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Charles University, Faculty of Pharmacy in Hradec Králové Department of Biological and Medical Sciences Candidate: Dagmar Dolinská Supervisor: PharmDr. Ondřej Janďourek, Ph.D. Work title: Advanced methods for testing antimicrobial activity Goal: The aim of the work in the theoretical part was to summarize methods of antimicrobial screening focusing on antimycotics and in the practical part to evaluate the antifungal activity of 47 tested substances using the microdilution broth method. Methods: The substances were tested using quantitative microdilution broth method on eight strains of yeast and fibrous fungi. These were Candida albicans, Candida krusei, Candida parapsilosis, Candida tropicalis, Aspergillus fumigatus, Aspergillus flavus, Absidia corymbifera and Trichophyton interdigitale. Results: The highest antimycotic activity was demonstrated by compound Ac-0a, where we recorded after 24 hours of incubation activity against all eight strains. However, it was not able to stop the growth of three strains after 48 hours of incubation, the strains concerned were Candida parapsilosis, Aspergillus fumigatus and Aspergillus flavus. Other samples which have shown activity were Cl-2, where activity was observed for Candida krusei, Aspergillus fumigatus and Trichophyton interdigitale strains, Cl-3 for...

[pt] A história recente da Lógica Matemática foi marcada por alguns conflitos entre diferentes correntes filosóficas, cada uma buscando contextualizar a atividade matemática a partir de seu próprio prisma analítico e, por meio disso, tentando conquistar para si mesma o pódio fundacional das Ciências Formais Tais discussões, perenes o bastante para ainda quedarem sem solução, foram fortemente impactadas pela apropriação semântica de alguns resultados técnicos obtidos no campo da teoria da prova, o que redefiniu a relação existente entre as abordagens clássica e intuicionista na matemática. Neste contexto, a presente dissertação tem por finalidade realizar uma descrição da emergente literatura de propostas integrativas entre diferentes sistemas lógicos e matemáticos (apelidadas por Dag Prawitz de ecumenismo lógico), além de investigar alguns impactos que mudanças formais poderiam ocasionar nas concepções filosóficas de algumas teorias matemáticas. No capítulo introdutório, traçamos um panorama geral desta nova proposta ecumênica e analisamos com mais atenção o conflito entre as lógicas Clássica, Intuicionista e Minimal, considerado por muitos como um dos mais influentes na literatura contemporânea. No segundo capítulo, este trabalho fornece uma contribuição original para a literatura ao criar uma nova abordagem ecumênica, além de provar algumas equivalências no interior do sistema Clássico-Intuicionista recentemente criado por Prawitz e compará-lo com uma lógica que criamos usando esta nova abordagem. No terceiro capítulo, contribuímos tanto com a abordagem tradicional quanto com nossa abordagem original ao criar e comparar dua lógicas ecumênicas Minimal-Intuicionistas. Por fim, realizamos uma breve revisão do tímido estado da arte no último capítulo, oferecendo um novo esquema conceitual de interpretação dos sistemas ecumênicos e comentando alguns aspectos promissores do campo, que poderão vir a ser melhor trabalhados no futuro. / [en] The recent history of Mathematical Logic was marked by some conficts between different philosophical positions, each trying to contextualize mathematical activity from its own analytical viewpoint and, with this, trying to conquer the foundational podium of the formal sciences for itself. Such discussions, lasting enough to remain without a solution, were strongly impacted by the semantical appropriation of some technical results obtained in the field of proof theory, which redefined the relation between the classical and intuitionistic approaches to mathematics. In this context, the present dissertation aims to describe the emergent literature about the integration of different logical and mathematical systems (nicknamed logical ecumenism by Dag Prawitz), in addition to investigating some impacts that those formal changes could have on the philosophical conceptions of some mathematical theories. In the introductory chapter, we have outlined a general overview of this new ecumenical proposal and analysed in greater depht the conflicts between Classical, Intuitionistic and Minimal logic, considered by many as one of the most influent on the contemporary literature. In the second chapter, this work provides an original contribution to the literature by creating a new ecumenical approach, in addition to proving some equivalencies within Prawitz s recently created Classical-Intuitionist system, and compares it with the logical system we have created using this new approach. In the third chapter, we contribute both to the traditional approach and our original approach by creating and comparing two Minimal-Intuitionist ecumenical logics. Finally, we briefly review the timid state of the art in the last chapter, offering a new conceptual framework for interpreting ecumenical systems, as well as commenting on some promising aspects of the field, which may be better analyzed in the future.

