Fabrics are unique materials which consist of various properties affecting their performance and end-uses. A computerized fabric property evaluation and analysis method plays a crucial role not only in textile industry but also in scientific research. An accurate analysis and measurement of fabric property provides a powerful tool for gauging product quality, assuring regulatory compliance and assessing the performance of textile materials. This thesis investigated the solutions for applying computerized methods to evaluate and intelligently interpret the texture and material properties of fabric in an inexpensive and efficient way. Firstly, a method which allows automatic recognition of basic weave pattern and precisely measuring the yarn count is proposed. The yarn crossed-areas are segmented by a spatial domain integral projection approach. Combining fuzzy c-means (FCM) and principal component analysis (PCA) on grey level co-occurrence matrix (GLCM) feature vectors extracted from the segments enables to classify detected segments into two clusters. Based on the analysis on texture orientation features, the yarn crossed-area states are automatically determined. An autocorrelation method is used to find weave repeats and correct detection errors. The method was validated by using computer simulated woven samples and real woven fabric images. The test samples have various yarn counts, appearance, and weave types. All weave patterns of tested fabric samples are successfully recognized and computed yarn counts are consistent to the manual counts. Secondly, we present a methodology for using the high resolution 3D surface data of fabric samples to measure surface roughness in a nondestructive and accurate way. A parameter FDFFT, which is the fractal dimension estimation from 2DFFT of 3D surface scan, is proposed as the indicator of surface roughness. The robustness of FDFFT, which consists of the rotation-invariance and scale-invariance, is validated on a number of computer simulated fractal Brownian images. Secondly, in order to evaluate the usefulness of FDFFT, a novel method of calculating standard roughness parameters from 3D surface scan is introduced. According to the test results, FDFFT has been demonstrated as a fast and reliable parameter for measuring the fabric roughness from 3D surface data. We attempt a neural network model using back propagation algorithm and FDFFT for predicting the standard roughness parameters. The proposed neural network model shows good performance experimentally. Finally, an intelligent approach for the interpretation of fabric objective measurements is proposed using supported vector machine (SVM) techniques. The human expert assessments of fabric samples are used during the training phase in order to adjust the general system into an applicable model. Since the target output of the system is clear, the uncertainty which lies in current subjective fabric evaluation does not affect the performance of proposed model. The support vector machine is one of the best solutions for handling high dimensional data classification. The complexity problem of the fabric property has been optimally dealt with. The generalization ability shown in SVM allows the user to separately implement and design the components. Sufficient cross-validations are performed and demonstrate the performance test of the system.

This thesis investigates the underlying causes of friction and ine ciency within an internal combustion engine, focusing on the ring-liner conjunction in the vicinity of the power-stroke top dead centre reversal. In such lubricated contacts, friction is the result of the interplay between numerous kinetics, with those at micro- and nano-scale interactions being signi cantly di erent than the ones at larger scales. A modi ed Elrod's cavitation algorithm is developed to determine the microscopic tribological characteristics of the piston ring-liner contact. Predicting lubricant tran- sient behaviour is critical when the inlet reversal leads to thin lms and inherent metal-to-metal interaction. The model clearly shows that cavitation at the trailing edge of the ring-liner contact generated pre-reversal, persists after reversal and pro- motes starvation and depletion of the oil lm. Hence, this will lead to boundary friction. A fractal based boundary friction model is developed for lightly loaded asperity con- tacts, separated by diminishing small lms, usually wetted by a layer of molecules adsorbed to the tips of the asperities. In nano-scale conjunctions, a lubricant layering e ect often takes place due to the smoothness of surfaces, which is governed by the surface and lubricant properties. A molecularly thin layer of lubricant molecules can adhere to the asperities, being the last barrier against direct surface contact. As a result, boundary friction (prevailing in such diminishing gaps) is actually determined by a combination of shearing of a thin adsorbed lm, adhesion of approaching as- perities and their plastic deformation. A model for physio-chemical hydrodynamic mechanism is successfully established, describing the formation of thin adsorbed lms between asperities. This model is e ectively integrated with separately devel- oped models that predict the adhesive and plastic contact of asperities.

