale. / In reliability and survival analysis, distributions that have a unimodalor $\cap-$shape hazard rate function are not too many, they include: the inverse Gaussian,log-normal, log-logistic, Birnbaum-Saunders, exponential Weibull and power generalized Weibulldistributions. In this thesis, we develop the modified Chi-squared tests for these distributions,and we give a comparative study between the inverse Gaussian distribution and the otherdistributions, then we realize simulations. We also construct the AFT model based on the inverseGaussian distribution and redundant systems based on distributions having a unimodal hazard ratefunction.

No description available.

Ultraprecision single point diamond turning is required to produce parts with sub-nanometer surface roughness and sub-micrometer surface profiles tolerances. These parts have applications in the optics industry, where tight form accuracy is required while achieving high surface finish quality. Generally, parts can be polished to achieve the desired finish, but then the form accuracy can easily be lost in the process rendering the part unusable. Currently, most mid to low spatial frequency surface finish errors are inspected offline. This is done by physically removing the workpiece from the machining fixture and mounting the part in a laser interferometer. This action introduces errors in itself through minute differences in the support conditions of the over constrained part on a machine as compared to the mounting conditions used for part measurement. Once removed, the fixture induced stresses and the part’s internal residual stresses relax and change the shape of the generally thin parts machined in these applications. Thereby, the offline inspection provides an erroneous description of the performance of the machine. This research explores the use of a single, high resolution, capacitance sensor to quickly and qualitatively measure the low to mid spatial frequencies on the workpiece surface, while it is mounted in a fixture on a standard ultraprecision single point diamond turning machine after a standard facing operation. Following initial testing, a strong qualitative correlation exists between the surface profiling on a standard offline system and this online measuring system. Despite environmental effects and the effects of the machine on the measurement system, the capacitive system with some modifications and awareness of its measurement method is a viable option for measuring mid to low spatial frequencies on a workpiece surface mounted on an ultraprecision machine with a resolution of 1nm with an error band of ±5nm with a 20kHz bandwidth. / Thesis / Master of Applied Science (MASc)