Le nombre croissant d’essais cliniques pour le traitement du cancer a conduit à la standardisation de l’évaluation de la réponse tumorale. Dans les essais cliniques de phase III des cancers avancés, la survie sans progression est souvent appliquée comme un critère de substitution pour la survie globale. Pour les tumeurs solides, la progression est généralement définie par les critères RECIST qui utilisent l’information sur le changement de taille des lésions cibles et les progressions de la maladie non-cible. Malgré leurs limites, les critères RECIST restent l’outil standard pour l’évaluation des traitements. En particulier, la taille tumorale mesurée au cours de temps est utilisée comme variable ponctuelle catégorisée pour identifier l’état d’un patient. L’approche statistique de la modélisation conjointe permet une analyse plus précise des marqueurs de réponse tumorale et de la survie. En outre, les modèles conjoints sont utiles pour les prédictions dynamiques individuelles. Dans ce travail, nous avons proposé d’appliquer un modèle conjoint trivarié pour des données longitudinales (taille tumorale), des évènements récurrents (les progressions de la maladie non-cible) et la survie. En utilisant des mesures de capacité prédictive, nous avons comparé le modèle proposé avec un modèle pour les progressions tumorales, définies selon les critères standards et la survie. Pour un essai clinique randomisé porté sur le cancer colorectal, nous avons trouvé une meilleure capacité prédictive du modèle proposé. Dans la deuxième partie, nous avons développé un logiciel en libre accès pour l’application de l’approche de modélisation conjointe proposée et les prédictions. Enfin, nous avons étendu le modèle à une analyse plus sophistiquée de l’évolution tumorale à l’aide d’un modèle mécaniste. Une équation différentielle ordinaire a été mise en œuvre pour décrire la trajectoire du marqueur biologique en tenant compte les caractéristiques biologiques de la croissance tumorale. Cette nouvelle approche contribue à la recherche clinique sur l’évaluation d’un traitement dans les essais cliniques grâce à une meilleure compréhension de la relation entre la réponse tumorale et la survie. / The increasing number of clinical trials for cancer treatments has led to standardization of guidelines for evaluation of tumor response. In phase III clinical trials of advanced cancer, progression-free survival is often applied as a surrogate endpoint for overall survival (OS). For solid tumors, progression is usually defined using the RECIST criteria that use information on the change of size of target lesions and progressions of non-target disease. The criteria remain the standard tool for treatment evaluation despite their limitations. In particular, repeatedly measured tumor size is used as a pointwise categorized variable to identify a patient’s status. Statistical approach of joint modeling allows for more accurate analysis of the tumor response markers and survival. Moreover, joint models are useful for individual dynamic predictions of death using patient’s history. In this work, we proposed to apply a trivariate joint model for a longitudinal outcome (tumor size), recurrent events (progressions of non-target disease) and survival. Using adapted measures of predictive accuracy we compared the proposed joint model with a model that considered tumor progressions defined within standard criteria and OS. For a randomized clinical trial for colorectal cancer patients, we found better predictive accuracy of the proposed joint model. In the second part, we developed freely available software for application of the proposed joint modeling and dynamic predictions approach. Finally, we extended the model to a more sophisticated analysis of tumor size evolution using a mechanistic model. An ordinary differential equation was implemented to describe the trajectory of the biomarker regarding the biological characteristics of tumor size under a treatment. This new approach contributes to clinical research on treatment evaluation in clinical trials by better understanding of the relationship between the markers of tumor response with OS.

The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.

Specified topic of the thesis is a multilevel evaluation of brittleness of selected building composites. The work deals with the opinions of fracture parameters of test specimens of lightweight and ordinary concrete. Specimens further differed fibres content in concrete mixtures, their type and length. The work is divided into two parts, theoretical and practical. The theoretical part conceives composite materials and introduction to fracture mechanics. The practical part describes the different steps for fracture-mechanical parameters evaluation using StiCrack and Excel Visual Basic software. The main part of the work is to evaluate the brittleness of different test specimens, taking into account the type of concrete mix and type of fibres.

The main subject of the diploma thesis is a market price modeling by real estates. As a tool for modeling, is used a multiple linear regression. As starting points, are used an econometrical theory and knowledge about real estate valuation. The main goal is to find optimal model for best capture in the time and place.

