Estimation of the degree of polarization through computational sensing

The degree of polarization of a refected field from active laser illumination can be used for object identifcation and classifcation. The goal of this study is to investigate methods for estimating the degree of polarization for refected fields with active laser illumination, which involves the measurement and processing of two orthogonal field components (complex amplitudes), two orthogonal intensity components, and the total field intensity. We propose to replace interferometric optical apparatuses with a computational approach for estimating the degree of polarization from two orthogonal intensity data and total intensity data. Cramer-Rao bounds for each of the three sensing modalities with various noise models are computed. Algebraic estimators and maximum-likelihood (ML) estimators are proposed. Active-set algorithm and expectation-maximization (EM) algorithm are used to compute ML estimates. The performances of the estimators are compared with each other and with their corresponding Cramer-Rao bounds. Estimators for four-channel polarimeter (intensity interferometer) sensing have a better performance than orthogonal intensities estimators and total intensity estimators. Processing the four intensities data from polarimeter, however, requires complicated optical devices, alignment, and four CCD detectors. It only requires one or two detectors and a computer to process orthogonal intensities data and total intensity data, and the bounds and estimator performances demonstrate that reasonable estimates may still be obtained from orthogonal intensities or total intensity data. Computational sensing is a promising way to estimate the degree of polarization.

Influence of traumatic impaction and pathological loading on knee menisci

Nearly half of the US population faces the risk of developing knee osteoarthritis (OA). Both in vitro and in vivo studies can aid in a better understanding of the etiology, progression, and advancement of this debilitating disorder. The knee menisci are fibrocartilagenous structures that aid in the distribution of load, attenuation of shock, alignment and lubrication of the knee. Little is known about the biochemical and morphological changes associated with knee menisci following altered loading and traumatic impaction, and investigations are needed to further elucidate how degradation of this soft tissue advances over time. The biochemical response of porcine meniscal explants was investigated following a single bout of dynamic compression with and without the treatment of the pharmaceutical drug, anakinra (IL-1RA). Dynamic loading led to a strain-dependent response in both anabolic and catabolic gene expression of meniscal explants. By inhibiting the Interleukin-1 pathway with IL-1RA, a marked decrease in several catabolic molecules was found. From these studies, future developments in OA treatments may be developed. The implementation of an in vivo animal model contributes to the understanding of how the knee joint behaves as a whole. A novel closed-joint in vivo model that induces anterior cruciate ligament (ACL) rupture has been developed to better understand how traumatic injury leads to OA. The menisci of knees from three different groups (healthy, ACL transected, and traumatically impacted) were characterized using histomorphometry. The acute and chronic changes within the knee following traumatic impaction were investigated. The works presented in this dissertation have focused on the characterization, implementation, and development of mechanically-induced changes to the knee menisci.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.