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico / CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Este trabalho tem como principal objetivo estudar as mÃtricas do funcional volume, volume mÃnimo e curvatura mÃnima em variedades compactas de dimensÃo quatro. Na primeira parte o objetivo à investigar as mÃtricas crÃticas do funcional volume sob a condiÃÃo de tais mÃtricas serem Bach-flats em uma variedade compacta com bordo ∂M. Provamos que uma mÃtrica crÃtica do funcional volume Bach-flat em uma variedade simplesmente conexa de dimensÃo quatro com bordo isomÃtrico a uma esfera padrÃo à necessariamente isomÃtrico a uma bola geodÃsica em um espaÃo forma simplesmente conexo R4, H4 ou S4. AlÃm disso, mostramos que em dimensÃo trÃs o resultado continua valido substituindo a condiÃÃo Bach-flat pela condiÃÃo mais fraca de M ter o tensor de Bach harmÃnico. Na segunda parte estudamos os invariantes geomÃtricos: volume mÃnimo e curvatura mÃnima. Em 1982, Gromov introduziu o conceito de volume mÃnimo para uma variedade suave como sendo o Ãnfimo de todos os volumes sob as mÃtricas de curvatura seccional limitada, em valor absoluto, por 1. Enquanto a curvatura mÃnima, que foi introduzido por Yun, à o menor pinching da curvatura seccional dentre as mÃtricas de volume 1. Em ambos os casos damos estimativas inferiores envolvendo alguns invariantes diferenciÃveis e topolÃgicos. Dentre elas mostraremos exemplos em que as estimativas sÃo Ãtimas. AlÃm disso, obtemos uma caracterizaÃÃo para o caso da igualdade em algumas estimativas. / This aim of this is to study the critical metrics of the volume functional, minimal volume and minimal curvature on four-dimensional compact manifolds. In the first part, we investigate Bach-flat critical metrics of the volume functional on a compact manifold M with boundary ∂M. Here, we prove that a Bach-flat critical metric of the volume functional on a simply connected 4-dimensional manifold with boundary isometric to a standard sphere must be isometric to a geodesic ball in a simply connected space form R4, H4 or S4. Moreover, we show that in dimension three the result even is true replacing the Bach-flat condition by the weaker assumption that M has divergence-free Bach tensor. In the second part we investigate the geometric invariants: minimal volume and minimal curvature. In 1982, Gromov introduced the concept of minimal volume for a smooth manifold as the greatest lower bound of the total volumes of Mn with respect to complete Riemannian metrics whose sectional curvature is bounded above in absolute value by 1. While the minimal curvature, introduced by G. Yun in 1966, is the smallest pinching of the sectional curvature among metrics of volume 1. In both cases we give below estimates to minimal volume and minimal curvature on 4-dimensional compact manifolds involving some differential and topological invariants. Among these ones, we get some sharp estimates. Moreover, we deduce characterizations for the equality case in some estimates.

Model generation and minimal model generation are useful for tasks such as model checking, query answering and for debugging of logical specifications. Due to this variety of applications, several minimality criteria and model generation methods for classical logics have been studied. Minimal model generation for modal logics how ever did not receive the same attention from the research community. This thesis aims to fill this gap by investigating minimality criteria and designing minimal model generation procedures for all the sublogics of the multi-modal logic S5(m) and their extensions with universal modalities. All the procedures are minimal model sound and complete, in the sense that they generate all and only minimal models. The starting point of the investigation is the definition of a Herbrand semantics for modal logics on which a syntactic minimality criterion is devised. The syntactic nature of the minimality criterion allows for an efficient minimal model generation procedure, but, on the other hand, the resulting minimal models can be redundant or semantically non minimal with respect to each other. To overcome the syntactic limitations of the first minimality criterion, the thesis moves from minimal modal Herbrand models to semantic minimality criteria based on subset-simulation. At first, theoretical procedures for the generation of models minimal modulo subset-simulation are presented. These procedures for the generation of models minimal modulo subset-simulation are minimal model sound and complete, but they might not terminate. The minimality criterion and the procedures are then refined in such a way that termination can be ensured while preserving minimal model soundness and completeness.

