Spectral properties of Google matrix of Wikipedia and other networks

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.     

COVID-19’s Impact on International Trade

We analyze how the COVID-19 pandemic affected the trade of products between countries. With this aim, using the United Nations Comtrade database, we perform a Google matrix analysis of the multiproduct World Trade Network (WTN) for the years 2018–2020, comprising the emergence of the COVID-19 as a global pandemic. The applied algorithms—PageRank, CheiRank and the reduced Google matrix—take into account the multiplicity of the WTN links, providing new insights into international trade compared to the usual import–export analysis. These complex networks analysis algorithms establish new rankings and trade balances of countries and products considering all countries on equal grounds, independent of their wealth, and every product on the basis of its relative exchanged volumes. In comparison with the pre-COVID-19 period, significant changes in these metrics occurred for the year 2020, highlighting a major rewiring of the international trade flows induced by the COVID-19 pandemic crisis. We define a new PageRank–CheiRank product trade balance, either export or import-oriented, which is significantly perturbed by the pandemic.     

Google matrix of business process management

Development of efficient business process models and determination of their characteristic properties are subject of intense interdisciplinary research. Here, we consider a business process model as a directed graph. Its nodes correspond to the units identified by the modeler and the link direction indicates the causal dependencies between units. It is of primary interest to obtain the stationary flow on such a directed graph, which corresponds to the steady-state of a firm during the business process. Following the ideas developed recently for the World Wide Web, we construct the Google matrix for our business process model and analyze its spectral properties. The importance of nodes is characterized by PageRank and recently proposed CheiRank and 2DRank, respectively. The results show that this two-dimensional ranking gives a significant information about the influence and communication properties of business model units. We argue that the Google matrix method, described here, provides a new efficient tool helping companies to make their decisions on how to evolve in the exceedingly dynamic global market.     

Analysis of world terror networks from the reduced Google matrix of Wikipedia

We apply the reduced Google matrix method to analyze interactions between 95 terrorist groups and determine their relationships and influence on 64 world countries. This is done on the basis of the Google matrix of the English Wikipedia (2017) composed of 5 416 537 articles which accumulate a great part of global human knowledge. The reduced Google matrix takes into account the direct and hidden links between a selection of 159 nodes (articles) appearing due to all paths of a random surfer moving over the whole network. As a result we obtain the network structure of terrorist groups and their relations with selected countries including hidden indirect links. Using the sensitivity of PageRank to a weight variation of specific links we determine the geopolitical sensitivity and influence of specific terrorist groups on world countries. The world maps of the sensitivity of various countries to influence of specific terrorist groups are obtained. We argue that this approach can find useful application for more extensive and detailed data bases analysis.     

Two-dimensional ranking of Wikipedia articles

The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.     

Google matrix analysis of C.elegans neural network

We study the structural properties of the neural network of the C.elegans (worm) from a directed graph point of view. The Google matrix analysis is used to characterize the neuron connectivity structure and node classifications are discussed and compared with physiological properties of the cells. Our results are obtained by a proper definition of neural directed network and subsequent eigenvector analysis which recovers some results of previous studies. Our analysis highlights particular sets of important neurons constituting the core of the neural system. The applications of PageRank, CheiRank and ImpactRank to characterization of interdependency of neurons are discussed.     

Impact of asymmetric information on market evolution

In this paper, we propose an agent-based model to study the impact of asymmetric information on market evolution. In each period, buyers and sellers are randomly matched. The condition for the transaction being performed depends on the comparison between valuations of buyers and sellers on the good they trade. We introduce cognitive capability to describe buyers’ valuation on a good and valuation ratio to reflect the gap between two kinds of traders’ valuations on the good. The market outcomes are sorted into four phases in the parameter space of these two variables. Computer simulations show us critical phenomena of phase transition. The model proposed herein is able to demonstrate how the asymmetry of information leads to the adverse selection effect. The model also explains the coexistence of low- and high-quality goods in a market with asymmetric information. We analyze the condition under which the asymmetry of information might not take its effect and find that the gap of valuations between buyers and sellers plays the key role.     

Convergence of reinforcement learning to Nash equilibrium: A search-market experiment

Since the introduction of Reinforcement Learning (RL) in Game Theory, a growing literature is concerned with the theoretical convergence of RL-driven outcomes towards Nash equilibrium. In this paper, we apply this issue to a search-theoretic framework (posted-price market) where sellers are confronted with a population of imperfectly informed buyers and take one decision per period (posted prices) with no direct interactions between sellers. We focus on three different scenarios with varying buyers’ characteristics. For each of these scenarios, we quantitatively and qualitatively test whether the learned variable (price strategy) converges to the Nash equilibrium. We also study the impact of the temperature parameter (defining the exploitation/exploration trade off) on these results.     