Fabrics are unique materials which consist of various properties affecting their performance and end-uses. A computerized fabric property evaluation and analysis method plays a crucial role not only in textile industry but also in scientific research. An accurate analysis and measurement of fabric property provides a powerful tool for gauging product quality, assuring regulatory compliance and assessing the performance of textile materials. This thesis investigated the solutions for applying computerized methods to evaluate and intelligently interpret the texture and material properties of fabric in an inexpensive and efficient way. Firstly, a method which allows automatic recognition of basic weave pattern and precisely measuring the yarn count is proposed. The yarn crossed-areas are segmented by a spatial domain integral projection approach. Combining fuzzy c-means (FCM) and principal component analysis (PCA) on grey level co-occurrence matrix (GLCM) feature vectors extracted from the segments enables to classify detected segments into two clusters. Based on the analysis on texture orientation features, the yarn crossed-area states are automatically determined. An autocorrelation method is used to find weave repeats and correct detection errors. The method was validated by using computer simulated woven samples and real woven fabric images. The test samples have various yarn counts, appearance, and weave types. All weave patterns of tested fabric samples are successfully recognized and computed yarn counts are consistent to the manual counts. Secondly, we present a methodology for using the high resolution 3D surface data of fabric samples to measure surface roughness in a nondestructive and accurate way. A parameter FDFFT, which is the fractal dimension estimation from 2DFFT of 3D surface scan, is proposed as the indicator of surface roughness. The robustness of FDFFT, which consists of the rotation-invariance and scale-invariance, is validated on a number of computer simulated fractal Brownian images. Secondly, in order to evaluate the usefulness of FDFFT, a novel method of calculating standard roughness parameters from 3D surface scan is introduced. According to the test results, FDFFT has been demonstrated as a fast and reliable parameter for measuring the fabric roughness from 3D surface data. We attempt a neural network model using back propagation algorithm and FDFFT for predicting the standard roughness parameters. The proposed neural network model shows good performance experimentally. Finally, an intelligent approach for the interpretation of fabric objective measurements is proposed using supported vector machine (SVM) techniques. The human expert assessments of fabric samples are used during the training phase in order to adjust the general system into an applicable model. Since the target output of the system is clear, the uncertainty which lies in current subjective fabric evaluation does not affect the performance of proposed model. The support vector machine is one of the best solutions for handling high dimensional data classification. The complexity problem of the fabric property has been optimally dealt with. The generalization ability shown in SVM allows the user to separately implement and design the components. Sufficient cross-validations are performed and demonstrate the performance test of the system.

En nuestra sociedad los derivados del petróleo son la fuente principal de energía. Los accidentes con hidrocarburos han protagonizado episodios de contaminación trágicos para la biosfera del océano. Se analizan algunos de ellos, sus efectos y sistemas de limpieza. La complejidad de los procesos físicos, químicos o biológicos que actúan sobre el crudo en el mar, hacen difícil su estudio en laboratorio. Para ello se hacen numerosas campañas de campo con distintas escalas y procesos físicos predominantes diferentes: zonas costeras (Delta del Ebro y playa de Vilanova); en aguas confinadas (puerto de Barcelona y puerto de Recife); y en aguas abiertas (Mediterráneo Occidental), con diferentes tecnologías (foto, vídeo, satélite), para seguir trazadores eularianos (manchas de leche y fluoresceína, flotantes o hidrocarburos) y lagrangianos (boyas lastradas), se miden los agentes forzadores: viento, oleaje, marea, etc. y se correlacionan para caracterizar los diferentes escenarios. También se revisa el estado del arte. El tratamiento digital de imágenes de vídeo permite numerosas aplicaciones en el campo de la hidromorfodinámica, pues es posible controlar