Fractal geometry is a new branch of mathematics. This report presents the tools, methods and theory required to describe this geometry. The power of Iterated Function Systems (IFS) is introduced and applied to produce fractal images or approximate complex estructures found in nature. The focus of this thesis is on how fractal geometry can be used in applications to computer graphics or to model natural objects.

A software process improvement study is presented. The literature on software development processes and their improvement is reviewed. The current peer review process at Software Engineering Directorate of the X Company, Ankara, T&uuml / rkiye (XCOM) is studied and the static software development metrics based on a recent proposal have been evaluated. The static software metrics based improvement suggestions and the author&rsquo / s improvement suggestions discussed with the senior staff are compared. An improved peer review process is proposed. The static software development metrics have been evaluated on the improved process to see the impacts of the improvements. The improved process has been already implemented at XCOM and preliminary results have been obtained.

Affected by continuous developments and innovations in information and communication technologies, governments have initiated the e-transformation process to adopt the knowledge based economy and to be competitive in global world. Throughout their journey of e-transformation, governments need to learn where they are in order to shift their position to advanced level. To assist governments in their evaluation of e-transformation, this thesis offers a metric system derived from some of the well known e-government evaluation studies. The system proposed is composed of metrics distributed into six main categories: &ldquo / Technology Infrastructure&rdquo / , &ldquo / e-Society&rdquo / , &ldquo / Human Capital&rdquo / , &ldquo / Political and Regulatory Environment&rdquo / , &ldquo / Economy Environment&rdquo / , and &ldquo / Online Services and Applications&rdquo / . Set of metrics to be attached in these categories are determined in terms of widely recognized measures of the tools reviewed. In order to implement the system, 30 countries are analyzed gathering data published by major research institutions. Additionally, this thesis examines Turkey&rsquo / s level on e-transformation from the perspectives of e-government evaluation studies reviewed.

In this paper, the gap metric is introduced to study the robustness of the stability of feedback systems. A relation between the gap metric and coprime fractions is also investigated. It is shown that the stability radius of the controller in the gap metric is equal to the stability margin of the controller. In the loop-shaping design procedure in the £h-gap metric, it is practically hard to formulate an ideal controller. Finally, this paper studied the conservatism of the gap metric, and proposed some properties that can help for control design and analysis.

We will study the solution stability of a parametric quasi-variational inequality without the monotonicity assumption of operators. By using the degree theory and the natural map we show that under certain conditions, the solution map of the problem is lower semi-continuous with respect to parameters.

<p>One way of modeling human knowledge is by using multidimensional spaces, in which an object is represented as a point in the space, and the distances among the points reflect the similarities among the represented objects. The distances are measured with some metric, commonly some instance of the Minkowski metric. The instances differ with the magnitude of the so-called r-parameter. The instances most commonly mentioned in the literature are the ones where r equals 1, 2 and infinity.</p><p>Cognitive scientists have found out that different metrics are suited to describe different dimensional combinations. From these findings an important distinction between integral and separable dimensions has been stated (Garner, 1974). Separable dimensions, e.g. size and form, are best described by the city-block metric, where r equals 1, and integral dimensions, such as the color dimensions, are best described by the Euclidean metric, where r equals 2. Developmental psychologists have formulated a hypothesis saying that small children perceive many dimensional combinations as integral whereas adults perceive the same combinations as separable. Thus, there seems to be a shift towards increasing separability with age or maturity.</p><p>Earlier experiments show the same phenomenon in adult short-term learning with novel stimuli. In these experiments, the stimuli were first perceived as rather integral and were then turning more separable, indicated by the Minkowski-r. This indicates a shift towards increasing separability with familiarity or skill.</p><p>This dissertation aims at investigating the generality of this phenomenon. Five similarity-rating experiments are conducted, for which the best fitting metric for the first half of the session is compared to the last half of the session. If the Minkowski-r is lower for the last half compared to the first half, it is considered to indicate increasing separability.</p><p>The conclusion is that the phenomenon of increasing separability during short-term learning cannot be found in these experiments, at least not given the operational definition of increasing separability as a function of a decreasing Minkowski-r. An alternative definition of increasing separability is suggested, where an r-value ‘retreating’ 2.0 indicates increasing separability, i.e. when the r-value of the best fitting metric for the last half of a similarity-rating session is further away from 2.0 compared to the first half of the session.</p>

