The aim of the diploma paper is valuation of economic effectiveness of the investment project in the sphere of optical production. The theoretical part introduces into the problems of investments and supplies a brief overview of standard evaluating methods. The practical part contains the description of the planned investment project, estimation of cash flow and determination of discount rate. After that, there is an application of the methods of effectiveness evaluation and sensitivity analysis for input parameters.

The main objective of this thesis is to provide management of specific company with valid information concerning intended investment in construction of a small photovoltaic power plant. Valuation of the investment is done using methods: payback period, discounted payback period, net present value, internal rate of return and profitability index. There is a comlete sensitivity analysis included in the thesis. Besides the valuation itself, the thesis provide also relevant information about the company, legal environment, czech and european renewable energy market and current state of the project.

La problématique de la gestion des données manquantes dans les études épidémiologiques est un sujet qui intéressera tous les chercheurs impliqués dans l’analyse des données recueillies et dans l’interprétation des résultats issus de ces analyses. Et même si la question de la gestion des données manquantes et de leur impact sur la validité des résultats obtenus est souvent discutée, cesont souvent les méthodes de traitement des données manquantes les plus simples mais pas toujours les plus valides qui sont utilisées en pratique. L’utilisation de chacune de ces méthodes suppose un certain nombre d’hypothèses sous lesquelles les résultats obtenus sont valides, mais il n’est pas toujours possible de tester ces hypothèses. L’objectif de ce travail était (i) de proposer une revue des différentes méthodes de traitement des données manquantes utilisées en épidémiologie en discutant les avantages et les limites de chacune de ces méthodes, (ii) de proposer une stratégie d’analyse afin d’étudier la robustesse des résultats obtenues via les méthodes classiques de traitement des données manquantes à l’écart aux hypothèses qui, bien que non testables, sont nécessaires à la validité de ces résultats, et (iii) de proposer quelques applications sur des données réelles des différents point discutés dans les deux premières parties. / The issue of how to deal with missing data in epidemiological studies is a topic which concerns every researcher involved in the analysis of collected data and in the interpretation of the results produced by these analyses. And even if the issue of the handling of missing data and of their impact on the validity of the results is often discussed, simple, but not always appropriate methods to deal with missing data are commonly used. The use of each of these methods is based on some hypotheses under which the obtained results are valid, but it is not always possible to test these hypotheses. The objective of this work was (i) to propose a review of various methods to handle missing data used in the field of epidemiology, and to discuss the advantages and disadvantages of each of these methods, (ii) to propose a strategy of analysis in order to study the robustness of the results obtained via classical methods to handle missing data to the departure from hypotheses which are required for the validity of these results, although they are not testable, and (iii) to propose some applications on real data of the issues discussed in the first two sections.

The purpose of this diploma paper is to present economic models used to evaluate the investment and its implementation in calculating merits of investment in photovoltaic power plant. It consists of theoretical and practical part. Most importantly, the discounted cash flow method is used to evaluate the investment. To calculate the impact of potential adverse scenarios, cash flow streams of each of them were multiplied by their probabilities. Next stage of the paper provides sensitivity analysis for major risk factors. Finally, the breakeven point was determined and presented as a subsidiary case for investment decision.

The thesis deals with the evaluation of the economic faculties of the universities in the Czech Republic using the WSA, TOPSIS and ELECTRE III methods. The theoretical part of the work describes the theory of multi-criteria decision making and focuses on the methods with the cardinal information and methods of calculation of the criteria weights. This part of the work is further devoted to the methodology of the world's most recognized rankings and evaluations of economic faculties in the Czech Republic. The practical part deals with the selection of appropriate criteria, the determination of their scales and evaluation of faculties using the Sanna MS Excel add-in application. In the scope of the sensitivity of the evaluation depending on the change in the weights of the criteria there is drawn up a questionnaire for students of schools with economic focus. The primary purpose is to create an objective ranking of economic faculties. The secondary aim of this work is to assess the sensitivity of the order of the faculties on the method used to calculate the weights of the criteria and on change of the weighting of the criteria itself.

This thesis is focused on describing chosen methods used in liabilities valuation of Life Insurance Company. This is the basis for a valuation of whole Insurance Company. Next goal is real valuation of liabilities and the whole company. The value of liabilities is computed with the Market Consistent Embedded Value methodology and valuation of the company is expresed with Appraisal Value, which is currently one of the most widely used methods for valuation of a life Insurance Company. The valuation is based on values of a fictious company, but the used insurance portfolio corresponds with real life data. The valuation is computed in pessimistic, middle and optimistic variant of company development. Closing this thesis is a sensitivity analysis of assumptions, influencing value of MCEV, where a change of the costs and commisions proved to be of most significance.

