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The lymphatic system consists of a network of vessels which work to return the interstitial fluid back to the blood circulation. Individual units called lymphangions, segments of lymphatic vessels between two valves, pump cyclically to propel lymph. Lymphangions are similar to the heart in that they are sensitive to both preload and afterload. To describe the heart independent of preload and afterload, investigators developed the concept of time-varying elastance. We evaluated the applicability of this concept to lymphangions by analyzing preliminary data obtained from the bovine mesenteric vessels. We found that there were some limitations to the applicability of this concept to lymphangions, as there was a high degree of variability with respect to contraction strength and frequency of individual time-varying elastance curves. To better characterize lymphangion mechanics, we built a device which would enable real-time isobaric, isometric and isotonic experiments in vitro. We performed all three experiments on lymphatic vessel segments and obtained input and output pressures, output flow, instantaneous radii and wall tension. The characterization of the lymphangion using these parameters can be the first step to simulate the behavior of a lymphatic vesssel and later the behavior of an entire lymphatic system.

Opinion dynamics is extensively used in studying large-scale social, economical, political and natural phenomena that involve many interacting agents. It also can be used to model the evolution of teams of autonomous vehicles operating in a coordinated fashion with civilian and military applications, when arbitration among individual goals needs to be negotiated. Recently, research was conducted on how opinion dynamics can be the core of collective decision-making mechanisms for swarm robotics. Opinion dynamics with a time varying opinion space, which is the set of all possible opinions an agent may have, is a relatively recent research topic. In this work, the Deffuant-Weisbuch model (DW model), which allows to model opinion dynamics in shrinking opinion spaces, was applied. In simulating this class of systems and in extracting information from them it is crucial to establish reliable algorithms and criteria for counting the numbers of clusters, as this ultimately affects the determination of the steady state of the system. A method was applied to combine Fuzzy c-means clustering and subtractive clustering to check convergence of the system and avoid negative influence of outliers. Different scenarios are simulated to study the influence of characteristic parameters on the formation of opinions, which is quantified by the formation of clusters in the opinion space. Additionally, we simulate the scenario of a two dimensional opinion space in which one side shrinks, and evaluate how the rate of shrinking influences the steady state opinion space. This is a simplified model to gain some insight on the effect of extreme changes of opinions in multi-dimensional opinion space.

Few model reduction techniques exist for dynamical systems whose parameters vary with time. We have particular interest here in linear time-periodic dynamical systems; we seek a structure-preserving algorithm for model reduction of linear time-periodic (LTP) dynamical systems of large scale that generalizes from the linear time-invariant (LTI) model reduction problem. We extend the familiar LTI system theory to analogous concepts in the LTP setting. First, we represent the LTP system as a convolution operator of a bivariate periodic kernel function. The kernel suggests a representation of the system as a frequency operator, called the Harmonic Transfer Function. Second, we exploit the Hilbert space structure of the family of LTP systems to develop necessary conditions for optimal approximations. Additionally, we show an a posteriori error bound written in terms of the $\\mathcal H_2$ norm of related LTI multiple input/multiple output system. This bound inspires an algorithm to construct approximations of reduced order. To verify the efficacy of this algorithm we apply it to three models: (1) fluid flow around a cylinder by a finite element discretization of the Navier-Stokes equations, (2) thermal diffusion through a plate modeled by the heat equation, and (3) structural model of component 1r of the Russian service module of the International Space Station. / Master of Science

This thesis deals with two different topics, both related to modelling time-varying variances in high frequency financial time series. The first topic concerns the estimation of unobserved component models with autoregressive conditional heteroscedastic (ARCH) effects. The second topic concerns the quasi-maximum likelihood estimation of stochastic variance processes. These are an alternative to ARCH processes for modelling conditionally heteroscedastic time series. The motivation of the work is based on the increasing interest in the financial area in modelling volatility. In financial markets, many decisions are based on the volatility of a specific stock or index, which is closely related to the variance. Therefore, it is important to develop good statistical models able to describe time-varying variances. 2

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The purpose of this study is to examine the teaching process with the integration of games which has been used in number and calculation instructions for fifth grade elementary school children with varying ability. The teaching models and game designs were modified according to viewpoints of students, parents and teachers. In this study, students were not only divided into basic and advanced groups based on their varying ability but also instructed separately. The researcher will adjust the difficulty level flexibly for the two groupings. The four teaching units were: multiplication and division, factor and multiple, four basic algorithms, and equivalent fractions. The researcher designs the mathematical games which are suitable for lessons with reference to prior research within the country and abroad. After carrying out the integration, the effects and improvements were examined through students¡¦ learning records, parents¡¦ questionnaires and interviews. The results indicated that game teaching can motivate students and have better effects on teaching students in accordance with their aptitude by ability grouping. There were several indicators of improving learning effects such as peers¡¦ mutual cooperation, clarifying mathematical concepts, be familiar with calculation and mathematical problem solving, the improvement of learning attitude, etc. The learning effects were gradually increasing in the process as well. Besides, students could timely offer their opinions for the improvement of game designs after the instruction. As to the parents, they considered that students improve calculating abilities and reduce fear in mathematics when there was an increase in learning motivation. Parents were having high satisfactions with the whole teaching models and observed obvious progress in students¡¦ achievements. To enhance the participation of students, game designs should avoid complex calculation and add in rules with more variations and probabilities. The consideration of low achievement students in integration of games, giving encouragement and reward system should work together at the right time to enhance participation. Besides, the impact of the labelling of ability grouping should be reduced to avoid negative viewpoints. Finally, the teaching surroundings with games integration not only improve students¡¦ learning attitude but also develop problem-solving ability and help to develop and upgrade their mathematical ability.