<p>During the last decade, potential theory and p-harmonic functions have been developed in the setting of doubling metric measure spaces supporting a <em>p</em>-Poincar´e inequality. This theory unifies, and has applications in several areas of analysis, such as weighted Sobolev spaces, calculus on Riemannian manifolds and Carnot groups, subelliptic differential operators and potential theory on graphs.</p><p>In this thesis we investigate the double obstacle problem for p-harmonic functions on metric spaces. We show the existence and uniqueness of solutions and their continuity when the obstacles are continuous. Moreover the solution is p-harmonic in the open set where it does not touch the continuous obstacles. The boundary regularity of the solutions is also studied.</p><p>Furthermore we study two kinds of convergence problems for the solutions. First we let the obstacles vary and fix the boundary values and show the convergence of the solutions. Second we consider an increasing sequence of open sets, with union Ω, and fix the obstacles and the boundary values. We show that the solutions of the obstacle problems in these sets converge to the solution of the corresponding problem in Ω.</p> / <p>Låt oss börja med att betrakta följande situation: Vi vill förflytta oss från en plats vid ena sidan av en äng till en viss punkt på andra sidan ängen. På båda sidor om ängen finns skogsområden som vi inte får gå in i. Ängen är tyvärr inte homogen utan består av olika sorters mark som vi har noggrant beskrivet på en karta. Vi vill göra förflyttningen på smidigast sätt, men då ängen inte är homogen ska vi förmodligen inte gå rakaste vägen utan ska anpassa vägen optimalt efter terrängen. Detta är ett exempel på ett dubbelhinderproblem där hindren är skogsområdena på sidorna som vi måste hålla oss utanför.</p><p>Mer abstrakt vill man minimiera energin hos funktioner som tar vissa givna randvärden (de givna start- och slutpunkterna i exemplet ovan) och som håller sig mellan ett undre och ett övre hinder. I denna avhandling studeras detta dubbelhinderproblem i väldigt allmänna situationer.</p><p>För att kunna lösa hinderproblemet krävs det att vi tillåter ickekontinuerliga lösningar och då visas i avhandlingen att hinderproblemet är entydigt lösbart. Ett huvudresultat i avhandlingen är att om våra hinder är kontinuerliga så blir även lösningen kontinuerlig. Vidare visas diverse konvergenssatser som visar hur lösningarna varierar när hindren eller området i vilket problemet löses varierar.</p><p>Hinderproblem har utöver eget intresse viktiga tillämpningar i potentialteorin, bland annat för att studera motsvarande energiminimeringsproblem utan hinder.</p>

In this research work, we propose a facial expression classification method using metric learning-based k-nearest neighbor voting. To achieve accurate classification of a facial expression from frontal face images, we first learn a distance metric structure from training data that characterizes the feature space pattern, then use this metric to retrieve the nearest neighbors from the training dataset, and finally output the classification decision accordingly. An expression is represented as a fusion of face shape and texture. This representation is based on registering a face image with a landmarking shape model and extracting Gabor features from local patches around landmarks. This type of representation achieves robustness and effectiveness by using an ensemble of local patch feature detectors at a global shape level. A naive implementation of the metric learning-based k-nearest neighbor would incur a time complexity proportional to the size of the training dataset, which precludes this method being used with enormous datasets. To scale to potential larger databases, a similar approach to that in [24] is used to achieve an approximate yet efficient ML-based kNN voting based on Locality Sensitive Hashing (LSH). A query example is directly hashed to the bucket of a pre-computed hash table where candidate nearest neighbors can be found, and there is no need to search the entire database for nearest neighbors. Experimental results on the Cohn-Kanade database and the Moving Faces and People database show that both ML-based kNN voting and its LSH approximation outperform the state-of-the-art, demonstrating the superiority and scalability of our method. / text

During the past few years there has been a significant interest in spectrum splitting systems to increase the overall efficiency of photovoltaic solar energy systems. However, methods for comparing the performance of spectrum splitting systems and the effects of optical spectral filter design on system performance are not well developed. This dissertation first establishes a method to analyze and compare spectrum splitting systems with different filters, PV cells types and geometries. The method examines the system conversion efficiency in detail and the role of optical spectral filters. A new metric termed the Improvement over Best Bandgap is defined which expresses the efficiency gain of the spectrum splitting system with respect to a similar system that contains the highest constituent single bandgap photovoltaic cell. Also, this work expands the analysis on dispersive spectrum splitting systems. The dispersive effects of transmission type filters are evaluated using a cross-correlation analysis. Lastly, this work presents a grating-over-lens design for dispersive spectrum splitting. In this geometry, a transmission grating is placed at the entrance of a lens. Part of the incident solar spectrum is diffracted off-axis from normal incidence to the lens. The diffracted spectral range comes to a focus at an off-axis point and the undiffracted spectrum comes to a focus at the paraxial focus of the lens. Since the diffracted wave is planar and off-axis, the off-axis focal points suffer from aberrations that increase system loss. In this work, a novel aberration compensation technique is presented using non-planar transmission gratings recorded using a conjugate object beam to modify the off-axis wavefront. Diverging sources are used as conjugate object and reference beams. The spherical waves are incident at the lens and the grating is recorded at the entrance aperture of the solar concentrator. The on-axis source is adjusted to produce an on-axis planar wavefront at the hologram plane. The off-axis source is approximated to a diffraction limited spot producing a non-planar off-axis wavefront on the hologram plane. Illumination with a planar AM1.5 spectrum reproduces an off-axis diffraction-limited spot on the focal plane. Models and experimental data are presented to quantify the reduction in losses achieved with aberration correction.

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