Pendant les deux dernières décennies l'idée d'une nature holographique de la gravité a pris forme à travers la correspondance AdS/CFT, aussi connue sous le nom de dualité jauge/gravité. CFT correspond à « conformal field theory », théorie conforme des champs, et dans la dualité il s'agit d'une théorie de jauge dans la limite de grand N 1. AdS représente l'espace d'anti-de Sitter, une solution maximalement symétrique des équations d'Einstein avec une constante cosmologique négative, et correspond au côté gravitationnel de la dualité. Dans certaines limites, des théories sur AdS avec de la gravité en d+1 dimensions peuvent être associées à des CFTs sans gravité en d dimensions, d'où le nom « dualité ». Cette dualité est aussi dite « holographique » par analogie avec le concept optique homonyme qui indique la possibilité de générer une image tridimensionnelle comme la projection d'un écran ou d'un film bidimensionnel. Le terme holographie vient des mots grecs holos, « en entier », et graphe, « écriture. Une telle projection, malgré le fait que l'information est stockée en 2 dimensions, contiendrait toute l'information pour reconstruire l'image tridimensionnelle. Dans la dualité jauge/gravité, la théorie de jauge se comporte comme un film d-dimensionnel qui contient la même information que l'image gravitationnelle (d+1)-dimensionnelle. Cette dualité relie la théorie gravitationnelle à la théorie quantique de champs (TQC) dual à travers des conditions aux limites sur des champs qui vivent dans AdS. Dans ce sens-là, la théorie de jauge peut être considérée comme définie sur le bord d'AdS, ce qui renforce l'analogie optique et, pour cela, la dualité est aussi connue comme la correspondance « bulk/boundary » ou « intérieur/bord ». Une de ses principales propriétés est l'association d'une TQC fortement couplée à une théorie gravitationnelle faiblement couplée et vice-versa. Pour cette raison, dans cette thèse j'utilise un intérieur faiblement couplé pour explorer et identifier des propriétés non-perturbatives de TQCs dans la limite de couplage fort. Cette thèse explore l'holographie à température nulle et finie. Nos objets d'intérêt sont des TQCs générées par la brisure de l'invariance d'échelle de CFTs et qui peuvent être étudiées à travers le groupe de renormalisation (GR). Le profil des champs au long de la dimension supplémentaire à l'intérieur est dual à des flots du GR sur la TQC vivant sur le bord, car la dimension supplémentaire est en correspondance avec l'échelle d'énergie. La correspondance va plus loin en identifiant les champs de l'intérieur comme duaux aux couplages renormalisés de la TQC, ce qui mène au concept du GR holographique. Avec le GR holographique, dans cette thèse je vais explorer des comportements qui sont d'une nature intrinsèquement non-perturbatifs du point de vue de la QFT. Les principaux résultats sont les suivants. A température nulle, pour un seul couplage, nous avons classifié toutes les solutions de notre système et identifié trois types de flots exotiques correspondant à des solutions qui inversent leur direction au long du flot, d'autres qui sautent des points fixes et des flots qui interpolent entre des minima du potentiel. Ces résultats ont été généralisés à plusieurs couplages à température nulle. Je présente également la relation entre la fonction principale de Hamilton et la nature du champ de vitesses des couplages: gradient ou non. À température finie nous avons considéré un seul couplage et exploré la thermodynamique des trois types de solutions exotiques mentionnées ci-dessus. Nous avons identifié une transition de phase entre des solutions qui sautent et qui ne sautent pas des points fixes, une discontinuité de l'énergie libre pour un potentiel admettant des solutions qui inversent le sens du flot à température nulle et la non-existence de solutions à température finie associées à un flot entre minima pour un potentiel qui admet une telle solution à température nulle. / Over the past twenty years the idea that gravity is holographic has become progressively concrete, materialised through the AdS/CFT correspondence, also known as the gauge/gravity duality. CFT stands for conformal field theory and in the correspondence it is a gauge-theory in the large N limit1. AdS stands for anti-de Sitter space-time, a maximally symmetric solution of Einstein’s equations with negative cosmological constant, it corresponds to the gravitational side of the duality. In some limits, theories on AdS with gravity in d + 1 dimensions can be mapped to CFTs without gravity in d dimensions and vice-versa, hence the name “duality”. Another term for the gauge/gravity duality is holographic duality. The term holography comes from the Greek words holos, “whole”, and graphe, “writing” or “drawing”. In physics, the term holography originates in optics, referring to the possibility of generating a 3-dimensional image as a projection from a bi- dimensional screen or film. In such a projection, despite of the fact that the film has one spatial dimension less than the projection, the film would contain all the information to recover the three-dimensional image. In the gauge/gravity duality, the gauge-theory behaves as a d-dimensional film which contains the same information as the (d + 1)-dimensional gravitational image. This analogy is reinforced by the fact that the duality relates the gravitational theory to the dual resulting quantum field theory (QFT) via boundary conditions of the fields living