The theoretical part of this work deals with evolutionary algorithms (EA), neural networks (NN) and their synthesis in the form of neuroevolution. From a practical point of view, the aim of the work is to show the application of neuroevolution on two different tasks. The first task is the evolutionary design of the convolutional neural network (CNN) architecture that would be able to classify handwritten digits (from the MNIST dataset) with a high accurancy. The second task is the evolutionary optimization of neurocontroller for a simulated Falcon 9 rocket landing. Both tasks are computationally demanding and therefore have been solved on a supercomputer. As a part of the first task, it was possible to design such architectures which, when properly trained, achieve an accuracy of 99.49%. It turned out that it is possible to automate the design of high-quality architectures with the use of neuroevolution. Within the second task, the neuro-controller weights have been optimized so that, for defined initial conditions, the model of the Falcon booster can successfully land. Neuroevolution succeeded in both tasks.

Tato práce popisuje metodu analýzy translačního pohybu užitím křížové korelace. Ukazujeme, jakým způsobem se chová funkce křížové korelace obrazů s navzájem posunutými objekty, a jak nám to umožňuje nacházet jejich vektory posunu. Pro následnou implementaci je nalezena efektivní metoda pro hledání pouze požadovaného počtu lokálních maxim funkce.

Cílem této práce je vytvořit neuronovou síť která bude schopna rekonstruovat obličeje z fotografií na kterých je část obličeje překrytá maskou. Jsou prezentovány koncepty využívané při vývoji konvolučních neuronových sítí a generativních kompetitivních sítí. Dále jsou popsány koncepty používané v neuronových sítích specificky pro rekonstrukci fotografií obličejů. Je představen model generativní kompetitivní sítě využívající kombinaci hrazených konvolučních vrstev a víceškálových bloků schopný realisticky doplnit oblasti obličeje zakryté maskou.

This thesis proposes tasks of exercises for mentioned course and design and creation of automated evaluation system for these exercises. This thesis focuses on discussion and exemplary solutions of possible tasks of each exercise and description of created automated evaluation system. For evaluation program are made tests with chosen special data sets, which will prove it’s functionality in general data sets.

This paper takes aim at creating a consistent form of study materials, supplemented with illustrative examples, for Signals and systems subject. The thesis starts with basic characteristics of acoustic, image, biological and communication signals. Characteristics of linear signals and AD&DA conversion has been added to the next part and to complete the submission, discrete signals follow. Diploma thesis as a whole contains basic theoretical description of problematics, which it tries to supplement with interesting examples, connections, graphs and matlab scripts for illustrative presentation of mentioned problematics.

Aim of this thesis is description of neural network based edge detection methods that are substitute for classic methods of detection using edge operators. First chapters generally discussed the issues of image processing, edge detection and neural networks. The objective of the main part is to show process of generating synthetic images, extracting training datasets and discussing variants of suitable topologies of neural networks for purpose of edge detection. The last part of the thesis is dedicated to evaluating and measuring accuracy values of neural network.

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Cette thèse est motivée par le diagnostic et l’évaluation des maladies neuro-dégénératives et dans le but de diagnostique sur la base de l’attention visuelle.Néanmoins, le dépistage à grande échelle de la population n’est possible que si des modèles de prédiction automatique suffisamment robustes peuvent être construits. Dans ce contexte nous nous intéressons `a la conception et le développement des modèles de prédiction automatique pour un contenu visuel spécifique à utiliser dans l’expérience psycho-visuelle impliquant des patients atteints des maladies neuro-dégénératives. La difficulté d’une telle prédiction réside dans une très faible quantité de données d’entraînement. Les modèles de saillance visuelle ne peuvent pas être fondés sur les caractérisitiques “bottom-up” uniquement, comme le suggère la théorie de l’intégration des caractéristiques. La composante “top-down” de l’attention visuelle humaine devient prépondérante au fur et à mesure d’observation de la scène visuelle. L’attention visuelle peut-être prédite en se basant sur les scènes déjà observées. Les réseaux de convolution profonds (CNN) se sont révèlés être un outil puissant pour prédire les zones saillantes dans les images statiques.Dans le but de construire un modèle de prédiction automatique pour les zones saillantes dans les vidéos naturels et intentionnellement dégradées, nous avons conçu une architecture spécifique de CNN profond. Pour surmonter le manque de données d’apprentissage,nous avons conçu un système d’apprentissage par transfert dérivé de la méthode de Bengio.Nous mesurons ses performances lors de la prédiction de régions saillantes. Les r´esultatsobtenus sont int´eressants concernant la r´eaction des sujets t´emoins normaux contre leszones d´egrad´ees dans les vid´eos. La comparaison de la carte de saillance pr´edite des vid´eosintentionnellement d´egrad´ees avec des cartes de densit´e de fixation du regard et d’autresmod`eles de r´ef´erence montre l’int´erˆet du mod`ele d´evelopp´e. / This thesis is motivated by the diagnosis and the evaluation of the dementia diseasesand with the aim of predicting if a new recorded gaze presents a complaint of thesediseases. Nevertheless, large-scale population screening is only possible if robust predictionmodels can be constructed. In this context, we are interested in the design and thedevelopment of automatic prediction models for specific visual content to be used in thepsycho-visual experience involving patients with dementia (PwD). The difficulty of sucha prediction lies in a very small amount of training data.Visual saliency models cannot be founded only on bottom-up features, as suggested byfeature integration theory. The top-down component of human visual attention becomesprevalent as human observers explore the visual scene. Visual saliency can be predictedon the basis of seen data. Deep Convolutional Neural Networks (CNN) have proven tobe a powerful tool for prediction of salient areas in static images. In order to constructan automatic prediction model for the salient areas in natural and intentionally degradedvideos, we have designed a specific CNN architecture. To overcome the lack of learningdata we designed a transfer learning scheme derived from bengio’s method. We measureits performances when predicting salient regions. The obtained results are interestingregarding the reaction of normal control subjects against degraded areas in videos. Thepredicted saliency map of intentionally degraded videos gives an interesting results comparedto gaze fixation density maps and other reference models.