la evolución espacial y temporal de cualquier parámetro con evidencias visibles y es una técnica no intrusiva que ofrece datos de oleaje de una zona, en contraposición a los datos puntuales de los sensores. Las imágenes sufren numerosas alteraciones, deformaciones, ruidos, etc., que hay que depurar previamente. Los coeficientes de difusión presentan una gran variedad condicionada a la dependencia característica con la escala temporal y espacial de los fenómenos predominantes. Los coeficientes de difusión medidos se agruparon según el número de Reynolds y se hizo una clasificación: hipodifusividad, hiperdifusividad y difusión anómala. Esta caracterización de escenarios permite parametrizar el medio para modelizar su comportamiento y poder predecir su evolución. En el campo del oleaje se pueden obtener espectros de energía y otros parámetros para su caracterización, detectar la morfología de barras sumergidas, identificar corrientes de retorno, caracterizar run-up, etc. En el puerto de Barcelona se tomaron numerosos datos de velocidades de viento (Vv) y corriente (Vc) llegando a una buena correlación entre ambas (Vcx (cm/s)= 2.306 Vvx (m/s)+ 0.148) y constatando que hay una influencia de otros efectos como la marea, reflexión de los muelles o difracción que no se pueden obviar. Las imágenes de Rádar de Apertura sintética SAR permiten detectar episodios de contaminación y analizar la vorticidad a gran escala del medio. Resultó sorprendente el gran número de manchas detectadas. Se comprobó que los vertidos siguen la Ley de Zipp (distribución hiperbólica entre los accidentes y su tamaño). Se vió que los remolinos siguen la dirección de los cañones submarinos. Con el análisis fractal y multifractal del contorno de la mancha se puede caracterizar su origen (antropogénico o natural como masas de plankton) y su envejecimiento o persistencia, etc. Se comprueba que es posible que la intermitencia de la turbulencia pueda parametrizarse mediante medidas fractales y que el uso de momentos de orden superior ayuda a comparar medidas de difusión a distintas escalas mediante la Ley de Richardson Generalizada. Así se relaciona la pendiente del espectro, la intermitencia y la dependencia temporal de la difusión efectiva. Los distintos agentes que producen difusión en el mar sufren interacciones no-lineales complejas. Con todo ello, se pretende contribuir a comprender mejor los procesos de dispersión de los contaminantes en el mar y, por consiguiente, ayudar en la lucha contra este fenómeno. / In our society the derivatives of petroleum are the main source of energy. The accidents with hydrocarbons have carried out tragic episodes of contamination for the biosphere of the ocean. Some of them, their effects and systems of cleaning are analyzed. The complexity of the physical, chemical or biological processes that act on the oil in the sea, makes their study in laboratory difficult. For it numerous campaigns of field with different scales and different predominant physical processes become: coastal zones (Delta of the Ebro and beach of Vilanova); in confined waters (port of Barcelona and port of Recife); and in open waters (West Mediterranean), with different technologies (photo, video, satellite), to follow Lagrangian tracers (milk spots and fluoresceine, floating or hydrocarbons) and Euler tracers (ballasted buoys), to measure the agents: wind, waves, tide, etc. and they are correlated to characterize the different scenes. Also the state-of-the-art is reviewed. Treatment digital of images of video allows many applications in field of hydromorfodynamics, because it is possible to control the space and temporary evolution of any parameter with visible evidences and is a nonintrusive technique that offers data of a zone, in contrast to the pointing data of the sensors. The images put up with numerous alterations, deformations, noises, etc., that have to purify previously. The diffusion coefficients present/display a great conditional variety to the dependency characteristic with the temporary and space scale of the main phenomena. The measured coefficients of diffusion were grouped according to the Reynolds number and a classification became: hypo-diffusion, hyper-diffusion and anomalous diffusion. This characterization of scenes allows obtaining the waves parameters, the average one to model its behavior and power to predict its evolution. In the field of the waves run-up, etc. can be obtained spectra of energy and other parameters for their characterization, the morphology of submerged