in the AdS bulk. In this sense, the gauge theory can be thought of as living at the boundary of AdS and the duality is also know as the bulk/boundary correspondence. One of the most important features of the correspondence is the mapping of a strongly coupled QFT into a weakly coupled gravitational theory and vice-versa. For this reason, in this thesis I will use a weakly coupled bulk theory to explore and identify non-perturbative features of QFT in the strong coupling regime. This thesis explores holography at zero and finite temperature. Our main concern are the CFTs in which scale invariance is either spontaneously or explicitly broken and the resulting QFT can be studied via the renormalisation group (RG). The profile of fields along the extra-dimension in the bulk is dual to renormalisation group flows in the QFT side (boundary), as the extra-dimension can be mapped to an energy scale. The mapping goes further by identifying bulk fields as dual to QFT running couplings, leading to the so-called holographic renormalisation group. With the holographic RG in what follows I will explore behaviours that are of an intrinsically non-perturbative nature from the QFT standpoint. The main results are as follows. At zero temperature, for a single coupling, we classified all possible solutions in our setup and identified three kinds of exotic flows corresponding to solutions reversing direction along the flow (bounces), flows skipping fixed points and solutions interpolating between minima of the potential. These results are generalised to many couplings at zero temperature. I also present a complete map between forms of the Hamilton's principal function and the gradient or non-gradient nature of the solutions. At finite temperature we considered a single coupling setup and explored the thermodynamics of the three kinds of above-mentioned exotic flows. We identified a phase transition between skipping and non-skipping solutions, a discontinuous free energy for a bouncing potential and the non-existence of a finite-temperature solutions for a chosen potential admitting a minimum-to-minimum solution.

Cette thèse porte sur la construction de nouveaux exemples de surfaces minimales dérivées de la famille de surfaces de Costa-Hoffman-Meeks. Il s'agit d'une famille de surfaces minimales complètes plongées avec trois bouts et genre k > 0. Soit M_k la surface de Costa_Hoffman_Meeks de genre k. Dans le chapitre 1, j'ai démontré que M_k est non dégénérée pour k > 37. J'ai donc étendu les résultats de S. Nayatani qui assuraient que la surface M_k est non dégénérée seulement pour k=1,...,37. Ce résultat permet de montrer dans les chapitres 2 et 3 l'existence de nouveaux exemples de surfaces minimales de genre g arbitraire à l'aide d'une procédure de collage d'autres surfaces déjà connues (parmi lesquelles y figure la surface M_k). Sans ceci, ces résultats ne seraient valables que pour k < 38. En particulier dans le chapitre 2, j'ai démontré l'existence, dans H^2 x R, (H^2 étant le plan hyperbolique) d'une famille de surfaces minimales plongées inspirées de M_k, pour tout k > 0. Ce résultat peut être censé un cas particulier d'un théorème générale de désingularisation de l'intersection de deux surfaces minimales annoncé par N. Kapouleas et jamais publié. Le chapitre 3 est consacré à la construction de trois familles de surfaces minimales simplement périodiques plongées dans R^3 dont le quotient a genre arbitraire. Les résultats présentés dans ce chapitre (obtenus en collaborations avec L. Hauswirth et M. Rodríguez) généralisent plusieurs anciennes constructions / This thesis is devoted to the construction of new examples of minimal surfaces derived from the family of surfaces if Costa-Hoffman-Meeks. Surfaces in this family are complete embedded with 3 ends and genus k > 0. Let M_k denote the surface of Costa-Hoffman-Meeks of genus k. In chapter 1 I showed M_k is non degenerate for k > 37. So I extended the results of S. Nayatani which insured M_k is non degenerate only for k=1,...,37. That allows to prove in chapters 2 and 3 the existence of new examples of minimal surfaces by a gluing procedure involving already known surfaces (among which figures M_k). Without it theses results would hold only for k < 38. In particular in chapter 2 I showed the existence in H^2 x R (where H^2 denotes the hyperbolic plane) of a family of surfaces inspired to M_k, for all k > 0, which are complete and embedded. This result can be considered as a particular case of a general theorem of desingularization of the intersection of two minimal surfaces announced by N. Kapouleas and never published. Chapter 3 is devoted to the construction of 3 families of singly periodic minimal surfaces, embedded in R^3, whose quotient has an arbitrary value of the genus. The results showed in this chapter (obtained in collaboration with L. Hauswirth and M. Rodríguez) generalize many previous constructions

