Evaluación del tiempo de reacción en velocistas con y sin discapacidad auditiva: aplicaciones para la inclusión

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.

Aerodynamic database error filtering via high order singular value decomposition

Esta Tesis presenta un nuevo método para filtrar errores en bases de datos multidimensionales. Este método no precisa ninguna información a priori sobre la naturaleza de los errores. En concreto, los errrores no deben ser necesariamente pequeños, ni de distribución aleatoria ni tener media cero. El único requerimiento es que no estén correlados con la información limpia propia de la base de datos. Este nuevo método se basa en una extensión mejorada del método básico de reconstrucción de huecos (capaz de reconstruir la información que falta de una base de datos multidimensional en posiciones conocidas) inventado por Everson y Sirovich (1995). El método de reconstrucción de huecos mejorado ha evolucionado como un método de filtrado de errores de dos pasos: en primer lugar, (a) identifica las posiciones en la base de datos afectadas por los errores y después, (b) reconstruye la información en dichas posiciones tratando la información de éstas como información desconocida. El método resultante filtra errores O(1) de forma eficiente, tanto si son errores aleatorios como sistemáticos e incluso si su distribución en la base de datos está concentrada o esparcida por ella. Primero, se ilustra el funcionamiento delmétodo con una base de datosmodelo bidimensional, que resulta de la dicretización de una función transcendental. Posteriormente, se presentan algunos casos prácticos de aplicación del método a dos bases de datos tridimensionales aerodinámicas que contienen la distribución de presiones sobre un ala a varios ángulos de ataque. Estas bases de datos resultan de modelos numéricos calculados en CFD. ABSTRACT A method is presented to filter errors out in multidimensional databases. The method does not require any a priori information about the nature the errors. In particular, the errors need not to be small, neither random, nor exhibit zero mean. Instead, they are only required to be relatively uncorrelated to the clean information contained in the database. The method is based on an improved extension of a seminal iterative gappy reconstruction method (able to reconstruct lost information at known positions in the database) due to Everson and Sirovich (1995). The improved gappy reconstruction method is evolved as an error filtering method in two steps, since it is adapted to first (a) identify the error locations in the database and then (b) reconstruct the information in these locations by treating the associated data as gappy data. The resultingmethod filters out O(1) errors in an efficient fashion, both when these are random and when they are systematic, and also both when they concentrated and when they are spread along the database. The performance of the method is first illustrated using a two-dimensional toymodel database resulting fromdiscretizing a transcendental function and then tested on two CFD-calculated, three-dimensional aerodynamic databases containing the pressure coefficient on the surface of a wing for varying values of the angle of attack. A more general performance analysis of the method is presented with the intention of quantifying the randomness factor the method admits maintaining a correct performance and secondly, quantifying the size of error the method can detect. Lastly, some improvements of the method are proposed with their respective verification.

Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Eyes With Previous Myopic Laser Refractive Surgery

Purpose: To calculate theoretically the errors in the estimation of corneal power when using the keratometric index (nk) in eyes that underwent laser refractive surgery for the correction of myopia and to define and validate clinically an algorithm for minimizing such errors. Methods: Differences between corneal power estimation by using the classical nk and by using the Gaussian equation in eyes that underwent laser myopic refractive surgery were simulated and evaluated theoretically. Additionally, an adjusted keratometric index (nkadj) model dependent on r1c was developed for minimizing these differences. The model was validated clinically by retrospectively using the data from 32 myopic eyes [range, −1.00 to −6.00 diopters (D)] that had undergone laser in situ keratomileusis using a solid-state laser platform. The agreement between Gaussian (PGaussc) and adjusted keratometric (Pkadj) corneal powers in such eyes was evaluated. Results: It was found that overestimations of corneal power up to 3.5 D were possible for nk = 1.3375 according to our simulations. The nk value to avoid the keratometric error ranged between 1.2984 and 1.3297. The following nkadj models were obtained: nkadj= −0.0064286r1c + 1.37688 (Gullstrand eye model) and nkadj = −0.0063804r1c + 1.37806 (Le Grand). The mean difference between Pkadj and PGaussc was 0.00 D, with limits of agreement of −0.45 and +0.46 D. This difference correlated significantly with the posterior corneal radius (r = −0.94, P < 0.01). Conclusions: The use of a single nk for estimating the corneal power in eyes that underwent a laser myopic refractive surgery can lead to significant errors. These errors can be minimized by using a variable nk dependent on r1c.

