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Several studies have been done to identify comorbidities of COVID-19. In this work, we developed an analytical bioinformatics framework to reveal COVID-19 comorbidities, their genomic associations, and molecular mechanisms accomplishing transcriptomic analyses of the RNA-seq datasets provided by the Gene Expression Omnibus (GEO) database, where normal and infected tissues were evaluated. Using the framework, we identified 27 COVID-19 correlated diseases out of 7,092 collected diseases. Analyzing clinical and epidemiological research, we noticed that our identified 27 diseases are associated with COVID-19, where hypertension, diabetes, obesity, and lung cancer are observed several times in COVID-19 patients. Therefore, we selected the above four diseases and performed assorted analyses to demonstrate the association between COVID-19 and hypertension, diabetes, obesity, and lung cancer as comorbidities. We investigated genomic associations with the cross-comparative analysis and Jaccard’s similarity index, identifying shared differentially expressed genes (DEGs) and linking DEGs of COVID-19 and the comorbidities, in which we identified hypertension as the most associated illness. We also revealed molecular mechanisms by identifying statistically significant ten pathways and ten ontologies. Moreover, to understand cellular physiology, we did protein-protein interaction (PPI) analyses among the comorbidities and COVID-19. We also used the degree centrality method and identified ten biomarker hub proteins (IL1B, CXCL8, FN1, MMP9, CXCL10, IL1A, IRF7, VWF, CXCL9, and ISG15) that associate COVID-19 with the comorbidities. Finally, we validated our findings by searching the published literature. Thus, our analytical approach elicited interconnections between COVID-19 and the aforementioned comorbidities in terms of remarkable DEGs, pathways, ontologies, PPI, and biomarker hub proteins.

The COVID-19 is one of the worst pandemics in modern history. We applied principal component analysis (PCA) to the daily time series of the COVID-19 death cases and confirmed cases for the top 25 countries from April of 2020 to February of 2021. We calculated the eigenvalues and eigenvectors of the cross-correlation matrix of the changes in daily accumulated data over monthly time windows. The largest eigenvalue describes the overall evolution dynamics of the COVID-19 and indicates that evolution was faster in April of 2020 than in any other period. By using the first two PC coefficients, we can identify the group dynamics of the COVID-19 evolution. We observed groups under critical states in the loading plot and found that American and European countries are represented by strong clusters in the loading plot. The first PC plays an important role and the correlations (C1) between the normalized logarithmic changes in deaths or confirmed cases and the first PCs may be used as indicators of different phases of the COVID-19. By varying C1 over time, we identified different phases of the COVID-19 in the analyzed countries over the target time period.

The global entropy and uniformity of three major commodities that exported most worldwide and all commodities combinedly were observed from 1995 to 2018. It is found that global entropy and uniformity of manufactured goods chiefly classified by material are higher than two other products machinery, transport equipment, and crude materials, inedible, except fuels, and it was fluctuating in two products. In 2018, they fall remarkably in manufactured goods and crude materials, inedible, except fuels. Further, local entropy and number of trade partners of two world’s most influencing countries China and USA were investigated and compared it with world’s average value of local entropy and trade partners. It is seen that local entropy and trade partners of two countries are much higher than world’s average value except some early cases of local entropy of China. It is also observed that when local entropy and number of partners both countries declined together, world’s average values fall significantly.

We analyze daily time series of stocks of S&P 500 to identify the financial states of US market from 1998 - 2012. The planar maximally filtered graph is constructed from correlation between companies. We measure the hierarchy of the financial graphs using hierarchical path. It is found that the networks are less hierarchical in the beginning of the crises and enhances with crises in the time period. Finally, graph alteration is measured by our propose method and also Jaccard index. We found that the big change of hierarchy altered the network structure. To observe the network variation, our approach gives better result than Jaccard index does.

