This work is focused on fractal dimension utilization for heart rate variability analysis. Both the theory of heart rate variability and the methods of HRV analysis in time domain and using the fractal dimesion are summarized. Short comparsion of time domain and fractal dimension method is presented.

Au cours des 20 dernières années, le développement des méthodes de télédétection et le succès des missions spatiales ont considérablement enrichi nos connaissances sur les surfaces planétaires révélant une immense diversité de morphologies. Etant le reflet de l'interaction et de la compétition entre des processus géologiques dont les modalités sont variables d'un corps à l'autre, elles sont largement étudiées pour retracer l'histoire géologique des planètes telluriques. En particulier, des informations précieuses sur la nature des processus et sur les lois générales qui contrôlent la formation et l'évolution des paysages sont enregistrées dans le champ topographique qui peut être analysé en tant que champ statistique. Nous rapportons dans cette thèse les résultats d'une étude comparative des propriétés statistiques de la topographie des principaux corps du système solaire en nous appuyant sur le volume croissant de données altimétriques et photogrammétriques. Notre approche est centrée sur la notion de loi d'échelle qui vise à caractériser les symétries du champ en traduisant le caractère auto-similaire des surfaces naturelles : les détails d'une surface ressemblent en général à des versions réduites de l'ensemble. Nous mettons en oeuvre plusieurs méthodes d'analyse de données dites «multifractales» pour dégager le meilleur modèle statistique capable de décrire la topographie dans différents contexte et proposons de nouveaux indicateurs de rugosité à l'échelle globale, régionale et locale. Nous montrons qu'en dépit de leur diversité, les surfaces du système solaire respectent des lois statistiques similaires que nous explicitons. En particulier nous montrons que la distribution globale des pentes d'un corps respecte en général des lois multifractales pour les échelles supérieures à 10-20km et présente une structure statistique différente pour les échelles inférieures. Enfin nous proposons une méthode pour générer des topographies synthétique sphériques dont le propriétés statistiques sont similaires aux topographie planétaire du système solaire. / Over the past 20 years, the development of remote sensing methods and the success of space missions have considerably enriched our knowledge of planetary surfaces revealing an immense diversity of morphologies. Being the reflection of the interaction and the competition between geological processes whose modalities are variable from one body to the other, they are widely studied to trace the geological history of the telluric planets. In particular, precise information on the nature of processes and general laws controlling the formation and evolution of landscapes is recorded in the topographic field which can be analyzed as a statistical field. We report in this thesis the results of a comparative study of the statistical properties of the topography of the main bodies of the solar system based on the increasing volume of altimetric and photogrammetric data. Our approach focuses on the notion of scaling law which aims to characterize the symmetries of the field by translating the self-similar nature of natural surfaces: the details of a surface generally look like reduced versions of the whole. We use several methods of analyzing so-called "multifractal" to derive the best statistical model capable of describing the topography in different contexts and propose new indicators of roughness at the global, regional and local scale. We show that in spite of their diversity, the surface of the solar system respects similar statistical laws. In particular, we show that the overall distribution of the slopes of a body generally respects multifractal laws for scales greater than 10-20 km and presents a different statistical structure for the lower scales. Finally, we propose a method for generating spherical synthetic topographies whose statistical properties are similar to the topographies in the solar system.

