The Integrative Neuropsychological Theory of Executive-Related Abilities and Component Transactions (INTERACT; Garcia-Barrera, 2011) is a novel perspective on executive function(s), and the functional interactions among those neural systems thought to underlie them. INTERACT was examined in this validation study using structural equation modeling. A novel battery of computerized tasks was implemented in a sample of 218 healthy, adult, university students. Each of the derived indicator variables represented a specific aspect of performance, and corresponded with one of the five distinct executive components of INTERACT. After eliminating tasks that demonstrated poor psychometric properties, overall model fit was excellent, χ2 = 36.38, df = 44, p = .786; CFI = 1.00; RMSEA = .000. Further, INTERACT was superior to six alternative measurement models, which were theoretically-based. Although the structural model of INTERACT was too complex to be tested here, a novel analysis of the data was introduced to test the interactions among INTERACT’s components. This analysis demonstrated the significant utility of INTERACT’s fundamental theoretical predictions. Given the outcome of this initial validation study, the predictive power of INTERACT should continue to be exploited in future studies of executive function(s), and should be extended to explore executive systems in unique populations. / Graduate

It can be shown that for the complete description of all the physical parameters in the flow behind an imtermediate strength unsteady shock, a knowledge of the particle trajectories within the flow is sufficient. This principle has been applied to determine the variation of the physical parameters throughout the length of a conventional shock tube. The particle trajectories were obtained by the high speed photography of cigarette smoke tracers, placed at 10 cm. intervals along the tube. By applying the conservation of mass equation to the particle trajectory data, the density variation was obtained throughout the flow including the rarefaction wave from the end of the compression chamber and behind the first reflected shock from the closed end of the expansion chamber. By means of the Rankine-Hugoniot relation, the pressures immediately behind the incident and reflected shock fronts were calculated, and by assuming isentropic flow between shocks along any particle trajectory, the complete pressure variation was determined. The temperature and local sound speed were subsequently calculated at all points and the particle velocities were determined from the time derivative of the particle trajectories. A complete mapping of all the parameters in the shock tube was thus obtained using a single photographic technique, which is simpler than previous methods. / Graduate / 0605

Feedback control is used in almost every aspect of modern life and is essential in almost all engineering systems. Since no mathematical model is perfect and disturbances occur frequently, feedback is required. The design of a feedback control has been widely investigated in finite-dimensional space. However, many systems of interest, such as fluid flow and large structural vibrations are described by nonlinear partial differential equations and their state evolves on an infinite-dimensional Hilbert space. Developing controller design methods for nonlinear infinite-dimensional systems is not trivial. The objectives of this thesis are divided into multiple tasks. First, the well-posedness of some classes of nonlinear partial differential equations defined on a Hilbert space are investigated. The following nonlinear affine system defined on the Hilbert space H is considered z ̇(t)=F(z(t))+Bu(t), t≥0 z (0) = z0, where z(t) ∈ H is the state vector and z0 is the initial condition. The vector u(t) ∈ U, where U is a Hilbert space, is a state-feedback control. The nonlinear operator F : D ⊂ H → H is densely defined in H and the linear operator B : U → H is a linear bounded operator. Conditions for the closed-loop system to have a unique solution in the Hilbert space H are given. Next, finding a single bounded state-feedback control for nonlinear partial differential equations is discussed. In particular, Lyapunov-indirect method is considered to control nonlinear infinite-dimensional systems and conditions on when this method achieves the goal of local asymptotic stabilization of the nonlinear infinite-dimensional system are given. The Kuramoto-Sivashinsky (KS) equation defined in the Hilbert space L2(−π,π) with periodic boundary conditions is considered. ∂z/∂t =−ν∂4z/∂x4 −∂2z/∂x2 −z∂z/∂x, t≥0 z (0) = z0 (x) , where the instability parameter ν > 0. The KS equation is a nonlinear partial differential equation that is first-order in time and fourth-order in space. It models reaction-diffusion systems and is related to various pattern formation phenomena where turbulence or chaos appear. For instance, it models long wave motions of a liquid film over a vertical plane. When the instability parameter ν < 1, this equation becomes unstable. This is shown by analyzing the stability of the linearized system and showing that the nonlinear C0- semigroup corresponding to the nonlinear KS equation is Fr ́echet differentiable. There are a number of papers establishing the stabilization of this equation via boundary control. In this thesis, we consider distributed control with a single bounded feedback control for the KS equation with periodic boundary conditions. First, it is shown that sta- bilizing the linearized KS equation implies local asymptotical stability of the nonlinear KS equation. This is done by establishing Fr ́echet differentiability of the associated nonlinear C0-semigroup and showing that it is equal to the linear C0-semigroup generated by the linearization of the equation. Next, a single state-feedback control that locally asymptot- ically stabilizes the KS equation is constructed. The same approach to stabilize the KS equation from one equilibrium point to another is used. Finally, the solution of the uncontrolled/state-feedback controlled KS equation is ap- proximated numerically. This is done using the Galerkin projection method to approximate infinite-dimensional systems. The numerical simulations indicate that the proposed Lyapunov-indirect method works in stabilizing the KS equation to a desired state. Moreover, the same approach can be used to stabilize the KS equation from one constant equilibrium state to another.