We consider the cross-correlation coefficients of the daily returns in the local and global stock markets. We generate the minimal spanning tree (MST) using the correlation matrix. We observe that the MSTs change their structure from chain-like networks to star-like networks during periods of market uncertainty. We quantify the measure of the hierarchical network utilizing the value of the hierarchy measured by the hierarchical path. The hierarchy and betweenness centrality characterize the state of the market regarding the impact of crises. During crises, the non-financial company is established as the central node of the MST. However, before the crisis and during stable periods, the financial company is occupying the central node of the MST in the Korean and the U.S. stock markets. The changes in the network structure and the central node are good indicators of an upcoming crisis.

This study investigates financial states and group dynamics by applying principal component analysis to the cross-correlation coefficients of the daily returns of commodity futures. The eigenvalues of the cross-correlation matrix in the 6-month timeframe displays similar values during 2010–2011, but decline following 2012. A sharp drop in eigenvalue implies the significant change of the market state. Three commodity sectors, energy, metals and agriculture, are projected into two dimensional spaces consisting of two principal components (PC). We observe that they form three distinct clusters in relation to various sectors. However, commodities with distinct features have intermingled with one another and scattered during severe crises, such as the European sovereign debt crises. We observe the notable change of the position of two dimensional spaces of groups during financial crises. By considering the first principal component (PC1) within the 6-month moving timeframe, we observe that commodities of the same group change states in a similar pattern, and the change of states of one group can be used as a warning for other group.

We consider the effects of the 2008 global financial crisis on the global stock market before, during, and after the crisis. We generate complex networks from a cross-correlation matrix such as the threshold network (TN) and the minimal spanning tree (MST). In the threshold network, we assign a threshold value by using the mean and standard deviation of cross-correlation coefficients. When the threshold is equal to the mean of these coefficients, we observe a giant cluster composed of three economic zones in all three periods. We find that during the crisis, the countries in the Asian zone were weakly connected and those in the American zone were tightly linked to the countries in the European zone. At a large threshold, the three economic zones were fragmented. The European countries connected tightly, but the Asian countries bound weakly. The MST constructed from the distance matrix. In the MST, France remained a hub node in all three periods. The size of the MST shrank slightly during the crisis. We observe a scaling relation between the network distance of nodes from the central hub (France) and the geometrical distance. We observe the topological change of the financial network structure during the global financial crisis. The TN and MST are complementary roles to understand the connecting structure of financial complex networks. The TN reveals to observe the clustering effects and robustness of the cluster during the financial crisis. The MST shows the central hub and connecting node among the economic zones., 18pages, 5figures

The core focus of the study is to investigate the impact of European crises on commodity and world stock market indices. To investigate the impact during and after crisis, the technique of threshold has been applied to make a complex network from the cross-correlations of the returns of 46 daily time series comprising of 23 global stock market indices and 23 commodity futures from 2010 to 2014. The networks are fragmented with the increase of threshold and the study detects a sturdy association between commodities and stock indices at high threshold during severe crisis of 2011. The dynamic of inter-links between two groups at threshold 0.1 show dissimilar behavior with the dynamic of inter-degrees of individual group of commodities with stock indices. The change of intra-degrees among individual groups of stock and commodities demonstrates that the effect of Cypriot crisis in first half of 2013 on financial indices is more shocking than those of commodity futures. The dynamic of clustering coefficient identifies that Asian financial indices and index of agricultural sector under commodity market are more responsive during as well as after crises. Finally, we propose a definition to measure the states of the network artifact. Identifying the dynamic movement of market state and network structure can be useful as an early warning of upcoming crisis and portfolio investment.