Rich-club and page-club coefficients for directed graphs

Rich-club and page-club coefficients and their null models are introduced for directed graphs. Null models allow for a quantitative discussion of the rich-club and page-club phenomena. These coefficients are computed for four directed real-world networks: Arxiv High Energy Physics paper citation network, Web network (released from Google), Citation network among US Patents, and email network from a EU research institution. The results show a high correlation between rich-club and page-club ordering. For journal paper citation network, we identify both rich-club and page-club ordering, showing that “elite” papers are cited by other “elite” papers. Google web network shows partial rich-club and page-club ordering up to some point and then a narrow declining of the corresponding normalized coefficients, indicating the lack of rich-club ordering and the lack of page-club ordering, i.e. high in-degree (PageRank) pages purposely avoid sharing links with other high in-degree (PageRank) pages. For UC patents citation network, we identify page-club and rich-club ordering providing a conclusion that “elite” patents are cited by other “elite” patents. Finally, for email communication network we show lack of both rich-club and page-club ordering. We construct an example of synthetic network showing page-club ordering and the lack of rich-club ordering.     

Blockchain based Scalable model for Secure Dynamic Spectrum Access

Conventional Cooperative spectrum sensing techniques either suffer from single point of failure attack or lack in providing incentives to users which makes them incompatible for Wireless Service Provider (WSP). We propose a dynamic spectrum access framework for WSP which gives prominence to automated sensing and sharing with the use of blockchain. In this system, the opportunity of spectrum access is first examined by sensor nodes and the access right is then allocated to the users when their transactions to WSP are authenticated in a decentralized manner. Apart from using blockchain as a reliable platform for automatic enforcement of spectrum sensing, we propose a novel mechanism for securing our network from the threats designed primarily for Cognitive Radio Networks. In addition to this, our proposed approach enhances the scalability of blockchain networks by using the sidechains for storing data and checkpointing it onto main chain after periodic intervals of time. Extensive simulations in Octave indicate superior performance offered by our proposed model.     

What Drives Bitcoin? An Approach from Continuous Local Transfer Entropy and Deep Learning Classification Models

Bitcoin has attracted attention from different market participants due to unpredictable price patterns. Sometimes, the price has exhibited big jumps. Bitcoin prices have also had extreme, unexpected crashes. We test the predictive power of a wide range of determinants on bitcoins’ price direction under the continuous transfer entropy approach as a feature selection criterion. Accordingly, the statistically significant assets in the sense of permutation test on the nearest neighbour estimation of local transfer entropy are used as features or explanatory variables in a deep learning classification model to predict the price direction of bitcoin. The proposed variable selection do not find significative the explanatory power of NASDAQ and Tesla. Under different scenarios and metrics, the best results are obtained using the significant drivers during the pandemic as validation. In the test, the accuracy increased in the post-pandemic scenario of July 2020 to January 2021 without drivers. In other words, our results indicate that in times of high volatility, Bitcoin seems to self-regulate and does not need additional drivers to improve the accuracy of the price direction.     

A reaction–diffusion model for market fluctuations – A relation between price change and traded volumes

Two decades ago Bak et al. (1997) [3] proposed a reaction–diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.     

An adaptive step-size spectrum auction mechanism for two-tier heterogeneous networks

Recently, with the rapid growth of demands for wireless communications, dynamic spectrum allocation is one of the key technologies in cognitive radio networks to resolve the realistic problem of low utilization efficiency of spectrum. It mainly focuses on how the spectrum owner dynamically allocates idle spectrum to secondary users who have no licensed spectrum for communications. In this paper, a dynamic spectrum allocation model based on auction theory in a two-tier heterogeneous network is proposed, in which the primary users (PUs) are the sellers, the central processor (CP) auctioneer is the coordinator, and femtocell base station (FBS) as the buyer bids for the idle spectrum and act as a wireless access point that provides communication services for secondary users (SUs). Its basic process is as follows: the auctioneer gradually raises the spectrum price from the reserved price; each bidder decides whether participates in the purchase or not. It is characterized by distributed execution and low complexity which can reduce unnecessary information exchange between primary users or secondary users. Meanwhile it can enhance the utilization of spectrum and improve the efficiency of the auction by generate the incentive mechanism.     

