The diploma thesis presents a collection of solved problems in binary relations. Students are familiarized with various applications of binary relations on high school mathematics and geometry. The work focuses on graphical representation of binary relations and their use in solving equations, inequalities and their sys- tems. It is a teaching text designated for a mathematics seminar at high school. In addition to exercises, it also includes an introduction of new concepts which are supplemented by relevant definitions and illustrative examples. 1

Apesar do grau relativamente alto de maturidade existente na área de pesquisa de aprendizado supervisionado em lote, na qual são utilizados dados originários de problemas estacionários, muitas aplicações reais lidam com fluxos de dados cujas distribuições de probabilidade se alteram com o tempo, ocasionando mudanças de conceito. Diversas pesquisas vêm sendo realizadas nos últimos anos com o objetivo de criar modelos precisos mesmo na presença de mudanças de conceito. A maioria delas, no entanto, assume que tão logo um evento seja classificado pelo algoritmo de aprendizado, seu rótulo verdadeiro se torna conhecido. Este trabalho explora as situações complementares, com revisão dos trabalhos mais importantes publicados e análise do impacto de atraso na disponibilidade dos rótulos verdadeiros ou sua não disponibilização. Ainda, propõe um novo algoritmo que reduz drasticamente a complexidade de aplicação do teste de hipótese não-paramétrico Kolmogorov-Smirnov, tornado eficiente seu uso em algoritmos que analisem fluxos de dados. A exemplo, mostramos sua potencial aplicação em um método de detecção de mudança de conceito não-supervisionado que, em conjunto com técnicas de Aprendizado Ativo e Aprendizado por Transferência, reduz a necessidade de rótulos verdadeiros para manter boa performance de um classificador ao longo do tempo, mesmo com a ocorrência de mudanças de conceito. / Despite the relatively maturity of batch-mode supervised learning research, in which the data typifies stationary problems, many real world applications deal with data streams whose statistical distribution changes over time, causing what is known as concept drift. A large body of research has been done in the last years, with the objective of creating new models that are accurate even in the presence of concept drifts. However, most of them assume that, once the classification algorithm labels an event, its actual label become readily available. This work explores the complementary situations, with a review of the most important published works and an analysis over the impact of delayed true labeling, including no true label availability at all. Furthermore, this work proposes a new algorithm that heavily reduces the complexity of applying Kolmogorov- Smirnov non-parametric hypotheis test, turning it into an uselful tool for analysis on data streams. As an instantiation of its usefulness, we present an unsupervised drift-detection method that, along with Active Learning and Transfer Learning approaches, decreases the number of true labels that are required to keep good classification performance over time, even in the presence of concept drifts.

We investigate here some aspects of cycle bases of undirected graphs that allow the iterative construction of all elementary cycles. We introduce the concept of quasi-robust bases as a generalization of the notion of robust bases and demonstrate that a certain class of bases of the complete bipartite graphs K m,n with m,n _> 5 is quasi-robust but not robust. We furthermore disprove a conjecture for cycle bases of Cartesian product graphs.

We present an Embedded Boundary with Adaptive Mesh Refinement technique for solving the compressible Navier Stokes equations in arbitrary complex domains; followed by a numerical studies for the effect of circular cylinders on the transient dynamics of the Richtmyer-Meshkov Instability. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost-fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The Navier Stokes equations are numerically solved by the second order multidimensional upwind method. Block-structured AMR, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the Embedded Boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The effects on the transient dynamics of the Richtmyer-Meshkov instability due to small scale perturbations introduced on the shock-wave or the material interface by a single or set of solid circular cylinders were computationally investigated using the developed technique. First, we discuss the RMI initiated on a flat interface by a rippled shock-wave that is disturbed by a single circular cylinder. Then, we study the effect of introducing a number of circular cylinders on the interface. The arrangement of the cylinders set mimic (in a two dimensional domain) the presence of the solid supporting grid wires used in the formation of the material interface in the experimental setup. We analyzed their effects on the mixing layer growth and the mixedness level, and qualitatively demonstrate the cylinders' perturbation effects on the mixing layer structure. We modeled the cylinders' influence based on their diameters; and showed the model ability to predict the variation of the mixing layer growth for different flow parameters.