The core focus of the study is to examine financial states using index effect on stock to stock correlations of developed, developing and emerging market. The three markets such as S&P 500, KOSPI 200 and DSE are declared as developed, developing and emerging market respectively. To study the similarity between stock price changes, we calculate the time series of the daily log return. Closing stock prices of the targeted markets have been used to measure the daily return of the stocks. To analyze the market mobility, Pearson correlation coefficient, partial correlation, and index effect on stock to stock correlation techniques have been applied. The study found that the companies of developed and emerging market are more strongly correlated than those of developing market during big crash. On the other hand, developing market shows less index effect on stock correlations during crisis. Moreover, insignificant index effect has been found in emerging market during calm state. No significant effect of DSE index on stock to stock correlations in the period of global financial crisis has been observed, implying that global financial crisis did not hit to the DSE in this period. Before the market crash, the interactions between stocks became low enough which corresponds to lower value of average correlation for all types of market. Finally, the change of correlation and partial correlation can be a good indicator to identify and predict the financial states of all the markets which will further helps the stakeholders to make proper economic decisions.

We analyze the structural change of the trade flow network for different commodities from 1995 to 2013. We investigate the hierarchical organization of Minimum Spanning Tree (MST) using the hierarchical path. The hierarchy for all products has been increased significantly with the evolution of time in last decade except the period of financial crises. We observe the remarkable increase of the hierarchy for the products of manufactured goods classified by materials, machinery and transport equipment, and crude oil from different periods. The man-made products such as machinery and transport equipment and manufactured goods are more hierarchical than the natural products such as mineral fuels. We observe that the role of China on some commodities in world trade is growing and predicts that China will be next giant hub on world trade network.

In this work, the financial data of 377 stocks of Standard & Poor’s 500 Index (S&P 500) from the years 1998–2012 with a 250-day time window were investigated by measuring realized stock returns and realized volatility. We examined the normal distribution and frequency distribution for both daily stock returns and volatility. We also determined the beta-coefficient and correlation among the stocks for 15 years and found that, during the crisis period, the beta-coefficient between the market index and stock’s prices and correlation among stock’s prices increased remarkably and decreased during the non-crisis period. We compared the stock volatility and stock returns for specific time periods i.e., non-crisis, before crisis and during crisis year in detail and found that the distribution behaviors of stock return prices has a better long-term effect that allows predictions of near-future market behavior than realized volatility of stock returns. Our detailed statistical analysis provides a valuable guideline for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.

Threshold methods in financial networks are important tools for obtaining important information about the financial state of a market. Previously, absolute thresholds of correlation coefficients have been used; however, they have no relation to the length of time. We assign a threshold value depending on the size of the time window by using the P-value concept of statistics. We construct a threshold network (TN) at the same threshold value for two different time window sizes in the Korean Composite Stock Price Index (KOSPI). We measure network properties, such as the edge density, clustering coefficient, assortativity coefficient, and modularity. We determine that a significant difference exists between the network properties of the two time windows at the same threshold, especially during crises. This implies that the market information depends on the length of the time window when constructing the TN. We apply the same technique to Standard and Poor’s 500 (S&P500) and observe similar results.

This paper considers stock prices in the Korean stock market during the 2008 global financial crisis by focusing on three time periods: before, during, and after the crisis. Complex networks are extracted from cross-correlation coefficients between the normalized logarithmic return of the stock price time series of firms. The minimal spanning trees (MSTs) and the hierarchical network (HN) are generated from cross-correlation coefficients. Before and after the crisis, securities firms are located at the center of the MST. During the crisis, however, the center of the MST changes to a firm in heavy industry and construction. During the crisis, the MST shrinks in comparison to that before and that after the crisis. This topological change in the MST during the crisis reflects a distinct effect of the global financial crisis. The cophenetic correlation coefficient increases during the crisis, indicating an increase in the hierarchical structure during in this period. When crisis hits the market, firms behave synchronously, and their correlations are higher than those during a normal period.

This study considers the effects of the 2008 global financial crisis on threshold networks of a local Korean financial market around the time of the crisis. Prices of individual stocks belonging to KOSPI 200 (Korea Composite Stock Price Index 200) are considered for three time periods, namely before, during, and after the crisis. Threshold networks are constructed from fully connected cross-correlation networks, and thresholds of cross-correlation coefficients are assigned to obtain threshold networks. At the high threshold, only one large cluster consisting of firms in the financial sector, heavy industry, and construction is observed during the crisis. However, before and after the crisis, there are several fragmented clusters belonging to various sectors. The power law of the degree distribution in threshold networks is observed within the limited range of thresholds. Threshold networks are fatter during the crisis than before or after the crisis. The clustering coefficient of the threshold network follows the power law in the scaling range.