bars, identification of return currents. In the port of Barcelona numerous speed data of wind (Vv) and current were taken (Vc) arriving at a good correlation between both (Vcx (cm/s) = 2,306 Vvx (m/s) + 0,148) and stating that an influence of other effects are as the tide, reflection of the wharves or diffraction that cannot be avoided. The images of Radar of synthetic Opening SAR allow to detect episodes of contamination and to analyze the vorticity on great scale of means. Was surprising the great number of spots identifies. It was verified that the spills follow the Law of Zipp (hyperbolic distribution between the accidents and their size). Saw that the eddies follow the direction of the submarine tubes. With the analysis fractal and multifractal of the contour of the spot it is possible to be characterized its origin (human or natural like masses of plankton) and its aging or persistence, etc. It is verified that it is possible that the intermitency of the turbulence can obtain parameters by means of measures fractals and that the use of moments of superior order aid to compare measures of diffusion on different scales by means of the Generalized Law of Richardson. Thus it is related the slope of the phantom, the intermitency and the temporary dependency of the effective diffusion. The different agents who produce diffusion in the sea undergo complex not-linear interactions. It, is tried yet to contribute to include/understand better the

The use of grading scales is common in clinical practice and research settings. A number of grading scales are available to the practitioner, however, despite their frequent use, they are only poorly understood and may be criticised for a number of things such as the variability of the assessments or the inequality of scale steps within or between scales. Hence, the global aim of this thesis was to study the McMonnies/Chapman-Davies (MC-D), Institute for Eye Research (IER), Efron, and validated bulbar redness (VBR) grading scales in order to (1) get a better understanding and (2) attempt a cross-calibration of the scales. After verifying the accuracy and precision of the objective and subjective techniques to be used (chapter 3), a series of experiments was conducted. The specific aims of this thesis were as follows: • Chapter 4: To use physical attributes of redness to determine the accuracy of the four bulbar redness grading scales. • Chapter 5: To use psychophysical scaling to estimate the perceived redness of the four bulbar redness grading scales. • Chapter 6: To investigate the effect of using reference anchors when scaling the grading scale images, and to convert grades between scales. • Chapter 7: To grade bulbar redness using cross-calibrated versions of the MC-D, IER, Efron, and VBR grading scales. Methods: • Chapter 4: Two image processing metrics, fractal dimension (D) and % pixel coverage (% PC), as well as photometric chromaticity (u’) were selected as physical measures to describe and compare redness in the four bulbar redness grading scales. Pearson correlation coefficients were calculated between each set of image metrics and the reference image grades to determine the accuracy of the scales. • Chapter 5: Ten naïve observers were asked to arrange printed copies of modified versions of the reference images (showing vascular detail only) across a distance of 1.5m for which only start and end point were indicated by 0 and 100, respectively (non-anchored scaling). After completion of scaling, the position of each image was hypothesised to reflect its perceived bulbar redness. The averaged perceived redness (across observers) for each image was used for comparison to the physical attributes of redness as determined in chapter 4. • Chapter 6: The experimental setup from chapter 5 was modified by providing the reference images of the VBR scale as additional, unlabelled anchors for psychophysical scaling (anchored scaling). Averaged perceived redness from anchored scaling was compared to non-anchored scaling, and perceived redness from anchored scaling was used to cross-calibrate grades between scales. • Chapter 7: The modified reference images of each grading scale were positioned within the 0 to 100 range according to their averaged perceived redness from anchored scaling, one scale at a time. The same 10 observers who had participated in the scaling experiments were asked to represent perceived bulbar redness of 16 sample images by placing them, one at a time, relative to the reference images of each scale. Perceived