Tato práce se zabývá buněčným cyklem kvasinky Saccgaromyces cerevisiae. Oblastí našeho zájmu je přechod mezi G1 a S fází, kde je naším cílem identifikovat velikosti buňky v době počátku DNA replikace. Nejprve se věnujeme nedávno publikovanému matematickému modelu, který popisuje mechanismy vedoucí k S fázi. Práce poskytuje detailní popis tohoto modelu, stejně jako časový průběh některých důležitých proteinů či jejich sloučenin. Dále se zabýváme pravděpodobnostním modelem aktivace replikačních počátků DNA. Nově uvažujeme vliv šíření DNA replikace mezi sousedícími počátky a analyzujeme jeho důsledky. Poskytujeme také senzitivní analýzu kritické velikosti buňky vzhledem ke konstantám popisujícím dynamiku reakcí v modelu G1/S přechodu.

The subject of my master’s thesis is creating a mathematical model of motor vehicle driving gear using the software programs MATLAB / Simulink. The results are presented via graphs of the data gained from the simulation of a car driving on a determined track. The parameters used in the model come from a specific file and they can be changed anytime in order to correspond with the particular vehicle.

Diploma thesis offers a new approach to the measuring of geometry errors in the machine tool workspace with the aid of laser tracker. There is a method of data acquisition and also the Matlab programs for data processing suggested in the thesis. This method can determine the accuracy and repeatibility of positioning and angular displacement of the numerical controlled axes of the measured machine tool and it compiles its mathematical model. All the gathered knowledge is used to evaluation of geometric accuracy of the virtual machined workpiece.

This thesis focuses on developing algorithms for brushless AC motor control. First part of the thesis contains derivation of mathematical model and overview of selected sensor and sensorless control methods. Second part introduces simulation model of the motor, developed in Matlab/Simulink environment, with usage of SimPowerSystems toolbox. Following chapter describes realization of control algorithm, utilizing Hall sensors and position estimation. After that, sensorless rotor position estimation module is developed, and its implementation into the model is mentioned. Last chapters deal with development of graphical user interface, meant for changing selected motor and control parameters, and they also summarize and compare achieved results.

This thesis deals with optimization of a vehicle’s (racing) drive on a track. The model of a vehicle and a track is built in this thesis. The first chapter is devoted to the fastest pass problem formulation. The problem optimizes (in the least time) the vehicle’s drive from a start line to a finish line. The problem is formulated as an optimal control theory problem. In the second chapter the optimal control theory problem is suitably discretised and transformed into a nonlinear programming problem. The transformation of the fastest pass problem into nonlinear programming problem, its detailed and illustrative derivation and reformulation form the main part of the thesis. Third chapter presents the implementation and solution of the problem using GAMS and MATLAB. This thesis is a part of a specific research project on which the author has participated. The main contribution of the author is an original formulation of the fastest pass problem as a nonlinear programming problem and its implementation and solving using GAMS.