Sedimentation is a fundamental operation in wastewater treatment works. A rational design of sedimentation tanks is currently achieved by plotting iso-percentile (iso-percentage) concentration removal profiles from flocculent settling data. A major drawback of the graphical iso-percentage method is that the iso-percentile lines are often manually interpolated and are mere hand drawn estimations. This is because the settling behaviour of sludge particles is highly non-linear. The manual analytical process is therefore very tedious, inaccurate and subjective. Hence, an optimised design of sedimentation tanks is necessary in order to eliminate the errors incurred during data analysis. In this study, a mechanistic iso-percentile flocculent model (referred to as the velocity flocculation model) is developed to simulate the behaviour of flocculating colloidal particles in turbid water. This model is based on the physical meanings of flocculent settling particles and on fractal theory. It is formulated to produce automated iso-percentile curves which are fundamental in the design of sedimentation tanks. The iso-percentile model was vertically integrated into a velocity model to produce a model expressing the velocity of particles as a function of removal rate. The velocity model has an obvious advantage over the iso-percentile model in that it is easy to contextualize. It can be reverted back to the iso-percentile trajectory analysis eliminating the need for extensive data interpolation and may in future eliminate the need for settling column analysis altogether. In the current study, the integrated velocity form is used to predict instantaneous flocculent settling velocity of fine suspended particles under near quiescent conditions. This is vital since it is difficult to obtain velocity values in-situ or directly from sedimentation tanks. Model validity and competency was tested by a direct comparison with existing literature models, such as Ozer’s model and Ramatsoma and Chirwa’s model. Model comparison was based on the goodness of fit, the least sum of square errors and mathematical consistency with known flocculent settling behaviour. The newly developed iso-percentile model achieved a more accurate simulation of physical experimental data, did not violate any of the mathematical constraints and yielded lower sum of square errors than originally achieved by Ozer and Ramatsoma and Chirwa. Notably, the proposed velocity model offers a distinctive advantage over conventional interpolated-iso-percentile based models which are prone to numerical errors during interpolation. Its performance (velocity model) was compared against Je and Chang’s velocity model. Higher velocity values were observed for the new model than for Je and Chang’s model implying that empirically based models would tend to under-predict the velocity values. The model developed in this study brings us one step closer to achieving full automation of the settling tank and clarifier design. / Dissertation (MEng)--University of Pretoria, 2013. / gm2014 / Chemical Engineering / unrestricted

The semiconductor industry was benefited by the advances in technology in the last decades. This fact has an impact on the sensors field, where the simple transducer was evolved into smart miniaturized multi-functional microsystems. However, commercially available gas and biological sensors are mostly bulky, expensive, and power-hungry, which act as obstacles to mass use. The aim of this work is gas and biological sensing using capacitive structures. Capacitive sensors were selected due to its design simplicity, low fabrication cost, and no DC power consumption. In the first part, the dominant structure among interdigitated electrodes (IDEs), fractal curves (Peano and Hilbert) and Archimedean spiral was investigated from capacitance density perspective. The investigation consists of geometrical formula calculations, COMSOL Multiphysics simulations and cleanroom fabrication of the capacitors on a silicon substrate. Moreover, low-cost fabrication on flexible plastic PET substrate was conducted outside cleanroom with rapid prototyping using a maskless laser etching. The second part contains the humidity, Volatile Organic compounds (VOCs) and Ammonia sensing of polymers, Polyimide and Nafion, and metal-organic framework (MOF), Cu(bdc)2.xH2O using IDEs and tested in an automated gas setup for experiment control and data extraction. The last part includes the biological sensing of C - reactive protein (CRP) quantification, which is considered as a biomarker of being prone to cardiac diseases and Bovine serum albumin (BSA) protein quantification, which is used as a reference for quantifying unknown proteins.

Internet of Things (IoT) is a new emerging paradigm which requires billions of wirelessly connected devices that communicate with each other in a complex radio-frequency (RF) environment. Considering the huge number of devices, recharging batteries or replacing them becomes impractical in real life. Therefore, harvesting ambient RF energy for powering IoT devices can be a practical solution to achieve self-charging operation. The antenna for the RF energy harvesting application must work on multiple frequency bands (multiband or wideband) to capture as much power as possible from ambient; it should be compact and small in size so that it can be integrated with IoT devices; and it should be low cost, considering the huge number of devices. This thesis presents a fully printed 3D cube Cantor fractal RF energy harvesting unit, which meets the above-mentioned criteria. The multiband Cantor fractal antenna has been designed and implemented on a package of rectifying circuits using additive manufacturing (combination of 3D inkjet printing of plastic substrate and 2D metallic screen printing of silver paste) for the first time for RF energy harvesting application. The antenna, which is in a Cantor fractal shape, is folded on five faces of a 3D cube where the bottom face accommodates rectifying circuit with matching network. The rectenna (rectifying antenna) harvests RF power from GSM900, GSM1800, and 3G at 2100 MHz frequency. Indoor and outdoor field tests of the RF energy harvester have been conducted in the IMPACT lab and the King Abdullah University of Science and Technology (KAUST) campus territory, and 252.4 mV of maximum output voltage is harvested.