PageRank model of opinion formation on social networks

We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of the Universities of Cambridge and Oxford, LiveJournal, and Twitter. In this model, the opinion formation of linked electors is weighted with their PageRank probability. Such a probability is used by the Google search engine for ranking of web pages. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion on a significant fraction of the society. However, for a homogeneous distribution of two opinions, there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that the LiveJournal and Twitter networks have a stronger tendency to a totalitarian opinion formation than the university networks. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.     

Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks

We use the methods of quantum chaos and Random Matrix Theory for analysis of statistical fluctuations of PageRank probabilities in directed networks. In this approach the effective energy levels are given by a logarithm of PageRank probability at a given node. After the standard energy level unfolding procedure we establish that the nearest spacing distribution of PageRank probabilities is described by the Poisson law typical for integrable quantum systems. Our studies are done for the Twitter network and three networks of Wikipedia editions in English, French and German. We argue that due to absence of level repulsion the PageRank order of nearby nodes can be easily interchanged. The obtained Poisson law implies that the nearby PageRank probabilities fluctuate as random independent variables.     

A dissipative network model with neighboring activation

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be ν ≈ 0.65 that corresponds to the fractal dimension of the network d ≈ 1.3. An independent computation of the fractal dimension by the cluster growing method, generalized for directed networks, gives a close value d ≈ 1.4. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension d < 2.     

Fat tails and multi-scaling in a simple model of limit order markets

We use a simple model where traders submit limit orders which are cleared in a double auction market. The limit prices are set by traders randomly, for buyers around a long-term trend and for sellers in a narrow band around their purchase price. Orders which are not filled within a specific time frame are randomly assigned a new limit price. In this framework we find evidence for the endogenous emergence of fat tails in the distribution of returns and multi-scaling whose origin is attributed to the market structure.     

A spectrum auction algorithm based on joint power control and beamforming in small cell networks

Spectrum auction is considered as a suitable approach to efficiently allocate spectrum among unlicensed users. However, in previous studies of spectrum auction, competition can hardly be reflected in the traditional spectrum allocation and the spectrum efficiency is still not high after the allocation. In this paper, we enhance the factor of competition in the auctions, in which bidders need to pay for the competition and the interference to macro cell users (MUs). We consider a communication system with one macro cell and several small cells, thus a licensed radio spectrum is shared by both MUs and small cell users (SUs). A truthful auction algorithm is proposed for spectrum allocation and the spectrum is divided into multiple channels in different time slots, so that SUs can make their choice for bidding under the guidance of history. In order to raise the communication quality, we propose a power control and beamforming algorithm in the heterogeneous network to enhance the system performance. Simulation results are presented to verify the effectiveness of the proposed algorithm in the small cell network.     

Dynamic Linkage between Bitcoin and Traditional Financial Assets: A Comparative Analysis of Different Time Frequencies

This study employs the ADCC-GARCH approach to investigate the dynamic correlation between bitcoin and 14 major financial assets in different time-frequency dimensions over the period 2013–2021, for which the risk diversification, hedging and safe-haven properties of bitcoin for those traditional assets are further examined. The results show that, first, bitcoin is positively linked to risk assets, including stock, bond and commodity, and negatively linked to the U.S. dollar, which is a safe-haven asset, so bitcoin is closer in nature to a risk asset than a safe-haven asset. Second, the high short-term volatility and speculative nature of the bitcoin market makes its long-term correlation with other assets stronger than the short-term. Third, the positive linkage between the prices of bitcoin and risk assets increases sharply under extreme shocks (e.g., the outbreak of COVID-19 in early 2020). Fourth, bitcoin can hedge against the U.S. dollar, and in the long term, bitcoin can hedge against the Chinese stock market and act as a safe haven for the U.S. stock market and crude oil. However, for most other traditional assets, bitcoin is only an effective diversifier.     

Sampling from complex networks with high community structures

In this paper, we propose a novel link-tracing sampling algorithm, based on the concepts from PageRank vectors, to sample from networks with high community structures. Our method has two phases; (1) Sampling the closest nodes to the initial nodes by approximating personalized PageRank vectors and (2) Jumping to a new community by using PageRank vectors and unknown neighbors. Empirical studies on several synthetic and real-world networks show that the proposed method improves the performance of network sampling compared to the popular link-based sampling methods in terms of accuracy and visited communities.