Randomness for Nucleotide Sequences of SARS-CoV-2 and Its Related Subfamilies

Analysing deaths and confirmed cases of COVID-19 pandemic by analytical approaches

In this work, the time series of growth rates regarding confirmed cases and deaths of COVID-19 for several sampled countries are investigated via an introduction of an orthonormal basis. This basis, which is served as the feature benchmark, reveals the hidden features of COVID-19 via the magnitude of Fourier coefficients. These coefficients are ranked in the form of ranking vectors for all the sampled countries. Based on these and Manhattan metric, we then perform spectral clustering to categorise the countries. Unlike the classical cosine similarity analysis which, relatively speaking, is a composite index and hard to identify the features of the categorised countries, spectral analysis delves into the internal structures or dynamical trend of the time series. This research shows there is no single feature that dominates the trend of the growth rates. It also reveals that results from the spectral analysis are different from the ones of cosine similarity. In the end, some approximated values of the confirmed cases and deaths are also calculated by the spectral analysis.

The Similarities and Distances of Growth Rates Related to COVID-19 Between Different Countries Based on Spectral Analysis

The COVID-19 pandemic has taken more than 1.78 million of lives across the globe. Identifying the underlying evolutive patterns between different countries would help us single out the mutated paths and behavior of this virus. I devise an orthonormal basis which would serve as the features to relate the evolution of one country's cases and deaths to others another's via coefficients from the inner product. Then I rank the coefficients measured by the inner product via the featured frequencies. The distances between these ranked vectors are evaluated by Manhattan metric. Afterwards, I associate each country with its nearest neighbor which shares the evolutive pattern via the distance matrix. Our research shows such patterns is are not random at all, i.e., the underlying pattern could be contributed to by some factors. In the end, I perform the typical cosine similarity on the time-series data. The comparison shows our mechanism differs from the typical one, but is also related to each it in some way. These findings reveal the underlying interaction between countries with respect to cases and deaths of COVID-19.

Extracted features of national and continental daily biweekly growth rates of confirmed COVID-19 cases and deaths via Fourier analysis

AIMS

By associating features with orthonormal bases, we analyse the values of the extracted features for the daily biweekly growth rates of COVID-19 confirmed cases and deaths on national and continental levels.

METHODS

By adopting the concept of Fourier coefficients, we analyse the inner products with respect to temporal and spatial frequencies on national and continental levels. The input data are the global time series data with 117 countries over 109 days on a national level; and 6 continents over 447 days on a continental level. Next, we calculate the Euclidean distance matrices and their average variabilities, which measure the average discrepancy between one feature vector and all others. Then we analyse the temporal and spatial variabilities on a national level. By calculating the temporal inner products on a continental level, we derive and analyse the similarities between the continents.

RESULTS

On the national level, the daily biweekly growth rates bear higher similarities in the time dimension than the ones in the space dimension. Furthermore, there exists a strong concurrency between the features for biweekly growth rates of cases and deaths. As far as the trends of the features are concerned, the features are stabler on the continental level, and less predictive on the national level. In addition, there are very high similarities between all the continents, except Asia.

CONCLUSIONS

The features for daily biweekly growth rates of cases and deaths are extracted via orthonormal frequencies. By tracking the inner products for the input data and the orthonormal features, we could decompose the evolutionary results of COVID-19 into some fundamental frequencies. Though the frequency-based techniques are applied, the interpretation of the features should resort to other methods. By analysing the spectrum of the frequencies, we reveal hidden patterns of the COVID-19 pandemic. This would provide some preliminary research merits for further insightful investigations. It could also be used to predict future trends of daily biweekly growth rates of COVID-19 cases and deaths.

Quantifying collective intelligence and behaviours of SARS-CoV-2 via environmental resources from virus' perspectives

Collective intelligence of viruses is witnessed in many research articles. Most of the researches focus on the qualitative properties or observations. In this research, we model the behaviours and collective intelligence of SARS-CoV-2 by minimal spanning trees (MSTs), which specify the underlying mechanisms of resource allocation in the viral colony. The vertices of the trees are 50 states, DC and NYC in the USA. The weights of the edges are assigned by the reciprocal of the sum of cases or deaths of COVID-19. The types of trees are decided by the chosen 18 factors. We sample 304 time-series data and compute their MST-based auto-correlations for stability analysis. Then we perform correlated analysis and comparative analysis on these stable factors. Our results show MST approach fits the collective intelligence modelling very well; the total cases and total deaths over areas are highly correlated in terms of MSTs; and these stable factors have little to do with the geographical distance. The results also indicate the colonisation of SARS-CoV-2 is pretty mature and organised. Based on the results, for environmental or health policies, we should also turn our attention to the transmission routes that are independent of or far away from human population or densities. The viruses' colonies might already exist in the wild in a large scale, not only in the populated or polluted cities. We shall build or conduct a monitoring system of their colonisation and survival techniques, in order to terminate, contain or live with their communities.

Track the dynamical features for mutant variants of COVID-19 in the UK

AIMS

The main purpose of this study is to explore whether the new variant SARS-CoV-2 VOC 202012/01 in the UK is equipped with some leading or underlying features.

METHODS

We apply a systematic and persuasive approach to reveal the underlying dynamical features of this variant. The approach utilises extracting the main features, which consist of 3-valued features, via the time-series data for new cases, 28-day deaths and 60-day deaths. The experimental samples chosen rely on the the rolling sets of regional data vectors whose dimensions are all 7 days. These data sets are projected onto the 3-valued features to yield the vector rejections. Then the minimal features are thus extracted by the minimal total norms. Then we map out the traces of the similarities between all the extracted time-varying features.

RESULTS

Our findings, no matter in preliminary or follow-up study, clearly show there is no consistent and substantial shift in the 3-valued features even after the occurrence of this new variant - this might validate the efficacy of the current vaccines against this variant.

CONCLUSIONS

Since the underlying features of the mutant is unchanged, and the leading feature of B1.1.7 is not yet present, it might help us make the lockdown decision "choose the lesser of the two evils: pandemic and economic woes", and validate vaccine developments or adopt preventive measures.