redness was taken as the measured position of the placed image from 0 and was averaged across observers. Results: • Chapter 4: Correlations were high between reference image grades and all sets of objective metrics (all Pearson’s r’s≥0.88, p≤0.05); each physical attribute pointed to a different scale as being most accurate. Independent of the physical attribute used, there were wide discrepancies between scale grades, with sometimes little overlap of equivalent levels when comparing the scales. • Chapter 5: The perceived redness of the reference images within each scale was ordered as expected, but not all consecutive within-scale levels were rated as having different redness. Perceived redness of the reference images varied between scales, with different ranges of severity being covered by the images. The perceived redness was strongly associated with the physical attributes of the reference images. • Chapter 6: There were differences in perceived redness range and when comparing reference levels between scales. Anchored scaling resulted in an apparent shift to lower perceived redness for all but one reference image compared to non-anchored scaling, with the rank order of the 20 images for both procedures remaining fairly constant (Spearman’s ρ=0.99). • Chapter 7: Overall, perceived redness depended on the sample image and the reference scale used (RM ANOVA; p=0.0008); 6 of the 16 images had a perceived redness that was significantly different between at least two of the scales. Between-scale correlation coefficients of concordance (CCC) ranged from 0.93 (IER vs. Efron) to 0.98 (VBR vs. Efron). Between-scale coefficients of repeatability (COR) ranged from 5 units (IER vs. VBR) to 8 units (IER vs. Efron) for the 0 to 100 range. Conclusions: • Chapter 4: Despite the generally strong linear associations between the physical characteristics of reference images in each scale, the scales themselves are not inherently accurate and are too different to allow for cross-calibration based on physical redness attributes. • Chapter 5: Subjective estimates of redness are based on a combination of chromaticity and vessel-based components. Psychophysical scaling of perceived redness lends itself to being used to cross calibrate the four clinical scales. • Chapter 6: The re-scaling of the reference images with anchored scaling suggests that redness was assessed based on within-scale characteristics and not using absolute redness scores, a mechanism that may be referred to as clinical scale constancy. The perceived redness data allow practitioners to modify the grades of the scale they commonly use so that comparisons of grading estimates between calibrated scales may be made. • Chapter 7: The use of the newly calibrated reference grades showed close agreement between grading estimates of all scales. The between-scale variability was similar to the variability typically observed when a single scale is repeatedly used. Perceived redness appears to be dependent upon the dynamic range of the reference images of the scale. In conclusion, this research showed that there are physical and perceptual differences between the reference images of all scales. A cross-calibration of the scales based on the perceived redness of the reference images provides practitioners with an opportunity to compare grades across scales, which is of particular value in research settings or if the same patient is seen by multiple practitioners who are familiar with using different scales.

This work details an O(n^2) algorithm for computing the spectra of discrete Schroedinger operators with periodic potentials. Spectra of these objects enhance our understanding of fundamental aperiodic physical systems and contain rich theoretical structure of interest to the mathematical community. Previous work on the Harper model led to an O(n^2) algorithm relying on properties not satisfied by other aperiodic operators. Physicists working with the Fibonacci Hamiltonian, a popular quasicrystal model, have instead used a problematic dynamical map approach or a sluggish O(n^3) procedure for their calculations. The algorithm presented in this work, a blend of well-established eigenvalue/vector algorithms, provides researchers with a more robust computational tool of general utility. Application to the Fibonacci Hamiltonian in the sparsely studied intermediate coupling regime reveals structure in canonical coverings of the spectrum that will prove useful in motivating conjectures regarding band combinatorics and fractal dimensions.

