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.

As ever more challenging designs are required in present-day industries, the traditional trial-and-error procedure frequently used for designing mechanical parts slows down the design process and yields suboptimal designs, so that new approaches are needed to obtain a competitive advantage. With the ascent of the Finite Element Method (FEM) in the engineering community in the 1970s, structural shape optimization arose as a promising area of application. However, due to the iterative nature of shape optimization processes, the handling of large quantities of numerical models along with the approximated character of numerical methods may even dissuade the use of these techniques (or fail to exploit their full potential) because the development time of new products is becoming ever shorter. This Thesis is concerned with the formulation of a 3D methodology based on the Cartesian-grid Finite Element Method (cgFEM) as a tool for efficient and robust numerical analysis. This methodology belongs to the category of embedded (or fictitious) domain discretization techniques in which the key concept is to extend the structural analysis problem to an easy-to-mesh approximation domain that encloses the physical domain boundary. The use of Cartesian grids provides a natural platform for structural shape optimization because the numerical domain is separated from a physical model, which can easily be changed during the optimization procedure without altering the background discretization. Another advantage is the fact that mesh generation becomes a trivial task since the discretization of the numerical domain and its manipulation, in combination with an efficient hierarchical data structure, can be exploited to save computational effort. However, these advantages are challenged by several numerical issues. Basically, the computational effort has moved from the use of expensive meshing algorithms towards the use of, for example, elaborate numerical integration schemes designed to capture the mismatch between the geometrical domain boundary and the embedding finite element mesh. To do this we used a stabilized formulation to impose boundary conditions and developed novel techniques to be able to capture the exact boundary representation of the models. To complete the implementation of a structural shape optimization method an adjunct formulation is used for the differentiation of the design sensitivities required for gradient-based algorithms. The derivatives are not only the variables required for the process, but also compose a powerful tool for projecting information between different designs, or even projecting the information to create h-adapted meshes without going through a full h-adaptive refinement process. The proposed improvements are reflected in the numerical examples included in this Thesis. These analyses clearly show the improved behavior of the cgFEM technology as regards numerical accuracy and computational efficiency, and consequently the suitability of the cgFEM approach for shape optimization or contact problems. / La competitividad en la industria actual impone la necesidad de generar nuevos y mejores diseños. El tradicional procedimiento de prueba y error, usado a menudo para el diseño de componentes mecánicos, ralentiza el proceso de diseño y produce diseños subóptimos, por lo que se necesitan nuevos enfoques para obtener una ventaja competitiva. Con el desarrollo del Método de los Elementos Finitos (MEF) en el campo de la ingeniería en la década de 1970, la optimización de forma estructural surgió como un área de aplicación prometedora. El entorno industrial cada vez más exigente implica ciclos cada vez más cortos de desarrollo de nuevos productos. Por tanto, la naturaleza iterativa de los procesos de optimización de forma, que supone el análisis de gran cantidad de geometrías (para las se han de usar modelos numéricos de gran tamaño a fin de limitar el efecto de los errores intrínsecamente asociados a las técnicas numéricas), puede incluso disuadir del uso de estas técnicas. Esta Tesis se centra en la formulación de una metodología 3D basada en el Cartesian-grid Finite Element Method (cgFEM) como herramienta para un análisis numérico eficiente y robusto. Esta metodología pertenece a la categoría de técnicas de discretización Immersed Boundary donde el concepto clave es extender el problema de análisis estructural a un dominio de aproximación, que contiene la frontera del dominio físico, cuya discretización (mallado) resulte sencilla. El uso de mallados cartesianos proporciona una plataforma natural para la optimización de forma estructural porque el dominio numérico está separado del modelo físico, que podrá cambiar libremente durante el procedimiento de optimización sin alterar la discretización subyacente. Otro argumento positivo reside en el hecho de que la generación de malla se convierte en una tarea trivial. La discretización del dominio numérico y su manipulación, en coalición con la eficiencia de una