Relationship among Corneal Biomechanics, Refractive Error, and Axial Length

Purpose: To evaluate the relationship between different ocular and corneal biomechanical parameters in emmetropic and ametropic healthy white children. Methods: This study included 293 eyes of 293 healthy Spanish children (135 boys and 158 girls), ranging in age from 6 to 17 years. Subjects were divided according to the refractive error: control (emmetropia, 99 children), myopia (100 children), and hyperopia (94 children) groups. In all cases, corneal hysteresis (CH) and corneal resistance factor (CRF) were evaluated with the Ocular Response Analyzer system. Axial length (AL) and mean corneal power were also measured by partial coherence interferometry (IOLMaster), and central corneal thickness (CCT) and anterior chamber depth were measured by anterior segment optical coherence tomography (Visante). Results: Mean (±SD) CH and CRF were 12.12 (±1.71) and 12.30 (±1.89) mm Hg, respectively. Mean (±SD) CCT was 542.68 (±37.20) μm and mean (±SD) spherical equivalent was +0.14 (±3.41) diopters. A positive correlation was found between CH and CRF (p < 0.001), and both correlated as well with CCT (p < 0.0001). Corneal resistance factor was found to decrease with increasing age (p = 0.01). Lower levels of CH were associated with longer AL and more myopia (p < 0.001 and p = 0.001, respectively). Higher values of CH were associated with increasing hyperopia. Significant differences in CH were found between emmetropic and myopic groups (p < 0.001) and between myopic and hyperopic groups (p = 0.011). There were also significant differences in CRF between emmetropic and myopic groups (p = 0.02). Multiple linear regression analysis showed that lower CH and CRF significantly associated with thinner CCT, longer AL, and flatter corneal curvature. Conclusions: The Ocular Response Analyzer corneal biomechanical properties seem to be compromised in myopia from an early age, especially in high myopia.

Estimation of the Central Corneal Power in Keratoconus: Theoretical and Clinical Assessment of the Error of the Keratometric Approach

Purpose: The aim of this study was to analyze theoretically the errors in the central corneal power calculation in eyes with keratoconus when a keratometric index (nk) is used and to clinically confirm the errors induced by this approach. Methods: Differences (DPc) between central corneal power estimation with the classical nk (Pk) and with the Gaussian equation (PGauss c ) in eyes with keratoconus were simulated and evaluated theoretically, considering the potential range of variation of the central radius of curvature of the anterior (r1c) and posterior (r2c) corneal surfaces. Further, these differences were also studied in a clinical sample including 44 keratoconic eyes (27 patients, age range: 14–73 years). The clinical agreement between Pk and PGauss c (true net power) obtained with a Scheimpflug photography–based topographer was evaluated in such eyes. Results: For nk = 1.3375, an overestimation was observed in most cases in the theoretical simulations, with DPc ranging from an underestimation of 20.1 diopters (D) (r1c = 7.9 mm and r2c = 8.2 mm) to an overestimation of 4.3 D (r1c = 4.7 mm and r2c = 3.1 mm). Clinically, Pk always overestimated the PGauss c given by the topography system in a range between 0.5 and 2.5 D (P , 0.01). The mean clinical DPc was 1.48 D, with limits of agreement of 0.71 and 2.25 D. A very strong statistically significant correlation was found between DPc and r2c (r = 20.93, P , 0.01). Conclusions: The use of a single value for nk for the calculation of corneal power is imprecise in keratoconus and can lead to significant clinical errors.

Error induced by the estimation of the corneal power and the effective lens position with a rotationally asymmetric refractive multifocal intraocular lens

AIM: To evaluate the prediction error in intraocular lens (IOL) power calculation for a rotationally asymmetric refractive multifocal IOL and the impact on this error of the optimization of the keratometric estimation of the corneal power and the prediction of the effective lens position (ELP). METHODS: Retrospective study including a total of 25 eyes of 13 patients (age, 50 to 83y) with previous cataract surgery with implantation of the Lentis Mplus LS-312 IOL (Oculentis GmbH, Germany). In all cases, an adjusted IOL power (PIOLadj) was calculated based on Gaussian optics using a variable keratometric index value (nkadj) for the estimation of the corneal power (Pkadj) and on a new value for ELP (ELPadj) obtained by multiple regression analysis. This PIOLadj was compared with the IOL power implanted (PIOLReal) and the value proposed by three conventional formulas (Haigis, Hoffer Q and Holladay). RESULTS: PIOLReal was not significantly different than PIOLadj and Holladay IOL power (P>0.05). In the Bland and Altman analysis, PIOLadj showed lower mean difference (-0.07 D) and limits of agreement (of 1.47 and -1.61 D) when compared to PIOLReal than the IOL power value obtained with the Holladay formula. Furthermore, ELPadj was significantly lower than ELP calculated with other conventional formulas (P<0.01) and was found to be dependent on axial length, anterior chamber depth and Pkadj. CONCLUSION: Refractive outcomes after cataract surgery with implantation of the multifocal IOL Lentis Mplus LS-312 can be optimized by minimizing the keratometric error and by estimating ELP using a mathematical expression dependent on anatomical factors.