This thesis deals with the topic of partial differential equations parallel solutions. First, it focuses on ordinary differential equations (ODE) and their solution methods using Taylor polynomial. Another part is devoted to partial differential equations (PDE). There are several types of PDE, there are parabolic, hyperbolic and eliptic PDE. There is also explained how to use TKSL system for PDE computing. Another part focuses on solution methods of PDE, these methods are forward, backward and combined methods. There was explained, how to solve these methods in TKSL and Matlab systems. Computing accuracy and time complexity are also discussed. Another part of thesis is PDE parallel solutions. Thanks to the possibility of PDE convertion to ODE systems it is possible to represent each ODE equation by independent operation unit. These units enable parallel computing. The last chapter is devoted to implementation. Application enables generation of ODE systems for TKSL system. These ODE systems represent given hyperbolic PDE.

Thesis is dedicated to evaluation of roundoff impact on numerical integration methods accuracy and effectivity. Contains theoretical expectations taken from existing literature, implementation of chosen methods, experimental measurement of attained accuracy under different circumstances and their comparison with regard to time complexity. Library contains Runge-Kutta methods to order 7 and Adams-Bashforth methods to order 20 implemented using C++ templates which allow optional arbitrary-precision arithmetic. Small models with known analytic solution were used for experiments.

This study seeks to develop a method that generalises the use of Adams-Bashforth to solve or treat partial differential equations with local and non-local differentiation by deriving a two-step Adams-Bashforth numerical scheme in Laplace space. The resulting solution is then transformed back into the real space by using the inverse Laplace transform. This is a powerful numerical algorithm for fractional order derivative. The error analysis for the method is studied and presented. The numerical simulations of the method as applied to the four-dimensional model, Caputo-Lu-Chen model and the wave equation are presented. In the analysis, the bifurcation dynamics are discussed and the periodic doubling processes that eventually caused chaotic behaviour (butterfly attractor) are shown. The related graphical simulations that show the existence of fractal structure that is characterised by chaos and usually called strange attractors are provided. For the Caputo-Lu-Chen model, graphical simulations have been realised in both integer and fractional derivative orders. / Mathematical Sciences / M. Sc. (Applied Mathematics)

When war broke out in Europe in 1939 a mother of two, the thirty-three-year-old Astrid Lindgren, begun keeping a journal. In this diary she wrote about the events of the war, the decisions of the government of Sweden and her own personal life in Stockholm. With a micro historical approach and with a theoretical framework from history of emotions this study aims to explore Lindgren´s emotional life and her emotions towards the changing aspects of the ordinary life, her government´s political agenda, and towards the international players and victims of the second world war. With the use of William K. Reddy´s terminology of emotive and emotional navigation as well as Hugo Nordland´s emotional strategies as analyzing tools the results showed that Lindgren´s initial emotion towards the ordinary life, now affected by the war, was despair, expressed in emotives such as chock, sadness and despondency. The emotion later shifted to gratitude (towards her own privileged situation) and blues (caused by war fatigue), existing simultaneously. The most common emotion expressed correlating to the Swedish government is the emotion of trust. Lindgren´s main emotions towards the victims of the war was compassion. At multiples times, in her diaries, she expressed pity for those who suffered and gratitude for not being among them. The emotions she expressed correlating to the great powers of the war was hate (Germany), fear (Soviet Union) and contempt (Italy). But she also felt conflicted when faced with the fact that she might have to make a choice between Germany and the Soviet Union. The fear of the Russians trumped her loathing of the Nazi regime, but when she gained a greater knowledge of the German atrocities, she came to regard both regimes as equally horrible. The frequent use of certain emotives (such as confidence, gratitude and pity) indicates an emotional navigation to consolidate her feelings and avoid other less desirable emotions. In the same way the uses of biblical metaphors, comparisons of beasts and the reference to brotherly love gives proof of emotional strategies in her handling of undesirable feelings such as hatred and shame. Lastly, this study concludes in a didactical discussion arguing that Astrid Lindgren´s war diaries is a material of great value when teaching of and developing a historical consciousness.

