The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being carried out worldwide by scientists to understand the nature of this catastrophic virus and find a potential vaccine for it. The most possible efforts have been taken to present this paper as a form of contribution to the understanding of this lethal virus in the first and second wave. This paper presents a unique technique for the methodical comparison of disastrous virus dissemination in two waves amid five most infested countries and the death rate of the virus in order to attain a clear view on the behaviour of the spread of the disease. For this study, the data set of the number of deaths per day and the number of infected cases per day of the most affected countries, the USA, Brazil, Russia, India, and the UK, have been considered in the first and second waves. The correlation fractal dimension has been estimated for the prescribed data sets of COVID-19, and the rate of death has been compared based on the correlation fractal dimension estimate curve. The statistical tool, analysis of variance, has also been used to support the performance of the proposed method. Further, the prediction of the daily death rate has been demonstrated through the autoregressive moving average model. In addition, this study also emphasis a feasible reconstruction of the death rate based on the fractal interpolation function. Subsequently, the normal probability plot is portrayed for the original data and the predicted data, derived through the fractal interpolation function to estimate the accuracy of the prediction. Finally, this paper neatly summarized with the comparison and prediction of epidemic curve of the first and second waves of COVID-19 pandemic to visualize the transmission rate in the both times.

No abstract

No abstract

No abstract

The shortest path algorithm is one of the best choices for implementation of data structures. The shortest path (SP) problem involves the problem of finding a suitable path between “two vertices or nodes in a graph” in such a way that the sum of the weights of its component edges is minimal. There are many theories for solving this problem one of the widely used way solution for solving this problem is Dijkstra’s algorithm (DA) which is also widely used in many engineering calculation works also. There are two types of DA one is the basic one and other one is optimized. This paper is focused on the basics one which provides a shortest route between source node and the destination node. Main focus has been kept on keeping the work simple and easy to understand with some basic concepts .Storage space and operational efficiency improvement has been tried to improve.

Fractal theory is the propelled technique to analyze the non-linear signals with more complexity.  Quantification of chaotic nature and complexity of the multifaceted therapeutic signals requires the estimation of the spectrum of Generalized Fractal Dimensions (GFD) where the complexity means greater inconstancy in the general form of fractal dimension range.  This paper has proposed a fuzzy multifractal technique to analyze the age related classifications by using the Fuzzy Generalized Fractal Dimensions (F–GFD) with Gaussian fuzzy valued function through the cardiac inter-beat interval dynamics in electrocardiogram (ECG) signals.  It has been revealed that, the designed Fuzzy GFD method accurately categorizes the young and old age subjects by graphical comparison with the typical GFD method.  The classification rate of young and elderly subjects has also supported statistically by ANOVA test.   Hence the fuzzified multifractal analysis accomplishes significantly to discriminate age groups than the classical multifractal analysis in heartbeat rate time series from ECG signals and also the conventional GFD is a specific case of the proposed F–GFD.

In this paper, we define the dominant set, zero divisor of the rough semiring (T, ∆, ∇). Also We prove that RS(X) is not a zero divisor for a dominant set X ⊆ U where U is the finite universal set on the set of all rough sets for the given information system together with the operations praba ∆ and praba ∇. We illustrate these concepts through examples.

In this work, we study the power of Saak features as an effort towards interpretable deep learning. Being inspired by the operations of convolutional layers of convolutional neural networks, multi-stage Saak transform was proposed. Based on this foundation, we provide an in-depth examination on Saak features, which are coefficients of the Saak transform, by analyzing their properties through visualization and demonstrating their applications in image classification. Being similar to CNN features, Saak features at later stages have larger receptive fields, yet they are obtained in a one-pass feedforward manner without backpropagation. The whole feature extraction process is transparent and is of extremely low complexity. The discriminant power of Saak features is demonstrated, and their classification performance in three well-known datasets (namely, MNIST, CIFAR-10 and STL-10) is shown by experimental results.