Investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by STACK

Students are increasingly being expected to use Computer Aided Assessment (CAA) systems as support for traditional courses. Assessing a full mathematical proof in an educational context and providing feedback and other outcomes to students is currently well beyond the capabilities of CAA systems. One possible approach to assessing students' answers has been to break up larger tasks into smaller individual steps to which automatic assessment can then be applied. However, the method of marking depends on the format of a mathematical response. This thesis aims to investigate the effectiveness of different formats in computer aided assessment of mathematics. A format effect occurs when the format of an exercise affects the rate of successful outcomes of the exercise. Having established the need to study the format effect when writing mathematical arguments particularly online, I consider three formats for writing open-ended questions: two-column, typing, and Separated Concerns. The first of three studies explored the impact of the two-column format in writing simple mathematical arguments. In conducting this research, I developed a coding scheme to describe and analyse the structure of individual mathematical arguments. The second study focused on the difference and the format effects between uploading handwritten and typing in writing mathematical responses. Another outcome of this study is to provide a further application of using the coding scheme on analysing students’ arguments. The third study focused on updating STACK potential response tree based on Separated Concerns. STACK is a System for Teaching and Assessment using a Computer algebra Kernel, is an open source computer aided assessment system for mathematics, and other STEM subjects. Separated Concerns is a phrase used to describe materials in which potential misconceptions are addressed directly. In this study, I focused exclusively on students’ responses, and misconceptions in learning proof by induction using STACK. Mathematical induction is used as a vehicle to illustrate the idea of Separated Concerns. The main goal of the third study is to understand how engagement with learning materials packaged into online quizzes to replace live lectures, a ``lecture quiz'', related to success on the weekly assessed quiz, and the course total. A second goal of the third study is to explore the common mistakes made by students when using online materials to prepare for mathematical induction. This study also illustrates how to use research to update the algorithms which assess students' answers, known as ``STACK potential response trees'', in questions written to support learning mathematical induction based on Separated Concerns

Survival implications vs. complications: unraveling the impact of vitamin D adjunctive use in critically ill patients with COVID-19—A multicenter cohort study

BackgroundDespite insufficient evidence, vitamin D has been used as adjunctive therapy in critically ill patients with COVID-19. This study evaluates the effectiveness and safety of vitamin D as an adjunctive therapy in critically ill COVID-19 patients.MethodsA multicenter retrospective cohort study that included all adult COVID-19 patients admitted to the intensive care units (ICUs) between March 2020 and July 2021. Patients were categorized into two groups based on their vitamin D use throughout their ICU stay (control vs. vitamin D). The primary endpoint was in-hospital mortality. Secondary outcomes were the length of stay (LOS), mechanical ventilation (MV) duration, and ICU-acquired complications. Propensity score (PS) matching (1:1) was used based on the predefined criteria. Multivariable logistic, Cox proportional hazards, and negative binomial regression analyses were employed as appropriate.ResultsA total of 1,435 patients were included in the study. Vitamin D was initiated in 177 patients (12.3%), whereas 1,258 patients did not receive it. A total of 288 patients were matched (1:1) using PS. The in-hospital mortality showed no difference between patients who received vitamin D and the control group (HR 1.22, 95% CI 0.87–1.71; p = 0.26). However, MV duration and ICU LOS were longer in the vitamin D group (beta coefficient 0.24 (95% CI 0.00–0.47), p = 0.05 and beta coefficient 0.16 (95% CI −0.01 to 0.33), p = 0.07, respectively). As an exploratory outcome, patients who received vitamin D were more likely to develop major bleeding than those who did not [OR 3.48 (95% CI 1.10, 10.94), p = 0.03].ConclusionThe use of vitamin D as adjunctive therapy in COVID-19 critically ill patients was not associated with survival benefits but was linked with longer MV duration, ICU LOS, and higher odds of major bleeding

Measuring and Improving the Reliability of Probabilistic Assessments in Petroleum Engineering

