The Use Of STEM Approaches To Widen Formula Derivation Steps In Material Science And Engineering Programmes At Higher Education Institutions

Many complex formula derivation steps found within material science and engineering programmes are essential skill-developing activities that enhance students’ learning. However, most students lack the required mathematical knowledge to fully comprehend some of those derivation steps. This work developed a framework of clarifying some of the formula derivations steps by adding further mathematical steps that support the students’ constructive and cognitive learning. Some derivation steps were added to the derivations of the theoretical tensile strength model as well as the Maxwell’s and the Voigt-Kelvin models. The idea was not to disrupt students’ constructive or cognitive learning processes but to facilitate their learning since their ultimate aim is not to derive but to apply the steps of the modified derivations in solving other material science and engineering problems. The students benefited from the activities in two folds; firstly, they understood the reasons behind each derivation step and secondly, it improved their self-study activities by reducing their study periods. These activities provide a platform to widen STEM activities at higher education institutions. The ongoing work will look at other important formula derivation steps within material science and engineering that can enhance students’ learning.

Seven Criteria of Severe COVID-19 (SCSC): A New Pre-Hospital Prognostic Scoring Tool Suggested for Screening of Probable/Confirmed COVID-19 Patients with Severe Outcomes

Introduction: COVID-19 pandemic led to various consequences in medical care that had been long provided for the patients referred to the hospitals. Objective: We conducted this study to derive and validate a new scoring system that can accurately differentiate COVID-19 patients who may have a worse outcome from others at the prehospital stage. Methods: This study was performed on probable/confirmed COVID-19 patients, who were transferred to the hospitals by Tehran emergency medical services (EMS). Occurrence of one of the items including: in-hospital death, intensive care unit (ICU) admission, or hospitalization for more than 20 days was considered to indicate a “severe disease”. Univariate and multivariate logistic regression were used for assessment of the relationship between all independent variables and the outcome. In the validity assessment step, area under the receiver operating characteristic (ROC) curve was calculated for a data set independent from the data based on which the model was designed. The sensitivity and specificity were also presented based on the best suggested cutoff point. Results: In this study, the data of 557 cases were analyzed in the derivation step and 356 cases were assessed in the validation step. The univariate logistic regression showed that age, weakness and fatigue, disease history, systolic blood pressure, SpO2, respiratory rate, and Glasgow coma scale (GCS) were statistically significant in severe disease group. The area under the ROC curve (AUC-ROC) of the tool was 0.808 (95% CI: 0.779, 0.834). The best cut-off point for screening was the score of ≥4, in which the sensitivity and specificity of the tool for the best cut-off point were 71.87% and 78.06%, respectively. In the validation step, the AUCROC of the tool was 0.723. Conclusions: Seven criteria of severe COVID-19 (SCSC) tool could properly differentiate probable/confirmed COVID-19 patients with severe outcomes in the pre-hospital stage.

Finding Small Proofs for Description Logic Entailments: Theory and Practice

Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand a consequence even if the individual derivation steps are easy to comprehend. This motivates our interest in finding small proofs for Description Logic (DL) entailments. Instead of concentrating on a specific DL and proof calculus for this DL, we introduce a general framework in which proofs are represented as labeled, directed hypergraphs, where each hyperedge corresponds to a single sound derivation step. On the theoretical side, we investigate the complexity of deciding whether a certain consequence has a proof of size at most n along the following orthogonal dimensions: (i) the underlying proof system is polynomial or exponential; (ii) proofs may or may not reuse already derived consequences; and (iii) the number n is represented in unary or binary. We have determined the exact worst-case complexity of this decision problem for all but one of the possible combinations of these options. On the practical side, we have developed and implemented an approach for generating proofs for expressive DLs based on a non-standard reasoning task called forgetting. We have evaluated this approach on a set of realistic ontologies and compared the obtained proofs with proofs generated by the DL reasoner ELK, finding that forgetting-based proofs are often better w.r.t. different measures of proof complexity.

From natural semantics to C: A formal derivation of two STG machines

The Spineless Tag-less G-machine (STG machine) was defined as the target abstract machine for compiling the lazy functional language Haskell. It is at the heart of the Glasgow Haskell Compiler (GHC) which is claimed to be the Haskell compiler that generates the most efficient code. A high-level description of the STG machine can be found in Peyton Jones (In Journal of Functional programming, 2(2), 127–202, 1992), Marlow & Peyton Jones (In Sigplan Not., 39(9), 4–5, 2004), and Marlow & Peyton Jones (In Journal of Functional Programming, 16(4–5), 415–449, 2006). Should the reader be interested in a more detailed view, then the only additional information available is the Haskell code of GHC and the C code of its runtime system.It is hard to prove that this machine correctly implements the lazy semantics of Haskell. Part of the problem lies in the fact that the STG machine executes a bare-bones functional language, called STGL, much lower level than Haskell. Therefore, part of the correctness should be—and it is—established by showing that the translation from Haskell to STGL preserves Haskell's semantics.The other part involves showing that the STG machine correctly implements the lazy semantics of STGL. In this paper we provide a step-by-step formal derivation of the STG machine and of its compilation to C, starting from a natural semantics of STGL. Thus, our starting point is higher level than the descriptions found Peyton Jones (In Journal of Functional programming, 2(2), 127–202, 1992) and Marlow & Peyton Jones (In Sigplan Not., 39(9), 4–5, 2004), and our arrival point is lower level than those works. Additionally, there has been substantial changes between the so-called push/enter model of the STG machine described in Peyton Jones (In Journal of Functional programming, 2(2), 127–202, 1992), and the eval/apply model of the STG machine described in Marlow & Peyton Jones (In Sigplan Not., 39(9), 4–5, 2004). So, in fact, we derive two machines instead of one, starting from the same initial semantics.At each step we provide enough intuitions and explanations in order to understand the refinement, and then the formal definitions and statements proving that the derivation step is sound and complete. The main contribution of the paper is to show that an efficient machine such as the STG can be presented, understood, and formally reasoned about at different levels of abstraction.