Exposing the Roots of Low Self-Efficacy for Math: A Multi-Case Study of Students in an Urban Middle School

This multi-case study of historically low-performing 7th grade students in a math class at an urban middle school employed a theoretical framework based upon Bandura’s Social Cognitive Theory to discover the causes of low self-efficacy for math. The study utilized a cross-case analysis of four students who demonstrated varying degrees of self-efficacy. To serve students similarly situated, Christian teachers need to know what these students are experiencing and an understanding of the causes of low self-efficacy can inform their professional practice. Christian teacher educators can also benefit from understanding the context into which teachers of such students will serve so as to aptly prepare them for effective practice

Fusing Binary Interface Defects in Topological Phases: The Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z}) case

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods can be applied to any Levin-Wen model. We also give physical interpretations for each of the defects in the $\mathbb{Z}/p\mathbb{Z}$ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion.Comment: 27+10 pages, 2+5 tables, comments welcom

Development of Force-Space Navigation for Surgical Robotics

Surgical robotics have been used for many years in orthopaedic procedures in the hip and knee. Robots tend to offer high accuracy and repeatability but add increased cost, complexity, time, and workflow disruption. This work outlines the design and development of a surgical robot that navigates using force feedback. Flexible components tether the patient to the robot and reaction loads are measured allowing the robot to “feel” its way around the pre-operative plan. Differences calculated between measured and desired loads are converted to Cartesian corrections that the robot used to navigate. The robot was tested first using simple square paths to test accuracy, repeatability and functionality. A pre-operative plan was established for implantation of the surgical system and allowed the robot to be tested doing a complex glenoid implant path. Finally, a study was performed and compared the robot’s surgical method to current surgical techniques of a trained surgical fellow on shoulder analogs. Based on this study, the robot performed as well as or better than the surgeon in almost every measurement parameter with less than 1 mm of implant placement error in many measurement metrics and less than 2° of implant orientation error in each angular measurement

Measurements and Mitigation of Scattered Light Noise in LIGO

The Advanced LIGO (aLIGO) detectors use 1064 nm lasers to measure the tiny fluctuations in spacetime that occur when gravitational waves pass through the earth. LIGO makes use of advanced coating methods and materials to limit the amount of light that scatters from the main beam, but some amount of light does scatter. This stray light can interact with surfaces inside the interferometer that are not seismically isolated and then recombine with the main beam, introducing excess noise into the gravitational wave channel. This thesis reviews the methods for modeling scattered light with ray tracing software and analytical models, for measuring scattered light with driven measurements of the vacuum enclosure, and for mitigating scattered light with baffles and changes to interferometer controls. It also details the process for finding correlations with auxiliary sensors in order to locate the sources of scattered light noise. The results of this work are improved sensitivity of the LIGO detectors in the frequency band from 20 Hz up to 200 Hz

Master of Science

thesisThe 2012 Great Utah Shakeout highlighted the necessity for increased coordination in the collection and sharing of spatial data related to disaster response during an event. Multiple agencies must quickly relay scientific and damage observations between teams in the field and command centers. Spatial Data Infrastructure (SDI) is a framework that directly supports information discovery and access and use of the data in decision making processes. An SDI contains five core components: policies, access networks, data handling facilities, standards, and human resources needed for the effective collection, management, access, delivery, and utilization of spatial data for a specific area. Implementation of an SDI will increase communication between agencies, field-based reconnaissance teams, first responders, and individuals in the event of a disaster. The increasing popularity of location-based mobile social networks has led to spatial data from these sources being used in the context of managing disaster response and recovery. Spatial data acquired from social networks, or Volunteer Geographic Information (VGI), could potentially contribute thousands of low-cost observations to aid in damage assessment and recovery efforts that may otherwise be unreported. The objective of this research is to design and develop an SDI to allow the incorporation of VGI, professional Geographic Information System (GIS) layers, a mobile application, and scientific reports to aid in the disaster management process. A secondary goal is to assess the utility of the resulting SDI. The end result of combining the three systems (e.g., SDE, a mobile application, and VGI), along with the network of relevant users, is an SDI that improves the volume, quality, currency, accuracy, and access to vital spatial and scientific information following a hazard event

Approaches to decision-making among late-stage melanoma patients: a multifactorial investigation.

PurposeThe treatment decisions of melanoma patients are poorly understood. Most research on cancer patient decision-making focuses on limited components of specific treatment decisions. This study aimed to holistically characterize late-stage melanoma patients' approaches to treatment decision-making in order to advance understanding of patient influences and supports.Methods(1) Exploratory analysis of longitudinal qualitative data to identify themes that characterize patient decision-making. (2) Pattern analysis of decision-making themes using an innovative method for visualizing qualitative data: a hierarchically-clustered heatmap. Participants were 13 advanced melanoma patients at a large academic medical center.ResultsExploratory analysis revealed eight themes. Heatmap analysis indicated two broad types of patient decision-makers. "Reliant outsiders" relied on providers for medical information, demonstrated low involvement in decision-making, showed a low or later-in-care interest in clinical trials, and expressed altruistic motives. "Active insiders" accessed substantial medical information and expertise in their networks, consulted with other doctors, showed early and substantial interest in trials, demonstrated high involvement in decision-making, and employed multiple decision-making strategies.ConclusionWe identified and characterized two distinct approaches to decision-making among patients with late-stage melanoma. These differences spanned a wide range of factors (e.g., behaviors, resources, motivations). Enhanced understanding of patients as decision-makers and the factors that shape their decision-making may help providers to better support patient understanding, improve patient-provider communication, and support shared decision-making

Singular matroid realization spaces

We study smoothness of realization spaces of matroids for small rank and ground set. For $\mathbb{C}$-realizable matroids, when the rank is $3$, we prove that the realization spaces are all smooth when the ground set has $11$ or fewer elements, and there are singular realization spaces for $12$ and greater elements. For rank $4$ and $9$ or fewer elements, we prove that these realization spaces are smooth. As an application, we prove that $\text{Gr}^{\circ}(3,n;\mathbb{C})$ -- the locus of the Grassmannian where all Pl\"ucker coordinates are nonzero -- is not sch\"on for $n\geq 12$

Investigation of Outlife Time on the Environmental Durability of P2-Etched, Adhesively-Bonded Aluminum Alloys Using the ASTM Wedge Test

P2 etchant is an environmentally-friendly aluminum etchant which has the potential to replace the Forest Products Laboratory (FPL) etchant as the industry standard. Environmental durability of adhesively-bonded aluminum surfaces etched using a paste version of the P2 etchant were tested using the Boeing-developed wedge test (ASTM D3762 - 03(2010)). This project specifically aimed to examine the relationship between outlife time (the time between etching and adhering) and the ability of bonded aluminum samples to pass the wedge test. Two aluminum alloys, 2024-T3 and 7075-T6, were wedge tested and the etched surfaces examined with an atomic force microscope (AFM) and a scanning electron microscope (SEM). The etchant improved durability of the bonded specimens and helped produce passing 2024 specimens for times ranging up to one week. Results of the 2024 testing demonstrated slightly decreased bond durability on average with increased outlife times, while the results of the 7075 testing were less conclusive and require more investigation to make meaningful conclusions. With more 2024 testing, the data could ideally be used to find a consistent critical outlife time near where bond durability decreases below the minimally-acceptable value. The results of this study may help Raytheon Company to improve their manufacturing procedures by defining a broader range of acceptable outlife times