Transportation planners have traditionally focused on physical travel only, and disregarded the fact that other modes of communication may influence travel demand. However, modern telecommunications are rapidly increasing the accessibility to activities that previously only could be reached by physical transportation. This development calls for methods to analyse interactions between telecommunications and transport systems. The objective of this thesis is to accomplish a better understanding of if and how impacts of information technology could be implemented in travel demand models. An important part of this issue is to investigate what kind of data that is needed. This thesis also aims at investigating whether the Communication Survey, KOM, collected by Swedish Institute for Transport and Communications, SIKA, can be used to improve transport modelling with respect to how modern telecommunications influence travel demand. KOM is a one-day travel and communication diary survey, including information on the respondents telecommuting habits as well as socio-economic status. One problem was the small sample size in KOM, which made the analyses uncertain. Since KOM is collected on a yearly basis, it is still possible to apply similar analysis methods within a few years, using a larger data set, which might enable extended analyses. The small sample in KOM available to date is best suited for general descriptive analyses of communication patterns in Sweden. The main conclusions of the paper are therefore connected to the methods and future data collection. The thesis includes three papers. The first paper tested a model approach that assumes substitution between travel and non-travel based communication, using the KOM database. Travel demand models are in general constructed as nested logit models with frequency, mode and destination choice levels. In the paper, non-travel based modes of communication were included in the choice set of such a model. The non-travel based modes of communication considered were Internet (and e-mail), ordinary mail and telephone contacts. The second and third papers investigate telecommuting. As a first step to reach the goal of forecasting telecommuting, the second paper examined the characteristics of current telecommuters by use of KOM. This was mainly accomplished by estimating a telecommuting adoption model of logit type. However, only 122 employees out of 7578 actually telecommutes full days at home. These telecommuters work primarily in information- and service-based industrial sectors concerned with computers, finance or communication. The difficulties in describing the utility of the telecommunications based alternatives (representing ”no travel”) concerned also the telecommuting adoption model. The third paper used data collected from a working site within the company Ericsson, located in the office district of Nacka Strand in Stockholm during the autumn 2002. The telecommuting frequency was substantially higher at Ericsson than in the workforce as a whole. The propensity to adopt telecommuting was modelled as a function of socio-economic variables and access to technical equipment, work task suitability and management attitudes, as perceived by the employees. The focus was to identify tools that the company can use to promote telecommuting, and to find incentives for the company to promote telecommuting. Technical equipment, suitable work tasks and managers attitude were identified as constraints for telecommuting. / <p>NR 20140805</p>

Exercise is widely recognized for its role in the health management and prevention of several chronic diseases. Exercise is considered as a stimulus in the form of physical stress to which a group of anatomical structures in the human body responds by generating a stress response that enables certain physiological modifications essential for restoring systemic homeostasis. A major component of the response is produced through the complex hypothalamic-pituitary-adrenal (HPA) axis mechanism that results in the release of cortisol which then intercedes with the effects of the stimulus. To investigate how cortisol helps the body adapt to this physical stress it is necessary to gain deep insight into the cortisol response mechanism. However, this is a complex mechanism, so to better understand the mechanics and to be able to analyze complex data, mathematical models are used. Various mathematical models have already been developed that describe different metabolic responses to exercise but to date, to my knowledge, none of these existing models has illustrated the HPA axis response mechanism, particularly cortisol response to physical exercise. Therefore, I have developed a mathematical model that describes cortisol variations on a normal day in the absence of any form of stress and on the day of exercise. The developed cortisol response model could fit simulation to experimental data and also passed the χ2- statistical test. Additionally, the model has been validated on different cortisol experimental data with satisfying results. At last, considering the positive outcome of this mathematical model, it could be used as a groundwork for developing a comprehensive model which can describe other metabolic processes response to exercise such as glucose metabolism together with the cortisol response mechanism in the future.

Environmental constraints can limit a population to a certain size, which is usually called the carrying capacity of a habitat. Besides to this 'external' factor, which is mainly determined by the limitation of resources, we investigate here another set of population-intrinsic factors that can limit a population size significantly below the maximum sustainable size. Firstly, density-independent mortality is a prominent factor in all organisms that show age-related and/or accidental death. Secondly, in sexually reproducing organisms the sex ratio and the success of pairing is important for finding reproductive partners. Using a simple model, we demonstrate how sex ratio, mating success and gender-specific mortality can strongly affect the speed of population growth and the maximum population size. In addition, we demonstrate that density-independent mortality, which is often neglected in population models, adds a very important feature to the system: it strongly enhances the negative influence of unbiased sex ratios and inefficient pairing to the maximum sustainable population size. A decrease of the maximum population size significantly affects a population's survival chance in inter-specific competition. Thus, we conclude that the inclusion of density-independent mortality is crucial, especially for models of species that reproduce sexually. We show that density-independent mortality, together with biased sex ratios, can significantly lower the abilities of a population to survive in conditions of strong inter-specific competition and due to the Allee effect. We emphasize that population models should incorporate the sex ratio, male success and density-independent mortality to make plausible predictions of the population dynamics in a gender-structured population. We show that the population size is limited by these intrinsic factors. This is of high ecological significance, because it means that there will always be resources available in any habitat that allows other species (e.g., invaders) to use these resources and settle successfully, if they are sufficiently adapted.

