Detection of various lung diseases including COVID-19 using extreme learning machine algorithm based on the features extracted from a lightweight CNN architecture.

Around the world, several lung diseases such as pneumonia, cardiomegaly, and tuberculosis (TB) contribute to severe illness, hospitalization or even death, particularly for elderly and medically vulnerable patients. In the last few decades, several new types of lung-related diseases have taken the lives of millions of people, and COVID-19 has taken almost 6.27 million lives. To fight against lung diseases, timely and correct diagnosis with appropriate treatment is crucial in the current COVID-19 pandemic. In this study, an intelligent recognition system for seven lung diseases has been proposed based on machine learning (ML) techniques to aid the medical experts. Chest X-ray (CXR) images of lung diseases were collected from several publicly available databases. A lightweight convolutional neural network (CNN) has been used to extract characteristic features from the raw pixel values of the CXR images. The best feature subset has been identified using the Pearson Correlation Coefficient (PCC). Finally, the extreme learning machine (ELM) has been used to perform the classification task to assist faster learning and reduced computational complexity. The proposed CNN-PCC-ELM model achieved an accuracy of 96.22% with an Area Under Curve (AUC) of 99.48% for eight class classification. The outcomes from the proposed model demonstrated better performance than the existing state-of-the-art (SOTA) models in the case of COVID-19, pneumonia, and tuberculosis detection in both binary and multiclass classifications. For eight class classification, the proposed model achieved precision, recall and fi-score and ROC are 100%, 99%, 100% and 99.99% respectively for COVID-19 detection demonstrating its robustness. Therefore, the proposed model has overshadowed the existing pioneering models to accurately differentiate COVID-19 from the other lung diseases that can assist the medical physicians in treating the patient effectively.

Generating binomial coefficients in a row of Pascal's triangle from extensions of powers of eleven.

Sir Isaac Newton noticed that the values of the first five rows of Pascal's triangle are each formed by a power of 11, and claimed that subsequent rows can also be generated by a power of 11. Literally, the claim is not true for the 5 t h row and onward. His genius mind might have suggested a deep relation between binomial coefficients and a power of some integer that resembles the number 11 in some form. In this study, we propose and prove a general formula to generate the values in any row of Pascal's triangle from the digits of ( 1 0 ⋯ 0 ︸ Θ zeros 1 ) n . It can be shown that the numbers in the cells in n t h row of Pascal's triangle may be achieved from Θ + 1 partitions of the digits of the number ( 1 0 ⋯ 0 ︸ Θ zeros 1 ) n , where Θ is a non-negative integer. That is, we may generate the number in the cells in a row of Pascal's triangle from a power of 11, 101, 1001, or 10001 and so on. We briefly discuss how to determine the number of zeros Θ in relation to n, and then empirically show that the partition really gives us binomial coefficients for several values of n. We provide a formula for Θ and prove that the ( n + 1 ) t h row of Pascal's triangle is simply Θ + 1 partitions of the digits of ( 1 0 ⋯ 0 ︸ Θ zeros 1 ) n from the right.