Tesis por compendio / [ES] La presbicia es el error refractivo con mayor incidencia en la población debido al envejecimiento de la misma. Existen múltiples medidas para corregirla, desde lentes oftálmicas, lentes de contacto, lentes intraoculares etc¿ Actualmente, los implantes intracorneales (corneal inlays) se encuentran entre las soluciones más novedosas. Estos dispositivos se sitúan en el estroma corneal mediante una cirugía mínimamente invasiva. Existen tres implantes intracorneales comerciales cuyos mecanismos difieren entre sí. El más estudiado es el KAMRA inlay® y utiliza el efecto estenopeico para aumentar la profundad de foco. Por otra parte, Flexivue Microlens® se basa en una estructura multifocal donde el centro focaliza en lejos mientras que la periferia focaliza en cerca. Por último, Raindrop Near Vision® modifica la estructura de la córnea para aumentar el radio de curvatura de la parte central de ésta y permitir enfocar a distancias próximas. Todos ellos deben permitir el paso de nutrientes y oxígeno a través de la córnea, ya sea mediante aperturas o siendo permeables. Existe un cuarto tipo de implante intracorneal no comercial desarrollado por el Diffractive Optics Group (DiOG), el cual distribuye los micro-agujeros, que permiten el paso de nutrientes y oxígeno, en las zonas transparentes de una placa zonal de Fresnel. Además, contiene un agujero central, que actúa como estenopeico. Este dispositivo tiene como nombre Diffractive Corneal Inlay (DCI). Esta Tesis pretende modificar y optimizar los parámetros de diseño del DCI y comparar sus propiedades ópticas con otros implantes intracorneales comerciales. / [EN] Presbyopia is the refractive error with the highest incidence in the population due to the aging of the population. There are many solutions to correct it, from ophthalmic lenses, contact lenses, intraocular lenses, etc... Currently the corneal inlays are among the newest solutions. These devices are placed in the corneal stroma by means of minimally invasive surgery. There are three commercial corneal inlays whose mechanisms differ from each other. The most studied is KAMRA inlay® which uses the pinhole effect to increase the depth of focus. On the other hand, Flexivue Microlens® is based on a multi-focal structure where the center focuses at distance vision while the periphery focuses at near vision. Finally, Raindrop Near Vision® modifies the structure of the cornea to increase the radius of curvature of the central part of it and allow focusing at near vision. All of them must all allow pass through to the cornea nutrients and oxygen, either by holes or being permeable. There is a fourth type of non-commercial corneal inlay developed by the Diffractive Optics Group (DiOG), which distributes micro-holes, allow the passage of nutrients and oxygen, in the transparent zones of a Fresnel zone plate. In addition, it contains a central hole, which acts as a pinhole. This device is called Diffractive Corneal Inlay (DCI). This Thesis aims to modify and optimize the design parameters of the DCI and to compare its optical properties with other commercial corneal inlays. / [CA] La presbícia es l'error refractiu amb major incidència en la població degut a l'envelliment d'aquesta. Hi existeixen múltiples solucions per corregir-la, des de lents oftàlmiques, lents de contacte, lents intraoculars, etc... Actualment, els implants intracorneales comercials es troben entre les solucions mes noves. Aquests dispositius es situen a l'estroma corneal mitjançant uns cirurgia mínimament invasiva. Hi existeixen tres tipus d'implants intracorneals amb diferents mecanismes. El mes estudiat es el KAMRA inlay® i utilitza l'efecte estenopeic per augmentar la profunditat de focus. Per altra banda, Flexivue Microlens® es basa en una estructura multifocal on el centre de la lent focalitza en el focus llunyà mentre que la perifèria focalitza prop. Per últim Raindrop Near Vision® modifica l'estructura de la còrnia per augmentar el radi de curvatura de la part central d'aquesta i permetre enfocar a distàncies pròximes. Tots ells deuen permetre el pas de nutrients i oxigen a través de la còrnia, ja siga mitjançant obertures o sent permeables. Existeix un quart tipus d'implant intracorneal no comercial desenvolupat pel Diffractive Optics Group (DiOG), el qual distribueix els micro-forats, que permeten el flux de nutrients i oxigen, en les zones transparents d'una placa zonal de Fresnel. A més, contenen un forat central, que actua com estenopeic. Aquest dispositiu rep el nom Diffractive Corneal Inlay (DCI). Aquesta tesi pretén modificar i optimitzar els paràmetres de disseny del DCI i comparar les seues propietats òptiques amb altres implantes intracorneals comercials. / Funding: Ministerio de Economía y Competitividad (DPI2015-71256-R); Generalitat Valenciana (PROMETEO/2019/048). D. Montagud-Martínez and V. Ferrando acknowledge the financial support from the Universitat Politècnica de València, Spain (fellowships FPI-2016 and PAID10-18, respectively). / Montagud Martínez, D. (2020). Diseño, realización y evaluación de implantes intracorneales difractivos multifocales [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/153474 / TESIS / Compendio