A web portal that publicly displays user-submitted content requires administration in order to ensure undesired content, that is potentially malicious, is excluded. Other administrative aspects that come with a web portal with user-submitted content include user-support and service maintenance. This project was formed in part to develop a new version of an existing web portal for advertising degree projects. The goal of the project is to develop an improved version of the old web portal and ensure that the new version requires as little manual administration work as possible. As how to minimize administration for this type of service was deemed unknown, this thesis takes an inductive approach to exploring how to minimize administration for a web portal with user-submitted content. This thesis results in the presentation of a web portal with new functionality and modified in aspects that the product owner wanted improved. The visual layout is presented along with information on what parts were reused from the old version of the web portal. Design choices that were made with a focus on minimizing administration and design choices in general that were deemed important are presented and motivated. Finally, the thesis concludes that possible areas where administrative work could be reduced depends heavily on the requirements set on the web portal and that the methods used in this thesis were successful in identifying administrative work aspects that can be reduced or eliminated on the web portal developed in this project. It is also concluded that sufficiently advanced automated systems could be useful in reducing the administrative work needed by any type of web portal with user-submitted content. / En webbportal som publikt visar användarskapat innehåll kräver administration för att försäkra att oönskat innehåll, som potentiellt är illvillig, exkluderas. Andra administrativa aspekter som medföljer en webbportal med användarskapat innehåll, inkluderar användarsupport och underhåll av tjänsten. Detta projekt skapades delvis för att utveckla en ny version av en redan existerande webbportal som används för annonsering av examensarbeten.Målet med projektet är att utveckla en förbättrad version av den gamla webbportalen och försäkra att den nya versionen kräver så lite manuellt administrativt arbete som möjligt. Hur minimering av administrativt arbete åstadkoms för denna typ av tjänst ansågs vara okänt, därav valdes ett induktivt tillvägagångssätt till detta projekt för att undersöka hur mängden administrativt arbete minimeras för en webbportal vars innehåll skapas av dess användare. Projektet resulterar i presentationen av en webbportal med ny funktionalitet med modifieringar inom olika aspekter beroende på det som efterfrågats av projektbeställaren. Visuella uppbyggnaden presenteras tillsammans med information angående vilka delar som återanvändes från den gamla version av webbportalen. Designval med fokus på minimering av administrativt arbete samt även generella designval som ansågs viktiga, presenteras och motiveras. Slutligen drar studien slutsatsen att möjliga områden där det administrativa arbetet kan reduceras till stor del beror på kraven satta för webbportalen och att metoderna som användes i denna studie var framgångsrika i att identifiera de aspekter av administrativt arbete som kan reduceras eller elimineras från webbportalen som utvecklades i detta projekt. Slutsatsen dras även att tillräckligt sofistikerade automatiska system kan vara användbara för att reducera administrativt arbete för webbportaler med användarskapat innehåll.

Este trabalho tem como foco principal estabelecer condições gerais suficientes para que uma expansão do corpo ordenado dos reais por funções com domínio em Rn seja modelo completa e o-minimal. Para tanto, faremos uma abordagem sob o ponto de vista de estruturas fracas o-minimais, conforme o trabalho de Charbonnel e Wilkie. Além disso, ao analisar condições adicionais, podemos obter a seguinte generalização de um trabalho de Gabrielov: uma expansão o-minimal do corpo ordenado dos reais por funções C infinito restritas, que é polinomialmente limitada e fechada sob diferenciação parcial, é modelo completa. / The main focus of this dissertation lies in establishing some general sufficient conditions for an expansion of the real ordered field by functions with domains Rn to be model complete and o-minimal. We approach this subject from the point of view of the o-minimal weak structures, by following the work of Charbonnel and Wilkie. Furthermore, when considering additional conditions, we are able to obtain the following generalization of a Gabrielovs result: an expansion of the real ordered field by restricted smooth functions, which is polynomially bounded and closed under partial differentiation, is model complete.

Este trabalho tem como foco principal estabelecer condições gerais suficientes para que uma expansão do corpo ordenado dos reais por funções com domínio em Rn seja modelo completa e o-minimal. Para tanto, faremos uma abordagem sob o ponto de vista de estruturas fracas o-minimais, conforme o trabalho de Charbonnel e Wilkie. Além disso, ao analisar condições adicionais, podemos obter a seguinte generalização de um trabalho de Gabrielov: uma expansão o-minimal do corpo ordenado dos reais por funções C infinito restritas, que é polinomialmente limitada e fechada sob diferenciação parcial, é modelo completa. / The main focus of this dissertation lies in establishing some general sufficient conditions for an expansion of the real ordered field by functions with domains Rn to be model complete and o-minimal. We approach this subject from the point of view of the o-minimal weak structures, by following the work of Charbonnel and Wilkie. Furthermore, when considering additional conditions, we are able to obtain the following generalization of a Gabrielovs result: an expansion of the real ordered field by restricted smooth functions, which is polynomially bounded and closed under partial differentiation, is model complete.