The global impact of COVID-19 has been significant and several vaccines have been developed to combat this virus. However, these vaccines have varying levels of efficacy and effectiveness in preventing illness and providing immunity. As the world continues to grapple with the ongoing pandemic, the development and distribution of effective vaccines remains a top priority, making monitoring prevention strategies mandatory and necessary to mitigate the spread of the disease. These vaccines have raised a huge debate on social networks and in the media about their effectiveness and secondary effects. This has generated big data, requiring intelligent tools capable of analyzing these data in depth and extracting the underlying knowledge and feelings. There is a scarcity of works that analyze feelings and the prediction of these feelings based on their estimated polarities at the same time. In this work, first, we use big data and Natural Language Processing (NLP) tools to extract the entities expressed in tweets about AstraZeneca and Pfizer and estimate their polarities; second, we use a Long Short-Term Memory (LSTM) neural network to predict the polarities of these two vaccines in the future. To ensure parallel data treatment for large-scale processing via clustered systems, we use the Apache Spark Framework (ASF) which enables the treatment of massive amounts of data in a distributed way. Results showed that the Pfizer vaccine is more popular and trustworthy than AstraZeneca. Additionally, according to the predictions generated by Long Short-Term Memory (LSTM) model, it is likely that Pfizer will continue to maintain its strong market position in the foreseeable future. These predictive analytics, which uses advanced machine learning techniques, have proven to be accurate in forecasting trends and identifying patterns in data. As such, we have confidence in the LSTM's prediction of Pfizer's ongoing dominance in the industry.

The subject matter of the article is to identify and equalize the parameters of telecommunication channels. The goal is to develop a new mathematical approach based on positive definite kernels on a Hilbert space. The tasks to be solved are: (a) to formulate a mathematical procedure based on a kernel; a kernel is a function that maps pairs of data points to a scalar value, and positive definite kernels are widely used in machine learning and signal processing applications; (b) to identify the channel parameters using the proposed method; and (c) to apply the Zero Forcing and MMSE equalizer to measure the performance of the proposed system. This article introduces a new method to address the problem of supervised identification of transmission channel parameters based on the positive definite kernel on Hilbert space, which implements Gaussian kernels. The input sequence, used as an input for a system or process, is assumed to be independent, have a zero mean, a non-Gaussian distribution, and be identically distributed. These assumptions are made to simplify the analysis and modeling. The proposed method for estimating the parameters of the channel impulse response yields promising results, indicating that the estimated parameters are close to the measured parameters of the model for various channels. The convergence of the estimated parameters toward the measured parameters of the model is particularly noticeable for BRAN A (indoor) and BRAN E (outdoor) channels. The method has been tested with different channel models, and the results remain consistent. Overall, the proposed method appears to be a reliable and effective approach for estimating channel impulse response parameters. The accuracy of the estimated parameters is particularly noteworthy considering the challenges inherent in modeling wireless channels, which can be influenced by various factors such as obstacles and interference. These findings have important implications for the design and optimization of wireless communication systems. Accurate estimates of channel impulse response parameters are essential for predicting and mitigating the effects of channel distortion and interference, and the proposed method represents a promising tool for achieving this goal. Further research and testing are needed to validate and refine the method and to explore its potential applications in different settings and scenarios. We evaluated the performance of the system using the estimated parameters obtained from the proposed method. Two equalizers, MMSE and ZF, were used, and the results show that MMSE outperforms ZF. Both equalizers produced highly satisfactory outcomes.