Carbon dioxide efflux rates (CER) of stems and roots of overstory and understory black cherry (<i>Prunus serotina</i> Ehrh., BC), red maple (<i>Acer rubrum</i> L., RM) and northern red oak (<i>Quercus rubra</i> L., RO) trees were monitored over two growing seasons at two contrasting sites in the Great Smoky Mountains to investigate diurnal and seasonal patterns in respiration and to develop prediction models based on environmental and plant parameters. CER of small roots (d<0-8 mm) was measured with a newly developed system which allows periodic <i>in situ</i> measurements by using permanently installed flexible cuvettes. Temperature-adjusted CER of roots showed no diel variation. The moderate long-term changes occurred simultaneously in all species and size classes, suggesting that they were driven mostly by environmental factors. Mean root CER ranged from 0.5 to 4.0 nmol g⁻¹ d.w. s⁻¹. Rates were up to six times higher for fine roots (d<2.0 mm) than for coarse roots. CER (per unit length) of boles (d>10 cm) and twigs (d<2 cm) was related to diameter by the function lnCER = a+<i>D</i>·lnd, with <i>D</i> between 1.2 and 1.8. A new, scale-invariant measure of CER, based on <i>D</i>, facilitated comparisons across diameters. Q₁₀ varied with the method of determination, and it was higher in spring (1.8-2.5) than in autumn (1.4-1.5) for all species. Daytime bole CER often fell below temperature-based predictions, likely due to transpiration. The reduction (usually <10%) was less pronounced at the drier site. Twig CER showed more substantial (often >±50%) deviations from the predictions. Deviations were higher in the canopy than in the understory. Mean bole maintenance respiration (at 20°C and d=20 cm) was 0.66, 0.43 and 0.50 μMol m⁻¹, while the volume-based growth coefficient was around 5, 6 and 8 mol cm⁻³ for BC, RM and RO, respectively. In a controlled study, BC and RM seedlings were fumigated in open-top chambers with sub-ambient, ambient and twice-ambient levels of ozone. The twice-ambient treatment reduced stem CER in BC by 50% (p=0.05) in July, but there was no treatment effect in September or in RM. Ozone reduced root/shoot ratio and diameter growth in BC, and P_max in both species. / Ph. D.

