OCCURRENCE OF LOWER EXTREMITY MUSCULOSKELETAL INJURIES DURING THE LOCKDOWN IN ATHLETES

Background of the Study: Lockdown was implemented worldwide to limit the spread of COVID-19. This sudden implementation of lockdown causes significant lifestyle changes for every individual. Along with the general population, it also has psychological, behavioral, and physical consequences on athletes. The study objective is to determine the occurrence of lower extremity musculoskeletal injuries during the COVID-19 lockdown in athletes. Methodology: Retrospective cross-sectional study design was used, and participants were recruited by a non-probability convenient sampling technique. A sample size of 147 was taken as calculated by the Raosoft software, and the study was completed 6 months. Both male and female athletes between the age group of 18-35 years, participants who did not participate in any official training session during the lockdown and registered at domestic level for at least 2 years were recruited from Pakistan Sports Board and Wapda Sports Complex Lahore. Data was collected using a semi-structured questionnaire. Nordic Musculoskeletal Questionnaire was used to identify the problematic painful areas of body. Data entry, analysis, and interpretation were done by using SPSS software version 22.0. Results: The mean age and BMI of participants were 25.6531±4.49 (years) and 23.28±3.24 (kg/m2) respectively. From the total, 39.5% of participants reported lower extremity musculoskeletal injuries. And most reported problematic areas include lower back and knee. 75% of participants continue to do workouts at home as a prevention strategy against injury occurrence. Conclusion: This concluded that the occurrence of lower extremity musculoskeletal injuries during the lockdown was moderate.

Formalization of Transform Methods Using Higher-Order-Logic Theorem Proving

Transform methods, such as the Laplace and the Fourier transforms, are widely used for analyzing the differential equations modeling the continuous dynamics of the engineering and physical systems. Traditionally, the transform methods based analysis is performed using paper-and-pencil proof and computer-based simulation techniques, such as sym bolic and numerical methods. However, due to their inherent limitations, such as the human-error proneness of paper-and-pencil proof methods and the presence of unverified symbolic algorithms, discretization and numerical errors in the simulations methods, these techniques cannot provide accurate results. The incomplete and inaccurate analysis poses a serious threat to the safety-critical domain, such as medicine and transportation, of engineering systems. To overcome these limitations, we propose to use higher-order-logic theorem proving to reason about the continuous dynamics of the engineering and physical systems using transform methods. The main advantages of this approach are the high expressiveness of the higher-order logic and the soundness of theorem provers, which provide absolute accu racy of the analysis. In particular, this thesis presents a higher-order-logic formalization of the Laplace and the Fourier transforms, which includes their formal definitions and the formal verification of their classical properties. The considered properties include integra bility, linearity, time shifting, frequency shifting, modulation, time scaling, time reversal, integration in time domain, differentiation in time domain, the Laplace and the Fourier transforms of a n-order differential equation and uniqueness. The formal reasoning about these properties involves multivariable calculus theories, i.e., the differential, integration, transcendental, topological, complex numbers, Lp spaces and vectors theories. Based on the availability of these theories in the HOL Light theorem prover, we chose it for our work. This thesis also provides the formal verification of a relationship between various transfor methods, i.e., the relationship between the Laplace and the Fourier transforms, and the relationship between the Fourier transform and the Fourier Cosine and Sine transforms. The proposed formalization plays a vital role in formally verifying the solutions of differential equations in both the time and the frequency domain and thus facilitates formal dynamical analysis of these systems. To illustrate the practical utilization and effectiveness, we use our proposed formalization for formally analyzing a 4-π soft error crosstalk model for Integrated Circuits (ICs), an audio equalizer, an Unmanned Free swimming Submersible (UFSS) vehicle and a platoon of automated vehicles using HOL Light.