Regression to the mean: what it is and how to deal with it

Background Regression to the mean (RTM) is a statistical phenomenon that can make natural variation in repeated data look like real change. It happens when unusually large or small measurements tend to be followed by measurements that are closer to the mean. Methods We give some examples of the phenomenon, and discuss methods to overcome it at the design and analysis stages of a study. Results The effect of RTM in a sample becomes more noticeable with increasing measurement error and when follow-up measurements are only examined on a sub-sample selected using a baseline value. Conclusions RTM is a ubiquitous phenomenon in repeated data and should always be considered as a possible cause of an observed change. Its effect can be alleviated through better study design and use of suitable statistical methods.

Gaussian processes for classification: mean field algorithms:mean-field algorithms

We derive a mean field algorithm for binary classification with Gaussian processes which is based on the TAP approach originally proposed in Statistical Physics of disordered systems. The theory also yields an approximate leave-one-out estimator for the generalization error which is computed with no extra computational cost. We show that from the TAP approach, it is possible to derive both a simpler 'naive' mean field theory and support vector machines (SVM) as limiting cases. For both mean field algorithms and support vectors machines, simulation results for three small benchmark data sets are presented. They show 1. that one may get state of the art performance by using the leave-one-out estimator for model selection and 2. the built-in leave-one-out estimators are extremely precise when compared to the exact leave-one-out estimate. The latter result is a taken as a strong support for the internal consistency of the mean field approach.

Gaussian processes and SVM: Mean field results and leave-one-out

In this chapter, we elaborate on the well-known relationship between Gaussian processes (GP) and Support Vector Machines (SVM). Secondly, we present approximate solutions for two computational problems arising in GP and SVM. The first one is the calculation of the posterior mean for GP classifiers using a `naive' mean field approach. The second one is a leave-one-out estimator for the generalization error of SVM based on a linear response method. Simulation results on a benchmark dataset show similar performances for the GP mean field algorithm and the SVM algorithm. The approximate leave-one-out estimator is found to be in very good agreement with the exact leave-one-out error.

TAP for parity check error correcting codes

We employ the methods presented in the previous chapter for decoding corrupted codewords, encoded using sparse parity check error correcting codes. We show the similarity between the equations derived from the TAP approach and those obtained from belief propagation, and examine their performance as practical decoding methods.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Data methods in optometry. Part 6: fitting a regression line to data

1. Fitting a linear regression to data provides much more information about the relationship between two variables than a simple correlation test. A goodness of fit test of the line should always be carried out. Hence, r squared estimates the strength of the relationship between Y and X, ANOVA whether a statistically significant line is present, and the ‘t’ test whether the slope of the line is significantly different from zero. 2. Always check whether the data collected fit the assumptions for regression analysis and, if not, whether a transformation of the Y and/or X variables is necessary. 3. If the regression line is to be used for prediction, it is important to determine whether the prediction involves an individual y value or a mean. Care should be taken if predictions are made close to the extremities of the data and are subject to considerable error if x falls beyond the range of the data. Multiple predictions require correction of the P values. 3. If several individual regression lines have been calculated from a number of similar sets of data, consider whether they should be combined to form a single regression line. 4. If the data exhibit a degree of curvature, then fitting a higher-order polynomial curve may provide a better fit than a straight line. In this case, a test of whether the data depart significantly from a linear regression should be carried out.

Bayesian error bars for regression

Regression problems are concerned with predicting the values of one or more continuous quantities, given the values of a number of input variables. For virtually every application of regression, however, it is also important to have an indication of the uncertainty in the predictions. Such uncertainties are expressed in terms of the error bars, which specify the standard deviation of the distribution of predictions about the mean. Accurate estimate of error bars is of practical importance especially when safety and reliability is an issue. The Bayesian view of regression leads naturally to two contributions to the error bars. The first arises from the intrinsic noise on the target data, while the second comes from the uncertainty in the values of the model parameters which manifests itself in the finite width of the posterior distribution over the space of these parameters. The Hessian matrix which involves the second derivatives of the error function with respect to the weights is needed for implementing the Bayesian formalism in general and estimating the error bars in particular. A study of different methods for evaluating this matrix is given with special emphasis on the outer product approximation method. The contribution of the uncertainty in model parameters to the error bars is a finite data size effect, which becomes negligible as the number of data points in the training set increases. A study of this contribution is given in relation to the distribution of data in input space. It is shown that the addition of data points to the training set can only reduce the local magnitude of the error bars or leave it unchanged. Using the asymptotic limit of an infinite data set, it is shown that the error bars have an approximate relation to the density of data in input space.