estructura jerárquica de datos, pueden ser explotados para ahorrar coste computacional. Sin embargo, estas ventajas pueden ser cuestionadas por varios problemas numéricos. Básicamente, el esfuerzo computacional se ha desplazado. Del uso de costosos algoritmos de mallado nos movemos hacia el uso de, por ejemplo, esquemas de integración numérica elaborados para poder capturar la discrepancia entre la frontera del dominio geométrico y la malla de elementos finitos que lo embebe. Para ello, utilizamos, por un lado, una formulación de estabilización para imponer condiciones de contorno y, por otro lado, hemos desarrollado nuevas técnicas para poder captar la representación exacta de los modelos geométricos. Para completar la implementación de un método de optimización de forma estructural se usa una formulación adjunta para derivar las sensibilidades de diseño requeridas por los algoritmos basados en gradiente. Las derivadas no son sólo variables requeridas para el proceso, sino una poderosa herramienta para poder proyectar información entre diferentes diseños o, incluso, proyectar la información para crear mallas h-adaptadas sin pasar por un proceso completo de refinamiento h-adaptativo. Las mejoras propuestas se reflejan en los ejemplos numéricos presentados en esta Tesis. Estos análisis muestran claramente el comportamiento superior de la tecnología cgFEM en cuanto a precisión numérica y eficiencia computacional. En consecuencia, el enfoque cgFEM se postula como una herramienta adecuada para la optimización de forma. / Actualment, amb la competència existent en la industria, s'imposa la necessitat de generar nous i millors dissenys . El tradicional procediment de prova i error, que amb freqüència es fa servir pel disseny de components mecànics, endarrereix el procés de disseny i produeix dissenys subòptims, pel que es necessiten nous enfocaments per obtindre avantatge competitiu. Amb el desenvolupament del Mètode dels Elements Finits (MEF) en el camp de l'enginyeria en la dècada de 1970, l'optimització de forma estructural va sorgir com un àrea d'aplicació prometedora. No obstant això, a causa de la natura iterativa dels processos d'optimització de forma, la manipulació dels models numèrics en grans quantitats, junt amb l'error de discretització dels mètodes numèrics, pot fins i tot dissuadir de l'ús d'aquestes tècniques (o d'explotar tot el seu potencial), perquè al mateix temps els cicles de desenvolupament de nous productes s'estan acurtant. Esta Tesi se centra en la formulació d'una metodologia 3D basada en el Cartesian-grid Finite Element Method (cgFEM) com a ferramenta per una anàlisi numèrica eficient i sòlida. Esta metodologia pertany a la categoria de tècniques de discretització Immersed Boundary on el concepte clau és expandir el problema d'anàlisi estructural a un domini d'aproximació fàcil de mallar que conté la frontera del domini físic. L'utilització de mallats cartesians proporciona una plataforma natural per l'optimització de forma estructural perquè el domini numèric està separat del model físic, que podria canviar lliurement durant el procediment d'optimització sense alterar la discretització subjacent. A més, un altre argument positiu el trobem en què la generació de malla es converteix en una tasca trivial, ja que la discretització del domini numèric i la seua manipulació, en coalició amb l'eficiència d'una estructura jeràrquica de dades, poden ser explotats per estalviar cost computacional. Tot i això, estos avantatges poden ser qüestionats per diversos problemes numèrics. Bàsicament, l'esforç computacional s'ha desplaçat. De l'ús de costosos algoritmes de mallat ens movem cap a l'ús de, per exemple, esquemes d'integració numèrica elaborats per poder capturar la discrepància entre la frontera del domini geomètric i la malla d'elements finits que ho embeu. Per això, fem ús, d'una banda, d'una formulació d'estabilització per imposar condicions de contorn i, d'un altra, desevolupem noves tècniques per poder captar la representació exacta dels models geomètrics Per completar la implementació d'un mètode d'optimització de forma estructural es fa ús d'una formulació adjunta per derivar les sensibilitats de disseny requerides pels algoritmes basats en gradient. Les derivades no són únicament variables requerides pel procés, sinó una poderosa ferramenta per poder projectar informació entre diferents dissenys o, fins i tot, projectar la informació per crear malles h-adaptades sense passar per un procés complet de refinament h-adaptatiu. Les millores proposades s'evidencien en els exemples numèrics presentats en esta Tesi. Estes anàlisis mostren clarament el comportament superior de la tecnologia cgFEM en tant a precisió numèrica i eficiència computacional. Així, l'enfocament cgFEM es postula com una ferramenta adient per l'optimització de forma. / Marco Alacid, O. (2017). Structural Shape Optimization Based On The Use Of Cartesian Grids [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/86195 / TESIS

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.