Computational analysis of the SARS-CoV-2 and other viruses based on the Kolmogorov's complexity and Shannon's information theories

Chaos theory in the understanding of COVID-19 pandemic dynamics

The chaos theory, a field of study in mathematics and physics, offers a unique lens through which to understand the dynamics of the COVID-19 pandemic. This theory, which deals with complex systems whose behavior is highly sensitive to initial conditions, can provide insights into the unpredictable and seemingly random nature of the pandemic's spread. In this review, we will discuss some literature data with the aim of showing how chaos theory could provide valuable perspectives in understanding the complex and dynamic nature of the COVID-19 pandemic. In particular, we will emphasize how the chaos theory can help in dissecting the unpredictable, non- linear progression of the disease, the importance of initial conditions, and the complex interactions between various factors influencing its spread. These insights are crucial for developing effective strategies to manage and mitigate the impact of the pandemic.

Zgli: A Pipeline for Clustering by Compression with Application to Patient Stratification in Spondyloarthritis

The normalized compression distance (NCD) is a similarity measure between a pair of finite objects based on compression. Clustering methods usually use distances (e.g., Euclidean distance, Manhattan distance) to measure the similarity between objects. The NCD is yet another distance with particular characteristics that can be used to build the starting distance matrix for methods such as hierarchical clustering or K-medoids. In this work, we propose Zgli, a novel Python module that enables the user to compute the NCD between files inside a given folder. Inspired by the CompLearn Linux command line tool, this module iterates on it by providing new text file compressors, a new compression-by-column option for tabular data, such as CSV files, and an encoder for small files made up of categorical data. Our results demonstrate that compression by column can yield better results than previous methods in the literature when clustering tabular data. Additionally, the categorical encoder shows that it can augment categorical data, allowing the use of the NCD for new data types. One of the advantages is that using this new feature does not require knowledge or context of the data. Furthermore, the fact that the new proposed module is written in Python, one of the most popular programming languages for machine learning, potentiates its use by developers to tackle problems with a new approach based on compression. This pipeline was tested in clinical data and proved a promising computational strategy by providing patient stratification via clusters aiding in precision medicine.

Complexity of COVID-19 Dynamics

With population explosion and globalization, the spread of infectious diseases has been a major concern. In 2019, a newly identified type of Coronavirus caused an outbreak of respiratory illness, popularly known as COVID-19, and became a pandemic. Although enormous efforts have been made to understand the spread of COVID-19, our knowledge of the COVID-19 dynamics still remains limited. The present study employs the concepts of chaos theory to examine the temporal dynamic complexity of COVID-19 around the world. The false nearest neighbor (FNN) method is applied to determine the dimensionality and, hence, the complexity of the COVID-19 dynamics. The methodology involves: (1) reconstruction of a single-variable COVID-19 time series in a multi-dimensional phase space to represent the underlying dynamics; and (2) identification of “false” neighbors in the reconstructed phase space and estimation of the dimension of the COVID-19 series. For implementation, COVID-19 data from 40 countries/regions around the world are studied. Two types of COVID-19 data are analyzed: (1) daily COVID-19 cases; and (2) daily COVID-19 deaths. The results for the 40 countries/regions indicate that: (1) the dynamics of COVID-19 cases exhibit low- to medium-level complexity, with dimensionality in the range 3 to 7; and (2) the dynamics of COVID-19 deaths exhibit complexity anywhere from low to high, with dimensionality ranging from 3 to 13. The results also suggest that the complexity of the dynamics of COVID-19 deaths is greater than or at least equal to that of the dynamics of COVID-19 cases for most (three-fourths) of the countries/regions. These results have important implications for modeling and predicting the spread of COVID-19 (and other infectious diseases), especially in the identification of the appropriate complexity of models.

Advances in the computational analysis of SARS-COV2 genome

Given a data-set of Ribonucleic acid (RNA) sequences we can infer the phylogenetics of the samples and tackle the information for scientific purposes. Based on current data and knowledge, the SARS-CoV-2 seemingly mutates much more slowly than the influenza virus that causes seasonal flu. However, very recent evolution poses some doubts about such conjecture and shadows the out-coming light of people vaccination. This paper adopts mathematical and computational tools for handling the challenge of analyzing the data-set of different clades of the severe acute respiratory syndrome virus-2 (SARS-CoV-2). On one hand, based on the mathematical paraphernalia of tools, the concept of distance associated with the Kolmogorov complexity and Shannon information theories, as well as with the Hamming scheme, are considered. On the other, advanced data processing computational techniques, such as, data compression, clustering and visualization, are borrowed for tackling the problem. The results of the synergistic approach reveal the complex time dynamics of the evolutionary process and may help to clarify future directions of the SARS-CoV-2 evolution.

Experimental Models of SARS-CoV-2 Infection: Possible Platforms to Study COVID-19 Pathogenesis and Potential Treatments

In December 2019, a novel coronavirus crossed species barriers to infect humans and was effectively transmitted from person to person, leading including vaccines and antiviral drugs that could prevent or limit the burden or transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a global health priority. It is thus of utmost importance to assess possible therapeutic strategies against SARS-CoV-2 using experimental models that recapitulate aspects of the human disease. Here, we review available models currently being developed and used to study SARS-CoV-2 infection and highlight their application to screen potential therapeutic approaches, including repurposed antiviral drugs and vaccines. Each identified model provides a valuable insight into SARS-CoV-2 cellular tropism, replication kinetics, and cell damage that could ultimately enhance understanding of SARS-CoV-2 pathogenesis and protective immunity. Expected final online publication date for the Annual Review of Pharmacology and Toxicology, Volume 62 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Clustering Perspective of the Collatz Conjecture

This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results.

New applications related to Covid-19

Analysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.