There are two sources of information available in empirical research in finance: one corresponding to historical data and the other to prices currently observed in the markets. When proposing a model, it is desirable to use information from both sources. However in modern finance, where stochastic differential equations have been one of the main modeling tools, the common models are typically different for historical data and for current market data. The former are usually assumed to be time homogeneous, while the latter are typically time in-homogeneous. This practice can be explained by the fact that a time-homogeneous model is stationary and easier to estimate, while time-inhomogeneous model are required in order to replicate market data sufficiently well without creating arbitrage opportunities. In this thesis, we study methods of statistical inference, both parametric and non-parametric, for stochastic differential equations with time-dependent parameters. In the first part, we propose a new class of stochastic differential equation with time-dependent drift and diffusion terms, where some of the parameters change according to a hidden Markov process. We show that under some technical conditions this innovative way of modeling switching times renders the resulting model stationary. We also explore different approaches to estimate parameters in our proposed model. Our simulation studies demonstrate that the parameters of the model can be efficiently estimated by using a version of the filtering method proposed in the literature. We illustrate our model and the proposed estimation method by applying them to interest rate data, and we detect significant time variations in early 1980s, when targets of the monetary policy in the United States were changed. One of the known drawbacks of parametric models is the risk of model misspecification. In the second part of the thesis, we allow the drift to be time-dependent and nonparametric, and our objective is to estimate it using a single trajectory of the process. The main idea underlying this method is to approximate the time-dependent function with a sequence of polynomials. Since we can estimate efficiently only a finite number of parameters for any finite length of data, in our method we propose to relate the number of parameters to the length of the observed trajectory. This idea is similar to the method of sieves proposed by Grenander (Abstract Inference, 1981). The asymptotic analysis that we present is based on the assumption that the length of available data $T$ increases to infinity. We investigate two cases, one is a Brownian motion with time-dependent drift and the other corresponds to a class of mean-reverting stochastic differential equations with time-dependent mean-reversion level. In both cases we prove asymptotic consistency and normality of a modified maximum likelihood estimator of the projected time-dependent component. The main challenge in proving our results in the second case stems from two features of the problem: one is due to the fact that coefficients of projections change with $T$ and the other is related to the confounding effect between the mean-reversion speed and the level function. By applying our method to the same interest rate data we use in the first part, we find another evidence of time-variation in the drift term.

This work extends modelling of high prequency electric-acoustic transducers beyong current limiting approxilations, which is of interest to such applications as ultrasonic imaging, testing, tomography etc. / Thesis (PhD)--University of South Australia, 2001.

This thesis is concerned with stochastic heat equation with memory and nonlinear energy supply. The main motivation to study such systems comes from Thermodynamics, see [85]. The main objective of this work is to study the existence and uniqueness of solutions to such equations and to investigate some fundamental properties of solutions like continuous dependence on initial conditions. In our approach we follow the seminal papers by Da Prato and Clement [10], where the stochastic heat equation with memory is tranformed into an integral equation in a function space and the so-called mild solutions are studied. In the aforementioned papers only linear equations with additive noise were investigated. The main contribution of this work is the extension of this approach to nonlinear equations. Our main tools are the theory of stochastic convolutions as developed in [33] and the theory of resolvent kernels for deterministic linear heat equations with memory, see[10]. Since the solution at time t depends on the whole history of the process up to time t, the resolvent kernel does not define a semigroup of operators in the state space of the process and therefore a ???standard??? theory of stochastic evolution equations as presented in the monograph [33] does not apply. A more delicate analysis of the resolvent kernles and the associated stochastic convolutions is needed. We will describe now content of this thesis in more detail. Introductory Chapters 1 and 2 collect some basic and essentially well known facts about the Wiener process, stochastic integrals, stochastic convolutions and integral kernels. However, some results in Chapter 2 dealing with stochastic convolution with respect to non-homogenous Wiener process are extensions of the existing theory. The main results of this thesis are presented in Chapters 3 and 4. In Chapter 3 we prove the existence and uniqueness of solutions to heat equations with additive noise and either Lipschitz or dissipative nonlinearities. In both cases we prove the continuous dependence of solutions on initial conditions. In Chapter 4 we prove the existence and uniqueness of solutions and continuous dependence on initial conditions for equations with multiplicative noise. The diffusion coefficients defined by unbounded operators are allowed.

This work extends modelling of high frequency electric-acoustic transducers beyond current limiting approximations, which is of interest to such applications as ultrasonic imaging, testing, tomography etc. The developed methodology includes transient modelling of the acoustic potential field with dynamic Green?s functions and linear formulation of wave propagation in the moving reference frame. A finite difference model is determined to achieve fast numerical implementation. Developed is also experimental methodology for impulse response measurements, offering modifications of the inverse Wiener filter and introducing novel transducer equalisation increasing signal bandwidth. / thesis (PhD)--University of South Australia, 2001.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (M.S. - Soils, Water and Engineering)--University of Arizona, 1982. / Bibliography: leaves 81-83.

Thesis (Ph.D.)--Auburn University, 2007. / Abstract. Includes bibliographic references (ℓ. 163-)