In this paper we investigate the potential of the analysis of noisy non-stationary time series by quantizing it into streams of discrete symbols and applying finite-memory symbolic predictors. The main argument is that careful quantization can reduce the noise in the time series to make model estimation more amenable given limited numbers of samples that can be drawn due to the non-stationarity in the time series. As a main application area we study the use of such an analysis in a realistic setting involving financial forecasting and trading. In particular, using historical data, we simulate the trading of straddles on the financial indexes DAX and FTSE 100 on a daily basis, based on predictions of the daily volatility differences in the underlying indexes. We propose a parametric, data-driven quantization scheme which transforms temporal patterns in the series of daily volatility changes into grammatical and statistical patterns in the corresponding symbolic streams. As symbolic predictors operating on the quantized streams we use the classical fixed-order Markov models, variable memory length Markov models and a novel variation of fractal-based predictors introduced in its original form in (Tino, 2000b). The fractal-based predictors are designed to efficiently use deep memory. We compare the symbolic models with continuous techniques such as time-delay neural networks with continuous and categorical outputs, and GARCH models. Our experiments strongly suggest that the robust information reduction achieved by quantizing the real-valued time series is highly beneficial. To deal with non-stationarity in financial daily time series, we propose two techniques that combine ``sophisticated" models fitted on the training data with a fixed set of simple-minded symbolic predictors not using older (and potentially misleading) data in the training set. Experimental results show that by quantizing the volatility differences and then using symbolic predictive models, market makers can generate a statistically significant excess profit. However, with respect to our prediction and trading techniques, the option market on the DAX does seem to be efficient for traders and non-members of the stock exchange. There is a potential for traders to make an excess profit on the FTSE 100. We also mention some interesting observations regarding the memory structure in the studied series of daily volatility differences. (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

This thesis explores new approaches to the analysis of functions by combining tools from the fields of complex bases, number systems, iterated function systems (IFS) and wavelet multiresolution analyses (MRA). The foundation of this work is grounded in the identification of a link between two-dimensional non-separable Haar wavelets and complex bases. The theory of complex bases and this link are generalized to higher dimensional number systems. Tilings generated by number systems are typically fractal in nature. This often yields asymmetry in the wavelet trees of functions during wavelet decomposition. To acknowledge this situation, a class of extensions of functions is developed. These are shown to be consistent with the Mallat algorithm. A formal definition of local IFS on wavelet trees (LIFSW) is constructed for MRA associated with number systems, along with an application to the inverse problem. From these investigations, a series of algorithms emerge, namely the Mallat algorithm using addressing in number systems, an algorithm for extending functions and a method for constructing LIFSW operators in higher dimensions. Applications to image coding are given and ideas for further study are also proposed. Background material is included to assist readers less familiar with the varied topics considered. In addition, an appendix provides a more detailed exposition of the fundamentals of IFS theory.

The use of grading scales is common in clinical practice and research settings. A number of grading scales are available to the practitioner, however, despite their frequent use, they are only poorly understood and may be criticised for a number of things such as the variability of the assessments or the inequality of scale steps within or between scales. Hence, the global aim of this thesis was to study the McMonnies/Chapman-Davies (MC-D), Institute for Eye Research (IER), Efron, and validated bulbar redness (VBR) grading scales in order to (1) get a better understanding and (2) attempt a cross-calibration of the scales. After verifying the accuracy and precision of the objective and subjective techniques to be used (chapter 3), a series of experiments was conducted. The specific aims of this thesis were as follows: • Chapter 4: To use physical attributes of redness to determine the accuracy of the four bulbar redness grading scales. • Chapter 5: To use psychophysical scaling to estimate the perceived redness of the four bulbar redness grading scales. • Chapter 6: To investigate the effect of using reference anchors when scaling the grading scale images, and to convert grades between scales. • Chapter 7: To grade bulbar redness using cross-calibrated versions of the MC-D, IER, Efron, and VBR grading scales. Methods: • Chapter 4: Two image processing metrics, fractal dimension (D) and % pixel coverage (% PC), as well as photometric chromaticity (u’) were selected as physical measures to describe and compare redness in the four bulbar redness grading scales. Pearson correlation coefficients were calculated between each set of image metrics and the reference image grades to determine the accuracy of the scales. • Chapter 5: Ten naïve observers were asked to arrange printed copies of modified versions of the reference images (showing vascular detail only) across a distance of 1.5m for which only