We study the dynamic interactions and structural changes in global financial indices in the years 1998-2012. We apply a principal component analysis (PCA) to cross-correlation coefficients of the stock indices. We calculate the correlations between principal components (PCs) and each asset, known as PC coefficients. A change in market state is identified as a change in the first PC coefficients. Some indices do not show significant change of PCs in market state during crises. The indices exposed to the invested capitals in the stock markets are at the minimum level of risk. Using the first two PC coefficients, we identify indices that are similar and more strongly correlated than the others. We observe that the European indices form a robust group over the observation period. The dynamics of the individual indices within the group increase in similarity with time, and the dynamics of indices are more similar during the crises. Furthermore, the group formation of indices changes position in two-dimensional spaces due to crises. Finally, after a financial crisis, the difference of PCs between the European and American indices narrows., Comment: 13 pages, 8 figures

In this paper, the change in topological hierarchy, which is measured by the minimum spanning tree constructed from the cross-correlations between the stock indices from the S & P 500 for 1998–2012 in a one year moving time window, was used to analyze a financial crisis. The hierarchy increased in all minor crises in the observation time window except for the sharp crisis of 2007–2008 when the global financial crisis occurred. The sudden increase in hierarchy just before the global financial crisis can be used for the early detection of an upcoming crisis. Clearly, the higher the hierarchy, the higher the threats to financial stability. The scaling relations were developed to observe the changes in hierarchy with the network topology. These scaling relations can also identify and quantify the financial crisis periods, and appear to contain the predictive power of an upcoming crisis.

This study examined how the correlation and network structure of 30 global indices and 145 local Korean indices belonging to the KOSPI 200 have changed during the 13-year period, 2000-2012. The correlations among the indices were calculated. The results showed that although the average correlations of the global indices increased with time, the local indices showed a decreasing trend except for drastic changes during crises. The average correlation of the local indices exceeded the global indices during the crises from 2000-2002, implying a strong correlation structure among the local indices during this period due to the detrimental effect of the dot-com bubble. The threshold networks (TN) were constructed in the observation time window by assigning a threshold value and determining the network topologies. A significant change in the network topologies was observed due to the financial crises in both markets. The Jaccard similarities were also determined using the common links of TNs. The TNs of the financial network were not consistent with the evolution of the time, and the successive TNs of the global indices were more similar than those of the successive local indices. Finally, the Jaccard similarities identified the change in the market state due to a crisis in both markets., 11 pages,4 figures

We analyzed cross-correlations between price fluctuations of global financial indices (20 daily stock indices over the world) and local indices (daily indices of 200 companies in the Korean stock market) by using random matrix theory (RMT). We compared eigenvalues and components of the largest and the second largest eigenvectors of the cross-correlation matrix before, during, and after the global financial the crisis in the year 2008. We find that the majority of its eigenvalues fall within the RMT bounds [{\lambda}_, {\lambda}+], where {\lambda}_- and {\lambda}_+ are the lower and the upper bounds of the eigenvalues of random correlation matrices. The components of the eigenvectors for the largest positive eigenvalues indicate the identical financial market mode dominating the global and local indices. On the other hand, the components of the eigenvector corresponding to the second largest eigenvalue are positive and negative values alternatively. The components before the crisis change sign during the crisis, and those during the crisis change sign after the crisis. The largest inverse participation ratio (IPR) corresponding to the smallest eigenvector is higher after the crisis than during any other periods in the global and local indices. During the global financial the crisis, the correlations among the global indices and among the local stock indices are perturbed significantly. However, the correlations between indices quickly recover the trends before the crisis.