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We have two main results. Our first main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs and show that many of these are minimal forbidden subgraphs for any field. Our second main result is a structural characterization of all graphs having minimum rank at most k for any k over any finite field. This characterization leads to a very strong connection to projective geometry and we apply projective geometry results to the minimum rank problem.

Accelerating the simulation of turbulence to stationarity is a critical challenge in various engineering applications. This study presents an innovative equation-free multiscale approach combined with a machine learning technique to address this challenge in the context of the one-dimensional stochastic Burgers' equation, a widely used toy model for turbulence. We employ an encoder-decoder recurrent neural network to perform super-resolution reconstruction of the velocity field from lower-dimensional energy spectrum data, enabling seamless transitions between fine and coarse levels of description. The proposed multiscale-machine learning framework significantly accelerates the computation of the statistically stationary turbulent Burgers' velocity field, achieving up to 442 times faster wall clock time compared to direct numerical simulation, while maintaining three-digit accuracy in the velocity field. Our findings demonstrate the potential of integrating equation-free multiscale methods with machine learning methods to efficiently simulate stochastic partial differential equations and highlight the possibility of using this approach to simulate stochastic systems in other engineering domains. / Master of Science / In many practical engineering problems, simulating turbulence can be computationally expensive and time-consuming. This research explores an innovative method to accelerate these simulations using a combination of equation-free multiscale techniques and deep learning. Multiscale methods allow researchers to simulate the behavior of a system at a coarser scale, even when the specific equations describing its evolution are only available for a finer scale. This can be particularly helpful when there is a notable difference in the time scales between the coarser and finer scales of a system. The ``equation-free approach multiscale method coarse projective integration" can then be used to speed up the simulations of the system's evolution. Turbulence is an ideal candidate for this approach since it can be argued that it evolves to a statistically steady state on two different time scales. Over the course of evolution, the shape of the energy spectrum (the coarse scale) changes slowly, while the velocity field (the fine scale) fluctuates rapidly. However, applying this multiscale framework to turbulence simulations has been challenging due to the lack of a method for reconstructing the velocity field from the lower-dimensional energy spectrum data. This is necessary for moving between the two levels of description in the multiscale simulation framework. In this study, we tackled this challenge by employing a deep neural network model called an encoder-decoder sequence-to-sequence architecture. The model was used to capture and learn the conversions between the structure of the velocity field and the energy spectrum for the one-dimensional stochastic Burgers' equation, a simplified model of turbulence. By combining multiscale techniques with deep learning, we were able to achieve a much faster and more efficient simulation of the turbulent Burgers' velocity field. The findings of this study demonstrated that this novel approach could recover the final steady-state turbulent Burgers' velocity field up to 442 times faster than the traditional direct numerical simulations, while maintaining a high level of accuracy. This breakthrough has the potential to significantly improve the efficiency of turbulence simulations in a variety of engineering applications, making it easier to study and understand these complex phenomena.

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[pt] Em UTI Neonatal estão internados bebês prematuros, sindrômicos ou com alguma malformação, havendo sempre um risco de morte. Diante das fragilidades de seus bebês e precipitados em um ambiente hostil onde há excesso de barulho, de luminosidade e de estímulos, os pais muitas vezes sentem-se angustiados, tristes e com raiva. Com os recursos psíquicos abalados e com sua capacidade de pensamento afetada, os pais podem lançar mão de mecanismos primitivos, como a identificação projetiva (Klein, 1946/1991a), para se defender. A equipe de saúde da UTI Neonatal, além de ser receptora das projeções parentais, necessita fazer face à constante ameaça de morte dos bebês. Acreditamos que diante desta ameça o ambiente da UTI Neonatal seria potencialmente traumático, inclusive para a equipe de saúde. O presente trabalho pretende, a partir da nossa experiência em UTI Neonatal, abordar o sofrimento psíquico a que está sujeito a equipe de saúde. Em razão do trabalho específico que desenvolvem, os membros da equipe de saúde podem chegar a um esgotamento emocional (Burnout). Pretendemos discutir como a equipe de saúde, para estar diante do sofrimento dos pais e dos bebês internados, necessita ela própria receber holding (Winnicott, 1975) e contenção (Bion, 1962) por parte da instituição de saúde. Acreditamos que os grupos de fala possuem importante função antitraumática para a manutenção da capacidade de pensar da equipe de saúde, para que possam continuar exercendo criativamente as suas atividades. / [en] In Neonatal ICU, premature, syndromic or malformed babies are hospitalized and there is always a risk to life. Faced with the vulnerabilities of their babies and precipitated in a hostile environment where there is too much noise, light and stimulation, parents often feel distressed, sad and angry. With unsettled psychological resources and impaired thinking ability, parents can use primitive mechanisms, such as projective identification (Klein, 1946/1991a), to defend themselves. Neonatal ICU health staff, in addition to receiving parental projections, needs to address the constant threat of infant death. Due to these circumstances, we believe that the environment of the Neonatal ICU would be potentially traumatic, including for the health staff. The present work intends, based on our experience in Neonatal ICU, to address the psychological suffering to which the health team is subjected. Because of their specific work, health staff members can experience emotional burnout. We intend to discuss how the health staff, in order to face the suffering of parents and hospitalized babies, needs to receive holding (Winnicott, 1975) and containment (Bion, 1962) by the health institution. We believe that conversation groups have an important anti-traumatic function to maintain the health team s ability to think so that they can continue to perform their activities creatively.

