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Fresh foods, including meats and produce are the fastest growing market in the supermarket and the class of foods most likely to cause a bacterial foodborne illness. As the rate of consumption of perishable products increases, rapid detection of pathogens within the food supply becomes a critical issue. Current methods used for the detection of bacteria that cause food-borne illnesses are time consuming, expensive and often require selective enrichment. In this study we adapted a separation technique originally developed for PCR to extract bacteria from ground beef using β-cyclodextrin (β-CD) and milk protein coated activated carbon (MP-CAC) as filtration agents. The recovered bacteria were bound to a gold slide via a 3-mercaptophenylboronic acid (3-MPBA) sandwich assay and detected with Surface Enhanced Raman Spectroscopy (SERS). The 3-MPBA sandwich assay used with the separation technique allowed detection of Salmonella enterica Enteritidis (BAA-1045), separated from a ground beef matrix, as low as 1x102 CFU/g. Detection at this level was accomplished in less than 8 hours, significantly faster than plate count or enrichment methods that require multiple days. Previously, SERS has been used to detect bacteria within simple matrices; this is the first study to have utilized SERS bacterial detection in a ground beef.

In the parametric development of statistical inference it often is assumed that observations are independent and Gaussian. The Gaussian assumption sometimes is justified on appeal to central limit theory or on the grounds that certain normal theory procedures are robust. The independence assumption, usually unjustified, routinely facilitates the derivation of needed distribution theory. In this thesis a variety of standard tests for scale parameters is considered when the observations are not necessarily either Gaussian or independent. The distributions considered are the spherically symmetric vector laws, i.e. laws for which x(nx1) and Px have the same distribution for every (nxn) orthogonal matrix P, and natural extensions of these to laws of random matrices. If x has a spherical law, then the distribution of Ax + b is said to be elliptically symmetric. The class of spherically symmetric laws contains such heavy-tailed distributions as the spherical Cauchy law and other symmetric stable distributions. As such laws need not have moments, the emphasis here is on tests for scale parameters which become tests regarding dispersion parameters whenever second-order moments are defined. Using the principle of invariance it is possible to characterize the invariant tests for certain hypotheses for all elliptically symmetric distributions. The particular problems treated are tests for the equality of k scale parameters, tests for the equality of k scale matrices, tests for sphericity, tests for block diagonal structure, tests for the uncorrelatedness of two variables within a set of m variables, and tests for the hypothesis of equi-correlatedness. In all cases except the last three the null and non-null distributions of invariant statistics are shown to be unique for all elliptically symmetric laws. The usual normal-theory procedures associated with these particular testing problems thus are exactly robust, and many of their known properties extend directly to this larger class. In the last three cases, the null distributions of certain invariant statistics are unique but the non-null distributions depend on the underlying elliptically symmetric law. In testing for block diagonal structure in the case of two blocks, a monotone power property is established for the subclass of all elliptically symmetric unimodal distributions. / Ph. D.

Most research on solving the N-electron Schrödinger equation has focused on ground states; excited states are comparatively less studied, and represent a greater challenge for many ab initio methods. The challenge is exacerbated for systems with substantial multiconfigurational character (i.e., strongly-correlated systems) for which standard many-electron wavefunction methods relying on a single electronic configuration give qualitatively incorrect descriptions of electron correlation. This thesis explores approaches to molecular excited state properties that are computationally efficient, yet applicable to multiconfigurational systems. Specifically, we explore strategies that combine the Equation-of-Motion (EOM) approach with the types of correlated wavefunction ansätze that are suitable for strongly-correlated systems. While it is known that the EOM method provides a general strategy for computing electronic transition energies, the significant flexibility in how one formulates the EOM approach and how it can be applied as a post-processing tool for different wavefunctions is not always appreciated. We begin by reviewing the EOM approach, focussing on methods that can be formulated using the 1- and 2-electron reduced density matrices. We assess the accuracy of different EOM approaches for neutral and ionic excited states. We focus on EOM-based alternatives to the traditional extended Koopams’ Theorem for ionization energies and electron affinities as well as an EOM formulation for double ionization transitions that constitutes an extension of the hole-hole/particle-particle random phase approximation (RPA) to multideterminant wavefunction methods. Then we introduce FanEOM, an EOM extension of the Flexible Ansatz for N-electron Configuration Interaction (FANCI) [Comput. Theor. Chem. 1202, 113187 (2021)], and explore its application to spectroscopic properties. Using the EOM methods for electronic excitation and double ionization/double electron affinity transitions described in the initial part of this thesis (i.e., the extended random phase approximations, ERPA), we study adiabatic connection formulations (AC) for computing the residual dynamic correlation energy in correlated wavefunction methods. The key idea in these approaches is that the perturbation strength dependent 2-RDM that appears in the AC formula can be approximated through the solutions from the different variants of ERPA [Phys. Rev. Lett. 120, 013001 (2018)]. Finally, we present PyEOM, an open-source software package designed to help prototype and test EOM-based methods. / Thesis / Doctor of Philosophy (PhD)

