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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 historical method of precise orbit determination is a dynamic approach. However, with the improvement of GPS tracking data and associated tracking networks, two newer methods have been developed: reduced-dynamic and kinematic. In addition to orbit determination, alternative methods of gravity field recovery have been developed using kinematic orbits which do not rely on any force modeling. However, one significant drawback of kinematic orbits is that they lack any velocity or acceleration information. These have to be derived numerically. Based on the results of this thesis, the Savitzky-Golay filter, without using a remove-restore procedure, is recommended for deriving kinematic velocities of the GRACE mission. In addition, the numerical differentiation methods are tested to see how well accurately they represent the satellite's acceleration for all three orbit types. Finally, with the kinematic orbits properly reconstructed, the results can also be compared to dynamic and reduced-dynamic orbits through K-Band Ranging residuals. / text