start and end point were indicated by 0 and 100, respectively (non-anchored scaling). After completion of scaling, the position of each image was hypothesised to reflect its perceived bulbar redness. The averaged perceived redness (across observers) for each image was used for comparison to the physical attributes of redness as determined in chapter 4. • Chapter 6: The experimental setup from chapter 5 was modified by providing the reference images of the VBR scale as additional, unlabelled anchors for psychophysical scaling (anchored scaling). Averaged perceived redness from anchored scaling was compared to non-anchored scaling, and perceived redness from anchored scaling was used to cross-calibrate grades between scales. • Chapter 7: The modified reference images of each grading scale were positioned within the 0 to 100 range according to their averaged perceived redness from anchored scaling, one scale at a time. The same 10 observers who had participated in the scaling experiments were asked to represent perceived bulbar redness of 16 sample images by placing them, one at a time, relative to the reference images of each scale. Perceived redness was taken as the measured position of the placed image from 0 and was averaged across observers. Results: • Chapter 4: Correlations were high between reference image grades and all sets of objective metrics (all Pearson’s r’s≥0.88, p≤0.05); each physical attribute pointed to a different scale as being most accurate. Independent of the physical attribute used, there were wide discrepancies between scale grades, with sometimes little overlap of equivalent levels when comparing the scales. • Chapter 5: The perceived redness of the reference images within each scale was ordered as expected, but not all consecutive within-scale levels were rated as having different redness. Perceived redness of the reference images varied between scales, with different ranges of severity being covered by the images. The perceived redness was strongly associated with the physical attributes of the reference images. • Chapter 6: There were differences in perceived redness range and when comparing reference levels between scales. Anchored scaling resulted in an apparent shift to lower perceived redness for all but one reference image compared to non-anchored scaling, with the rank order of the 20 images for both procedures remaining fairly constant (Spearman’s ρ=0.99). • Chapter 7: Overall, perceived redness depended on the sample image and the reference scale used (RM ANOVA; p=0.0008); 6 of the 16 images had a perceived redness that was significantly different between at least two of the scales. Between-scale correlation coefficients of concordance (CCC) ranged from 0.93 (IER vs. Efron) to 0.98 (VBR vs. Efron). Between-scale coefficients of repeatability (COR) ranged from 5 units (IER vs. VBR) to 8 units (IER vs. Efron) for the 0 to 100 range. Conclusions: • Chapter 4: Despite the generally strong linear associations between the physical characteristics of reference images in each scale, the scales themselves are not inherently accurate and are too different to allow for cross-calibration based on physical redness attributes. • Chapter 5: Subjective estimates of redness are based on a combination of chromaticity and vessel-based components. Psychophysical scaling of perceived redness lends itself to being used to cross calibrate the four clinical scales. • Chapter 6: The re-scaling of the reference images with anchored scaling suggests that redness was assessed based on within-scale characteristics and not using absolute redness scores, a mechanism that may be referred to as clinical scale constancy. The perceived redness data allow practitioners to modify the grades of the scale they commonly use so that comparisons of grading estimates between calibrated scales may be made. • Chapter 7: The use of the newly calibrated reference grades showed close agreement between grading estimates of all scales. The between-scale variability was similar to the variability typically observed when a single scale is repeatedly used. Perceived redness appears to be dependent upon the dynamic range of the reference images of the scale. In conclusion, this research showed that there are physical and perceptual differences between the reference images of all scales. A cross-calibration of the scales based on the perceived redness of the reference images provides practitioners with an opportunity to compare grades across scales, which is of particular value in research settings or if the same patient is seen by multiple practitioners who are familiar with using different scales.

In this thesis, the study focuses on the tunable frequency ratio of Sierpinski Gasket fractal antennas and we use the SAW substrate of piezoelectric material. By using the fractal structure and the substrate of piezoelectric material, the goal of the miniaturized antenna is achieved. The proposed antenna can be widely used in wireless communication products. Firstly, we design the Sierpinski Gasket fractal antenna on the FR4 substrate. The asymmetric geometry of Sierpinski Gasket fractal structure is proposed and we choose the proper discontinuity locations to design the three-band and tunable antenna for IEEE 802.11b/g/a wireless communication systems. The preliminary design of the Sierpinski Gasket fractal structure on the piezoelectric substrate allows us to compare simulated and measured results to improve the non-ideal processing factors. Finally, comparing with the existing products, we reduce the size of the miniaturized fractal antenna to 5x5mm^2 on the SAW substrate by coplanar waveguide, coupled-fed, shorting with conductive adhesive and high iteration stage of half-Sierpinski Gasket fractal structure for GPS band and IEEE 802.11b/g applications.