Mathematical modelling is playing an increasingly important role in helping us to understand biological systems. The construction of biological models typically requires the use of experimentally-measured parameter values. However, varying degrees of uncertainty surround virtually all parameters in these models. Sensitivity analysis is one of the most important tools for the analysis of models, and shows how the outputs of a model, such as concentrations and reaction fluxes, are dependent on the parameters which make up the input. Unfortunately, small changes in parameter values can lead to the results of a sensitivity analysis changing significantly. The results of such analyses must therefore be interpreted with caution, particularly if a high degree of uncertainty surrounds the parameter values. Global sensitivity analysis methods can help in such situations by allowing sensitivities to be calculated over a range of possible parameter values. However, these techniques are computationally expensive, particularly for larger, more detailed models. Software was developed to enable a number of computationally-intensive modelling tasks, including two global sensitivity analysis methods, to be run in parallel in a high-throughput computing environment. The use of high-throughput computing enabled the run time of these analyses to be drastically reduced, allowing models to be analysed to a degree that would otherwise be impractical or impossible. Global sensitivity analysis using high-throughput computing was performed on a selection of both theoretical and physiologically-based models. Varying degrees of parameter uncertainty were considered. These analyses revealed instances in which the results of a sensitivity analysis were valid, even under large degrees of parameter variation. Other cases were found for which only a slight change in parameter values could completely change the results of the analysis. Parameter uncertainties are a real problem in biological systems modelling. This work shows how, with the help of high-throughput computing, global sensitivity analysis can become a practical part of the modelling process.

The goal of this master thesis is to evaluate an investment project to a biogas power plant. The first part of the master thesis defined the essential theory needed for the capital investment decisions. There is overview of the most important investment criteria like net present value and methods and sources of project financing. In the analytical part I calculate the necessary values like revenues, operational costs and depreciation in order to find out projects cash flow. The investment is then evaluated by investment criteria. In order to make the analysis more accurate the sensitivity analysis is made. In the last part of the thesis there is an overview of results and a investment recommendation.

abstract: Cancer is a worldwide burden in every aspect: physically, emotionally, and financially. A need for innovation in cancer research has led to a vast interdisciplinary effort to search for the next breakthrough. Mathematical modeling allows for a unique look into the underlying cellular dynamics and allows for testing treatment strategies without the need for clinical trials. This dissertation explores several iterations of a dendritic cell (DC) therapy model and correspondingly investigates what each iteration teaches about response to treatment. In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies. In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined. Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2020

L’industrie éolienne et l’aéronautique ont des besoins importants en matière de mesure de vent dans les premières centaines de mètres de l’atmosphère. Les lidars sont des instruments répandus et éprouvés pour ce type de mesure. Cependant, leurs qualités d’acquisition sont atténuées par un bruit de mesure systématique. En utilisant des techniques sur le filtrage nonlinéaire nous avons participé au développement d'un algorithme qui améliore l’estimation du vent et de la turbulence. Cet algorithme est basé sur une représentation de l’atmosphère par des particules fluides. Il utilise un modèle lagrangien stochastique de turbulence et un filtrage par sélection génétique. Son efficacité dépend du réglage de certains paramètres, fixés à une valeur acceptable à l’issue de la phase de développement. Mais l’influence de ces paramètres n’a jamais été étudiée. Ce travail de thèse répond à cette question par une analyse de sensibilité basée sur la décomposition de variance. De nouveaux estimateurs pour les indices de Sobol, utilisant des régression pénalisées, ont été testés. Ces estimateurs mettent les indices de Sobol les plus petits automatiquement à zéro pour faciliter l’interprétation globale. L’analyse de sensibilité permet de réduire le système à 9 entrées et 5 sorties à un système de 3 entrées (le nombre de particules, le bruit d’observation réel et le bruit d’observation donné au filtre) et 2 sorties (la pente du spectre de vent et l’erreur sur le vent). Grâce à ce système réduit, nous mettons en évidence une méthode de réglage des paramètres d’entrée les plus importants. Le bruit d’observation donné au filtre est bien réglé lorsque la pente du spectre est à la valeur cible de -5/3. Une fois ce bruit réglé, l’erreur sur le vent est minimale avec une expression connue. / Wind energy industry and airport safety are in need of atmospheric observations. Remote sensors, such as lidars, are well proven and common technology to provide wind measurements in the first hundreds of meters of altitude. However, acquisition abilities of lidars are polluted by measurement noise. Using non-linear filtering techniques, we took part at the development of an algorithm improving wind and turbulence estimations. The process is based on a representation of the atmosphere with fluid particles. It uses a stochastic Lagrangian model of turbulence and a genetic selection filtering technique. Its efficiency depends of the setting of various parameters. Their values were fixed experimentally during the development phase. But their influence has never been assessed. This work addresses this question with a variance-based sensitivity analysis. New estimators of Sobol indices, using penalized regression have been tested. These estimators ensure the lowest Sobol indices automatically go to zero so the overall interpretation is simplified. The sensitivity analysis allows to reduce the system from 5 outputs and 9 inputs to 3 inputs (number of particles, real observation noise, observation noise given to the filter) and 2 outputs (wind spectrum slope, root-mean-squared error on wind). With this reduced system we determined a procedure to correctly set the most important parameters. The observation noise given to the filter is well set when the wind spectrum slope has the expected value of -5/3. Once it is set correctly, the error on wind is minimum and its expression is known.