Correction to: A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally.

[This corrects the article DOI: 10.1007/s12652-022-03772-6.].

A study of plithogenic graphs: applications in spreading coronavirus disease (COVID-19) globally.

During the last two decades, the world has experienced three major outbreaks of Coronaviruses, namely severe acute respiratory syndrome (SARS- CoV), middle east respiratory syndrome (MERS-CoV), and the current ongoing pandemic of severe acute respiratory syndrome 2 (SARS-CoV-2). The SARS-CoV-2 caused the disease known as Coronavirus Disease 2019 (COVID-19). Since its discovery for the first time in Wuhan, China, in December 2019, the disease has spread very fast, and cases have been reported in more than 200 countries/territories. In this study, the idea of Smarandache's pathogenic set is used to discuss the novel COVID-19 spread. We first introduced plithogenic graphs and their subclass, like plithogenic fuzzy graphs. We also established certain binary operations like union, join, Cartesian product, and composition of pathogenic fuzzy graphs, which are helpful when we discuss combining two different graphs. In the end, we investigate the spreading trend of COVID-19 by applying the pathogenic fuzzy graphs. We observe that COVID-19 is much dangerous than (MERS-CoV) and (SARS-CoV). Moreover, as the SARS-CoV and MERS-CoV outbreaks were controlled, there are greater chances to overcome the current pandemic of COVID-19 too. Our model suggests that all the countries should stop all types of traveling/movement across the borders and internally too to control the spread of COVID-19. The proposed model also predicts that in case precautionary measures have not been taken then there is a chance of severe outbreak in future.

Optical Coherence Tomography-guided Intervention in STEMI Patients with Normal Looking Coronaries.

Optical coherence tomography (OCT) is an increasingly available intracoronary imaging modality that provides highresolution imaging of coronary arteries and guides operators in percutaneous coronary intervention (PCI) by accurately defining luminal geometry and detailed plaque composition. The two cases under discussion in this report, presented with acute ST elevation myocardial infarction (STEMI) with angiography showing minor narrowing (<30%) with TIMI III flow in which OCT-guided approach was used regarding the management owing to its improved temporal and axial resolution, thus providing proper plaque assessment and subsequent proper management.

Effects of Lower Limb Cycle Training on Echocardiographic Parameters of Left Ventricle in Dilated Cardiomyopathy Patients.

OBJECTIVE: To determine the effect of lower limb ergometric training on echocardiographic parameters of left ventricle in dilated cardiomyopathy (DMC) patients. STUDY DESIGN: Randomized control trial. PLACE AND DURATION OF STUDY: Rawalpindi Institute of Cardiology, Rawalpindi, Pakistan, from September 2016 to February 2017. METHODOLOGY: Clinically stable patients with DCM (n=60), were randomly allocated into an interventional group with two-month interventional program and a non-trained control group (n=30 each). Treatment protocol for interventional group was lower limb ergometer exercise for 8 weeks, 4 days/week. Pre and post-treatment echocardiography was done in both groups at baseline and after 8 weeks. SPSS 21 was used for data analysis. RESULTS: The median (IQR) age of the patients was 51 (18) years in interventional group and 62 (11) years in control group. Male to female ratio was 18:9 in control group and 17:12 in Interventional group. Statistically significant results were detected within the groups regarding ejection fraction (EF), left ventricular internal dimension systole (LVIDS) and left ventricular internal diastolic dimension (LVIDD) (p <0.001). CONCLUSION: Exercise training with lower limb ergometer was effective in improving the ejection fraction and left ventricular dimensions in patients with dilated cardiomyopathies.