On doit à Friedrich Knop un étonnant théorème qui établit un lien entre algèbres de Lie simples de type A-D-E, et singularités simples de même type. Le résultat est le suivant : on considère la projectivisation de l'orbite de plus haut poids pour l'action adjointe d'un groupe de Lie simple sur son algèbre de Lie (une telle variété est appelée variété adjointe). Il existe alors un hyperplan tangent à l'orbite ayant un unique point singulier du même type que celui de l'algèbre de Lie. Ce théorème est le point de départ de nos travaux. Afin de mieux comprendre ce lien, nous étudions la géométrie des variétés duales des variétés adjointes. Dans le premier chapitre nous prouvons une version duale du théorème de Knop. Notre théorème permet d'obtenir le discriminant d'une singularité simple à partir de la duale de la variété adjointe. L'hyperplan considéré par Knop s'interprète alors comme un point très singulier de la duale. Dans le deuxième chapitre nous considérons le lieu singulier de la duale pour une variétés projective lisse. Nous montrons que l'existence de certaines strates de dimensions maximales équivaut à l'existence de section hyperplane de la variété d'origine admettant des points singuliers d'un type donné. Nous insistons alors sur l'importance de deux strates qui ont un sens géométrique : la duale de la variété des tangentes et la duale de la variété des sécantes. Enfin dans un dernier chapitre nous appliquons ces résultats à l'étude de la normalité des duales des variétés homogènes.

Cette thèse porte sur différentes problématiques liées à la détection, l'ajustement et l'identification de structures elliptiques en images. Nous plaçons la détection de primitives géométriques dans le cadre statistique des méthodes a contrario afin d'obtenir un détecteur de segments de droites et d'arcs circulaires/elliptiques sans paramètres et capable de contrôler le nombre de fausses détections. Pour améliorer la précision des primitives détectées, une technique analytique simple d'ajustement de coniques est proposée ; elle combine la distance algébrique et l'orientation du gradient. L'identification d'une configuration de cercles coplanaires en images par une signature discriminante demande normalement la rectification Euclidienne du plan contenant les cercles. Nous proposons une technique efficace de calcul de la signature qui s'affranchit de l'étape de rectification ; elle est fondée exclusivement sur des propriétés invariantes du plan projectif, devenant elle même projectivement invariante / This thesis deals with different aspects concerning the detection, fitting, and identification of elliptical features in digital images. We put the geometric feature detection in the a contrario statistical framework in order to obtain a combined parameter-free line segment, circular/elliptical arc detector, which controls the number of false detections. To improve the accuracy of the detected features, especially in cases of occluded circles/ellipses, a simple closed-form technique for conic fitting is introduced, which merges efficiently the algebraic distance with the gradient orientation. Identifying a configuration of coplanar circles in images through a discriminant signature usually requires the Euclidean reconstruction of the plane containing the circles. We propose an efficient signature computation method that bypasses the Euclidean reconstruction; it relies exclusively on invariant properties of the projective plane, being thus itself invariant under perspective

The Fairy Tale Test (FTT) is a projective personality test designed for children aged 6 to 12 years. FTT is based on the association between fairy tales and unconscious processes. Its goal is to assess the child's personality profile and to offer information not only about single personality traits but also their interrelations. It is possible it effectively employed as a method to assess eventual personality changes over time or as a tool in clinical or cross-cultural research as well. The Fairy Tale Test was standardized in five countries of the world Greece, Russia, China, India and Turkey, at the present time we effort to set up standard specification also in the Czech Republic. This diploma paper should also contribute to the standardization with administrating FTT and its evaluation to the selected sample of six and seven-years old children. Key words Fairy tales, interpretation of the fairy tales, projective tests, the Fairy Tale Test, younger school age.

Title: The marketing research of the image of sports brands Objectives: The objective of the inquiry is to identify the image of the 5 best known sports brands on the Czech market from the Prague generation Y point of view, whose age limit is defined by Bergha (2012). At the very end of the survey we then compare the acquired results with one another. Methods: The center of interest was the brand and how the consumer perceives it. The marketing research, used in this survey in the form of the electronic inquiry, can be assessed as quantitative with the use of qualitative techniques. It is based on studying the respondents' approach to competitive brands from one market segment. As crucial in the questionnaire was a battery of personal qualities, which was however supplemented by modified projective techniques, i.e. association tests and emotional connection of brands with colours. Results: The inquiry results show that among strongly perceived personal qualities of the examined sports brands is "trustworthy" which gives the impression of active life and health. Among neutrally perceived attributes is "exciting" and quite unapt characteristic is "aggressive". When evaluating the emotionality of the brands by means of limbic mapping, colours like black, white, blue and red predominantly dominate....

The work focuses on qualitative research of possibilities and limits of the use of picture cards symbols (including Tarot) that would serve the clients in coaching and therapy as a projective technique leading to their deeper self-knowledge and personal development. Respondents told their life story based on picture cards. We show here under what conditions this projective technique brought them new information and inspiration for their self- development, in what forms the method can be applied and what methodical procedures are most effective. The simple clients' description of the selected images did not bring them much substantially new. It began to be more inspirational for them when a consultant added targeted questions, his reflections and hypothetical interpretations, or even explained standard meanings of symbols. Then this technique started to speak to clients more and brought them new impulses. Even more inspiring for them it became, once an element of chance was incorporated - when they pulled out some cards at random. The thesis finally formulates detailed recommended general methodology for projective technique application for personal growth and discusses possibilities and limits of the use of projective methods in coaching, therapy and personal development seminars.