Rumination consists of voluntary regurgitation of partially digested food, followed by chewing and re-swallowing or expulsion of regurgitated stomach contents (DM-ID2). Little research has systematically analyzed the differential effects of type or quantity of food on rumination across extended observations. This analysis demonstrated that certain (isolated) foods may differentially affect the rate of rumination. Furthermore, patterns of responding and manipulations of quantity may provide evidence for naturally occurring contingencies of punishment for the rumination of particular foods. These results may provide an avenue for minimally invasive, sustainable treatment for individuals with severe and chronic rumination.

The success of any racing car hinges on three key factors: its speed, handling, and reliability. In a highly competitive environment where lap times are extremely tight, even slight variations in components can significantly affect performance and, consequently, lap times. At the heart of a race car's performance lies the upright—a critical component of its suspension system. The upright serves to link the suspension arms to the wheels, effectively transmitting steering and braking forces to the suspension setup. Achieving optimal performance requires finding the right balance between lightweight design and ample stiffness, crucial for maintaining precise steering geometry and overall vehicle dynamics, especially under intense loads. Furthermore, there is a need to explore the system of structural optimization and seamlessly integrate Finite Element (FE) Models into the mathematical optimization process. This thesis explores a technique for parametric structural optimization utilizing finite element analysis and response surfaces to minimize the weight of the upright. Various constraints such as frequency, stress, displacement, and fatigue are taken into consideration during this optimization process. A parametric finite element model of the upright was designed, along with the mathematical formulation of the optimization problem as a nonlinear programming problem, based on the design objectives and suspension geometry. By conducting parameter sensitivity analysis, three design variables were chosen from a pool of five, and response surfaces were constructed to represent the constraints and objective function to be used to solve the optimization problem using Sequential Quadratic Programming (SQP). To streamline the process of parameter sensitivity analysis and response surface development, a Python scripting procedure was employed to automate the finite element job analysis and results extraction. The optimized upright design resulted in overall weight reduction of 25.3% from the maximum weight design of the parameterized upright. / Master of Science / The success of any racing car depends on three key factors: its speed, handling and reliability. In a highly competitive environment where lap times are extremely tight, even slight variations in components can significantly affect performance and consequently, lap times. At the heart of a race car's performance lies the upright—a critical component of its suspension system. The upright serves to link the suspension arms to the wheels, effectively transmitting steering and braking forces to the suspension setup. To achieve the best performance, upright must be as light as possible but it needs to be strong enough to ensure that the car is predictable when turning in a corner or while braking. Additionally, there is a need to explore methods of structural optimization and integrate finite element analysis seamlessly into the optimization process. Finite element analysis (FEA) is the use of part models, simulations, and calculations to predict and understand how an object might behave under certain physical conditions. This thesis examines a technique for optimizing the upright by designing it with numerous adjustable features for testing and then utilizing response surfaces to minimize its weight. Throughout this process, factors such as vibration, stress, deformation, and fatigue are carefully considered. A detailed parametric finite element model of the upright was developed, alongside the formulation of the optimization problem as a nonlinear programming problem, based on the objectives of the design and the geometry of the suspension. Through rigorous testing of parameters for optimization potential, design variables are selected for optimization. Response surfaces were then constructed to represent the constraints and objective function necessary to solve the optimization problem using Sequential Quadratic Programming (SQP). To enhance the efficiency of this process, a Python script was created to handle specific tasks within the finite element solver. This automation streamlined the analysis of the finite element model and the extraction of results. Ultimately, the optimized design of the upright yielded a 25.3% reduction in weight compared to its maximum weight configuration.