Sensors, as a crucial part of autonomous driving, are primarily used for perceiving the environment. The recent deep learning development of different sensors has demonstrated the ability of machines recognizing and understanding their surroundings. Automotive radar, as a primary sensor for self-driving vehicles, is well-known for its robustness against variable lighting and weather conditions. Compared with camera-based deep learning development, Object detection using automotive radars has not been explored to its full extent. This can be attributed to the lack of public radar datasets. In this thesis, we collect a novel radar dataset that contains radar data in the form of Range-Azimuth-Doppler tensors along with the bounding boxes on the tensor for dynamic road users, category labels, and 2D bounding boxes on the Cartesian Bird-EyeView range map. To build the dataset, we propose an instance-wise auto-annotation algorithm. Furthermore, a novel Range-Azimuth-Doppler based multi-class object detection deep learning model is proposed. The algorithm is a one-stage anchor-based detector that generates both 3D bounding boxes and 2D bounding boxes on Range-AzimuthDoppler and Cartesian domains, respectively. Our proposed algorithm achieves 56.3% AP with IOU of 0.3 on 3D bounding box predictions, and 51.6% with IOU of 0.5 on 2D bounding box predictions. Our dataset and the code can be found at https://github.com/ZhangAoCanada/RADDet.git.

Kartézské genetické programován (CGP) je evoluc inspirovaná metoda strojového učen, která je primárně určená pro automatizovaný návrh programů a čslicových obvodů. CGP je úspěšné v řešen mnoha úloh z reálného světa. Avšak k nalezen inovativnch řešen obvykle potřebuje značný výpočetn výkon. Každý kandidátn program navržený pomoc CGP mus být spuštěn, aby se zjistilo, do jaké mry tento program řeš zadaný problém, a mohla mu být přiřazena fitness hodnota. Právě vyhodnocen fitness bývá výpočetně nejnáročnějš část návrhu pomoc CGP. Tato práce se zabývá využitm koevoluce prediktorů fitness v CGP za účelem zrychlen procesu evolučnho návrhu prováděného pomoc CGP. Prediktor fitness je malá podmnožina trénovacch dat použvaná pro rychlý odhad fitness hodnoty namsto náročného vyhodnocen objektivn fitness hodnoty. Koevoluce prediktorů fitness je optimalizačn metoda modelován fitness, která snižuje náročnost a frekvenci výpočtu fitness. V této práci je koevolučn algoritmus přizpůsoben pro CGP a jsou představeny a zkoumány tři přstupy k zakódován prediktorů fitness. Představená metoda je experimentálně vyhodnocena v pěti úlohách symbolické regrese a v úloze návrhu obrazových filtrů. Výsledky experimentů ukazuj, že pomoc této metody lze významně snžit výpočetn čas, který CGP potřebuje pro řešen zkoumané třdy úloh.

This thesis deals with image filter design using coevolutionary algorithms. It contains a description of evolutionary algorithms, focusing on genetic programming, cartesian genetic programming and coevolution, the reader can learn about image filters too. The next chapters contain the design of image filters and noise detectors using cooperative coevolution, and the implementation and testing of the proposed filter. In the last chapter the proposed filter is compared to other filters created using evolutionary algorithms but without coevolution.

The aim of this work is to design and implement a program for automated design of convolutional neural networks (CNN) with the use of evolutionary computing techniques. From a practical point of view, this approach reduces the requirements for the human factor in the design of CNN architectures, and thus eliminates the tedious and laborious process of manual design. This work utilizes a special form of genetic programming, called Cartesian genetic programming, which uses a graph representation for candidate solution encoding.This technique enables the user to parameterize the CNN search process and focus on architectures, that are interesting from the view of used computational units, accuracy or number of parameters. The proposed approach was tested on the standardized CIFAR-10dataset, which is often used by researchers to compare the performance of their CNNs. The performed experiments showed, that this approach has both research and practical potential and the implemented program opens up new possibilities in automated CNN design.

This master thesis describes stochastic optimization algorithms inspired in nature that use population of individuals - evolutionary algorithms. Genetic programming and its variant - cartesian genetic programming is described in a greater detail. This thesis is further focused on the analysis and visualization of digital circuit evolution records. Existing tools for visualization of the circuit evolution were analysed, but because no suitable tool allowing complex analysis of the circuit evolution was found, a new set of functions was proposed and the principles of a new tool were formulated. These functions were implemented in form of an interactive GUI application in Java programming language. The application was described in detail and then used for analysis of digital circuit evolution records.

This thesis deals with the usage of coevolution in the task of symbolic regression. Symbolic regression is used for obtaining mathematical formula which approximates the measured data. It can be executed by genetic programming - a method from the category of evolutionary algorithms that is inspired by natural evolutionary processes. Coevolution works with multiple evolutionary processes that are running simultaneously and influencing each other. This work deals with the design and implementation of the application which performs symbolic regression using coevolution on test-based problems. The test set was generated by a new method, which allows to adjust its size dynamically. Functionality of the application was verified on a set of five test tasks. The results were compared with a coevolution algorithm with a fixed-sized test set. In three cases the new method needed lesser number of generations to find a solution of a desired quality, however, in most cases more data-point evaluations were required.