Viele Probleme der Riss- und Bruchmechanik sowie der mathematischen Physik lassen sich auf Lösungen von singulären Integralgleichungen über einem Intervall zurückführen. Diese Gleichungen setzen sich im Wesentlichen aus dem Cauchy'schen singulären Integraloperator und zusätzlichen Integraloperatoren mit festen Singularitäten in den jeweiligen Kernen zusammen. Zur numerischen Lösung solcher Gleichungen werden polynomiale Kollokations-Quadraturverfahren betrachet. Als Ansatzfunktionen und Kollokationspunkte werden dabei gewichtete Polynome und Tschebyscheff-Knoten gewählt. Die Gewichte sind so gewählt, dass diese das asymptotische Verhalten der Lösung in den Randpunkten widerspiegeln. Mit Hilfe von C*-Algebra Techniken, werden in dieser Arbeit notwendige und hinreichende Bedingungen für die Stabilität der Kollokations-Quadraturverfahren angegeben. Die theoretischen Resultate werden dabei durch numerische Berechnungen anhand des Problems der angerissenen Halbebene und des angerissenen Loches überprüft.

This work addresses the question of the efficient numerical solution of time-domain boundary integral equations with retarded potentials arising in the problems of acoustic and electromagnetic scattering. The convolutional form of the time-domain boundary operators allows to discretize them with the help of Runge-Kutta convolution quadrature. This method combines Laplace-transform and time-stepping approaches and requires the explicit form of the fundamental solution only in the Laplace domain to be known. Recent numerical and analytical studies revealed excellent properties of Runge-Kutta convolution quadrature, e.g. high convergence order, stability, low dissipation and dispersion. As a model problem, we consider the wave scattering in three dimensions. The convolution quadrature discretization of the indirect formulation for the three-dimensional wave equation leads to the lower triangular Toeplitz system of equations. Each entry of this system is a boundary integral operator with a kernel defined by convolution quadrature. In this work we develop an efficient method of almost linear complexity for the solution of this system based on the existing recursive algorithm. The latter requires the construction of many discretizations of the Helmholtz boundary single layer operator for a wide range of complex wavenumbers. This leads to two main problems: the need to construct many dense matrices and to evaluate many singular and near-singular integrals. The first problem is overcome by the use of data-sparse techniques, namely, the high-frequency fast multipole method (HF FMM) and H-matrices. The applicability of both techniques for the discretization of the Helmholtz boundary single-layer operators with complex wavenumbers is analyzed. It is shown that the presence of decay can favorably affect the length of the fast multipole expansions and thus reduce the matrix-vector multiplication times. The performance of H-matrices and the HF FMM is compared for a range of complex wavenumbers, and the strategy to choose between two techniques is suggested. The second problem, namely, the assembly of many singular and nearly-singular integrals, is solved by the use of the Huygens principle. In this work we prove that kernels of the boundary integral operators $w_n^h(d)$ ($h$ is the time step and $t_n=nh$ is the time) exhibit exponential decay outside of the neighborhood of $d=nh$ (this is the consequence of the Huygens principle). The size of the support of these kernels for fixed $h$ increases with $n$ as $n^a,a<1$, where $a$ depends on the order of the Runge-Kutta method and is (typically) smaller for Runge-Kutta methods of higher order. Numerical experiments demonstrate that theoretically predicted values of $a$ are quite close to optimal. In the work it is shown how this property can be used in the recursive algorithm to construct only a few matrices with the near-field, while for the rest of the matrices the far-field only is assembled. The resulting method allows to solve the three-dimensional wave scattering problem with asymptotically almost linear complexity. The efficiency of the approach is confirmed by extensive numerical experiments.