This dissertation examines the application of the Liouville operator to problems in classical mechanics. An approximation scheme or methodology is sought that would allow the calculation of the position and momentum of an object at a specified later time, given the initial values of the object's position and momentum at some specified earlier time. The approximation scheme utilizes matrix techniques to represent the Liouville operator. An approximation scheme using the Liouville operator is formulated and applied to several simple one-dimensional physical problems, whose solution is obtainable in terms of known analytic functions. The scheme is shown to be extendable relative to cross products and powers of the variables involved. The approximation scheme is applied to a more complicated one-dimensional problem, a quartic perturbed simple harmonic oscillator, whose solution is not capable of being expressed in terms of simple analytic functions. Data produced by the application of the approximation scheme to the perturbed quartic harmonic oscillator is analyzed statistically and graphically. The scheme is reapplied to the solution of the same problem with the incorporation of a drag term, and the results analyzed. The scheme is then applied to a simple physical pendulum having a functionalized potential in order to ascertain the limits of the approximation technique. The approximation scheme is next applied to a two-dimensional non-perturbed Kepler problem. The data produced is analyzed statistically and graphically. Conclusions are drawn and suggestions are made in order to continue the research in several of the areas presented. / Ph. D.

Eigenstructure based techniques have been studied extensively in the last decade to estimate the number and locations of incoming radiating sources using a passive sensor array. One of the early limitations was the computational load involved in arriving at the eigendecompositions. The introduction of VLSI circuits and parallel processors however, has reduced the cost of computation A tremendously. As a consequence, we study eigendecomposition algorithms with highly parallel and A localized data flow, in order to take advantage of VLSI capabilities. This dissertation presents a fast Recursive/Iterative Toeplitz (Hermitian) Eigenspace (RITE) algorithm, and its extension to the generalized strongly regular eigendecomposition situation (C-RITE). Both procedures exhibit highly parallel structures, and their applicability to fast passive array processing is emphasized. The algorithms compute recursively in increasing order, the complete (generalized) eigendecompositions of the successive subproblems contained in the maximum size one. At each order, a number of independent, structurally identical, non-linear problems is solved in parallel. The (generalized) eigenvalues are found by quadratically convergent iterative search techniques. Two different search methods, a restricted Newton approach and a rational approximation based technique are considered. The eigenvectors are found by solving Toeplitz systems efficiently. The multiple minimum (generalized) eigenvalue case and the case of a cluster of small (generalized) eigenvalues are treated also. Eigenpair residual norms and orthonormality norms in comparison with IMSL library routines, indicate good performance and stability behavior for increasing dimensions for both the RITE and C-RITE algorithms. Application of the procedures to the Direction Of Arrival (DOA) identification problem, using the MUSIC algorithm, is presented. The order-recursive properties of RITE and C-RITE permit estimation of angles for all intermediate orders imbedded in the original problem, facilitating the earliest possible estimation of the number and location of radiating sources. The detection algorithm based on RITE or C-RITE can then stop, thereby minimizing the overall computational load to that corresponding to the smallest order for which angle of arrival estimation is indicated to be reliable. Some extensions of the RITE procedure to Hermitian (non-Toeplitz) matrices are presented. This corresponds in the array processing context to correlation matrices estimated from non-linear arrays or incoming signals with non-stationary characteristics. A first—order perturbation approach and two Subspace Iteration (SI) methods are investigated. The RITE decomposition of the Toeplitzsized (diagonally averaged) matrix is used as a starting point. Results show that the SI based techniques lead to good approximation of the eigen-information, with the rate of convergence depending upon the SNR ar1d the angle difference between incoming sources, the convergence being faster than starting the SI method from an arbitrary initial matrix. / Ph. D.