In the past several years, the Defense Advanced Research Projects Agency (DARPA) has sponsored two Grand Challenges, races among autonomous ground vehicles in rural environments. These vehicles must follow a course delineated by Global Positioning System waypoints using no human guidance. Airborne LIDAR data and GIS can play a significant role in identifying barriers and least cost paths for such vehicles. Least cost paths minimize the sum of impedance across a surface. Impedance can be measured by steepness of slope, impenetrable barriers such as vegetation and buildings, fence lines and streams, or other factors deemed important to the vehicle's success at navigating the terrain. This research aims to provide accurate least cost paths for those vehicles using airborne LIDAR data. The concepts of barrier identification and least cost path generation are reviewed and forty-five least cost paths created with their performance compared to corresponding Euclidean paths. The least cost paths were found superior to the corresponding Euclidean paths in terms of impedance as they avoid barriers, follow roads and pass across relatively gentler slopes. / Master of Science

Shuffled linear regression concerns itself with linear models with an unknown correspondence between the input and the output. This correspondence is usually represented by a permutation matrix II*. The model we are interested in has one more complication which is that the design matrix is itself latent and is observed with noise. This is considered as a type of errors-in-variables (EIV) model. Our interest lies in the recovery of the permutation matrix. We propose an estimator for II* based on the total least squares (TLS) technique, a common method of estimation used in EIV model. The estimation problem can be viewed as approximating one matrix by another of lower rank and the quantity it seeks to minimize is the sum of the smallest singular values squared. Due to identifiability issue, we evaluate the proposed estimator by the normalized Procrustes quadratic loss which allows for an orthogonal rotation of the estimated design matrix. Our main result provides an upper bound on this quantity which states that it is required that the signal-to-noise ratio to go to infinity in order for the loss to go to zero. On the computational front, since the problem of permutation recovery is NP-hard to solve, we propose a simple and efficient algorithm named alternating LAP/TLS algorithm (ALTA) to approximate the estimator, and we use it to empirically examine the main result. The main idea of the algorithm is to alternate between estimating the unknown coefficient matrix using the TLS method and estimating the latent permutation matrix by solving a linear assignment problem (LAP) which runs in polynomial time. Lastly, we propose a hypothesis testing procedure based on graph matching which we apply in the field of digital humanities, on character social networks constructed from novel series.

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<p> The work in this thesis is to develop a tool for calculating the parameters corresponding to certain theoretical model of dielectric relaxation phenomena and then doing the curve fitting using the result after fetching the data from the user. To our best knowledge, this the first such tool to calculate the parameters corresponding to certain theoretical model of dielectric relaxation phenomena while the user only need to provide the experimental data. The parameters are calculated by using a nonlinear least square algorithm implemented in Matlab and a nonlinear function minimizer available in Matlab. The way to do the curve fitting is not by the traditional way such as cubic spline but by calculating the simulated data using the chosen model and the calculated result for the parameters. </p> <p> The available mathematical models include all of popular theoretical models, the Cole-Davidson (DC), the Kohlrausch-Williams-Watts (KWW), the Havriliak-Negami (HN) and the model proposed by R. Hilfer (FD). </p> <p> There are two ways to calculate the parameters for each model as mentioned before. The result returned by this system may not be unique. Especially if the frequency range of data is not wide enough, the result would most likely be non-unique. Since the iterative method is used in the system, it is suggested that the user provides the initial values for the system with his best knowledge or background for the data and the tested sample related to dielectric relaxation process. </p> <p> It is normal if there is a part having worse fitting than the other parts. One of reasons could be the mathematical model's defect, which the model does not work for that part. For the further information, please contact me by email at zouhaijun at yahoo.com. </p> / Thesis / Master of Science (MSc)

Optimization based domain decomposition methods for the solution of partial differential equations are considered. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains; the constraints are the partial differential equations. First, we consider a linear constraint. The existence of optimal solutions for the optimization problem is shown as is its convergence to the exact solution of the given problem. We then derive an optimality system of partial differential equations from which solutions of the domain decomposition problem may be determined. Finite element approximations to solutions of the optimality system are defined and analyzed as is an eminently parallelizable gradient method for solving the optimality system. The linear constraint minimization problem is also recast as a linear least squares problem and is solved by a conjugate gradient method. The domain decomposition method can be extended to nonlinear problems such as the Navier-Stokes equations. This results from the fact that the objective functional for the minimization problem involves the jump in dependent variables across the interfaces between subdomains. Thus, the method does not require that the partial differential equations themselves be derivable through an extremal problem. An optimality system is derived by applying a Lagrange multiplier rule to a constrained optimization problem. Error estimates for finite element approximations are presented as is a gradient method to solve the optimality system. We also use a Gauss-Newton method to solve the minimization problem with the nonlinear constraint. / Ph. D.

A new approach to determining mode vectors is presented which uses predetermined global parameters and an improved residual model to iteratively determine modal residues. The motivation for such a technique is to determine modal parameters rapidly so that, as data acquisition techniques become faster, more structural degrees of freedom can be measured without significantly slowing down the parameter estimation process. The technique requires an accurate determination of the global parameters of natural frequency and damping by means of an FRF curve fit. More than one structural point is recommended to determine the global parameters since they will be used in determining the mode vectors. A structurally damped curve fitter which uses one or two FRFs is described and can be used for determining the global parameters. Examples of curve fitting simulated and measured data are presented and a comparison is made to a commercially available curve-fitter. Once a frequency range-of-interest is selected, frequencies will be chosen at which the mobility is measured using sine excitation. The in-range modal response is represented by a matrix-vector product where the vector contains the residues for the modes of interest. The out-of-range modal content is also represented by a matrix-vector product and forms the improved residual model. The residual content is removed from the measured mobility by an iterative technique which allows for an accurate determination of the residues of interest. An evaluation of the technique is carried out by simulating a dynamic system including the shaker and power supply. The simulated system is closely modeled after a real system used to evaluate the technique on experimental data. Convergence rates are shown for cases of close modes, low amplitude modes and errors in the global parameters. The results of using the technique on experimental data shows that convergence typically occurs in under 15 iterations. Regenerating the FRF from the modal parameters shows close agreement to the original FRF and better agreement than the regeneration from modal parameters derived from a commercially available curve fitter.> / Ph. D.