A bilinear formulation is used for developing the time finite element method (TFM) to obtain transient responses of both linear, nonlinear, damped and undamped systems. Also the formulation, used in the h-, p- and hp-versions, is extended and found to be readily amenable to multi-degree-of-freedom systems. The resulting linear and nonlinear algebraic equations for the transient response are differentiated to obtain the sensitivity of the response with respect to various design parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with other methods, excellent results for both the transient response and its sensitivity to system parameters. Mostly, the results were obtained using the Legendre polynomials as basis functions, though, in some cases other orthogonal polynomials namely, Hermite, Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of TFM, and the one often overlooked in its past applications, is the ease in which the sensitivity of the transient response with respect to various design parameters can be obtained. Since a considerable effort is spent in determining the sensitivity of the response with respect to system parameters in many algorithms for parametric identification, an identification procedure based on the TFM is developed and tested for a number of nonlinear single-and two-degree-of-freedom system problems. An advantage of the TFM is the easy calculation of the sensitivity of the transient response with respect to various design parameters, a key requirement for gradient-based parameter identification schemes. The method is simple, since one obtains the sensitivity of the response to system parameters by differentiating the algebraic equations, not original differential equations. These sensitivities are used in Levenberg-Marquardt iterative direct method to identify parameters for nonlinear single- and two-degree-of-freedom systems. The measured response was simulated by integrating the example nonlinear systems using the given values of the system parameters. To study the influence of the measurement noise on parameter identification, random noise is added to the simulated response. The accuracy and the efficiency of the present method is compared to a previously available approach that employs a multistep method to integrate nonlinear differential equations. It is seen, for the same accuracy, the present approach requires fewer data points. Finally, the TFM for optimal control problems based on Hamiltonian weak formulation is proposed by adopting the p- and hp-versions as a finite element discretization process. The p-version can be used to improve the accuracy of the solution by adding more unknowns to each element without refining the mesh. The usage of hierarchical type of shape functions can lead to a significant saving in computational effort for a given accuracy. A set of Legendre polynomials are chosen as higher order shape functions and applied to two simple minimization problems for optimal control. The proposed formulation provides very accurate results for these problems. / Ph. D.

Since the mid 1980's many statisticians have studied methods for combining parametric and nonparametric esimates to improve the quality of fits in a regression problem. Notably in 1987, Einsporn and Birch proposed the Model Robust Regression estimate (MRR1) in which estimates of the parametric function, ƒ, and the nonparametric function, 𝑔, were combined in a straightforward fashion via the use of a mixing parameter, λ. This technique was studied extensively at small samples and was shown to be quite effective at modeling various unusual functions. In 1995, Mays and Birch developed the MRR2 estimate as an alternative to MRR1. This model involved first forming the parametric fit to the data, and then adding in an estimate of 𝑔 according to the lack of fit demonstrated by the error terms. Using small samples, they illustrated the superiority of MRR2 to MRR1 in most situations. In this dissertation we have developed asymptotic convergence rates for both MRR1 and MRR2 in OLS and GLS (maximum likelihood) settings. In many of these settings, it is demonstrated that the user of MRR1 or MRR2 achieves the best convergence rates available regardless of whether or not the model is properly specified. This is the "Golden Result of Model Robust Regression". It turns out that the selection of the mixing parameter is paramount in determining whether or not this result is attained. / Ph. D.

This dissertation describes methods of mitigating radio frequency interference (RFI) in the frequency range 10-100 MHz, developing and evaluating coherent methods with which RFI is subtracted from the afflicted data, nominally resulting in no distortion of the underlying signals. This approach is of interest in weak signal applications such as radio astronomy, where the signal of interest may have interference-to-noise ratio much less than one, and so can be easily distorted by other methods. Environmental noise in this band is strong and non-white, so a realistic noise model is developed, with which we characterize the performance of signal parameter estimation, a key component of the proposed algorithms. Two classes of methods are considered: "generic" parameter estimation/subtraction (PE/S) and a modulation-specific form known as demodulation-remodulation ("demod--remod") PE/S. It is demonstrated for RFI in the form of narrowband FM and Broadcast FM that generic PE/S has the problem of severely distorting underlying signals of interest and demod-remod PE/S is less prone to this problem. Demod-remod PE/S is also applied and evaluated for RFI in the form of Digital TV signals. In both cases, we compare the performance of the demod-remod PE/S with that of a traditional adaptive canceling method employing a reference antenna, and propose a hybrid method to further improve performance. A new metric for "toxicity" is defined and employed to determine the degree to which RFI mitigation damages the underlying signal of interest. / Ph. D.