Petroleum industry performance has been consistently below expectations. This underperformance has been attributed in part to the existence of cognitive biases in project evaluation, resulting in poor project valuation and selection. It was demonstrated in the literature that chronic overconfidence and optimism (estimated distributions of project value too narrow and shifted positively), both common in industry, produce substantial disappointment (realized portfolio values less than estimated). In this work, I aim to evaluate the impact of overconfidence as well as underconfidence (estimated distributions too wide) on portfolio performance, to determine if it is more beneficial to reduce biases and improve calibration or to reduce uncertainty, to provide a simple way of measuring biases from historical assessments, to determine the relationship between the number of probabilistic assessments and the accuracy of these measurements, and to determine guidelines for minimizing biases in new assessments using external adjustment. I simulated the performance of projects selected in a typical portfolio of O&G projects to determine the effects of biases on portfolio performance and to compare reducing biases against reducing uncertainty. Next, I generated calibration curves for historical probabilistic assessments and used these curves to calculate different reliability measures. Then I generated different numbers of biased assessments and used them to determine the relationship between the number of assessments and the accuracy of the bias measurements. Furthermore, I used the calibration curve to adjust new forecasts and measured the reliability of the new forecasts after adjustment as a function of the number of historical assessments and other parameters. This research demonstrates that underconfidence is just as detrimental to portfolio performance as overconfidence. Decision error will be minimized and portfolio value will be maximized only when there is no bias in project estimation. Furthermore, I found that reducing biases consistently generates more value than reducing uncertainty. Moreover, this research shows that using more historical assessments to measure biases typically improves the accuracy of the bias measurements. However, even a low number of assessments is enough to detect moderate and extreme biases. Finally, this research shows that production forecasts that were updated frequently over time using newly available data and externally adjusted using the most recent bias measurements were superior in terms of calibration to forecasts that were not updated or externally adjusted. The methods presented in this work can be used to measure and improve the reliability of probabilistic assessments in many petroleum engineering applications. Implementing these methods will result, over the long run, in the best calibrated assessments. Well-calibrated assessments result in better identification of superior projects and inferior projects, and ultimately, better investment decision making and increased profitability

Early hemi-diaphragmatic plication following intraoperative phrenic nerve transection during complete AV canal repair

Unilateral diaphragmatic palsy reduces pulmonary function by about 25% in older children and usually it is well tolerated; however, it causes severe respiratory distress in infants and young children. Diaphragmatic plication performed later than 10 days after cardiac surgery for patients under 1 year of age was associated with higher incidence of pneumonia and mortality. The management of the diaphragmatic paralysis due to phrenic nerve injury aiming mainly to preserve the respiratory function. Until now, the optimal management of diaphragmatic palsy in children who have undergone cardiac surgery remains controversial and consists of prolonged ventilation or diaphragmatic plication. In our case, many factors supported early diaphragmatic plication, the age of the patient, post-operative AV canal repair with severe pulmonary hypertension, and clear transection of the left phrenic nerve diagnosed intraoperatively

UFODMV: Unsupervised Feature Selection for Online Dynamic Multi-Views

In most machine learning (ML) applications, data that arrive from heterogeneous views (i.e., multiple heterogeneous sources of data) are more likely to provide complementary information than does a single view. Hence, these are known as multi-view data. In real-world applications, such as web clustering, data arrive from diverse groups (i.e., sets of features) and therefore have heterogeneous properties. Each feature group is referred to as a particular view. Although multi-view learning provides complementary information for machine learning algorithms, it results in high dimensionality. However, to reduce the dimensionality, feature selection is an efficient method that can be used to select only the representative features of the views so to reduce the dimensionality. In this paper, an unsupervised feature selection for online dynamic multi-views (UFODMV) is developed, which is a novel and efficient mechanism for the dynamic selection of features from multi-views in an unsupervised stream. UFODMV consists of a clustering-based feature selection mechanism enabling the dynamic selection of representative features and a merging process whereby both features and views are received incrementally in a streamed fashion over time. The experimental evaluation demonstrates that the UFODMV model has the best classification accuracy with values of 20% and 50% compared with well-known single-view and multi-view unsupervised feature selection methods, namely OMVFS, USSSF, and SPEC

Prevalence and risk factors of dry eye disease among adults in Saudi Arabia

Background: Environmental and epidemiological factors increase the risk of dry eye in Saudi Arabia, but most studies have limited generalizability. Objective: To determine the prevalence of dry eye disease (DED) among adults across Saudi Arabia and the associated risk factors. The secondary objective was to estimate the economic burden of DED by calculating lubricant usage and its annual costs. Methods: This cross-sectional study invited adults from across Saudi Arabia to complete a questionnaire that collected data regarding demographics, symptoms related to DED, previous diagnosis of DED, use of contact lenses, and use of eye lubricants. Results: A total of 2042 responses were received, of which 784 (38.4%) respondents had previously been diagnosed with DED and 752 (36.8%) were symptomatic but undiagnosed. Between the DED diagnosed and symptomatic-undiagnosed groups, a significant difference was found in terms of age (P < 0.001), gender (P = 0.002), presence of diabetes mellitus (P = 0.004), smoking status (P = 0.007), duration of electronic screen use (P = 0.05), number of ocular complaints (P < 0.001), and frequency of lubricants use (P < 0.001). Between the DED-diagnosed and non-DED groups, significant differences were found in terms of age (P < 0.001), gender (P < 0.001), presence of diabetes mellitus (P = 0.001), allergy (P = 0.001), autoimmune disease (P = 0.005), smoking status (P < 0.001), and history of refractive surgery (P < 0.001). The mean estimated annual cost of using lubricating agents was SAR 328.2 ± 210.3 (USD 87.5 ± 56.1), and this was significantly higher in the diagnosed group (P = 0.01) than the symptomatic-undiagnosed group. Conclusions: The prevalence of DED is high among adults in Saudi Arabia. High-risk population include elderly, female, and using electronic screens for >2 hours/day