Stationary viscoelastic wave fields generated by scalar wave functions

The usual Helmholtz decomposition gives a decomposition of any vector valued function into a sum of gradient of a scalar function and rotation of a vector valued function under some mild condition. In this paper we show that the vector valued function of the second term i.e. the divergence free part of this decomposition can be further decomposed into a sum of a vector valued function polarized in one component and the rotation of a vector valued function also polarized in the same component. Hence the divergence free part only depends on two scalar functions. Further we show the so called completeness of representation associated to this decomposition for the stationary wave field of a homogeneous, isotropic viscoelastic medium. That is by applying this decomposition to this wave field, we can show that each of these three scalar functions satisfies a Helmholtz equation. Our completeness of representation is useful for solving boundary value problem in a cylindrical domain for several partial differential equations of systems in mathematical physics such as stationary isotropic homogeneous elastic/viscoelastic equations of system and stationary isotropic homogeneous Maxwell equations of system. As an example, by using this completeness of representation, we give the solution formula for torsional deformation of a pendulum of cylindrical shaped homogeneous isotropic viscoelastic medium

Opinion formation driven by PageRank node influence on directed networks

We study a two states opinion formation model driven by PageRank node influence and report an extensive numerical study on how PageRank affects collective opinion formations in large-scale empirical directed networks. In our model the opinion of a node can be updated by the sum of its neighbor nodes' opinions weighted by the node influence of the neighbor nodes at each step. We consider PageRank probability and its sublinear power as node influence measures and investigate evolution of opinion under various conditions. First, we observe that all networks reach steady state opinion after a certain relaxation time. This time scale is decreasing with the heterogeneity of node influence in the networks. Second, we find that our model shows consensus and non-consensus behavior in steady state depending on types of networks: Web graph, citation network of physics articles, and LiveJournal social network show non-consensus behavior while Wikipedia article network shows consensus behavior. Third, we find that a more heterogeneous influence distribution leads to a more uniform opinion state in the cases of Web graph, Wikipedia, and Livejournal. However, the opposite behavior is observed in the citation network. Finally we identify that a small number of influential nodes can impose their own opinion on significant fraction of other nodes in all considered networks. Our study shows that the effects of heterogeneity of node influence on opinion formation can be significant and suggests further investigations on the interplay between node influence and collective opinion in networks.Comment: 10 pages, 6 figures. Published in Physica A 436, 707-715 (2015

Effect of changing data size on eigenvalues in the Korean and Japanese stock markets

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features

Statistical Investigation of Connected Structures of Stock Networks in Financial Time Series

In this study, we have investigated factors of determination which can affect the connected structure of a stock network. The representative index for topological properties of a stock network is the number of links with other stocks. We used the multi-factor model, extensively acknowledged in financial literature. In the multi-factor model, common factors act as independent variables while returns of individual stocks act as dependent variables. We calculated the coefficient of determination, which represents the measurement value of the degree in which dependent variables are explained by independent variables. Therefore, we investigated the relationship between the number of links in the stock network and the coefficient of determination in the multi-factor model. We used individual stocks traded on the market indices of Korea, Japan, Canada, Italy and the UK. The results are as follows. We found that the mean coefficient of determination of stocks with a large number of links have higher values than those with a small number of links with other stocks. These results suggest that common factors are significantly deterministic factors to be taken into account when making a stock network. Furthermore, stocks with a large number of links to other stocks can be more affected by common factors.Comment: 11 pages, 2 figure

Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles

How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles. With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank and 2DRank. In particular, we focus on articles related to persons, identify top 30 persons for each rank among different editions and analyze distinctions of their distributions over activity fields such as politics, art, science, religion, sport for each edition. We find that local heroes are dominant but also global heroes exist and create an effective network representing entanglement of cultures. The Google matrix analysis of network of cultures shows signs of the Zipf law distribution. This approach allows to examine diversity and shared characteristics of knowledge organization between cultures. The developed computational, data driven approach highlights cultural interconnections in a new perspective.Comment: Published in PLoS ONE (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074554). Supporting information is available on the same webpag

Topological Properties of the Minimal Spanning Tree in Korean and American Stock Markets

We investigate a factor that can affect the number of links of a specific stock in a network between stocks created by the minimal spanning tree (MST) method, by using individual stock data listed on the S&P500 and KOSPI. Among the common factors mentioned in the arbitrage pricing model (APM), widely acknowledged in the financial field, a representative market index is established as a possible factor. We found that the correlation distribution, $\rho_{ij}$, of 400 stocks taken from the S&P500 index shows a very similar with that of the Korean stock market and those deviate from the correlation distribution of time series removed a nonlinearity by the surrogate method. We also shows that the degree distribution of the MSTs for both stock markets follows a power-law distribution with the exponent $\zeta \sim$ 2.1, while the degree distribution of the time series eliminated a nonlinearity follows an exponential distribution with the exponent, $\delta \sim 0.77$. Furthermore the correlation, $\rho_{iM}$, between the degree k of individual stock, $i$, and the market index, $M$, follows a power-law distribution, $\sim k^{\gamma}$, with the exponent \gamma_{\textrm{S&P500}} \approx 0.16 and $\gamma_{\textrm{KOSPI}} \approx 0.14$, respectively. Thus, regardless of the markets, the indivisual stocks closely related to the common factor in the market, the market index, are likely to be located around the center of the network between stocks, while those weakly related to the market index are likely to be placed in the outside

Concurrent enhancement of percolation and synchronization in adaptive networks

Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems' collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.Comment: Published in Scientific Report