A method utilizing H2 control concepts and the numerical method of Polynomial Chaos was developed in order to create a novel robust probabilistically optimal control approach. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. As such, the development of new methods utilizing probability density functions (PDFs) was desired. From a more theoretical viewpoint, the utilization of Polynomial Chaos for studying and designing control systems has not been very thoroughly investigated. The current work looks at expanding the H2 and related Linear Quadratic Regulator (LQR) control problems for systems with parametric uncertainty. This allows solving deterministic linear equations that represent probabilistic linear differential equations. The application of common LTI (Linear Time Invariant) tools to these expanded systems are theoretically justified and investigated. Examples demonstrating the utilized optimization process for minimizing the H2 norm and parallels to LQR design are presented. The dissertation begins with a thorough background section that reviews necessary probability theory. Also, the connection between Polynomial Chaos and dynamic systems is explained. Next, an overview of related control methods, as well as an in-depth review of current Polynomial Chaos literature is given. Following, formal analysis, related to the use of Polynomial Chaos, is provided. This lays the ground for the general method of control design using Polynomial Chaos and H2. Then an experimental section is included that demonstrates controller synthesis for a constructed probabilistic system. The experimental results lend support to the method. / Ph. D.

Without noise, a wireless system would be able to transmit and receive signals over an arbitrary long-distance. However, practical wireless systems are not noise-free, leading to a limited communication range. Thus, the design of low-noise devices (such as antennas, amplifiers, and filters) is essential to increase the communication range. Also, it is well known that the noise performance of a receiving radio is primarily determined by the frontend including the antenna, filter, and a low-noise amplifier. In our first design, we intend to reduce the noise level of the receiving system by integrating a parametric amplifier into the slot antenna. The parametric amplifier utilizes nonlinear and/or time-variant properties of reactive elements (capacitors and/or inductors) to amplify radio frequency signals. Also, the parametric amplifier offers superior noise performance due to its reactive nature. We utilize the parametric amplifier to design a low-noise active matching circuit for electrically small antennas in our second design. Using Chu's limit and the Bode-Fano bound, we show a trade-off between the noise and bandwidth of the electrically small antennas. In particular, to make the small antenna wideband, one needs to introduce a mismatch between the antenna and the amplifier. Due to the mismatch, the effect of the low-noise amplifier becomes even more critical and that is why we choose the parametric amplifier as a natural candidate. As a realized design, a loop antenna is configured as a receiver, and the up-converter parametric amplifier is connected to it leading to a low-noise and wideband active matching circuit. The structure is simulated using a hybrid simulation technique and its noise performance is compared to the transistor counterpart. Our simulation and measurement results show more than 20 times bandwidth improvement at the expense of a 2 dB increase in the noise figure compared to the passive antenna counterpart. / Doctor of Philosophy / Nowadays, there is a high demand for compact and high-speed electronic devices such as cellphones, tablets, laptops, etc. It is therefore essential to design a miniaturized wideband antenna. Unfortunately, a trade-off exists between the bandwidth and gain of small antennas. The trade-off is based on some fundamental limits and extends to all small and passive antennas, regardless of their shape or structure. By using an active component such as an amplifier, the gain-bandwidth trade-off can be improved. However, we show that the active component adds noise to the receiving system leading to a new trade-off between noise and bandwidth in the receiving structures. In other words, utilizing the active component does not solve the problem and just replaces the gain-bandwidth trade-off with the noise-bandwidth trade-off. To improve the noise-bandwidth trade-off, we propose a new receiving structure in which we use the parametric amplifier instead of a commercially available transistor amplifier. The noise performance of the parametric amplifier is extremely better than the transistor amplifier leading to lower noise for the specified bandwidth. In particular, we improved the noise performance of the receiving system by 3 dB leading to doubling the communication distance.