- Jakub Machek Prague Illustrated Courier. The Prague Penny-press as a Window into the World of Common Men. This work is dedicated to early sensational pictorial press (Pražský Illustrovaný Kurýr and its less successful predecessors) and its urban readers, as an example of the rising Fin de siècle popular culture in the Czech lands and its significance for revealing fundamental social and political changes that took place at the turn of the 20th century. During this era, even the members of lower social classes broadened their economical and cultural potency and thus capacity to absorb the development of new common culture generated by the rapid industrialization and urbanization. Production and reception of emerging popular press is analysed as a marker of the new modern urban experience and its social influences. Global pattern of successful mass daily press was, however, modified for Prague audience, its specific local beliefs, values and desires, distinctively different from those of western urban centre dwellers.

Chez les patients infectés par le VIH, les traitements antirétroviraux empêchent la réplicationvirale, ce qui est suivi, dans la plupart des cas, par une restauration de la population des lymphocytesT CD4+ (CD4). Néanmoins ce n’est pas le cas pour certains patients appelés patients àfaible réponse immunitaire. Des injections d’interleukine-7 (IL7) exogène, une cytokine impliquéedans l’homéostasie des CD4, sont considérées afin de maintenir les taux de CD4 au-dessus de500 cellules par μL, taux au-dessus duquel les patients ont une espérance de vie comparable auxpersonnes non infectées par le VIH. Les essais INSPIRE ont évalué l’effet d’injections répétéesd’IL7 chez les patients à faible réponse immunologique.Nous présentons plusieurs modèles mécanistes de l’effet des injections d’IL7 sur les CD4, quiincluent des effets aléatoires afin de tenir compte de la variabilité inter-individuelle. En utilisantces modèles avec une approche Bayésienne, les paramètres individuels d’un nouveau patient sontéchantillonnés, ce qui nous permet de faire des prédictions sur sa dynamique de CD4 et donc depersonnaliser le traitement. Nous proposons quatre protocoles adaptatifs permettant de limiter letemps passé sous 500 CD4 par μL, sans pour autant augmenter le nombre d’injections. Ces protocolesont été implémentés dans une application Shiny présentant une interface facile d’utilisation,et pourront être testés lors d’essais cliniques.Le réservoir viral, principalement constitué de CD4 quiescentes infectées, est la première barrièreà l’éradication du VIH. Les injections d’IL7 entrainent une augmentation du nombre deCD4 et donc du réservoir viral ; la question est alors de savoir si les injections provoquent denouvelles infections cellulaires ou si le réservoir augmente de la même façon que les CD4. Nousconcluons que si quelques patients ont présenté des dynamiques de marqueurs compatibles avecla survenue de nouvelles infections de cellules, ce n’est pas le cas de la majorité des patients. Laconfirmation de ces phénomènes et la caractérisation de potentiels patients à risque nécessite desdonnées supplémentaires mesurables dans un essai clinique. / In HIV infected patients, antiretroviral therapy suppresses the viral replication which is followedin most patients by a restoration of the CD4+ T cells (CD4) pool. However, it is not the case forsome patients called low immunological responders. Injections of interleukin-7 (IL7), a cytokineinvolved in the CD4 homeostasis, are considered in order to maintain the CD4 levels above 500cells per μL, the level at which life expectancy is similar to that of the non-infected. INSPIREtrials evaluated the effect of repeated injections of IL7 on low immunological responders.We present a few mechanistic models of the effect of IL7 injections on CD4, which includerandom effects to account for inter-individual variability. Using these models with a Bayesianapproach, the individual parameters of a new patient are sampled, which allows us to makepredictions about its CD4 dynamics and thus to personalize the treatment. We propose fouradaptive protocols that limit the time spent under 500 CD4 per μL, without increasing thenumber of injections. Those protocols are implemented into a Shiny app with an easy to useinterface, and they could be tested during clinical trials.The viral reservoir, mainly made up of quiescent infected CD4, is the main obstacle to HIVeradication. IL7 injections induce an increase of the level of CD4, hence of the viral reservoir ; thequestion is then to determine if the injections induce new cell infections or if the reservoir increasesin the same way as CD4. We conclude that while some patients presented marker dynamicsconsistent with the occurrence of new cell infections, this is not the case for the majority ofpatients. Confirmation of these events and characterization of potential at-risk patients requiresadditional measurable data in a clinical trial.