Tesis por compendio / The diffractive optical elements have enhanced his importance in the last decades due to the improvement of the technology which allows its construction and the greater computing power that helps predicting the behaviour of the diffractive structures in function of the design parameters without en extra cost. The periodic symmetry become a key factor in order to understand the performance of these elements, and it allows to study the properties and the applicability of the different diffractive elements. However, this periodicity also introduces certain limitation in the design of the elements and their properties, such as high chromatic aberration when they are used as image forming elements. To overcome this limitations it was proposed the use of deterministic aperiodic sequences in the design of the diffractive optical elements. In this Thesis work I study different aperiodic sequences and their effect in the design of new diffractive structures. In particular, we use the Cantor fractal set, the Fibonacci sequence and the Thue--Morse series in the design of devices with different purposes. Along the development of the Thesis there have been generated new diffractive elements which overcome some limitations, opening new field for the application of pre-existing technologies. Between them, they can be highlighted the optical alignment systems, the generation of optical vortex, the reduction of the chromatic aberration and the enhancement of the focal depth in image forming elements. / Los elementos ópticos difractivos han ganado importancia en las últimas décadas debido al avance de la tecnología que permite su construcción y al aumento de la potencia de cálculo computacional que permite predecir, con un coste mínimo, su comportamiento en función de los múltiples parámetros que definen su estructura. La periodicidad constituye un factor clave a la hora de entender su funcionamiento y estudiar las propiedades y aplicabilidad de los diferentes tipos de elementos difractivos. Ahora bien, esta periodicidad también introduce ciertas limitaciones en el diseño de los elementos y en sus propiedades, como por ejemplo una alta aberración cromática al ser utilizados como elementos formadores de imagen. Para superar estas limitaciones se propuso la aplicación de secuencias aperiódicas deterministas al diseño de los elementos ópticos difractivos. En este trabajo de Tesis se han estudiado diferentes secuencias aperiódicas y sus efectos en el diseño de nuevas estructuras difractivas. En particular, se ha utilizado la secuencia fractal de Cantor, la serie de Fibonacci y la serie de Thue--Morse en el diseño de dispositivos difractivos con diferentes finalidades. A lo largo del desarrollo del trabajo de Tesis se han generado nuevos elementos difractivos que superan ciertas limitaciones, abriendo nuevos campos de aplicación a tecnologías preexistentes. Entre ellos, podemos destacar los sistemas de alineación óptica, la generación de vórtices ópticos, la reducción de la aberración cromática y el aumento de la profundidad de foco en elementos formadores de imagen. / Els elements òptics difractius han guanyat importancia les últimes dècades degut a l'avanç de la tecnología que permet la seua construcció y a l'augment de la potència de càlcul computacional que permet predir, amb un cost mínim, el seu comportament en funció dels diferents parámetres que defineixen la seua estructura. La periodicitat constitueix un factor clau a l'hora d'entendre el seu funcionament y estudiar les propietats y aplicabilitat dels diferents tipus d'elements difractius. Ara be, aquesta periodicitat tambe introdueix certes llimitacions en el disseny dels elements y les seus propietats, com per exemple una elevada aberració cromàtica quan actuen com a elements formadors d'imatges. Per superar aquestes llimitacions es va proposar l'aplicació de diferents sequencies aperiòdiques deterministes al disseny dels elements òptics difractius. En aquest treball de Tesi estudie diferents sequencies aperiòdiques y els seus efectes en el disseny de noves estructures difractives. En particular, s'han utilitzat la secuencia fractal de Cantor, la serie de Fibonacci y la serie de Thue--Morse en el disseny de dispositius difractius amb diferents finalitats. Al llarg del desenvolupament del treball de Tesi s'han generat nous elements difractius que superen certes llimitacions, obint nous camps d'aplicació a tecnologies preexistents. Entre ells, podem destacar els sistemes d'alineació òptica, la generació de vòrtex òptics, la reducció de l'aberració cromàtica y l'augment de la profunditat de fòcus d'elements formadors d'imatges. / Ferrando Martín, V. (2017). Diseño y aplicaciones de nuevas estructuras difractivas aperiódicas [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/79508 / TESIS / Premios Extraordinarios de tesis doctorales / Compendio

This thesis study two promising methods used to define the multiscale CAPM - the wavelet-based decomposition and the fractal regression. Their estimates, obtained on monthly excess return on ten portfolios formed on beta in the US market, are compared in the period from November 2000 to October 2020 and, subsequently, in the period from November 1965 to October 2020. In the first period, the multiscale beta is not significantly different from the original single-scale beta for most of the portfolios. Contrary, both methods uncover significant multiscale behavior of the beta in the second period. Specifically, the high-beta portfolios have higher multiscale beta at longer investment horizons, mainly at wavelet scale 3 and scales 12-24 of the fractal regression. Overall, both methods deliver consistent results, and seem suitable for extending the CAPM with an investment horizon. JEL Classification Keywords G12, C20 CAPM, asset pricing, multiscale analysis, wavelets, fractal regression Title Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression

This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.