Dynamical systems are mathematical models of physical phenomena widely used throughout the world today. When a dynamical system is too large to effectively use, we turn to model reduction to obtain a smaller dynamical system that preserves the behavior of the original. In many cases these models depend on one or more parameters other than time, which leads to the field of parametric model reduction. Constructing a parametric reduced-order model (ROM) is not an easy task, and for very large parametric systems it can be difficult to know how well a ROM models the original system, since this usually involves many computations with the full-order system, which is precisely what we want to avoid. Building off of efficient 𝐻-infinity approximations, we develop a greedy algorithm for efficiently modeling large-scale parametric dynamical systems in an 𝐻₂-sense. We demonstrate the effectiveness of this greedy search on a fluid problem, a mechanics problem, and a thermal problem. We also investigate Bayesian optimization for solving the optimization subproblem, and end with extending this algorithm to work with MIMO systems. / Master of Science / In the past century, mathematical modeling and simulation has become the third pillar of scientific discovery and understanding, alongside theory and experimentation. Mathematical models are used every day, and are essential to modern engineering problems. Some of these mathematical models depend on quantities other than just time, parameters such as the viscosity of a fluid or the strength of a spring. These models can sometimes become so large and complicated that it can take a very long time to run simulations with the models. In such a case, we use parametric model reduction to come up with a much smaller and faster model that behaves like the original model. But when these large models vary highly with the parameters, it can also become very expensive to reduce these models accurately. Algorithms already exist for quickly computing reduced-order models (ROMs) with respect to one measure of how "good" the ROM is. In this thesis we develop an algorithm for quickly computing the ROM with respect to a different measure - one that is more closely tied to how the models are simulated.

Infrastructure management must move from a perspective that may singularly emphasize facility condition assessment to a broader view that involves nonphysical factors, which may substantially impact facility performance and shorten its service life. Socioeconomic, technological, regulatory, and user value changes can substantially increase the service expectations of existing facilities. Based on a theoretical framework drawn from prior work, this research develops a new approach to model infrastructure performance and assess factors that influence the remaining service life of highway bridges. Key parameters that impact the serviceability of highway bridges are identified and incorporated into a system dynamics model. This platform supports parametric scenario analysis and is applied in several cases to test how various factors influence bridge service life and performance. This decision support system provides a new approach for modeling serviceability over time and gives decision-makers an indication of: (a) the gap between society's service expectations and the service level provided and (b) the remaining service life of a highway bridge. / Ph. D.

The architectural opportunity to develop the sound and light lock of a performance venue as a space that engages and prepares the audience for a performance is one that is sadly missing from most halls. I have explored the development of this threshold as a true architectural space, one that enhances the overall experience for the audience members. And by introducing a parametric process into the architectural and acoustic development, have proposed a unique process for the design of concert halls. From physical model building to analysis by computer simulation, digital technology has undoubtedly advanced the realm of acoustic prediction. But common computer prediction programs that exist today are still essentially digitized applications of the analog model building process. Being: construct a model, analyze, make adjustments and repeat until the desired results are achieved. By implementing a parametric approach to model building it allows for design changes and the significance of those changes to be recognized in real time, an invaluable tool in the development of a sound-sensitive space. Utilizing the 3D software Rhinoceros and its scripting plug-in Grasshopper, it becomes possible to easily visualize crucial first-order reflections relative to surfaces that can be controlled and manipulated in very precise ways. This software is becoming more popular amongst architects and designers, and the prediction process will be an extension of this software into the field of acoustics. By using software already in the design vernacular, there is a seamless transition between design and analysis, making for a more cohesive project / Master of Architecture