Climate change is likely to disrupt the timing of developmental events (phenology) in insect populations in which development time is largely determined by temperature. Shifting phenology puts insects at risk of being exposed to seasonal weather extremes during sensitive life stages and losing synchrony with biotic resources. Additionally, warming may result in loss of developmental synchronization within a population, making it difficult to find mates or mount mass attacks against well-defended resources at low population densities. It is unknown whether genetic evolution of development time can occur rapidly enough to moderate these effects. The work presented here is largely motivated by the need to understand how mountain pine beetle (MPB) populations will respond to climate change. MPB is an important forest pest from both an economic and ecological perspective, because MPB outbreaks often result in massive timber loss. Recent MPB range expansion and increased outbreak frequency have been linked to warming temperatures. We present a novel approach to modeling the evolution of phenology by allowing the parameters of a phenology model to evolve in response to selection on emergence time and density. We also develop a temperature-dependent phenology model for MPB that accounts for multiple types of developmental variation: variation that persists throughout a life stage, random variation, and variation due to the MPB oviposition mechanism. This model is parameterized using MPB development time data from constant temperature laboratory experiments. We use Laplace's method to approximate steady distributions of the evolution model under stable temperatures. Here the mean phenotype allows for parents and offspring to be oviposited at exactly the same time of year in consecutive generations. These results are verified numerically for both MPB and a two-stage model insect. The evolution model is also applied to investigate the evolution of phenology for MPB and the two-stage model insect under warming temperatures. The model predicts that local populations can only adapt to climate change if development time can adapt so that individuals can complete exactly one generation per year and if the rate of temperature change is moderate.

Indiana University-Purdue University Indianapolis (IUPUI) / Glaucoma is a multi-factorial ocular disease associated with death of retinal ganglion cells and irreversible vision loss. Many risk factors contribute to glaucomatous damage, including elevated intraocular pressure (IOP), age, genetics, and other diseases such as diabetes and systemic hypertension. Interestingly, alterations in retinal hemodynamics have also been associated with glaucoma. A better understanding of the factors that contribute to these hemodynamic alterations could lead to improved and more appropriate clinical approaches to manage and hopefully treat glaucoma patients. In this thesis, we develop several mathematical models aimed at describing ocular hemodynamics and oxygenation in health and disease. Precisely we describe: (i) a time-dependent mathematical model for the retinal circulation that includes macrocirculation, microcirculation, phenomenological vascular regulation, and the mechanical effect of IOP on the retinal vasculature; (ii) a steady-state mathematical model for the retinal circulation that includes macrocirculation, microcirculation, mechanistic vascular regulation, the effect of IOP on the central retinal artery and central retinal vein, and the transport of oxygen in the retinal tissue using a Krogh cylinder type model; (iii) a steady-state mathematical model for the transport of oxygen in the retinal microcirculation and tissue based on a realistic retinal anatomy; and (iv) a steady-state mathematical model for the production and drainage of aqueous humor (AH). The main objective of this work is to study the relationship between IOP, systemic blood pressure, and the functionality of vascular autoregulation; the transport and exchange of oxygen in the retinal vasculature and tissue; and the production and drainage of AH, that contributes to the level of IOP. The models developed in this thesis predict that (i) the autoregulation plateau occurs for different values of IOP in hypertensive and normotensive patients. Thus, the level of blood pressure and functionality of autoregulation affect the changes in retinal hemodynamics caused by IOP and might explain the inconsistent outcomes of clinical studies; (ii) the metabolic and carbon dioxide mechanisms play a major role in the vascular regulation of the retina. Thus, the impairment of either of these mechanisms could cause ischemic damage to the retinal tissue; (iii) the multi-layer description of transport of oxygen in the retinal tissue accounts for the effect of the inner and outer retina, thereby improving the predictive ability of the model; (iv) a greater reduction in IOP is obtained if topical medications target AH production rather that AH drainage and if IOP-lowering medications are administrated to patients that exhibit a high initial level of IOP. Thus, the effectiveness of IOP-lowering medications depend on a patient’s value of IOP. In conclusion, the results of this thesis demonstrate that the insight provided by mathematical modeling alongside clinical studies can improve the understanding of diseases and potentially contribute to the clinical development of new treatments.